i 

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ii

Technical Report Documentation Page

1. Report No. NHI-15-044 2. Government Accession No. 3. Recipient’s Catalog No.

4. Title and Subtitle

Engineering for Structural Stability in Bridge Construction

5. Report Date

April 2015 

6. Performing Organization 

Code:

7. Author(s)

Michael J. Garlich, S.E., P.E.; Thomas H. Pechillo, P.E.; Jason 

M. Schneider, P.E., S.E.; Todd A. Helwig, PhD., P.E.; Mary 

Anne O’Toole, P.E.; Stan-Lee C. Kaderbek, P.E., S.E.; Michael 

Grubb, P.E.; John Ashton, S.E., P.E.

8. Performing Organization 

Report No.

9. Performing Organization on Name and Address

Collins Engineers, Inc.

123 North Wacker Drive, Suite 900

Chicago, Illinois 60606

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-09-T-70027

12. Sponsoring Agency Name and Address 

Office of Bridge Technology

Federal Highway Administration

1200 New Jersey Avenue, S.E.

Washington, DC 20590

13. Type of Report and 

Period Covered

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract:

This manual is intended to serve as a reference. It will provide technical information which will 

enable Manual users to perform the following activities:

• Describe typical erection practices for girder bridge superstructures and recognize 

critical construction stages

• Discuss typical practices for evaluating structural stability of girder bridge 

superstructures during early stages of erection and throughout bridge construction

• Explain the basic concepts of stability and why it is important in bridge erection

• Explain common techniques for performing advanced stability analysis along with their 

advantages and limitations

• Describe how differing construction sequences effect superstructure stability

• Be able to select appropriate loads, load combinations, and load factors for use in 

analyzing superstructure components during construction

• Be able to analyze bridge members at various stages of erection

• Develop erection plans that are safe and economical, and know what information is 

required and should be a part of those plans

• Describe the differences between local, member and global (system) stability

17. Key Words

Bridge construction, bridge erection, bridge 

superstructures, bridge stability

18. Distribution Statement

19. Security Classif. (of this 

report)

Unclassified 

20. Security Classification (of 

this page)

21. No of 

Pages

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
iii
iv

APPROXIMATE CONVERSIONS TO SI UNITS

SYMBOL WHEN YOU KNOW MULTIPLY BY TO FIND SYMBOL

LENGTH

in inches 25.4 millimeters mm

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME

fl oz fluid ounces 29.57 milliliters mL

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3

yd3 cubic yards 0.765 cubic meters m3

NOTE: volumes greater than 1000 L shall be shown in m3

MASS

oz ounces 28.35 grams g 

lb pounds 0.454 kilograms kg 

T short tons (2000 lb) 0.907 megagrams (or 

"metric ton")

Mg (or "t")

TEMPERATURE (exact degrees)

o

F Fahrenheit 5 (F-32)/9

or (F-32)/1.8

Celsius oC 

ILLUMINATION

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS

lbf pound-force 4.45 newtons N 
v 

lbf/in2 pound-force per square 

inch

6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS

SYMBOL WHEN YOU KNOW MULTIPLY BY TO FIND SYMBOL

LENGTH

mm millimeters 0.039 inches in

m meters 3.28 feet ft

m meters 1.09 yards yd

km kilometers 0.621 miles mi

AREA

mm2 square millimeters 0.0016 square inches in2

m2 square meters 10.764 square feet ft2

m2 square meters 1.195 square yards yd2

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2

VOLUME

mL milliliters 0.034 fluid ounces fl oz

L liters 0.264 gallons gal

m3 cubic meters 35.314 cubic feet ft3

m3 cubic meters 1.307 cubic yards yd3

MASS

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric 

ton")

1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees)

o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION

lx lux 0.0929 foot-candles fc

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS

N newtons 0.225 pound-force lbf

kPa kilopascals 0.145 pound-force per 

inch2

lbf/in2

*SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 

of ASTM E380.

(Revised March 2003)
vi

Engineering for Structural Stability in Bridge Construction 

Report No. NHI-15-044

April 2015
vii
viii

TABLE OF CONTENTS

CHAPTER 1 INTRODUCTION .................................................................................... 1.1

SECTION 1. MANUAL SCOPE 1.1

SECTION 2. SURVEY OF STATE DEPARTMENTS OF 

TRANSPORTATION 1.6

1.2.1 Survey Description..................................................................... 1.6

1.2.2 Summary of Responses............................................................. 1.6

CHAPTER 2 CONSTRUCTION FAILURE CASE STUDIES ....................................... 2.1

SECTION 1. INTRODUCTION 2.1

SECTION 2. ROUTE 17 (FUTURE I-86), NEW YORK (2010) 2.1

SECTION 3. MARCY BRIDGE, NEW YORK (2002) 2.2

SECTION 4. RED MOUNTAIN FREEWAY, ARIZONA (2007) 2.5

SECTION 5. EAST BOUND I-80/94 TO NORTH BOUND IL 394, RAMP J 2.7

2.5.1 General Description ................................................................... 2.7

2.5.2 Ramifications of Collapse ........................................................ 2.12

SECTION 6. I-70 BRIDGE, COLORADO (2004) 2.12

SECTION 7. SR69 OVER THE TENNESSEE RIVER (1995) 2.15

SECTION 8. SOUVENIR BOULEVARD BRIDGE, QUEBEC (2000) 2.18

SECTION 9. QUEBEC BRIDGE OVER ST. LAWRENCE (1907) 2.19

SECTION 10. I-80 GIRDER FAILURE (2005) 2.23

SECTION 11. CASE STUDIES – STEEL BOX-GIRDER BRIDGE FAILURES 

DURING ERECTION OUTSIDE OF NORTH AMERICA 2.25

2.11.1 Introduction .............................................................................. 2.25

2.11.2 Fourth Danube Bridge.............................................................. 2.26

2.11.3 Cleddau Bridge ........................................................................ 2.27

2.11.4 West Gate Bridge..................................................................... 2.28

2.11.5 Rhine Bridge ............................................................................ 2.30

2.11.6 Zeulenroda Bridge ................................................................... 2.32

SECTION 12. SUMMARY AND CONCLUSIONS 2.32

CHAPTER 3 TYPICAL BRIDGE CONSTRUCTION PRACTICE................................. 3.1

SECTION 1. INTRODUCTION 3.1

SECTION 2. ERECTION SEQUENCING 3.1

3.2.1 Site Conditions........................................................................... 3.1

3.2.2 Girder Shipping.......................................................................... 3.1
ix

3.2.3 Erection Sequence..................................................................... 3.3

3.2.3.1 Initial Preparation ..................................................................3.3

3.2.3.2 Steel Girder Bridges..............................................................3.5

3.2.3.3 Concrete Girder Bridges........................................................3.7

SECTION 3. GIRDER HANDLING 3.10

3.3.1 Center of Gravity...................................................................... 3.10

3.3.2 Rigging for Straight and Curved Steel Girders......................... 3.11

3.3.3 Rigging for Concrete Girders ................................................... 3.12

3.3.4 Local Stresses from Beam Clamps.......................................... 3.13

3.3.5 Lifting Beams & Spreader Beams............................................ 3.14

3.3.7 Bolting Procedures................................................................... 3.17

3.3.8 Field Welding Considerations .................................................. 3.18

3.3.9 Concrete Girders...................................................................... 3.18

SECTION 4. CRANES 3.19

3.4.1 Typical Crane Data .................................................................. 3.19

3.4.2 Holding Cranes ........................................................................ 3.25

3.4.3 Soil Pressures and Structures Influenced by Crane Location .. 3.26

SECTION 5. BRACING 3.27

3.5.1 Girder Bracing.......................................................................... 3.27

3.5.2 Temporary Bracing and Hold Downs ....................................... 3.29

3.5.2.1 Chain Down to Standard Bearings ......................................3.30

3.5.2.2 Erecting on Multi-Rotational Bearings ................................. 3.36

3.5.2.3 Bracing to Adjacent Structures – Phased Construction .......3.37

3.5.2.4 Uplift Hold-Down ................................................................. 3.38

SECTION 6. SHORING TOWERS 3.39

SECTION 7. DECK CONSTRUCTION 3.42

3.7.1 Placing Sequence.................................................................... 3.42

3.7.2 Overhang Brackets .................................................................. 3.43

SECTION 8. BRIDGE DEMOLITION 3.48

SECTION 9. SUMMARY 3.49

CHAPTER 4 STABILITY FUNDAMENTALS............................................................... 4.2

SECTION 1. INTRODUCTION 4.2

SECTION 2. GEOMETRICAL IMPERFECTIONS AND RESIDUAL 

STRESSES 4.3

SECTION 3. COLUMN BUCKLING 4.8

4.3.1 Flexural Buckling........................................................................ 4.9

4.3.2 Torsional Buckling.................................................................... 4.13
x 

4.3.2.1 Elastic Torsional Buckling about the Shear Center..............4.15

4.3.2.2 Elastic Torsional Buckling Cases with Twist about a Restrained 

Axis .....................................................................................4.18

4.3.3 Elastic Flexural Torsional Buckling .......................................... 4.19

4.3.4 Inelastic Effects for Torsional and Flexural Torsional Buckling 4.21

SECTION 4. PLATE BUCKLING AND LOCAL BUCKLING 4.22

4.4.1 Plate Buckling .......................................................................... 4.23

SECTION 5. GIRDER BUCKLING 4.25

4.5.1 Uniform Moment Loading......................................................... 4.26

4.5.2 Moment Gradient Loading........................................................ 4.28

4.5.3 Effect of Load Position on Cross-section ................................. 4.28

SECTION 6. SUMMARY 4.29

CHAPTER 5 STABILITY IN BRIDGE ERECTION....................................................... 5.1

SECTION 1. INTRODUCTION 5.1

SECTION 2. LATERAL RESISTANCE OF PARTIALLY ERECTED 

SUPERSTRUCTURES 5.2

5.2.1 General Considerations ............................................................. 5.2

5.2.2 Lateral Resistance Effects ......................................................... 5.3

5.2.3 Lateral Bracing Classifications................................................... 5.5

5.2.3.1 Relative Bracing ....................................................................5.6

5.2.3.2 Nodal (Discrete) Bracing .......................................................5.7

5.2.3.3 Lean-On Bracing ...................................................................5.7

5.2.3.4 Continuous Bracing...............................................................5.8

SECTION 3. BRACING REQUIREMENTS 5.10

5.3.1 I-Girder Bracing........................................................................ 5.10

5.3.2 Skew Effects ............................................................................ 5.18

SECTION 4. SYSTEM BUCKLING OF GIRDERS 5.19

SECTION 5. BRACING TO ADJACENT STRUCTURES 5.23

SECTION 6. UPLIFT DURING ERECTION AND DECK POUR 5.24

5.6.1 Uplift Considerations................................................................ 5.24

5.6.2 Additional Deck Pour Considerations....................................... 5.26

SECTION 7. ROLL STABILITY OF CURVED SPANS 5.27

SECTION 8. ROLL STABILITY OF FASCIA GIRDERS 5.30

SECTION 9. ADDITIONAL CONSIDERATIONS FOR STEEL BOX 

GIRDERS 5.33

5.9.1 Differential Deflections ............................................................. 5.33
xi

5.9.2 Top Flange Lateral Bracing...................................................... 5.34

5.9.3 Bottom Flange Stiffeners.......................................................... 5.34

SECTION 10. SUMMARY 5.35

CHAPTER 6 ANALYSIS FOR STABILITY.................................................................. 6.1

SECTION 1. INTRODUCTION 6.1

SECTION 2. COMPUTATIONAL MODELING 6.1

6.2.1 Grillage Models .......................................................................... 6.3

6.2.2 Three Dimensional Models ........................................................ 6.5

SECTION 3. TYPES OF ANALYSES 6.7

6.3.1 First Order Analyses .................................................................. 6.8

6.3.2 Eigenvalue Buckling Analysis .................................................... 6.8

6.3.3 Second-Order Analysis ............................................................ 6.16

SECTION 4. BEHAVIOR OF STRAIGHT AND HORIZONTALLY CURVED 

GIRDERS DURING LIFTING 6.22

SECTION 5. BEHAVIOR OF STRAIGHT AND HORIZONTALLY CURVED 

GIRDERS DURING ERECTION AND CONSTRUCTION 6.32

6.5.1 UT Bridge................................................................................. 6.32

6.5.2 Determining the Critical Erection Stages ................................. 6.38

6.5.3 Evaluation of Concrete Placement........................................... 6.46

SECTION 6. COMPARISONS BETWEEN AASHTO DESIGN 

EXPRESSIONS AND EIGENVALUE BUCKLING ESTIMATES6.51

6.6.1 Girder Geometry ...................................................................... 6.51

6.6.2 Comparisons Between AASHTO Equations and Eigenvalue 

Buckling Solutions.................................................................... 6.52

SECTION 7. SUMMARY 6.56

CHAPTER 7 DESIGN CRITERIA ................................................................................ 7.1

SECTION 1. INTRODUCTION 7.1

SECTION 2. STRUCTURE ANALYSIS 7.5

7.2.1 Member and Component Evaluation.......................................... 7.5

7.2.2 Critical Erection Stages.............................................................. 7.5

7.2.3 Analytical Modeling.................................................................... 7.6

7.2.3.1 Selection of Analysis Methods for Steel I-Girder Bridges.......7.8

7.2.3.2 Selection of Analysis Methods for Steel Tub-Girder Bridges7.11

7.2.4 General Girder Proportions...................................................... 7.15

7.2.4.1 Steel I-Girders.....................................................................7.15

7.2.4.2 Steel Box-Girders................................................................7.15
xii

7.2.4.3 Steel I-Girder Erection Conditions .......................................7.16

7.2.5 General Concrete Girder Proportions ...................................... 7.16

SECTION 3. LOAD COMBINATIONS AND LOAD FACTORS 7.16

SECTION 4. LOADS 7.18

7.4.1 Material Weights ...................................................................... 7.18

7.4.2 Permanent Dead Load (DC) .................................................... 7.18

7.4.3 Construction Dead Load (CDL) ................................................. 7.19

7.4.3.1 Construction Live Load (CLL) .................................................7.19

7.4.3.2 Dynamic Load Allowance ....................................................7.20

7.4.3.3 Incidental Loads..................................................................7.21

7.4.4 Wind Load (Cw) ........................................................................ 7.21

7.4.5 Seismic Loading....................................................................... 7.36

SECTION 5. GIRDER LIFTING 7.36

7.5.1 General Considerations ........................................................... 7.36

7.5.2 Steel Girders............................................................................ 7.37

7.5.2.1 Straight Girders...................................................................7.37

7.5.2.2 Curved Girders....................................................................7.38

7.5.3 Concrete Girders...................................................................... 7.41

SECTION 6. STEEL GIRDER STABILITY AND BRACING 7.44

7.6.1 General .................................................................................... 7.44

7.6.2 Lateral Bracing......................................................................... 7.45

7.6.3 Global Stability......................................................................... 7.45

SECTION 7. CONCRETE GIRDER STABILITY AND BRACING 7.46

7.7.1 General .................................................................................... 7.46

7.7.2 Simply Supported Condition - Girder Rollover ......................... 7.47

SECTION 8. CONCENTRATED LOAD EFFECTS 7.51

7.8.1 Bearing Stiffeners .................................................................... 7.51

7.8.2 Local Effects of Lifting Clamp Loads........................................ 7.51

SECTION 9. DEFLECTION CONTROL 7.54

SECTION 10. CONNECTIONS 7.54

7.10.1 Steel Connections.................................................................... 7.54

7.10.2 Concrete Connections ............................................................. 7.55

SECTION 11. TEMPORARY SUPPORTS (FALSEWORK) 7.55

SECTION 12. BEARINGS 7.56

SECTION 13. DECK PLACEMENT 7.56

SECTION 14. SUMMARY 7.56
xiii

CHAPTER 8 ERECTION PLANS AND PROCEDURES ............................................. 8.1

SECTION 1. INTRODUCTION 8.1

SECTION 2. PLAN PREPARATION 8.1

SECTION 3. ERECTION PLANS 8.2

8.3.1 General ...................................................................................... 8.2

8.3.2 General Plan............................................................................ 8.13

8.3.3 Erection Sequencing................................................................ 8.13

8.3.4 Calculations ............................................................................. 8.14

SECTION 4. GIRDER SETTING 8.15

SECTION 5. GIRDER STABILIZATION 8.21

SECTION 6. SUBMITTALS 8.22

SECTION 7. ERECTION CHECKISTS 8.26

SECTION 8. BRIDGE REMOVAL PLANS 8.31

SECTION 9. SUMMARY 8.31

CHAPTER 9 MAJOR AND UNUSUAL BRIDGE CONSTRUCTION ........................... 9.1

SECTION 1. INTRODUCTION 9.1

SECTION 2. ARCH BRIDGES 9.1

9.2.1 Steel........................................................................................... 9.2

SECTION 3. TRUSSES 9.4

9.3.1 Stick Built Truss Erection Analysis............................................. 9.5

9.3.2 Pre-Assembly Erection Analysis ................................................ 9.8

SECTION 4. CABLE-STAYED BRIDGES 9.8

SECTION 5. BRIDGE LIFTING AND MOVING 9.9

SECTION 6. MOVABLE BRIDGE STABILITY 9.11

SECTION 7. SUMMARY 9.16

APPENDIX A REFERENCES.....................................................................................A.1

APPENDIX B DESIGN EXAMPLES............................................................................B.0

EXAMPLE PROBLEM #1: 2-SPAN MULTI-GIRDER SKEWED STEEL 

BRIDGE B.1

EXAMPLE PROBLEM #2: 3-SPAN MULTI-GIRDER CURVED STEEL

STRUCTURE B.54

EXAMPLE PROBLEM #3: CONCRETE SPLICED GIRDER B.138

EXAMPLE PROBLEM #4: 3-SPAN BOX GIRDER CURVED STEEL 

STRUCTURE B.171
xiv

APPENDIX C SURVEY ON ENGINEERING FOR STRUCTURAL SAFETY ..............C.0

APPENDIX D RECOMMENDED ENGINEERING CRITERIA......................................D.0

D-1. MEMBER AND COMPONENT EVALUATION D.1

D-1.1 GENERAL D.1

D-1.2 ANALYSIS D.2

D-2. LOAD COMBINATIONS AND LOAD FACTORS D.2

D-3. LOADS D.4

D-3.1 PERMANENT DEAD LOADS (DC) D.4

D-3.2 CONSTRUCTION DEAD LOADS (CDL) D.4

D-3.3 CONSTRUCTION LIVE LOADS (CLL) D.4

D-3.4 WIND LOADS (CW) D.5

D-3.5 SEISMIC LOADS D.7

D-4. GIRDER LIFTING D.8

D-4.1 GENERAL D.8

D-4.2 STEEL GIRDERS D.8

D-4.3 CONCRETE GIRDERS D.9

D-5. GIRDER STABILITY D.10

D-5.1 GENERAL D.10

D-5.2 STEEL GIRDER BRACING D.11

D-5.3 CONCRETE GIRDER BRACING D.14

D-5.4 STEEL GIRDERS GLOBAL STABILITY D.16

D-6. CONCENTRATED LOADS EFFECTS D.17

D-7. DEFLECTION CONTROL D.18

D-8. STEEL CONNECTIONS D.18

D-9. CONCRETE CONNECTIONS D.18

D-10. TEMPORARY SUPPORTS (FALSEWORK) D.18

D-11. BEARINGS D.20

D-12. DECK D.20

D-12.1 FORMS D.20

D-12.2 OVERHANGS D.20

D-12.3 DECK PLACEMENT D.21

GLOSSARY................................................................................................................ G.1
xv 

TABLE OF FIGURES

Figure 1-1 Collapse of Steel Girder Bridge during Construction .............................. 1.1

Figure 1-2 States Responding to Survey ................................................................. 1.9

Figure 2-1 Route 17 Collapsed Shoring and Girders ............................................... 2.2

Figure 2-2 Marcy Bridge Plan .................................................................................. 2.3

Figure 2-3 Marcy Bridge Cross-section – Including Formwork................................. 2.4

Figure 2-4 Marcy Bridge after Collapse.................................................................... 2.5

Figure 2-5 Red Mountain Freeway Showing Collapsed Concrete Girders on Ground

................................................................................................................ 2.6

Figure 2-6 Ramp J Plan Showing Units 1 Through 3 ............................................... 2.8

Figure 2-7 Girder Layout Plan – Unit 1 on Which Girders Misaligned ...................... 2.9

Figure 2-8 Girder Layout Plan – Unit 2. Erection Was from Pier 7........................... 2.9

Figure 2-9 Typical Cross-frame Details (from Design Drawings) ........................... 2.10

Figure 2-10 Post-Collapse Photograph - Unit 2 Looking toward Pier 6.................... 2.11

Figure 2-11 I-70 Bridge Showing Collapsed Girder.................................................. 2.13

Figure 2-12 Girder Collapse - Note Girder Deflected Down Into Lane ..................... 2.15

Figure 2-13 Typical Cross-Section of SR 69 Bridge River Spans ............................ 2.16

Figure 2-14 State Route 69 Bridge Erection Progress at Collapse ......................... 2.17

Figure 2-15 SR69-Bridge Site Showing Collapsed Spans ....................................... 2.18

Figure 2-16 Quebec Bridge under Construction Shortly before Collapse (Modjeski 

et.al, 1919 – used by permission of Library and Archives of Canada).. 2.20

Figure 2-17 Quebec Bridge after Collapse (Modjeski et.al, 1919 – used by permission 

of Library and Archives of Canada) ...................................................... 2.21

Figure 2-18 Quebec Bridge after Collapse – End View (Modjeski et.al, 1919 – used by 

permission of Library and Archives of Canada) .................................... 2.22

Figure 2-19 I-80 Elevation and Erection Sequence.................................................. 2.23

Figure 2-20 Incorrect Bracing at Pot Bearing, Pier 1 and Abutment 1...................... 2.24

Figure 2-21 End view of I-80 Bridge under Construction Prior to the Collapse ........ 2.25

Figure 2-22 Cleddau Bridge Buckled over Pier........................................................ 2.27

Figure 2-23 West Gate Bridge after Collapse .......................................................... 2.28

Figure 2-24 West Gate Bridge Construction Site after Collapse .............................. 2.29

Figure 2-25 Rhine Bridge Longitudinal Stiffener Splice............................................ 2.31

Figure 3-1 Bridge Plate Girder Loaded for Transport to Project Site........................ 3.2

Figure 3-2 Concrete Girder in Transport with Escort Vehicles ................................. 3.3

Figure 3-3 Splicing Girder Segments at Grade Prior to Lifting ................................. 3.4

Figure 3-4 Curved Girder Being Erected with Cross-Frames Attached.................... 3.6

Figure 3-5 Setting Drop-in Span with Strongbacks Attached ................................... 3.8

Figure 3-6 Girder Supported on Strongback (Shown on the Right).......................... 3.8

Figure 3-7 Typical Strongback Arrangement............................................................ 3.9

Figure 3-8 Girder Rigging with Spreader Beam ..................................................... 3.10

Figure 3-9 Beam Clamps on Steel Girder .............................................................. 3.11

Figure 3-10 Crane Rigged to Concrete Girder at Lifting Loops ................................ 3.12

Figure 3-11 Basket Hitch Rigging............................................................................. 3.13

Figure 3-12 Beam Clamp......................................................................................... 3.13

Figure 3-13 Spreader Beam..................................................................................... 3.15
xvi

Figure 3-14 Lifting Beam.......................................................................................... 3.15

Figure 3-15 Girder Splice Bolts Being Installed and Drift Pins in Place.................... 3.16

Figure 3-16 Ironworkers Tools of the Trade............................................................. 3.17

Figure 3-17 Crane Mounted on Barge...................................................................... 3.20

Figure 3-18 Sample Load Chart for 350-Ton Capacity Crane.................................. 3.21

Figure 3-19 Sample Load Charts for 45-Ton Capacity Crane.................................. 3.24

Figure 3-20 Multiple Cranes Lifting Girder – Aerial View.......................................... 3.25

Figure 3-21 Lower Lateral Bracing........................................................................... 3.27

Figure 3-22 Wind Load Distribution.......................................................................... 3.28

Figure 3-23 Box Girder Top Lateral Bracing and Diaphragms ................................. 3.28

Figure 3-24 Steel Girder Tie Down Using Chain Binders to Pier.............................. 3.30

Figure 3-25 Steel Girder Tie Down Using Strut and Chain Binders ......................... 3.31

Figure 3-26 Concrete Girder Bracing Example Using Tie-down Rods ..................... 3.32

Figure 3-27 Typical Concrete Girder Bracing Arrangements at Pier or Abutment.... 3.33

Figure 3-28 Concrete Girder Erection Bracing – Example Plan ............................... 3.33

Figure 3-29 Concrete Girder Erection Bracing Detail at Abutment or Pier Using Cable 

and Timber Strut ................................................................................... 3.34

Figure 3-30 Concrete Girder Erection Bracing Detail between Girders Using Timbers 

and Top Tie Bar.................................................................................... 3.34

Figure 3-31 Concrete Girder Erection Bracing Detail between Girders Using Timbers 

and Tie Rod .......................................................................................... 3.35

Figure 3-32 Timber X-Bracing for Concrete I-girders ............................................... 3.35

Figure 3-33 Conceptual Guided HLMR Bearing Lock .............................................. 3.36

Figure 3-34 Temporary Brace to Existing Bridge Deck During Phased Construction

.............................................................................................................. 3.37

Figure 3-35 Hold-Down Assembly for Steel Girders................................................. 3.38

Figure 3-36 Shoring Towers Supporting Girders during Erection............................. 3.39

Figure 3-37 Tower Flexibility Effects Under Lateral Load......................................... 3.40

Figure 3-38 Shoring Towers Supported on Timber Mats ......................................... 3.41

Figure 3-39 Deck Finishing Equipment for Deck Pour ............................................. 3.43

Figure 3-40 Typical Overhang Bracket – Steel Girder.............................................. 3.44

Figure 3-41 Typical Overhang Bracket – Concrete Girder ....................................... 3.45

Figure 3-42 Overhang Brackets Being Set on a Tub Girder..................................... 3.46

Figure 3-43 Overhang Bracket Bracing Examples ................................................... 3.47

Figure 3-44 Bridge Deck Demolition Removing Deck in Sections............................ 3.49

Figure 4-1 Camber and Sweep in Steel Members ................................................... 4.4

Figure 4-2 Effects of Residual Stresses on Stress-strain ......................................... 4.5

Figure 4-3 Typical Residual Stress Distribution on a Rolled Wide Flange Section .. 4.7

Figure 4-4 Flexural Buckling of Wide Flange Column .............................................. 4.9

Figure 4-5 Effective Length Factor......................................................................... 4.10

Figure 4-6 K factors for Idealized Support Conditions............................................ 4.11

Figure 4-7 Typical Doubly and Singly-Symmetric Sections.................................... 4.13

Figure 4-8 Warping Stiffness and Bending Stiffness of the Plate Elements........... 4.14

Figure 4-9 Ineffective Torsional Brace ................................................................... 4.16

Figure 4-10 Lateral Bracing Offset from Shear Center............................................. 4.19

Figure 4-11 Definitions of yo and xo .......................................................................... 4.21
xvii

Figure 4-12 Moment of Inertia Sample Calculations ................................................ 4.22

Figure 4-13 Plate Buckling Coefficients for Axial Compression in a Long Plate....... 4.24

Figure 4-14 Bending Stresses in Doubly and Singly Symmetric Girders.................. 4.26

Figure 4-15 Buckled Shape of I-Girder..................................................................... 4.27

Figure 4-16 Effect of Load Position on Cross-section .............................................. 4.29

Figure 5-1 Relative Bracing System for Columns and Girder................................... 5.6

Figure 5-2 Nodal Bracing System for Bridge Girders ............................................... 5.7

Figure 5-3 Lean-on Bracing for Bridge Girders ........................................................ 5.8

Figure 5-4 Cross-frames in Skewed Application ...................................................... 5.9

Figure 5-5 Bending Stresses in Singly Symmetric Section .................................... 5.10

Figure 5-6 Torsional Bracing Stiffness ................................................................... 5.12

Figure 5-7 Stiffness Formulas for Twin Girder Cross-frames (assumes no connection 

eccentricity) ........................................................................................... 5.13

Figure 5-8 Web Stiffness Geometry ....................................................................... 5.15

Figure 5-9 Web Stiffness Geometry at Cross-frames............................................. 5.16

Figure 5-10 Brace Orientations for Bridges with Skewed Supports ......................... 5.18

Figure 5-11 System Buckling of a Twin Girder Widening......................................... 5.20

Figure 5-12 System Buckling Mode ......................................................................... 5.21

Figure 5-13 Elastic Deformation of Guy Wire Bracing.............................................. 5.23

Figure 5-14 Typical Pour Sequence for Two Span Bridge ....................................... 5.25

Figure 5-15 Uplift Effect on Two Span Deck Pour.................................................... 5.25

Figure 5-16 Typical Pour Sequence for Three Span Bridge..................................... 5.26

Figure 5-17 Center of Gravity and Destabilizing Moment Arm of Single Curved Girder

.............................................................................................................. 5.27

Figure 5-18 Center of Gravity and Stabilizing Moment Arm of a Pair of Curved Girders

.............................................................................................................. 5.29

Figure 5-19 Free-body Diagram of Concrete Beam with Eccentric Overhang Loading 

at Lift-off................................................................................................ 5.31

Figure 6-1 Line Element Versus Shell Element........................................................ 6.3

Figure 6-2 Indicating Torsional Deformations with Line Elements ........................... 6.5

Figure 6-3 Euler Column with Length of 30 ft......................................................... 6.10

Figure 6-4 Determining Buckling Capacity based upon Eigenvalue Buckling Solution 

and Magnitude of Reference Load........................................................ 6.11

Figure 6-5 Girder Properties for Beam Buckling Analysis ...................................... 6.12

Figure 6-6 Beam Modeled in MASTAN2 Subjected to Uniform Moment Loading .. 6.13

Figure 6-7 Beam Subjected to Uniform Moment Modeled in BASP....................... 6.13

Figure 6-8 Problem not Well Suited for Eigenvalue Buckling Analysis................... 6.15

Figure 6-9 Second Order Effects as a Result of Imperfections .............................. 6.17

Figure 6-10 Second Order Analysis on Column with Initial Imperfection.................. 6.18

Figure 6-11 Simple Problems for Use in Becoming Familiar with Software Capabilities 

and Modeling Decisions........................................................................ 6.21

Figure 6-12 Schematic of Girder Segment during Lifting ......................................... 6.22

Figure 6-13 Stabilizing Effect of Girder Self-Weight Acting below Crane Pick Point 6.23

Figure 6-14 Bolted Air Space [Stith et al. 2010] ....................................................... 6.24

Figure 6-15 Sample Input Page for Girder Properties in UT Lift............................... 6.25

Figure 6-16 Sample Cross-frame Input for UT Lift ................................................... 6.26
xviii

Figure 6-17 Sample Output of Optimum Lift Locations for Girder Segment for UT Lift

.............................................................................................................. 6.28

Figure 6-18 Sample Input Page for Actual Spreader Beam and Lift Locations from UT 

Lift......................................................................................................... 6.29

Figure 6-19 Sample UT Lift Output of Girder Stresses and Rotation at Ends and 

Middle of Segments .............................................................................. 6.30

Figure 6-20 Sample UT Lift Graphs of Girder Displacements and Torque............... 6.31

Figure 6-21 Typical UT Bridge Input Panel for Basic Bridge Geometry ................... 6.33

Figure 6-22 UT Bridge Pop-Up Screen with Additional Information on Skew Sign 

Convention............................................................................................ 6.34

Figure 6-23 UT Bridge Input Screen for Girder Properties ....................................... 6.35

Figure 6-24 Information Panel on the Defined Model for UT Bridge......................... 6.36

Figure 6-25 Plan View and Elevation of Two Span Bridge Modeled ........................ 6.39

Figure 6-26 Plan View of Erected Girders for Eight Erection Stages ....................... 6.40

Figure 6-27 Buckled Shape of Girder 1 with No Intermediate Bracing (Case 1) ...... 6.42

Figure 6-28 Buckled Shape of Girders 1 and 2 in Case 2........................................ 6.42

Figure 6-29 Case 5 Buckled Shape ......................................................................... 6.43

Figure 6-30 Case 8 Buckled Shape ......................................................................... 6.43

Figure 6-31 Buckled Shape for Case 1 with Shoring Tower 90 ft from Bent 1 ......... 6.44

Figure 6-32 Buckled Shape for Case 1 with a Holding Crane 90 ft from Bent 1....... 6.45

Figure 6-33 Potential Uplift in Horizontally Curved Girder during Erection............... 6.46

Figure 6-34 Cross-section of Four Girder Bridge Considered in the Concrete 

Placement Evaluation ........................................................................... 6.48

Figure 6-35 Critical Loading to Check Uplift When Continuous Deck Cast is Proposed

.............................................................................................................. 6.48

Figure 6-36 UT Bridge Results for Potential Uplift during Continuous Deck Cast .... 6.48

Figure 6-37 Estimated Dead Load Deflections from Uniform Load from Simulated 

Continuous Deck Placement................................................................. 6.50

Figure 6-38 Concrete Pouring Sequence................................................................. 6.50

Figure 6-39 Differential Deflection due to Early Stiffening of the Concrete .............. 6.51

Figure 7-1 Matrix for Recommended Level of Analysis – I-Girder Bridges............... 7.9

Figure 7-2 Matrix 1 for Recommended Level of Analysis – Tub-Girder Bridges .... 7.11

Figure 7-3 Matrix 2 for Recommended Level of Analysis – Tub-Girder Bridges .... 7.14

Figure 7-4 Concrete-placing and Finishing Equipment on Bridge Deck................. 7.20

Figure 7-5 Basic Wind Speeds (with permission from ASCE)................................ 7.25

Figure 7-6 Basic Wind Speeds (cont.) (with permission from ASCE)..................... 7.26

Figure 7-7 Exposure B - Suburban Residential Area with Mostly Single Family 

Dwellings (with permission from ASCE)................................................ 7.28

Figure 7-8 Exposure B - Urban Area with Numerous Closely Spaced Obstructions 

With Size of Single Family Dwellings or Larger (with permission from 

ASCE)................................................................................................... 7.29

Figure 7-9 Exposure C - Flat Open Grassland with Scattered Obstructions (with 

permission from ASCE) ........................................................................ 7.30

Figure 7-10 Exposure C - Open Terrain with Scattered Obstructions (with permission 

from ASCE)........................................................................................... 7.31

Figure 7-11 Exposure D - A Building at the Shoreline (with permission from ASCE)7.32
xix

Figure 7-12 Girder Wind Load Terminology ............................................................. 7.34

Figure 7-13 Girder Lifting Length Installation ........................................................... 7.38

Figure 7-14 Effect of Eccentricity on Curved I-Girder Tilt......................................... 7.39

Figure 7-15 Zero Rotation/Equal Force Lift Equation for Curved I-Girder ................ 7.40

Figure 7-16 Final Equilibrium Position of Hanging Concrete Precast Beam ............ 7.42

Figure 7-17 Equilibrium of Girder on Elastic Support ............................................... 7.48

Figure 7-18 Definition of Radius of Stability (r)......................................................... 7.50

Figure 7-19 Steel Girder Lifting Clamp Load Distribution......................................... 7.53

Figure 8-1 Steel Girder Erection Drawings 1 – Plan Stages 1 and 2........................ 8.3

Figure 8-2 Steel Girder Erection Drawings 2 – Plan Stages 3-5 and 6 .................... 8.4

Figure 8-3 Steel Girder Erection Drawings 3 – Plan Stages 7-10 ............................ 8.5

Figure 8-4 Steel Girder Erection Drawings 4 – Shoring Elevations.......................... 8.6

Figure 8-5 Steel Girder Erection Drawings 5 – Shoring Towers............................... 8.7

Figure 8-6 Steel Girder Erection Drawings 6 – Lifting and Local Bracing Details..... 8.8

Figure 8-7 Concrete Girder Erection Plan 1 – South Span Girders Plan and 

Clearances.............................................................................................. 8.9

Figure 8-8 Concrete Girder Erection Plan 2 – South Span Girders Plan................ 8.10

Figure 8-9 Concrete Girder Erection Plan 3 – North Span Girders Plan and 

Clearances............................................................................................ 8.11

Figure 8-10 Concrete Girder Erection Plan 4 – North Span Girders Plan ................ 8.12

Figure 8-11 Crane Track Pressures for Crawler Crane............................................ 8.17

Figure 8-12 Truck Crane on Outriggers Supported on Timber Mats ........................ 8.18

Figure 8-13 Plan for Crane Operating from Barge ................................................... 8.19

Figure 8-14 Plan Notes for Crane on Barge............................................................. 8.20

Figure 8-15 Precast Concrete Girder Supported on Strongback.............................. 8.22

Figure 8-16 Checklist: Plan Drawings (to Scale) for Each Erection Stage ............... 8.26

Figure 8-17 Checklist: Detail Drawings .................................................................... 8.27

Figure 8-18 Checklist: Written Procedures and/or Drawing Notes ........................... 8.28

Figure 8-19 Checklist: Calculations at all Stages of Erection................................... 8.29

Figure 8-20 Checklist: Additional Submittal Data ..................................................... 8.30

Figure 8-21 Checklist: Demolition Checklist............................................................. 8.31

Figure 9-1 Arch Bridges – Tied and True Types ...................................................... 9.1

Figure 9-2 Arch Bridge Erection Staging on Falsework............................................ 9.2

Figure 9-3 Erection of Tied Arch Bridge Using Falsework........................................ 9.3

Figure 9-4 Typical Truss Configurations .................................................................. 9.5

Figure 9-5 Temporary Kingpost Supporting Cantilever Construction of Bridge Truss 

Over the Mississippi River ...................................................................... 9.7

Figure 9-6 New Truss on Temporary Trestle for Slide-In ....................................... 9.10

Figure 9-7 Initial Balancing of the Congress Avenue Bridge over the Chicago River

.............................................................................................................. 9.11

Figure 9-8 Intermediate Balancing of the Congress Avenue Bridge over the Chicago 

River ..................................................................................................... 9.14

Figure 9-9 Late Stage Balancing of Congress Ave Bridge over the Chicago River 9.15

Figure B1-1: Example 1 General Plan and Elevation ....................................................B.3

Figure B1-2: Example 1 Framing Plan ..........................................................................B.4

Figure B1-3: Example 1 Cross-section .........................................................................B.5
xx 

Figure B1-4: Example 1 Girder Elevation ......................................................................B.6

Figure B1-5: Wind Load to Girder Group During Partially-Erected or Fully-Erected

Condition...............................................................................................B.10

Figure B1-6: Wind Load to 1st Girder During Its Setting (One Day) .............................B.10

Figure B1-7: Bridge Modeled in 3D Finite ElementAnalysis Software to Determine

Forces to Girders (Note Skew is Present But Difficult to See Due to

Perspective)..........................................................................................B.10

Figure B1-8: Case 1 (Dead = Selfweight, Wind = 26.6 lb/ft).........................................B.11

Figure B1-9: Case 2 (Dead = Selfweight, Wind = 198.5 lb/ft).......................................B.11

Figure B1-10: Case 3 (Dead = Selfweight, Wind = 198.5 lb/ft).....................................B.12

Figure B1-11: Case 4 (Dead = Selfweight, Wind = 198.5 lb/ft).....................................B.12

Figure B1-12: Case 5 ................................................................................................. B.13

Figure B1-13: Example 1 Single Girder Pick ...............................................................B.14

Figure B1-14: Example 1 Girder Clamp Loading.........................................................B.20

Figure B1-15: Major-Axis Bending Moment Diagram ..................................................B.21

Figure B1-16: Example 1 Overhang Bracket Loading.................................................B.37

Figure B1-17: Case 1 Eigenvalue Analysis ................................................................B.42

Figure B1-18: Case 2 Eigenvalue Analysis ................................................................B.43

Figure B2-1: Example 2 Cross-section .......................................................................B.57

Figure B2-2: Example 2 Framing Plan ........................................................................B.58

Figure B2-3: Example 2 Field Section 1 ......................................................................B.59

Figure B2-4: Example 2 Field Section 2 ......................................................................B.60

Figure B2-5: Example 2 Field Section 3.....................................................................B.61

Figure B2-6: Page 1 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames

..............................................................................................................B.65

Figure B2-7: Page 2 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames

..............................................................................................................B.66

Figure B2-8: Page 3 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames

..............................................................................................................B.67

Figure B2-9: Page 4 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames

..............................................................................................................B.68

Figure B2-10: Page 5 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames

..............................................................................................................B.69

Figure B2-11: Page 6 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames

..............................................................................................................B.70

Figure B2-12: Page 2 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames..................................................................................................B.72

Figure B2-13: Page 2 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames..................................................................................................B.73

Figure B2-14: Page 3 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames..................................................................................................B.74

Figure B2-15: Page 4 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames..................................................................................................B.75

Figure B2-16: Page 5 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames..................................................................................................B.76
xxi

Figure B2-17: Page 6 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames..................................................................................................B.77

Figure B2-18: Page 2 of UT Lift Output for Girder G3 Field Section 3 ..........................B.79

Figure B2-19: Page 3 of UT Lift Output for Girder G3 Field Section 3 ..........................B.80

Figure B2-20: Page 3 of UT Lift Output for Girder G3 Field Section 3 ..........................B.81

Figure B2-21: Page 4 of UT Lift Output for Girder G3 Field Section 3 ..........................B.82

Figure B2-22: Page 5 of UT Lift Output for Girder G3 Field Section 3..........................B.83

Figure B2-23: Page 6 of UT Lift Output for Girder G3 Field Section 3..........................B.84

Figure B2-24: Page 2 of UT Lift Output for Girder G2 Field Section 3..........................B.86

Figure B2-25: Page 3 of UT Lift Output for Girder G2 Field Section 3 ..........................B.87

Figure B2-26: Page 3 of UT Lift Output for Girder G2 Field Section 3 ..........................B.88

Figure B2-27: Page 4 of UT Lift Output for Girder G2 Field Section 3 ..........................B.89

Figure B2-28: Page 5 of UT Lift Output for Girder G2 Field Section 3 ..........................B.90

Figure B2-29: Page 6 of UT Lift Output for Girder G2 Field Section 3 ..........................B.91

Figure B2-30: Page 2 of UT Lift Output for Girder G1 Field Section 3 ..........................B.93

Figure B2-31: Page 3 of UT Lift Output for Girder G1 Field Section 3 ..........................B.94

Figure B2-32: Page 3 of UT Lift Output for Girder G1 Field Section 3 ..........................B.95

Figure B2-33: Page 4 of UT Lift Output for Girder G1 Field Section 3 ..........................B.96

Figure B2-34: Page 5 of UT Lift Output for Girder G1 Field Section 3 ..........................B.97

Figure B2-35: Page 6 of UT Lift Output for Girder G1 Field Section 3Erection of G3 and 

G4 in Span 3 (with all cross-frames and no shoring) ............................B.98

Figure B2-36: Analysis of Fully Erected Bridge ..........................................................B.99

Figure B2-37: Girder Deflection During Two Girder Erection ...................................B.100

Figure B2-38: Girder Stresses and Eigenvalue Analysis During Two Girder Erection

............................................................................................................B.100

Figure B2-39: Girder Deflection During Two Girder Erection with Shoring...............B.102

Figure B2-40: Girder Stresses and Eigenvalue Analysis, Two Girders with ShoringB.102

Figure B2-41: Girder Stresses and Eigenvalue Analysis, Two Girders with Shoring, Half 

of the Cross-Frames ...........................................................................B.103

Figure B2-42: Girder Stresses and Eigenvalue Analysis, Four Girders with no Shoring

............................................................................................................B.105

Figure B2-43: Girder Deflection During Four Girder Erection with no Shoring ..........B.105

Figure B2-44: Girder Deflection During Four Girder Erection with Shoring ..............B.106

Figure B2-45: Girder Deflection During Span 1 Erection..........................................B.107

Figure B2-46: Girder Stresses and Eigenvalue Analysis During Span 1 

ErectionAdequacy of the Bearings During Erection ............................B.107

Figure B2-47: Reactions During Case 1 (1st Deck Pour)..........................................B.109

Figure B2-48: Normal Stresses During Case 1 (1st Deck Pour) ..............................B.109

Figure B2-49: Girder G4 Normal Stresses at Left Tip of Bottom Flange for Analysis 

Case 1 (1st Deck Pour).......................................................................B.110

Figure B2-50: Girder G4 Normal Stresses at Right Tip of Bottom Flange for Analysis 

Case 1 (1st Deck Pour)Resistance of Girder G4, Field Section 1 for First

Cast During Concrete Deck Pour, continued.....................................B.110

Figure B2-51: Girder G4 Normal Stresses at Left Tip of Top Flange for Analysis Case 1 

(1st Deck Pour)...................................................................................B.111
xxii

Figure B2-52: Girder G4 Normal Stresses at Right Tip of Top Flange for Analysis Case 1 

(1st Deck Pour)...................................................................................B.111

Figure B2-53: Normal and Warping Stresses in Curved I-Girders .............................B.112

Figure B2-54: Top Flange Splice Bolt Configuration .................................................B.126

Figure B2-55: Web Splice Bolt Configuration............................................................B.127

Figure B2-56: Girder Stresses and Eigenvalue Analysis, Two Girders with Holding Crane

at Top Flange......................................................................................B.131

Figure B2-57: Girder Deflection During Two Girder Erection with Holding Crane at

Bottom Flange.....................................................................................B.133

Figure B2-58: Girder Stresses and Eigenvalue Analysis, Two Girders with Holding Crane

at Bottom Flange ................................................................................B.133

Figure B3-1: Example 3 Plan ....................................................................................B.140

Figure B3-2: Example 3 Elevation.............................................................................B.141

Figure B3-3: Example 3 Sections for Constant Depth Girders ..................................B.142

Figure B3-4: Example 3 Sections at Critical Locations ..............................................B.143

Figure B3-5: Example 3 Stages of Construction .......................................................B.144

Figure B3-6: Typical Strongback System..................................................................B.157

Figure B3-7: Minor Axis Moment of Inertia Calculation for BT-78...............................B.158

Figure B3-8: Minor Axis Moment of Inertia Calculation for BT-78, continued.............B.159

Figure B3-9: MinorAxis Moment of Inertia Calculation for BT-90 ..............................B.160

Figure B3-10: Minor Axis Moment of Inertia Calculation for BT-90, continued ...........B.161

Figure B3-11: MinorAxis Moment of Inertia Calculation for BT-180...........................B.162

Figure B3-12: MinorAxis Moment of Inertia Calculation for BT-180, continued .........B.163

Figure B3-13: Prestress Layout for End Girder Segments........................................B.164

Figure B3-14: Prestress Layout for Girder Segments at Splices in Spans 1 & 3......B.164

Figure B3-15: Prestress Layout for Pier Girder Segments .......................................B.165

Figure B3-16: Prestress Layout for Drop-In Girder Segments..................................B.166

Figure B4-1: Example 4 Cross-section .....................................................................B.173

Figure B4-2: Example 4 Framing Plan ......................................................................B.174

Figure B4-3: Example 4 Composite Box Cross-section, Girder 2 ..............................B.175

Figure B4-4: Problem Setup.....................................................................................B.176

Figure B4-5: Problem Input.......................................................................................B.176

Figure B4-6: Pour Sequence Loads (Analysis Case 1) ........................................B.177

Figure B4-7: Pour Sequence Loads (Analysis Cases 2 and 3)................................. B.178

Figure B4-8: Maximum Positive Moment Magnitude and Location for Cumulative

Analysis Case 2 ..................................................................................B.178

Figure B4-9: Max. External Brace Axial Stress for Cumulative Analysis Case 2 ........B.179

Figure B4-10: Normal Stresses Before Location of Maximum Positive Moment for

Cumulative Analysis Case 2 ................................................................B.180

Figure B4-11: Normal Stresses Beyond Location of Maximum Positive Moment for

Cumulative Analysis Case 2 ................................................................B.180

Figure B4-12: Normal And Warping Stresses In Curved I-Girders......................B.181

Figure B4-13: Loading Computation For Steel Dead Load (Dc) In Field Section 1 ..B.194

Figure B4-14: Loading Computation for Steel Dead Load (DC) in Field Section 2a ..B.195

Figure B4-15: Loading Computation for Steel Dead Load (DC) in Field Section 2b ..B.196
xxiii

Figure B4-16: Loading Computation for Average Steel Dead Load (DC) in Field Section

2 ..........................................................................................................B.197

Figure B4-17: Loading Computation for Steel Dead Load (DC) in Field Section 3 ....B.198

Figure B4-18: Loading Computation for Concrete Dead Load (DC) and Temporary

Forms Dead Load (CDL) ....................................................................B.199

Figure B4-19: Loading Computation for Construction Live Load (CLL).....................B.200

Figure B4-20: First Buckling Mode for Cumulative Analysis Case 2 ........................B.201

Figure B4-21: Problem Setup for Missing Brace Scenario ........................................B.202

Figure B4-22: First Buckling Mode for Cumulative Analysis Case 2 with Missing Brace

............................................................................................................B.203

Figure C-23 Lateral Pressure and Structure Height..................................................C.28
xxiv

TABLES

Table 6-1 Summary of Eigenvalues for Erection Scenario in Figure 6- 25 (half crossframes installed) ................................................................................... 6.41

Table 6-2 Summary of Eigenvalues for Erection Scenario in Figure 6- 25 All Crossframes Installed and Holding Crane for Case 1 .................................... 6.45

Table 6-3 Summary of analysis cases. ................................................................. 6.55

Table 7-4 Load Factors and Load Combinations .................................................. 7.17

Table 7-5 Wind Velocity Modification Factors ....................................................... 7.23

Table 7-6 Velocity Pressure Exposure Coefficient Kz ........................................... 7.33

Table 7-7 Wind Net Force Coefficient, Cf, for Girder Bridges during Construction 7.35

Table 7-8 Wind Net Force Coefficient, Cf for Truss Bridges (during Construction) 

(After ASCE 7-10)................................................................................. 7.36

Table B1-9 Erection Analysis Output Summary.......................................................B.12

Table B1-10 Deck Pour Analysis Output Summary ................................................... B.13

Table B3-11 Section Properties of Florida 78" Bulb Tee with Variable Web Depth...B.139

Table D-1 Load Combinations and Load Factors.........................................................D.3

Table D-3.1 Velocity Pressure Exposure Coefficient, Kz ............................................D.6

Table D-3.2 Wind Velocity Modification Factors, Vm...................................................D.7

Table D-3.3 Wind Net Force Coefficient, Cf, (For Girder Bridges During Construction)

................................................................................................................D.7

Table D-3.4 Wind Net Force Coefficient, Cf (For Truss Bridges During Construction)D.7
xxv 

PHOTOGRAPH/ILLUSTRATION CREDITS

Photographs and illustrations used in the figures in this manual have been provided by 

the following:

ASCE 7-10, used with permission of the American Society of Civil Engineers, 

Figures 7-5 through 7-11

CTL Group, Project No. 262291 (Arizona Department of Transportation) - Figure 2-5 

Danny’s Construction Company—Figures 3-4, 3-20, 3-36

Dunnett Bay Construction—Figures 3-39, 3-44

High Steel Structures—Figure 3-1 

Illinois Department of Transportation—Figure 2-10

Kansas Department of Transportation—Figure 1-1 

Knife River—Figures 3-2, , 3-10, 3-11, 3-32

McHugh Construction—Figure 9-6 

National Archives Canada, Figures 2-16 through 2-18.

National Transportation Safety Board Report HW-1-04-M21-023 – Figures 2-11 & 2-12

New York State Department of Transportation—Figure 2-1 

Pennsylvania Department of Transportation—Figure 2-21

Royal Commission into the Failure of West Gate Bridge – Figures 2-23 & 2-24

University of Texas-Austin – Figure 5-11

The Commercial Appeal, Memphis, used with permission, Figure 2-15

Walsh Construction Company—Figures 3-5, 3-6, 3-38, 7-4, 9-3, 9-5, 9-7, 9-8, 9-9 

Wisconsin Department of Transportation—Figures 8-1 through 8-10
xxvi 

GLOSSARY OF ACRONYMS

3D Three Dimensional

3D-FEM Three Dimensional Finite Element Method

2D Two Dimensional

AASHTO American Association of State Highway and Transportation Officials

ACI American Concrete Institute

AISC American Institute of Steel Construction

ASCE American Society of Civil Engineers

ASD Allowable Strength Design

ASTM American Society for Testing and Materials

BDS Bridge Design Specifications

DOF Degrees of Freedom 

DSW Design Speed Wind

FEM Finite Element Method

FHWA Federal Highway Administration

FDOT Florida Department of Transportation

FOS Factor of Safety

FS Factor of Safety

IDOT Illinois Department of Transportation

KDOT Kansas Department of Transportation

LF Load Factor

LRFD Load and Resistance Factor Design 

MRI Mean Recurrence Interval

NCHRP National Cooperative Highway Research Program 

NYSDOT New York State Department of Transportation

OSHA Occupational Safety and Health Administration

PCI Precast/Prestressed Concrete Institute

PennDOT Pennsylvania Department of Transportation

PE Professional Engineer

SSRC Structural Stability Research Council

TXDOT Texas Department of Transportation

US United States

UT University of Texas at Austin
xxvii 

LIST OF SYMBOLS

Symbol Definition

≤ less than or equal to

≥ greater than or equal to

< less than

> greater than

= equal to

a overhang beyond lift point (in)

a center-to-center spacing of top flanges in box girder (in)

a area (in2

) 

a the distance from the shear center to the location where the lateral brace

frames into the section (in)

Ab bolt area (in2

) 

A0 the enclosed area of the cross-section of the closed shape (in2

) 

Abar area of hanger bar (in2

) 

Abf area of bottom flange (in2

) 

Ac area of diagonal member (in2) 

Ad wind directionality factor

adi cantilever overhang during lift of drop-in girder (in)

Af exposed projected area of girder or truss (ft2

) 

Ag gross cross-sectional area of section (in2

) 

Ag_di gross area of concrete of drop-in girder (in2) 

Ag_ps gross area of concrete of pier segment girder (in2) 

Ah area of horizontal member (in2

) 

An net area of cross-section (in2

) 

Ao the enclosed area of the cross-section of the closed shape (in2

) 

aps cantilever overhang during lift of pier segment girder (in)

Af area of flange (in2) 

Atf area of top flange (in2

) 

Aw area of web (in2

) 

awc ratio of two times the web area in compression to the area of the 

compression flange

b the distance from the shear center to the location where the lateral brace 

frames into the section (in)

b the width of a plate element (in)

bb width of bottom flange (in)

bbf width of bottom flange (in)

bb_ps width of bottom flange of pier segment girder (in)

bf width of the flange (in)

bfc width of the compression flange (in) 

bflange unstiffened plate width of WT flange (in)

bft width of tension flange (in)

bi plate width for use in computing J (in)

bs width of stiffener plate (in)
xxviii 

bstem unstiffened plate width of WT stem (in)

bt width of top flange (in)

bt_di width of top flange of drop-in girder (in)

btf width of top flange (in)

c centroidal distance to extreme compression fiber (in)

C torsional stiffness (in4) 

Cb, CbL lift adjustment factor 

Cb moment modification factor 

Cd 1.0 for single curvature and 2.0 for the brace closest to the inflection point 

for a beam in double curvature

CDL, CDL construction dead load

Cf wind net force coefficient

C.G. center of gravity

CL length of clamp along flange (in)

CLE effective length for bending check (in)

CLL, CLL construction live load

Cmc ratio of shear buckling resistance to yield strength in hanger beam

CR equipment reactions

cu depth of neutral axis at ultimate load (in)

CW, Cw construction wind load

Cw warping constant (in6

) 

Cw14 ratio of shear buckling resistance to yield strength in strongback

d depth of cross-section (in)

d depth of girder (in)

D radial distance to center of gravity (in)

D girder depth (in)

dbr distance from top of beam to blocking (in)

Dc depth of web in compression (in)

Di depth of web measured along incline (in)

do transverse stiffener spacing in hanger beam (in)

do.w14 transverse stiffener spacing in strongback (in)

Dweb depth of web (in)

Dweb.w14 depth of web of strongback (in)

DC permanent dead load

deck_width deck width (out-to-out) (in)

DL dead load

DWS design wind speed (mph)

e eccentricity (in)

e eccentricity of overhang force (in)

E modulus of elasticity (ksi)

Ec concrete modulus of elasticity (ksi)

edi eccentricity of prestressing strands in drop-in girder (in)

ei initial eccentricity of center of gravity (in) 

ei_di initial lateral eccentricity at midspan during lift of drop-in girder (in)

ei_ps initial lateral eccentricity at midspan during lift of pier segment girder (in)
xxix

emax analysis error

eps eccentricity of prestressing strands in pier segment girder (in)

es eccentricity of prestressing strands (in)

Es steel modulus of Elasticity (ksi)

ET tangent stiffness

ew eccentricity from wind overturning moment (in)

f axial stress (ksi) 

f1 smaller stress at end of unbraced length assuming linear stress 

distribution (ksi) 

F eccentric force (kips)

°F degrees Fahrenheit

f0 and f2 respectively, smaller and larger stresses at the ends of the unbraced 

length (ksi)

Fb required bracing force (kips)

fb_ps compressive stress in bottom fiber of pier segment girder from gravity load 

and prestress (ksi)

Fbr required force couple in the brace (kips)

Fbr required strength of brace (kips)

Fbr factored chord forces in cross-frame (kip) (See Figure 5-7)

Fbrc required strength of compression brace (kips)

Fbrt required strength of tension brace (kips)

fbu stress in compression flange without consideration of lateral bending (ksi)

fbuc stress in compression flange without consideration of lateral bending (ksi)

fbut stress in tension flange without consideration of lateral bending (ksi)

fc concrete strength (ksi)

Fcr elastic lateral torsional buckling stress (ksi)

Fcrw nominal web bend-buckling resistance (ksi)

FE Euler buckling stress (ksi)

FL lateral force on flange from overhang bracket (klf)

fL1 first order stress due to lateral bending (ksi)

flb local flange bending stress (ksi) 

fLC approximated second order lateral bending stress (ksi) 

fL1c first order stress due to lateral bending in compression flange (ksi) 

fLt first order stress due to lateral bending in tension flange (ksi) 

Flongvert longitudinal force in bolt from vertical bending stress (kips)

Flonglat longitudinal force in bolt from flange lateral bending stress (kips)

Flongtotal total longitudinal force in bolt (kips)

fmid stress at middle of unbraced length (ksi) 

Fnc controlling nominal flexural resistance (ksi)

Fnc1 local buckling resistance (ksi)

Fnc2 lateral torsional buckling resistance (ksi)

FOS factor of safety

fr modulus of rupture of concrete (ksi) 

FQPL quarter point lift-off force (kips)

FSc factor of safety for cracking

FSf factor of safety for rollover
xxx 

FSc_di factor of safety for cracking of drop-in girder

FSc_ps factor of safety for cracking of pier segment girder

FSf_di factor of safety for failure of drop-in girder

FSf_ps factor of safety for failure of pier segment gider

ft. feet

ft2 square feet

ft compressive stress at top fiber due to gravity load and prestress (ksi)

ft_di compressive stress in top fiber of drop-in girder from gravity load and 

prestress (ksi)

ftop flange force from strong-axis moment (kips)

Ftrans transverse force in bolt from flange lateral bending stress (kips)

Fu tensile strength of steel (ksi) 

Fub tensile strength of bolt (ksi) 

Fu.bar tensile strength of hanger bar (ksi) 

Fy, Fy yield stress of steel (ksi) 

Fy.bar yield strength of hanger bar (ksi) 

Fyw14 yield strength of strongback (ksi)

Fyc yield stress of compression flange steel (ksi)

Fyf specified minimum flange yield strength (ksi) 

g dead load factor

G shear modulus (ksi)

G gust effect factor 

h exposed wind height (in)

h height of cross-section (in) 

h clear distance between flanges less the fillet for rolled shapes; distance 

between flanges for welded built-up girders or adjacent lines of fasteners 

(in)

H 1 minus the square of yo divided by the square of ro

H height of axis of rotation about the top of girder (in)

hb height of cross-frame (in)

H C.G. depth to center of gravity (in)

ho distance between flange centroids of the girder (in)

ho girder height (in)

hr distance from bottom of girder to roll axis (in)

hset exposed height for single girder being set (in)

I moment of inertia (in4) 

Ic connectivity index (in4) 

lgx gross moment of inertia about the x axis (in4) 

lgy gross moment of inertia about the y axis (in4) 

in2 square inches

in3 cubic inches

in. inches

lp polar moment of inertia (in4

) 

Is skew index

Ix moment of inertia about the x axis (in4) 

Ix_di major axis moment of inertia of drop-in girder (in4

) 
xxxi 

Ix_ps major axis moment of inertia of pier segment girder (in4) 

ly moment of inertia about the y axis (in4

) 

lyc moment of inertia of the compression flange about an axis through the 

web (in4) 

Iy_di minor axis moment of inertia of drop-in girder(in4) 

Iy,eff, Ieff equivalent moment of inertia about y axis for shape with unsymmetric 

flanges (in4

) 

Iy_ps minor axis moment of inertia of pier segment girder(in4) 

lyt moment of inertia of the tension flange about an axis through the web (in4) 

J St. Venant torsional constant (in4) 

k plate bucking coefficient 

k shear buckling coefficient

k distance from outer face of flange to web toe of fillet (in)

k, kip kilopounds

K effective length factor

kb combined stiffness of two fascia girder elastomeric bearings (k-in/rad)

Kd, kd wind directionality factor

kflange plate buckling coefficient for flange of WT

Kno sway effective length factor for columns that cannot sway

kstem plate buckling coefficient for stem of WT

kr height of roll center (in)

ksi kips per square inch

Ksway effective length factor for columns that can sway

kw14 shear buckling coefficient in strongback

Kz, kz velocity pressure exposure coefficient 

Kz effective length factor for torsion 

Kzt, kzt topographic factor 

Ky effective length factor for buckling about y axis

KΘ sum of rotational spring constants of supports (k-in/rad)

l beam length (in)

L length (in)

L span length (in)

l1 distance between lift points (in)

L length along girder to center of gravity (in)

lb pounds

lb length of bearing (in) 

Lb unbraced length (in)

Lb, Llift total length of a girder pick (in)

lbf poundforce

lbf/in2 poundforce per square inch

Lb.w14 unbraced length of strongback (in)

Lc length of diagonal member (in)

Ldi length between lifting points for drop-in girder (in)

Lg girder length (in)

Lg_di length of drop-in girder (in)
xxxii 

Lg_ps length of pier segment girder (in)

Lid eccentricity of Wid (in)

Lift L average length from the lift points to the ends of the girder (in)

Llift1 length along girder to Lift point 1 (in)

Llift2 length along girder to Lift point 2 (in)

Lp limiting unbraced length to achieve the maximum nominal flexural 

resistance under uniform bending (in)

Lp.w14 limiting unbraced length to achieve nominal plastic moment (in)

Lps length between lifting points for pier segment girder (in)

Lr limiting unbraced length to achieve the onset of nominal yielding in either 

flange under uniform bending with consideration of compression flange 

residual stress effects (in)

Lr.w14 limiting unbraced length to achieve nominal moment based on inelastic 

lateral-torsional buckling (in)

Ls length between supports (in)

LS span length at the bridge centerline (in)

Ly length for buckling about y axis (in)

LZ the spacing between locations restrained from twist (in)

m a constant taken to equal 1 for simple-span bridges and 2 for continuousspan bridges

M the bending moment at the particular cross-section (k-in) 

M 

MA moment at the quarter point of the unbraced length (kip-in)

MB moment at the middle of the unbraced length (kip-in)

Mbr moment in the brace (kip-in)

Mbr in-plane flexural resistance of brace (k-in)

Mbr skew moment in the brace for a skewed bridge. (kip-in)

MC moment at the three quarter point of the unbraced length (kip-in)

Mcr elastic critical buckling moment (kip-in)

Mf maximum moment within the span (kip-in)

Mfl lateral flange moment (kip-in)

Mg applied gravity moment (k-in)

Mg_di gravity moment at midspan during lift of drop-in girder (k-in)

Mg_ps gravity moment at midspan during lift of pier segment girder (k-in)

Mgs buckling capacity of a girder in the system buckling mode (kip-in)

ML lateral moment in flange from overhang bracket (k-in)

Mlat service level weak-axis moment that would cause cracking in top flange of 

girder (k-in)

Mlat moment in flange due to lateral bending from curvature (k-in)

Mlat lateral moment capacity of PPC girder (k-in)

Mlat_di lateral moment capacity of drop-in girder (k-in)

Mlat_ps lateral moment capacity of pier segment girder (k-in)

MLu factored lateral moment in flange from overhang bracket (k-in)

Mmax maximum moment in the beam segment (kip-in)

Mn nominal flexural resistance (k-in)
xxxiii 

Mnc nominal flexural resistance based on compression flange (k-in)

Mny nominal weak-axis bending resistance (k-in)

Mn.w14 nominal flexural resistance for strongback (k-in)

Mo overturning moment (kip-in)

Mo plastic moment (k-in)

Mp plastic moment resistance (k-in)

Mp.w14 plastic moment for strongback (k-in)

Mr resisting moment (kip-in)

Mr required flexural strength (k-in) 

Mrx flexural resistance about strong axis (k-in)

Mry weak axis flexural resistance (k-in)

mph miles per hour

Mu elastic buckling strength (k-in)

Mu factored maximum moment (k-in)

Mu_w14 maximum moment in strongback (k-in)

Mu_mc maximum moment in MC hanger beam (k-in) 

Mx applied unfactored strong-axis moment (k-in)

Mux applied factored major axis bending forces (k-in)

Muy applied factored minor axis lateral bending forces (k-in)

Mw applied wind moment at midspan (k-in)

N lateral bending constant

n number of braces in a span, excluding supports

N newtons

ncf number of intermediate cross-frames in the span

Nfb number of flange bolts

ng number of girders connected by cross-frames 

Ns number of shear planes

Nwb number of web bolts

P prestress force (kips)

P lifting clamp load (kips)

Pbr required brace strength (kips)

pcf pounds per cubic foot

Pe_FB flexural buckling resistance (kips)

Pcr critical buckling load (kips)

Pdi prestress force in drop-in girder (kips)

Pdi design load for MC hanger beam at drop-in segment (kips)

Pe governing elastic critical buckling resistance (kips)

Pe_FTB governing flexural-torsional buckling resistance (kips)

Pey flexural-torsional buckling resistance about y axis (kips)

PEy flexural buckling capacity

Pez flexural-torsional buckling resistance about z axis (kips)

PE critical elastic buckling (Euler) load (kips)

PEx flexural buckling capacity about the x axis (kips) 

plf pounds per linear foot

Pmax yield capacity of bracing (kips)

Pn nominal buckling strength (kips)
xxxiv 

Po equivalent nominal yield resistance (kips)

Pps prestress force in pier segment girder (kips)

Pr elastic torsional buckling capacity (kips)

Prc axial compression resistance (kips)

Pr axial tension resistance (kips)

Pref applied force (kips)

Prt axial tension resistance (kips)

Pr.u, Pru axial tension resistance for fracture (kips)

Pr.y, Pry axial tension resistance for yielding (kips)

psf pounds per square foot

psi pounds per square inch

PT elastic torsional buckling capacity (kips)

Pu applied factored axial force (kips)

Puc axial compression force (kips)

Put axial tension force (kips)

Py force resulting in full yielding of the cross-section (kips) 

Q slender element reduction factor

Q total force effect

Qflange slender element reduction factor for WT flange

Qi appropriate force effect

Qstem slender element reduction factor for WT stem

Qs slender element reduction factor for unstiffened elements

Qs_flange slender element reduction factor for unstiffened WT flange

Qs_stem slender element reduction factor for unstiffened WT stem

qz velocity pressure at height z above grade (psf)

Qz net wind pressure (psf)

Qzset one day girder setting net pressure (psf)

qzset one day girder setting velocity pressure (psf) 

qzsh shielding velocity pressure (psf) 

r radius (in)

r radius of stability (in) 

r radius of gyration (in) 

R radius of curvature of the girder (in)

Rapproxmax maximum of the component forces determined by the approximate 

analysis minus the corresponding estimate from the 3 Dimensional Finite 

Element Analysis, and that difference divided by the estimate from the 

from the 3 Dimensional Finite Element Analysis. 

Ratio1 web slenderness in hanger beam

Ratio1w14 web slenderness in strongback

Ratio2 limiting web slenderness in hanger beam

Ratio2w14 limiting web slenderness in strongback

Rb web load shedding factor 

Rc service level concentrated force at each flange edge (kips)

Rh hybrid factor

Rn nominal resistance of the web to local web yielding (Eq 7. 17) (kips)

Rn nominal shear resistance of bolt (kips)
xxxv 

ro polar radius of gyration (in)

Rp reduction factor for holes

Rr shear resistance of bolt (kips)

rt effective radius of gyration (in)

Ru total force in bolt (kips)

rx radius of gyration with respect to the x axis (in)

ry radius of gyration with respect to the y axis (in)

rz radius of gyration for minor principal axis (in)

S, s girder spacing (in)

Sb, Sbx elastic section modulus of the bottom fiber about the x axis (in3) 

Sf elastic section modulus of flange (in3) 

St, Stx elastic section modulus of the top fiber about the x axis (in3

) 

Sx elastic section modulus about the x axis (in3) 

Sxc elastic section modulus about the x axis to the compression flange (in3) 

Sy elastic section modulus about the y axis (in3) 

Syc elastic section modulus of compression flange about y axis (in3

) 

Syt elastic section modulus of tension flange about y axis (in3) 

t centroidal distance to extreme tension fiber (in)

t thickness of a plate element (in)

T short tons (2000 lb)

Tbar tension in hanger bar (kips)

tbf thickness of the bottom flange (in)

tf thickness of the flange (in)

tfc thickness of the compression flange (in)

tflange thickness of WT flange plate element (in)

ti plate thickness used in computing J (in)

ts thickness of the stiffener plate (in)

tstem thickness of WT stem plate element (in)

tT thickness of the top flange (in)

tft thickness of the tension flange (in)

ttf thickness of the top flange (in)

tw, tweb web thickness (in)

tweb.w14 thickness of web of strongback (in)

U shear lag reduction factor

V basic wind speed (mph)

Vm wind velocity modification factor

Vn nominal shear resistance (kips)

Vn.w14 nominal shear resistance in strongback (kips)

Vp plastic shear force (kips) 

Vp.w14 plastic shear force in strongback (kips) 

Vu maximum shear (kips) 

Vu_mc maximum shear in MC hanger beam (kips) 

Vu_w14 maximum shear in strongback (kips) 

w girder weight per unit length (klf)

W total weight of beam (kips)

W wind load
xxxvi 

W1 force to girder group during partially-erected or fully-erected condition (plf)

wb width of elastomeric bearing (in)

wbracket total uniform load at overhang bracket (klf)

wdi weight per unit length of drop-in girder (klf)

wDC uniform permanent dead load

wforms form weight at overhang bracket (klf)

Wo weight of beam + haunch (kips)

wps weight per unit length of pier segment girder (klf)

wfascia concrete weight at overhang bracket (klf)

Wg weight of the girder (kips)

wg width of the section (in)

wg width of the bridge measured between fascia girders (in)

Wid weight of half of slab between fascia girder and 1st interior girder (kips)

wrail screed rail weight at overhang bracket (klf)

Wset force to first girder during its setting (plf)

Wx weight of cross-frame (kips)

ww line load from wind (plf)

x additional overhang distance of deck relative to bottom flange of box girder 

(in)

x approximate location of splice (in)

X distance from the center of curvature to the axis of rotation (in)

 distance from the center of curvature to the center of gravity of the curved 

girder segment (in)

xo distance between the shear center and the geometric centroid measured 

about x axis (in)

xdi distance from lift point to midspan during lift of drop-in girder (in)

xps distance from lift point to midspan during lift of pier segment girder (in)

y height of center of gravity of beam above roll axis (in)

Yb, yb centroidal distance to bottom fiber (in)

ybf centroidal distance to bottom flange, referenced to bottom of girder (in)

yo distance between the shear center and the geometric centroid measured 

along y axis (in)

yb_di distance from centroid to bottom fiber of drop-in girder (in)

yb_ps distance from centroid to bottom fiber of pier segment girder (in)

yr height of the roll axis above the center of gravity of the beam (in)

yr_di height of roll axis above centroid of drop-in girder (in)

yr_ps height of roll axis above centroid of pier segment girder (in)

Yt, yt centroidal distance to top fiber (in)

yt_di distance from centroid to top fiber of drop-in girder (in)

yt_ps distance from centroid to top fiber of pier segment girder (in)

ytf centroidal distance to top flange, referenced to bottom of girder (in)

yw centroidal distance to web, referenced to bottom of girder (in)

z height of top of bridge deck above grade or water (ft)

zmax maximum resisting moment arm (in)

zo lateral deflection of center of gravity of beam with the full dead weight 

applied laterally (in)
xxxvii 

o, zo.bar lateral deflection of center of gravity of beam (in)

 

, zo.bar.p lateral deflection of center of gravity of beam including rotation effects (in) 

zo_di lateral deflection of center of gravity of drop-in girder with full dead weight 

applied laterally (in)

zo.p_di lateral deflection of center of gravity of drop-in girder including rotation 

effects (in)

zo.p_ps lateral deflection of center of gravity of pier segment including rotation 

effects (in)

zo_ps lateral deflection of center of gravity of pier segment girder with full dead 

weight applied laterally (in)

Zx.w14 plastic section modulus of strongback (in3

) 

Zx plastic section modulus about x axis (in3) 

Zy plastic section modulus about y axis (in3) 

α angle of overhang bracket relative to fascia girder web (rad)

α angle of overhang bracket relative to horizontal line (rad)

α superelevation or tilt angle of support (rad)

α one-half of the degree of curvature of the curved girder segment (rad)

β stiffness

βb attached brace stiffness (k-in/rad)

βbr required brace stiffness (k/in)

βbskew attached brace stiffness for a skewed bridge

βconn connection stiffness

βg in-plane girder system stiffness(k-in/rad)

βi ideal stiffness (k-in)

βL lateral bracing stiffness

βr reduced weak axis flexural stiffness accounting for imperfections (k-in)

βsec web distortional stiffness (k-in/rad)

βskew attached brace stiffness for a skewed bridge 

βT torsional bracing system stiffness (k-in/rad)

βTreqd required nodal bracing system stiffness (k-in) 

βTreqd5 required nodal bracing system stiffness for Case 5 (k-in)

 continuous bracing stiffness (k-in/rad-in)

βw warping stiffness (k-in)

appropriate load factor (LRFD)

δh horizontal deflection (in)

δv vertical deflection (in)

Δ deformation (in)

Δh horizontal deformation (in)

ΔL chord length to lift point 2 (in) 

Δo initial deformation or imperfection (in)

Δw lateral deflection at midspan due to wind on uncracked section (in)

ε strain (in/in)

ε ratio of solid area of truss members to gross area of truss
xxxviii 

θ skew angle measured from a line perpendicular to the tangent of the 

bridge centerline (deg)

θ equilibrium roll angle (rad) 

θ lateral deflection (in)

θ roll angle of major axis of beam with respect to vertical (rad)

θ inclination angle of web plate in box girder, measured from vertical (rad)

Θ angular distance to center of gravity (rad)

θ' angular distance from lift points to center of gravity (rad)

θ1 angle of rotation at liftoff (rad)

θ1 skew angle at first support (deg)

θ2 angle of rotation after liftoff (rad)

θ2 skew angle at second support (deg)

θ3 skew angle at third support (deg)

θBrY = angle of rotation at reinforcing bar rupture (rad)

Θdi equilibrium roll angle of drop-in girder (rad)

θi ei/yr = initial roll angle (rad)

Θi_di initial roll angle of drop-in girder (rad)

θ lift 1 angular distance to lift point 1 (rad)

θ lift 2 angular distance to lift point 2 (rad)

Θmajor roll angle of major axis with respect to vertical (rad)

Θmax tilt angle at which cracking begins (rad) 

Θmax_di maximum roll angle for cracking of drop-in girder (rad) 

Θmax.p & Θ'max tilt angle at failure (rad)

Θmax.p_di maximum roll angle for failure of drop-in girder (rad)

Θmax.p_ps maximum roll angle for failure of pier segment girder (rad)

Θps equilibrium roll angle of pier segment girder (rad)

Θmax_ps maximum roll angle for cracking of pier segment girder (rad)

Θi_ps initial roll angle of pier segment girder (rad)

Θtotal out-of-plumb total twist at end of girder (deg)

λ eigenvalue

λ slenderness ratio

λeff effective slenderness ratio

λlimit limiting slenderness ratio

λf slenderness ratio of the compression flange

λpf limiting slenderness ratio for a compact flange

λrf limiting slenderness for a noncompact flange

λrw limiting slenderness ratio for a noncompact web

μ Poisson’s Ratio

π pi, irrational number equal to circumference of a circle divided by its 

diameter

σ bending stress (ksi)

σcr elastic buckling stress (ksi)

σdiff warping stress in flange (ksi)

σp proportional limit stress (ksi)

σsum vertical bending stress in flange (ksi)
xxxix 

σTop LT, σL1, σL2 stress at the top left corner of the girder (ksi)

σTop RT, σR1, σR2 stress at the top right corner of the girder (ksi)

σBot LT stress at the bottom left corner of the girder (ksi)

σBot RT stress at the bottom right corner of the girder (ksi)

σTotal stress at the center of gravity of the girder (ksi)

σy yield strength (stress)(ksi)

φ resistance factor

φb resistance factor for lateral torsional buckling

φbk resistance factor for girder system buckling

φbr resistance factor for steel girder bracing

φf resistance factor for flexure 

φfx resistance factor for flexure about x axis

φfy resistance factor for flexure about y axis

φc, φc LRFD system factor

φc resistance factor for axial compression

φMn ultimate bending resistance (k-in)

φr factored resistance 

φu resistance factor for axial fracture (tension)

φy resistance factor for axial yielding (tension)
1.1

CHAPTER 1

INTRODUCTION

SECTION 1. MANUAL SCOPE

The design and construction of bridges has changed over the years to reflect the needs 

of the traveling public and advances in structural analysis techniques and materials 

developments. Highway geometrics, particularly in urban areas, often require curved 

girder structures, and the availability of higher strength materials has led to lighter 

weight members and longer spans. Current design practice also looks to minimize 

lateral bracing, particularly in steel bridges, where bracing connections must be detailed 

for fatigue.

Figure 1-1 Collapse of Steel Girder Bridge during Construction

Along with changes in bridge design, the ability of bridge contractors to set longer and 

heavier girders has increased with new high capacity mobile crane availability. 

Increased use of curved girders and composite construction, where the concrete deck 

contributes to lateral load resistance as well as providing lateral stability for the top 

flange, places added responsibility on contractors to understand bridge superstructure 

performance during construction. 

This manual provides guidance to bridge erection engineers, resident/construction 

engineers, and design engineers to assist in the design and evaluation of bridge 

superstructures during construction. It is intended primarily to cover common steel and 

concrete multi-girder I-girder and tub, or box-girder, bridges. Proper assessment of 

bridge superstructure performance during construction is critical to ensure that member 
1.2

instability or deformations do not lead to unsafe conditions or to poor geometry control 

that may be reflected in the finished structure. 

For many bridge structures, the most critical conditions for design occur during 

construction, particularly when concrete decks intended to provide lateral support to the 

girders are not yet in place. Bridge girder collapses during construction, due to 

instability, have occurred in the United States as well as other countries, and several 

case studies are presented in Chapter 2. In some cases, excessive girder deformations 

have necessitated superstructure bracing modifications and even removal and 

re-erection of girders. The survey results reported in Section 3 indicate that 75% of the 

responding states have experienced such occurrences. Bridge superstructure collapses 

due to instability have resulted in injuries and deaths to construction personnel as 

reported in numerous news reports (WECT, 2009; Roads & Bridges, 2005; Yura, Ji and 

Windeanto, 2005; Ex

ponent, 2011; Star News Online, 2008), as well as deaths to the 

public (NTSB, 2006). Collapses have occurred during reconstruction as well as during 

construction of new structures (KCCI News, Des Moines, 2011). 

These collapses and related girder erection problems not only affect the public due to 

fatalities and injuries, but such instances increase construction costs, either directly or 

indirectly, due to rework, extended project completion, and inconvenience to motorists. 

The case studies included in Chapter 2 show several failures within the United States 

within the 2002 – 2010 time frame, without even accounting for instances of excessive 

deformations or related lesser problems. Clearly, this incidence of failure is too high.

Considerable research has been conducted over the past 20 years to provide a better 

understanding of the performance of bridge superstructures during construction, and 

establish or confirm methods of analysis and member and system design. Many of 

these studies are cited herein or listed as additional references. Much of this work 

includes effects and design requirements related to structural stability, an area of 

structural theory that generally receives limited course time in undergraduate 

engineering programs. 

General theory of structural stability is addressed in numerous standard structural 

mechanics and analysis, as well as design, textbooks. Works on classic stability theory 

include the Theory of Elastic Stability by Timoshenko and Gere, and Buckling Strength 

of Metal Structures by Bleich, which is no longer in print. The Guide to Stability Design 

Criteria for Metal Structures, R. Ziemian ed., addresses not only theoretical aspects of 

stability, but the development of currently utilized design equations. Various technical 

papers addressing member and system stability have also been published in the 

journals of the American Institute of Steel Construction (AISC), the American Society of 

Civil Engineers (ASCE) Structural Engineering, Bridge Engineering, and Structural 

Design and Construction journals, the American Concrete Institute, (ACI), the PrecastPrestressed Concrete Institute, (PCI), and others.

Numerous reports and research papers addressing issues related to bridge erection 

and stability are available. In many cases these documents may be obtained 
1.3

electronically, often at no cost. Among those which provide information on bridge girder 

erection and stability are the following: 

• National Cooperative Highway Research Program (NCHRP) Synthesis 345, 

Steel Bridge Erection Practices (2005) examines and discusses issues relating to 

steel I-girder, tub-girder and box-girder bridges that influence bridge erection. 

The synthesis reports results from questionnaires and interviews with bridge 

owners, fabricators and erectors on issues such as girder fit-up, stability, erection 

sequencing and owner requirements. 

• NCHRP Report 725, “Guidelines for Analysis Methods and Construction 

Engineering of Curved and Skewed Steel Girder Bridges” (2012) evaluates the 

accuracy of one dimensional (line-girder based) and two dimensional (grid type) 

analysis procedures to predict constructed geometry and evaluate bridge 

constructability as opposed to three dimensional models. Recommendations 

relating bridge configurations and the desired analysis output data to appropriate 

analysis models are provided. The effects on bridge locked-in forces from crossframe detailing using either steel dead load fit (SDLF) or total dead load fit 

(TDLF) are also examined and procedures to account for these in the analysis 

are provided. The report also provides recommendations for analysis and plan 

submittal content for erection engineering.

• “Stability Analysis of Single and Double Steel Girders during Construction”, 

Coffelt, et. al, University of Tennessee (2010) looks at torsional buckling of single 

and double girder systems. This work indicates that under lateral wind, the lateral 

girder deflection of each girder of a pair is essentially the same and thus the 

weak axis moment of inertia of the girder pair is twice that of the single girder. 

Results of the work support Yura’s buckling equation (Yura, J. and Windeanto, 

2005) for twin girders, but suggest use of an unbraced length factor, Cb, of 3 for 

the cantilever case.

• “Stability of Precast Prestressed Concrete Bridge Girders Considering Sweep 

and Thermal Effects” Georgia Transportation Research Council Project No. E-20-

860, Zurieck, et al., (2009), is a report prepared by Georgia Institute of 

Technology for the Georgia Department of Transportation. This report includes a 

comprehensive summary of prior research and design recommendations for 

stability of both reinforced and prestressed concrete girders, both under lifting 

conditions and after setting. Recommended provisions for design based on 

theoretical and load test data are presented. The thermal effects of the 

performance of a 100 foot long 54 inch bulb tee are also modeled and discussed. 

It is noted, for the case studied, that internal thermal deflections were 

approximately 0.5 inch; however, instability due to this deformation was not 

predicted by in the finite element model. The model did not, however, include 

initial sweep or the effects of uneven support conditions. 

• “Guidance for Erection and Construction of Curved I-Girder Bridges”, Stith, et al., 

Report No. FHWA / TX–1010–5571–1, Center for Transportation Research, 

University of Texas at Austin (2010). The report summarizes the results of a 

research investigation on the behavior of horizontally curved girders during 
1.4

construction. The role of bracing in preventing girder buckling and excessive 

deformations is addressed theoretically and compared to field research results. 

Effects of holding cranes and shoring towers are included, as well as lifting 

considerations. The report also discusses computer programs to analyze girders 

during lifting, UT Lift, and steel I-girder bridges during erection, UT Bridge, that 

were developed as part of the overall project.

• “Impact of Overhang Construction on Girder Design”, Yang, et. al., Report No. 0-

5706-1, Center for Transportation Research, University of Texas at Austin 

(2010). This report presents research results and analytic studies to investigate 

the effects of deck overhang brackets on the performance of both concrete and 

steel girder bridges. System stability for concrete and steel girders is addressed 

as well as local web stability for steel girders, and analysis provisions are 

provided. A number of practical recommendations for handling field conditions 

are included. 

• “Design Guidelines for Steel Trapezoidal Box-Girder Systems”, Helwig, et. al., 

Report No. FHWA / TX-0710-4307-1, Center for Transportation Research, 

University of Texas at Austin (2004). This report provides theoretical background 

and analysis and design recommendations for trapezoidal box-girders with an 

emphasis on bracing system requirements to control flange buckling and girder 

distortion in permanent and constructions stages. The use of external k-frame 

braces used to control relative deformation between adjacent girders during deck 

placement is presented along with design methodology. 

• “Guidelines for Analyzing Curved and Skewed Bridges and Designing Them for 

Construction”, Dr. Daniel G. Linzell, et. al., The Thomas D. Larson Transportation 

Institute The Pennsylvania State University (2010). This report provides results of 

a series of parametric studies to evaluate the influence of construction 

methodology and sequence on stresses and deformations in both curved and 

skewed steel I-girder bridges. The bridge structures were numerically 

constructed and the influence of web-plumbness, temporary shoring location and 

settlement, sequencing of girder and cross-frame placement, cross-frame 

detailing practices (SDLF vs. FDLF), and several other variables were assessed 

as to their effects on the completed bridge. Models were correlated to field data, 

and these were then used to examine a wide range in the variables. The report 

provides recommendations on erection sequencing, use of cross-frames vs. solid 

diaphragms, web out-of-plumbness, shoring tower location and settlement limits, 

and cross-frame detailing practices for both curved and skewed bridges. 

Temperature effects during construction were found to be negligible. 

• “Lateral Bracing of Long-Span Florida Bulb-Tee Girders”, Consolazio, et. al., 

Department of Civil and Coastal Engineering, University of Florida (2007). The 

stability of Florida long span bulb-tee girders during the erection process was 

studied. Predicted girder buckling capacities include the effects of span length,

bridge skew, girder sweep, bearing pad creep, and bracing. Design equations to 

assess the buckling capacity including the effects of the above listed variables 
1.5

were developed. Lateral wind loading effects are also discussed, as are the 

effects on stability of elastomeric bearing pad orientation. 

During superstructure construction, it is also necessary that the engineers performing 

the construction stage analysis be knowledgeable in field erection practices, 

construction equipment, and construction load conditions — which may differ from those 

used in the design of the final structure. 

This manual provides background information in stability concepts and provides 

guidance on performing stability analysis. This manual also discusses some of the 

advantages and limitations of bridge stability analysis methods. Recommendations are 

included that address construction loading conditions, and identify critical stages within 

the bridge superstructure construction process. Primarily girder bridges are addressed 

since they constitute the majority of the bridge inventory. 

Chapter 2 of this manual presents several failure case histories, noting the prevalence 

of stability related failures, and the importance of proper temporary bracing. It is also 

noted that these failures are often preceded by various warning signs such as difficulty 

in member fit-up on visual deformations.

During bridge erection, the member support conditions, loads and stresses are affected 

by the erection practices such as lifting, installation of bracing, bearing conditions, 

temporary supports and placing sequence. Deck placing equipment, overhang brackets 

and staging can also have significant effects on girder stability. Chapter 3 presents 

information on construction practices as it relates to these considerations. 

Chapters 4, 5, and 6 present the theoretical background for analyzing girder stability as 

well as how to integrate the theory into design practices. Both individual member 

stability and multi-girder stability are presented. Chapter 6 includes advanced stability 

analysis methods and Eigenvalue analysis. 

Engineering design criteria for use in evaluating bridges during erection are presented 

in Chapter 7. Loading criteria and load factors for analysis are provided along with 

discussion of their applicability. Equations for checking member conditions during 

erection are included. Appendix D presents a summary of the engineering criteria for 

erection in a format suitable for inclusion in a specification.

Recommendations for the contents of erection engineering submittals are presented in 

Chapter 8. Submittal requirements are related to two categories of bridge complexity. 

Check lists are included to assist both the design engineer and submittal reviewer. 

Chapter 9 contains guidance on erection stability of several non-girder type bridges. 

Appendices are provided that include the results of the erection survey sent to each 

state, four example problems demonstrating the application of the design methods and 

criteria presented in the manual, design criteria provisions provided in a specification 

format, and references.
1.6

SECTION 2. SURVEY OF STATE DEPARTMENTS OF 

TRANSPORTATION

1.2.1 Survey Description

In an effort to better understand the past experiences in bridge superstructure erection 

in individual states, and their requirements as they relate to superstructure erection, a 

survey was sent to all states that are AASHTO members. Distribution of the survey was 

facilitated by Technical Committee T-4, Construction, of the AASHTO Subcommittee on 

Bridges and Structures (SCOBS). The survey included 18 questions, starting with any 

past problems related to girder erection (either steel or concrete), but concentrating on 

erection standards, erection design criteria, and submittal and review practices utilized. 

Additional survey results for steel bridge fabrication and erection practices can be found 

in NCHRP Synthesis 345, Steel Bridge Erection Practices, and Guidelines for Design 

and Safe Handling of Curved I-Shaped Steel Girders (Stith, Petruzzi, et. al). 

1.2.2 Summary of Responses

Survey responses were provided by 33 states, as shown in Figure 1.2. A compilation of 

the survey responses is included in Appendix C. A summary of the responses is given 

below. 

1. How often have you experienced any collapses or near collapses due to lifting, 

handling or instability of a member during construction? 

o Though nine respondents noted this rarely or never happens, 20 states 

provided at least brief descriptions of some type of problem. Exterior 

girder rotation during concrete placement, girder lifting difficulties, and 

insufficient temporary bracing were the primary problems. 

2. How often have you experienced member deformation / stability / alignment 

problems during deck placement? 

o Six respondents noted never having this problem, while 25 indicated it 

happens rarely too often. Problems for skewed girders and insufficient 

bracing were identified as well as fascia girder rotation.

3. How often have you experienced problems in the final geometry / alignment of 

superstructures during or at the end of erection?

o Twenty-eight respondents indicated never or rarely experiencing such 

problems, while five replied occasionally or often. Fifteen respondents 

noted problems related to survey errors or alignment / fit-up. 

4. When checking a girder for stability during handling and erection, do you require 

AASHTO LRFD be used?

o Eighteen states replied yes. Of those replying no, eight use a variety of 

AASHTO 17th edition, AASHTO Guide Specifications for Temporary 

Works, or State requirements.

5. Do you require an erection procedure to be submitted by the bridge erector?
1.7

o Of the 32 respondents, 27 answered yes.

6. If the answer to question 5 is yes, are they required for all bridges?

o Of the 26 respondents, 16 who answered yes to question 5 replied yes.

7. If the answer to question 6 is no, is there a size, span length, geometry feature or 

other threshold consideration that triggers the requirement?

o Fifteen respondents provided criteria. Triggering mechanisms included: 

erection over traffic, railroads, steel plate girders, long spans / curved / 

skewed, or as required by design engineer.

8. Do you have requirements for the erection procedure contents and format?

o Of the 32 respondents, 19 replied yes, 14 replied no.

9. Do you specify criteria to erectors for design wind load considerations during 

erection?

o Only six respondents specify criteria. California has a table of wind 

pressures, varying with height, while two reference the AASHTO Guide 

Specification for Bridge Temporary Works. 

10.Do you specify criteria to erectors for maximum lateral deflection of girders due to 

wind load?

o One state, Pennsylvania, provides criteria.

11.Do you specify a minimum safety factor with regard to global stability of a 

partially erected or demolished structure for global structural stability?

o None of the respondents specify this.

12.Do you provide guidance or design criteria for the strength and stability checks 

for cantilever girder sections during lifting and placement? 

o Two states, Kansas and Virginia, replied yes.

13.Do you require a bridge demolition procedure to be submitted for bridge 

removal?

o Twenty-seven respondents do require a demolition plan; only six do not.

14.If the answer to 13 is yes, is there a size, span length, geometry feature or other 

threshold consideration that triggers the requirement?

o Nineteen respondents indicated requirements. The most common 

triggering considerations are bridges over, or adjacent to, live traffic or 

railroads, structure length, or it is done on a case specific basis. 

15.Do you have requirements as to the qualifications of those who prepare the 

erection plan?

o Twenty-five respondents require the person to be a registered engineer.

16.Do you have requirements as to the qualifications of those who prepare the 

demolition plans?
1.8

o Twenty respondents have requirements. Fifteen require the persons to be 

a registered engineer, while the other five may require a P.E. based on 

bridge complexity.

17.Do you have requirements as to the level / degree of engineering analysis that is 

performed by the erector?

o Ten respondents indicated some type of requirements; however, these 

appear to be of a more general nature.

18.Who reviews erector supplied erection plans?

o Eight respondents perform reviews within the construction or resident 

engineering group, while twenty two perform reviews within the design 

group or by the Engineer of Record. Pennsylvania uses consultants for 

larger projects. Ohio uses a peer review system with no department 

review. One respondent did not indicate any reviews. Kansas uses 

different criteria for different erection categories.
1.9

Figure 1-2 States Responding to Survey
1.10

In reviewing the overall responses, several conclusions may be drawn:

• Though each of the respondents generally considers the occurrence of collapse, 

near-miss, or problems with stability and alignment to be infrequent, taken 

together, such incidents appear to be rather common. 

• The requirement to perform erection design checks to the AASHTO LRFD is 

referenced by the majority of respondents.

• Most respondents do require an erection and demolition procedure, though the 

requirement may be dependent on the bridge complexity, or adjacent traffic. 

• Approximately one half of the respondents provide requirements for the erection 

procedure.

• Detailed design requirements for erection design provided by the owner are rare. 

• Virtually all respondents require erection or demolition procedures to be prepared 

by a registered professional engineer.

• Review of erection procedures is most often performed in-house by construction 

or design staff. When not performed in-house, the design engineer-of-record 

performs the review. 

It is evident that problems do occur as a result of bridge erection operations and that, at 

least from a procedure and submittal process, the respondents require engineering for 

the erection or demolition work. Guidance for that engineering is considered to be 

provided by AASHTO along with the engineers’ experience. 

Survey responses show that owner requirements on girder deflections, global stability 

safety factors, strength, and stability of cantilever sections and wind load criteria during 

erection are rarely provided. Design criteria and the related discussion contained in 

Chapter 7 are provided so that consistent criteria are available to guide design in these 

areas.
2.1

CHAPTER 2

CONSTRUCTION FAILURE CASE STUDIES 

SECTION 1. INTRODUCTION

The failure of the Quebec Bridge over the St. Lawrence River in 1907 demonstrates that 

bridge failures during construction are not a recent phenomenon. Indeed, the collapse 

of bridges both during construction and while in service have been a prime motivator in 

the development of the design and construction specifications that we use today. 

However, despite advances in engineering knowledge and specifications, failures during 

construction continue to occur as the case studies that follow demonstrate. Failures not 

only include cases of total or partial collapse, but also include bridge deflection or local 

member buckling that require remedial measures. The failures discussed illustrate the 

importance of adequately addressing superstructure stability through both analysis and 

attention to field construction practices and erection details, noting that warning signs of 

potential problems are often present.

SECTION 2. ROUTE 17 (FUTURE I-86), NEW YORK (2010)

The structure under construction consisted of a two-span continuous parallel steel plate 

girder bridge that was planned to carry I-86 in New York State. The girders were each 

fabricated in three segments, with a center section spanning over the pier, and two end 

pieces, which originated at field splices and ended at the abutments. The girders were 

erected on temporary steel shoring frames located on each side of the pier. Each frame 

consisted of two steel towers and a single steel W33 shoring beam spanning between 

the towers in a simple span configuration. The W33 beam rested on a W12 transfer 

beam at the top of each tower. Each frame was founded on two timber distribution mats, 

one at the base of each tower. See Figure 2-1.

The center five girder segments over the pier were erected on a Thursday during the 

summer and reportedly had all cross-frames and bottom flange diagonals installed, but 

with partially bolted connections. Due to a poor weather forecast on Friday, no 

additional work was planned. 

On Saturday evening, the engineer in charge was notified of a loud bang and arrived at 

the site to find the bridge girders sitting precariously on the pier cap and partially 

collapsed shoring, as shown in Figure 2-1. The weather from the time of erection to the 

collapse was not unusual, with winds averaging 7 to 10 mph and occasional gusts as 

high as 25 mph. 

A subsequent forensic analysis by the owner uncovered multiple issues with the 

temporary shoring. Deficiencies were identified in the capacity of the W33 shoring beam 

with respect to lateral torsional buckling and for local web crippling and yielding where 

the bridge girders rested on the top flange of the W33. Additionally, the investigation 
2.2

determined that the W12 transfer beam at the top of each tower had inadequate flexural 

strength, and the pins used to splice the shoring tower segments together were 

significantly overstressed. A review of survey data from before and after the failure 

determined that one of the distribution mats supporting one of the temporary shoring 

towers had settled 31⁄2 inches between the time of erection and the forensic 

investigation.

Figure 2-1 Route 17 Collapsed Shoring and Girders

SECTION 3. MARCY BRIDGE, NEW YORK (2002)

The Marcy Bridge was designed to span approximately 170 feet across an expressway 

in New York State and was to serve as a pedestrian bridge. The bridge was designed 

as a composite structure incorporating a steel tub-girder with a 14-foot-wide, cast-inplace concrete deck. The bridge cross-section including the deck formwork is shown in 

Figure 2-3(Corr, et. al 2004). The structure collapsed during the concrete deck 

placement in the fall of 2002, at a time when the concrete placement had reached

approximately midspan. The collapse resulted in one fatality and nine serious injuries. A 

photograph of the bridge after the collapse is shown in Figure 2-4.

The design consisted of a single trapezoidal steel tub-girder with a composite reinforced 

concrete deck. The bridge was straight in plan. A subsequent forensic investigation 

determined that the failure mode was lateral-torsional buckling of the steel tub-girder in 

which the entire girder cross-section participated, as opposed to the typical failure mode 

of the compression flanges only as shown in Figure 2-4. Such bridges are particularly 
2.3

susceptible to this type of failure because they are very flexible in a twisting mode prior 

to deck hardening. A plan view of the bridge, showing the locations of the struts and K 

braces is shown in Figure 2-2. The spacing of the internal bracing was sufficient to 

prevent lateral flange buckling (Yura, J.A. and Widianto, 2005)

Figure 2-2 Marcy Bridge Plan

Since the shear center of the tub-girder is located below the tub-girder cross-section, 

construction loads can generate torsional loads in the open cross-section. The ratio of 

the moment of inertia about the vertical, y, axis over the moment of inertia about the 

horizontal, x, axis for the girder was 1.75, and hence lateral torsional buckling was not 

considered as a mode of failure. However, the Marcy bridge tub-girder behaved like a 

double I-girder bridge due to the absence of top flange bracing. The cross-frames did 

not provide out-of-plane rigidity, allowing each girder to deflect individually, and the 

entire tub girder cross-section failed in global lateral-torsional buckling. 
2.4

Figure 2-3 Marcy Bridge Cross-section – Including Formwork

Several things could have been done to avoid this collapse. A structural analysis of the 

bridge behavior during concrete placement would have indicated that temporary 

falsework, such as shoring towers, was required to ensure stability until the concrete 

attained sufficient strength. Optionally, additional top flange lateral bracing could have 

been added to create a quasi-closed cross-section and increase the global lateraltorsional stiffness to prevent buckling. The 1978 US Steel publication titled, 

Steel/Concrete Composite Box-Girder Bridges, A Construction Manual, recommends a 

full length internal top flange lateral system in spans over 150 feet. A third option could 

have utilized stay-in-place formwork engineered to act as top flange lateral bracing. The 

bridge did utilize stay-in-place formwork; however, the formwork and its connection to 

the top flanges were not engineered to provide the lateral strength and stiffness needed 

to prevent the girder from buckling.
2.5

Figure 2-4 Marcy Bridge after Collapse

One outcome of the Marcy Bridge collapse was a requirement issued by the New York 

Department of Transportation in 2003 that all tub girders include a full length lateral 

bracing system. Similar provisions were also subsequently included in the AASHTO 

Specifications (Corr, D.J. et. al 2009).

SECTION 4. RED MOUNTAIN FREEWAY, ARIZONA (2007)

The Red Mountain Freeway collapse occurred during the construction of the Red 

Mountain Freeway near Power Road in Mesa, Arizona. Two bridges were under 

construction, an eight-span structure carrying westbound traffic and a nine-span 

structure carrying eastbound traffic. The collapse occurred in Span 5 of the westbound 

structure, which consisted of 5 foot 3 inch deep AASHTO Type V modified prestressed 

concrete girders in a 114-foot simple span configuration (ENR, 2007). 
2.6

During July 2007, the Span 5 girders of the westbound structure had been erected and 

were seated on their elastomeric bearings. No temporary cross bracing had been 

installed to provide lateral stability. On August 9, 2007, nine of the eleven precast, 

prestressed concrete girders in Span 5 collapsed prior to placement of the cast-in-place 

concrete deck and diaphragms.

A forensic investigation (CTL Group, 2007) initiated by the Owner concluded that the 

likely cause of the failure was lateral instability of the one of the exterior girders, Girder 

A5-9. This instability led to a rolling and/or sliding failure of the girder, which triggered a 

progressive collapse of the eight adjacent girders. The report stated that the instability 

of the girder was likely due to simultaneous bearing eccentricity, bowing of the girder 

(sweep), and a non-level slope of the bearing surface. Additionally, thermal creep, 

concrete creep, wind, and construction loads between girder erection and the collapse, 

and the failure to fully remove the stainless steel bearing plate protection material 

compounded the initial eccentricity, sweep, and bearing surface slopes in both the 

transverse and longitudinal directions, increasing the likelihood of the collapse.

Figure 2-5 Red Mountain Freeway Showing Collapsed Concrete Girders 

on Ground
2.7

In their article “Rollover stability of precast, prestressed concrete bridge girders with 

flexible bearings,” Hurff and Kahn (Hurff, H.B. and Kahn, L.F., 2012) also conclude that 

the girder failure was due to rollover and not buckling. The CTL report provided 

recommendations to improve resistance of girders to rollover to include:

• Assuring all bearing surfaces are clean

• Assuring the girders are centered on the bearings

• Installing temporary bracing for lateral stability at the girder ends as soon as they 

are erected.

SECTION 5. EAST BOUND I-80/94 TO NORTH BOUND IL 394, 

RAMP J

2.5.1 General Description

Reconstruction of the I-80/94 / IL 394 interchange included widening and 

reconfiguration of the interchange to provide improved traffic flow. The improved 

geometrics required construction of two elevated curved ramp structures, designated 

Ramps G and J. Due to construction scheduling and contract packages, the two ramps 

were erected by different contractors. During steel erection for the three-span Unit 2 of 

Ramp J, a collapse occurred.

Ramp J incorporated a cast-in-place concrete deck supported on six concentrically 

curved, welded steel plate girders. The ramp had two, three span continuous units, and 

one four-span continuous unit separated by expansion joints, with an overall centerline 

length of 2,344 feet - 8 inches. The arrangement of the ramp and the unit designations 

are shown in Figure 2.6. 
2.8

Figure 2-6 Ramp J Plan Showing Units 1 Through 3

The I-shape girders were spaced radially at 5 feet-53

/8 inches center-to-center, with 

bolted radial cross fames spaced at approximately 15 feet. See Figure 2-7 and Figure 2-

8 for the girder layout and splice locations for Units 1 and 2 respectively, and Figure 2-9 

for the typical cross-frame details. The girders’ webs were 102 inches deep by 3⁄4 inches 

thick, and the flange sizes varied by location. Flange width to thickness ratios varied 

between (approximately) 15 and 18 inches in positive moment regions. The three outer 

girders had larger flanges than the three inside girders. The girders were curved to 

approximately 990 feet radius and the ramp had a superelevation of approximately 6 

percent. 
2.9

Figure 2-7 Girder Layout Plan – Unit 1 on Which Girders Misaligned

Figure 2-8 Girder Layout Plan – Unit 2. Erection Was from Pier 7.
2.10

Figure 2-9 Typical Cross-frame Details (from Design Drawings)

Drawing notes indicated the bridge was designed to AASHTO Standard Specifications 

for Highway Bridges 2002, and the 1993 Guide Specifications for Horizontally Curved 

Highway Bridges (with revisions through 1997). Structural steel was AASHTO M270M, 

Grade 345 (Fy = 50 ksi). Cross-frame connections stipulated M22 (7/8-in. diameter) high 

strength bolts in M27 (11

/16 in. diameter) oversize holes. The drawings also contained 

the following Construction Note: 

“The stability of the partially erected curved steel components is the Contractor’s 

responsibility during all phases of construction. Temporary shoring towers may 

be required at locations determined by the Steel Erector”. 

A further, Steel Erection Note stated:

“Contractor to submit for Engineer’s review, detailed erection plans and procedures 

taking into account traffic maintenance including but not limited to staging positions, 

falsework locations and sequence of girder erection and provisions for stability of 

girders and bearings during erection.”

A further note required bearings to be blocked during erection.

Construction of the ramp began with Unit 1, for which steel erection was mostly 

completed at the time Unit 2 erection began, although end cross-frames were not 

completed and interior cross-frame connection bolts were not tightened. The erector 
2.11

planned to adjust the steel alignment and complete cross-frame bolt tightening prior to 

forming and casting the deck. Unit 1 shoring was left in place until all steel work was 

erected.

Unit 2 erection started with Span 6 from the expansion joint at Pier 7 and progressed 

toward Unit 1, setting the girders from the outside of the curve inward. See Figure 2-8 

for the girder layout in Unit 2. Span 6 girders had two field bolted splices, and the splice 

nearest Pier 7 was bolted on the ground before the combined segments were lifted. A 

shoring tower was placed near midspan to support the two outside girders (#5 and #6). 

Some of the lateral bracing was bolted finger tight. The next girder segments, extending 

over Pier 6, were erected and the splices fully bolted. 

Once all six rows of girders were in place in Span 6, the shoring tower was to be 

relocated. A crane applied uplift to a girder at the tower to reduce pressure and allow 

the shoring tower jacks to be loosened. After the jacks were released, workers began 

disassembling the tower, but then the Span 6 girders moved outward, became unstable, 

and collapsed, resulting in the death of one ironworker and injuries to three others. 

Figure 2-10 is a photograph taken after the collapse, looking toward Pier 6. Due to the 

position of Unit 2 in the interchange, the steelwork did not land on the traveled roadway, 

resulting in minimal traffic disruption.

Figure 2-10 Post-Collapse Photograph - Unit 2 Looking toward Pier 6
2.12

A subsequent survey of the erected steel for Unit 1 of the ramp, Figure 2-7, performed 

to verify alignment and elevations preparatory to placing the concrete deck showed that 

the in-place geometry did not match the design documents. Both the girder alignment 

and elevations varied from requirements. Vertical deflections were most severe in the 

outside girder of Span 2 of Unit 1, where deflections exceeded design values by several 

inches. Horizontal deflections of several inches outward were also measured in Span 2 

of Unit 1. These deflections were severe enough that the Illinois Department of 

Transportation mandated the contractor install additional shoring until methods to 

realign or even re-erect the steel work were investigated and applied.

2.5.2 Ramifications of Collapse

At the time of the collapse, the erection of Unit 3 had not started. Prior to starting the 

Unit 3 erection, a detailed erection plan and construction procedure was developed to 

address both girder stability and geometry control based on a piece-by-piece erection 

analysis. Shoring towers were placed for temporary support and were designed with 

sufficient capacity to allow jacking of the girder needed for adjusting elevation during 

erection.

The Span 6 in Unit 2 steel was replaced with new girders, and the existing pier cap 

concrete was repaired. A plan for removal of the collapsed steel and erection of the new 

girder was also developed for this unit. The Unit 1 steel was realigned prior to deck 

placement.

SECTION 6. I-70 BRIDGE, COLORADO (2004)

Two steel plate girders, each 194 feet long, composed of a 154-foot span and 50-foot 

cantilever over the center pier were scheduled to be erected to support the widening of 

an existing structure during a nighttime closure of the highway below. The contractor 

encountered problems in setting the first girder. Reportedly, the contractor used 

improper tools and set the first piece backwards. These problems caused delays and 

only one of the two girders was erected during the nighttime closure (NTSB, 2006). 

Horizontal temporary steel angle lateral braces from the erected single girder to the 

existing bridge deck were planned to be installed. Bolts were to be used to connect the 

angle braces to the steel girder and expansion bolts were to be used to connect the 

braces to the bridge deck. The NTSB Highway Accident Report indicates that the 

Erector’s Safety Officer, with no training or certification in engineering, developed the 

bracing plan for the single girder utilizing a hand drawn sketch.
2.13

Figure 2-11 I-70 Bridge Showing Collapsed Girder 

A cold and windy forecast postponed the erection of the second and third girder needed 

for the widening, as well as the cross-frames, for more than three days. At that time, the 

single erected girder collapsed, rolling onto its side and causing three deaths. Figures 2-

11 and 2-12, from the NTSB report, show the collapsed girder.

The subsequent forensic investigation indicated several problems with the girder 

installation. The girder had been installed over four degrees out of plumb at the 

abutment, leaning toward the existing bridge, and over two degrees out of plumb at the 

pier. The NTSB determined that failure of the braces occurred at the existing bridge 

deck, when the lateral force from the girder’s distortion placed loads on the expansion 

anchors, separating the expansion bolts from the existing bridge deck. The expansion 

bolts were not installed in accordance with the manufacturer’s instructions. The 0.75-

inch diameter bolts were set in oversized, 0.90 inch diameter holes, and four of the five 

bolts were not embedded into the concrete the minimum specified depth of 3.25 inches. 

Only one bolt was embedded more than 2.5 inches deep, and one bolt was embedded 
2.14

only 1.25 inches deep. Additionally, the five lateral braces were to be bolted flush with 

the existing bridge deck and none were actually flush with the deck.

A finite element analysis of the girder collapse was conducted by the FHWA TurnerFairbank Highway Research Center (Wright, Kogler, et.al, 2005) to assist in determining 

the likely or possible sequence of events between the girder erection and collapse. 

Although the wind loading had minimal effect on the girder, cyclical forces in the braces 

due to lateral vibrations and wind loads were identified as primary factors in weakening 

the incorrectly installed expansion bolts over time. The second angle brace (from the 

south) of the five braces was critical in providing stability for the girder. The analysis 

indicated that the removal of this brace caused immediate instability for the out-of-plumb 

girder. 

As part of the response to this accident, the State DOT issued post-accident revisions to 

its Standard Specifications, including: 

1. An erection plan must be developed. It must be reviewed and approved by the 

Contractor’s Professional Engineer at least 4 weeks prior to the erection of a 

structural steel member.

2. Details for falsework, bracing, or other connections should be shown on the 

erection plan.

3. A pre-erection conference must be held two weeks prior to erection, attended by 

the Contractor’s Professional Engineer.

4. Written approval of each phase of installation must be provided by the 

Contractor’s Professional Engineer before vehicles or pedestrians are allowed on 

or below the structure.

5. Daily inspections of erected steel are required by the Contractor until completion 

of the deck concrete.

This accident also demonstrates the need to have contingency plans in place at each 

stage of erection. 
2.15

Figure 2-12 Girder Collapse - Note Girder Deflected Down Into Lane

SECTION 7. SR69 OVER THE TENNESSEE RIVER (1995)

The SR69 Bridge over the Tennessee River consisted of 16 spans totaling 2893 feet – 9 

inches in length. The 13 approach spans consisted of prestressed precast bulb tee 

girders. The three river-crossing spans, 14, 15, and 16 were: 340 feet, 525 feet, and 

340 feet – 6 inches long, respectively. Each was supported by three continuous steel 

girders spaced 20 feet - 10 inches on center transversely, with intermediate W24 steel 

stringers centered between the girders. The girders were braced by transverse crossframes spaced at 24 to 25 feet on center. A cross-section of the river spans is shown in 

Figure 2-13.
2.16

Figure 2-13 Typical Cross-Section of SR 69 Bridge River Spans
2.17

In May of 1995, erection work was progressing on the main river span. Two girders 

were erected and cross-frames were installed and bolted in Spans 14 and 15. The 

girders were cantilevered over Pier 15 to field splice locations in Span 16. As the final 

girder was being erected in Span 15, the contractor had difficulty in the girder fit-up 

(Wiss, Janney, Elstner Assoc., Inc., 1995). The fit-up problem was related to a sweep in 

the girder that caused it to miss its bearing at the pier and a bolt hole pattern 

misalignment in matching pieces. As the erection crew made efforts to correct this 

sweep through come-a-longs and over-booming of cranes, they buckled a cross-frame 

that was in place between this last girder and the adjacent girder. When they removed 

the damaged cross-frame in order to replace it, the last girder erected was left with 

approximately a 200 foot unbraced length, and the bridge collapsed shortly thereafter. 

Figure 2-14 shows the progression of erection, looking downstream, at the time of the 

collapse. The collapse resulted in one fatality and several injuries. 

Figure 2-14 State Route 69 Bridge Erection Progress at Collapse
2.18

Figure 2-15 is a photograph from the Wiss, Janney, Elstner Associates, Inc. report, 

reportedly taken within hours of the collapse. The cross-frame that had been removed 

can be seen in the right side of the photograph still attached to the crane’s whip line. A 

subsequent forensic analysis attributed the collapse to lateral torsional buckling of the 

girder because of the large unbraced length of the compression flange with the crossframe removed. 

Figure 2-15 SR69-Bridge Site Showing Collapsed Spans

SECTION 8. SOUVENIR BOULEVARD BRIDGE, QUEBEC (2000)

The Souvenir Boulevard Bridge, which crosses Highway 15 in Laval, Quebec, was 

under construction in June 2000 when a partial collapse of the structure occurred. The 

4-span, 472 foot long structure consisted of AASHTO Type V prestressed concrete 

girders and an 8-inch thick concrete deck. Per industry standard in Quebec, the 

structure was designed to have only one expansion joint to increase durability and 

reduce maintenance. To accommodate the single expansion joint, fiber reinforced 

elastomeric bearings were provided at the point of fixity at the west abutment (Line 1), 

and pot bearings designed to accommodate longitudinal movement were provided at 

the piers and east abutment (Lines 2-5). Due to the significant width of the bridge, the 

pot bearings at Girders 1-4 and 12-15 (exterior girders) were also designed to allow for 

transverse movement (Tremblay, R. and Mitchell, D., 2006).

On June 18, 2000, Girders 1-8 had been erected and were seated on their bearings, 

and threaded tie rods and timber blocking had been installed between the top flanges at 
2.19

the ends of the girders, as had been used as in precast girder construction supported 

on elastomeric bearings. At approximately 10:45 a.m., the four exterior girders in the 

interior spans on the south side of the structure slid off their bearings, tilted over, and 

collapsed onto Highway 15, killing one person and seriously injuring another. The four 

exterior girders in the end spans also slid off their bearings, but were prevented from 

collapsing onto the highway below by the abutment wing walls.

A committee of experts was created to investigate the collapse, identify the causes of 

the collapse, and provide guidance on how to evaluate the adequacy of bracing for this 

type of construction. The committee collected mechanical, geometric, climatic, and 

loading data after the collapse, and a three-dimensional model of the girder-bearing 

system was developed. The analysis showed that sliding pot bearings do not offer 

significance resistance to the twisting of the girders about their longitudinal axis. This 

allowed the bearings to slide off their supports where transverse movements were 

permitted. Because the tie rods and timber blocking which only ran between the top 

flanges did not provide adequate bracing against girder rotation, the girders were 

unstable and a small load or disturbance could potentially lead to a collapse.

To mitigate the likelihood of the collapse of similar structures, the committee determined 

that adequate temporary bracing must be provided for girders supported by pot 

bearings prior to placement of the concrete deck and diaphragms. This bracing should 

include diagonal and lower lateral bracing to restrain rotation of the girder ends. 

Additionally, a stability analysis of the individual girders and the girder systems should 

be performed as a part of the design of the temporary bracing and to ensure the overall 

stability of the structure during construction.

SECTION 9. QUEBEC BRIDGE OVER ST. LAWRENCE (1907)

At 5:31 p.m. on the afternoon of August 29, 1907, the south arm of the cantilever truss 

bridge under construction north of Quebec over the St. Lawrence River collapsed. The 

New York Times reported that the sound of the collapse was clearly heard in Quebec, 

nine miles away. Of the 86 workers on the bridge at the time of collapse, 75 died; most 

bodies were never recovered (Rosenberger, J., 2004).

The Quebec Bridge was designed as a cantilever bridge with a clear span of 1,800 feet, 

the longest in the world at that time. The bridge had originally been designed by the 

Phoenix Company, who was responsible for design and erection, with a clear span of 

1,600 feet, but this was increased to 1,800 feet. by Theodore Cooper on the basis that 

this would allow the foundations to be founded in shallower water, reduce ice loads and 

speed construction. 

Theodore Cooper, author of the 1890 book, General Specifications for Iron and Steel 

Railroad Bridges and Viaducts and developer of Cooper’s E Loading, was considered to 

be one of the preeminent bridge engineers in the United States. He had been retained 

as a consulting engineer on the project due to the lack of design experience of the 

Phoenix Company with a bridge of such large size.
2.20

During erection of chord members in the south anchor arm in June it was noted that 

some members were out of alignment (Pearson, C., and Delatte, N., 2006). This was 

attributed to fabrication tolerances and member adjustments were made in the field to 

allow riveting of the connections. As work progressed, additional member deformations 

were reported, including the compression chords near the pier. Jacking of members 

was required to achieve alignment and allow riveting of connections. Figure 2-16 shows 

the bridge under construction with the cantilever span to the left of the pier and anchor 

span to the right of the pier.

Figure 2-16 Quebec Bridge under Construction Shortly before Collapse 

(Modjeski et.al, 1919 – used by permission of Library and 

Archives of Canada)

In early August, bending was reported in two lower (compression) chords of the 

cantilever arm. When the deformations were reported to the chief design engineer for 

the Phoenix Company, he attributed them to shop fabrication, while others believed the 

deformations were due to accidental impacts or mishandling. Norman McClure, 

Cooper’s on-site inspector, insisted however that the deformations were due to stresses 

that had occurred after the members were erected. Deformations were sufficient to 

cause some ironworkers to stop working, and on August 27, the construction foreman 

stopped work pending resolution of the observed problems.

On August 27, inspections of member compression chord A9L, the lower chord to the 

pier in the anchor arm, showed an increase in deflection from 3⁄4 inch to 21⁄4 inch in two 
2.21

weeks, and that the opposite chord also was deflected in the same direction. On the 

afternoon of August 28, McClure left to meet with Cooper at his New York City office. 

After their meeting on the morning of August 29, Cooper telegraphed the Phoenix 

Bridge Company’s office in Pennsylvania, “Add no more load to the bridge until due 

consideration of facts. McClure will be over at five o’clock”. McClure then left by train for 

the Phoenix Bridge Company’s office to discuss the matter with Jon Deans, the Chief 

Engineer, and Peter Szlapka the Chief Designing Engineer for the Phoenix Bridge 

Company. Meanwhile, Alex Beauville, a riveting foreman on the bridge reported 

sheared rivets on the bottom chord, and others reported the bridge as becoming 

“springy”.

Figure 2-17 Quebec Bridge after Collapse (Modjeski et.al, 1919 – used by 

permission of Library and Archives of Canada)

McClure arrived shortly after 5:00 p.m. and found that Deans had received Cooper’s 

telegram, but had not forwarded it, or other directives, to the bridge site. After 

preliminary discussions, they decided to await further field information before deciding 

on a course of action, and meet again in the morning. A few minutes after that decision 

was made, the bridge collapsed. Figures 2-17 and 2-18 show the collapsed bridge.

A Royal Commission was convened by the Governor General of Canada, comprised of 

three civil engineers. The Commission’s report concluded that the immediate cause of 

the collapse was buckling of the A9R and A9L compression chords in the anchor arm, 

the design of which was found to be defective. Among factors cited as contributing to 

the failure were:
2.22

• Failure to adequately determine the true dead load resulting in stresses 

exceeding the design specification allowable. Actual dead load of the cantilever 

arm was 19.7% greater, and the anchor arm 30% greater than that used for 

design.

• The state of professional knowledge of the behavior of steel columns was not 

sufficient for design of the bridge.

• Lack of qualified on-site oversight.

The compression chords consisted of four ribs connected by riveted lacing bars. Testing 

performed after the collapse showed these behaved as four separate compression 

members rather than a single unit. Under load, the lacing and rivets failed, followed 

immediately by buckling.

Figure 2-18 Quebec Bridge after Collapse – End View (Modjeski et.al, 1919 

– used by permission of Library and Archives of Canada)

Design of the Quebec Bridge, which would be the largest cantilever bridge in the world, 

pushed the limits of design knowledge in its time. The use of high allowable stresses, 

failure to fully redesign the bridge after increasing the length of the main span, and 

requirements for specialized fabrication and erection practices should have led to a 

heightened sensitivity to field observations and any unexpected occurrences during 

construction. Instead, the designers dismissed or attempted to explain observed 

member deformations as due to causes other than overstress, even in conflict with 

reports from their own field engineer. Even when the obvious signs of overstress and 

the onset of buckling were finally acknowledged, the designers failed to recognize the 

severity and immediately halt construction.
2.23

SECTION 10. I-80 GIRDER FAILURE (2005)

In March 2005, girder erection began for the construction of dual seven span bridges 

carrying I-80 in Clearfield County, Pennsylvania. Each 150 foot span was composed of 

five AASHTO, 28-by 96-inch deep prestressed concrete I-girders. The bearing types 

varied with location. 

Figure 2-19 shows a simplified bridge elevation indicating the erection sequence. The 

abutments and Piers 1 and 6 used multi-rotational pot bearings with non-guilded 

bearings at the exterior girders, and guided bearing at the interior girders. The 

remainder of the spans were supported on elastomeric bearings.

Figure 2-19 I-80 Elevation and Erection Sequence

Temporary girder bracing requirements varied with the bearing type. At Abutment 2 and 

Pier 6, spans supported by multi-rotational bearings, the bracing included dual diagonal 

bracing of the fascia girder and blocking of the non-guilded bearings. This was in 

accordance with the erection drawings. For spans 2 through 5, supported on 

elastomeric bearings, the temporary bracing, as required by the erection drawings, 

consisted of a single diagonal brace at the fascia girder. A view of the bridge prior to 

collapse showing temporary bracing installed is shown in Figure 2-21.

Though the bearing type and thus temporary bracing requirements changed from 

elastomeric to multi-rotational at Pier 1 and Abutment 1, the temporary bracing was 

actually installed as though the girders were on elastomeric bearings, contrary to the 

erection plans. Figure 2-20 shows the bracing incorrectly used at the pot bearings on 

Pier 1 and Abutment 1. 
2.24

Figure 2-20 Incorrect Bracing at Pot Bearing, Pier 1 and Abutment 1

The unguided pot bearing provides no lateral restraint at the girder support. As a result, 

bracing only the top flange did not prevent the girder from rolling about the pot bearing 

which provided no lateral restraint. Investigation of the collapse included consideration 

of possible non-uniform thermal effects causing an increased sweep in the girders. An 

increased sweep would add an eccentric load due to girder self-weight that could 

contribute to a rolling instability about the bearing. Subsequent research work at 

Georgia Institute of Technology sponsored by PennDOT (Hurff, J., 2010), while 

indicating that thermal effects had minor effects, has provided important information 

regarding precast girder stability during erection. A major lesson from the I-80 collapse 

is the need to carefully review erection bracing details for bridges with varying bearing 

types to ensure adequate bracing design details and to provide field supervision to 

ensure that proper bracing is installed at each location.
2.25

Figure 2-21 End view of I-80 Bridge under Construction Prior to the 

Collapse

SECTION 11. CASE STUDIES – STEEL BOX-GIRDER BRIDGE 

FAILURES DURING ERECTION OUTSIDE OF NORTH AMERICA

2.11.1 Introduction

The importance of considering forces imparted during construction, in addition to the 

final configuration intended by the designers, is illustrated in the following case studies.

Between 1969 and 1973, five steel box-girder bridges failed during construction outside 

of North America. Four of these occurred within a two-year period and were well 

publicized at the time of each failure. The fifth failure occurred two years after the fourth 

and was only publicized many years later. Each of these collapses reveals specific 

lessons and the loss of 57 lives as a result of these failures underscores the importance 

of considering all possible loading combinations when developing erection methods.
2.26

2.11.2 Fourth Danube Bridge

The Fourth Danube Bridge in Vienna, Austria, was designed using three-span 

continuous welded twin steel box-girders with an overall length of 1,351 feet and span 

lengths of 394 feet, 689 feet, and 269 feet. Each rectangular box cross-section was 25 

feet wide, and the overall depth of the haunched girder was 17 feet at midspan. The 

flanges were longitudinally stiffened by flat plates, rather than T-sections or similar 

configurations that would come to be used in more modern construction of this type 

(Akensson, Bjorn 2008).

Span 2 of the bridge was being erected by the free cantilever method in November of 

1969. Spans 1 and 3 were fully in place, with cantilever sections extending from both 

piers. When the final section of Span 2 was ready for placement, it was determined that 

the warm temperatures experienced on the final day of erection caused the cantilever 

sections to deflect downward more than expected, due to the tops of the sections 

having undergone additional temperature-induced deformations relative to the bottoms 

of the sections. As a result, the final section did not fit as intended.

In an attempt to mitigate this problem, it was determined that the closure section would 

be shortened by 5⁄8 inch at the top, which represented the difference in temperature 

deformation. It was recognized at the time that this would introduce undesirable 

constraining forces and a resulting distribution of forces and moments that the system 

was not designed to resist. Specifically, in this configuration, the bottom flange would 

experience a higher compressive force than intended. The intended solution was to 

lower the interior supports at the piers in order to artificially introduce tension in the 

bottom flange.

However, due to the required modifications of the closure section, there was not enough 

time remaining in the workday to lower the supports and this operation was rescheduled 

for the following day. During the evening and overnight hours, the bridge was not in the 

direct heat of the sun, and the temperature dropped to more seasonable levels. This 

temperature swing introduced significant compressive forces into the bottom flange. 

These forces were exacerbated by the poor longitudinal stiffener detailing. As a result, 

the superstructure buckled near the right-hand dead load moment contraflexure point in 

Span 2, which was not designed to resist significant bending forces. This buckle 

redistributed the forces in the system and a second buckle occurred approximately at 

the midspan of Span 1. These two locations buckled enough to form nearly pure hinges 

at these locations. A third buckle, at the closure section, occurred, but this was not as 

pronounced as the first two.

The first two hinges transformed the structure from twice statically indeterminate to 

statically determinate. This enabled the internal forces to redistribute and relieve the 

constraining forces, preventing a collapse. Had the buckle at the closure section been 

pronounced enough to form a third hinge, a collapse mechanism would have 

developed.
2.27

2.11.3 Cleddau Bridge

The Cleddau Bridge in Milford Haven, Wales was designed as a seven-span continuous 

welded single-cell steel box-girder with an overall length of 2,688 feet - 9 inch The box 

cross-section consisted of a 41-foot wide top flange, a 22-foot wide bottom flange, and 

two 18 foot deep inclined webs. Other than traditional longitudinal and transverse 

stiffening elements, there were no interior plate diaphragms or other stiffeners, except 

those at the piers (Akesson, Bjorn 2008).

At the time of collapse, in June of 1970, Span 7 (the southernmost span, 252 feet long) 

was fully erected and shored approximately 140 feet from the abutment. Span 6 (also 

252 feet long) was being erected by the cantilever method. Individual box segments 

were incrementally launched from Pier 6 northward toward the free end of the 

cantilever. When the bridge collapsed, 196 feet of Span 6 had been erected and was 

cantilevered out from Pier 6. An additional box section, having a length between 50 and 

60 feet, was being launched, when the cantilevered section of Span 6 collapsed. The 

section buckled about Pier 6 and fell to the ground. At the time of collapse, the 

cantilever section weighed approximately 500 tons. Four people were killed in the 

collapse. 

Figure 2-22 Cleddau Bridge Buckled over Pier
2.28

After an investigation, it was determined that the mode of failure was buckling of the pier 

diaphragm, which was designed to resist loads imparted in the final configuration of the 

bridge, but was insufficient to resist the erection loads.

2.11.4 West Gate Bridge

The West Gate Bridge in Melbourne, Australia, with an overall length of 8,530 feet, was 

oriented in an east-west direction. The approach spans consisted of reinforced concrete 

and the center five spans consisted of a continuous welded steel box-girder structure. 

The middle three spans were supplemented by stay cables. 

The cross-section consisted of a 13-feet deep, three-cell box-girder. The top flange was 

123 feet wide, and the bottom flange was 63-feet wide. The interior web plates were 

vertical, while the exterior web plates were inclined.

Figure 2-23 West Gate Bridge after Collapse
2.29

Due to a series of delays, construction fell behind schedule, and as a result, the 

contractor devised a method of erection that would help bring the project back on 

schedule. The chosen method of erection, along with a series of poor decisions 

associated with this method of erection, eventually led to the collapse of this bridge 

(West Gate Bridge Memorial Committee, 1990).

The method selected was to split the box-girder longitudinally into two halves and 

introduce a longitudinal splice. The two halves would then each be lifted separately into 

place by hydraulic jacks and then rolled into place and spliced. This method of erection 

was intended to speed construction because of the greatly reduced number of crane 

lifts compared to conventional construction. However, it left long unsupported lengths of 

flange on each half.

Figure 2-24 West Gate Bridge Construction Site after Collapse
2.30

Construction began on the east side by assembling the two halves on the ground. 

However, because the flanges were unsupported on their free edges due to the division 

of the three-celled box section into two halves, the top flange buckled while the girder 

halves were still on the ground in a simply supported configuration. The amplitude of 

these buckles was up to 15 inches. In spite of this, the contractor elected to continue 

with the erection.

Initially, each half was moved into place as described above. Before completing the 

longitudinal splice, the contractor needed to address the buckles at the free edges of 

the top flanges. To relieve the distortion caused by the buckles, the contractor unbolted 

several transverse splices, allowing the adjacent top flange plates to slip past each 

other in the longitudinal direction. New holes were drilled, or existing holes enlarged, in 

order to re-bolt the transverse splices (Morrison et.al, 1971).

Construction then proceeded to the west side. Considering the lessons learned from the 

free edge buckling of the top flanges that occurred on the east side, the construction 

team utilized additional stiffening elements on the top flanges of the two halves of the 

west sections, which initially controlled the free edge buckling. However, when the two 

halves were about to be longitudinally spliced, it was noticed that the north half was 

cambered 4 1⁄2 inches more than the south half.

In order to make the longitudinal splice, it was decided that the camber of the north half 

would be reduced by placing concrete blocks on this portion of the structure. It was due 

to this loading configuration that the free edge of the top flange of the north half 

eventually buckled, as the supplementary stiffening elements were unable to resist the 

additional buckling stresses caused by the dead weight of the concrete blocks. At this 

point it was decided that the buckles would be taken out in a similar manner as the east 

side; that is, some of the transverse splices would be unbolted, which in turn would 

allow the top flange plates to slide past one another in the longitudinal direction. 

However, the additional load of the concrete blocks was not taken into account in this 

case, and unbolting of the splice caused additional stresses in the top flange. The entire 

section buckled and collapsed to the ground, taking the lives of 36 workers.

2.11.5 Rhine Bridge 

The Rhine Bridge in Koblenz, West Germany was designed as a three-span continuous 

welded single cell steel box-girder with an overall length of 1,450 feet and span lengths 

of 338 feet, 774 feet and 338 feet. The box cross-section consisted of a 97-feet wide top 

flange, a 36-feet wide bottom flange, and two inclined webs. The overall depth of the 

haunched girder was 19 feet at midspan. The bottom flanges were longitudinally 

stiffened with T-sections. 

Span 2 of the bridge was being erected by the free cantilever method. Spans 1 and 3 

were fully in place, with cantilever sections extending from both piers. The crane was 

positioned at the end of one of the cantilever sections and was in the process of lifting 

the 85-ton closure section into place when this cantilever section collapsed, failing in 
2.31

negative bending moment. The section that failed was not at the pier, the point of 

maximum moment, but rather at approximately the 1⁄4 point of the span.

Neither the reason for the location of the failure, nor the actual cause of the failure, was 

immediately clear. As a part of the investigation, these became apparent. First, the 

location of the failure was within the section of the span for which the minimum depth of 

the cross-section was used. Second, this location was near the point of dead load 

moment contraflexure; therefore, this section would have been designed for a much 

lower level of stress than was experienced during the construction phase. Finally, and 

most importantly, the root cause of the failure was determined to be the inadequate 

detailing of the longitudinal stiffener at this location (Akesson, B., 2008).

The failure occurred at the location of a transverse splice. Longitudinal stiffeners were 

welded to the bottom flanges at these locations, but the stiffeners stopped 

approximately 9 inch short of the centerline of the splice in order to facilitate the welded 

splice. Following the splicing of the girder section, it was determined that what was 

labeled a supplementary T-section stiffener would be spliced to the main longitudinal 

stiffeners; however, this supplementary section was positioned such that a 1 inch gap 

was introduced between this stiffener and the bottom flange (See Figure 2-25). The gap 

was introduced, in part, to avoid intersecting welds; however, the resulting configuration 

did very little, if anything, to stiffen the bottom flange at the location of this splice. It was 

determined through the ensuing investigation that the bottom flange buckled at the 

splice location. If the longitudinal stiffener had been configured to function properly, this 

would very likely not have occurred. 

Figure 2-25 Rhine Bridge Longitudinal Stiffener Splice
2.32

2.11.6 Zeulenroda Bridge

The four bridge failures described above are well-known examples of steel box-girders 

failing during erection. However, a fifth failure occurred in Zeulenroda, East Germany in 

August of 1973. This was not reported until the archives were opened to the public in 

the late 1990’s (Akesson, B., 2008).

This bridge was designed as a single-cell six-span continuous welded steel box-girder 

bridge. The overall length of the bridge was 1,188 feet, two end spans of 180 feet, and 

four center spans of 207 feet. The cross-section consisted of a 36-feet wide top flange, 

a 13-feet wide bottom flange, and two inclined webs, and an overall girder depth of 7 

feet.

One of the end spans and about half of the adjacent span had been erected using the 

free cantilever method. Near midspan (just beyond the point that had already been 

erected), a shoring tower was in place to assist with the erection. However, the bridge 

collapsed just short of the shoring tower during the erection of one of the box-girder 

segments.

No formal investigation was performed regarding the cause of collapse; however, 

Åkesson, after performing load and capacity calculations on the failed section using the 

speculated erection loading, concluded that the bottom flange was inadequately 

designed to handle the erection loads, and the longitudinal stiffeners were inadequately 

designed and detailed for the required loading during erection.

SECTION 12. SUMMARY AND CONCLUSIONS

Although the circumstances surrounding the failures discussed in this chapter varied 

widely, some common conclusions can be drawn from the summaries of these failures 

that were presented:

• Loading for both primary and secondary members, including loading from jacks, 

cranes, support towers, thermal creep, concrete creep, wind, and construction 

loads must be considered at every point of the construction sequence.

• The contractor’s erection engineer must be cognizant of the various stages of 

erection, how each stage affects the loads and capacities of the sections being 

loaded, and how changes during construction due to fabrication errors, changes 

in construction methodologies and other considerations affect the manner in 

which load is applied and resisted.

• Secondary elements such as stiffeners must be properly designed and detailed 

to account for the required loading conditions during each stage of construction 

as well as for the final configuration of the structure.

• A stability analysis of both the individual components and overall systems should 

be performed as a part of the design of temporary bracing and shoring to ensure 
2.33

the overall stability of the structure during construction. Lateral instability must be 

considered at every point during the construction.

• At each point in the construction sequence, all bracing, bolting, and framing 

assumed in the design of that construction sequence must be in place.

• The geometry of the structure must be monitored at each step of the 

construction.

• Bridges relying on the deck for structural stability must be checked for conditions 

when the deck is not yet providing that stability. A structural analysis of the bridge 

behavior during concrete placement should always be performed.

• Box girders may need additional top flange bracing to accommodate the 

construction loads.

• Field personnel should be alert to unexpected deformations, member fit-up 

difficulties, unusual sounds, etc. and report them to supervisory and engineering 

staff. The reason for such occurrences should be carefully investigated.

• No modifications to the permanent structure or temporary works should be made 

without an engineering analysis
2.34

. 
3.1

CHAPTER 3 

TYPICAL BRIDGE CONSTRUCTION PRACTICE 

SECTION 1. INTRODUCTION

Various construction activities and considerations that can affect girder stability occur in 

the erection of bridge superstructures. Chapter 3 discusses the processes followed 

during erection, various options in erection methods and sequencing, and presents an 

overview of typical equipment used along with some of its limitations. Providing stability 

at all stages of erection is critical and various methods of achieving stability and 

geometry control may be utilized. The effect of deck placement and demolition 

sequencing on overall structural behavior must also be considered. Detailed designs of 

shoring are beyond the scope of this chapter, but references to pertinent AASHTO 

provisions are included.

SECTION 2. ERECTION SEQUENCING

3.2.1 Site Conditions

The site conditions often dictate the sequence and method of erection. Locations of 

roadways, site topography, railroad tracks, existing structures, waterways, overhead 

and underground utilities, and maintenance and protection of traffic through the work 

zone typically control where cranes and shoring can be placed and where girders can 

be delivered by truck. When girders cannot be erected directly from trucks or other 

delivery methods, adequate laydown space must be available and prepared for 

temporary girder storage. Based on available crane locations, a lifting or pick radius 

from the delivery or laydown location and a setting radius to the final girder location can 

be determined and an appropriately-sized crane can be chosen.

Soil pressures under crane tracks, wheels, or outriggers that develop during lifting must 

be compared to allowable soil bearing capacities to preclude crane tipping due to 

outrigger or track settlement. Compacted stone pads or timber mats are often 

constructed to facilitate crane operations and distribute the loads.

3.2.2 Girder Shipping 

Shipping weights and piece lengths for girder segments can typically be found on the 

fabricator’s or precaster’s shop drawings. The engineer preparing the erection 

procedure should perform take-offs of the girder weights for determining crane 

requirements and preparing stability calculations and center of gravity calculations. 

These calculations also serve as a second check on the fabricator’s estimation of girder 

weight.
3.2

Girders are typically shipped with webs in the vertical position and the girder is chained 

to the truck dollies – refer to Figure 3-1. Depending on the constraints of the project site 

and whether the truck has to be backed in at the site, the erector will select the 

orientation of the girder and relay that information to the fabricator so that the pieces 

arrive in the desired orientation. 

Figure 3-1 Bridge Plate Girder Loaded for Transport to Project Site

Transporting the girders from the fabrication shop to the project site typically requires an 

in-depth analysis of possible routes, including routing clearance checks, loading 

analysis and permitting with applicable routing agencies. Girders may occasionally be 

shipped by water or rail, in which case an intermediate step of off-loading to trucks for 

local transport may be necessary. 

Though size and weight limits for truck transport vary with available highway access, 

typical limits on over-the-road shipping applicable to both steel and concrete girders 

include:

Length – Maximum length is normally in the 120-140 foot range, though lengths up to 

185 feet may be possible for some routes, and by utilizing steerable trailers.

• Width – Widths over 8 to 10 feet require permits. Maximum permitted widths 

normally are limited to 12 to 16 feet.

• Height – Height of trailer plus girder is normally limited to 12 feet above the 

roadway without an over-dimension permit and 14 feet if permitted.

• Weight – Depending upon available transportation equipment and state 

regulations, loads up to 110 tons may be transportable. The ability to transport a 

heavy load may be governed by sufficient member length to accommodate the 

number of axles needed for the load.
3.3

Transport of large or heavy loads requires permitting and may be limited by construction 

zone width restrictions on some routes and allowable travel hours. Routes should also 

be evaluated for high cross slopes which could result in instability of loads with high 

centers of gravity. Over-dimension loads will also require escort vehicles as shown in 

Figure 3-2. As part of the shipping plan, the supplier should complete an analysis of the 

girder to ensure that stresses during shipping remain within the AASHTO limits.

Figure 3-2 Concrete Girder in Transport with Escort Vehicles

3.2.3 Erection Sequence

3.2.3.1 Initial Preparation

Each bridge will require an erection sequence that meets site and design conditions for 

that bridge. Although the sequence is the responsibility of the bridge erector, the 

following outlines the concerns that must be taken into account. Prior to the start of 

girder erection, the bridge bearings are set and their elevation and location verified. 

Bearing support surfaces, particularly for elastomeric bearings, must be flat within 

specified tolerances in order to provide uniform bearing.

Erection often begins at a fixed bearing, or at one end of the bridge, where the bearing 

stiffener in the web of the girder is used to locate the bearing centerline and establishes 

a control point at the start of girder erection. For bridges located on a grade, erection 

normally starts at the abutment with the lowest elevation, and in these cases it may be 

necessary to block the girders to the backwall or install restraint blocking to the girder 

seats to maintain girder location. 
3.4

On longer bridges, some of the initial pieces may intentionally not be set on the 

centerline of bearing but rather be offset on the bearing by one to two inches toward the 

backwall to provide a larger gap into which the final girder piece can be set. Once the 

final piece is in position the bridge is jacked longitudinally to close the gap and final 

bolting of the field splices is performed. When this procedure is used, the girders must 

be checked to ensure they possess sufficient axial capacity under self-weight to resist 

the jacking forces.

Figure 3-3 Splicing Girder Segments at 

Grade Prior to Lifting
3.5

3.2.3.2 Steel Girder Bridges

When sufficient crane capacity is available to lift the combined weight, girder segments 

are spliced at grade to yield longer sections for placing as shown in Figure 3-3. When 

the girders are erected at grade, some or all of the cross-frames are attached at that 

time. If girders are to be set one-by-one, the erection process usually starts with setting 

the fascia girder, stabilizing the girder, unhooking the crane and then setting the first 

interior girder with cross-frames already attached to the girder. 

Once the first interior girder is in place the cross-frames are swung into place and 

connected to the fascia girder prior to the crane releasing the load. The number of 

cross-frames attached to the second girder is dependent upon what is needed for lateral 

stability of the girders. Remaining cross-frames and lateral bracing (if specified) are then 

erected. The third girder then is erected and the cross-frames hanging off of the second 

girder are connected to the third. Similarly, the fourth girder is erected with cross-frames 

attached, and then any additional girders with each pick alternating between plain 

girders and girders with cross-frames already attached. Figure 3-4 depicts a curved 

girder being erected with cross-frames attached. In this photo, the temporary shoring is 

actually above the girders and the girders are suspended from an adjustable chain-fall 

system.

An alternate erection process is to install the cross-frames between a pair of girders 

working at grade, and then lift and set the girder pair. While a higher capacity crane may 

be needed than for setting single girders, setting pairs eliminates the need to provide 

temporary bracing at the ends of the first girder set. Subsequent girder pairs are then 

set, and the cross-frames between pairs installed.
3.6

Figure 3-4 Curved Girder Being Erected with Cross-Frames Attached 

When the bridge consists of multiple spans, due to the expense associated with the 

main lifting crane, the crane will usually be relocated to its next position to erect the 

subsequent span or girder segment. A smaller crane is then mobilized to complete the 

erection of cross-frames and any lateral bracing in the first span.

In curved girder bridges, the first individually erected curved girder will not be stable if 

set in place on the bearings by itself. Therefore, it is common for the first two girders to 

have the cross-frames installed while the girders are on the ground and lifted as an 

assembly. Otherwise, additional cranes and/or shoring systems are required to hold the 

first girder in place while a second and perhaps a third, or more, adjacent girder(s) are 

lifted and connected with cross-frames. Even with a paired erection scheme, temporary 

shoring systems may still be required. An engineering analysis of the system at each

stage of erection is required to determine the arrangement of the shoring system and 

the applied loads and deformations as successive girders are set.

Studies of curved and skewed girder erection sequencing conducted for the 

Pennsylvania Department of Transportation (Linzell, David, et. al. 2010) found that 

setting curved girder pairs reduced vertical deflections during erection, particularly 

compared to erecting single girders beginning on the outside of the curve. Based on 

their studies, the best erection scheme for controlling deflections, especially for tight 

radii, is to erect girder pairs working outward from the inside of the curve. 
3.7

Cross-frames must be installed as the girders are set and be secured with full-size pins 

and high strength bolts. Partially installed or insufficiently secured cross-frames lead to 

poor control of girder alignment and complicate fit-up as erection progresses.

3.2.3.3 Concrete Girder Bridges

The preferred method of erecting long precast concrete girders is with two cranes, with 

one located at each bridge girder support. Single cranes are generally limited to placing 

precast concrete girders with spans of 60 feet or less. Single-crane lifts require a 

sufficient boom length and lifting cables of sufficient length to keep the lifting cables at a 

minimum angle from the horizontal, typically specified as 60 degrees. Spreader bars or 

struts can also be used to control this minimum angle. 

Erection using two cranes is usually faster than with one crane. The method is normally 

used when long girders can be delivered along the bridge span, and cranes positioned 

near the girder supports can lift and swing the girders from the delivery vehicle directly 

to their final position. It is also used where precast girder sections are spliced at grade. 

Dual–crane lifts can utilize shorter booms than single–crane lifts, which can be 

important where headroom is limited. 

Girder erection normally begins with the fascia girder which is set and braced to the 

abutment or pier cap. The adjacent girder is then set and braced individually or, more 

commonly, to the previously set girder.

Once the girders are positioned, required temporary bracing remains in place until the 

end diaphragms, and any required intermediate diaphragms, are placed / cast. 

For spliced girder and similar erection, the initial pier girder segments are set on their 

piers, with supplemental support from shoring towers or bracing extending back to the 

pier shaft. In the latter case, the bracing design must account for potential unbalanced 

loads to the pier. Once the pier girders are placed, the drop-in girders are placed, as 

shown in Figure 3-5. These are typically supported on separate or shared shoring, or 

are suspended by a strongback, Figure 3-6 and Figure 3-7, hanger assembly. The 

selection of a temporary support system depends upon bridge elevation, presence of 

waterways, and contractor preferences. A work platform may also be provided to allow 

for completion of the girder splicing operations.
3.8

Figure 3-5 Setting Drop-in Span with Strongbacks Attached

Figure 3-6 Girder Supported on Strongback (Shown on the Right) 
3.9

Figure 3-7 Typical Strongback Arrangement
3.10

SECTION 3. GIRDER HANDLING

3.3.1 Center of Gravity

A critical component to erecting the bridge girders and other components is determining 

the center of gravity of each piece. The center of gravity is a point on the girder where 

the total weight of the piece may be thought to be concentrated. If the girder was 

supported at the center of gravity, it would be in a balanced condition and the moment 

from the weight of the right portion of the girder about the center of gravity would equal 

the moment from the weight of the left portion of the girder. 

Figure 3-8 Girder Rigging with Spreader Beam

Erectors will often verify the calculated location of the center of gravity in the field by 

lifting the girder a few inches off the delivery truck to see if it hangs level. Slight 

adjustments to the theoretical center of gravity that was calculated can then be made in 

the field.
3.11

3.3.2 Rigging for Straight and Curved Steel Girders 

On single crane picks the crane hook is located over the center of gravity of the girder. 

On shorter pieces, a single beam clamp or pair of beam clamps with slings is often 

utilized, whereas on longer heavier pieces a spreader beam or lifting beam along with a 

pair of clamps is utilized to pick the girder segments as shown in Figure 3-8. A typical 

beam clamp is shown in Figure 3-9. Beam clamps are commonly available in 15 ton, 25 

ton, and 35 ton capacities and connect to the top flange of the girder. Local stresses in 

the top flange due to the beam clamp need to be investigated, as discussed later in this 

chapter. 

Single crane picks with a single lift point are not recommended for curved girders. Use 

of a lifting beam with two lift points spaced so that the lifting points lie on the center of 

gravity of the curved girder will minimize rotation during lifting. For larger girders, the 

use of two cranes with a total of four lifting points will improve girder stability and 

facilitate fit-up of the splices. 

Figure 3-9 Beam Clamps on Steel Girder
3.12

3.3.3 Rigging for Concrete Girders

Concrete girders typically involve a two crane pick both due to their weight and the 

crane attachment points are at each end of the girder. Lifting loops, most often 

consisting of one or more prestressing strands, are typically cast into the girder near the 

girder ends and the loops are connected to a shackle and a sling as shown in Figure 3-

10. Lifting points used to erect the girders should be the same as used by the precaster 

to move and ship the girders. The critical condition for the lifting loops is when the 

girders are removed from the casting beds since the concrete has not yet achieved its 

full strength. 

If concrete girder segments are light enough for the available crane capacity a single 

crane pick using a spreader beam can be used to pick the girder. If inclined lifting 

cables (or straps) are used, the axial force in the girder segment due to the inclined 

cables must be included in the lifting analysis by the precast and erection engineers. 

Figure 3-10 Crane Rigged to Concrete Girder at Lifting Loops

Other options for rigging of concrete girders include utilizing a basket hitch near the end 

of the girder as shown in Figure 3-11. The basket hitch is typically positioned so that it 

does not interfere with the abutment or pier when the girder is set.
3.13

Figure 3-11 Basket Hitch Rigging

When multiple lifting points are used, for instance, lifting at four points along the girder, 

techniques for equalizing the load on each lifting point are used. This may be done with 

roller blocks, spreader beams or lifting trusses.

3.3.4 Local Stresses from Beam Clamps

Figure 3-12 Beam Clamp
3.14

Beam clamps grip the beam at three points: the underside of the top flange on each 

side and the top of the girder. When properly balanced and safely guided, the beam can 

be handled even if the clamp is slightly away from the center of gravity of the piece. 

Good safety procedures providing control of the lifted beam must be used. Snubbing 

lines (tag lines) at each end must be used to control excessive twisting or swinging, and 

to guide the beam to its proper place.

The weight of the beam clamp automatically opens its tongs, which slide under the 

flanges of the beam (refer to Figure 3-12). When the clamp is lifting, its center plate and 

gripping tongs work against each other—the heavier the beam, the greater the clamping 

pressure. Some models of clamps have a recessed base to accept studs welded to a 

beam surface.

When utilizing beam clamps to pick steel girders, significant localized stresses are 

produced in the top flange of the girder. These stresses should be checked (see Section 

7-6.3) and, if necessary, the area reinforced. This is usually accomplished by adding a 

loose plate on top of the flange under the clamp or adding a plate or angle between the 

tongs and the bottom of the flange.

3.3.5 Lifting Beams & Spreader Beams 

Spreader beams like that shown in Figure 3-13, or lifting beams as shown in Figure 3-

14, are typically utilized to handle longer straight members and horizontally curved steel 

girders. The design of lifting beams and spreader beams should be in accordance with 

ASME BTH-1 Design of Below-the-Hook Lifting Devices. This reference requires all 

below-the-hook lifting devices to be designed for specified rated loads, load geometry, 

Design Category and Service Class. The resolution of loads into forces and stresses 

affecting structural members, mechanical components and connections used in rigging 

are performed using classical strength of material methods although other analysis 

techniques can be used.

Spreader beams are designed as compression members along with some minor 

bending due to self-weight and possible eccentricity from the sling attachment. Lifting 

beams are primarily bending members that typically attach in their center directly to the 

crane hook, and then suspend beam clamps or lifting cables from each end to attach to 

the girder. 
3.15

Figure 3-13 Spreader Beam

Figure 3-14 Lifting Beam

Assembly can generally be thought of as maneuvering of the pieces with cranes into 

their final positions in the structure, whereas fit-up consists of aligning the members and 

field splice plates.

During the assembly phase, a ground crew selects pieces based on the shop or 

erection drawings. The crew typically dresses the girders, provides any additional 

rigging such as safety cables or tag lines, and hooks the crane to the pieces to be 

erected. The ‘top men’ guide the pieces into their appropriate positions and secure them 

to the structure or temporary shoring if required by the erection plan. 

Fit-up is the process of aligning the members and the plies through the use of drift pins, 

and erection or ‘fit-up’ bolts. Erection bolts are used to draw the plates in the splice or 

connection into contact. Drift pins are steel pins tapered at each end and cylindrical in 

the middle (Figure 3-16). The cylindrical portion has the same nominal diameter as the 

open bolt hole. The drift pins are driven into the splice through all plies at the corners of 

the connection plates, thereby drifting into alignment the flanges and webs of the 

girders. Once this is accomplished, about 25% of the remaining holes also have drift 

pins driven into them uniformly throughout the connection (Figure 3-15). 
3.16

Members are typically first aligned vertically through the web splice, and then aligned 

horizontally through the flange splice. High strength bolts are then installed as the drift 

pins are removed. Typically, 50% of the holes are filled with high strength bolts and 

erection pins prior to the crane releasing the load; however, bridge owners may have 

differing requirements, which must be followed. The AASHTO LRFD Bridge 

Construction Specifications require a minimum of 75% of the holes be filled if the 

structure is carrying traffic during erection, as may occur during rehabilitation projects. 

Cross-frames and diaphragms should be pinned and bolted to a snug condition but not 

fully tightened until all of the girder lines are complete. This provides for stability and 

allows for adjustment as erection proceeds. On curved girder lines, the cross-frame 

connections also typically have 50% of the holes filled with high strength bolts or pins 

prior to the crane releasing its load, though some owners may require a higher 

percentage.

The final bolts are installed typically from the center of the connection toward the 

outward edges. Erection bolts can be used as many times as necessary, but cannot be 

used as the final bolts. 

Figure 3-15 Girder Splice Bolts Being Installed and Drift Pins in Place
3.17

Figure 3-16 Ironworkers Tools of the Trade

3.3.7 Bolting Procedures 

Bolts are typically ASTM A325, A490 or F1852 as specified in the contract documents. 

The bolt installation method should be in accordance with the AASHTO LRFD Bridge 

Construction Specifications and owner requirements.

Bridge girder lines are usually made up of several pieces that are bolted together in the 

field. These bolted connections must be properly aligned and tightened before the splice 

can perform as designed. Field splices are generally located near a point of zero dead 

load bending stress. The field splices are labeled on the erection sheets of the shop 

drawings and may differ from those shown on the design plans if the fabricator or 

erector requests, and has received approval for an alternate location to facilitate 

erection or shipping.

Access for the ironworkers to assemble and bolt the splice may utilize man lifts, 

suspended platforms, cages or other methods. Providing room for this equipment may 

preclude installation of bracing or cross-frames near the girder splice until the splice is 

complete. Though splice size varies widely, an initial estimate of the time required to 

make up a splice is around 30 minutes. Pins and bolts placed at the edges of a splice 

are more effective in maintaining member alignment (and in web splices, moment 

capacity). This is of particular importance where splices are initially only partially bolted.

In order to reduce the time that large cranes are required on the jobsite for erection, 

contractors may initially erect the structure using partially bolted connections and then 
3.18

complete bolting as a follow-up activity. Similar situations occur when erection work 

periods are of limited duration due to traffic or access restrictions. 

The common requirement for installation of at least 50% of the high strength bolts in a 

connection, prior to releasing it from support, is recognition that the self-weight of the 

steelwork produces lower loads on the splice than do the final design loads. These bolts 

must be properly tightened, not only to carry their loads, but to prevent connection 

slippage and maintain member alignment. The erection engineer should review 

connection configuration and location and ensure that loads during erection do not 

exceed the assumption of the 50% bolted criteria for each erection stage. For instance, 

continuous girders cantilevering beyond a support pier develop stresses on the splice in 

the trailing span that differ from the steel self-weight stresses in the final configuration. 

Partially bolted connection capacity evaluation must recognize that the splice bolts 

constitute a bearing connection until final tightening. 

3.3.8 Field Welding Considerations

Field welded connections are not widely used in bridge structures. However, field 

welded girder splices and cross-frame connections may be encountered. When field 

welds are part of the load resisting system, the welded members should not be loaded 

until welds are fully completed, unless an engineering stress analysis is performed that 

demonstrates sufficient capacity for intermediate conditions. Temporary supports and 

guides for field welded members must be sufficiently rigid to assure that the required 

weld joint geometry is maintained during welding.

Erectors may wish to field weld connections for temporary bracing, tie-offs, temporary 

stiffeners, etc. Field welding of such brackets, lugs, reinforcing bar ties, screed rails, etc. 

to permanent members should not be allowed unless approved by the Engineer of 

Record. High strength rod conforming to ASTM A722 is often used in temporary works 

for bracing or hangers. Welding of A722 rods can result in brittle fracture and should be 

prohibited. All welding must conform to owner requirements.

Girder temporary bracing connection plates or stiffeners required for erection should 

preferably be shop installed. When this is not possible, their field welding should 

conform to the Bridge Welding Code, AWS D1.5.

3.3.9 Concrete Girders

Various methods may be used to create continuous girder systems from precast 

concrete beams. Methods for coupling individual beams to create continuous girders 

include post-tensioning and coupling with either high-strength rods or prestressing 

strands. Drop-in spans are discussed in Section 3.2.3.3. Continuity of the girders does 

not take place until all bar splices, post-tensioning and concrete placement at joints is 

complete; thus any temporary works must remain until continuity is achieved. In some 

cases, staged post-tensioning may be used. 
3.19

Temporary girder support and bracing must provide for proper alignment of splice bars 

or strands so that bar connections may be made. Alignment of ducts is also critical to 

avoid additional friction losses during tendon stressing.

SECTION 4. CRANES

3.4.1 Typical Crane Data

Typically, mobile cranes are utilized to erect and demolish bridge superstructures. 

During lifting, the crane is supported either by its tracks, for a crawler crane, or for truck 

cranes, on outriggers that extend out from the crane frame to provide discrete support 

points. For mobile cranes, the stability-limited rated load for a crawler crane is 75% of 

the tipping load. The stability-limited rated load for a mobile hydraulic or lattice-boom 

truck crane supported on outriggers is 85% of the tipping load. The American Society of 

Mechanical Engineers specifies these limits along with additional safety-related aspects 

of the crane design.

It is common for mobile cranes to be mounted on barges to facilitate erection of bridges 

over rivers or over large bodies of water (Figure 3-17). Typically, the published crane 

lifting capacity charts for barge mounted cranes are downrated 25% to 33% to account 

for the dynamic effect of barge vessel motion. Additionally, overall barge stability needs 

to be considered in the downrating, inasmuch as barges that allow greater pitch or yaw 

would require greater downrating of the cranes. Barge stability must be ensured for all 

crane operating conditions, and the barge deck evaluated for the crane loads and track 

pressures.
3.20

Figure 3-17 Crane Mounted on Barge

Newer cranes feature load moment indicators in plain view of the crane operator that 

display the crane boom radius, boom angle, rated load, actual load, wind speed and 

other data as well as displays with messages and alarms to alert the crane operator and 

prevent dangerous conditions from developing. Most new cranes are also equipped with 

automatic shutoffs if the load moment indicator is exceeded. The load moment indicator 

combines the effect of the load and its radius on the crane capacity.

The crane manufacturer publishes load charts for each crane. The charts dictate the 

allowable load that may be lifted based on the desired factors of safety compared to the 

radius of the boom of the crane. A sample load chart is shown in Figure 3-18 for a 350-

ton capacity hydraulic truck crane. The top portion of the chart indicates that the chart 

covers boom lengths of 51 feet to 197 feet, the crane has 220,400 lbs. of counterweight, 

the outriggers are fully extended and set, and that the ratings listed are good for any 

pick geometry over a 360 degree swing of the crane. The lower portion of the chart is 

similar except the counterweight is 110,200 pounds.
3.21

Figure 3-18 Sample Load Chart for 350-Ton Capacity Crane
3.22

Figure 3-19 depicts a sample load chart for a 45-ton capacity all-terrain crane. Like the 

previous chart, this load chart identifies allowable load on the crane hook at various lift 

radii and boom configurations. The chart on the upper left is for 20 feet - 10 inches x 20 

feet - 4 inches outrigger spacing, main boom lengths from 25.6 feet to 102.3 feet, and is 

good for any lift geometry over the 360 degree swing of the crane. 

The chart in the lower left of Figure 3-19 rates the crane for a reduced outrigger 

configuration of 20 feet – 10 inches x 7 feet – 8 inches and limits the boom length to 

64.0 feet when the crane is operating with the reduced outrigger spacing. In contrast, 

the chart on the upper right of Figure 3-19 rates the crane with no outriggers and a 

boom position of 0 degrees, which means that the chart is only good for lifts over the 

rear of the crane, and the boom length is limited to 44.6 feet

In selecting a crane and appropriately describing it on erection documents, it is 

important to be very specific. A given crane may be available in several configurations 

of boom types and lengths, counterweight configurations, tracks extended (or not), etc. 

These variations affect the crane lifting capacities, and track or outrigger loads. 

Maximum crane capacity can be controlled by boom structural capacity, as well as 

crane tipping. When determining the allowable lifted load, the weight of all rigging below 

the crane hook must be subtracted from the rated load capacity. Where large spreader 

beams are required, this can substantially reduce the allowable weight of the lifted 

girder. 

Where multiple cranes are used to pick a single girder, or girder pair, (Figure 3-20), 

close operator control must be maintained to ensure load shifting does not take place, 

causing one crane to become overloaded. 

The crane type and capacity selected for a given project depends upon many factors 

including the method of bridge field assembly, site access and the resulting radius to lift, 

turn, and set the members, and local crane availability. Mobilization and demobilization 

costs as well as project sequencing and staging must also be considered. Some large 

crawler cranes may require field assembly, even requiring use of a smaller crane to 

handle crane components.

General guidance on crane capacity may fall in the following ranges:

• Setting single girders or sections with weights in the 25 to 40 ton range might use 

conventional truck or crawler cranes with a main lifting capacity between 150 and 

250 tons. To account for typical working radii, a 60 to 70 ton holding crane may 

also be needed. (Refer to SECTION 3-4.2 for a discussion of holding cranes.)

• For spliced segments or heavier girders in the 50 to 100 ton weight range, 300 to 

550 ton capacity hydraulic cranes may be used. Smaller cranes may be sufficient 

if they can be positioned for minimal picking radius.
3.23

• For lifts of 100 to 200 tons such as large girders or girder assemblies, hydraulic 

cranes in the 500 to 650 ton capacity range or crawler cranes of 300 to 450 ton 

capacity might be used. These heavy lifts are often multiple crane lifts.
3.24

Figure 3-19 Sample Load Charts for 45-Ton Capacity Crane
3.25

Figure 3-20 Multiple Cranes Lifting Girder – Aerial View

3.4.2 Holding Cranes

Holding cranes are often utilized to temporarily stabilize girders or control geometry 

during erection. The holding crane typically accepts a portion of the erected girder load 

while the main lifting crane releases the load in order to pick another girder segment for 

erection. Holding cranes are typically utilized when the use of temporary shoring is not 

feasible due to limitations from live rail or vehicular traffic lanes beneath the structure, 

waterways, and the like that would conflict with the desired placement of the temporary 

shoring.

Research by the FHWA/TXDOT/University of Texas at Austin, (Stith, Jason, et. al. 

2010), studied various cases of curved girder bridges utilizing holding cranes during 

erection. These research results can also be applied to straight girders. Their research 

indicates that the optimum location for placing a holding crane is at the maximum

positive moment location in the girder, which will maintain a web vertical and minimize 

displacements along the length of the girder, facilitating fit-up. Unlike shore towers, 

placing a holding crane at the location of maximum positive moment tends to give the 

lowest displacements and warping stresses of any location along the girder. 
3.26

The research also showed that the load that the holding crane applies significantly 

affects the behavior of the girder being supported and recommends that the holding 

crane lift with a load equivalent to that of a rigid support reaction placed at the same 

location. The crane should be sized to enable it to provide the required lift capacity, 

accounting for its job site location relative to the girder being held.

Holding cranes are normally, and preferably, attached to the top flange of the girder, 

thus providing an upward force above the girder’s center of gravity. Thus, if the girder 

rotates, a component of the holding force creates a restoring secondary moment that 

decreases deflections from those predicted by a linear analysis. 

Because support for the girder provided by the holding crane is through the crane 

rigging which has minimal lateral stiffness, the holding crane does not provide a lateral 

or torsional brace point for the girder. However, by sizing the holding crane as though it 

were a rigid support, the bending moment within the supported girder is reduced. This is 

further discussed in Chapter 4.

3.4.3 Soil Pressures and Structures Influenced by Crane Location

Cranes may produce bearing pressures beneath tracks or outriggers of several 

thousand pounds per square foot, and the existing soil conditions must be evaluated for 

their allowable bearing capacity. The available soil bearing capacity can be determined 

using the AASHTO LRFD Specifications; however, the available bearing pressures 

should account for the short-term effect of the maximum loads. When computed bearing 

pressure exceeds that available, compacted stone pads or timber mats are commonly 

used to distribute the loads. Crane loading data is available from crane suppliers, or can 

be calculated from crane dimension and weight data. The book Cranes and Derricks by 

Howard I. Shapiro, et al., provides calculation guidance.

The cost of renting and operating a crane is directly proportional to the lifting capacity of 

the crane. In order to minimize the expense associated with crane capacity it is 

generally desired to have the crane as close as possible to the girder segment that is 

being set. This results in cranes being set up or operated directly adjacent to 

abutments, and wingwalls, as well as atop buried structures. The surcharge load 

caused by the crane self-weight and the lifted load weight on these portions of the 

structure are often large and well in excess of the anticipated loads accounted for during 

the design of these components. All structures within the zone of influence of an 

outrigger or the tracks of a crawler need to be evaluated to ensure adequate capacity 

prior to approving a crane position. Additionally, when tracks or outriggers are placed 

near a slope or excavation, the resulting load effects on stability and bearing capacity 

must be investigated.
3.27

SECTION 5. BRACING

3.5.1 Girder Bracing

Bracing is used to perform various functions in bridge superstructures. Bracing normally 

consists of cross-frames or diaphragms between girders and lower, and possibly upper, 

lateral bracing systems as shown in Figure 3-21. Cross-frames may be composed of 

angles, tees, or channel sections and are generally shipped to the bridge site as 

fabricated assemblies with high strength bolted connections to the girders. Diaphragms 

may be fabricated from channels, wide flange sections or bent plates, and are field 

bolted to the girders. Cross-frames and diaphragms provide vertical load distribution 

between girders, serve to laterally brace girders for stability prior to casting the deck, 

laterally brace the compression flange in negative moment regions, and provide transfer 

of lateral loads to piers and abutments. 

Lateral bracing systems (Figure 3-21) provide a truss system to carry lateral loads to the 

piers and abutments. Figure 3-22 shows the distribution of wind loads between the 

concrete deck and lower lateral bracing system in the completed bridge. Without the 

deck or lateral bracing, the lateral loads produce weak axis bending of the girder 

flanges. These bracing systems also help prevent relative lateral movement of the 

girders, and provide added control of bridge geometry during construction. This is 

particularly important in curved girder spans. 

Figure 3-21 Lower Lateral Bracing
3.28

Figure 3-22 Wind Load Distribution

Figure 3-23 Box Girder Top Lateral Bracing and Diaphragms
3.29

Cross-frames or diaphragms used in box section members, as shown in Figure 3-23, 

perform much the same functions as in I-girder spans. Stability and geometric control 

during erection and casting of the deck are dependent on proper bracing design. Lateral 

top flange bracing should be provided to prevent flange buckling during deck placement, 

as well as control deformations. At least partial length bracing should be provided in 

straight box girders, and full length in curved box girders. External cross-frames or 

diaphragms between boxes may be needed to maintain proper deck geometry and 

thickness during deck placement, due to relative displacements resulting from girder 

twist.

The erection plan must consider the sequence and extent of cross-frame / diaphragm 

and lateral bracing installation required for each stage of erection. This erection 

sequence will also determine the need for any temporary bracing. The load and 

stiffness demands on permanent bracing may differ under erection conditions from that 

used for the permanent bridge design, and should be verified. 

Erection schedules may limit the time available for field activities, particularly when 

traffic flow may need to be stopped to allow overhead operations. The erector may want 

to reduce the extent of bracing initially placed, or the completion of bracing connections, 

completing the installation at a later time. Such practices require careful evaluation and 

control, if the bridge’s stability is to be maintained. 

Temporary bracing may be required due to construction operations, such as stabilizing 

girders at piers or abutments, bracing of girders to an adjacent structure during 

widening projects, transferring loads from deck overhang brackets, and other purposes. 

The erection engineer must properly design any such bracing considering strength and 

stiffness requirements, as well as special requirements, such as allowing controlled 

vertical movement of adjacent members. 

The bridge erector must ensure that girders are adequately braced at all times. Erectors 

should closely monitor weather conditions and have contingency plans and materials in 

place so that in the event of unforeseen wind activity or storms added bracing or holddowns can be quickly placed. A review of bracing requirements should be conducted 

each day prior to leaving the site.

3.5.2 Temporary Bracing and Hold Downs

Temporary bracing is normally required to provide stability for girders, at least until the 

permanent bracing or diaphragms are installed. Bracing at girder ends and piers is 

needed to provide global stability to the girder and restraint to girder twist. 

Hold down systems may be needed to restrain girders, and temporary restraint is 

needed to eliminate movement at rotational and sliding bearings. 

Designs for these temporary items can take many forms depending on details of the 

bridge design, erector preferences, erection engineer experience and owner 
3.30

requirements. Temporary bracing and hold-downs should be located so that they do not 

interfere with installing the permanent bracing or cast-in-place concrete diaphragms. 

Several methods of providing this temporary bracing are shown in the following 

subsections.

3.5.2.1 Chain Down to Standard Bearings

Figure 3-24 Steel Girder Tie Down Using Chain Binders to Pier

One method for holding girders in position at piers and abutments on common fixed or 

expansion elastomeric bearings is to chain the girders to the bearings themselves. Two 

details to achieve this are illustrated in Figure 3-24 and Figure 3-25.

The first detail, Figure 3-24 binds the girder to the bearing through the use of chains and 

load binders and incorporates the anchor bolts for the bearing. It is also common to use 

temporary anchor bolts embedded in the top of the pier cap or abutment seat in lieu of 

the bearing anchor bolts. This detail is common in situations where the girder is still 

supported by the crane and is in the process of having cross-frames connected 

between the girder and the adjacent previously erected girder line. 

The second detail, Figure 3-25, is commonly used when erecting the first single girder 

where the girder will be subjected to wind loads. 
3.31

Figure 3-25 Steel Girder Tie Down Using Strut and Chain Binders

The chain and load binder will prevent the girder from rolling over when subjected to 

wind loads from the right, while the pipe strut will handle wind loads from the left. This 

detail also restrains the girder from twisting.

Figure 3-26, which is based on a Commonwealth of Pennsylvania Department of 

Transportation bracing detail shows a variation of the arrangement suitable for concrete 

girders utilizing threaded rods in place of the chains. The top channel member provides 

load distribution across the flange rather than at the flange tips, as would happen if 

chain were used on the bulb tee. Note the use of neoprene pads for load distribution.
3.32

Figure 3-26 Concrete Girder Bracing Example Using Tie-down Rods

Several brace options for bracing girders at abutments or piers, similar to those in 

Florida Department of Transportation Standards are shown in Figure 3-27. Connection 

to the precast concrete girders is made using threaded inserts cast into the girder. 

Tension only members are normally cable, while angles or pipe are commonly used for 

members that carry tension and compression. In these details, the braces connect to 

the abutment or pier face using brackets secured with expansion anchors. In these 

arrangements, the loads are transferred through the expansion anchors in shear, thus 

anchor design is simplified.
3.33

Figure 3-27 Typical Concrete Girder Bracing Arrangements at Pier or 

Abutment

Figures 3-28 through 3-31 show concrete girder bracing details based on Texas 

Department of Transportation standards. Figure 3-32 shows timber X-bracing and top 

flange lateral struts for I-girders at the abutment. Many bracing systems used for 

concrete girders utilize timber members as compression elements. It is important that 

these be secured by wedging or connections to adjacent members to preclude 

loosening and displacement due to construction and wind induced vibrations.

Figure 3-28 Concrete Girder Erection Bracing – Example Plan
3.34

Figure 3-29 Concrete Girder Erection Bracing Detail at Abutment or Pier 

Using Cable and Timber Strut

Figure 3-30 Concrete Girder Erection Bracing Detail between Girders 

Using Timbers and Top Tie Bar
3.35

Figure 3-31 Concrete Girder Erection Bracing Detail between Girders 

Using Timbers and Tie Rod

Figure 3-32 Timber X-Bracing for Concrete I-girders
3.36

3.5.2.2 Erecting on Multi-Rotational Bearings

When erecting girders on multi-rotational bearings, the bearing must be restrained so 

the girder does not roll. Wooden or steel shims can be driven between the load plate 

and the masonry plate (cylinder plate) on all sides of the bearing to prevent unwanted 

displacements of the girder at the bearings. The girder itself would be chained down in a 

manner similar to the elastomeric bearing examples.

A method of locking a guided high load multi-rotational (HLMR) bearing, after a 

Pennsylvania DOT standard detail, is shown in Figure 3-33. The locking assembly is 

placed prior to setting the girder, which is then secured with local bracing.

Figure 3-33 Conceptual Guided HLMR Bearing Lock
3.37

3.5.2.3 Bracing to Adjacent Structures – Phased Construction

Many bridge replacement projects are conducted without detour routes when sufficient 

width is available. This may require that the first new girder erected adjacent to the 

existing bridge be braced to that bridge. Inasmuch as the existing bridge is subject to 

vehicular loading, the existing structure is subjected to vibrations and deflections that 

the new girder is not subjected to. Special attention should be given to providing details 

that will allow differential deflection between the existing structure and the new structure 

as well as engineering connection details that will not be susceptible to vibration.

Figure 3-34 illustrates a possible connection that meets the criteria. This detail allows 

vertical movement while providing a lateral brace point along the new girder flange in 

positive moment regions. These temporary braces must be located to preclude 

instability of the new girder. Bracing at the abutment or pier may be as shown in Figure 

3-27.

Figure 3-34 Temporary Brace to Existing Bridge Deck During Phased 

Construction
3.38

3.5.2.4 Uplift Hold-Down

Unbalanced load conditions while setting girders or casting the deck can cause reduced 

pressure from the girders on the bearings. This not only can cause alignment issues 

with the bearings, but also reduce the lateral restraint to the girder bottom flange, or 

allow sliding. A typical hold-down detail is shown in Figure 3-35. The rod can be 

preloaded to provide a net compression to the bearings when the uplift is present. For 

concrete girders, the channels will bear on the top slope of the bottom flange, which 

may require installation of a horizontal tension rod through the lower webs or similar 

tension tie configuration to prevent spreading of the girders due to the horizontal 

component of the vertical load. 

Figure 3-35 Hold-Down Assembly for Steel Girders
3.39

SECTION 6. SHORING TOWERS

Shoring towers, such as those shown in Figure 3-36, are primarily used to control 

deformations and stresses in the girders during erection. They may also be used to 

temporarily support concrete girder segments prior to those segments being made into 

a continuous girder. The location of a shoring tower affects the behavior of the girders 

as well as required design forces on the shoring tower. The specific location where a 

shoring tower can be placed, however, may be affected by many nonstructural 

restrictions such as site access, construction methodology, and girder stiffness 

variations. 

It is recommended that shoring towers be placed at locations where the maximum 

positive bending moment occurs between permanent supports. This positioning will 

have the greatest effect on minimizing the total deflections, and in general, it places a 

tower near the position where it will be required to support the least load of any position 

along the girder. It should be noted that adding a shoring tower results in a large 

concentrated force and it is thus advisable for steel girders to place the shoring tower 

under a stiffener location, or alternatively, to check local yielding and stability of the 

girder web at the shoring tower location. 

Figure 3-36 Shoring Towers Supporting Girders during Erection

Shoring tower loads should be computed for the various erection stages to ensure the 

maximum loads are accounted for. The design of shoring towers should be in 
3.40

accordance with the AASHTO Guide Design Specifications for Bridge Temporary 

Works. 

Towers have to be designed to resist the bracing force imparted by externally applied 

lateral forces, as well as the force imparted by the bracing member to the tower. Towers 

will also deflect at the top and may rotate, both of which will lead to the reduction of 

restraining forces, as shown in Figure 3-37. To mitigate this, this deflection needs to be 

accounted for in the bracing scheme, and the towers need to be designed to be stiff 

enough to be able to develop the required restraining force. Tower deflections should be 

monitored at the time of load application (member release) and periodically thereafter. 

Observation of any unanticipated or unusual deflections should be cause to immediately 

stop work until the cause of the deflections is resolved and any remedial measures 

completed.

Figure 3-37 Tower Flexibility Effects Under Lateral Load
3.41

In order to ensure that towers are installed to the required elevations, both tower 

shortening and settlement should be evaluated. The AASHTO LRFD Bridge 

Construction Specifications, Article 11.8.5.2, requires top of tower elevations to be set 

so that they support the girders at their cambered no-load elevations. Hydraulic jacks 

are sometimes installed at the tops of towers to allow for adjustment in girder elevation 

as erection progresses. The shoring towers are normally released prior to placing the 

concrete deck, and a sequence for releasing should be determined. The method of 

release, whether by shoring tower screw jacks, hydraulic jack systems, sand jacks, or 

other means should provide for gradual and controlled release of loads from the shoring 

system. 

Temporary shoring towers are often placed on timber mats or precast slabs set at 

grade. For poor soils or very heavy loads, cast-in-place concrete footings or pile bents 

may be required. Figure 3-38 shows shoring towers supported on timber mats carrying 

spliced bulb-tee sections. 

Figure 3-38 Shoring Towers Supported on Timber Mats
3.42

SECTION 7. DECK CONSTRUCTION

3.7.1 Placing Sequence

In continuous girder bridges, a concrete deck placing sequence is normally provided in 

the design plans, or addressed in the owner’s specifications. Typically, the positive 

moment regions of the deck are placed first, followed by the negative moment regions, 

in an effort to minimize deck cracking in the negative moment region. This results in a 

discontinuous deck placement, generally not favored by contractors. Contractors will 

often develop an alternate placing sequence, which starts at one end of the bridge and 

moves across. Aside from issues such as deck elevation control and concrete cracking / 

mix control, placing the deck in this manner can create uplift at piers or abutments that 

must be addressed in the erection plan. Uplift is most pronounced where a short end 

span is followed by a longer interior span, with maximum uplift occurring as concrete 

placement reaches mid-span of the longer span. Hold-down assemblies as discussed in 

Article 3.5.2.5 may be needed.

Skewed supports and/or curvature can complicate the deck-casting sequence. Keeping 

the deck placement reasonably symmetrical laterally minimizes eccentric or unbalanced 

loading and helps reduce differential deflections between adjacent girders. On skewed 

bridges where the anticipated differential deflections between girders are reasonably 

small, it is preferable to set up the finishing machine normal to the girders as it reduces 

the length of the machine. However, in cases with severe skews that may lead to large 

differential deflections, it may be preferable to set up the finishing machine to align with 

the bridge’s skew. With this arrangement, as the finishing machine progresses along the 

bridge, each girder carries an equal concrete load with resulting similar deflection along 

its length.

In wide structures that have multiple girders and/or with severe skews, multiple deck 

placements may have to be made in the lateral direction which will result in the 

introduction of longitudinal construction joints.
3.43

Figure 3-39 Deck Finishing Equipment for Deck Pour

3.7.2 Overhang Brackets

Almost all steel and concrete bridges include a deck overhang beyond the fascia girder. 

Overhang brackets are used to support the overhang concrete loads, and often the 

loads from the finishing machine. Figure 3-39 shows a typical finishing machine, which 

runs on screed rails set atop the overhang forms or fascia girder. Figure 3-40 and 

Figure 3-41 show typical overhang brackets for steel and concrete girders, respectively. 

Overhang brackets are manufactured items for which dimensional and load capacity 

data are available from the manufacturer. Typical bracket spacing is approximately 4 

feet. Figure 3-42 shows brackets being set on a tub-girder. 

AASHTO LRFD Article 6.10.3.1 requires that the effect of forces from deck overhang 

brackets acting on the fascia girders be considered by the bridge design engineer. The 

magnitude and application of the overhang loads assumed in the design should be 

shown on the contract documents. Loads from the contractor’s selected overhang 

brackets should be compared to these loads to determine if further analysis is required. 

The eccentricity of the deck weight and other loads acting on the overhang brackets 

creates torsional moments on the fascia girders. On curved bridges, overhang bracket 

loads are particularly critical for the girder on the outside of the curve. As the loads are 

applied to the brackets, the top flange is pulled outward causing flange lateral moments 

of the same type as the flange lateral moments due to curvature in regions of positive 

flexure. The opposite is true for the girder on the inside of the curve. 
3.44

The girder top flange must have sufficient capacity to resist these lateral overhang 

bracket loads acting in combination with the vertical loads resulting from the deck 

casting. The bracket should be sized so that the reaction from the bracket’s diagonal 

strut is applied to the girder just above the bottom flange. Placing the bottom of the 

overhang bracket above the base of the girder web may result in web overstresses and 

distortion in areas between cross-frames or transverse stiffness. Temporary bracing 

may be needed to control these deformations. This may especially be a concern on 

deep steel girders due to the depth limits of available brackets.

Figure 3-40 Typical Overhang Bracket – Steel Girder
3.45

Figure 3-41 Typical Overhang Bracket – Concrete Girder
3.46

Figure 3-42 Overhang Brackets Being Set on a Tub Girder

Torsional loads can be resisted by the use of ties, usually reinforcing bars placed above 

the top flange, and timber compression struts located at the bottom flange. The 

computer design tool TAEG (Torsional Analysis for Exterior Girder), developed by the 

University of Kansas for the Kansas Department of Transportation (KDOT), is a public 

domain program, available from KDOT, that can be used to evaluate these systems 

including girder and cross-frame forces. 

Figure 3-43 illustrates examples of temporary bracing used to control the local effects of 

the overhang brackets. When possible, the tie rods should run the full width of the 

bridge. Tie bars attached to U-stirrups of precast girders must be attached near the 

bottom of the U-stirrups to limit stirrup lateral deformations. Timber blocking can be 

carried across the bridge width, but often an angled wood brace runs from the lower 

flange of the outside, or perhaps first inside girder, to the underside of the top flange of 

the next girder to the inside. All blocking must be made tight by wedging, and be 

secured against loosening due to relative movements between the girders, vibration, or 

accidental impacts. 
3.47

Figure 3-43 Overhang Bracket Bracing Examples
3.48

SECTION 8. BRIDGE DEMOLITION

Demolition of existing bridges may include full bridge removal to allow for new 

construction, or partial removal for widening, refurbishment, redecking, or similar 

activities. When concrete bridge decks are removed, composite action of the deck and 

girders is lost and lateral support for girders is reduced or eliminated. Thus, the girder 

capacity alone must be sufficient to prevent overstress or instability under these 

configurations. In some cases, temporary lateral bracing or supports were used during 

bridge erection; reinstallation of similar measures may be required during bridge 

demolition.

While of less concern where bridges are to be fully demolished, demolition activities for 

bridges being redecked or with girders otherwise reused should not cause girder 

damage that could adversely affect capacity. Concrete decks are normally removed 

either by demolishing the deck with hydraulic breakers with the debris retained by a 

temporary work deck supported on the girder lower flanges, or by saw cutting into large 

pieces, as shown in Figure 3-44, which are then lifted off using cranes, back-hoes or 

similar equipment. As the left girder in Figure 3-44 shows, when large hydraulic 

breakers are used, girder flanges may suffer impact damage causing deep dents, flange 

twisting, flange tears, and other defects that can reduce girder capacity. In removing 

decks in slabs, saw cuts are made both parallel and perpendicular to the girders to yield 

slabs of such size that they can be readily removed. If the depth of cut of the saws is not 

well controlled, girder flanges may experience cuts that can significantly reduce girder 

capacity. For redecking projects, it is recommended that the girder top flange location 

be marked on the deck and hammer sizes limited in order to minimize any girder 

damage.

Girder removal normally follows a sequence that is the reverse of erection. Unless 

girders are to be reclaimed for reuse, members are separated into sizes convenient for 

lifting by flame cutting rather than unbolting connections. Stability must be maintained at 

each stage of removal.

In determining crane capacities for demolition, consideration must be given to increased 

girder weight due to concrete that remains attached. In addition, an allowance should be 

made for the possibility of girders hanging up during removal due to corrosion, possible 

misalignment remaining from installation, possible structure movements over time, and 

similar factors. Thus, cranes should be sized using generous allowances for unknowns.

As seen in Figure 3-44, demolition is often performed by equipment located on the 

bridge. The effects of these loads must be evaluated and account for equipment loads 

as well as changes in girder capacity as demolition proceeds. These activities may 

create uplift at supports, and girder behavior may change from continuous to simple 

span or cantilever depending on stages in removal.
3.49

In removing decks from post-tensioned concrete girder bridges, evaluation should 

consider whether post-tensioning was applied before or after the deck was cast. If the 

deck was placed prior to stressing, the bare beams may not have sufficient capacity to 

resist the prestressing force when no longer composite, possibly resulting in girder 

cracking. 

Figure 3-44 Bridge Deck Demolition Removing Deck in Sections

SECTION 9. SUMMARY

Erection schemes for girder bridges, though well developed, require evaluation 

considering the specific requirements of each structure. Those responsible for the 

design of erection methods and sequencing must be knowledgeable in how construction 

practices affect the bridge superstructure at each stage of erection. In presenting an 

overview of construction practices and noting the relationship of these to girder erection 

and stability, this chapter provides a background to the girder design and stability 

discussions presented in the following chapters.
3.50
4.2

CHAPTER 4 

STABILITY FUNDAMENTALS 

SECTION 1. INTRODUCTION

Much of the analysis that is performed on steel and concrete bridge systems assumes 

that the structure is geometrically stable and that the deformations of the structure will 

not have a significant impact on the geometry of the structural components. However, 

depending on the configuration of the structure and the applied loading, instabilities can 

have a significant impact on the safety and performance of the structure, primarily 

during construction stages. Although some limit states are similar for steel and concrete 

structural elements, for many situations the controlling limit states are often substantially 

different between the two materials. The following two sub-sections provide a general 

introduction to the general topics of stability that will most likely apply to steel and 

concrete structures. 

4.1.1 Steel Structures

Stability limit states often control the design of compression members in steel 

structures. The stability of structural elements and systems can generally be divided into 

two areas: local buckling and global buckling. Local buckling modes typically involve 

buckling of elements of the cross-section, such as the flanges (flange local buckling) or 

the web (web bend buckling), both of which are usually controlled by limiting the 

geometric profile of the section. Global buckling modes include both individual member 

buckling as well as system buckling involving a group of structural members. Global 

member stability is a function of several parameters, including the member geometry, 

unbraced length, and boundary (support) conditions. Depending on the cross-sectional 

geometry and bracing that is provided, the potential global buckling modes for columns 

can consist of flexural buckling, torsional buckling, or flexural-torsional buckling. The 

global buckling mode for girders is always flexural-torsional (also often referred to as 

lateral-torsional). In addition to members buckling, interconnected girders (such as a 

multi-girder system with cross-frames) can also fail in a system buckling mode. System 

buckling of interconnected girders is covered in Chapter 5. Although this chapter is 

presented primarily from a steel perspective, most of the principles also apply to 

concrete structural members and systems. In addition to buckling modes, concrete 

girders (and steel girders in the absence of bracing) should be evaluated for roll stability 

of the girder to ensure that the member does not fail as a result of overturning. Roll 

stability is not discussed in this chapter but is discussed in Chapter 5.
4.3

4.1.2 Concrete Structures

Although much of this chapter is presented primarily from a steel perspective, most of 

the principles also apply to concrete structural members and systems. This is 

particularly true for concrete column elements. Although it is possible that a concrete 

beam may experience lateral-torsional buckling between brace points, in many 

situations the torsional constant of the girder is relatively large and therefore, provided 

twist is restrained at a few points along the girder length, the lateral-torsional buckling 

strength is often not an issue. However, in addition to buckling modes, concrete girders 

(and steel girders in the absence of bracing) should be evaluated for roll stability of the 

girder to ensure that the member does not fail as a result of overturning. Roll stability is 

not discussed in this chapter but is discussed in Chapter 5.

4.1.3 Analysis for Stability

Although many designers make use of a first-order structural analysis to determine 

design forces, such an analysis does not provide an estimate of buckling-related 

deformations, nor can such an analysis provide an estimate of the buckling strength. 

Two types of analyses are generally associated with stability: a critical load analysis and 

a large-displacement analysis. A critical load analysis is found from an eigenvalue 

buckling analysis as outlined in Chapter 6. Many commercially available software 

packages are capable of determining eigenvalues. Many of the expressions that are 

presented in this chapter for evaluating the buckling capacity of plates and elements are 

synonymous with the critical loads that are predicted by eigenvalues. The critical load 

provides a valuable indicator of the maximum capacity of the section under ideal 

conditions. However, because of local and global imperfections, the actual capacity is 

often lower than predicted by the critical load. Methods of stability analyses are 

discussed in Chapter 6. This chapter focuses on the stability buckling behavior of 

structural members and has been divided into six sections, including this introduction. 

The buckling capacity is significantly affected by geometrical imperfections and residual 

stresses, both of which are discussed in the following section. The subsequent sections 

focus on the buckling behavior of columns, plates, and girders. The final section of the 

chapter provides a discussion on the fundamental strength and stiffness requirements 

for proper stability bracing. Bracing is discussed in more detail in Chapter 5.

SECTION 2. GEOMETRICAL IMPERFECTIONS AND RESIDUAL 

STRESSES 

There are a number of geometrical imperfections that can have a substantial impact on 

the buckling resistance of the section. Many of the imperfections in steel sections come 

as a result of the manufacturing process. The imperfections may consist of 

inconsistencies or distortions of the cross-section, out-of-straightness of the member, as 

well as plumbness limits in the erected structure. Most codes and standards including 

the AASHTO Specification (2012) reference the American Society of Testing and 
4.4

Materials (ASTM) A6/A6M (2012) for tolerances on plates, rolled shapes, and fabricated 

steel sections. Although inconsistencies and distortions of the cross-section may have 

some impact on the global buckling behavior, the effect will generally be more severe 

on the local buckling capacity.

Although the manufacturing process can also lead to imperfections in concrete 

structures, imperfections can also come from prestressing and long-term creep 

deformations. Due to the weight of the concrete members, lateral imperfections can 

cause large over-turning moments. Problematic situations that have occurred during 

construction on the concrete girders have often been due to inadequate or incorrectly 

installed braces that are intended to stabilize the girders. Tolerance limits for sweep, 

camber, cross-section and other properties of precast concrete girders are provided in 

the PCI Manual for Quality Control for Plants and Production of Structural Precast 

Concrete Products (MNL 116-99)

Figure 4-1 Camber and Sweep in Steel Members

Global buckling modes are much more sensitive to variations in the profile of the 

member along the length. For rolled shapes, ASTM A6 provides tolerances on the 

camber and sweep of the member as depicted in Figure 4-1. Camber is generally 

defined as the intentional bending of the member to account for dead load deflections, 

while sweep is an out-of-plane imperfection from the member’s designed geometry. The 

ASTM A6 tolerance on sweep for sections that are likely to be used in bridges is equal 

to L/960. 
4.5

In addition to the magnitude of the imperfection, the shape of the imperfection has an 

impact on the buckling capacity. If the shape of the imperfection is similar to the 

controlling buckling mode, the imperfection has a more substantial effect on the 

buckling capacity. When analyzing members for stability using a large displacement 

analysis, the potential imperfection should be included in the geometry of the member. 

The critical shape of the imperfection in these analyses is dependent on the controlling 

buckling mode. For buckling modes that primarily include lateral translation, a 

translation such as those depicted in Figure 4-1 are generally critical. However, for 

mode shapes involving a torsional deformation, the critical imperfection includes twist of 

the section as well. An effective method of incorporating the critical shape imperfection 

is to use the eigenvalue from an eigenvalue solution to create a seed imperfection for 

the large displacement analysis. Modeling the imperfections in the large displacement 

analysis is covered in more detail in Chapter 6. 

Figure 4-2 Effects of Residual Stresses on Stress-strain

The buckling strength of a member is often significantly affected by residual stresses, 

which are stresses that are locked into the cross-section and are typically caused during 

manufacturing or fabrication. The locked-in stresses consist of a combination of tensile 

and compressive stresses with force resultants that are in equilibrium. Although residual 

stresses will cause a member to experience inelasticity at an applied stress lower than 

the yield strength of the material, because the tensile and compressive force resultants 

are in equilibrium, the ultimate strength of a member in tension is not generally reduced. 

This is demonstrated in Figure 4-2, which depicts a stress-strain curve for a steel 

section with residual stresses. The dashed line represents the idealized stress-strain 

curve for mild-carbon steel with a well-defined yield plateau. The idealized stress-strain

curve typically comes from a test on a coupon of the material cut from the main 

member. The residual stresses are released when the coupon is cut from the material, 

and therefore, the resulting curve is often not representative of the behavior of the entire 
4.6

cross-section. The presence of residual stresses leads to yielding of parts of the crosssection at applied stress levels lower than the yield strength of the material. However, 

because the tensile residual stresses are counter-balanced by compressive residual 

stresses, the total yield capacity of the entire section is still the same: Py equals sy times

Ag, where Py is the force resulting in full yielding of the cross-section, sy (in practice also 

sometimes denoted by Fy) is the yield strength of the material, and Ag is the gross 

cross-sectional area of the member. The magnitude of the maximum tensile residual 

stress in the cross-section is the difference between the yield strength, sy, and the 

proportional limit stress, sp, which is the stress where the s−ε curve becomes nonlinear. 

A curve similar to that shown in Figure 4-2 will result when a member is subjected to 

compression, provided that the length of the member is short enough (a stub column 

section) so that the member will not buckle. As is discussed in the following section, the 

buckling strength is a function of the stiffness (modulus) of the material. Above the 

proportional limit stress, the tangent stiffness (ET) of the material is less than the elastic 

stiffness (E). As a result, the buckling strength of a member can be significantly reduced 

by the presence of residual stresses on the cross-section. Although the applied stress 

may be less than the yield strength of the material, the residual stresses lead to 

premature yielding of elements of the cross-section that reduce the effective stiffness of 

the member compared to the full elastic stiffness. Therefore, to account for the effects of 

residual stresses, most design specifications have both elastic and inelastic buckling 

solutions. The inelastic buckling solution takes into account the impact of residual 

stresses on the stiffness of the member. 

As noted earlier in this section, residual stresses are often caused by the manufacturing 

or fabrication processes of the steel member. For example, in rolled W-shapes residual 

stresses are primarily caused during the manufacturing process at the mill. To facilitate 

the rolling process, a steel billet for the W-shape is raised to a high temperature so that 

the modulus of the material is relatively low, thereby making the shape easy to roll 

without excessively wearing the mechanical rollers. Once the W-shape has been rolled 

and achieved a shape within applicable tolerances, the member is left to cool. 

As the member cools, the steel begins to regain the full elastic stiffness and also 

shortens as dictated by the thermal properties of expansion and contraction. However, 

thermal gradients exist as the shape gradually cools. The first portions of the crosssection to cool are the regions that have the most surface area exposed to the 

atmosphere, such as the flange tips. As these regions cool and contract, the modulus of 

elasticity of the material increases to the full elastic value. 

Although some parts of the section may have cooled and possess nearly the full elastic 

modulus, other regions are still hot, and as they cool, will continue to contract. However, 

in order to contract, regions of the section with significant material stiffness must be 

stressed to accommodate the thermal contraction of the hotter regions — which 

therefore leads to residual stresses. In general, portions of the section that cool first 

develop compressive residual stresses, while portions that cool last develop tensile 

residual stresses. As noted earlier, the tensile and compressive force resultants from 
4.7

the stresses must be equal for static equilibrium. There have been a number of previous 

studies on the magnitude and distribution of residual stresses in steel members (SSRC 

2010). A typical residual stress pattern in a rolled W-shape is depicted in Figure 4-3. 

Because the tips of the flanges and mid-depth of the web cool first, these sections 

experience compressive residual stresses while the flange to web intersection cools last 

and material in that area typically experiences tensile residual stresses. 

Figure 4-3 Typical Residual Stress Distribution on a Rolled Wide Flange 

Section

Sections built-up from welded plates also develop substantial residual stresses. The 

high localized heat input from the welding process coupled with the high thermal 

conductivity of steel can result in a quenching effect in the welds as the steel plates 

draw heat away from the weld. The residual stresses that develop from welds can be 

significantly higher than those found in rolled shapes. Preheating the plates in the weld 

area helps to minimize the large thermal gradient and can reduce the magnitudes of the 

residual stress as well as the plate distortions in the welded regions. Residual stress 

distributions are also affected by the straightening and cambering of girders by cold 

working the steel material. Rolled sections can be straightened by either a rotarizing 

process or by gag straightening. Many mills use the rotarizing process in which the 

shape is passed through a series of rollers that cold work the section back and forth to 

achieve a straight section. 

On a W-shape, the rollers typically react on the fillets (often referred to as the K-zone) of 

the shape. Although rotarizing is a quick method to straighten the section, the large 

reactions from the rotarizing on a localized region of the shape may affect the ductility of 

the steel at the roller contact point and can lead to a region of low fracture toughness for 
4.8

crack initiation. The rotarizing process produces residual stresses all along the length. 

The other straightening process is referred to as gag straightening in which hydraulic 

presses act at a few locations and deform the member inelastically to achieve a 

member that satisfies the required sweep (or camber) tolerances. The method of gag 

straightening is a manual process that is more labor intensive than the automated 

rotarizing process; however gag straightening does not generally lead to the issues with 

low fracture toughness at localized regions of the member as outlined for rotarized 

sections. 

The impact of residual stresses on the buckling behavior differs depending on the axis 

of the section. For example, the effects of residual stresses have a more significant 

impact for buckling about the weak axis of a wide flange section compared to the 

buckling about the strong axis. Some past studies have recommended different buckling 

solutions depending on the axis that the section is buckling about; however the 

suitability of these different solutions is questionable. Although there have been 

numerous studies in the past on the magnitude and distribution of residual stresses, 

there is a great deal of variability. Numerous factors play a role in the actual distribution 

and magnitude. Although there is significant scatter in the test results due to variations 

in the distribution of residual stresses, inelastic buckling solutions have been developed 

for design specifications that provide a reasonable estimate of the impact of residual 

stresses on the buckling behavior. The following section focuses on the buckling 

behavior of column sections. Although elastic buckling behavior is discussed first, 

methods of accounting for inelastic effects on the buckling behavior are also covered. 

SECTION 3. COLUMN BUCKLING

There are several applications for axially loaded compression members in bridge 

applications, including: piers, truss members, and temporary supports, such as shore 

towers. There are three buckling modes possible for axially loaded compression 

members: flexural buckling, torsional buckling, and flexural-torsional buckling. The 

following subsections provide an outline of the solutions for the different modes. The 

controlling mode is generally the value that provides the lowest capacity. Although a 

complete stability design considers all three modes, with a little insight into the buckling 

solutions, a designer can eliminate the need to evaluate some of the modes depending 

on the shape of the cross-section and the bracing details. A discussion of when the 

particular modes need to be evaluated is provided in the following subsections. 
4.9

Figure 4-4 Flexural Buckling of Wide Flange Column

4.3.1 Flexural Buckling 

The buckling mode that is generally covered in all courses on structural steel design is 

the flexural buckling mode. As a result, most engineers are the most familiar with 

flexural buckling, which involves a lateral translation of the cross-section about one of 

the principle axes as depicted in Figure 4-4. The pin-ended column in Figure 4-4 is often 

referred to as an Euler column as a tribute to Leonhard Euler who was the first 

individual to develop a mathematical formulation in the mid-1700s to predict the elastic 

buckling capacity of axial loaded columns. 

The elastic solution developed by Euler for the pin-ended column is given in the 

following expression:

Equation 4-1

Where: 

PE = the critical elastic buckling load (Euler load) (kips)

E = the modulus of elasticity (ksi)

I = the moment of inertia of the section about the buckling axis (y-y axis in 

figure) (in4

) 

L = the unbraced length of the column (in)

The controlling buckling capacity of the column in Figure 4-4 would be the smaller of 

buckling about the x-x and y-y axis. If the unbraced length is the same about the two 

axes, the smaller moment of inertia will dictate the buckling capacity. For this reason, 

the y-y axis is often referred to as the weak axis since Iy<Ix in I-shaped members, 
4.10

generally referred to as I-girders. However, the strong axis can still control buckling if 

the unbraced length is larger about that axis or if the translational or rotational support 

conditions are different about the two axes. 

Equation 4-1 is applicable to columns with pinned ends. For more general problems, an 

effective length factor (K) is often incorporated, resulting in the following expression:

Equation 4-2 

The effective length factor converts a column in a structural system to an equivalent 

Euler column. A physical representation of the effective length factor is depicted in 

Figure 4-5. The columns in the portal frame are pinned at the base and restrained by 

the girder at the top. The effective length factor for a column in the structural system is a 

function of the relative stiffness between the columns and the restraining girder at the 

top of the frame. The effective length factor converts the columns in the frame to the 

equivalent length of the pin-ended Euler column in the figure.

Figure 4-5 Effective Length Factor

Effective length factors for flexural buckling are often divided into two categories as a 

function of the bracing condition of the column. The columns in Figure 4-5 are part of an 
4.11

unbraced frame that can side-sway. The range for the effective length factors for 

unbraced frames is 1.0 ≤ Ksway < ∞. For braced members in which the ends cannot 

translate relative to one another, the range for the effective length factor is 0.5 ≤ Kno sway

≤ 1.0. Many specifications or the associated commentary sections provide a figure 

similar to the one shown in Figure 4-6 that tabulate the K-factors for idealized support 

conditions. Such a figure is useful to provide an indication of the range of K-factors for 

idealized columns; however, most structures do not match the idealized support 

conditions. Therefore, for design, a solution that can account for the variable support 

conditions is typically desired. A more general solution is available with the alignment 

chart that that is commonly provided in most design specifications (AASHTO Section 

4.6.2.5). 

Figure 4-6 K factors for Idealized Support Conditions

As noted earlier, design specifications typically provide both elastic and inelastic 

buckling solutions. Since the solutions will typically be a function of the material yield 

strength, the buckling solutions are sometimes provided in terms of stress instead of 

force. Dividing both sides of Equation 4-2 by the cross-sectional area results in a stress 

and gives the following formulation:
4.12

Equation 4-3 

Where:

 

FE = the Euler buckling stress (ksi)

r = the radius of gyration which is equal to g

I r A = (in)

Ag = the gross area of the cross-section (in2

) 

The ratio KL/r is a unitless quantity that is referred to as the slenderness of the column. 

Most design specifications use an elastic buckling solution that is some function of the 

Euler solution given by Equation 4-3.

The inelastic buckling solution in most specifications is tangent to the elastic solution at 

a selected column slenderness and then tends to the nominal yield strength (usually 

including a resistance factor, φ) at a column slenderness of 0. The combined elastic and 

inelastic solutions are usually referred to as the column curve. The AASHTO LRFD

specification has adopted the column curve from the AISC Specification (2010) as given 

in the following equations:

Equation 4-4 

Equation 4-5 

Where:

Pn = the nominal buckling strength (k)

PE = the Euler buckling load given by Equation 4-2(k)

Po = the yield load of the section given by FyAg (k)

Fy = the nominal yield strength of the column material (ksi)

Ag = the gross area of the column (in2) 

The AASHTO specification also includes a Q factor in the calculation of Po, which is a 

factor that accounts for slender cross-sectional elements that may be affected by local 

buckling. Flexural buckling is a buckling mode that may control the design of either 

doubly-symmetric or singly-symmetric sections. The term doubly-symmetric refers to a 

section with two axes of symmetry, while a singly-symmetric section possesses a single 

axis of symmetry. Some typical doubly-symmetric and singly-symmetric sections are 

depicted in Figure 4-7.
4.13

4.3.2 Torsional Buckling 

Another potential mode to be considered for axially-loaded columns is torsional 

buckling, in which the instability involves a pure twist of the section. The point that the 

section twists about is dependent on the cross-sectional properties and the bracing

details that are used. The assumed center of twist for most columns is the shear center 

of the section; however as is subsequently discussed in this section, depending on the 

lateral bracing details, some columns may twist about a restrained axis. Before the 

buckling behavior is discussed, a brief overview of the torsional properties of the section 

is prudent.

The torsional resistance in thin-walled members results from either Saint-Venant 

torsional stiffness or warping torsional stiffness. The Saint-Venant stiffness is often 

referred to as uniform torsion, since the stiffness does not vary along the length and is 

also not sensitive to the support conditions of the section. Saint-Venant torsion results in 

a pure shear deformation in the plane of the plates that make up the member. 

Figure 4-7 Typical Doubly and Singly-Symmetric Sections

The warping torsional resistance, on the other hand, is often referred to as non-uniform 

torsion since the stiffness is associated with the bending deformation in the plane of the 

individual plates that comprise the section. The warping stiffness of a section is related 

to the member’s resistance to warping deformation. 
4.14

Two I-girders subjected to a torque at the ends are shown in Figure 4-8 to illustrate 

warping deformation and also warping stiffness. The applied torque is indicated using 

the right-hand rule convention (direct thumb of right hand in the direction of double 

arrow heads and fingers curl in direction of applied torque). Figure 4-8 shows that 

warping deformation consists of a twist of the flanges relative to each other about a 

vertical axis through the web. Warping deformation distorts the cross-section such that it 

no longer is a plane section because the two flanges have distorted relative to one 

another. Twist about the longitudinal axis of the member in Figure 4-8A is prevented at 

one end; however the warping deformations are not restrained. Since the section is free 

to warp along the entire length, the flanges remain straight as they twist relative to each 

other and the member only possesses Saint-Venant torsional stiffness. 

Figure 4-8 Warping Stiffness and Bending Stiffness of the Plate Elements

The wide flange section in Figure 4-8B has both twist and warping deformation 

prevented at one end. With warping restrained at just one location along the length, the 

member cannot twist without bending the flanges. Since the flanges must bend if the 

member twists, the section therefore has warping stiffness. The warping torsion 

produces longitudinal stresses in the flanges of the member.

Many members do not have a physical restraint preventing warping as shown in Figure 

4-8B; however, the member still has warping stiffness if twist is prevented at a minimum 

of two points along the longitudinal axis. The twist restraint end conditions prevent the 

section from rotating about the longitudinal axis, but otherwise do not specifically 

restrain warping deformation of the section. Since the bending stiffness is very sensitive 

to the unsupported length, the warping stiffness is highly variable with the magnitude of 

the unbraced length. Larger bending lengths of the plate elements from the member 

twist lead to lower torsional warping resistance compared to shorter bending lengths.
4.15

4.3.2.1 Elastic Torsional Buckling about the Shear Center 

Based upon the torsional stiffness components outlined above, the torsional buckling 

resistance potentially includes both Saint-Venant and warping components. For doublysymmetric sections, the elastic torsional buckling capacity is given as follows: 

Where: Equation 4-6 

E = the modulus of elasticity (ksi)

G = the shear modulus (ksi)

J = the torsional constant (in4

) 

Cw = the warping constant (in6

) 

Kz = the effective length factor for torsion 

Lz = the spacing between locations restrained from twist (in)

Ag = the area of the gross cross-section (in2) 

Ix = the moment of inertia about the x axis (in4) 

Iy = the moment of inertia about the y axis (in4

) 

The first term in the brackets is related to the warping stiffness while the second term is 

related to the Saint-Venant stiffness. The effective length factor in Equation 4-6 reflects 

the beneficial effects of warping restraint on the stiffness of the section. A pinned end in 

torsion has twist restrained; however, the section is free to warp. A fixed end in torsion 

is one that has twist restrained and full warping restraint. Therefore, if twist is restrained 

at both ends of the unbraced length, the effective length factor for torsion is as follows:

• Section free to warp at both ends of the unbraced length: Kz = 1.0 

• Section free to warp at one end, warping restrained at the other: Kz = 0.7

• Section fixed from warping at both ends: Kz = 0.5

• Effective length factors similar to the sway mode can be found if twist is 

only restrained at one end, in which case Kz ≥ 1.0

The shear modulus in Equation 4-6 is given by the expression G = ( ) 12 + μ

E , where is 

Poisson’s Ratio (0.3 for metals). Therefore, since the elastic modulus for steel is 29,000 

ksi, the value of G = 11,200 ksi. For open cross-sections, the torsional constant is given 

by the following expression:

Equation 4-7 
4.16

where bi and ti are the respective width and thickness of the plate elements that make 

up the cross-section of the girder. The torsional buckling behavior of closed crosssections is discussed at the end of this subsection. For doubly-symmetric I-girders, the 

warping constant is equal to:

Equation 4-8 

Where, h0 is the distance between flange centroids which is equal to the total girder 

depth minus flange thickness, which equals d-tf. 

Figure 4-9 Ineffective Torsional Brace

For I-girders, weak axis flexural buckling will always control over torsional buckling 

when the unbraced length is the same for the two modes. When the unbraced length for 

torsional buckling is larger than for weak axis flexure, then both modes need to be 

evaluated. Figure 4-9 shows the case where the unbraced length for flexural buckling 

and torsional buckling are different. In many applications, rods are used to provide 

bracing as shown in Figure 4-9a. The detail that is commonly used to connect the rod to 

the wide flange section consists of a hole in the web as indicated in Figure 4-9b. 

Although the large axial stiffness of the rod provides good control of the lateral 

movement of the section, the low flexural stiffness of the rod makes such a brace 

ineffective at controlling twist as depicted in Figure 4-9c. As a result, with twist 

restrained at the top and bottom of the column, the unbraced length for torsional 
4.17

buckling would be the full column length, L, while the unbraced length for weak axis 

flexure is L/2. As a result, both weak axis flexural buckling and torsional buckling need 

to be considered. 

The solution given in Equation 4-6 is for sections with substantial warping stiffness. 

Cross-sections that are composed of plates that intersect at a single point do not have 

significant warping stiffness. Although the AISC Manual (2012) provides values of Cw for 

WT-sections, the torsional stiffness of the section primarily is the result of Saint-Venant 

stiffness. The contribution of the warping term in Equation 4-6 for WT sections is often 

less than 1% of the total and is therefore not worth including in the calculation. Sections 

with insignificant warping stiffness include angles, cruciforms, WT, and built-up double 

angle sections. The elastic torsional buckling capacity for these sections consists of only 

the Saint-Venant term:

Equation 4-9 

Although closed cross-sections do have warping stiffness, the contribution is a relatively 

small percentage of the total stiffness due to the extremely large Saint-Venant stiffness 

of the closed shape and therefore, the warping stiffness is often conservatively 

neglected. The torsional constant of the closed shape is much larger than the value for 

a comparable open section. The torsional constant for a rectangular tube is given by the 

following expression:

Equation 4-10

Where Ao is the enclosed area of the cross-section of the closed shape, and the 

variables bi and ti in the summation are the respective width and thickness of the ith

plate that make up the cross-section. For example, considering a rectangular crosssection made up of four plates, the denominator in Equation 4-10 is calculated by simply 

summing the width-to-thickness ratios of the four plate elements. In a circular tube 

section (pipe or HSS section), the torsional constant can be found in Equation 4-10 by 

replacing the summation in the denominator with (2πr/t), where r is the radius of the 

pipe measured to the mid thickness of the wall and t is the wall thickness. Ao in 

Equation 4-10 is typically defined by the area enclosed from the mid-thickness of the 

plates that make up the cross-section. Because the torsional constant for closed crosssections is so large, the resulting torsional buckling capacity predicted by Equation 4-10 

is also very large. If the load is converted to a stress, the elastic buckling stress is of the 

order of G = 11,200 ksi, which obviously means the section would yield. As a result, 

torsional buckling of closed cross-sections is not a concern and the mode does not 

need to be evaluated. Flexural buckling will always control for columns made from 

closed shapes.
4.18

4.3.2.2 Elastic Torsional Buckling Cases with Twist about a Restrained 

Axis

The bracing detail that is shown in Figure 4-9 results in a case where the section can 

twist about mid height and the torsional unbraced length is larger than the weak axis 

flexure unbraced length. In some instances, the lateral bracing may frame into the 

cross-section at a location offset from the shear center. Two cases are shown in Figure 

4-10 in which the lateral bracing may be offset on either the weak or strong axis. The 

bracing in this case only stops lateral translation and does not restrain twist. The column 

section can fail in these cases by torsional buckling about a restrained axis. 

Timoshenko and Gere (1970) provided the following two expressions for columns with 

the respective cases of the lateral bracing offset on the strong or weak axis:

Equation 4-11

Equation 4-12

Where, PE is the Euler buckling load given by Equation 4-1 with the unbraced length 

equal to the total spacing between locations where twist is restrained, and a or b are the 

distance from the shear center to the location where the lateral brace frames into the 

section as indicated in Figure 4-10. The other terms are as specified in the last section. 

As expected, if a or b is equal to zero (lateral bracing at the shear center), Equation 4-

11 and Equation 4-12 reduce to Equation 4-6. However, if the bracing is offset from the 

shear center, the expressions can be used to evaluate the torsional buckling resistance. 

If the lateral bracing is offset along the weak axis, the torsional buckling capacity will be 

smaller than the corresponding capacity if the lateral bracing was positioned at the 

shear center. Depending on the section properties, if the bracing is offset along the 

strong axis, the torsional buckling capacity can increase or decrease relative to shear 

center bracing. Further discussion and comparisons of the expressions with Equation 4-

6 are provided in Helwig and Yura (1999). Common cases in which the bracing is offset 

from the shear center are found in trusses. The chords can be oriented as shown in 

Figure 4-10. If the deck is located above the top chord, the lateral bracing may be offset 

and Equation 4-11 or Equation 4-12 may be applicable.
4.19

Figure 4-10 Lateral Bracing Offset from Shear Center

4.3.3 Elastic Flexural Torsional Buckling

Flexural torsional buckling has a mode shape in which the cross-section translates and 

twists. Many sections may be susceptible to either flexural buckling about one of the 

principle axes or flexural torsional buckling about the other principle axis. Although 

expressions can be presented for these cases (and are given at the end of this 

subsection), better insight into the buckling behavior can be obtained by first reviewing 

the general buckling expression that is valid for any shape section. The general solution 

is given as follows:

Equation 4-13

Where: 

Pcr = the critical buckling load (kips) 

PEx = the flexural buckling capacity given by Equation 4-2 using Ix (kips) 

PEy = the flexural buckling capacity given by Equation 4-2 using Iy (kips) 

PT = the torsional buckling capacity given by Equation 4-6 (kips)

The values of xo and yo are demonstrated in Figure 4-11 and represent the distance 

between the shear center and the geometric centroid measured about either the weak 
4.20

axis or the strong axis. The term r0 represents the polar radius of gyration and is given 

by the expression: 

Equation 4-14

Where:

Ag = the gross area of the cross-section. 

Although Equation 4-13 appears relatively complex, the expression is applicable to any 

shape cross-section and also provides valuable insight into the behavior of various 

types of cross-section with regards to the potential modes that may control column 

buckling capacity. For example, in a doubly-symmetric section, the center of gravity and 

the shear center coincide. Therefore, xo and yo are equal to zero and Equation 4-13 

reduces to the following:

Equation 4-15

Equation 4-15 has three potential roots. The critical buckling load may be either flexural

buckling about the x or y axis, or torsional buckling about the shear center. In a singlysymmetric section, either xo or yo is equal to zero. For example, in the WT section 

shown in Figure 4-11, xo is equal to zero and Equation 4-13 reduces to the following 

expression:

Equation 4-16

One root to the equation is Pcr = PEx, which represents flexural buckling about the x-x 

axis. The other root is given by the remaining quadratic expression and represents 

flexural-torsional buckling in which the section translates about the y-y axis and twists 

about the shear center. Although the flexural torsional mode can be found directly using 

Equation 4-13 many design specifications, such as AASHTO, provide a separate 

equation for the flexural torsional mode of singly symmetric shapes:

Equation 4-17

Where:

, and 
4.21

Figure 4-11 Definitions of yo and xo 

Equation 4-17 is simply the quadratic solution to Equation 4-16 after the (Pcr-PEx) is 

factored out. The solution can be used to calculate the flexural torsional mode when the 

y-axis is the axis of symmetry. If a designer is considering a section such as a channel, 

as shown in Figure 4-11, xo is equal to zero. Therefore, when the section is symmetric 

about the x-axis, PEy is replaced with PEx and yo is replaced with xo in Equation 4-17.

4.3.4 Inelastic Effects for Torsional and Flexural Torsional Buckling

The torsional and flexural torsional buckling expressions given up to this point 

represent the elastic torsional buckling capacities. The St. Venant term is not as 

severely affected by inelasticity compared to the warping term. For singlysymmetric sections without significant warping stiffness (WT-sections or double 

angles), the AISC specification uses the elastic torsional buckling capacity, PT, in 

Equation 4-17 and uses the inelastic buckling capacity given by Equation 4-4 and 

Equation 4-5 for PEy. 

For all other sections AISC simply calculates the elastic critical torsional or 

flexural torsional buckling capacity, and uses that value for PE in Equation 4-4 

and Equation 4-5. Such an approach reduces both the warping and St. Venant 

torsional components to account for inelasticity, which is conservative. The 

AASHTO Specification uses the same conservative approach and uses the 

elastic critical torsional or flexural-torsional buckling load for PE in Equation 4-4 

and Equation 4-5 for all cross-sections.
4.22

SECTION 4. PLATE BUCKLING AND LOCAL BUCKLING

The resulting configuration of the I-shape in Figure 4-12 maximizes the moment of 

inertia of the section about the X-X axis which improves the resistance to bending or 

global buckling about that axis. The numerical breakdown of the terms that contribute to 

the moments of inertia in Figure 4-12 show the terms that tend to dominate the 

calculation of Ix and Iy. For example, in the evaluation of Ix, the moments of inertia of the 

flange plates about their centroidal axes contribute very little compared to the Ad2 term. 

In a similar fashion, the web contributes very little towards the moment of inertia about 

the Y-axis. In design, the terms that have small contributions to the moments of inertia 

can often be neglected with little impact on the accuracy of the calculation. 

Figure 4-12 Moment of Inertia Sample Calculations

However, in the process of design, engineers often must make decisions on proportions 

of the member to improve the efficiency of the section. For example, if the designer 

desires to increase the moment of inertia about the Y-axis, the calculations demonstrate 

that increasing the flange width will increase Iy much more substantially than increasing 

the thickness. If the flange area is maintained at 12 in2, but a flange size of 24 in. x 0.5 

in. is used, Iy increases by a factor of 4 to 1152 in4. The large increase is due to the 

cubed exponent on the flange width. Therefore, a wider plate with a smaller thickness 

results in a much more significant increase in the moment of inertia compared to a 

thicker plate with a smaller width. From a flexural buckling perspective that is heavily 

dependent on the cross-section moment of inertia, this observation is valid. However, in 

addition to the global buckling modes discussed earlier in this chapter, another limit 

state that may control the capacity of the member is local buckling of one of the 
4.23

elements of the cross-section. For the example given above, the cross-section with the 

24 in. wide flanges that are 0.5 in. thick will be much more susceptible to local buckling 

of the flange plates compared to the section with the 1 in. thick flanges. However, 

before local buckling is discussed, an overview of plate buckling is first outlined in the 

following subsection.

4.4.1 Plate Buckling 

There are a number of fundamental differences in the stability behavior of plates 

compared to some of the global buckling modes discussed earlier in this chapter. One 

of the primary differences between plate buckling and global buckling is associated with 

the post-buckling behavior. In global buckling modes, the ultimate strength of the 

members is typically very close to the global buckling capacity. However, in plate 

buckling problems, there can be substantial post buckling strength in which the load 

carrying capacity of the cross-section can be substantially higher than predicted from 

the plate buckling solution. A common example of this increased strength is found in the 

webs of plate girders. As outlined later in this section, the shear capacity of the webs 

can be much higher than predicted by shear buckling formulations. 

A discussion of plate buckling can be found in several texts on stability (Bleich, 

Timoshenko and Gere, SSRC Guide). The elastic plate buckling capacity is commonly 

expressed as follows: 

Equation 4-18

Where, scr is the elastic plate buckling stress (ksi), k is the plate buckling coefficient, E 

is the modulus of elasticity of the plate material, μ is Poisson’s ratio of the material, 

while b and t are the respective width and thickness of the plate. Poisson’s ratio for 

metals is 0.3. The plate buckling coefficient, k, accounts for variations in the support 

conditions and distribution of stress in the plate. 

The plate buckling coefficients can be divided into three primary categories: axial 

compression, bending, and shear. The values shown in Figure 4-13 show the plate 

buckling coefficients for a long plate subjected to axial compression. The support 

conditions have a significant impact on the plate buckling coefficient. Although many 

plates may not match exactly the idealized boundary conditions that are depicted in 

Figure 4-13, the values shown can be used to bracket the critical buckling stress.
4.24

Figure 4-13 Plate Buckling Coefficients for Axial Compression in a Long 

Plate

An example of the ability to bracket the plate buckling coefficient would be the web plate 

of an I-shaped member such as the section depicted in Figure 4-12. For the case of 

pure compression, the web will likely receive some restraint from the two flange plates. 

The flange plates have sufficient lateral stiffness so that the edges of the plate can be 

assumed as supported against out-of-plane translation. Therefore, the idealized support 

conditions from Figure 4-13 will be somewhere between Cases 1 and 3, which 

correspond to the respective cases of simply supported conditions and fully fixed 

conditions. The simply-supported conditions will provide a conservative estimate of the 
4.25

plate buckling coefficient. The actual amount of restraint that the flanges provide is a 

function of the stiffness of the flange plates compared to the web plate. The stiffness of 

the flange plates are a function of the magnitude of the axial compressive stress 

compared to the flange buckling stress. If the flange plates are providing restraint to the 

web plate, then the web can provide no rotational restraint to the flanges, and therefore, 

the plate buckling coefficient for the flange would be Case 4 with one edge free and the 

other edge pinned. The width of the plate in that case would be half the flange width 

(bf/2).

The plate buckling coefficients in Figure 4-13 are for the case of a “long” plate. The 

number of waves that the plate buckles in along the length (perpendicular to the 

dimension “b” in the plate of the plate) can be sensitive to the total plate length. If the 

plate length is defined as “a”, many stability texts (Timoshenko and Gere, Bleich, SSRC 

Guide) provide graphs of the corresponding plate buckling coefficient, k, as a function of 

the aspect ratio of the plate, a/b. Variations in the plate aspect ratio, a/b, results in a 

series of curves with lower bound solutions that match the tabulated plate buckling 

coefficients given in Figure 4-13. For plates subjected to combined bending and axial 

compression, Equation 4-18 is applicable with the appropriate plate buckling coefficient. 

Due to the wide variability of potential stress distributions there is a wide range of 

potential plate buckling coefficients; however tabulated values for specific cases can be 

found in sources such as the SSRC Guide (2010). 

SECTION 5. GIRDER BUCKLING 

Flexural bending of girders results in a state of stress that includes both tension and 

compression on the cross-section. Figure 4-14 shows the typical elastic stress 

distributions that may develop in doubly- and singly-symmetric I-shapes from gravity 

loading. The maximum stresses occur at the extreme fibers of the cross-section. Elastic 

bending of a member about an axis of symmetry leads to a stress distribution such as 

that depicted in Figure 4-14(A) in which the neutral axis is located at the middle of the 

section and the magnitude of the maximum tensile and compressive stresses are equal. 

For bending about the unsymmetric axis for a singly-symmetric I-shape, the stress 

distribution in Figure 4-14(B) shows that the neutral axis will be closer to the larger 

flange and the maximum elastic bending stress occurs at the extreme fiber in the 

section with the smaller flange. The location of the neutral axis is dictated by horizontal 

equilibrium of the cross-section with recognition that the compression and tensile 

resultants must be equal. The bending stress,s at any location on the cross-section a 

distance, y, from the neutral axis is given by the expression:

Equation 4-19

Where:

M = the bending moment at the particular cross-section (k-in) 

I = the moment of inertia of the section about the axis of bending (in4) 
4.26

The magnitude of the maximum bending stress is determined by inserting the maximum 

distance, c, from the neutral axis to the extreme fibers. 

Figure 4-14 Bending Stresses in Doubly and Singly Symmetric Girders

4.5.1 Uniform Moment Loading 

Because both tensile and compressive stresses result from bending, the buckling 

modes for girders include both lateral translation and twisting of the cross-section. 

Therefore, the mode of buckling is often referred to as lateral-torsional buckling (LTB). 

The buckled shape of a simply supported girder with compression in the top flange is 

depicted in Figure 4-15. The expression for the elastic critical buckling moment, Mcr, of a 

doubly-symmetric shape that was derived by Timoshenko (Timoshenko and Gere, 

1961) is given in the following equation:

Equation 4-20

Most of the terms in Equation 4-20 were defined in the section on torsional buckling 

earlier. Lb is the unbraced length and is equal to the spacing between cross-frames or 

the panel points of a lateral truss on the compression flange. The first term under the 

radical is related to the St. Venant torsional stiffness while the second term is related to 

the warping torsional stiffness. 
4.27

The AASHTO Specification Appendix A6 uses the following equation for evaluating the 

lateral-torsional buckling capacity:

Equation 4-21

Equation 4-22

Where, Fcr is the critical lateral-torsional buckling stress, equal to Mcr/Sxc, Sxc is the 

elastic section modulus about the major axis of the section to the compression flange, 

bfc is the width of the compression flange, tfc is the thickness of the compression flange, 

Dc is the depth of web in compression, tw is the thickness of the web, and rt is the 

effective radius of gyration of the section for lateral-torsional buckling. 

Figure 4-15 Buckled Shape of I-Girder
4.28

For doubly-symmetric I-sections, Equation 4-21 essentially produces the same solution 

as Equation 4-20; however the AASHTO expression is also applicable for singlysymmetric I-sections with different flange sizes. 

4.5.2 Moment Gradient Loading 

The buckling expressions shown in the last section were developed for the case of 

uniform moment loading. The effects of moment gradient are accounted for with a 

moment modification factor, Cb, which is applied to the expressions. The AISC 

specification recommends the following expression for Cb: 

Equation 4-23

Where Mmax is the maximum moment in the girder segment defined by Lb, MB is the 

moment at the middle of the unbraced length, while MA and MC are the values of the 

moment at the quarter points of the unbraced length. The absolute value is used for all 

values of the moment in Equation 4-23. Past editions of the AASHTO Specification 

included Equation 4-23; however the most current edition of the AASHTO LRFD 

specification uses the following expression:

Equation 4-24

The values of f1 and f2 represent stresses at the ends of the unbraced length and 

involve a number of different cases outlined in the AASHTO specification depending on 

the distribution of stress. The above expression is similar in form to a long-standing 

formulation that was expressed in terms of moment, but was only applicable to straight 

line moment diagrams. The current AASHTO specification includes variable definitions 

of the stress to approximate the impact of non-linear moment diagrams to improve the 

range of applications for which the expression can be used. The AASHTO commentary 

frequently refers to Equation 4-21 as the “more accurate” expression.

4.5.3 Effect of Load Position on Cross-section

The Cb expressions outlined above are applicable to cases in which the applied loads 

are applied at midheight of the section. In situations where the loads are not applied at 

midheight, the buckling capacity can be substantially different than predicted by the Cb

expressions. Figure 4-16 shows three different cases where the load is applied at the 

top flange, midheight, and the bottom flange. For example, when the load is applied at 

the top flange as depicted in Figure 4-16(A), the buckling capacity will be less than for 

cases with the load applied at midheight. The reason for the reduction in the buckling 

capacity is because the applied load leads to an overturning torque that tends to further 

destabilize the member compared to midheight loading. In a similar fashion, when the 
4.29

load is applied at the bottom flange the load produces a stabilizing torque that tends to 

straighten the girder and results in an increase in the buckling capacity compared to 

midheight loading. The effects of load position are more significant for members without 

intermediate (between the supports) bracing. Intermediate bracing tends to reduce the 

impact of load position. In cases with intermediate bracing, the impact of load position

can generally be neglected. For cases without intermediate bracing, solutions 

accounting for the impact of load position are presented in the literature (SSRC Guide, 

Helwig et al.). 

Figure 4-16 Effect of Load Position on Cross-section

Effective bracing of girders can be obtained by either preventing twist of the section or 

by preventing lateral movement of the compression flange. The most common form of 

girder bracing is cross-frames or plate diaphragms that control the twist of the girder 

cross-section. Therefore, Lb in the buckling expressions above are typically taken as the 

spacing between cross-frames or diaphragms. Bracing for girders is discussed in more 

detail in Chapter 5. 

SECTION 6. SUMMARY

This chapter has provided an overview of the stability fundamentals necessary to 

understand the many factors that can affect the behavior of bridge structures during 

construction. A discussion of the various local and global buckling modes that are 

possible for column and beam systems was provided. Understanding the many factors 

that affect these different buckling modes can provide engineers and erectors insight 

into potential problems that might be encountered in the field as well as possible 

remedies for these problems. The subsequent chapters build from the fundamental 

material that is presented in this chapter.
5.1

CHAPTER 5 

STABILITY IN BRIDGE ERECTION 

SECTION 1. INTRODUCTION

There are a number of critical stages that need to be considered in the design of steel 

and concrete bridge systems. The widely accepted role of the bridge designer is to 

provide a safe and economical system in the completed structure, while the safety of 

the bridge during erection and construction is generally the responsibility of the 

contractor. Although the members of the bridge industry accept these roles, the 

distribution of responsibilities can result in some difficult challenges towards ensuring a 

safe environment during construction. In most situations, girder proportions are based 

upon the behavior of the finished bridge when the girders are composite with the 

concrete bridge deck. In addition to substantially improving the flexural strength of the 

girders, the cured concrete deck also provides continuous lateral and torsional restraint 

to the girders. This continuous restraint greatly improves the stability resistance of the 

girders. Therefore, the critical stages for structural stability generally occur during 

construction before the concrete deck has cured. 

Assessing the stability during construction can be particularly complex due to the limited 

presence of bracing during early erection stages. Contractors also face challenging 

problems that often limit the position of cranes or falsework, such as shore towers, due 

to traffic congestion or geographical limitations of the job site. Most bridge owners 

require the contractor to present erection and construction schemes along with 

supporting calculations that show the scheme to be safe. However, verifying the safety 

of the construction scheme requires proper modeling of the structural system during the 

critical construction stages. From a stability perspective, there are generally three 

different stage classifications that present complicated scenarios: 

1. the stability of individual girder segments during lifting with a crane, 

2. the evaluation of the stability of the partially erected structural system, and 

3. the stability and behavior of the structural system during placement of the 

concrete bridge deck. 

Much of the behavior that is mentioned in these three points is addressed through the 

proper analysis of the structure, which is covered in Chapter 6. However, the stability 

and lateral load resistance of the structure is also highly dependent on the proper 

design and detailing of the bracing, which must be completed before a proper erection 

scheme can be investigated.

This chapter addresses the global stability of erected or partially erected 

superstructures. An overview is provided of some of the changing requirements that 

develop as girder erection and deck concrete placement progresses. In addition, 

sources of stability that are provided by previously completed structural elements and 

temporary structures are discussed.
5.2

SECTION 2. LATERAL RESISTANCE OF PARTIALLY ERECTED 

SUPERSTRUCTURES

5.2.1 General Considerations

Throughout the construction process, fully- or partially-erected bridge superstructures 

are subjected to lateral force effects from a variety of potential sources. These force 

effects may be due to externally applied loads, such as wind, or may be caused by 

internal force effects from girder curvature or buckling-induced forces caused from 

stability effects. This chapter focuses on the externally applied loads as well as stabilityinduced forces and potential sources of restraint.

A suitable load path must be provided to resist the lateral loads that are applied to the 

structure at various stages during construction. A force transfer mechanism must be 

provided that will transfer the applied loads to the foundations, which may consist of 

either permanent or temporary elements. Permanent foundations will generally be the 

piers or abutments of the structure, while temporary foundations are found in crane 

supports, rigging or temporary shoring towers. 

Buckling-induced forces are generally the result of second-order effects which are 

related to the applied forces and deformations in the structure. In many cases, the 

lateral loads on the structure will result in deformations that intensify the second-order 

effects. The buckling resistance of the structure is enhanced by the use of bracing to 

reduce the unsupported length of main members. In many situations, the bracing that is 

provided may serve the dual purpose of providing stability as well as acting as a 

component of the load path for the resistance of lateral forces on the structure. The 

bracing can be attached to portions of the existing structure already completed, a 

temporary structure, or an adjacent structure. Some examples of these sources of 

support are as follows: 

• Existing Structure: abutments, piers, or an adjacent girder

• Temporary Structure: falsework, a deadman block, a crane, or a shoring tower

• Adjacent Structure: existing bridge or structure adjacent to construction

Various bracing types and schemes are discussed in this chapter. While the primary 

functions of bracing in concrete bridges are usually to prevent roll of the girders and to 

provide load distribution, bracing in steel bridges often provides additional functions. 

Some of the fundamental characteristics that the bracing in steel bridges must possess 

include the following:

• The bracing must have adequate strength to resist the stability-induced forces. 

From this perspective, the brace should not have strength issues that may be 

associated with material inelasticity or a potential instability of the brace itself that 

may preclude the brace from functioning properly.

• A clear load path must be provided between the primary member and the brace. 

The connection to the brace is often a critical component to the system both from 
5.3

a strength and stiffness perspective. As is noted later in the chapter, a bracing 

system is only as stiff as the most flexible component. Therefore, providing a stiff 

brace with an overly-flexible connection will usually result in an ineffective brace. 

• Because the braces may resist both stability-induced forces and also serve as a 

member of a lateral load path, the bracing must be designed to resist the 

combination of both the externally applied loads and the stability-induced forces. 

5.2.2 Lateral Resistance Effects

Lateral stability is often attained by providing structural elements to offer restraint to the 

primary members that would otherwise lack sufficient stability to resist the applied loads. 

In most situations, these elements are discrete bracing members, such as diaphragms, 

cross-frames, or blocking that span between adjacent girders. In addition, lateral 

resistance can also be obtained by alternative means such as falsework or other 

sources of temporary support. In some situations, restraint may come from sources that 

are not relied upon in conventional bridge design, such as stay-in-place forms, for the 

concrete bridge deck. 

In steel girder systems, cross-frames or diaphragms are required at all points of 

support, including at temporary shoring towers, in order to transfer lateral and torsional 

forces from the superstructure to the support. Intermediate (between supports) crossframes are also required to ensure adequate transfer of lateral and rotational forces to 

the system. A rational analysis should be performed to determine the intermediate 

cross-frame spacing during all stages of construction to ensure:

• Sufficient lateral support of the bottom flange is provided for deck overhang 

brackets; 

• Sufficient transfer of lateral wind loads on the girders to the foundation;

• Stability of the bottom flange for loads producing compression in the bottom 

flange;

• Stability of the top flange for loads producing compression in the top flange, 

especially during the deck placement before the fresh concrete begins to act 

compositely with the girders;

• Control of flange lateral bending effects; and

• Adequate distribution of vertical dead and live loads (including construction 

loads) applied to the structure.

It should be noted that for deck replacement projects, the top flanges experience 

various permutations of bracing demand as sections of deck are subsequently removed. 

Each stage needs to be analyzed to ensure adequate stability and transference, as well 

as resistance to dead, live, wind and construction loads.
5.4

Cross-frames should be proportioned to be as deep as possible to efficiently transfer 

vertical and lateral forces to the flanges and to control girder rotation to the extent 

possible. In composite systems subjected to positive bending (compression in the top 

flange), the top flange is generally located near the neutral axis of the final composite 

section. In the positive moment region, the composite girders are essentially 

continuously braced by the concrete deck and therefore the top flange is not susceptible 

to significant instability or lateral demand from wind load or other lateral forces. As a 

result, construction dead and wind loads may be the most critical load cases that should 

be considered in the stability design of the member and the necessary bracing; 

however, these loads are typically not considered by the designer. The location and 

magnitudes of the forces are in part determined by the contractor’s chosen erection 

method and sequence. In addition, when positioning bracing near the top flange, care 

should be taken so that it does not interfere with the placement of the deck formwork.

The cross-frame connections to the girders should be designed and detailed such that 

undesirable fatigue-sensitive details are avoided. If the situation necessitates fatiguesensitive details, a detailed fatigue analysis should be performed for the final 

configuration of the bridge to ensure that this detail will not control the design.

Because many concrete girder systems do not have permanent cross-frames or 

diaphragms with a positive connection to the primary members, or because permanent 

cross-frames or diaphragms are installed after the primary members have been set, 

blocking or other temporary means of restraint are often required to provide a stable 

system that is capable of resisting lateral forces. The blocking provides a load path that 

is capable of distributing lateral loads from sources such as wind as well as resisting 

forces from the overhang construction. 

Bracing to resist torsional forces imparted to the system as a result of deck overhangs is 

particularly important. This situation is problematic for both steel and concrete bridges. 

Deck overhangs are nearly always constructed using overhang brackets. The dead load 

of the wet concrete in the overhang, combined with the load imparted by the outer 

wheel of the screed machine, leads to a significant force in the overhang bracket that 

imparts a torque on the fascia girder. 

If these forces are not properly accounted for in the design of a bracing system, a failure 

of an individual girder or a collection of girders is possible. In steel girders, the failure 

may manifest itself as either a local instability of the girder flange or web, lateraltorsional buckling of the fascia girder, or a global stability failure of multiple girders. In 

concrete girder systems, the failure mode is typically overturning (roll) of one or more of 

the concrete girders. In addition, rotational displacement due to overstressing and 

eccentric loading can occur for both steel and concrete girders, which can lead to 

shifting of the deck reinforcement and loss of cover. In such a case, the durability of the 

deck will likely be compromised, leading to poor long-term performance of the deck.

Stay-in-place (SIP) forms are increasingly used in bridge deck construction. In building 

construction, the commonly-used SIP forms are relied upon as lateral beam bracing. 
5.5

However, SIP forms in the building industry are continuous over the top flanges of the 

girders and connected by welding the shear studs through the deck to the flange. 

Alternatively, the building connections may consist of puddle welds or self-tapping 

screws to achieve lateral load transfer. These connection techniques in the building 

industry provide a good force transfer between the SIP forms and the girders, thereby 

providing a good source of lateral bracing to the girders. 

In the bridge industry, longer girder spans often lead to variations in flange thickness 

along the bridge length as well as differential camber between adjacent girders. As a 

result, the SIP forms require a connection that will permit the adjustment of the form 

elevation so as to achieve a uniform deck thickness along the bridge length. The 

connection that is typically used in bridges consists of a leveling angle that allows the

contractor to adjust the form elevation and provide uniform deck thickness along the 

length and width of the bridge. Although the leveling angles are beneficial for solving 

many of the constructability issues with the deck, they are considered a flexible 

connection to the girder flange. As a result, the lateral bracing potential of the SIP form 

is greatly reduced and may be highly dependent on workmanship. 

Due to such concerns, the AASHTO LRFD Bridge Design Specifications do not allow 

SIP forms to be considered to provide lateral flange stability. Direct attachment of SIP 

forms to flanges (Chen, Yura, Williamson, and Frank, 2005) of U-girders and use of 

improved details of leveling angles to provide lateral resistance (Egilmez, Helwig, 

Jetann, and Lowery, 2007) have, however, demonstrated that SIP forms can act as 

lateral bracing when properly connected to the flanges.

5.2.3 Lateral Bracing Classifications

Effective stability bracing can be achieved through a number of different means, 

however for the purposes of design, bracing systems are usually classified into four 

categories: (a) relative, (b) nodal (also called discrete), (c) lean-on, and (d) continuous. 

In many situations, a given bracing application may fit into multiple classifications; 

however the design methods that have been developed are based upon individual 

categories. 
5.6

5.2.3.1 Relative Bracing

A relative brace system, such as diagonal bracing in column or beam systems, is 

attached at two locations along the length of the member that define the unbraced 

length, Lb. For the two columns in Figure 5-1(A) or the two girders in Figure 5-1(B), the 

diagonals and the horizontal struts combine to control the relative movement at the 

ends of the unbraced length. In this figure, the ends of the unbraced length are labeled 

A, B, and C. Considering the bracing panel with the ends labeled A and B, the brace 

controls the relative movement of point A with respect to point B and is therefore a 

relative brace. 

Although there are two diagonals within each bracing panel, the diagonals are often 

designed as tension-only members since they often consist of slender members with a 

minimal buckling capacity. In this case the compression diagonal is neglected since its 

buckling capacity is often relatively small and the tension diagonal is designed to 

provide enough stiffness and strength to brace the structure. 

Both the diagonal and the strut contribute to the strength and stiffness of the bracing 

system. For beams and trusses, a relative bracing system can consist of a top flange 

(chord) lateral truss system that may be provided to help resist lateral loads such as 

wind. Generally, if a perpendicular cut everywhere along the unbraced length passes 

through the brace, then the brace system is relative.

Figure 5-1 Relative Bracing System for Columns and Girder
5.7

5.2.3.2 Nodal (Discrete) Bracing

A nodal brace controls the movement only at the particular brace point, without direct 

interaction with adjacent braced points along the length of the member. Nodal braces 

can be designed to control either the lateral movement of the compression flange or to 

control twist of the cross-section as depicted in Figure 5.1. Figure 5-2(A) shows a crossframe which is generally the most commonly used type of bracing that is used in steel 

bridges. The cross-frame ties the two girders together at a specific location along the 

girder length and is categorized as a torsional nodal brace since the brace controls twist 

of the girders at a single point. In staged construction, a lateral nodal brace might 

consist of a strut that is used to restrain the lateral movement of the compression flange 

of a girder as depicted in Figure 5-2(B). In the case depicted in Figure 5-2(B), the 

compression flange of the girder on the right is braced off of the two composite steel 

girders that have previously-placed concrete. 

In this case, care needs to be taken so that the unsupported length of the bottom flange 

does not become too large so that the torsional flexibility leads to excessive lateral 

deformation. In addition, the ability for the non-composite girder on the right to deflect 

vertically relative to the existing composite girders during concrete placement should be 

taken into consideration. In situations where the laterally unrestrained length of the 

bottom flange becomes too large, both a top and bottom strut may be necessary, as is 

frequently used in lean-on bracing applications, which is discussed in the next 

subsection. 

Figure 5-2 Nodal Bracing System for Bridge Girders

5.2.3.3 Lean-On Bracing

In some applications, the efficiency of the system and the behavior can improve by 

using lean-on techniques such as those depicted in Figure 5-3. The case shown 

previously in 5-2(B) is really an application of lean-on bracing; however the size of the 

strut necessary to brace the girders off of the hardened concrete slab would generally 

be based on nodal bracing concepts and the example was therefore shown in that 

section. In lean-on bracing cases with torsional bracing, the cross-frames are replaced 

by top and bottom struts that allow several girders to lean on a single cross-frame. 

Applications where such a bracing system is particularly useful are in bridges with large 
5.8

support skews such as the one shown in Figure 5-4. Large support skews can make the 

cross-frames difficult to install and also may lead to large forces induced in the crossframes from truck traffic on the bridge. The large live load induced forces increase the 

likelihood of fatigue cracking in the girders around the cross-frames. In lean-on bracing 

applications, cross-frames within a given bracing line are located as far away from the 

support as possible, such as the case labeled “A” in Figure 5-4 (Helwig, 2005). Top and 

bottom struts are used between the other girders to lean the girders on the bracing. In 

skewed girder applications, bracing lines (such as the point labeled as “B” in Figure 5-4) 

should be offset from the supports by about 4 to 5 feet to make the bracing easier to 

install and to also prevent large forces that would develop if the bracing line frames 

directly into the support. 

Figure 5-3 Lean-on Bracing for Bridge Girders

5.2.3.4 Continuous Bracing

The last category of bracing is continuous bracing, in which case the bracing is fastened 

all along the length of the member. As noted earlier, in the building industry the stay-inplace (SIP) forms are often relied upon for stability bracing, which is a form of 

continuous bracing. In the bridge industry, the connections between the forms and 

girders are too flexible and therefore, the forms are not permitted to be relied upon for 

bracing. Cases with continuous bracing during construction are not commonly found in 

bridge applications. The cured concrete slab provides continuous bracing to the steel 

girders in composite construction (with shear studs). The concrete slab actually 
5.9

provides continuous lateral and torsional restraint to the girders. Due to the limited 

applications of continuous bracing in bridges, no further discussion is warranted. 

Figure 5-4 Cross-frames in Skewed Application
5.10

SECTION 3. BRACING REQUIREMENTS

5.3.1 I-Girder Bracing 

Both steel and concrete girders normally require bracing during the various stages of 

erection. Though the high torsional stiffness of standard precast concrete girders 

typically precludes lateral torsional buckling, bracing to assure roll stability is often 

required. Roll stability is addressed in Sections 7 and 8 of this chapter and Section 7 of 

Chapter 7.

For steel I-girder systems, effective bracing systems can be designed to provide 

torsional (βT), lateral (βL) or warping (βW) restraints. The discussion presented in this 

chapter focuses on torsional bracing and lateral bracing since these types of bracing are 

the most commonly used stability bracing systems in bridges.

The most common forms of torsional bracing are cross-frames or diaphragms that 

prevent twist of the section at the brace location. If two adjacent beams are 

interconnected at a point by properly designed cross-frames or diaphragms, that 

location can be considered as torsionally braced in relation to the beam buckling 

strength. Though the pair of beams can move laterally at midspan, the two flanges must 

move laterally together and twisting of the flanges is prevented. Since twist is prevented 

at that point, it acts as a brace point.

Figure 5-5 Bending Stresses in Singly Symmetric Section
5.11

The torsional bracing requirements for beam systems are provided in the AISC 

Specification for Structural Steel Buildings (2010) and the provisions are directly 

applicable to bridge systems. Because steel bridge girders may consist of singlysymmetric I-shaped sections, the provisions in the Commentary of the AISC 

Specification for Structural Steel Buildings (2010) are the most applicable. The required 

strength and stiffness of the cross-frames or diaphragms can be determined from the 

following expressions:

 (Strength) Equation 5-1

 (Stiffness) Equation 5-2 

Where:

Mbr = Design brace moment in torsional brace (kip-in)

Mu = maximum factored girder moment within the span (kip-in)

Cb = moment gradient magnification factor based upon girder moments 

between cross-frame locations (use Cb = 1.0 or AISC Chapter F to 

calculate alternate values)

φφbr = 0.75

L = span length (in)

Lb = unbraced length equal to the spacing between cross-frames (in)

ho = distance between flange centroids of the girder (in)

hb = vertical distance between cross-frame bracing chords or work points (see 

Figure 5-7) (in)

n = number of braces in span

Ieff = Iyc + (t/c) Iyt (see Figure 5-5 for t and c definitions) (in4

) 

Iyc = out-of-plane moment of inertia of the compression flange about the weak 

axis of girder (in4

) 

Iyt = out-of-plane moment of inertia of the tension flange, about the weak axis 

of girder (in4) 

βT = torsional bracing system stiffness (kip-in/rad)

Fbr = factored chord forces in cross-frame (kip) (See Figure 5-7)

Equation 5-2 provides the stiffness requirements for the torsional bracing system, which 

is a function of the stiffness of the following components:

βb = attached brace (cross-frame) stiffness (See Figures 5-6 and 5-7)

βsec = web distortional stiffness

βg = in-plane girder system stiffness
5.12

Each of the above three components are subsequently discussed in the remainder of 

this section. Bracing systems generally follow the classic equation for springs in series. 

Therefore, the system stiffness, βT, is governed by the following expression: 

Equation 5-3 

By considering the mathematical formulation of Eq. 5.3, the system stiffness, βT, is less 

than the smallest value of βb, βsec, or βg. Therefore, it is important to properly consider 

the stiffness of each of the system components. 

Figure 5-6 Torsional Bracing Stiffness

The brace stiffness, βb, for common bridge girder bracing systems is shown in Figure 5-

6 and Figure 5-7 (from Yura, et al. 2005). The torsional bracing stiffness of the 

diaphragms in Figure 5-6 depends upon the ability of the diaphragm to force the girder 

flanges to displace in the same direction. In locations where the girder top flange is in 

compression, locating the diaphragm above mid-height of the girder will usually cause 

the compression flanges to displace laterally in the same direction. If the diaphragm is 

located below midheight, such as cases with a through-girder system, the two flanges 

will displace in opposite directions resulting in a lower stiffness.
5.13

In order to achieve the torsional bracing stiffness shown in Figure 5-7, the connection 

between the brace and girder must be capable of developing the bracing moment, Mbr. 

In most situations, the brace moment is relatively small and can be obtained with simple 

connections. For example, although a wide flange or channel shape may be used for 

the diaphragm, it is usually not necessary to connect the flanges of the diaphragm to 

develop Mbr.

Figure 5-7 Stiffness Formulas for Twin Girder Cross-frames (assumes no 

connection eccentricity)

Figure 5-7 provides the stiffness of various cross-frame configurations. The stiffnesses 

shown in Figure 5-7 were derived from an elastic truss analysis. If the truss members in 

an x-bracing system are designed as tension-only members, then a horizontal member 

is required. Provided the two diagonals have adequate compression resistance, a 

compression system can be used with or without the top struts since they are zero force 
5.14

members. For k-bracing, a top horizontal member should be used, even though it 

carries no force, to ensure equal lateral top flange displacement.

Cross-frames are often composed of angles with an eccentric connection. Work by 

Wang (2013) has shown that the eccentricity in the angle connections results in a 

reduction in the stiffness of the cross-frame. To account for the reduction in the 

stiffness from the eccentric connections, the stiffness from the equations shown in 

Figure 5-7 should be reduced by 50% when members with eccentric connections (such 

as angles) are used. If a tension-only system is considered, there is no reduction 

necessary due to the conservatism by neglecting the compression diagonal.

The web distortional stiffness, βsec, accounts for the flexibility introduced into the bracing 

due to deformation of the girder web. The following expression for βsec takes into 

account the flexibility of both the web and a web stiffener:

Equation 5-4 

Where the terms are as shown in Figure 5-8, the effective width of the web is 

taken as 1.5ho. For diaphragm connections configured as shown in Figure 5-9, 

βsec is computed from the stiffness of the separate areas so that 1/ βsec can be 

computed as shown in Equation 5-5. 
5.15

Figure 5-8 Web Stiffness Geometry

Equation 5-5 

Equation 5-6 

Compared to Equation 5-4, Equations 5-5 and 5-6 are the more accurate formulations 

for accounting for the effects of cross-sectional distortion since the web can be divided 

up into regions above and below the brace. For plate or channel diaphragms or crossframes, the region of the web within the depth of the brace can be considered rigid 
5.16

since web distortion will be minimal within the depth of the brace. Therefore, for full 

depth braces such as diaphragm or cross-frames, the cross-sectional stiffness can be 

considered infinitely stiff.

The brace moment, Mbr, at the ends of a cross-frame or diaphragm produces a vertical 

force couple that acts on the girders. The resulting force couple produces a differential 

displacement in adjacent girders that reduces the torsional stiffness of the cross-frame. 

For a brace only at midspan in a multi-girder system, the contribution of the in-plane 

girder flexibility to the brace system stiffness is (Yura and Philips, 1992):

Equation 5-7 

Where ng is the number of girders across the width of the bridge interconnected by the 

cross-frames. 

The effect of girder stiffness decreases as the number of girders increases. For a pair of 

girders, the βg factor is significant (Helwig, Frank and Yura, 1997), and the above 

equation can be used in cases of multiple braces along the span as well. If βg

dominates the torsional brace stiffness, βb, then a system mode of buckling as 

discussed in Section 5-4 is possible. 

Figure 5-9 Web Stiffness Geometry at Cross-frames

The diaphragm and cross-frame stiffnesses shown in Figures 5-6 and 5-7 assume rigid 

connections exist between the braces and the girders. For flexible connections such as 

clip angles bolted only through one leg or welded only along the toe will flex, reducing 

the system stiffness. For any connection with a given stiffness, βconn, the impact on the 
5.17

system stiffness can be accounted for by adding the term 2/βconn (there is a connection 

at both ends of the brace) to the right hand side of Equation 5-3.

The brace force requirements are directly proportional to the magnitude of the initial outof-straightness of the girders (Ziemian SSRC, 2010). The brace force requirements 

given above were developed for an assumed out-of-straightness of 0.002 L. If oversize 

holes are used in the bracing details, the brace force will increase if connection slip 

takes place. This can be accounted for in the design by increasing the magnitude of the 

brace force by the factor (1 + oversize/Lb/500).

Besides cross-frames, another frequently used bracing system in steel bridges is a 

lateral truss that acts as a relative brace to control the movement of a braced point with 

respect to adjacent braced points. The AISC Specifications provide the following 

equations for the design of the relative beam bracing: 

(Strength) Equation 5-8A 

(Stiffness) Equation 5-8B 

For a lateral brace connecting to a rigid structure (e.g., adjacent bridge), this nodal 

lateral bracing is governed by the following set of equations from the AISC 

Specification:

(Strength) Equation 5-9A 

(Stiffness) Equation 5-9B 

Where:

Pbr = The required brace strength (kip)

bbr = The required brace stiffness (kip/in)

ho = distance between flange centroids (in)

Lb = length between brace points (in)

Mu = maximum factored moment (kip-in)

Cd = 1.0 except as follows:

2.0 for the brace closest to inflection point for a beam subject to 

double curvature 

φφbr = 0.75
5.18

For design of the overall girder bracing system, the girder stability-induced bracing 

forces computed from the above equations should be added to the bracing forces due 

to wind, skew, curvature and any other induced effects. The total bracing force, due to 

the combined effects, is then used for member design.

5.3.2 Skew Effects 

Skew angles, as shown in Figure 5-10, increase the interaction between the girders and 

bracing. When the cross-frames are oriented perpendicular to the girder longitudinal 

axis, the skew angle does not impact the stability-induced forces and the provisions 

previously outlined can be used for the bracing design. However, the bridge deflections 

in a bridge with skewed supports do vary across the width of the bridge creating 

differential deflections between the ends of the bracing. For larger skew angles, the 

differential deflections can result in significant forces induced into the cross-frame that 

are additive to the stability-induced forces. For skew angles larger than approximately 

45 degrees, the forces from the differential deflection often exceed the stability-induced

forces. The forces due to differential deflections should be added to the stability forces 

when designing the bracing. Forces in the bracing resulting from casting of the bridge 

deck can generally be satisfactorily predicted from a first-order computer model of the 

girders and bracing system.

Figure 5-10 Brace Orientations for Bridges with Skewed Supports

Although AASHTO requires cross-frames to be oriented perpendicular to the girders for 

skew angles larger than 20 degrees, for skew angles less than 20 degrees, the 

intermediate braces can be oriented parallel to the skew angle. When the cross-frames

are oriented parallel to the skew angle, the skew angle impacts both the stability 

stiffness and strength requirements for the bracing. Expressions for the required 

strength and stiffness are given as (Wang and Helwig, 2008): 

Equation 5-10
5.19 

Where βb is given in Equation 5-6 and 5.7, βbskew is then used in the previous equations 

in place of βb. The value “s” in the stiffness equations should be the skewed bracing 

length as opposed to the girder spacing. The moment in the skewed bracing then 

becomes: 

Equation 5-11

SECTION 4. SYSTEM BUCKLING OF GIRDERS

The most common braces that are utilized in steel bridge systems are cross-frames or 

diaphragms that control twist of the adjacent girders that they connect. The unbraced 

length, Lb, that designers typically use in buckling solutions such as the expressions 

shown in Chapter 4, is the distance between the cross-frames along the length of the 

bridge. In most applications, the cross-frame locations do behave as braced points 

against girder buckling. However, the cross-frames may not serve as a brace point for 

systems with a relatively large length-to-width ratio in which case the girder systems are 

susceptible to a system mode of buckling that is relatively insensitive to the spacing 

between the cross-frames. 

Twin girder systems or cases during construction when only a few girders have been 

erected can produce systems with a large length-to-width ratio. There have been a 

number of applications during construction in which the girders have been close to 

buckling in the system mode. For example, the two-girder widening shown in Figure 5-

11 had relatively close cross-frames, however the girder experienced significant twisting 

during placement of the concrete deck as evidenced by the 10 in. lateral deformation of 

the bottom flange relative to the plumb line. The load on the twin girder system was 

balanced and did not have an eccentricity. The behavior exhibited in the bridge 

widening was very nearly a buckling failure of the entire girder system as described 

below. 
5.20

Figure 5-11 System Buckling of a Twin Girder Widening

The buckled shape of the compression flange that is typically envisioned in a properly 

braced girder system is depicted in Figure 5-12(a), which shows a plan view of a twin 

girder system. By reducing the spacing between the braces, the engineer can reduce 

the size of Lb and thereby improve the buckling capacity of the girders that results from 

the lateral-torsional buckling expressions. However in girder systems with a relatively 

large length to width ratio, the controlling mode is the buckled shape depicted in Figure 

5-12(b). In the system buckling mode, the girder system behaves as a unit and the 

resulting resistance is not significantly affected by the spacing or size of the braces. 
5.21

Figure 5-12 System Buckling Mode

Yura et al. (2005) presented the following solution for doubly-symmetric girders that can 

be used to evaluate the buckling capacity of girders in the system buckling mode:

Equation 5-12

Where:

Mgs = nominal buckling resistance of the girder system (kip-in)

S = the girder spacing (in)

Lg = the total length of the girder (in)

E = the modulus of elasticity of the steel girder (ksi)

Iy = the moment of inertia of a single girder about the weak axis (in4) 

Ix = the moment of inertia of a single girder about the strong axis (in4) 

The expression can be divided by the number of girders, n, to estimate the capacity of 

one of the girders for comparison with the girder design moment. A resistance factor, φφ, 

of 0.9 should be used to compare capacity with the factored design moment, Mu. 
5.22

For singly-symmetric girders, ly, in Equation 5-12 can be replaced with Ieff (Yura et al. 

2005): 

Equation 5-13

Where: 

Iyc and Iyt = the respective moments of inertia of the compression and tension 

flanges about an axis through the web

c and t = the respective distances from the centroidal axis to the compression 

and tension flanges as shown previously in Figure 5-5. 

For a doubly-symmetric section, Ieff given by Equation 5-13 reduces to Iy since c = t. 

Equation 5-12 is a closed form solution that can be used to evaluate the system 

buckling capacity of twin girder systems. For a three girder system, replace Iyc in 

Equation 5-13 with 3/2 Iyc, and define S in Equation 5-12 as the distance between the 

two outside girders (twice the spacing between adjacent girders). For a four girder 

system, replace Iyc in Equation 5-13 with 2Iyc and define S in Equation 5-12 as the 

distance between the two outside girders (or 3S, where S is the girder spacing).

Equation 5-11 shows that for a given girder span (Lg), the system buckling mode can be 

improved by either increasing the stiffness of the individual girders or by increasing the 

girder spacing. An alternative method of improving the buckling capacity is presented in 

Yura et al (2005) and consists of adding a few panels of a top and bottom flange lateral 

truss near the ends of the girders. 

Lateral load effects, when combined with the system global buckling resistance 

calculated in Equation 5-12, may be computed using Equation A6.1.1-1 from the 

AASHTO Specifications, where the term replaces the φφfMnc term on the right 

hand side of the equation.

The Yura equation: has recently been incorporated into AASHTO 

LRFD as Eq. 6.10.3.4.2-1 for checking system buckling during deck pour. The approach 

presented above is applicable for intermediate steel checks prior to the deck pour 

( ), but the AASHTO approach omits the φφ factor and limits the total sum of 

the factored positive girder moments to 50% Mgs during the deck pour (Strength VI load 

combination). Should the sum of the moments exceed 50%, the design can add flange 

level lateral bracing, revise the girder spans/sizes to increase system stiffness, or 

evaluate the amplified girder second-order displacements and verify that they are within 

owner tolerances. Note that amplification can also occur under steel-only dead load as 

the buckling limit is approached, but the recommended system buckling φφ factor and 

Strength I/III load factors should provide an adequate level of safety for most narrow 

systems subject to buckling in the steel-only condition.
5.23

SECTION 5. BRACING TO ADJACENT STRUCTURES

Adjacent structures, adjacent portions of the existing structure, or adjacent portions of 

the newly-constructed structure, can be used as brace points. In these situations, guy 

wires are commonly used for bracing elements. However, when guy wires are long, one 

needs to account for the elastic deformation of the guy wires. The flexibility of the long 

cable needs to be considered in evaluating the stiffness requirements. Excessive 

elastic elongation may lead to a reduction of the anticipated bracing restraint as well as 

unanticipated deflection of the member being braced. This is illustrated in Figure 5-13. 

For guys attached to deadmen, the deadmen need to be designed for pullout of the 

anchorage, as well as global stability (sliding and overturning). In cases where the 

girder may deflect from additional loading added after the brace is installed (such as 

concrete placement), a turnbuckle should be included in the guy wire so that the slack 

can be removed from the brace due to the girder deflection. In continuous girder 

applications, the brace may develop additional tension when concrete is placed in an 

adjacent span and the use of a turnbuckle can also be used to release the added 

tension.

In addition, when external bracing is provided, the bracing force can lead to forces in the 

member being braced for which the designer did not account. For this reason, bracing 

points need to be evaluated to ensure that local and global stability is satisfied, and that 

the resulting forces do not result in overstressing the braced member. Additional 

supports, tie-downs and stiffening elements are frequently required in these cases.

Figure 5-13 Elastic Deformation of Guy Wire Bracing
5.24

SECTION 6. Uplift During Erection And Deck Pour

5.6.1 Uplift Considerations

Uplift can occur at supports due to a variety of different scenarios. One of the most 

common causes for uplift is due to unbalanced loading during a deck pour sequence in 

continuous girder construction. Uplift can also occur at the corners of skewed bridges. 

Uplift can also occur at supports for partially erected spans due to the primary member 

dead weight alone, particularly in horizontally curved girders. Uplift considerations are 

much more common for steel bridges because the self-weight of a steel primary 

member is generally significantly less than that of a concrete primary member. 

Therefore, the discussion in this section will be focused on steel girder bridges, but the 

reader should bear in mind that potential uplift should also be investigated for concrete 

girder bridges.

For multiple-span bridges, a deck pour sequence must be developed that minimizes 

construction stresses in the primary member as well as the deck. In continuous span 

girders, contractors often like to have the option for a continuous concrete casting 

sequence from one end of the bridge to the other. Although a continuous casting 

sequence is desirable for ease of construction, such a scenario creates one of the most 

likely circumstances for uplift at a support. Uplift can also occur even when a 

segmented casting sequence is used. Typically, the positive moment sections are 

poured first, followed by the negative moment sections. This procedure is utilized to 

minimize undesirable cracking in the top of the deck in the negative moment areas.

For two-span bridges a portion of one of the spans (from the end support to the 

approximate point of contraflexure) will be poured first, followed by a similar portion of 

the other span, followed by the negative moment area. As depicted in Figure 5-14 and 

Figure 5-15, when the first span is poured, net uplift may occur at the opposite end 

support. 
5.25

Figure 5-14 Typical Pour Sequence for Two Span Bridge

Figure 5-15 Uplift Effect on Two Span Deck Pour

This is because the necessary downward reaction (R3) to the dead load of the wet 

concrete in the first span being poured will generally be greater than the upward 

reaction caused by the self-weight of the steel girder alone (See Figure 5-15), therefore 

leading to uplift at the support. Tie-downs will almost always be required in this case. 

The effect of uplift can be reduced by adjusting the length of the first stage of the 

concrete pour. If the span lengths are different, the best solution is generally to pour the 

shorter span first.
5.26

For three-span bridges, a portion of one of the end spans is generally poured first. This 

is because if the center span were poured first, uplift is likely to occur at both end 

supports. By pouring one of the end spans first, uplift may occur at the opposite interior 

support. However, due to the increased continuity of a three-span bridge compared to a 

two-span bridge, uplift occurs less frequently for a three-span bridge than for a two-span 

bridge, unless one of the outside spans is relatively short. Once again, the potential for 

uplift, as well as its magnitude, can be reduced by pouring the shorter end span first. 

After the shorter end span is poured, the other end span is typically poured, followed by 

the center span, and finally, the negative moment areas (see Figure 5-16).

Figure 5-16 Typical Pour Sequence for Three Span Bridge

Bridges that consist of four or more spans should also be checked for uplift that could 

occur during deck pouring, but uplift occurs for these types of bridges less frequently 

than for two- or three-span bridges.

It should be noted that the foregoing is typically used as a starting point when 

developing pour sequences; however, other considerations may govern, such as 

equipment placement, access, construction staging and others that may require 

modifying the pour sequence to suit the specific condition encountered.

5.6.2 Additional Deck Pour Considerations

When developing the deck pour sequence, one should be aware that the engineer 

typically designs the bridge elements for the final condition of the fully poured deck, and 

that additional stresses imparted due to the contractor’s choice of deck pour sequence 

are often not considered by the original designer. Even if a suggested pour sequence is 
5.27

indicated in the design plans, it is important that this pour sequence is analyzed to 

account for the contractors’ means and methods.

Consider the two-span bridge shown in Figure 5-15. The designer would typically check 

the member stresses assuming the fully cast deck is in place, which would generally be 

composite with the steel in the positive moment regions and may or may not be 

considered to be composite with the reinforcing bars in the negative moment regions. 

However, when the first span of the deck is poured, the stresses in the member in that 

span will exceed the design dead load stresses because the counteracting stresses 

from the concrete in the opposite span are not in place. Further, since the concrete in 

the first span will often have cured and become composite, when the second span is 

poured the reduction in stress in the member in the first span will be less than if the 

entirety of the deck were to have been poured at one time.

Girder camber should also be calculated based on the chosen deck pour sequence. 

These can sometimes be markedly different than the final condition cambers that are 

typically computed by the designer, particularly for two-span bridges. For single-span 

and multiple (greater than two) span bridges, cambers computed based on a deck pour 

sequence are usually close to those computed for the final condition, except for unusual 

(unbalanced) span configurations and very long spans.

SECTION 7. ROLL STABILITY OF CURVED SPANS

The geometry of horizontally curved girders generally leads to a de-stabilizing or 

overturning moment that needs to be considered in the erection plan. The overturning 

moment is the result of the offset of the center of gravity with respect to the line of 

support of the girder as shown in Figure 5-17. As shown in the figure, the axis of 

rotation is defined by a line connecting the end points of support of a curved girder 

segment. The center of gravity can be approximated by assuming that the girder is a 

line segment (i.e. has zero width).

Figure 5-17 Center of Gravity and Destabilizing Moment Arm of Single 

Curved Girder
5.28

This approximation leads to the center of gravity being defined as:

Equation 5-14

Where:

x

-

 = distance from the center of curvature to the center of gravity of the 

curved girder segment (ft)

R = radius of curvature of the curved girder segment (ft)

a = one-half of the degree of curvature of the curved girder segment (rad)

The distance from the center of curvature to the axis of rotation is:

Equation 5-15

Therefore, the overturning moment arm is:

Equation 5-16

As an example, for a curved girder segment with a radius (R) of 1000 ft. and a length (L) 

of 200 ft., the overturning moment arm can be computed as follows:

 L/ 2 R 200 ft / 2*1000 ft 0.1 rad a = = ( ) =

x R = = sin / 1000 ft * sin 0.1 rad / 0.1 rad 998.33 ft a a ( ) =

X R = = cos 1000 ft *cos 0.1 rad 995.00 ft a ( ) =

x X −= − = 998.33 ft 995.00 ft 3.33 ft

In cases where overturning is a concern, intermediate points of support, such as shoring 

towers or holding cranes can be added to reduce the likelihood for such problems. 

However, in any case, erecting a single curved girder will require significant bracing to 

ensure that the segment in question does not overturn. 

The potential for overturning is dramatically reduced, and in most cases, eliminated, by 

erecting curved girder segments in pairs, as depicted in Figure 5-18. In this case, the 

axis of rotation moves out to the line connecting the end points of support of the 

outermost curved girder segment. The effect of a pair of girders can be demonstrated 

with the same geometry as in the above example. For a girder spacing of 10 ft. and 

properly designed cross-frame bracing between the girders, the calculation of 

overturning moment is as follows:
5.29

For the inside girder (Girder 1):

a11 1 = = L R / 2 200 ft / 2 2*1000 ft 0.1rad ( ) = as above, and

x R 1 1 = = sin / 1000 ft *sin 0.1 rad / 0.1 rad 998.33 ft a a ( ) = as above.

For the outside girder (Girder 2):

2 R =1010 ft and 2 L = 202 ft , which leads to:

( ) 2

2

2

202 ft / 2*1010 ft 0.1 rad

2

L

R

a = = =

( ) 2 2

2

2

sin 1010 ft *sin 0.1 rad / 0.1 rad 1008.32 ft R

x

a

a = = =

The center of gravity of the pair of girders is:

( ) 1 2 1003.33 ft

2

+ = = x x

x

The distance from the center of curvature to the axis of rotation is:

X R = = 2 2 cos 1010 ft *cos 0.1 rad 1004.95 ft a ( ) =

The resulting moment arm is then:

x X − = − =− 1003.33ft 1004.95ft 1.63ft

Since the moment arm is negative, there is no overturning moment and the pair of 

curved girder segments will be globally stable for roll over.

Figure 5-18 Center of Gravity and Stabilizing Moment Arm of a Pair of 

Curved Girders
5.30

SECTION 8. ROLL STABILITY OF FASCIA GIRDERS

The torsional loading from the deck overhang can potentially cause problems in both 

concrete and steel girder bridges during construction. The main issue with concrete 

girder bridges is that the overhang load can generate excessive torsional rotation in the 

fascia girder. For steel girder bridges, the torque from the overhang can lead to both 

global and local stability issues. Most global stability issues with the overhangs occur in 

bridge widening projects. The widening is often isolated from the original construction to 

permit vertical deflections during deck casting. Therefore, the widening often consists of 

a two- or three-girder system with a large length-to-width ratio. 

From a lateral-torsional buckling perspective, the girders are susceptible to the system 

buckling mode outlined in Section 5.4 that is relatively insensitive to the spacing 

between intermediate cross-frames. The low resistance to lateral torsional buckling, 

coupled with the torque from the overhang brackets, has led to systems that may have 

been dangerously close to failure. In addition to the global stability issues, potential 

problems are related to the local stability of the girder webs. In many instances, the 

overhang brackets exert large concentrated forces on the webs of the steel girders. The 

forces from the overhang bracket can distort the web, thereby leading to local 

instabilities or large web imperfections that can get locked into the girders once the deck 

cures. 

Many bridge owners specify limits on overhang width in order to keep the torsional load 

on the fascia girder reasonably balanced. Article 6.10.3.4 of the AASHTO LRFD Bridge 

Specifications provides a method of computing the flange lateral bending stress in steel 

girders due to overhang brackets. 

The torsional loads can be resisted by the use of ties, usually reinforcing bars placed 

above the top flange, and timber compression struts located at the bottom flange. The 

computer design tool TAEG (Torsional Analysis for Exterior Girder), developed by KTRAN, is a public domain program that can be used to evaluate these systems 

including girder and cross-frame forces. 

Yang et. al. (2010) have developed a recommended design procedure for overhangs on 

concrete I-girder bridges for both flexible and stiff connections. For flexible connections, 

the design procedure is based on the eccentric loading causing rigid body rotation of the 

I-girder. The limiting rotation in their procedure is the rotation that causes lift-off of the 

girder from the elastomeric bearing pad over 1⁄4 of the pad width. The bearing pad 

stiffness after lift-off actually changes depending upon the axial load, but this is complex 

to determine and the refinement may not be warranted. The rotation is further restricted 

by limiting the angle of rotation to 0.5 degrees based on serviceability; Figure 5-19 

shows a free-body diagram of the fascia girder/overhang model; for notation see 

Equation 5-17.
5.31

The girder rotation causes the deck reinforcing steel mat to also rotate, which can 

reduce the concrete cover over the reinforcing. The Florida DOT, for example, limits 

girder rotation so that the maximum reduction in cover is less than 1⁄4-inch. Bracing may 

be required to control this rotation.

Figure 5-19 Free-body Diagram of Concrete Beam with Eccentric Overhang 

Loading at Lift-off

The summarized procedure is as follows:

Step 1 – Calculate the effective eccentric force and its eccentricity. Forces to be 

considered include the weight of the fresh concrete on the overhang, the weight of the 

work bridge and workers, the weight of the finishing equipment, and the weight of the

formwork. The analysis is based upon simple statics.

Step 2 – Calculate the quarter point lift-off force and check it against the effective 

eccentric force.

Equation 5-17
5.32

Where:

FQPL = quarter point lift-off force (kips)

Wid = weight of half of slab between fascia girder and 1st interior girder (kips)

Lid = eccentricity of Wid (in)

Pmax = yield capacity of bracing (kip)

dbr = distance from top of beam to blocking (in)

wb = width of elastomeric bearing (in)

Wo = weight of beam + haunch (kips)

e = eccentricity of overhang force (in)

Step 3 – Check beam rotations to ensure angles of rotation (θ1 and θ2) are less than 0.5 

degrees.

Equation 5-18

Equation 5-19

Where:

F = eccentric force (kips) 

θ1 = angle of rotation at lift-off (deg) 

θ2 = angle of rotation after lift-off (deg) 

kb = combined stiffness of two fascia girder elastomeric bearings (k/in per in 

width of bearing) 

For stiff connections, the design procedure is based on rupture of the reinforcing bar. 

The summarized procedure is as follows:

Step 1 – Calculate the effective eccentric force and its eccentricity. Forces to be 

considered include the wet weight of the overhang concrete, the weight of the work 

bridge and workers, the weight of the finishing equipment, and the weight of the 

formwork. This is done using simple statics.

Step 2 – Check for rupture of reinforcing bar by ensuring that the beam rotation at 

rupture, θBrY, is less than the beam rotation for a given overhang width, θ. 
5.33

Equation 5-20

Equation 5-21

Where:

θBrY = angle of rotation at reinforcing bar rupture (rad)

θ = angle of rotation for a given overhang (rad)

 kst = combined stiffness of top bracing bars (k/in)

kwd = combined stiffness of wood blocking (k/in)

SECTION 9. ADDITIONAL CONSIDERATIONS FOR STEEL BOX 

GIRDERS

Erecting steel box (also known as tub) girders present some issues that are not 

addressed elsewhere in this Manual. This section describes, in general terms, some of 

these issues and how they should be addressed.

5.9.1 Differential Deflections

For multi-girder I-girder type bridges, cross-frames or diaphragms are almost always 

provided by the designer to provide bracing against buckling during throughout the 

construction process. In addition to stability bracing, the cross-frames also control 

construction-induced differential deflections between the girders.

For steel box girders, however, the design typically calls for top flange lateral bracing, 

which serves to provide torsional stiffness to the box section by developing a quasiclosed section. This lateral bracing also serves as brace points for the top flanges 

during the wet concrete stage. Due to the large torsional stiffness of the girders, both in 

the quasi-closed state and in the finished bridge, intermediate external cross-frames or 

diaphragms are usually not necessary.

The absence of permanent external cross-frames could present issues with respect to 

differential deflection between adjacent girders. Depending on the contractor’s chosen 

pour sequence and methodology, along with any potential changes to the staging that 

may have occurred during construction, temporary external cross-frames, if not 

specified on the design plans, may be required.
5.34

5.9.2 Top Flange Lateral Bracing

As stated above, top flange lateral bracing is typically provided in steel box girders to 

develop a quasi-closed section in order to provide torsional stiffness. The top flange 

lateral bracing controls differential longitudinal displacements between the two webs; 

thus, this bracing must be designed to resist the warping stresses (both torsional and 

normal) induced in the box girder. The need for top flange lateral bracing is especially 

critical for curved steel box girders, since these braces are primary members that 

actively participate in the distribution of force due to the curvature.

WT-sections are often used for the top flange lateral truss in tub girders. Since the 

warping stresses are greatest near the ends of the girders, the strength requirements 

for the design of the top flange lateral bracing are greatest at these locations. Often 

(particularly in the case of curved girders), top flange lateral bracing is provided 

throughout the span, although the section and/or spacing may be reduced near the 

center of the span.

The bridge designer would have designed the top flange lateral bracing for the final 

erected condition (in addition to the deck pour stages shown on the plans). Therefore, 

the erection engineer should evaluate the potential need for more robust top flange 

lateral bracing for the various temporary conditions that reflect the contractor’s chosen 

means and methods, including, but not limited to the contractor’s chosen deck pour 

sequence. If the erection engineer adds top flange lateral bracing, he should avoid the 

use of fatigue-sensitive connection details that may result from this change. These 

details are usually avoided by providing bolted connections to the primary member in all 

tension or reversal stress zones.

5.9.3 Bottom Flange Stiffeners

Bottom flanges for steel box girders are inherently wide. For simply-supported box 

girders, the bottom flange will be in tension during all stages analyzed by the designer. 

Because the design of a tension flange is based purely on the required cross-sectional 

area of the flange to resist the design stresses (or moments), the design typically results 

in a thin bottom flange. Moreover, due to the bottom flange being designed for a 

tension-only condition, the designer typically will not provide bottom flange stiffeners.

For continuous steel box girders, the bottom flanges at the intermediate support 

locations are designed to resist the design compression forces; therefore, the bottom 

flange thickness in these locations is more robust. This required thickness sometimes 

results in a bottom flange with a width-to-thickness (b/t) ratio that satisfies the AASHTO 

threshold for not requiring a bottom flange stiffener, even though the flange may 

experience significant compressive force.

During construction, however, the contractor’s chosen means and methods often will 

result in compressive forces in the bottom flanges of steel box girders well in excess of 
5.35

those envisioned by the designer. Intermediate shoring and the contractor’s chosen pick 

points are two of the primary reasons for this. The contractor’s engineer should 

therefore be aware of the potential need for bottom flange stiffeners for erection.

Bottom flange stiffeners are most often T-sections that are longitudinally welded to the 

bottom flange at the center of the flange. When provided for erection purposes, these 

stiffeners are usually left in place. If this is the case, the allowable stress associated with 

the fatigue category of the weld should be checked against the design live load stress 

range to ensure that all of the long-term fatigue requirements are satisfied.

SECTION 10. SUMMARY

This chapter has provided an overview of a number of stability issues that need to be 

included when evaluating the behavior of a bridge during the erection and deck 

construction stages. The chapter included a discussion of a number of potential stability 

modes that need to be evaluated including system buckling modes or girder rolling 

modes that can happen during construction. A number of other issues were also 

discussed such as problems associated with uplift at supports and other considerations 

that may be affected by the deck pouring sequence. An overview of the available design 

expressions for stability bracing were provided as well as an overview of analytic

modeling decisions that the erection engineer should consider when deciding on how to 

model the bridge. A number of the factors discussed in the chapter provide a good 

segue in the next chapter which focuses on the methods of stability analysis.
5.36
6.1

CHAPTER 6 

ANALYSIS FOR STABILITY

SECTION 1. INTRODUCTION

Chapter 6 extends the stability fundamentals presented in Chapter 4 to look at the 

behavior and analysis of individual members, partially erected systems of members, 

and the behavior during concrete deck placement. Although the primary focus of the 

examples in the chapter are on steel girders, the basic principles that are covered also 

apply to concrete systems. Advanced stability concepts such as non-linear analysis 

and 2nd order effects are presented. Effects of computer modeling parameters and 

software limitations on the accuracy of predicted behavior are considered, as well as 

techniques for verification of computer models. Representative outputs with buckled 

shapes are included to show the effects of properly designed bracing.

This chapter provides an overview of computational modeling techniques for evaluating 

the stability of bridge systems during the various construction stages. The primary 

emphasis is on steel girder systems, however many of the techniques are also 

applicable to concrete girder systems. Following this introductory section, important 

considerations for proper modeling of the girders and boundary conditions are 

discussed. The types of analyses are then covered including geometric linear, 

eigenvalue buckling, and geometric non-linear analyses. Because the stresses during 

construction are typically well below the yield strength of the material, the emphasis in 

this chapter is on elastic materials. 

SECTION 2. COMPUTATIONAL MODELING

Computational abilities have dramatically improved in recent years. The speed and data 

storage capabilities of personal computers have made it possible for engineers to 

quickly carry out sophisticated analyses on complex systems. By nature, stability 

problems often require iterative analyses that, in the 1980’s and 1990’s, may have 

required several days on super computers to solve large-sized problems. With modern 

computers, these analyses may be completed in a relatively short period of time on a 

desktop or laptop computer. In addition to improvements in the computational 

capabilities, the sophistication of the software has also improved dramatically. 

Engineers have a variety of software choices available and they must have a clear 

understanding of the behavior that is to be captured in the analysis when selecting a 

suitable software package. 

Many of the commercial software packages that are available specifically for bridge 

systems make use of two-dimensional grillage models in which the girders are modeled 

as line elements. Beyond the grillage models, engineers also have available a variety of 
6.2

full 3D finite element programs that make it possible to develop detailed models of the 

components on the entire bridge system. The different software packages come with 

varying levels of complexity and analytical abilities. This section outlines the basic 

capabilities of some of the different classifications of software packages. Throughout the 

chapter, results from some specific software packages (MASTAN2, BASP, UT LIFT, 

and UT Bridge) are referred to or shown. It should be noted that the analysis discussed 

in this chapter can be carried out with a wide array of commercially available software. 

The software packages that are referred to in this chapter are available in the public 

domain and are free for download at the following sites: MASTAN2: 

http://www.mastan2.com/; BASP, UT LIFT, and UT Bridge: 

http://fsel.engr.utexas.edu/software/index.cfm. The goal of the discussions in this 

chapter is not to endorse any specific brand of software, but to instead provide an 

overview so that engineers can understand the necessary analytical capabilities to 

predict the type of behavior that is desired. The material presented in this chapter 

should help the engineer in selecting a suitable software package to satisfy the needs 

for their particular application as well as potentially understanding the abilities and 

proper use of the software packages that they may already be using. 

The discussions on the modeling techniques often refer to “nodes” and “elements”, 

which are important characteristics of computer models that are used to define the 

structural system. As shown in Figure 6-1, nodes represent a point in space that is used 

to define the geometry of the basic model. The nodes in a structural model may 

possess translational and rotational degrees of freedom (DOF) that define the structural 

displacements. Depending on the types of elements that are used, each node in the 

model will usually have between two to six degrees of freedom (depends on the number 

of translational or rotational degrees of freedom in 2D or 3D space). The size of the 

model is related to the total number of DOFs.

The elements represent the structural member with the boundaries or geometries of the 

individual elements defined by the nodes. The two models shown in Figure 6-1 could be 

used to represent the same I-shaped cross-section. As shown in Figure 6-1(a), the 

connectivity of the line element is defined by the two nodes at the ends of the element. 

The cross-section in Figure 6-1(b) is composed of four-node shell elements and directly 

models the I-shape of the member. 

The two models depicted in Figure 6-1 demonstrate the potential differences in the 

relative size of models. Only three nodes and two elements are required to define two 

sequential segments of the beam in Figure 6-1(a), whereas 27 nodes and 16 elements 

were used to define two sequential segments of the I-shaped beam in Figure 6-1(b). In 

a 3D model with six DOF per node, the two element representation of the I-shaped 

girder contributes 18 DOF to the model, while the two segments of the shell element 

model contribute 162 DOF to the model. 

In general, due to concerns about element aspect ratios, shell element models will 

require many more element divisions along the length of the girders compared to line 

element models. Therefore, in addition to possessing many more nodes through the 
6.3

cross-section, shell element models will generally have more cross-sectional divisions 

along the length resulting in much larger models (more DOFs) compared to line element 

models. Thus, the size of the shell element model obviously is much larger than the 

corresponding line element model; however, such a shell element model also potentially 

has the ability to capture much more complex behavior than the more simple line 

element model. The following two subsections provide a simple overview of some basic 

models that may be used to represent a given structural system. 

Figure 6-1 Line Element Versus Shell Element

6.2.1 Grillage Models

Most of the software packages that are commonly used in bridge design fit into the 

category of 2D grillage models. The software can be used to analyze either straight or 

horizontally curved girder systems. The term “grillage model” may also be referred to as 

a “grid model” in AASHTO and other documents. The girders are modeled as line 

elements and the concrete deck may be modeled by shell elements. Typical input for a 

grillage model consists of defining the nodal geometry, the cross-sectional properties of 

the girders, and the slab geometry. Based upon the desired model, the user can 

position nodes at specific locations so as to be able to define supports, concentrated 

forces, cross-frame locations, and transitions or changes in the shape of the crosssection. The nodes are positioned so that the analysis provides deformations and 

force/stress results. In many situations the software may allow the engineer to subdivide 

the elements after they are defined so as to add supplementary nodes in the structure 

to provide additional output. In some cases, the software may also internally subdivide 

the elements to provide a better representation of the structural system. Engineers 

should have an understanding of whether the software package internally subdivides 

elements to provide a more robust solution so that they can decide how many nodes 
6.4

they should specify to achieve a sufficient level of accuracy. Methods of checking 

modeling accuracy are discussed later in the chapter. 

Grillage models are attractive from a design perspective due to the ease of defining the 

model as well as the solution efficiency with respect to computational effort. The user 

generally has to simply specify the coordinates of the desired nodes as well as the 

girder properties along the length of the bridge. Although some grillage model software 

may allow the engineer to specify plate sizes for the flanges and webs and have section 

properties computed by the software, other programs require the engineer to input 

section properties such as areas, moments of inertia, and torsional properties of the 

girders. 

The attractive feature of grillage models is the ease by which the model can be defined. 

The models generally have sufficient accuracy to provide good estimates of the design 

forces and deformations in the finished bridge. Although grillage models can be used to 

predict some behavior during construction stages, the programs are often not 

sufficiently accurate representations of the system to capture stability issues with most 

bridges during construction. One limitation of the line element representation of the 

girders is that such a model does not represent the local flexibility of the cross-section. 

In cases where braces, such as cross-frames or plate diaphragms, are not full depth, 

the effects of cross-sectional distortion play a very important role in the effectiveness of 

the bracing. In other situations the locations of supports or applied loads on the crosssection can play an important role in the overall behavior and line element models do 

not adequately capture these effects. 

Another drawback to line element models is the ability to observe the displaced shape 

of the model. Because the girder cross-section is represented by a line, the displaced 

shape does not tend to show twist of the cross-section and as a result the user may not 

have a clear indication of the structural displacements. For example, consider the 

buckled shape of the beam in Figure 6-2(a). The beam has simple supports and is 

subjected to uniform moment loading. The buckling mode for the beam is lateraltorsional buckling; however the line element model does not show twist of the section. 

Some grillage or frame element programs have graphical interfaces that will extrapolate 

the line element model to show up graphically with depth and can therefore show twist 

of the cross-section. For programs that do not have this feature, the user can create 

“flags” at a few locations along the length to demonstrate twist of the cross-section. For 

example, the same model in Figure 6-2(a) was modified to include a “flag” at select 

locations along the length as shown in Figure 6-2(b). The flags were made by defining 

nodes and connecting them with elements. The element properties for these flags are 

not too important since the flag essentially acts as a deformation indicator and does not 

retrain the model. If material density is specified, it is important to not give the flags an 

area that will lead to a large self-weight contribution. 
6.5

Figure 6-2 Indicating Torsional Deformations with Line Elements

The flags have the same rotation as the girder nodes to which they are connected and 

provide an indication of the rotational deformation along the length. In this case, 

“flanges” and the “web” were included in the flags; however, simply putting a vertical 

element at the locations provides the visual indication of the twist. Since the nodes on 

the flags are not restrained in any way, the solution to the problem does not change 

compared to the model in Figure 6-1(a). The effects of load position on the crosssection were discussed in Chapter 4. Gravity loads applied at the top flange are 

generally more critical than loads applied at the centroid or at the bottom flange. In a 

line element solution, a reasonable approximation of the effects of load position can be 

obtained by defining an element similar to the “flags” in Figure 6-2(b). For example, if 

concentrated forces were applied to the nodes at the simulated top flange location in 

Figure 6-2(b), the model will provide a reasonable approximation of the effects of load 

position in the buckling behavior. However, in this case, the properties of the flag 

elements may be important since they are loaded elements, and the user should 

consider the effects of the cross-sectional stiffness on the element properties. 

Considering the tributary area of the web/flange cross-section between the “flags”, the 

user can estimate an appropriate area and moment of inertia of the flag section.

6.2.2 Three Dimensional Models 

There are a number of general purpose finite element programs that can be used to 

model structural systems. Most 3D finite element programs have an extensive library of 

element types that allow the user to model a wide variety of structural systems. The 

programs will usually include truss, beam, shell, or solid elements. The use of solid 

elements is not discussed in this document since these elements generally result in 

extremely large models and will not typically be required in bridge modeling. However, 

truss, beam, and shell elements are frequently used to model bridge systems and some 

of the basics of each element are covered. 

As the name implies, truss elements are line elements that possess axial stiffness but 

not flexural stiffness. The elements are defined by two nodes at the ends that generally 

only possess translational DOF. Another type of line element is a beam element that 
6.6

has both translational and rotational DOFs. Beam elements potentially have axial, 

bending, and torsional stiffness and can be used to model a variety of structural 

members; however as noted earlier, these elements are mainly able to model global 

member behavior and will not capture localized distortions of the cross-section. Shell 

elements as previously depicted in Figure 6-1 can be used to model a variety of 

structural members. General purpose programs may have a variety of different types of 

shell elements depending on the desired characteristics to be modeled. Some 

commonly-used shell elements may consist of four-noded or eight-noded elements that 

allow the user to model straight or curved plate elements. 

An important feature of modeling with shell elements is to keep the aspect ratio 

(length/width of the individual shells) as close to unity as possible; however, good 

results can often be achieved with aspect ratios as high as three or more. The accuracy 

of the finite element model is often a function of the mesh density that is used. As is 

discussed later in the chapter, a mesh sensitivity analysis can be conducted to ensure 

that a sufficiently fine mesh density is utilized. The mesh density that is used may 

sometimes be dictated by the need to maintain a reasonable aspect ratio of the shell 

elements. Achieving an element aspect ratio close to unity will often not be possible for 

all of the elements in the cross-section. The engineer will often have to consider the 

number of elements necessary in the web depth versus the flange widths and balance 

the number of element divisions along the length to result in a satisfactory aspect ratio. 

As noted above, aspect ratios of two to three are not uncommon and still often yield 

good results. 

To reduce the size of the model, a combination of shell and beam elements may be 

selected to model the members. A common practice for 3D models of girder systems is 

to use shell elements to model the webs and to use beam elements to model the 

flanges and web stiffeners. Utilizing beam elements for the flange can still capture both 

the St. Venant and warping stiffness of the beam, and can also reduce the size of the 

problem, since extra nodes for the flanges are not necessary. 

3D modeling allows for the most accurate representation of the member cross-sections 

and allows the user to accurately model the locations of supports and load points on the 

cross-section, which can have a significant impact on the stability of the system. 

Because the web and stiffeners are represented in the model, the interaction of the 

bracing members and the girders can be more accurately captured compared to 2D 

models. An accurate representation of the interaction between the bracing and the 

girder cross-section is extremely important since cross-sectional distortion can render 

the bracing ineffective.

While three-dimensional models provide the most accurate rendering of the bridge 

elements, the drawback is the difficulty in creating the models. Although performance of 

computers and the capabilities of structural analysis software have dramatically 

improved over the past two decades, the bottleneck with regards to the ability to model 

and study structural behavior is in the efficient use of the software. The learning curve 

for users to become familiar with 3D modeling techniques is relatively steep. The length 
6.7

of time necessary for an engineer to become familiar and efficient with 3D modeling 

software can take several months, and even then the time necessary to create the 

models for complex bridge systems is significant. 

Efforts have been put forth to develop a user-friendly program that can be used to 

facilitate the creation of models to study the behavior of steel bridge systems during 

erection and construction (Stith et al., 2010). The resulting program is UT Bridge, which 

includes a preprocessor and a post processor that specifically target the modeling of 

steel I-girder bridge systems during erection and construction. Such an approach to 

model creation is limited by the necessary modeling assumptions; however, engineers 

can effectively use the software to quickly create 3D models to study complex bridge 

geometries and to consider a wide variety of erection or construction scenarios. Over 

time, modeling advances in commercial programs are likely to introduce products that 

the bridge industry can use to accurately and efficiently model a wider variety of 

systems. 

Before important modeling scenarios and other specific problems can be discussed, it is 

important to cover some of the basic decisions that need to be made with regards to the 

types of analysis that are available to capture the structural behavior. Modern day 

programs have several options for different types of analyses that can be conducted, 

and engineers should have a proper understanding of the meaning and capabilities of 

these analyses. The following section provides a discussion of some of the different 

types of analyses that can be carried out.

SECTION 3. TYPES OF ANALYSES 

In addition to the modeling options for the engineer, there are also a number of 

considerations with regard to the type of analysis to carry out when evaluating the 

safety of a structural system during construction. Although proper material models are 

often a major concern in evaluating the strength of a given structural system, the bridge 

elements will generally remain elastic throughout the construction stages. Therefore, 

linearly elastic materials will typically be utilized in most analyses. However, making 

decisions on the type of analysis can be a major decision and engineers should have a 

good understanding for the types of analyses they should be conducting to evaluate the 

structure. The analysis types that are discussed below include first order, eigenvalue 

buckling, and second order (nonlinear geometry) analyses. Regardless of the type of 

analysis that is utilized, in all cases the first step is to properly define the geometry of 

the model so that the structural representation and appropriate boundary (support) 

conditions are defined. How the load is applied to the structure may be somewhat 

dependent on the specific type of analysis that is to be carried out, as is discussed in 

the following sections.
6.8

6.3.1 First Order Analyses

The most common analysis that is generally carried out on bridge systems is a firstorder analysis that assumes that the deformations in the structure will not significantly 

change the geometry. A first order analysis does not consider the stability of the system. 

With the exception of axial deformations in the structural members, equilibrium is taken 

on the undisplaced members. Such an analysis will typically provide good estimates of 

the reactions at supports or shore towers, as well as necessary holding crane lifting 

forces. In addition, from a girder design perspective, a first order analysis will usually 

provide good estimates of the moments and torsion induced in straight or horizontally 

curved girders. However, from a stability perspective, a first order analysis will not 

provide any indication of the stability-induced forces in the girders or the braces. 

Although a second-order analysis with non-linear geometry is generally necessary to 

capture deformations and forces related to girder stability, in many situations a secondorder analysis may not be necessary as is discussed in more detail in Section 6-3.3.

The number of steps with which the load is applied to the system does not generally 

have any impact on the solution in a first order structural analysis. Therefore, the 

engineer can typically define the loads to be applied in a single load step.

6.3.2 Eigenvalue Buckling Analysis

Many programs have the ability to evaluate the global and potentially the local stability 

using an eigenvalue buckling analyses. The analysis option in the software may be 

referred to as a “critical load analysis” or a “buckling analysis”, both of which generally 

indicate that the program can solve for the buckling modes and the corresponding 

buckling loads. The program documentation likely includes some theory related to 

generalized eigenvalue problems, or if engineers desire additional information there are 

a variety of textbooks such as McGuire et al. (2000) that include a discussion on the 

matrix formulation. In order to properly utilize the results of an eigenvalue buckling 

analysis, the engineer needs to understand the significance of the eigenvalue and the 

corresponding eigenvector (mode shape).

The eigenvalue solution will give the user an indication of the elastic buckling capacity 

of the section and therefore does not consider the effects of material inelasticity. Since 

the stresses are typically well within the elastic buckling range during construction, the 

eigenvalue solutions provide a good indicator of the buckling capacity. However, the 

eigenvalue solutions are primarily applicable for problems in which prebuckling 

deformations are small. Cases where prebuckling deformations are not small are 

discussed toward the end of this subsection.

After the model is properly defined and the appropriate boundary conditions have been 

defined, the loads can be applied to the structure. However, the meaning of the 

resulting eigenvalue is directly dependent on the magnitude of the applied loads. The 

loads that are applied to the structure represent a “reference” load that the program 
6.9

uses to compute the geometric stiffness matrix for the structure based upon a linear 

elastic structural analysis. Once the linear elastic stiffness matrix and the geometric 

stiffness matrix have been formed, the program solves the eigenvalue problem that 

yields the requested number of eigenvalues and corresponding eigenvectors. Many 

programs may allow the user to request multiple modes (eigenvectors); however, the 

mode that is usually of interest is the first mode since that will have the lowest 

eigenvalue. The eigenvalue, λ, represents a factor that is applied to the reference load 

to determine the critical buckling load using the following expression:

Equation 6-22

Where, Pcr is the corresponding buckling load, λ is the eigenvalue, and Pref is the 

magnitude of the applied force. For example, consider the column with the cross-section 

shown in Figure 6-3. The column has pinned ends with a length of 30 ft 

The column was modeled in MASTAN2 and the results are summarized in Figure 6-4. 

Three different cases were used for the applied “reference” load. In Case 1, a unit axial 

load of 1 kip was applied at the top of the column and resulting eigenvalue, λ, was 

368.1. Referring back to Equation 6-1, since a reference load of 1 kip was used, the 

buckling load is directly equal to the eigenvalue. If instead a reference load of 10 kips is 

used, as is shown for Case 2, the eigenvalue must be multiplied by 10 to obtain the 

critical buckling load. In Case 3, the applied reference load was 368.1 kips and as 

expected, the resulting eigenvalue is 1.0. 
6.10

Figure 6-3 Euler Column with Length of 30 ft

The moment of inertia about the y-axis of the column cross-section shown in Figure 6-3 

is 167.7 in4

. Since the column has the boundary conditions of a classic Euler column, 

Equation 6-2 can be used to calculate the buckling capacity:

Equation 6-23

 

As expected, the eigenvalue buckling analysis exactly predicts the critical load for this 

classic column buckling case. 
6.11

Figure 6-4 Determining Buckling Capacity based upon Eigenvalue 

Buckling Solution and Magnitude of Reference Load

Eigenvalue analyses can also be utilized in the cases of beam buckling problems. For 

example, consider the beam cross-section shown in Figure 6-5. The beam was 

modeled in MASTAN2 with a span of 50 ft (600 in.) and subjected to uniform moment 

loading. The corresponding buckled shape of the beam is shown in Figure 6-6. The 

beam elements in grillage or frame programs can often capture the torsional warping 

stiffness of the beams; however, the user may have to specify the types of torsional 

connections at the ends of the individual beam elements. For example, in MASTAN2 

the connections at the ends of the beam elements can be “free”, “fixed”, or “continuous”. 

The “free” and “fixed” options either make the section warping free or warping fixed. In 

most situations, the user will want the section to be “continuous” which links the warping 

stiffness of the adjacent elements but does not imply a warping fixed condition. 
6.12

To help show the buckled shape in Figure 6-6, the flagged model discussed earlier in 

the chapter was used. Because a concentrated moment of 1k-in was applied at the two 

ends, the eigenvalue is equal to the critical buckling load and gave a buckling moment 

of 7578 k-in. 

The same beam was also modeled in the finite element program BASP (Akay et al. 

1977), which is an acronym that stands for Buckling Analysis of Stiffened Plates. BASP 

is an eigenvalue buckling program that can capture both local and global buckling of 

stiffened plate elements. The program is a 2D finite element program that can capture 

plate buckling modes. Since the web of a girder is essentially a plate stiffened by the 

flanges, the program can be used to model global buckling of columns and beams. The 

program can be used to model doubly- and singly-symmetric sections; however, the 

sections must be symmetric about the web plate. Therefore although a doubly- or 

singly-symmetric I-section can be modeled, a channel section cannot be modeled since 

the flanges are not symmetric about the web. BASP uses four-node shell elements to 

model the webs and uses beam elements to model the flanges and stiffeners. 

Figure 6-5 Girder Properties for Beam Buckling Analysis

The beam section depicted in Figure 6-5 was modeled in BASP to determine the 

buckling mode and the corresponding buckled shape is shown in Figure 6-7. The web 

was meshed with four elements through the depth, and 50 elements along the length, 

which gives an aspect ratio of unity for the web elements (i.e. 48 in/4 = 12 in. and 600 

in/50=12 in.). Because the flanges are modeled with beam elements, the aspect ratio is 

not an issue. The BASP model demonstrates some new aspects for discussion for 

modeling considerations when dealing with finite element models. BASP allows the user 

to apply concentrated forces at a node in either the x or y direction (the z direction is out 

of the plane of the plate). The program does not have a feature for applying 

concentrated moments. Therefore, a force couple must be used to model a 

concentrated moment. For the model shown in Figure 6-7, the couple consisted of two 

forces of magnitude “1/d” applied in opposite directions at the flanges, where d is the 

depth of the beam. Therefore, the magnitude of the applied concentrated moment was 
6.13

(1/d) x d = 1 k-in. The predicted buckling capacity in BASP was 7193 k-in which results 

in a difference of approximately 5% from the capacity predicted by MASTAN. Part of the 

difference is likely due to local effects that occur around the locations of the 

concentrated forces; however, in general, the two programs have reasonable 

agreement despite very different model characteristics. 

Figure 6-6 Beam Modeled in MASTAN2 Subjected to Uniform Moment 

Loading

Figure 6-7 Beam Subjected to Uniform Moment Modeled in BASP

The elastic lateral-torsional buckling expression given in Equation 6-3 can be used to 

predict the buckling capacity of the beam modeled with MASTAN2 and BASP. 

Equation 6-24
6.14

Inserting the section properties from Figure 6-5 into the above expression gives an 

estimate of the buckling moment of 7547 k-in, which has good agreement with the 

eigenvalue predictions from the two different computer models. The comparisons of the 

eigenvalue buckling solutions and the elastic buckling expressions for the column and 

beam problems demonstrate that the eigenvalue buckling solutions are analogous to 

the solutions that are predicted from the elastic buckling equations. While the two 

problems considered were the idealized cases for which theoretical solutions are readily 

available, eigenvalue buckling solutions can be used to model more general problems 

for which the theoretical solutions must rely on approximate modifiers such as K-factors 

for column buckling and Cb factors for beams with moment gradient. Provided the 

problems are properly modeled, the eigenvalue buckling programs can provide more 

accurate solutions for the specific problems. 

The load cases that were used in the respective column and beam buckling problem 

consisted of a pure axial load and the case of uniform moment. The loading that is used 

in actual structures is more complicated and therefore the selection of a “reference load” 

to use in the eigenvalue problem is not always clear. For the case of gravity loads from 

self-weight, most engineers simply put the self-weight on the structure and conduct the 

eigenvalue buckling analysis. In this case, the eigenvalue represents a multiplier on the 

self-weight that will result in buckling. Some engineers think of this as a factor of safety; 

however this is not necessarily a correct interpretation since there are nonlinear effects 

associated with the stability problem. The degree of non-linearity is a function of how 

close the applied load is to the buckling load. 

Questions are often raised with regard to how large the eigenvalue should be relative to 

the full service loading applied to the structure to have a safe condition. An eigenvalue 

of unity or less for cases where the full service load is applied to the structure clearly 

demonstrate cases in which the structure will likely have stability issues. Cases where 

the eigenvalue is substantially larger than unity, such as three or four, present cases 

where stability is not likely an issue. However, an exact limit that should be targeted with 

regards to the magnitude of the eigenvalue is highly dependent on the buckling mode. 

The slenderness of the element that is being considered should be taken into 

consideration since the flexibility of the element is more likely to lead to larger second 

order effects. A target “load factor” during construction might be of the order of 1.4~1.5 

and therefore the eigenvalue based upon service loads should at least be in this range. 

If an extra 25%-30% safety margin is placed to avoid flexibility issues with slender 

elements a target eigenvalue of 1.75 may be appropriate for some problems. If an 

engineer is not comfortable with the buckling capacity predicted from an eigenvalue 

analysis, bracing should be added, or a more detailed analysis considering non-linear 

geometry, such as discussed in the next subsection, should be considered. 

Engineers should pay careful attention to the buckled shape to see if it coincides with 

their expectations. In some cases the engineer may be expecting a global buckling 

mode and instead a local instability may control the buckled shape. Although there is 

typically a significant difference in the buckling capacity for different modes for global 
6.15

buckling, local instabilities often have numerous potential mode shapes clustered 

around a small range of loads.

Engineers should have a good understanding of when an eigenvalue solution may not 

provide good insight into the buckling behavior. A primary assumption in an eigenvalue 

analysis is that pre-buckling deformations do not significantly affect the geometry of the 

structure. The pre-buckling deformations that adversely affect the accuracy of the 

eigenvalue solution are generally in the same direction that is being predicted in the 

analysis. For example, in the two problems considered in this section (the column and 

the beam buckling problems), the pre-buckling deformations were not in the same 

direction as the buckling mode that was being predicted. In the case of the column, the 

applied load causes axial shortening but does not cause any flexural deformations in 

the direction of buckling. Therefore, the magnitude of the reference load has no impact 

on the predicted buckling capacity. The same can be said for the beam buckling 

problem. Although a larger reference load will lead to larger bending about the strong 

axis of the beam, the buckling mode primarily involves twisting about the longitudinal 

axis and bending about the weak axis. As a result, the magnitude of the reference load 

has no significant impact on the buckling load. If the reference load is doubled, the 

eigenvalue will be halved. 

The type of problem that is not well-suited for an eigenvalue buckling analysis is 

depicted in Figure 6-8. The shallow frame may be susceptible to in-plane buckling and 

the prebuckling deformations, ∆, are in the same direction as the potential buckling 

direction. 

The linear eigenvalue problem is based on a linear elastic analysis; however, the 

analysis still does reflect the effects of axial shortening. As a result, the buckling 

capacity in this case will generally be sensitive to the magnitude of the reference load. 

For problems such as this, a second-order analysis should be conducted to evaluate the 

stability of the system. 

A common problem in the bridge industry in which the eigenvalue will often not provide 

a definitive solution is in horizontally curved girders. Studies (Stith, et.al. 2009 and Stith 

Figure 6-8 Problem not Well Suited for Eigenvalue Buckling Analysis
6.16

et. al., 2010) have shown that the eigenvalue solution is not generally sensitive to the 

degree of curvature in the bridge. For example, if the effective girder span is maintained 

but the radius of curvature of the girder is increased, the eigenvalue does not 

significantly change. However, it is relatively clear that for a given load the torsional 

deformations will increase as the radius of curvature of the girder is reduced. The larger 

girder twist can lead to second order effects that are not predicted by the eigenvalue 

analysis. 

6.3.3 Second-Order Analysis

Many software packages have the ability to carry out a second-order analysis that 

considers the impact of deformations on the structural behavior. A second-order 

analysis is also sometimes referred to as a large displacement analysis or an analysis 

with nonlinear geometry. Second-order effects from an analysis perspective can 

generally be referred to as amplifications in member forces and displacements as a 

result of the changes in geometry of the structure. For example, the perfectly straight 

column subjected to pure axial load in Figure 6-9(a) only experiences axial stress until 

the buckling load is reached at which point the member must bend. If a more realistic 

column is considered with an imperfection, Δo, as shown in Figure 6-9(b), the column 

will begin to bend immediately when load is applied due to the PΔ moments that 

develop in the column. Whereas first-order deformations can be solved for directly since 

the analysis is conducted on the original geometry of the structure, second-order 

deformations result in non-linear behavior that requires an iterative solution. Secondorder effects develop in structures as a result of several factors, including combined 

bending and axial force, the impact of imperfections, or due to geometrical effects in the 

structural elements. Although the most accurate approach to predicting the behavior is 

to carry out a second-order analysis that includes the impact of deformations on the 

structural response, in many cases the impact of neglecting second-order effects is 

insignificant and, therefore, such an analysis may not be warranted. This section 

provides a discussion of some of the factors that should be taken into consideration 

when conducting a second-order analysis. Some discussion is also provided on when a 

second-order analysis may be required, as well as cases that may not necessitate the 

more detailed analysis. 

The magnitude and shape of the initial imperfection has a significant impact on the 

behavior of the main members as well as the requirements for bracing. The shapes of 

the imperfections that should be modeled are dependent on the type of buckling that is 

critical. The critical shape for column members that are susceptible to flexural buckling 

generally consist of pure lateral sweeps, while members susceptible to either torsional 

or flexural-torsional modes (such as beams) will potentially have lateral sweep and 

twist. The impact of imperfections and the critical shapes and magnitudes are covered 

in more detail later in the chapter. 
6.17

Figure 6-9 Second Order Effects as a Result of Imperfections

The degree of nonlinearity in a second-order analysis is sensitive to the magnitudes of 

the applied loads relative to the buckling load as well as the imperfections in the 

structure. For example, Figure 6-10 shows the load versus deformation curve for the 

column section shown previously in Figure 6-3 with a lateral sweep imperfection. The 

maximum sweep imperfection at midheight had a magnitude of L/500. The vertical axis 

was normalized by the eigenvalue buckling load (Pcr = 368.1k) that was covered earlier 

in the last subsection. The buckling load that was determined from the eigenvalue 

analysis is essentially an upper bound on the load carrying capacity since the column 

experiences very large lateral displacements as the buckling load is approached. At 

load levels of 50-60% of Pcr, the degree of non-linearity is not that significant; however, 

as the buckling load is approached, the load-deformation curve is relatively flat and the 

column experiences very large deformations for small increases in the applied load. 

This type of behavior is important for engineers and construction personnel to 

understand. The concept of buckling is often perceived to be a “sudden” event. In 

reality, the instabilities that occur due to global buckling modes are often a gradual 

softening in the structure. As the structure nears the buckling capacity, the stiffness 

decays and the structure may experience large deformations due to the increased 

flexibility. Therefore, engineers should be aware of potential problems when field 

personnel complain of fit-up problems or flexibility in the structure. Although in many 

situations the problem may just be a fabrication or erection issue, potential stability 

problems should not be ruled out without proper consideration and/or analysis.

The manner in which the load is applied in a second-order analysis can significantly 

impact the accuracy of the solution. Whereas in a linear elastic analysis, the load can be 
6.18

applied in a single load step, the load in a second-order analysis should typically be 

applied in several steps, the size of which depend on the relative magnitude of the total 

load compared to the buckling load. For this reason, it is usually prudent to first conduct 

an eigenvalue buckling analysis before carrying out a second-order analysis. The 

knowledge of the load level compared to the critical buckling load will likely be an 

important consideration in the load steps that are selected for the analysis. For 

example, in a large displacement analysis where the full load may be close to the critical 

buckling load, the user can generally begin the first few load steps with larger 

percentages of the buckling load, but should gradually taper the steps as the buckling 

load is approached. This practice will often result in more accurate predictions of the 

deformations, as well as quicker convergence in the solution. Some of the software 

packages may offer different solution approaches with regard to how the load is applied. 

For example, the software may offer an automatic load stepping option where the 

program establishes the sizes of the load steps and if convergence is not reached within 

a certain number of iterations, the load increment is reduced until either: a) convergence 

is achieved, b) the time or load steps allotted to the analysis is exceeded, or c) the 

solution diverges. 

Figure 6-10 Second Order Analysis on Column with Initial Imperfection
6.19

Other important aspects in the accuracy of the second order analysis are the 

convergence tolerances, which some programs allow the user to specify. The large 

displacement analysis is based upon an iterative solution process that will continue until 

either 1) convergence is achieved, 2) the load step may be reduced (automatic load 

stepping) until convergence is achieved, 3) the solution diverges, or 4) the time or 

number of iterations allotted to the analysis is exceeded. Some programs will not allow 

the user to specify convergence tolerances; however, others allow user-specified limits 

such as force and displacement convergence limits. Care should be taken in selecting 

the convergence limits since too large of a tolerance can result in the accumulation of 

errors in the solution that can lead to poor estimates of the structural behavior. On the 

contrary, specifying too tight of a tolerance convergence can substantially increase the 

length of time for the analysis with very little impact on the accuracy of the solution. 

Methods of determining appropriate tolerance limits are discussed in the following subsection that focuses on model verification.

This chapter has focused on three analysis methods that may be used in the analysis of 

bridge systems: 

4. first-order analysis, 

5. eigenvalue buckling analysis, and 

6. second-order analysis. 

Of the three different analysis methods, the most accurate is the second-order analysis 

that reflects the impact of deformations on the overall behavior. However, the improved 

accuracy also requires potentially more complexity that may not be justified. For 

example, it can be stated that the most accurate analysis technique is to use a secondorder analysis with non-linear material capabilities. Although the proper material model 

can be developed with sufficient user effort, these efforts are a waste of time if the 

structure is then found to remain in the elastic range. Similarly, the decision to carry out 

a second-order analysis should be based upon expectations or concerns of the impact 

of deformations on the structural performance. 

In many instances, a second-order analysis may not be required. The decisions on 

whether to conduct a second-order analysis should be based upon considerations of the 

potential structural behavior and experience can help dictate these decisions. Including 

the impact of imperfections on straight girder systems is mandatory in order for a large 

displacement analysis to provide meaningful results. Other factors that will affect the 

large displacement analysis are effects of support skew as well as the impact of

horizontal curvature on the behavior. Parametric studies conducted as part of a TxDOT 

sponsored research study on curved girders (Stith et. al., 2009) found that the impact of 

second order effects in horizontally curved girders were significantly affected by the 

lateral and torsional stiffness of the girder system. The study considered the geometry 

of the proportioning of the girders and recommended a ratio of the flange width/girder 

depth greater than approximately 0.25 to minimize the impact of second-order effects. 

The minimum value of the ratio of the flange width/girder depth permitted in AASHTO 
6.20

(2012) is 1/6, which results in relatively slender girder sections that may experience 

significant second order effects. The TxDOT study also considered the impact of 

holding cranes versus shore towers. Because holding cranes support the girders from 

the top flange, the cranes result in a restoring force that tends to reduce the second 

order effects. Therefore a first-order analysis will often actually be conservative 

compared to a second-order analysis, when considering the impact of the holding 

cranes. Second-order effects for shore towers will tend to destabilize the girders unless 

twist of the girder is also restrained at the shore tower. 

When considering bracing requirements for stability, a large displacement analysis is 

required on the imperfect system in order determine the necessary stability forces.

This chapter has focused on some of the different analysis options that are available to 

the engineer and also highlighted some of the decisions that need to be made in 

developing the model. The modeling decisions that are made can be critical to ensure 

sufficient accuracy in the analysis. Before a new software package is used to model a 

complex structural system, the user should always begin with a relatively simple 

problem for which the behavior is well understood. For example, the problems that have 

been considered thus far in this chapter were an Euler column and a simply supported 

beam subjected to uniform moment. These basic problems were selected for simplicity 

in discussion and also because the solutions for the problems were readily available for 

comparative purposes in discussing the accuracy of the computer models. Simple 

problems and experimentation should always be the starting point when beginning with 

a new software package. For example, the simply supported beams shown in Figure 6-

11 represent good problems that an engineer can use to make sure that they 

understand how to input basic support conditions, load types, and cross-sectional 

properties. The user has a good indication of the expected reactions and deformations 

for the problem and therefore can ensure that they are properly specifying the 

necessary input for the problem. Additional problems to those depicted in Figure 6-11 

are available from a variety of sources such as basic structural analysis books or other 

sources. The users may want to also consider fixed ended beams or other idealized 

support or load conditions in the analysis to ensure that they are properly inputting the 

appropriate boundary conditions or applied loading.
6.21

Figure 6-11 Simple Problems for Use in Becoming Familiar with Software 

Capabilities and Modeling Decisions

While simple problems should always be used as a starting point in becoming familiar 

with new analysis packages, it is also important that to understand techniques for 

ensuring that the appropriate modeling decisions are made instead of blindly accepting 

the results of an analysis. One of the most critical decisions that affects both accuracy 

and computational efficiency of a computer model is the appropriate mesh density for 

the problem. The accuracy of a finite element model generally improves with increased 

mesh density. Increasing mesh density generally involves providing more elements to 

model the structure. Provided the aspect ratio of the elements is maintained, increasing 

the number of elements in the model will lead to improved accuracy. However, with 

more elements the number of degrees of freedom in the structure also increases which 

therefore reduces the computational efficiency of the problem. The decrease in the 

computational efficiency results in longer analysis times as well as a higher demand on 

computer resources such as memory and disk space. The user must therefore weigh 

the benefits of the increase in accuracy compared to the reduction in computational 

efficiency.

The last subsection focused on second order analysis methods in which nonlinear 

geometry is considered. As discussed, some of the software packages may allow the 

user to establish the tolerance limits that will be used for evaluating convergence. 

Utilizing too large of a tolerance limit may lead to errors in the solution, while too small 

of a tolerance will lead to longer computational times with very little impact on the 
6.22

accuracy. The user can experiment with the tolerance limits to determine appropriate 

limits that provide good estimates of the structural behavior. This is accomplished by 

starting out with relatively large limits and reducing the limits while comparing the 

relative change in the solution. The point when the changes in convergence tolerances 

have little impact on relative change in the solution usually signifies acceptable 

tolerances that will provide sufficient accuracy and computational efficiency. 

SECTION 4. BEHAVIOR OF STRAIGHT AND HORIZONTALLY 

CURVED GIRDERS DURING LIFTING 

The behavior of girders during lifting can be difficult to assess. Although a variety of 

lifting configurations may be used, a survey of erectors, contractors, and engineers 

conducted on TxDOT study 0-5574 (Stith et. al., 2009) found that most girder segments 

are lifted by a single crane with a spreader beam as depicted in Figure 6-12. The 

stability of the girder is a function of many factors. The connection to the crane typically 

consists of a simple lifting clamp connected to the top flange. The primary source of 

stability is the girder self-weight that acts at the center of gravity on the cross-section 

hanging below the crane lifting point. The girder receives a stabilizing effect because 

the self-weight acts at a location below the support point from the crane as depicted in 

Figure 6-13. Twisting of the girder results in a stabilizing component. However, lateraltorsional buckling is a major concern due to the long unsupported lengths of the girder. 

Depending on the locations of the crane pick points, stability can be controlled by either 

the overhang region of length “a” or by the region between the pick points of length “LLift” 

as indicated in Figure 6-12. 

Figure 6-12 Schematic of Girder Segment during Lifting
6.23

The stability of girders during lifting was studied by Schuh (2008) and Farris (2008) who 

developed moment modification factors, Cb, that can be used to estimate the buckling 

behavior of girders during lifting. The moment modification factors are a function of the 

length of the overhang, a, versus the middle region of the girder, LLift. 

Figure 6-13 Stabilizing Effect of 

Girder Self-Weight 

Acting below Crane 

Pick Point

Another major problem that erectors face is the lifting of horizontally curved girder 

segments that can experience a rigid body rotation during lifting. Depending on the 

location of the lifting points, the geometric centroid of the horizontally curved segment 

may have an eccentricity to the line of support from the cranes as depicted in Figure 6-

13 (Stith et. al., 2010). As a result, the girder will rotate until the geometric centroid of 

the segment lies beneath the line of support. As demonstrated in the figure, the girder 

rotation may be towards the outside or inside of the curve depending on the location of 

the lifting points. The rotation of the girder can be a major concern for erectors since 

excessive rotation of the lifted girder can make air splices such as the connection 

shown in Figure 6-14 difficult to complete. 
6.24

Figure 6-14 Bolted Air Space [Stith et al. 2010]

A computational tool, UT lift, was developed as part of TxDOT research study 0-5574 to 

assist erection engineers with evaluating the lifting behavior of girder segments. The 

tool consists of an Excel-based spreadsheet that is applicable to straight and 

horizontally curved steel girder segments lifted at two locations along the length of the 

girder. The spreadsheet is available for free download at 

http://fsel.engr.utexas.edu/software/index.cfm. The spreadsheet consists of five sheets, 

one of which requires user input. The other pages provide calculations on the girder 

behavior during lifting. An input page for a sample girder segment is shown in Figure 6-

15. The cells that are shaded are areas for requested input. In addition to some basic 

title and project information, the input allows the user to specify the number of section 

changes along the length of the segment. The problem shown in this example consists 

of a girder with a dapped end that has six section transitions along the length. The plate 

sizes for the flanges and webs, as well as the length of each section along the segment, 

are input. The weights of the various sections are calculated and the user can also 

specify a “girder scale factor” to account for the weight of stiffeners or other fabricated 

parts of the section. Also on the first sheet is information about the cross-frames that 

may be lifted with the girder segment as depicted in Figure 6-16. The user can specify 

the number of cross-frames that will be include on the segment and also provide the 

weight of the cross-frames so that the impact on the girder torque (and resulting twist) 

can be considered. The user can experiment with the behavior considering whether 

cross-frames are included only on the inside of the curve (I), only on the outside (O), or 

both inside and outside (I/O). The weight of the cross-frames are assumed to be applied 

a distance of s/2 from the girder centerline, where s is the girder spacing. If desired, the 

erector can also adjust the weight of one of the cross-frames to determine the 

necessary counterweight that could be applied to reduce the twist of the segment so 

that the splice is easier to complete. 
6.25

Figure 6-15 Sample Input Page for Girder Properties in UT Lift
6.26

Figure 6-16 Sample Cross-frame Input for UT Lift
6.27

The next sheet of the spreadsheet provides information on the location of the geometric 

centroid of the section, as well as the optimum lift location for the girder segment as 

shown in Figure 6-17. The optimum lift location is the position that results in zero 

rotation of the segment during lift. The program also estimates the required spreader 

beam length that would be required for the problem. For the sample case in the figure, a 

spreader beam length of 98.684 ft with the first end positioned 23.78 ft from the first end 

will result in zero rigid body rotation in the segment. 

The information on the optimum lift locations is provided primarily for information 

purposes, since erectors will generally not have the ability to exactly match the optimum 

lifting equipment. Therefore, as shown in Figure 6-18, the erector can input the length of 

the spreader beam that is in stock and adjust the lifting point locations on the beam to 

achieve a rigid body rotation that is acceptable to the desired performance. The user 

can also go back to the cross-frame information and adjust the number and location of 

the cross-frames to help modify the twist of the section. The spreadsheet provides a 

warning that the lifting forces may not be equal as indicated in the sheet; however, in 

this case the forces are within a few hundred pounds of each other which will not be an 

issue. If the forces are too much out of balance, the segment and spreader beam will 

rotate until equilibrium is achieved, which may result in difficulty making the connection. 

In this case, the location of the lift points can be adjusted until the forces are 

approximately equal. There is a button on the lower part of the page that the user can 

push to calculate the rotations and stresses in the girder. Because the program includes 

macros, the user will have to enable the macros in the spreadsheet. A one-dimensional 

finite element was incorporated into the macros of the spreadsheet to compute the twist 

of the girder segment from the torque that results from the geometry. Therefore, the 

program estimates both the rigid body rotation as well as the girder rotation due to 

torsion. 

Figure 6-19 shows the sample output of the girder stresses and segment rotations with 

the input spreader beam and lifting locations. In this case the two ends of the segment 

are estimated to rotate 3.127° at one end and 1.900° at the other end. If these rotations 

are larger than the erector feels is necessary to make the connections at the ends of the 

girder, the lifting properties can be adjusted or the contractor can experiment with crossframes included in the lift on the inside or outside of the girder to adjust the torque. This 

page also allows the user to estimate the buckling load of the segment with input of a 

dead load factor (g) and a resistance factor. The spreadsheet shows the maximum 

factored moment based upon the self-weight of the steel section (and load factor) and 

also estimates the buckling capacity using the AASHTO elastic buckling expression and 

the Cb factor from the work of Farris (2008). The buckling expression will be reasonably 

accurate for straight (or mildly curved) girders; however, for girders with significant 

curvature, the elastic buckling load is not necessarily a good indicator of safety due to 

the nonlinear response of the girder. The user can get an indication of potential 

problems with the girders by considering the magnitudes of the deformations that may 

occur during lifting. To help understand the girder behavior, sample graphs as depicted 

in Figure 6-20 are provided on the last page of the spreadsheet. If the deformations 

seem excessive, more detailed analysis of the girders may be necessary. 
6.28

Figure 6-17 Sample Output of Optimum Lift Locations for Girder Segment 

for UT Lift
6.29

Figure 6-18 Sample Input Page for Actual Spreader Beam and Lift 

Locations from UT Lift
6.30

Figure 6-19 Sample UT Lift Output of Girder Stresses and Rotation at Ends 

and Middle of Segments
6.31

Figure 6-20 Sample UT Lift Graphs of Girder Displacements and Torque
6.32

SECTION 5. BEHAVIOR OF STRAIGHT AND HORIZONTALLY 

CURVED GIRDERS DURING ERECTION AND CONSTRUCTION 

As noted earlier in the chapter, there are a variety of models and analysis methods that 

can be used to study the stability behavior of steel bridge systems. The accuracy of the 

various modeling techniques depend heavily on the types of details that are used in the 

bracing as well as the combination of temporary and permanent supports that may be 

used during construction. While grillage models are by far the easiest models to create, 

the simple models that result may be lacking sufficient detail to accurately capture the 

behavior of the system at critical stages in the construction. The stability of the system 

can be significantly affected by the support locations on the girder cross-section, as well 

as the interaction of the braces with the cross-sectional stiffness. The most accurate 

modeling method is, therefore, 3D models that can more accurately capture the impact 

of details and cross-sectional distortion on the bridge behavior. However, the drawback 

to utilizing 3D modeling is the time necessary to properly model the bridge, as well as 

validation methods that are necessary. The modeling time increases dramatically for 

bridges with horizontal curvature combined with potential support skew. Further 

complicating the modeling issues is identifying and modeling the critical stages in the 

partially-erected bridge. As part of TxDOT project 0-5574, a computational analysis tool 

named UT Bridge was developed to specifically address the analysis issues with steel 

bridges during construction. The UT Bridge program is a 3D finite element program that 

is free to download at http://fsel.engr.utexas.edu/software/index.cfm. 

The goal of the software is to create accurate representations of the structural system 

during construction through the use of a user-friendly graphical user interface (GUI). 

The software consists of 14 input screens that prompt the user for input related to the 

basic bridge geometry, the erection sequence, locations of shore towers or temporary 

holding cranes, and the concrete deck casting sequence.

This section focuses on the determination of critical stages that should be evaluated 

throughout the construction process. Because the critical stages vary among bridges, 

results from the UT bridge program will be used to describe how the various stages can 

be identified and analyzed. Therefore this section has been divided into four 

subsections. Following this introduction, an overview of the UT Bridge software is 

provided. A typical erection sequence for a two-span horizontally curved girder is then 

presented followed by an evaluation of a staged concrete deck placement. 

6.5.1 UT Bridge

The UT Bridge Software is a 3D finite element program that was specifically developed 

to target the behavior of straight and horizontally curved girders during erection. The 

software is capable of conducting a first-order structural analysis or an eigenvalue 

buckling analysis. The software consists of 14 input screens that prompt the user for 

input that is readily available from shop drawings or bridge plans. The software allows 

the user to fully define the steel bridge system and then experiment with a variety of 
6.33

erection or concrete deck placement scenarios to evaluate the behavior of the bridge 

during construction and provide confidence in the erection and construction plans. 

At the start of the program, the user can select to either start a new project or continue 

with an existing project. The user selects between conducting an erection analysis or a 

deck placement analysis on either a straight or horizontally curved girder system. The 

input panels prompt the user for the necessary information on the basic geometry of the 

bridge. For example, Figure 6-21 shows the third of fourteen input panels that prompts 

the user for the span lengths and types of bearings. In addition to the basic span 

lengths of the girders, the user can specify support skew. Many of the panels have a 

button with a magnifying glass that provides the user with additional information. For 

example, if the user selects the magnifying glass on the third panel, the information 

panel shown in Figure 6-22 appears and provides the user with the sign convention for 

the support skews.

Figure 6-21 Typical UT Bridge Input Panel for Basic Bridge Geometry
6.34

Figure 6-22 UT Bridge Pop-Up Screen with Additional Information on Skew 

Sign Convention

Figure 6-23 shows the input screen for the girder properties in which plate sizes are 

defined for the different girders in the bridge. Many of the input screens have options for 

the user to define the properties for girder 1 and then select “All Girders Uniform” so that 

the properties are copied to each girder. If the option is selected for horizontally curved 

girders the program assumes that the plate transitions are radial for the other girders. If 

the girders have skewed supports, the properties of each girder must be defined since 

the girder lengths and plate transitions may be much more variable. Some of the input 

screens have a button that shows a “pencil” which, if selected, initiates a pop-up window 

with the schematic of the defined element. For example, if the button is pushed while on 

the “girder 1” tab for the girder input shown in Figure 6-23, the pop up screen shows an 

elevation of girder 1 with the defined plate sizes as shown in Figure 6-24. The user can 

select to show either the plate thickness or the plate widths. 
6.35

Figure 6-23 UT Bridge Input Screen for Girder Properties
6.36

Figure 6-24 Information Panel on the Defined Model for UT Bridge

The support and intermediate cross-frames are specified separately. The program 

assumes that there is a connection plate (stiffener) at each cross-frame location and the 

user specifies the plate size on the same panel the cross-frame member sizes are 

specified. The cross-frames are assumed to be “X-Type” cross-frames with two 

diagonals and lateral struts at the top and bottom; however a tension-only diagonal 

system is assumed in which case only the tension diagonal contributes to the stiffness. 

For different cross-frames systems, equations for the stiffness relative to “X-type” crossframes are available and the member sizes can be adjusted accordingly. For radial 

cross-frames, the software has a “uniform spacing tool” that can help to define crossframes along the length of the girders. If the cross-frames are not radial, the user can 

specify the cross-frames separately between each set of girders. The user also 

specifies the cross-frames’ sizes at the supports and the size of the bearing stiffeners. 

The program offers two options for the bearing stiffeners, plate stiffeners or pipe 

stiffeners. Pipe stiffeners have been utilized on bridges with heavily skewed supports to 

facilitate stiffer connections between the cross-frames and the girders at the supports 

(Quadrato, et. al., 2010). The pipe stiffeners also offer a significant amount of warping 

restraint to the girders and the program is capable of including the benefits of these 

stiffeners on the torsional behavior. The user is prompted for the plate and width if a 

plate bearing stiffener is selected or the pipe diameter and thickness if a round pipe 

stiffener is specified at the support locations. 
6.37

By the ninth input screen, the erection model has been fully defined and the user then 

begins to focus on the erection sequence. The user specifies the number of analysis 

runs that are to be conducted to analyze the entire erection sequence. The user can 

analyze the behavior as each individual girder segment is erected or may choose to 

only consider the analysis cases that are deemed “critical”. The following section 

outlines methods to evaluate the critical analysis cases that need to be considered. The 

software allows the user to input wind loads if desired to evaluate the behavior of 

partially erected systems under wind loads. 

The software can allow the user to consider the effectiveness and placement of either 

shore towers or temporary holding cranes. For holding cranes, the user specifies the 

location of the holding crane force along the girder length and also on the cross-section, 

as well as the magnitude of the holding crane force. In many situations, the desired 

behavior of the holding crane is that it acts like a rigid support much in the way shore 

towers are considered to act. To determine the required crane force, the analysis can 

first be conducted by putting a shore tower at the particular location and determining the 

reaction. The analysis can then be rerun by replacing the shore tower with a temporary 

holding crane applying an upward force at the specified location. 

The user can decide to either conduct a first order structural analysis or an eigenvalue 

buckling analysis for up to five buckling modes. As noted earlier in the chapter, the first 

mode is the primary mode of interest since it will have the lowest buckling load. Before 

the analysis is conducted the user has the ability to first visualize the bridge to make 

sure that the proper geometry has been captured and that the correct erection 

sequence that was desired is being modeled.

UT Bridge automatically creates the three-dimensional finite element mesh of the girder 

systems using a combination of shells and beam elements. The user can choose one of 

three meshing options located under the “Tools” category on the Menu Bar. There are 

three meshing options: Coarse, Normal, or Fine. In the coarse meshing option, element 

divisions are at a 4-foot-spacing along the length of the girder with four web elements 

through the depth of the web. In the normal meshing option, element divisions along the 

girder length are at a 2-foot-spacing with four elements through the depth of the web. In 

the fine meshing option, the element divisions are at a 1-foot-spacing along the girder 

length with four elements through the depth of the web. In most applications, the normal 

meshing option results in good estimates of the behavior, however if computer 

resources are short the user may opt to use the coarse mesh or the fine mesh may be 

selected to provide more nodes along the length to better capture the behavior. The 

finer mesh may provide better estimates of the behavior if local plate buckling is an 

issue on the bridge. 

In addition to conducting a girder erection analysis, UT Bridge also allows the user to 

conduct a deck placement analysis from the same model that was described in the 

erection analysis. On input form 10, the user provides the information about the 

concrete deck properties. The pertinent geometrical information includes the thickness 

of the deck, the haunch properties, and the overhang widths on the two sides of the 
6.38

bridge. The user also defines how many deck segments are cast and the number of 

concrete placements. The deck segments are usually divided into the number of 

individual positive moment regions and negative moment regions where the deck is 

likely to have construction joints. The number of deck placements refers to how many 

different time periods that the concrete will be placed. For example, the contractor may 

decide to place all of the positive moment regions in succession and allow that concrete 

to cure for a day or more before placing the negative moment regions. The reason that 

the number of concrete placements is important is that UT Bridge allows the user to 

take into consideration the time-dependent stiffness gain in the concrete based upon 

test results from Topkaya (2002). 

Topkaya conducted experiments on the stiffness gain in the concrete during the hours 

immediately after casting. The concrete can quickly gain stiffness and create composite 

action between the freshly placed slab and the steel girders. Although the strength of 

the concrete is obviously not adequate to develop large increases in the bending 

strength of the cross-section, the stiffness gain can substantially affect the deformations 

in the girders and the required bracing. Therefore, UT Bridge allows the user to express

the concrete placement in terms of hours from the start of the deck construction. The 

analysis then takes into consideration the impact of the freshly placed concrete on the 

bridge behavior. While the program allows the stiffness to be directly taken from the 

work from Topkaya (2002), the user can also directly input a different stiffness if the 

value is known or to obtain a measure of the impact of the variation of the stiffness on 

the behavior. If the user does not wish to consider the impact of the concrete stiffening 

on the behavior, a single placement can be specified and only the weight of the wet 

concrete is considered.

Because the program automatically generates the mesh, isolated cases have been 

found where a flange width transition or other localized discontinuity may lead to a 

meshing problem that has issues running. Changing the meshing option to one of the 

other two options (i.e. Normal to Course or Fine) typically fixes this problem.

6.5.2 Determining the Critical Erection Stages

As noted at the outset of the chapter, the difficult aspect of erection engineering is 

ensuring the stability of the bridge at early stages in the erection when not all of the 

bracing is present in the structure. In many situations the most precarious condition of 

the bridge is the first girder segment when there is no existing structure besides the pier 

caps/abutments to brace the girder. The use of shore towers or temporary holding 

cranes can significantly increase the cost and time of erection and therefore such 

falsework is preferred only in cases where it is absolutely necessary. Because the 

system generally becomes more stable as more of the structure is erected, not all 

stages of the erection need to be modeled. However, without experience, it is not 

always clear which stages need to be considered. In this section, the erection of a fourgirder steel bridge is evaluated to demonstrate some of the critical stages that need to 

be considered in the erection. Due to the variability of geometries and loading 

conditions on bridges, the critical stages will vary from bridge to bridge; however with 

experience, most engineers will be able to rule out some of the specific stages that 
6.39

need not be considered. The bridge that is to be modeled is depicted in Figure 6-25. 

The two-span unit represents a bridge that is simple enough in this example that the 

erection sequence can be covered in an efficient manner; however there are enough

complexities that some of the difficulties in analysis can be discussed. The girders are 

doubly-symmetric and the plate sizes in the bridge are indicated. The bridge has two 

175 ft-spans. The girders have 14 in. x 1 in. flanges in the positive moment regions and 

16 in. x 1.5 in. flanges in the negative moment region. The web is 66 in. deep and 0.5 

in. thick. The girders have a splice at the locations of the flange transitions so each 

girder will be shipped to the job site in three segments: two 135 ft segments and the 80 

ft segment for the negative moment region. The cross-frames are spaced 25 ft on 

center along the bridge length; however, in many situations, not all of the cross-frames 

are installed as the girders are lifted into place. UT Bridge allows the user to fully define 

the bracing layout but to leave out every other cross-frame during the analysis for the 

erection scenario, which was assumed in this analysis.

Figure 6-25 Plan View and Elevation of Two Span Bridge Modeled
6.40

There are a variety of methods that could be used to erect the four-girder system 

depicted in Figure 6-25. Perhaps the “easiest” method of erecting the girders is to place 

a shore tower between Bents 1 and 2 so that the 135 ft long segments can first be lifted 

into place and then the 80 ft long segments can be lifted and the splice can be 

completed in the air so that the girders cantilever over Bent 2 leaving the 135 ft long 

segments to be lifted and spliced to complete the girder erection. However, the 

drawback to such a scenario is the time required to assemble and erect the shore tower 

as well as the potential traffic interruption that such a tower will cause below the bridge 

area. As a result, the first preference for most cases will be to erect the bridge without 

the use of a shore tower. Therefore, in a different and more likely scenario, one of the 

girder splices would be completed on the ground to make 215 ft long segments that can 

be lifted into place and set on two of the supports (Bent 1 and Bent 2). Therefore the 

girders will cantilever over Bent 2 after the first segments are erected and the bridge 

would be completed in the manner described above with the final 135 ft long segment of 

each girder lifted and connected with an air splice, thereby completing each girder line. 

Since the girder segments would be lifted individually in the latter scenario, there are 

eight separate lifts for the steel girder bridge as denoted in Figure 6-26. Although each 

case can be analyzed to evaluate the safety of the erection scenario, some of the cases 

are more critical than others and therefore each case does not necessarily have to be 

considered when evaluating the potential scenarios.

Figure 6-26 Plan View of Erected Girders for Eight Erection Stages
6.41

Table 6-1 shows a summary of eigenvalue buckling results for the eight different load 

cases. Some erectors may opt to initially only install half the cross-frames, so the 

analytical results are for cases where every other intermediate cross-frame was 

installed. The erector would then come back and install all the cross-frames prior to 

deck placement. The applied loading on the girders consisted of the unfactored selfweight of the steel section. Therefore, an eigenvalue greater than 1 indicates that the 

critical load is higher than the self-weight and a value less than 1 means that the critical 

load is less than the self-weight, indicating that the section will definitely buckle during 

erection. 

Case Eigenvalue

1 0.48

2 1.57

3 1.84

4 1.96

5 1.32

6 2.36

7 3.15

8 3.55

Table 6-1 Summary of Eigenvalues for Erection Scenario in Figure 6- 25 

(half cross-frames installed)

With an eigenvalue of 0.48, the girder is clearly not adequate to support its self-weight 

in the case 1 lift where girder 1 is erected onto the abutments. Figure 6-27 shows the 

buckled shape of girder 1 from the Case 1 erection. The analysis assumes that the 

girder will be braced at the pier locations, but the eigenvalue shows that additional 

bracing or a temporary support will be required. When Girder 2 is added the eigenvalue 

increases to 1.57, which indicates that the critical load is 57% higher than the selfweight of the section. The buckled shape of Girders 1 and 2 for Case 2 in the erection 

scenario is shown in Figure 6-28. In analyzing the different cases, it is clear that Case 1 

will usually always be one of the most critical cases. Depending on the length of the lifts, 

Cases 1 and 5 are potentially critical, since these cases will have the largest 

unsupported length of any of the cases. For this particular analysis, Case 5 has an 

eigenvalue of 1.32 which is probably borderline with regards to safety. Adding 

temporary bracing or a holding crane would probably be considered at this stage. 

Considering the Case 5 buckled shape, Figure 6-29, the unbraced length of Girder 1 is 

150 ft since there is one cross-frame on the cantilevered portion of the girders (i.e. 135 

ft + 15 ft = 150 ft). The buckling capacity of Case 5 can be improved if the erector was 

able to add temporary bracing at the end of the cantilever section. The benefit can be 

found in UT Bridge by adding another cross-frame line located at 215 ft along the length 

of the bridge, which increases the eigenvalue to 1.50. The actual bracing that is used by 

the erector will not consist of a permanent cross-frame, but instead could consist of 

some wide flange shapes spanning between the cantilever portion of Girders 1 and 2 
6.42

that could be clamped to the top and bottom flanges. Once the remainder of Girder 2 is 

added (Case 6), the eigenvalue increases to 2.36 and the temporary bracing could be 

removed.

Figure 6-27 Buckled Shape of Girder 1 with No Intermediate Bracing (Case 1)

Figure 6-28 Buckled Shape of Girders 1 and 2 in Case 2
6.43

Figure 6-30 shows the buckled shape for Case 8 when all of the girders have been fully 

erected, but only half of the cross-frames are included. The behavior of the system if the 

full bracing is added is discussed later in this section. 

Figure 6-29 Case 5 Buckled Shape

Figure 6-30 Case 8 Buckled Shape
6.44

Based upon the eigenvalues, the erection scenario is inadequate for the Case 1 

condition. In an effort to improve the behavior of the girder during erection, the behavior 

with the addition of a holding crane is evaluated. However, if a holding crane is to be 

used, the force that the crane should apply to the girder at the lift point typically needs to 

be specified. If a shore tower were to be used in the erection scheme, the tower would 

have been erected to a height that puts the girder splice at the proper elevation to 

facilitate completion of the splice. To determine the required lifting force for the holding 

crane, an analysis will first be conducted in UT Bridge by modeling a shore tower in 

Analysis Case 1 with only Girder 1 erected. UT Bridge allows the user to specify the 

location of the shore tower/holding crane along the length of the girder. Depending on 

the site layout, the engineer may have limitations on where the shore tower or holding 

crane can be placed and therefore should select the appropriate location. Since there 

are no limitations in this problem, a location 90 ft from the first bent was selected for the 

support location, which is very near the middle of the 175 ft-span. 

The buckled shape of the analysis with the shore tower is shown in Figure 6-31. The 

eigenvalue with the shore tower is 5.81 and the vertical reaction is 21.3 kips. Using this 

reaction, the shore tower can be replaced in UT Bridge with a holding crane in the form 

of an upward force of 21.3 kips at the same location, except the load is applied at the 

top flange since most holding cranes will connect to the girders with a flange clamp at 

the top flange. The buckled shape for the load case with the holding crane is shown in 

Figure 6-32. The eigenvalue with the holding crane is 4.58, which is less than the value 

of 5.81 for the case of the shore tower. The difference in the eigenvalues for these two 

cases with the falsework is due to the assumptions that twist and lateral movement is 

restrained at the shore tower. For the case with the holding crane, the analysis only 

applies an upward force, but the girder can still translate and twist at that location. 

Figure 6-31 Buckled Shape for Case 1 with Shoring Tower 90 ft from Bent 1
6.45

Figure 6-32 Buckled Shape for Case 1 with a Holding Crane 90 ft from Bent 1

If the holding crane is removed after Girder 2 is erected, the eigenvalue will be 1.57 as 

was given in Table 6-1. If the engineer requires all intermediate cross-frames to be 

installed between each girder at the time of erection (instead of only half), the buckling 

capacities of the system will increase to the values given in Table 6-2. The percent 

increase is substantial, however the engineer can evaluate the behavior and make 

decisions that are the most efficient in terms of time and resources available for the job. 

Case Eigenvalue Percent Change Compared to 

Table 6.1 (half Cross-frames)

1 4.58 (holding crane) 854% (due to holding crane)

2 1.87 19% 

3 2.59 41%

4 3.12 59%

5 1.33 1%

6 4.65 97%

7 5.74 82%

8 6.56 85%

Table 6-2 Summary of Eigenvalues for Erection Scenario in Figure 6- 25 

All Cross-frames Installed and Holding Crane for Case 1

With the addition of the holding crane, Case 5 is the most critical case. As noted earlier, 

temporary bracing added near the end of the cantilever can raise the eigenvalue to 1.5. 
6.46

A temporary holding crane could also be considered, which would greatly increase the 

stability much like the outcome of Case 1.

In the erection of curved girder systems, there are a number of other 

considerations that the engineer needs to be aware of. For example, 

consideration of the torsional stability of the partially erected system is a major 

consideration. In the curved girder system shown in Figure 6-27, when only two 

girders are on the supports, the interior girder has a negative vertical reaction 

which indicates uplift. UT Bridge gives a warning when uplift is a problem; 

however engineers need to check the vertical reactions to make sure that a 

typical erection scenario doesn’t have uplift cases. For the example in Figure 6-

27, the engineer may need to ensure that a tie down is provide at the first support 

to make sure that the girder system has adequate torsional stability. 

Figure 6-33 Potential Uplift in Horizontally Curved Girder during Erection

6.5.3 Evaluation of Concrete Placement 

Another critical stage for the stability of a girder system is during the placement of the 

concrete deck. Although the full bracing is installed to the girders at this stage, the 

applied loads during deck placement are significantly higher compared to the erection 

stage where the loads only consist of the weight of the steel section. During placement, 

the concrete is a fluid and offers no restraint to the steel girder system. As a result, the 

deck placement conditions offer another critical stage that must be evaluated. 
6.47

Consideration of the stability of the system during the deck placement will typically rely 

upon the resistance of steel girders and the bracing system, which usually consists of 

the cross-frame systems. Although stay-in-place forms do enhance the stability of the 

girder system, due to flexibility in the connections between the form work and the 

girders, AASHTO does not permit the forms to be relied upon for bracing. The UT 

bridge software can be used to conduct an eigenvalue analysis to evaluate the stability 

of the girder system during deck placement. 

As discussed in Section 6-3.2, the eigenvalue represents a multiplier on the applied 

load. The loads will consist of the self-weight of the girders, concrete deck, formwork, 

and the construction personnel/equipment. There is often some unpredictability in the 

distribution of the applied construction loads during the deck placement. Relative to the 

applied serviced loads to the structure, a target eigenvalue during the deck placement 

will usually be in the range of 1.5-1.75. This range of eigenvalues will usually account 

for some of the uncertainty in the load distribution on the structure. In some cases, the 

engineer may be able to account for some of the beneficial restraint that comes from 

previously set concrete as is explained later in this subsection.

In addition to the stability of the system, there are a number of other behavioral 

concerns that must be evaluated during deck placement. Some of the factors include 

potential lift-off at the supports of continuous and/or horizontally curved girders as well 

as cambering requirements so as to achieve the proper deck stiffness. As noted earlier, 

UT Bridge includes the ability to consider the time dependent stiffness gain in the 

concrete. The stiffness gain of the concrete during the cast impacts the brace forces 

that develop in the cross-frames, the rotational behavior of the girders during 

construction, and also the vertical displacements of the bridge during deck placement. 

For an example, the two-span straight girder considered in Section 6.5.2 was evaluated 

during a simulated deck placement. The deck consisted of a 10 in. thick concrete deck 

with 4 ft overhangs as shown in Figure 6-34. Although the 350 ft total length of the 

bridge may be a bit long to complete in a single cast, some contractors would like to 

conduct a single cast starting at one end of the bridge and placing the concrete towards 

the other. However, it’s important to ensure that the girders will not lift off the support 

during the deck placement. The critical stage to check for lift-off will be when the 

concrete has been totally placed on one span as depicted in Figure 6-35. The UT 

Bridge solution for the critical case that might cause uplift is shown in Figure 6-36. The 

analysis shows that uplift would not occur; however the reactions at the far support are 

relatively small (approximately 1000 lbs. and 1500 lbs. at the exterior and interior 

girders respectively). Since a load factor of 1.0 was used in the analysis, these forces 

are generally too close to uplift and either a tie-down at the supports should be used or 

a staged deck cast should be used. 
6.48

Figure 6-34 Cross-section of Four Girder Bridge Considered in the 

Concrete Placement Evaluation

Figure 6-35 Critical Loading to Check Uplift When Continuous Deck Cast is 

Proposed

Figure 6-36 UT Bridge Results for Potential Uplift during Continuous Deck 

Cast
6.49

UT Bridge also provides graphs of nodal data such as stresses or displacements. 

Figure 6-37 shows a graph of the vertical displacement along the bridge length. As 

expected, the vertical displacements for the simulated continuous deck cast essentially 

give symmetric displacements in the two spans. There is a very small difference due to 

the rounding of the span lengths that happens in the meshing; however the predicted 

vertical displacement is approximately 8.5 in. 

As noted earlier, these values can be affected due to the time dependent stiffness gain 

in the material. The program calculates the increase in concrete stiffness with age and 

incorporates these values in subsequent analyses. The effect of the concrete stiffening 

can be considered in cases where concerns exist about the stability of the systems 

since the partially cured concrete contributes to the girder stability; however neglecting 

this effect is generally conservative. The early stiffening of the concrete can also have 

an impact on the resulting camber and the software can account for the potential partial 

composite action that may develop. For example, instead of a continuous deck pour, a 

case where the deck is divided into three segments of length 135 ft, 80 ft, and 135 ft as 

depicted in Figure 6-38 was considered. The time of placement for the deck casting was 

taken as 0 hours for deck segment 1, 8 hours for deck segment 2, and 48 hours for 

deck segment 3 (the negative moment region). The difference in time between these 

stages can impact the vertical displacements during the deck pour. Figure 6-39 shows 

the unsymmetrical displacements that result from the concrete deck placement when 

early stiffening is accounted for. The maximum displacement occurs in the first span 

and has a value of approximately 10 in. The deflection in the second span is only about 

7 in. Recall that the displacements in both spans were the average of these values, 

about 8.5 in, for the monolithic pour (Figure 6-37).
6.50

Figure 6-37 Estimated Dead Load Deflections from Uniform Load from 

Simulated Continuous Deck Placement

Figure 6-38 Concrete Pouring Sequence
6.51

Figure 6-39 Differential Deflection due to Early Stiffening of the Concrete

SECTION 6. COMPARISONS BETWEEN AASHTO DESIGN 

EXPRESSIONS AND EIGENVALUE BUCKLING ESTIMATES

As noted earlier in the chapter, critical loads predicted from an eigenvalue buckling 

analysis will often have good correlation with estimates from closed-form equations that 

are included in design specifications such as AASHTO. However, simplifying 

assumptions have been made in some of the specification equations and the designer 

also must often make assumptions in using the expressions that can lead to differences 

between the buckling capacity predicted by the eigenvalue and specification 

expressions. This section provides a comparison between the eigenvalue buckling 

solutions and the AASHTO design expressions so that engineers can understand the 

source of the differences between these buckling estimates. For the purposes of 

comparison, variations in the geometries of a girder that is used in Example 1 of

Appendix B are used to demonstrate potential differences in the buckling solutions. The 

eigenvalue solutions are obtained using the program BASP outlined earlier in the 

chapter. Comparisons are made with the buckling expressions included in AASHTO 

Section 10.6 and AASHTO Appendix A6. 

6.6.1 Girder Geometry
6.52

Although the bridge geometry in Example 1 from Appendix B consists of a two-span 

bridge with six girders across the width of the bridge, comparisons in this section will 

focus on the stability of a single girder during the first lifting stage. The geometry of the 

Example 1 girder is shown in Figure 6-40 in which the girder consists of a non-prismatic 

section with larger flanges in the negative moment region compared to the positive 

moment region. In the positive moment region, a smaller top flange is used compared 

to the bottom flange, thereby creating a singly-symmetric section. In the positive 

moment region, the same size flanges are provided, resulting in a doubly-symmetric 

section. The flange transitions occur at the two splice points on the girder. During 

erection of the first segment, twist will often be provided by preventing lateral movement 

at the top and bottom of the girder as denoted by the “X” at these locations. A common 

erection scheme for the girder that would likely be considered would be to complete 

Splice 1 on the ground and lift a 212 ft long segment onto the supports with a 48 ft

overhang to Splice 2. Because the girder is a non-prismatic section, an engineer 

desiring to use the AASHTO buckling expressions will need to make some simplifying 

assumptions. The most common approach to this problem is to treat the girder as a 

prismatic section with the properties of the positive moment region and an unbraced 

length of 164 ft, which is the total length of the first span. 

0.875” plate x 18”

48’ 48’ 116’

2” plate x 18” 0.75” plate x 16”

2” plate x 18”

0.5” web plate x 60” 0.5675” web plate x 60” 0.5” web plate x 60”

116’

X

X

X

X

X

X

X – lateral restraint

Splice 1 Splice 2

Figure 6-40: Geometry of Two-Span Non-Prismatic Girder

6.6.2 Comparisons Between AASHTO Equations and Eigenvalue Buckling 

Solutions

The AASHTO Specification has two different expressions that can be used to evaluate 

the lateral-torsional buckling capacity. AASHTO Section 6.10.8 has the following 

lateral-torsional buckling expression (Note Rb for the beam is 1.0 and is not shown in the 

equation):

 

AASHTO Equation 6.10.8.2.3-8 

This particular AASHTO expression neglects the St. Venant torsional stiffness and 

therefore only reflects the capacity based upon the warping torsional stiffness. 

Alternatively, the following AASHTO expression in Appendix A6 (Equation A6.3.3-8) can 
6.53

be used to consider the contribution of both the warping and St. Venant torsional 

stiffness: 

2 2

1 0.078 b b cr t b xc

t

C E J L F

L S h r

r

π   = +          

AASHTO Equation A6.3.3-8 

The term inside the radical of the AASHTO Appendix A6 expression represents the St. 

Venant Stiffness of the section, while the term outside the radical is identical to the 

AASHTO Eq. 6.10.8.2.3-8. Since the actual plate sizes can be included in a finite 

element program, there will likely be additional differences between buckling estimates 

using the AASHTO expressions and the eigenvalue buckling solution. To demonstrate 

potential differences between eigenvalue solutions and the AASHTO expressions, the 

girder geometries shown in Figure 6-41 are considered. In Case 1, the girder is treated 

as a simply-supported prismatic girder with a total length of 164 ft In Case 2, the girder 

is still treated as a prismatic section; however the 48 ft long overhang is considered. In 

Case 3, the non-prismatic girder with the overhang is considered. 
6.54

0.875” plate x 18”

116’ + 48’ = 164’

0.75” plate x 16”

0.5” web plate x 60”

A) Case 1 – Simply Supported Prismatic Girder

B) Case 2 – Overhanging Prismatic Beam

C) Case 3 – Overhanging Non-Prismatic Beam

0.875” plate x 18”

48’

0.75” plate x 16”

0.5” web plate x 60”

0.875” plate x 18”

48’ 48’

0.75” plate x 16”

2” plate x 18”

0.5” web plate x 60” 0.5675” web plate x 60”

164’

164’

2” plate x 18”

X

X

X

X

X – lateral restraint

X

X

X

X

X

X

X

X

Figure 6-41: Cases Considered in Comparison of AASHTO Equations and 

Eigenvalue Buckling Solutions
6.55

The loading case that was considered consisted of uniform moment loading so that Cb = 1.0. 

For the purposes of comparison, the program BASP (Buckling Analysis of Stiffened Plates) was 

used with uniform moment loading to demonstrate the differences between the eigenvalue 

solution and the AASHTO expressions given above. Three different analyses were conducted 

in BASP to demonstrate the behavior. The results are summarized in the following table:

Analysis 

Case

Description AASHTO Eq. 

6.10.8.2.3-8 

AASHTO Eq. 

A6.3.3-8 

BASP 

(Eigenvalue)

1 No Overhang, 

Prismatic, 

Section

95.7 k-ft

(49.6%)

185 k-ft

(2.6%)

190 k-ft

2 Cantilever 

Overhang, 

Prismatic Section

N/A N/A 208 k-ft

3 Cantilever 

Overhang Nonprismatic Section

N/A N/A 318 k-ft

Table 6-3 Summary of analysis cases.

In analysis Case 1, the beam was modeled as a prismatic section with a 16” x 0.75” top 

flange, 18” x 0.875” bottom flange, and a 60” x 0.5” web. As shown in Figure 6.41, the 

beam in BASP for this case was modeled without the overhang beyond the interior 

support. This beam has the same section properties as utilized in the two AASHTO 

equations. The eigenvalue solution in this case has good agreement with the AASHTO 

Appendix A6 equation that includes both the St. Venant and warping stiffness. The 

percentages shown below the AASHTO expressions are the percent differences relative 

to the BASP Analytical Case 1 solution. The AASHTO Equation 6.10.8.2.3-8 that is 

frequently used in practice was nearly 50% conservative compared to the eigenvalue 

solution since the St. Venant stiffness is conservatively neglected in the AASHTO 

equation. Most designers would approximate the cross-section as shown in Case 1 for 

the geometries in Case 2 and 3, and therefore solutions are not given for these cases. 

In the Analysis Case 2, the portion of the erected beam that overhangs the interior 

support was included, which resulted in nearly a 10% increase to 208 k-ft in the 

eigenvalue buckling solution. The increase in the buckling capacity occurs because the 

overhanging beam provides some additional restraint at the support since the 

overhanging section does possess St. Venant stiffness. In the analysis Case 3, the 

much larger section in the negative moment region was included thereby forming a nonprismatic beam. The larger section in the negative moment region, increased the 

uniform moment buckling capacity to 318 k-ft 

Another source of conservatism that will often exist in solutions using the expressions 

from AASHTO are the moment gradient factor. In many cases, engineers will use a Cb

=1.0 due to complexities associated with non-prismatic sections or moment 

distributions. The finite element solution will often reflect the benefits of moment 

gradient, which may often lead to additional capacity reflected in the eigenvalue 

solution. The factors outlined above will often lead to significant differences between 

hand calculations using the AASHTO equations and critical loads predicted from a finite 

element program. Such is the case as outlined later in Example 1 in Appendix B. 
6.56

SECTION 7. SUMMARY

This chapter has provided a summary of several potential analytical methods for 

evaluating the stability of bridge systems during construction. In addition to the methods 

of analysis, several modeling considerations were outlined ranging from the necessary 

detail of the models, types of analyses and specific construction stages that might 

critical. Simplified models consisting of line element representations of girders were 

discussed as well as detailed three-dimensional shell element models. The different 

stages that may control the stability of girders during erection were discussed including 

cases during lifting of individual girder segments, partially erected girder systems, and 

critical stages during concrete deck placement. The analytical procedures that were 

discussed in this chapter can be carried out on a variety of software packages that 

commercially available as well as others that are in the public domain.
7.1

CHAPTER 7

DESIGN CRITERIA

SECTION 1. INTRODUCTION

At each stage of the erection of a girder bridge superstructure, both the member loads 

and the available resistances will differ as the configuration changes. Also, at each 

stage the member loads and available resistances will differ from those in the finished 

structure. For example, performance of an individual girder may be controlled by lifting 

conditions, or after placement of the girder but prior to its connection to the adjacent 

girders. Wind effects on an open girder grillage will also differ from those on the 

completed bridge. Criteria for the evaluation of girder-bridge superstructures during 

erection should take into account these varying conditions, and may differ from those 

provided for the finished bridge. In addition, criteria for evaluating members at some 

erection stages, i.e. lifting of girders, is not explicitly addressed in the AASHTO Bridge 

Design Specifications. The supplementary evaluation criteria presented in this chapter 

address conditions that affect the stability and performance of the girder-bridge 

superstructure during erection that are not directly addressed in the AASHTO Bridge 

Design Specifications. Bridge owners may also have provisions covering engineering 

analysis for construction conditions and required submittals. These account for owner 

practices, local load conditions and other factors, and must be adhered to in preparing 

erection analysis and procedures. Appendix D in this Manual provides recommended 

engineering criteria for girder-bridge superstructure evaluation during construction in a 

format suitable for possible inclusion in specifications that might be developed by the 

bridge owner.

The recommended engineering criteria are presented in an LFRD format to be 

consistent with the AASHTO LRFD Bridge Design Specifications (AASHTO 

Specifications). The applicable requirements provided in the AASHTO Specifications 

are not restated; however, relevant evaluation criteria and formulas not included in the 

AASHTO Specifications are presented herein. The recommended engineering criteria 

have been developed assuming that the design engineer and contractor have 

reasonable control over some erection activities, but perhaps less over others. For 

instance, an erection plan may limit lifting and setting of a girder to periods where the 

wind speeds are less than 20 mph. However, once the work for that shift ends, the wind 

speeds to which the partially erected girder is subjected and the scheduling of 

subsequent construction activity may be under the control of Mother Nature rather than 

the contractor. 

The design of bridges is governed by the AASHTO Specifications, whereas the 

AASHTO LRFD Bridge Construction Specifications provides requirements pertaining to 

construction practices. Both Specifications reflect the directive made by the Federal 

Highway Administration (FHWA) that all bridges designed after 2007 use the load and 

resistance factor design, or LRFD, methodology. Various articles of these specifications 
7.2

address matters related to the erection and performance of bridge superstructures 

during construction.

Article 2.5.3 of the AASHTO Specifications notes that constructability issues should 

include, but not be limited to, deflection and stability during critical stages of 

construction. It further requires that where a designer has assumed a particular 

sequence of construction to control dead load stresses, that the sequence be defined in 

the contract documents. For complex bridges, or bridges where an experienced 

contractor would not be expected to be able to predict and estimate a suitable erection 

procedure while bidding the project, at least one feasible method of construction should 

be included in the contract documents. Requirements for temporary bracing or support 

to execute the given erection plan should be included; however, this is generally limited 

to providing loads and recommended locations for the vertical shoring.

Article 3.4.2 of the AASHTO Specifications provides load factors for construction loads 

for use in evaluating structure strength and serviceability. The commentary defines 

construction loads as, “permanent loads and other loads that act on the structure only 

during construction”. The specified load factors, which are intended for use when 

investigating the applicable load combinations in Table 3.4.1-1 during construction, are 

in some cases reduced from those used for permanent loading cases. 

The AASHTO “Guide Design Specifications for Bridge Temporary Works” includes 

provisions for bridge construction loads, deck construction, and design of falsework or 

shoring. This information should be referenced where appropriate in developing erection 

studies and temporary support design. It should be noted, however, that this document 

was developed primarily to address the design of falsework for cast-in-place concrete, 

and does not directly address girder erection issues. 

Concrete girder design is covered under SECTION 5: Concrete Structures of the 

AASHTO Design Specifications. Specific guidance for construction conditions for girder 

bridges is limited. Article 5.5.4.3 – Stability, does state that “Buckling of precast 

members during handling, transportation, and erection should be investigated,” but the 

provision is silent regarding methods to perform the necessary investigations. In 

addition, Article 5.6.1, under Article 5.6 – Design Considerations, requires members and 

connections to be designed to accommodate construction loads. The AASHTO LRFD 

Bridge Construction Specifications provides requirements summarized as follows:

8.13.5 Storage and Handling: Requires precast girder support points to be 

within 2.5 ft. of the location shown in the shop drawings.

8.13.6 Erection: The contractor is responsible for safety of the precast 

members during all construction stages. Members should be 

temporarily braced as required to resist wind or other loads.

8.16.3.2 Design Calculations for Construction Procedures: Requires that 

calculations be prepared by a registered professional engineer for 

falsework, erection devices, or other temporary construction that may 

carry calculated stresses.
7.3

No specific guidance is provided as to what constitutes adequate methodology or 

submittal requirements to satisfy these responsibilities. 

The design of steel structures, including steel girders, is covered in SECTION 6: Steel 

Structures of the AASHTO Specifications. The provisions of Article 6.10: I-Section 

Flexural Members address both straight and curved girders in a consistent manner, and 

include a unified approach for the investigation of the effects of combined major-axis 

bending and flange lateral bending stresses regardless of the source. Attention is called 

to the considerations of flange lateral bending stresses during construction for straight 

girders, as well as flange lateral bending stresses due to curvature in horizontally 

curved bridges, both during construction and in the final structure. Design equations that 

address the nominal flexural resistance of discretely braced compression flanges, a 

common case to be investigated during construction, are provided, which include 

provisions to account for the effects of flange lateral bending due to deck overhang 

bracket loads.

Articles 6.10.3 and 6.11.3 of the AASHTO Design Specifications for steel I-girder and 

box-girder members, respectively, present required design criteria for investigating the 

adequacy of the members during critical stages of construction. Criteria for deck 

placement effects are also provided. Article 6.10.3.1 requires stresses during erection to 

remain below nominal yield levels for all main load-carrying members, and reliance on 

post-buckling resistance is not permitted, except for potential local web yielding in 

hybrid sections. 

Provisions for bracing design are limited. While bracing locations can be determined to 

control flange stresses using the flexure design equations, determining required 

strength and stiffness of the bracing members is addressed only through the 

requirement for a rational analysis. Design of individual bracing members is addressed 

in this Manual, and general guidance on bracing locations and configurations is noted in 

several articles. 

One of the significant changes that was implemented in the AASHTO Design 

Specifications, which dates back to the First Edition (1994) of the specifications, was the 

removal of the maximum 25 foot cross-frame spacing limit for straight steel-girder 

bridges. The cross-frame spacing is now to be based on a “rational analysis”, and the 

tendency is to attempt to minimize the number of cross-frames in order to eliminate 

fatigue prone details and improve economy. Special maximum cross-frame spacing 

requirements remain for curved steel girders. The tendency to reduce the number of 

cross-frames makes proper design checks of the girders and the bracing at critical 

construction stages more important.

Section 11 - Steel Structures of the AASHTO LRFD Bridge Construction Specifications 

requires the contractor to provide calculations verifying erection methods that vary from 

the contract documents, and to be responsible for any temporary bracing or shoring. 

Additional requirements are provided for curved girders. The contractor should provide 
7.4

a construction plan detailing fabrication, erection procedures, and deck placement for 

curved girder bridges based either on the plan shown in the contract documents or the 

contractor’s own plan. The plan, in either event, should “demonstrate the general 

stability of the structure and individual components during each stage of construction” 

and be stamped by a registered Professional Engineer. 

In addition to the AASHTO provisions, several other engineering specifications and 

industry publications provide guidance or design provisions that can be used for 

erection evaluation. The American Institute of Steel Construction (AISC) requirements 

for the design flexural strength of steel I-section members are covered in Chapter F of 

the Specification for Structural Steel Buildings (2010) and includes a design equation to 

determine when lateral-torsional buckling needs to be considered. The available lateraltorsional buckling capacity is determined based on the length of the compression flange 

between brace points, and a moment-gradient modification factor, Cb, to account for the 

beneficial effect of a nonuniform moment between brace locations. This is consistent 

with the AASHTO provisions, which should be used in the erection evaluation of steelgirder bridges in lieu of the AISC provisions. Once the location of brace points is 

determined to provide the required member strength, the bracing can be designed using 

the provisions of Appendix 6 of the AISC Specification. Appendix 6 provides equations 

to determine the required brace strength as well as required stiffness for both lateral 

bracing and torsional bracing. The brace strength and stiffness requirements are 

dependent upon the required flexural strength and the Cb factor (among other inputs). 

Equations are included for both the LRFD and Allowable Strength Design (ASD) load 

combinations. Once the required brace strength and stiffness is determined, member 

design is completed in the standard manner for the member type(s) selected. These 

equations are not currently provided in the AASHTO provisions, but are provided and 

discussed further herein.

The Precast Prestressed Concrete Institute, PCI, provides design, production, and 

installation guidance for a wide range of products, including building components, piling, 

and bridge members. The PCI Bridge Design Manual, Chapter 3 Fabrication and 

Construction, provides general information concerning member lifting, lifting loop 

installation, and girder setting. PCI also produces the “Erector’s Manual: Standards and 

Guidelines for the Erection of Precast Products, MNL-127-99.” Chapter 8, Design 

Theory and Procedure, of the PCI Bridge Design Manual provides methods to calculate 

lateral stability of precast members during transporting, lifting, and placement in Section 

8.10, Lateral Stability of Slender Members.

While the American Concrete Institute’s “Building Code Requirements for Structural 

Concrete and Commentary” (ACI 318) are not written to address concrete bridges, the 

provisions of Appendix D, Anchoring to Concrete, provide design information not in 

AASHTO that may be required in design of the connections for bracing or hold downs to 

concrete during erection. Chapter 10 – Flexure and Axial Loads, limits the unbraced 

length of a girder to 50 times the least width of the compression flange.
7.5

SECTION 2. STRUCTURE ANALYSIS

7.2.1 Member and Component Evaluation

Bridge girders must be designed to provide adequate strength and stability during all 

stages of erection. The loads to which each erection stage is subjected not only differ 

from those used for the design of the finished structure, but generally also vary with the 

particular erection stage. For many simple structural systems, the erector or their 

engineer can justify the erection procedures by judgment or documented experience on 

bridges of similar span, slenderness, lateral stiffness, and bracing configuration. The 

justification of these erection procedures can be made through hand-calculations, an 

eigenvalue buckling analysis, and comparisons with previous erection procedures on 

similar structural systems. However, in cases where significant uncertainty exists in the 

system stability as a result of procedures or geometrical conditions, a global stability 

analysis that considers the impact of deformations on the geometry of the system 

should be conducted to verify adequate stability for the erection scheme and 

appropriate load conditions. Girder design must be based on the most critical 

conditions, and these may not be the same for every girder in a system. Similarly, 

calculated loads used to size cranes, and design shoring systems and bracing must 

represent the most severe load conditions. In addition:

• All members should be shipped, lifted, supported, connected, and braced in such 

a way that no limit states are violated at any time and damage such as yielding, 

buckling and concrete cracking is avoided. Stability includes local, member, 

global and rigid body (rollover) stability.

• Analysis methods used should be sufficiently refined to evaluate the limit states 

of concern for each stage of girder erection. For setting of a single girder, a line 

girder analysis may be satisfactory; however, refined grid or 3D analysis methods 

are necessary for girder systems unless it is determined that girder interaction 

effects can safely be neglected.

• The boundary conditions assumed used in the analysis model should be 

representative of those specified in the erection plans, and provided in the field. 

• The boundary conditions should recognize the absence of any vertical restraint in 

the investigation of uplift scenarios. 

• Nominal yielding or reliance on post-buckling resistance should not be permitted 

for main steel load-carrying members for all construction conditions, except for 

potential local yielding of the web in hybrid sections.

7.2.2 Critical Erection Stages

The erection plan and supporting engineering calculations must address both strength 

and stability at each stage of erection. Deformations associated with each stage should 

also be evaluated. Critical erection stages for the girder bridge structure during 

construction normally consist of at least the following:
7.6

• Lifting of girders/members

• Placement of the initial girder and any associated temporary bracing used to hold 

the girder in place

• First pair of girders set with permanent bracing installed

• All girders and bracing installed prior to the deck placement

• All girders and bracing installed during the deck placement 

• Application of the deck overhang bracket loads to the fascia girders during the 

deck placement

The last two stages shown above are evaluated by the Engineer of Record; however, if 

the deck placement sequence changes from that shown in the contract documents, 

these stages must be re-evaluated. Each of these conditions for the partially completed 

structure is accompanied by differing loading. Primary loads include structure and deck 

concrete self-weight (dead load), wind load, construction loads from formwork, 

materials, workers and concrete-placing equipment.

7.2.3 Analytical Modeling

The selection of an analytical model and analysis method must consider the type of 

information required in subsequent analyses of the structural components. To 

investigate a single girder placed into position, a line girder analysis may be readily 

used with the girder dead load acting vertically and wind acting laterally on the girder 

face. As additional girders are set, the load distribution becomes affected by the 

stiffness contributed to the system by diaphragms or cross-frames, the effects of which 

are not accounted for in a line-girder analysis. For curved or skewed bridges, these 

effects are of increased importance, though they can have effects even on parallel 

girder spans, particularly as skews increase (Fisher 2006).

The stability issues that often occur with concrete systems are primarily related to roll 

stability. Many solutions for evaluating roll stability are based upon simple free-body 

diagrams and are discussed in Sections 5-7 and 7-7.2.

A two-dimensional (2D) grid analysis (also referred to as a grillage analysis) is a finite 

element application that models the structure as a grid of elements and is often used in 

bridge design. The AASHTO Specification provides some guidance on the use of 2D 

grillage models in Chapter 4, Structural Analysis and Evaluation. Two-dimensional 

beam elements capture flexure, shear, and Saint Venant torsion effects, but do not 

normally model flange bending (warping) stresses, which are important for curved girder 

analyses. The cross-frames or diaphragms in 2D grid analyses are modeled as line 

elements, requiring the designer to input appropriate stiffness properties based on the 

diaphragm or cross-frame configuration. One approach is to model the equivalent 

flexural stiffness of the cross-frame separately, by applying a unit force couple to one 

end, calculating the resulting deflection, and computing the end rotation. This rotation is 
7.7

then applied to a propped cantilever beam with length equal to the cross-frame width, 

so that the associated moment of inertia for the propped cantilever can be back 

calculated and used as the line element stiffness for the cross-frame. 

Another approach is to compute the shear stiffness of the cross-frame due to a unit 

vertical deflection, and utilize this as the cross-frame stiffness for the line element. The 

cross-frame support conditions assumed in the above models can provide additional 

variations to the modeling, with each model providing different results. Both the flexural 

and shear stiffness of the brace influence a bridge’s behavior. Differential girder 

deflections are predominately affected by cross-frame shear stiffness, while rotation of 

the girders is more likely to be affected by the flexural stiffness. Running several 

analyses using varying cross-frame stiffness values can provide a means to determine 

the structure’s sensitivity to the stiffness variations and provide a range of values for 

design. 

White et al. (2012) as part of their work under the National Cooperation Highway Research 

Project 725, provided recommendations for improved modeling techniques in 2D analysis. The 

use of a shear-deformable (Timoshenko) beam element improves the accuracy of the 2D-grid 

analysis method. This approach involves calculation of both an equivalent moment of inertia 

along with an equivalent shear area. Guidance on appropriate calculation methods is provided 

in the National Steel Bridge Alliance publication “G13.1 Guidelines for Steel Girder Bridge 

Analysis” (2014).

Three-dimensional finite element analyses (3D-FEM) use a computerized structural 

analysis model of the structure in three dimensions. Various software packages 

possess the ability to model the bridge components with a variety of different element 

types. The girder flanges and webs, bracing members, and deck can be modeled with a 

wide array of element configurations including line/beam elements, plate/shell elements, 

truss elements, solid elements, etc. as appropriate. Three-dimensional FEM is 

considered the most “precise” method for analysis; however, structure modeling and 

subsequent output analysis requires more time than with other analysis techniques. In 

addition, although these modeling concepts are perceived to be the “most accurate”, the 

actual accuracy is contingent on a number of key factors. Users of 3D-FEM computer 

programs must understand the element formulations and results can be sensitive to 

proper modeling and input. 

Advantages of the 3D-FEM include output that provides translation and rotation at each 

node in the structural model. This allows determination of member deflections and 

rotations both vertically and laterally at discrete points along the length of the girder 

flanges and webs. The three-dimensional model has the capability of modeling the 

flexibility in the web and flanges that can therefore capture local effects on the crosssection. The solution results from such a model have the ability to better predict 

potential erection stability issues or other significant problems compared to simple 

models. Bracing forces and deformations can be directly obtained from the analysis.
7.8

Analysis of models for erection typically do not consider composite action or live loads. As a 

result, the load modeling and the extraction of moments and shears is less complicated than 

that for “full design” in 3D.

Advances in computer capabilities and software development have made the use of 3DFEM analysis more wide spread. The use of the software packages for the erection 

analysis of complex straight and curved girder bridges can avoid problematic situations 

that result in unsafe conditions or expensive field solutions. 

7.2.3.1 Selection of Analysis Methods for Steel I-Girder Bridges 

Part of the work completed under the National Cooperative Highway Research Project 

(NCHRP 725) ( NCHRP, 2012), was a comparative study of the analysis results for 

curved, skewed, and curved bridges with skew obtained from different bridge structural 

analysis methods to those obtained from a detailed 3D finite element solution, deemed 

to provide the “correct” results. A review of a large data base of bridges resulted in an 

overview of the accuracy of the various methods of analysis. Based upon the results, 

limitations of the methods were identified and recommendations for the usage of 

simplified grid models were developed. 

This information was then assembled into a matrix to aid in the selection of an 

appropriate approximate method of analysis of for I-girder bridges, and tub-girder 

bridges. 

The results indicate that traditional 2D-grid and 1D-line girder analysis methods predict 

major-axis bending stresses and vertical deflections within 20% accuracy for I-girder 

bridges, except for girders with small radii of curvature. While both methods were able 

to compute cross-frame stresses and flange lateral bending stresses for curved girders 

within 7% - 20% accuracy, they were not able to determine these forces for skewed 

bridges. Complete details are available in the NCHRP 725 Report. 

Figure 7-1 summarizes the results for the various methods and responses monitored for 

I-girder bridges. Figure 7-1 can be used to assess when a certain analysis method can 

be expected to give acceptable results. The grading rubric used to assign the letter 

“grades” to each method for the required analysis output data was as follows: 

• A grade of ‘A’ is assigned when the normalized mean error is less than or equal 

to 6%, reflecting excellent accuracy of the analysis predictions. 

• A grade of ‘B’ is assigned when the normalized mean error is between 7% and 

12%, reflecting a case where the analysis predictions are in “reasonable 

agreement” with the benchmark analysis results.

• A grade of ‘C’ is assigned when the normalized mean error is between 13% and 

20%, reflecting a case where the analysis predictions start to deviate 

“significantly” from the benchmark analysis results. 
7.9

• A grade of ‘D’ is assigned when the normalized mean error is between 21% and 

30%, indicating a case where the analysis predictions are poor, but may be 

considered acceptable in some cases. 

• A score of ‘F’ is assigned if the normalized mean errors are above the 30% limit. 

At this level of deviation from the benchmark analysis results, the subject 

approximate analysis method is considered unreliable and inadequate for design. 

Figure 7-1 Matrix for Recommended Level of Analysis – I-Girder Bridges

Information on the development of the grading system and the methodology of 

determining the normalized mean error can be found in the NCHRP 12-79 Report.

In Figure 7-1, scoring for the various measured responses is subdivided into six 

categories based on the bridge geometry. These categories are defined as follows: 

• Curved bridges with no skew are identified in the Geometry column by the letter 

“C.” 
7.10

• The curved bridges are further divided into two sub-categories, based on the 

connectivity index, defined as: 

Equation 7-1 

Where: 

R = the minimum radius of curvature at the centerline of the bridge crosssection throughout the length of the bridge (ft)

ncf = the number of intermediate cross-frames in the span

m = a constant taken equal to 1 for simple-span bridges and 2 for continuousspan bridges

In bridges with multiple spans, IC is taken as the largest value obtained from any of the 

spans. 

• Straight skewed bridges are identified in the Geometry column by the letter “S.” 

• The straight skewed bridges are further divided into three sub-categories, based 

on the skew index: 

Equation 7-2 

Where:

wg = the width of the bridge measured between fascia girders (ft)

θ = the skew angle measured from a line perpendicular to the tangent of the 

bridge centerline (degrees)

Ls = the span length at the bridge centerline (ft)

In bridges with unequal skew of their bearing lines, θ is taken as the angle of the 

bearing line with the largest skew. Bridges that are both curved and skewed are 

identified in the Geometry column by the letters “C&S.”

Two letter grades are indicated for each of the cells In Figure 7-1. The first grade 

corresponds to the worst-case results encountered for the bridges studied by NCHRP 

Project 12-79 within the specified category. The second grade indicates the mode of the 

letter grades for that category, i.e., the letter grade encountered most often for that 

category. It is useful to understand the qualifier indicated on the “C&S” bridges, i.e., “(IC

> 0.5 & IS > 0.1)” in Figure 7-1. If a bridge has an IC < 0.5 and an IS > 0.1, it can be 

considered as a straight-skewed bridge for the purposes of assessing the expected 

analysis accuracy. Furthermore, if a bridge has an IC > 0.5 and an IS < 0.1, it can be 

considered as a curved radially-supported bridge for these purposes.
7.11

7.2.3.2 Selection of Analysis Methods for Steel Tub-Girder Bridges

Similar to the matrix developed for I-girder bridges, NCHRP 725 developed a matrix to 

aid in the selection of an appropriate approximate method of analysis for tub-girder 

bridges, Figure 7-2. 

Figure 7-2 Matrix 1 for Recommended Level of Analysis – Tub-Girder 

Bridges

Figure 7-2 scores for the major-axis bending stresses and vertical displacements are 

relatively good for all analysis methods. However, the worst-case scores for the internal 

torques are generally quite low. These low scores are largely due to the fact that the 

internal torques in tub-girder bridges can be sensitive to various details of the framing, 

such as the use and location of external intermediate cross-frames or diaphragms, the 

relative flexibility of these diaphragms as well as the adjacent internal cross-frames 

within the tub-girders, skewed interior piers without external cross-frames between the 

piers at the corresponding bearing line, incidental torques introduced into the girders 

due to the specific orientation of the top flange lateral bracing system members 

(particularly for Pratt-type TFLB systems), etc. 

Similar to the considerations for I-girder bridges, the external diaphragms and/or crossframes typically respond relatively rigidly in their own plane compared to the torsional 

stiffness of the girders (even though the torsional stiffness of tub-girders is generally 
7.12

significantly large with respect to comparable I-girders). Therefore, the girder layovers at 

skewed bearing lines tend to be proportional to the major-axis bending rotation of the 

girders at these locations. As a result, the errors in the girder layover calculations 

obtained from the approximate methods tend to be similar to the errors in the major-axis 

bending displacements.

The connectivity index, IC, does not apply to tub-girder bridges. This index is primarily a 

measure of the loss of accuracy in I-girder bridges due to the poor modeling of the Igirder torsion properties. For tub-girder bridges, the conventional Saint Venant torsion 

model generally works well as a characterization of the response of the pseudo-closed 

section tub-girders. Hence, IC is not used for characterization of tub-girder bridges in 

Figure 7-2. Furthermore, there is only a weak correlation between the accuracy of the 

simplified analysis calculations and the skew index Is for tub-girder bridges. Therefore, 

the skew index is not used to characterize tub-girder bridges in Figure 7-2 either. 

Important differences in the simplified analysis predictions do exist, however, as a 

function of whether the bridge is curved, “C,” straight and skewed, “S,” or curved and 

skewed “C&S.” Therefore, these characterizations are shown in the table. 

A discussion of the specific characteristics of the 2D – Program 1 computer program 

showing the tables can be found in the NCHRP 725 Report.

In addition to the above assessments, the accuracy of the bracing component force 

calculations in tub-girder bridges is assessed separately in Figure 7-3. It is useful to 

address the accuracy of these response calculations separately from the ones shown in 

Figure 7-2, since the simplified bracing component force calculations take the girder 

major-axis bending moments, torques, and applied transverse loads as inputs and then 

apply various useful mechanics of 51 material approximations to obtain the force 

estimates. That is, there are two distinct sources of error in the bracing component 

forces relative to the 3D FEA benchmark solutions: 

7. The error in the calculation of the input quantities obtained from the 1D line-girder 

or 2D-grid analysis, and 

8. The error introduced by approximations in the bracing component force 

equations. 

Chapter 2 of the NCHRP 12-79 Task 8 report provides an overview of the bracing 

component force equations evaluated here, which are used frequently in current 

professional practice. It should be noted that the calculation of the top flange lateral 

bending stresses in tub-girders is included with the bracing component force 

calculations. This is because these stresses are influenced significantly by the 

interaction of the top flanges with the tub-girder bracing systems.

The NCHRP 725 research observed that in many situations, the bracing component 

force estimates are conservative relative to the 3D FEA benchmark solutions. 

Therefore, it is useful to consider a signed error measure for the bracing component 

force calculations. In addition, the bracing component dimensions and section sizes 

often are repeated to a substantial degree throughout a tub-girder bridge for the 

different types of components. Therefore, it is useful to quantify the analysis error as the 
7.13

difference between the maximum of the component forces determined by the 

approximate analysis minus the corresponding estimate from the 3D FEA benchmark, 

i.e.:

max ( max max ) max / approx FEA FEA eR R R = −

for a given type of component. The grades for these responses were assigned based on 

the same scoring system used for the assessments based on the normalized mean 

error with one exception: Separate grades were assigned for the positive (conservative) 

errors and for the negative (unconservative) errors in Figure 7-3. In situations where no 

negative (unconservative) errors were observed in all of the bridges considered in a 

given category, the symbol “--” is shown in the cells of the matrix and the cells are 

unshaded.

The mode of the grades is shown only for the top flange diagonal bracing forces in 

Figure 7-3. The mode of the grades for the other component force types are not shown 

because of substantial positive and negative errors in the calculations that were 

encountered in general for the tub-girder bridges, and because, in cases where a clear 

mode for the grades existed, the mode of the grades was the same as the worst-case 

grade.

In addition to the above considerations, it should be noted that current simplified 

estimates of the tub-girder bridge bracing component forces are generally less accurate 

for bridges with Pratt-type top flange lateral bracing (TFLB) systems compared to 

Warren-and X-type systems. A small number of tub-girder bridges with Pratt-type TFLB 

systems were considered in the NCHRP 725 research. Therefore, the composite scores 

for these bridges are reported separately in Figure 7-3.

Equation 7-3
7.14

Figure 7-3 Matrix 2 for Recommended Level of Analysis – Tub-Girder 

Bridges
7.15

7.2.4 General Girder Proportions

7.2.4.1 Steel I-Girders

The flange width provides a significant contribution to the warping stiffness, and hence 

torsional stiffness, of I-girders, which is particularly important during construction of the 

bridge superstructure. Article 6.10.2.2 of the AASHTO Design Specifications, limits the 

flange width, bf, for steel I-girders to a minimum of one-sixth of the girder depth, D (bf ≥ 

D/6). Owners may have more stringent requirements; for instance, the Texas 

Department of Transportation limits flange widths to bf ≥ D/4 for straight girders and bf ≥ 

D/3 for curved girders. Work by Stith, Petruzzi, et.al, 2010, showed that limiting the bf/D 

ratio to a minimum of 1⁄4 significantly reduces second-order effects in curved girders. For 

these cases, it was shown that cross-frame forces due to curvature could usually be 

well predicted by a first-order structural analysis. 

A minimum flange width is generally sought by designers though for reasons of 

materials costs in the finished structure. Girder dimensions are determined in 

accordance with AASHTO and Owner requirements by the design Engineer of Record 

and are provided in the contract drawings. Thus, it is highly unlikely that any of these 

dimensions are subject to change based on the erection engineer’s evaluation.

7.2.4.2 Steel Box-Girders

Article 6.11.2 of the AASHTO Design Specification, provides limits for web and flange 

proportions for steel box-girders. These limit the web thickness of unstiffened webs to 

the web depth divided by 150, and to the web depth divided by 300 if the web has 

longitudinal stiffeners. The requirements for top flanges of box sections are the same as 

for the top flange of I-sections: 

bf / 2tf ≤ 12

bf ≥ D/6

tf ≥ 1.1tw 

Where:

bf = flange width (in)

tf = flange thickness (in)

D = girder depth (in)

tw = web thickness (in)

The National Steel Bridge Alliance, “Practical Steel Tub Girder Design” recommends 

that girder webs be at least 5 ft. high, with typical span-to-girder depth ratios between 

25 to 35. The maximum width/thickness (bf/tf) ratio of bottom flanges in compression is 

60, and longitudinal stiffeners are typically required when the bf/tf ratio exceeds 45. A 

minimum bottom flange thickness of 0.5 in. is recommended for tension zones, with 

minimum bf/tf ratios in the range of 80 to 120. The Texas Department of Transportation, 
7.16

as an example, limits the bf/tf for the bottom flange to 80, with a minimum plate 

thickness of 0.75 in.

7.2.4.3 Steel I-Girder Erection Conditions

The use of the ratio of the girder length to flange width (L/bf) to judge stability of a steel 

girder during erection has a long and generally successful history. The limit of L/bf less 

than 85 appears in U.S. Steel erection manuals for straight girders. While erectors use 

various limits, they generally range as follows (Zhao, Yu, Burdette, 2010):

• Less than 60, girder will be stable

• 60-80, girder should be checked by calculation 

• Over 80, temporary shoring will be required

• Use one-half of limits for cantilevers

Based on the work of Zhao, et. al (2009), when the L/bf limits for cantilever beams are 

below 30, stability will be satisfactory, while values over 60 require temporary support. 

For values between these limits, calculations should be performed. Similar values for 

simply supported beams were 45 and 85. Clearly, these are large ranges, and such 

rules-of-thumb should be used only as rough guidelines. 

7.2.5 General Concrete Girder Proportions

Article 5.14.1.2 of the AASHTO Design Specifications provides minimum thicknesses 

for precast concrete beams as follows:

Top flange 2 inches

Web 5 inches

Web (post tensioned) 6.5 inches

Bottom flange 5 inches

The bottom flange minimum thickness primarily relates to box-type sections. Actual 

dimensions are established by flexural design efficiency and durability considerations. A 

review of standard AASHTO girder sections indicates that actual thicknesses, 

particularly for flanges, exceed the minimum. As noted previously, the resulting girder 

cross-sections normally possess large torsional stiffness such that roll stability, rather 

than lateral-torsional buckling, governs erection stability design.

SECTION 3. LOAD COMBINATIONS AND LOAD FACTORS

Article 3.4.2.1 of the AASHTO Design Specifications provides load factors and 

combinations for strength load combinations to be used for construction loading cases. 

The totaled factored force effect at each stage of construction should be taken as:
7.17

 

Where:

Q = Total factored force effect

γi = Load factors specified in Table 7-5

Qi = Force effects from loads during construction specified herein

For the cases of construction dead load, live load and wind load, the AASHTO load 

factors provided in Article 3.4.2.1 are similar to those presented in ASCE 37-0 2 for 

structures under construction. Recommended load factors and combinations for 

evaluating structures during erection, based on the provisions of Article 3.4.2.1, are 

given in Table 7-1.

DC CDL CLL(d) CW

Strength I 1.25 1.50 1.50 — 

Strength III 1.25 1.25 — 1.0(b)

Strength VI(a) 1.40 1.40 1.40 — 

Service 1.00 1.00 1.00 0.7(b)

Uplift (c) 0.90/1.35 0.90/1.35 — 1.0(b)

Table 7-4 Load Factors and Load Combinations

The Strength VI load case is only used to verify the strength and stability of the 

completed steel superstructure under the loads from deck placement. Due to normal 

construction practices and common limits on wind during deck concrete-placement due 

to drying shrinkage concerns, wind load is not included in Strength VI. The intermediate 

stages of steel erection may be evaluated from the Strength I or Strength III load 

combinations. The use of the 1.25 load factor on DC in these load combinations 

recognizes that steel self-weight, taken from shop drawings, is known with a high 

Equation 7-4 

a) Steel structures only for the case of placing deck on completed steel. Use Strength 

I or III for intermediate steel conditions.

b) The specified load factor of 1.0 for wind load force effects is based on basic wind 

speed maps wherein the load factor of 1.4 is built into the maps to increase the 

applied wind speed to the acceptable risk recurrence level. Wind loads may be 

computed using a wind velocity based on the Wind Velocity Modification Factor 

specified in Table 7-2 for the construction phase duration under investigation.

Note that the wind load factor is less than 1.0 for the service load combination.

c) Where a construction load produces uplift at the location being investigated, the 

maximum load factor should be applied to the load effect and where the load 

resists uplift, the load effect should be multiplied by the smaller load factor.

d) Include dynamic load allowance if applicable.
7.18

degree of accuracy, while the 1.4 load factor in Strength VI accounts for variability in 

how the deck concrete is placed (i.e., mounding of concrete, vertical drop dynamic 

effects, etc.).

The resistance, or phi ( ), factors utilized for the evaluation should conform to the 

AASHTO Design Specifications for steel and concrete as appropriate. Additional 

resistance factors for equations presented in this Manual are as follows:

, resistance factor for lateral-torsional buckling = 0.90

, resistance factor for steel girder bracing stiffness = 0.75

, resistance factor for girder system buckling = 0.90

Safety factors on lifting accessories, jacks, and other manufactured items shall be in 

accordance with manufacturer’s recommendations.

SECTION 4. LOADS

7.4.1 Material Weights

In the absence of more precise information, material unit weights used in the 

computation of permanent dead loads may be taken from Table 3.5.1-1 of the AASHTO 

Design Specifications. The weight of steel members should be computed using a unit 

weight for steel of 490 pounds per cubic foot. The weight of cast-in-place concrete 

should be computed based on an in-place unit weight of 150 pounds per cubic foot (pcf) 

for normal weight concrete and 125 pcf for structural lightweight concrete, unless mixspecific data is available. The above unit weights for concrete include the weight of 

prestressing steel and reinforcing steel, assumed as 5 pcf. For high strength concretes 

or heavily reinforced members, member weight calculation in accordance with AASHTO 

Table 3.5.1-1 is recommended.

7.4.2 Permanent Dead Load (DC)

Permanent dead load includes the weight of the partially completed structure, including 

the weight of the deck concrete during placement and any stay-in-place forms. Dead 

loads of the girders, framing, and deck, should be computed from design plans or shop 

fabrication drawings (when available). As a result, the dead loads and their distributions 

along the span may be expected to be accurate. Material unit weights used in 

computing dead loads should be in accordance with AASHTO Design Specifications, as 

discussed above. The weight of stiffeners, splices, studs, bolts, paint and other 

miscellaneous items may be taken as an equivalent uniformly distributed weight along 

the girder, or accounted for using an increased material density. However, when large 

field splice components are present at the end of cantilever segments during erection, 
7.19

including the concentrated load effect may be warranted. The weight of stay-in-place 

corrugated metal deck formwork may be taken as 20 pounds per square foot, including 

the weight of concrete in the flutes. Where stay-in-place precast concrete deck forms 

are used, the weight should be computed from formwork drawings.

7.4.3 Construction Dead Load (CDL) 

Construction dead load should include the weight of removable formwork and any

shielding or work platforms that are only on the bridge during construction. The weight 

of formwork is normally taken at 10 pounds per square foot (psf) for wood or metal deck 

forms to account for material weight plus miscellaneous fillers, connectors, etc. 

Cantilever formwork, including walkway and railing, may weigh in the 15 to 20 psf 

range. A project specific value may be calculated as well. 

7.4.3.1 Construction Live Load (CLL) 

Construction live loads include the weight of workers, miscellaneous tools and supplies, 

materials and equipment that are only on the bridge during construction. A minimum 

uniform live load of 20 psf should be applied to the deck area to account for workers 

and miscellaneous light tools, etc. A 75 pound per linear foot (plf) live load should be 

applied along the outside edge of bridge deck overhangs. The construction live load 

should also include the actual weight of any equipment or materials loads, applied as a 

concentrated or locally uniform load to the appropriate location on the deck. 

Equipment reactions should include the full weight of any equipment based on its 

maximum operating weight unless specific means are in place to ensure a reduced 

loading. Loads should be calculated based on data obtained from the equipment 

manufacturer or supplier for the specific equipment to be utilized. 

Equipment, other than concrete-placing/finishing equipment, commonly termed a 

Bidwell® or Gomaco® machine, is not normally present on new bridge decks during 

construction, however in some cases other equipment may be present. When concrete 

is placed using motorized buggies, an additional 25 psf construction uniform live load 

should be applied to account for their use. If concrete is to be placed using a conveyor 

system as shown in Figure 7-4 the support reactions should be treated as equipment 

loads. In Figure 7-4, the conveyors for concrete delivery are shown on each side of the 

deck. 

Jacks or jacking systems may be used during erection operations to allow adjustments 

in elevation, or to shift members laterally. Jacking force effects should be based upon 

the maximum jack capacities unless positive means are provided to limit the applied 

jacking forces. Safety factors on jack capacity should follow manufacturer’s 

recommendations.
7.20

When bridges are being demolished or rehabilitated, loads from construction equipment 

may be present on portions of a bridge adjacent to areas of removed deck or in other 

locations that can produce adverse effects on member stability. In these cases, the 

actual equipment loads and their locations, including moving load effects, should be 

used in evaluating the adequacy of the structure at the various stages of construction. 

Figure 7-4 Concrete-placing and Finishing Equipment on Bridge Deck

7.4.3.2 Dynamic Load Allowance

Dynamic load allowance, or impact, should be applied to equipment loads to account for 

effects of equipment moving on the structure as well as operating effects when 

stationary. The dynamic load allowance for operating equipment should be as 

recommended by the equipment manufacturer; however, a minimum dynamic load 

allowance of 0.10 of the equipment weight for equipment that can move on the 

structure, and 0.10 of the operating load for equipment when stationary should be used. 

Since equipment moving atop the structure does so at a very slow speed, a dynamic 

load allowance less than used for normal bridge traffic can be appropriate. Dynamic 

load allowance is typically not applied to the loads from the deck concreteplacing/finishing machine.
7.21

A dynamic load allowance is also not normally applied to a crane’s lifted load. This is 

consistent with crane design and reflects the controlled procedures for lifting as well as 

the crane operational characteristics. When crane lifts involve removal of existing 

members, the calculated lifted load should include the member weight and rigging plus 

the addition of a minimum dynamic load allowance equal to twenty percent of the 

calculated member weight. This is added to account for lifting resistance due to 

interaction with other members, miscellaneous debris on the member, etc.

In investigating construction load effects for concrete segmental bridges, Article 5.14.2.3 

of the AASHTO Design Specifications specifies a dynamic load allowance to account for 

the effect of accidental release of a precast segment or “sudden application of an 

otherwise static load...” The dynamic load allowance is specified as 100 percent of the 

segment dead load, to be added to the dead load of the segment. While this load 

condition is for segmental construction, similar dynamic effects might be applicable to 

specialized girder bridge lifting configurations using cables or winches or similar 

arrangements.

During bridge demolition or reconstruction, heavy equipment such as hydraulic concrete 

breakers, end loaders, trucks, etc. may operate from portions of the structure. In these 

cases, the dynamic load effects should be as recommended by the equipment 

suppliers, but not be less than the vehicle’s dynamic load allowance computed from the 

AASHTO Specifications.

7.4.3.3 Incidental Loads 

During superstructure erection, incidental loads may affect the stability of the members. 

As an example, a crane hook or lifted load might bump a member previously placed, or 

equipment operating beneath previously placed girders may accidentally strike a 

member. While these loads are not definable, consideration should be given to such 

accidental occurrences. It is recommended that bridge girders be designed to resist a 

minimum lateral load, (5 psf is suggested herein), to account for these possibilities. 

Some owners may require design for higher minimum lateral loads. This load should be 

applied to the vertical face area of the girder at the centroid of the loaded area.

7.4.4 Wind Load (Cw) 

Article 3.8.1 of the AASHTO Design Specifications provides wind loads applicable to the 

design of the finished bridge structure. The minimum total wind load on the windward 

beam or girder is given as 300 plf of span and is applied to the girders with the deck in 

place. However, until the deck is placed, the girders form an open system that may 

behave differently under wind load than the finished structure.

Though not stated explicitly, it may be inferred that the specified load on the permanent 

structure is based on a wind speed recurrence interval of 50 years, or longer. Since the 

construction duration for a bridge superstructure is much less than this, it is reasonable 
7.22

to base the construction period wind speed on some lesser recurrence interval, resulting 

in a reduced design wind speed. 

During the actual lifting and setting of girders and other members, wind speeds will 

seldom exceed 20 mph due to girder positioning and fit-up difficulties as well as safety 

considerations. Permissible crane operating loads are typically reduced for wind speeds 

exceeding 15 to 20 mph. Manitowoc® Crane Manufacture’s lifting charts for their crane 

models 888 and 2250, as examples, prohibit even reduced operations for wind speeds 

above 35 mph. Based on these considerations, a one-day duration wind speed of 20 

mph can be used to assess girder stability up to the time that construction operations 

cease for the shift or the day, provided that the wind velocity limits are included as part 

of the erection procedures. 

When investigating the girders in their final erected condition for the loads due to deck 

placement, the wind load may be neglected. While restrictions on equipment operation 

and worker safety would preclude placement in winds exceeding perhaps 20 to 25 miles 

per hour, restrictions on wind speed to preclude rapid water loss from the concrete deck 

(associated with deck cracking) limit winds to much less than even these values. The 

strength gain of the deck concrete is such that even if stronger winds should occur only 

a few hours after deck casting, the deck will have gained adequate strength to provide 

lateral bracing to the girders.

Where reduced wind speeds are used in design, provisions must be made to address 

any unanticipated high wind events due to sudden storms. These provisions need to 

recognize that the erection contractor may only have control of the project site for 

limited time periods, and hence coordination with the general contractor is necessary to 

assure that someone will be available at all times should supplementary bracing be 

required on short notice. The erection plans must clearly state the design wind loads 

associated with each stage of erection and provide provisions for any supplementary 

bracing.

Wind speed maps used by ASCE 7-10 Minimum Design Loads for Buildings and Other 

Structures to compute wind pressures are based on a 3-second gust wind speed 

measured at 33 feet above grade. When comparing wind speeds from weather 

forecasts to those used for design, the sampling periods used in the predictions must be 

known so the forecast, or reported, wind speed can be adjusted to be consistent with 

the design basis wind. ASCE 37-02 Design Loads on Structures during Construction, 

notes that to convert fastest-mile or 1-minute average wind speeds to 3-second gust 

speeds, the speed must be multiplied by 1.25, and to convert mean-hourly speeds to 3-

second gust speeds, the speed must be multiplied by 1.55.

It is recommended that wind pressures and loads for superstructure erection stages be 

calculated in accordance with the provisions of Chapter 29, Wind Loads on other 

Structures and Building Appurtenances MWFRS of ASCE 7-10 Minimum Design Loads 

for Building and Other Structures, as modified herein. The wind velocity for the required 

Risk Category should be used along with the appropriate Velocity Modification Factor 
7.23

from Table 7-4 to calculate the design velocity pressure. The Velocity Modification 

Factors in Table 7-4 are similar to those contained in ASCE 37-02, but have been 

computed to account for the changes in the wind provisions of ASCE 7-10. The 

recalculation reflects the fact that the wind velocity maps of ASCE 7-10 now directly 

include the Importance Factor and Wind Load Factor, which previously were separately 

applied to the wind velocity obtained from the wind maps.

Construction Duration Velocity Modification Factor (Vm) 

0 – 6 weeks 0.65

6 weeks – 1 year 0.75

1 year – 2 years 0.80

2 years – 5 years 0.85

Table 7-5 Wind Velocity Modification Factors

Wind velocity should be adjusted for height effects based on the top of bridge elevation, 

including superelevation, above grade. Table 7-3 provides height effect adjustments to 

the velocity pressure for various Exposure Categories.

Based on Table 1.5-1, ”Risk Category of Buildings and Other Structures for Flood, 

Winds, Snow, Earthquake, and Ice Loads,” of ASCE 7-10, a Risk Category of II should 

be used for bridge structures during erection, unless otherwise required by the bridge 

Owner. Circumstances for which the engineer or owner may consider a higher risk 

category include construction immediately adjacent to essential facilities in which an 

erection failure could imperil facility operation or occupant safety. For a Risk Category 

other than II, the appropriate wind speed maps of ASCE 7-10 should be used, in lieu of 

Figures 7-5 and 7-6.

The design wind load, Cw, should be determined from the following formula:

Where:

qz = Velocity pressure at height z above grade (psf) (see Equation 7- 7-6)

G = gust effect factor, use 0.85

Cf = net force coefficient (Tables 7-4, 7-5)

Af = exposed projected area of girder or truss (ft2

) 

The effects of superelevation and horizontal curvature are to be considered in 

determining the exposed projected area. Velocity pressure, qz, in psf evaluated at height 

‘z’ should be calculated from the following equation:

 

Equation 7-5 

Equation 7-6 
7.24

Where:

Kz = velocity pressure exposure coefficient (from Table 7-5) 

Kzt = topographic factor, use 1.0 

Kd = wind directionality factor, use 0.85

V = basic wind speed (Figures 7-5, 7-6) (mph)

Vm = wind velocity modification factor (Table 7-2)

z = height of top of bridge deck above grade / water (ft)

Basic wind speed, V, should be taken from Figure 7-5 and Figure 7-6, Basic Wind 

Speeds, which give Risk Category II wind speeds, and then be adjusted for the 

construction duration period in accordance with the Wind Velocity Modification Factors 

from Table 7-2. The wind velocity for a single work shift, or multiple shifts not exceeding 

one day should not be taken as less than 20 mph, except for deck placement where 

wind may be neglected.

In determining the design wind speed and selecting a velocity modification factor, both 

local site conditions and seasonal weather variations should be considered. For 

instance, when it can be ensured that erection will not take place during hurricane 

season, a basic wind speed reflecting this condition may be considered. Local 

conditions, perhaps erection within a canyon, where high winds might develop rapidly, 

must also be considered based on local experience.

The velocity pressure exposure coefficient, Kz, is a function of the ground surface 

roughness and height above grade and should be determined from Table 7-5. 

For each wind direction considered, the upwind exposure should be based on ground 

surface roughness that is determined from natural topography, vegetation, and 

constructed facilities. For bridge girder evaluation during erection, only the wind 

direction perpendicular to the girder is normally evaluated. A ground surface roughness 

category should be determined for a distance upwind of the site, and should be used to 

establish the exposure category.

Surface Roughnesses are defined as follows:

Surface Roughness B: Urban and suburban areas, wooded areas, or other terrain with 

numerous closely spaced obstructions having the size of single-family dwellings or 

larger.

Surface Roughness C: Open terrain with scattered obstructions having heights 

generally less than 30 ft. This category includes flat open country and grasslands.

Surface Roughness D: Flat, unobstructed areas and water surfaces. This category 

includes smooth mud flats, salt flats, and unbroken ice.
7.25

Figure 7-5 Basic Wind Speeds (with permission from ASCE)
7.26

Figure 7-6 Basic Wind Speeds (cont.) (with permission from ASCE)

Notes: 

1. Values are nominal design 3-second gust wind speeds in miles per hour (mph) at 33 ft. 

(10 m) above ground for Exposure C category.

2. Linear interpolation between contours is permitted.

3. Islands and coastal areas outside the last contour should use the last wind speed 

contour of the coastal area.

4. Mountainous terrain, gorges, ocean promontories, and special wind regions should be 

examined for unusual wind conditions.

5. Wind speeds correspond to approximately a 7% probability of exceedance in 50 years 

(Annual Exceedance Probability = 0.00143, MRI = 700 Years).
7.27

Exposure Categories should be determined as follows:

Exposure B: For bridges less than or equal to 30 feet high, Exposure B should apply 

where the ground surface roughness, as defined by Surface Roughness B, prevails in 

the upwind direction for a distance greater than 1,000 feet. For bridges with a mean 

height greater than 30 feet, Exposure B should apply where Surface Roughness B 

prevails in the upwind direction for a distance greater than 2,600 feet or 20 times the 

height of the bridge, whichever is greater. Figure 7-7 shows an example of Exposure B 

with low rise structures in a suburban setting. The buildings are generally less than 30 

feet high with Surface Roughness Category B terrain around the site for a distance 

greater than 1500 feet in any wind direction. Figure 7-8 shows an example of Exposure 

B in an urban setting where terrain representative of Surface Roughness Category B 

extends more than 20 times the height of the structure or 2600 feet whichever is 

greater, in the upwind direction.

Exposure C: Exposure C should apply for all case where Exposure B or D does not 

apply. Figure 7-9 shows an example of Exposure C with open grassland and scattered 

obstructions generally less than 30 feet high. Figure 7-10 shows an example of 

Exposure C with open terrain and scattered obstructions generally less than 30 feet 

high for most wind directions. The structures are less than 1500 feet or 10 times the 

height of the structure, whichever is greater, from an open field. This prevents the use of 

Exposure B.

Exposure D: Exposure D should apply where the ground surface roughness, as defined 

by Surface Roughness D, prevails in the upwind direction for a distance greater than 

5,000 feet or 20 times the bridge height, whichever is greater. Exposure D should also 

apply where the ground surface roughness immediately upwind of the site is B or C, and 

the site is within 600 feet or 20 times the bridge height, whichever is greater, from an 

Exposure D condition as defined in the previous sentence. Figure 7-11 shows an 

example of Exposure D. The wind is flowing over open water for at least one mile. 

Shorelines with Exposure D include inland waterways, The Great Lakes, and coastal 

areas of California, Oregon, Washington and Alaska.

For a site located in the transition zone between exposure categories, the category 

resulting in the largest wind forces should be used. 
7.28

Figure 7-7 Exposure B - Suburban Residential Area with Mostly Single 

Family Dwellings (with permission from ASCE)
7.29

Figure 7-8 Exposure B - Urban Area with Numerous Closely Spaced 

Obstructions With Size of Single Family Dwellings or Larger 

(with permission from ASCE)
7.30

Figure 7-9 Exposure C - Flat Open Grassland with Scattered Obstructions 

(with permission from ASCE)
7.31

Figure 7-10 Exposure C - Open Terrain with Scattered Obstructions (with 

permission from ASCE)
7.32

Figure 7-11 Exposure D - A Building at the Shoreline (with permission from 

ASCE)
7.33

Height above ground level, z Exposure Category

ft (m) B C D

0-15 (0-4.6) 0.57 0.85 1.03

20 (6.1) 0.62 0.90 1.08

25 (7.6) 0.66 0.94 1.12

30 (9.1) 0.70 0.98 1.16

40 (12.2) 0.76 1.04 1.22

50 (15.2) 0.81 1.09 1.27

60 (18) 0.85 1.13 1.31

70 (21.3) 0.89 1.17 1.34

80 (24.4) 0.93 1.21 1.38

90 (27.4) 0.96 1.24 1.40

100 (30.5) 0.99 1.26 1.43

120 (36.6) 1.04 1.31 1.48

140 (42.7) 1.09 1.36 1.52

160 (48.8) 1.13 1.39 1.55

180 (54.9) 1.17 1.43 1.58

200 (61.0) 1.20 1.46 1.61

250 (76.2) 1.28 1.53 1.68

300 (91.4) 1.35 1.59 1.73

350 (106.7) 1.41 1.64 1.78

400 (121.9) 1.47 1.69 1.82

450 (137.2) 1.52 1.73 1.86

500 (152.4) 1.56 1.77 1.89

Table 7-6 Velocity Pressure Exposure Coefficient Kz 

Notes: Linear interpolation for intermediate values of height z is acceptable.

The wind net force coefficient, Cf for girder bridges should be taken from Figure 

7-4, while Cf for truss bridges should be taken from Figure 7-5. 

As noted above, during erection, bridge girders form an open system of members 

exposed to the wind. Depending upon girder depth and spacing, the windward girder(s) 

may shield the more leeward girders from the wind loads, see Figure 7-12. This 

shielding effect will increase as the ratio of girder spacing to girder depth, s/d, 

decreases. This effect is accounted for in this Manual in the wind net force coefficient, 

Cf, used to calculate the wind load to the girder system. The wind net force coefficients, 

Cf, in Table 7-4, are taken from the Florida Department of Transportation 2010 

Structures Manual, Section 2.4.3, “Wind Loads during Construction” pressure 

coefficients, Cp. 
7.34

Figure 7-12 Girder Wind Load Terminology

The shielding effects of a two-girder system can be considered using information from 

“Wind Effects on Structures (3rd Edition)” by E. Simiu and R. Scanlan. Based on limited 

test data on a two-girder system, a Cf value of 2.2 is appropriate for systems where the 

s/d ratio is less than 2, which is normally the case for multi-girder bridges. The

theoretical Cf for a single plate girder is given as 2.04 in Table 4.5.1 of “Wind Effects on 

Structures”. 

The provisions of British Standard 5400, Design Manual for Roads and Bridges, Volume 

1, Section 3, Part 14 (Loads for Highway Bridges), specify a force coefficient of 2.2 for a 

single girder, or Cf = 2(1+0.05s/d) with a minimum Cf of 2.2, for multi-girder systems. 

This equates to the use of Cf = 2.2 for girder spacing up to twice the girder depth, which 

covers the usual cases. Note that the Cf = 2.2 is consistent with the values computed 

from Simiu and Scanlan’s book, as well as the Florida DOT values. 

Based upon the information discussed above, the Cf for girder bridges should be taken 

as 2.2 applied to the windward area of the windward girder for single girders or for 

multiple girders where s/d is 2 or less. Where s/d is greater than 2, Cf = 2(1+0.05s/d) ≤ 4 

should be used. For bridges with superelevation, the windward area should be taken 

based on the overall superstructure depth; however, critical loading conditions typically 

occur with only one or two girders in place.

Research of wind loads on open girder systems recently completed under sponsorship 

of the Florida DOT (Consolazio and Gurley, 2013) suggests that for some wide multigirder configurations the effective drag coefficient may be larger than has commonly 

been used. This research also indicates that the bracing between the windward and 

first interior girder may see increased loads due to suction between the girders. 

However, until additional verification of the proposed wind load model from the report is 

completed, any use of the proposed wind shielding model should be made with caution 

so that it is not inappropriately applied.
7.35

For box girders with sloping webs, the vertical wind load component should be 

considered.

The vertical wind effect on girder bridges during erection before deck formwork is 

placed acts on a relatively small exposed horizontal area and counteracts the selfweight of the girders; thus, it need not normally be included as a design loading. Even 

with deck forms in place, uplift effects on the girders are rarely a concern, since the 

formwork weight opposes the wind uplift, although the formwork itself may be affected. 

When erection takes place over active traffic, some vertical wind load is produced by 

truck traffic passing under the bridge. As there is evidence that these loads are small 

and affect only a limited tributary area they are normally neglected. Where girder 

bridges are built on a significant grade or superelevation, or where unique terrain is 

present, such as a bridge along a hillside or canyon wall, the effects of uplift may need 

to be considered. In this case, the uplift may be computed from provisions of ASCE 7-

10 treating the girders, and formwork if present, as a roof.

COMPONENT TYPE CONSTRUCTION 

CONDITION

FORCE COEFFICIENT (Cf) 

I-Shaped Girder 

Superstructure

Deck forms not in place 2.2 (1)

Deck forms in place 1.1

U-Shaped and Box-Girder 

Superstructure

Deck forms not in place 1.5

Deck forms in place 1.1

Flat Slab or Segmental BoxGirder SuperstructureAny 1.1

Table 7-7 Wind Net Force Coefficient, Cf, for Girder Bridges during 

Construction

(1) When s/d is greater than 2, where s is the girder spacing and d is the girder depth, Cf

is equal to 2(1+0.05 s/d) ≤ 4.0
7.36

ε FORCE COEFFICIENT (Cf)

<0.1 2 

0.1 to 0.29 1.8 

0.29 to 0.7 1.7

Where ε is the Solid Area of the Truss Members divided by the Gross Area of the Truss

Table 7-8 Wind Net Force Coefficient, Cf for Truss Bridges (during 

Construction) (After ASCE 7-10)

7.4.5 Seismic Loading

Seismic loads are not usually applied to girder bridges while under construction. Some 

owners may have requirements where girders are erected over traffic or other specific 

conditions. Reduced seismic loads are appropriate and should be based on owner 

guidance. 

SECTION 5. GIRDER LIFTING

7.5.1 General Considerations

Lifting procedures should be developed to ensure that the girder has adequate strength 

and buckling resistance during lifting operations. Girder weight should be based on 

shop drawing weight or computed from member dimensions accounting for fabrication 

tolerances in finished dimensions. Steel girders should be lifted near their quarter points 

whenever possible, while concrete girders are normally lifted near the ends. Where a 

spreader beam is employed, the line of support, or line running through the girder lifting 

points, should pass through the center of gravity of the member, and the lifting reactions 

at each pick point should be equal. Cross-frames attached to the girders prior to lifting, 

and any other variations to the girder configuration should be considered in determining 

the center of gravity.

The girder bending moments should be determined by treating the girder as simply 

supported at the lift points. Lift points should not be assumed to provide any lateraltorsional restraint.
7.37

7.5.2 Steel Girders

7.5.2.1 Straight Girders

Lifting at two points is recommended. When I-girders are lifted by a single lifting cable, 

the girder is treated as two cantilever sections. If the girder is lifted at two locations 

using inclined cables, the girder is analyzed as a beam-column on two supports with the 

axial load equal to the horizontal load component in the lifting cables. Where the girder 

is lifted at two locations along its length using vertical lifting cables (or slings), analysis 

of the beam can be performed based on a beam with two supports. Ideally, lift points 

should be set at the girder quarter points, as discussed above.

For straight, doubly-symmetric girders lifted at two points (Figure 7-13), the elastic 

buckling moment capacity can be computed from the following:

















=< + 2

2

2

b

y wy

b

bu cr bb L L

EI GJ CIE

L

CMM π π φφ

Where:

Mu = Factored maximum moment from static analysis

Mcr = Critical buckling moment

φφb = Buckling resistance factor = 0.9

Lb = Unbraced length = L (total length of girder segment)

E = Modulus of elasticity (ksi)

Iy = Weak axis moment of inertia (in4

) 

G = Shear modulus (ksi)

J = Torsional constant( )= ∑ 3

3

4 bt in

Cw = Warping constant ( ) 4

2

6 hI

in y = 

CbL = Lift adjustment factor

= 2.0 0.225 ≤ Lift

bL

L

C for L

= << 6.0 0.225 0.3 Lift

bL

L

C for L

= 4.0 0.3 ≥ Lift

bL

L

C for L

Equation 7-7

Equation 7-8

Equation 7-9

Equation 7-10
7.38

Where:

Lift L = Average length from the lift points to the ends of the girder (Figure 7-13)

Figure 7-13 Girder Lifting Length Installation

The CbL factors were developed by Schuh and Farris (2008). For singly-symmetric 

members, Mcr may be evaluated in accordance with the AASHTO Design Specifications 

Appendix D6.4.2.

7.5.2.2 Curved Girders

Curved girders are subject to a rigid-body rotation and cross-sectional twisting during 

lifting. Curved girders are normally lifted at two points using a spreader beam. When 

possible, the line of support, the line running between the lifting points, should pass 

through the center of gravity of the girder. Otherwise twisting will occur as shown in 

Figure 7-14. When girders are lifted with cross-frames attached, their contribution as 

well as variation in girder configuration must be included in determining the center of 

gravity. To maintain rotational stability of the spreader beam, the lifting reactions at each 

pick point must be equal. 
7.39

Figure 7-14 Effect of Eccentricity on Curved I-Girder Tilt

Figure 7-14 shows the geometry associated with lifting a curved girder. Girder pairs or 

box-girders may be handled in a similar manner. The lift points are to be selected to 

pass through the center of gravity. To produce equal lift cable loads, the lift points are 

placed equidistant from the center of gravity, Figure 7-15, as determined by the 

following equations (Stith, Schuh, et al 2010):

cos ′ = D

R

θ

1 cos−   ′ =    

D

R

θ

Equation 7-11

Equation 7-12
7.40

1 = − ′ θ θθ Lift

L R Lift Lift 1 1 = θ

2 1 = + ( ) 2* ′ L R Lift θ θ Lift

Where the terms are as shown in Figure 7-15:

Figure 7-15 Zero Rotation/Equal Force Lift Equation for Curved I-Girder

The lift cable load is then one half the total girder weight, and the spreader beam length 

is: 

L R = 2 sin ' ( ) θ

When the central angle subtended by the girder length for a curved girder is less than 3 

degrees, the girder buckling capacity may be calculated as a straight girder using 

Equation 7-7 

When the girder(s) cannot be lifted through their center of gravity, girder roll and 

torsional loading should be investigated. A calculation method for this case can be 

Equation 7-13

Equation 7-14

Equation 7-15

Equation 7-16
7.41

found in Stith, Schuh, et al (2010). Solution of this problem can be performed using a 

public domain spreadsheet program developed by the University of Texas, UT Lift, as 

discussed in Chapter 6. 

7.5.3 Concrete Girders

When a precast, prestressed concrete beam hangs from flexible supports, such as 

cables during erection, it is free to roll about the line passing through the center of 

rotation at each lifting point, or the roll axis, as shown in Figure 7-16. Due to beam 

sweep tolerances and lifting point placement tolerances, the center of gravity of the 

beam will be located on one side or the other of the roll axis. This eccentricity causes 

the beam to rotate about the roll axis by a small angle, which causes a component of 

the beam self-weight to be applied about the weak axis of the beam. The lateral

component of the self-weight creates a lateral deflection of the beam and increases the 

roll angle, which causes further lateral deflection. Depending on the lateral stiffness of 

the beam, it will reach equilibrium at a slightly larger roll angle or the roll angle will 

increase to a point where the lateral bending is sufficient to initiate failure of the beam. 

The final equilibrium position of the hanging beam is shown In Figure 7-16.
7.42

Figure 7-16 Final Equilibrium Position of Hanging Concrete Precast Beam

The hanging beam can be analyzed using the equations presented in the PCI Bridge 

Design Manual, Third Edition (2011). The equations presented herein are taken from 

Chapter 8 of that publication and were originally developed in the work of Mast (1993). 

Critical conditions for lifting normally occur when the girders are initially moved from the 

casting beds by the precaster as the concrete strength will be less than when the girder 

is set in the bridge. Analysis of the girders for lifting at the plant and for transport to the 

job site is carried out by the precaster and is not discussed further in this Manual. 

Should re-transport of girders be necessary after site delivery and unloading, the girders 

should be re-evaluated using the equations for transport presented in the PCI Bridge 

Design Manual. 
7.43

Based upon past successful experience, a safety factor of 1.0 is used in checking beam 

cracking and 1.5 is used for girder roll stability (PCI, 2011). Thus the controlling 

equations are as follows:

Rollover: r max

'

o max i

y 1.5 

z e

  θ ≤     ′θ +

′

Cracking: 

max

1.0 1 o i

r

z

y

θ

θ

 

≤÷ +    

The tilt angle at rollover (failure), , may be taken as:

max 2.5

i

o

e

z

θ′ =

In which:

ei = the initial lateral eccentricity of the center of gravity with respect to the 

roll axis (in).

yr = the height of the roll axis above the center of gravity of the beam (in).

o = the theoretical lateral deflection of the center of gravity of the beam, 

computed with the full weight applied as a lateral load, measured to the 

center of gravity for the deflected arc of the beam (in).

θi = ei / yr (rad)

θmax = tilt angle at which cracking begins, based on tension at the top corner 

equal to the concrete modulus of rupture (rad)

o z′ = lateral deflection of girder center of gravity including rotation effects (in) 

= o ( ) m xa ′ 1 2.5z + ⋅ θ′

The assumed eccentricity, ei, may be taken as a minimum of 1/4 inch to account for 

misplacement of the lifting device (loops, etc.) plus 1/8 inch for each 10 feet of beam 

length or fraction thereof. This is based on standard PCI fabrication tolerances, and the 

recommendations of PCI (2011).

Use of a total sweep of 1/16-inch per 10 feet of beam length is based on using the 

beam sweep tolerance for I-girders or bulb-tee girders as given in the PCI Manual for 

Quality Control for Plants and Production of Structural Precast Concrete Products, MNL 

116-99, Fourth Edition. Work by Cojocaru (2012), based on field measurements of 

precast girders, concluded that the PCI sweep tolerance is a reasonable value. 

However, for longer girders or where girders are stored for extended time periods, 

actual measurements of sweep are recommended to be used in stability calculations.

The effect of camber should be included in computing the center of gravity of the girder.

Equation 7-17

Equation 7-18

Equation 7-19
7.44

For a beam with overall length, l, and equal overhangs beyond the lifting points of 

length, a, at each end: 

( ) ( ) ( ) ( ) 5 3 24 5

11 1 0.1 3 1.2

12 o

y

w

z l al al a

EI l

= −++    

Where: 

l1 = l – 2a

θmax = the tilt angle at cracking which equals Mlat divided by Mg 

Mg = service level strong-axis moment in girder due to self-weight

Mlat = service level weak-axis moment that would cause cracking in top flange of 

girder

SECTION 6. STEEL GIRDER STABILITY AND BRACING

7.6.1 General 

As discussed in Chapter 5, girder bracing systems provide stability to the girders and 

improve the lateral and torsional stiffness of the bridge during construction and in its 

completed state. The AASHTO Design Specifications consider bracing members that 

carry calculated loads based on a structural analysis to be primary members, e.g. 

bracing members in curved steel bridges, otherwise bracing members may be 

considered to be secondary members. A first-order analysis of a straight bridge under 

construction may indicate zero forces in the bracing members, yet failure to properly 

install the necessary bracing during construction can lead to failure due to instability. 

Lateral-torsional buckling often controls steel I-girder design during construction. In 

order to control girder stresses and deformation bracing systems must possess 

adequate strength as well as stiffness. Further discussion on strength and stiffness 

requirements for bracing is contained in Chapter 5.

Cross-frames or diaphragms between adjacent girders are termed nodal torsional 

braces herein since the bracing restrains girder twist at the brace location. The distance 

between the nodal braces defines the girder unbraced length. For straight steel girder 

bridges, the bracing system design is normally dominated by stability and skew effects. 

The effects of torsion and lateral flange bending generally control bracing design for 

curved steel girder bridges.

In assessing the stability of the bridge during construction, the bracing requirements 

should be investigated at each stage of the erection sequence. The investigation of the 

need for bracing in I-girder bridges should consider the following as a minimum:

• Transfer of lateral wind loads between girders and to the supports. Wind loads 

will be carried by both flanges in proportion to their lateral stiffness.

Equation 7-20
7.45

• Stability of the top flange in compression, particularly during initial girder 

placement and deck placement

• Stability of the bottom flange in compression zones

• Global stability for the girder system

• Provision of lateral support to the bottom flange when deck overhang brackets 

are used

• Control of flange lateral bending

• Control of girder geometry

These checks should also be performed on bridges undergoing renovation, particularly 

during redecking of composite girder spans and box-girders. 

7.6.2 Lateral Bracing

In steel I-girder bridges, lateral bracing may be required to resist wind loads and provide 

girder stability prior to deck construction. When lateral bracing is deemed necessary, it 

should ideally be connected directly to the flange being braced using a bolted 

connection. However, bolting directly to the top flange may interfere with construction 

using stay-in-place forms. In these cases bracing should connect as near the top flange 

as practical. The lateral-bracing system is designed as a truss.

Placing flange lateral bracing in the same plane as the top flange minimizes live load 

lateral bracing stresses in the finished bridge. Permanent bottom lateral bracing in Igirder bridges has the effect of creating a quasi-closed section in combination with the 

hardened concrete deck, and the bracing may attract significant forces due to live load 

bending of the girders. In some cases, removal of lower lateral bracing that is only 

required during construction might be considered. This also minimizes potential fatigue 

prone details. 

Bracing design forces include computed forces due to vertical and lateral loads as well 

as stability induced forces. Design of bracing at each stage of erection must be 

consistent with the forces and bracing that are associated with that stage. Design of 

bracing components should be in accordance with the design equations presented in 

Section 3 of Chapter 5 for this particular bracing configuration.

7.6.3 Global Stability

Systems of two to four noncomposite I-girders interconnected by cross-frames or 

diaphragms should be investigated to assure that failure in a system buckling mode as 

discussed in Section 4 of Chapter 5 does not occur. System buckling may be 

investigated using Equation 5-12, or an eigenvalue analysis as discussed in Chapter 6. 
7.46

When evaluating global stability using Equation 5-12, use of a 1.25 dead load factor is 

recommended. Appropriate ranges of eigenvalues are discussed in Chapter 6.

The effects of lateral load in combination with the system bucking resistance calculated 

from Equation 5-12 may be evaluated using the AASHTO Specifications Equation 

A6.1.1-1, by replacing the term φφf Mnc on the right hand side of the equation with φφbk Mgs 

calculated by Equation 5-12 (and adjusted for the number of girders in the system). 

Note that φφbk is defined above in Section 3.

The Yura equation: has recently been incorporated into AASHTO 

LRFD as Eq. 6.10.3.4.2-1 for checking system buckling during deck pour. The approach 

presented above is applicable for intermediate steel checks prior to the deck pour 

( ), but the AASHTO approach omits the φφ factor and limits the total sum of 

the factored positive girder moments to 50% Mgs during the deck pour (Strength VI load 

combination). Should the sum of the moments exceed 50%, the design can add flange 

level lateral bracing, revise the girder spans/sizes to increase system stiffness, or 

evaluate the amplified girder second-order displacements and verify that they are within 

owner tolerances. Note that amplification can also occur under steel-only dead load as 

the buckling limit is approached, but the recommended system buckling φφ factor and 

Strength I/III load factors should provide an adequate level of safety for most narrow 

systems subject to buckling in the steel-only condition.

SECTION 7. CONCRETE GIRDER STABILITY AND BRACING

7.7.1 General

Precast concrete girders may be susceptible to lateral-torsional buckling or rollover 

instability prior to the girders being stabilized by the casting of the top slab, which 

provides continuous lateral support to the girders, preventing buckling. The condition 

when the girder is set on the bearings during erection is represented by a simply 

supported girder, supported on bearings at the ends, with no overhangs. The supports 

typically allow rotation about both the girder’s strong and weak axes, with elastomeric 

bearings pads most commonly used. Factors such as bearing slope, bearing skew 

relative to the girder centerline, bearing type, and girder imperfections can have 

significant effects on the stability behavior. 

The School of Civil and Environmental Engineering of the Georgia Institute of

Technology prepared a study of the stability of precast prestressed girders for the 

Georgia Department of Transportation (Sureick, Kahn, et. al., 2009). This work included 

calculation of lateral-torsional buckling and rollover stability for simply supported 

AASHTO Type I through Type IV girders, with a minimum concrete compressive 

strength of 6 ksi, and their ends restrained against rotation. The results are shown in 

Table 7-6, and provide girder lengths below which detailed analysis for lateral-torsional 

buckling and rollover may not be required. These lengths include a safety factor of 1.5. 
7.47

AASHTO Girder Type Length below which lateraltorsional buckling does not 

occur (feet)

Length below which 

rollover about support 

does not occur (feet)

I 127 75

II 133 80

III 155 100

IV 175 110

V 197 135

VI 193 140

Table 7-6 AASHTO Concrete Girder Stability Limits

Prestressed, precast concrete bridge girders are designed to preclude flexural cracking 

under their self-weight. As a result, the girder section weak axis bending moment of 

inertia and torsional stiffness are sufficiently large to prevent lateral-torsional buckling 

for AASHTO and PTI standard bulb-tee and similarly stiff sections (Hurff and Kahn, 

2012). Stability is therefore controlled by rollover. This is consistent with the guidance in 

Chapter 8 of the PCI Bridge Design Manual. 

7.7.2 Simply Supported Condition - Girder Rollover
7.48

For prestressed concrete bridge girders, rollover will typically control over buckling for 

cases where the ends are not laterally braced because the elastic buckling load will be 

greater than the self-weight. Rollover is caused by initial girder rotation compounded by 

a lack of flatness of the bottom flange of a prestressed concrete girder and the roll 

flexibility of the bearings increasing the girder rotation. The rotation of a girder causes a 

component of the girder weight to be applied about the weak axis of the girder, which 

causes lateral deflection and further shifts the center of gravity of the girder which 

causes further lateral deflection. Figure 7-17 shows lateral deflection and rotation 

imperfections at equilibrium of a prestressed girder on elastic supports. Note that for 

skewed supports out-of-plane rotations need to be considered in addition to in-plane 

rotations.

Figure 7-17 Equilibrium of Girder on Elastic Support

Rollover of a simply supported girder is determined primarily by the properties of the 

support rather than the girder. Prestressed concrete girders of ordinary proportions 

have been found to usually have sufficient lateral bending strength to withstand greater 

angles of inclination than can be resisted by the supports. Therefore, it is necessary to 

determine the properties of the supports in order to perform the rollover analysis. 

Elastomeric bearing pads are the most common bearing type used with precast girders 

and provide a springy support for the concrete girders. The rotational stiffness constant, 

Kθ, is determined by the dimensions and properties of the pad and may be calculated 

from the pad’s vertical stiffness properties as shown in Yazdani et.al. (2000). Girder 

camber and roll effects contribute to an uneven load distribution to the bearing pad 

which effectively reduces its stiffness. Refer to NCHRP Report 298, “Performance of 

Elastomeric Bearings” and NCHRP Report 596, “Rotation Limits for Elastomeric 

Bearings” for information on bearing pad properties. 

When the bearing pads are set on a skew to the girder centerline, an additional uneven 

load distribution to the pad is created that further reduces its effective stiffness. In 

addition, the variation in bearing pad stiffness is not linear with load. The axial stiffness 
7.49

under girder self-weight alone will be less than that under service load. Girders should 

be evaluated to ensure a sufficient safety factor on rollover and cracking. A minimum 

safety factor on rollover of 1.5 is recommended by Mast (1993) and PCI (2013) along 

with a minimum safety factor on cracking of 1.0.

Equation 7-21 below can be used to compute the factor of safety for a simply supported 

precast concrete girder against cracking (Mast, 1993):

 

( ) max

max max

1.0 o i

r

z ey

− ≤

+ +

θ a

θ θ

Where: 

ei = initial lateral eccentricity of center of gravity with respect to roll axis (in) 

(minimum of 1 inch plus 1/8 inch for each 10 feet of girder length or 

fraction thereof)

hr = distance from bottom of girder to roll axis 

w = girder weight per unit length (k/in)

Ec = modulus of elasticity of concrete

 = moment of inertia of beam about weak axis (in.4) 

L = girder span (in)

zmax = maximum resisting moment arm (typically half of bottom flange width) (in)

θmax = Mlat/Mg 

Mlat = service level weak-axis moment that would cause cracking in top flange 

of girder (k-in)

Mg = service level strong-axis moment in girder due to self-weight (k-in)

r = radius of stability = KΘ /W (see Figure 7-19)

Kθ = sum of rotational spring constants of supports (k-in/rad)

W = total weight of beam (k)

y = height of center of gravity of beam above roll axis (in)

α = tilt angle of support (rad)

( ) ( ) max

max rad r z h

r

a θ a − ′ = +

4 1

120 o

c y

wL

z

E I

    =        

( ) max 1 2.5 o o z z ′ ′ = + θ

The height of the center of gravity of the beam above the roll axis should include beam camber. 

The tilt angle of the support should include both the out of flatness tolerance of the bottom fo the 

beam and the bearing seat cross slope.

Equation 7-21
7.50

Figure 7-18 Definition of Radius of Stability (r)

Equation 7-22 below can be used to compute the factor of safety against rollover for a 

simply supported precast concrete girder (Mast, 1993)

( ) max

max max

1.5 o i

r

z ey

′ − ≤ ′′ ′ + +

θ a

θ θ

Where the terms are defined above.

The effects on roll stability of skewed elastomeric bearing pads may be accounted for 

by use of a modification factor applied to the bearing pad stiffness. The modified 

stiffness equals the calculated stiffness multiplied by the modification factor. Based 

upon the results of physical bearing pad tests (Consolazio and Hamilton, 2012), as well 

as computational studies (Consolazio and Hamilton, 2007), the Florida Department of 

Transportation developed the bearing pad stiffness modification factors shown in 

Table 7.7. These values are based on Florida DOT bearing dimensions so may not be

applicable for other states; however the general trend should be similar. These factors 

include the effect of girder end rotation due to camber, as well as skew. Linear 

interpolation may be used for skew angles between zero and 15 degrees and between 

15 degrees and 60 degrees.

Equation 7-22
7.51

Skew Angle (degrees) 0 15 30 45 60

Stiffness Modifier 1 0.40 0.32 0.26 0.21

Table 7-7 Skew Angle Bearing Pad Stiffness Modification Factors

Lateral wind load effects are added by computing equivalent eccentricities that are 

added to the assumed initial eccentricity, ei, to compute a total eccentricity to use in the 

above equations. The eccentricities due to wind include the lateral wind deflection for 

the uncracked girder, plus an overturning moment eccentricity equal to the wind 

overturning moment computed about the bottom of the bearing pad divided by the girder 

self-weight.

Increasing the bottom flange width is the most effective way to increase the stability of a 

simply supported precast concrete girder. This will also increase the bearing pad width, 

which should preferably be equal to the width of the girder bottom flange, minus the 

chamfers, as a minimum (Mast, 1993).

In order to avoid the complexity of the rollover analysis which relies on variables such 

as bearing rotational stiffness and the tilt angle of the bearings, it is important to brace 

the precast concrete girders at the supports during erection. The girders can be braced 

from the top flange down to the abutment or pier seats, or multiple adjacent girders can 

be braced to one another. Chapter 3, Figures 3-26 through 3-32 illustrate typical bracing 

options for precast concrete beams.

SECTION 8. CONCENTRATED LOAD EFFECTS

7.8.1 Bearing Stiffeners

At bearing locations and at other locations on steel girders subjected to concentrated 

loads, where the loads are not transmitted through a deck or deck system, webs without 

bearing stiffeners shall be investigated for the limit states of local web yielding and local 

web crippling according to the provisions of Appendix D6.5 – Concentrated Loads 

Applied to Webs without Bearing Stiffeners of the AASHTO Design Specifications. Web 

sideway buckling, if applicable, shall be investigated according to AISC Specification 

J10.4.

7.8.2 Local Effects of Lifting Clamp Loads 

The local effects of lifting clamp loads on the girder flange should be addressed as part 

of the erection evaluation. A commonly used approximate load distribution model to 

assess flange bending is shown in Figure 7-19. The bending moment due to the clamp 

load is considered distributed over an effective flange length, CLE, and the bending 

stress in the flange is computed considering that part of the flange as a cantilever beam. 

The resulting stress (or applied moment) is compared to the allowable plate bending 

stress (or nominal plate bending capacity). While this is a simplified and conservative 
7.52

approach, this conservatism helps to minimize any flange distortion. Using this method 

the local flange bending stress may be taken as:

( ) ( )2

/ 6

c

lb

f Lf

R k f

bCt

=

+

 

≤ 0.75 lb yf f F

Where:

Rc = service level concentrated force at each flange edge (kip)

Fyf = specified minimum flange yield stress (ksi)

bf = flange width (in)

tf = flange thickness (in)

CL = length of clamp along flange (in)

k = distance from outer face of flange to web toe of fillet (in)

Equation 7-23

Equation 7-24
7.53

Figure 7-19 Steel Girder Lifting Clamp Load Distribution
7.54

SECTION 9. DEFLECTION CONTROL

Control of the girder vertical and horizontal deflections and girder rotations is important 

in assuring that erection fit-up can be achieved without applying excessive force to 

mating components, and that accumulated deformations are within finished structure 

limits. Deflections should be computed using the service load combination. Wind load is 

not normally included when computing deflections during deck placement.

Large lateral deflections which cause the girders to be out-of-plumb (i.e. rotate about 

the girder longitudinal axis) will also introduce secondary stress in girders that could be 

important. NCHRP Report 725 found that while a girder out-of-plumb of one percent had 

a negligible effect on girder or bracing stresses for curved steel I-girders, a six percent 

out-of-plumb increased girder stresses and lateral deflection by up to 20 percent. 

Control of the rotation about the longitudinal axis of the girder during erection is 

particularly important in curved girder bridges, since both the supported girder and the 

girder being lifted for field connection will tend to rotate due to torsional effects. Rotation 

of the in-place girder should be minimized by installation of the permanent or temporary 

bracing, preferably at locations adjacent to the field splices. Limits for deflections and 

rotations during erection should be established by the erector, with input from the 

erector’s engineer so that member fit-up is achieved without forcing members into 

position. Deflections must be kept within elastic limits such that the overall girders are in 

proper alignment upon completion of erection. While some variations in vertical dead 

load deflection can be accommodated in establishing final screed elevations, excessive 

girder twist makes setting formwork difficult and can effect reinforcing steel clearances. 

As an example of lateral deflection limits, the Pennsylvania DOT limits the lateral 

deflection under service wind load to a value equal to the girder span over 150. This 

represents a transient load, and would not occur during active erection. Based on 

evaluation of data from a questionnaire sent to erectors, as well as girder analysis 

studies, Stith (Stith, Petruzzi, et. al. 2010) recommended limiting the girder out-of-plumb 

during erection for curved girders to 1.5 percent of the girder depth to facilitate fit-up of 

connections. Survey data indicated that a value of one percent to two percent was 

generally found by erectors to be a workable range. 

SECTION 10. CONNECTIONS

7.10.1 Steel Connections 

Connections to steel structures or components required as part of the erection 

operations must be designed in accordance with the applicable provisions of Article 

6.13 of the AASHTO design specifications. Existing connections and splices should be 

evaluated for each stage of construction under consideration according to the same 

provisions, as applicable. Any proposed changes to the owner’s standard specified 
7.55

bolting procedures must be supported by engineering analysis addressing erection 

conditions. Reaming of bolt holes during erection should be permitted only with the 

approval of the engineer. Field drilling may be required in some situations.

7.10.2 Concrete Connections 

Anchorage and other connections to concrete structures or components required as 

part of the erection operations should be designed in accordance with Appendix D of 

ACI 318, Building Code Requirements for Structural Concrete. Existing anchorages and 

connections should be evaluated for each stage of construction under consideration 

according to the same provisions, as applicable. When temporary connections are 

made to the permanent structure, provisions should be made for removal of the 

anchorage and repairs as may be required by the owner.

SECTION 11. TEMPORARY SUPPORTS (FALSEWORK)

Temporary supports and their associated components should be designed to carry 

vertical and lateral loads due to self-weight of the girders and wind and any loads that 

are applied to the temporary supports as the erection progresses. Temporary support 

design shall conform to the AASHTO Guide Specifications for Temporary Works. The 

effects of any longitudinal jacking during the erection should also be investigated. The 

elevation of the temporary supports should be such as to support the girders at their 

cambered no-load elevation. The use of temporary supports must not result in any 

overstressing of the girders. Jacks used in conjunction with the temporary supports 

should have a stroke adequate to permit full unloading. Unloading of temporary 

supports should be performed such that all temporary supports at each cross-section 

are unloaded uniformly. The deflections of the erected girders at the temporary supports 

when they are removed should be evaluated, and stability of the girders should be 

ensured prior to removal of the temporary supports. 

Where appropriate, holding cranes may be used to temporarily support girders from 

above rather than use shoring towers located below the girders. Holding cranes will not 

provide a lateral brace. However, by altering the girder moment distribution and 

associated Cb value for the girder, bending stresses may be decreased.
7.56

SECTION 12. BEARINGS

Computed bearing rotations during each stage of construction under investigation 

should not exceed the rotational capacity of the bearing. Bearings should be installed 

such that, after dead load has been applied, sufficient rotation capacity should be 

available to accommodate rotations due to environmental loads and live loads. 

Expansion bearings should be installed so that they will be in the center of the permitted 

travel at an ambient temperature of 60°F, unless otherwise specified by the owner. 

Where required for erection stability, designs for blocking of the bearings or other 

methods of locking the structure in position should be designed and detailed based on 

the associated loads and local rotations.

SECTION 13. DECK PLACEMENT

Concrete-placements shall either be made in the sequence specified in the contract 

documents, or may be based on a sequence developed entirely by the contractor, in 

which case the contractor’s engineer must evaluate the effects of the desired placement 

sequence according to the criteria specified in Article 6.10.3.4 of the AASHTO design 

specifications. 

The duration of each placement should be specified in the construction plan. The time 

between placements should be determined to be such that the concrete in prior pours 

has reached an age or strength specified in the construction plan. Placements that 

include both negative and positive dead load moment regions should be placed such 

that the positive moment region is poured first. Any accelerating or retarding agents to 

be used in the concrete mix shall be specified. When changes in the deck placement 

sequence are made, revised deck drawings and associated fillet heights and girder 

elevations need to be prepared.

SECTION 14. SUMMARY

Design criteria for use in evaluation girder bridges during construction should account 

for the open configuration of the girders prior to deck placement and the likelihood of 

environmental loads that may occur over relatively short construction time durations. 

The criteria contained in this chapter were developed recognizing those conditions as 

well as AASHTO guidance on loads and load factors. The application of the criteria 

must achieve a structure that provides adequate strength and stability at all stages of 

erection.
8.1

CHAPTER 8 

ERECTION PLANS AND PROCEDURES 

SECTION 1. INTRODUCTION

The contractor’s erection plans and procedures describe the detailed means and 

methods to be used by the contractor or erector in constructing the bridge girders and 

associated structural elements. The erection plans are developed from information in 

the contract drawings and specifications, the fabricator or precaster’s shop drawings, 

and the engineering calculations prepared by (or for) the bridge erector. The erection 

plans must be job specific and include details of any temporary works required during 

erection. Complex erection projects may require input from the structural engineer of 

record in addition to the original design calculations such that the contractor can confirm 

constructability during various erection stages.

State departments of transportation and other bridge owners typically provide at least 

general requirements for erection plan submittal, with which the contractor must comply. 

Guidance on girder erection submittals is also included in the AASHTO/NSBA Steel 

Bridge Collaboration “Steel Bridge Erection Guide Specifications” and in Appendix B of 

NCHRP Report 725. This chapter provides information to supplement those 

requirements and address the type and level of detail that should be provided in 

erection plans and procedures.

Facilities owners adjacent to the bridge construction site may have erection 

requirements to protect their property that must also be satisfied. Railroads, in 

particular, may have very detailed submittal requirements, including design provisions 

for shoring that must be followed for work adjacent to or over tracks.

SECTION 2. PLAN PREPARATION

Erection plan submittals are prepared by the bridge erection contractor or 

subcontractor. The submittals should normally require at least a sketch of the work area 

and site logistics, as well as the sequence of erection and any supporting data, such as 

maximum pick weights and crane capacity charts. Submittals for larger or more complex 

projects may include preparation of detailed drawings and engineering calculations, 

piece-by-piece erection sequences, lifting diagrams and crane information, and detailed 

design and drawings of any temporary works. 

The preparation of the submittal documents may be completed in-house by the erector, 

particularly for simple projects, or may involve an engineering consulting firm retained 

by the erector to provide support services. While erectors may have engineers as part 

of their staff, project commitments, as well as the extent and complexity of engineering 
8.2

required for some projects, can result in retention of outside engineering services. Close 

collaboration between the erector and his consultant is needed to develop an erection 

plan that is efficient for the erector, satisfies engineering requirements for stability and 

strength at each erection stage and accommodates the specific site conditions. 

Selection of erection methods, equipment, and temporary support systems is generally 

based on past erector experience and available equipment and materials, and this must 

be reflected in the engineering calculations.

In the preparation of the erection plans and supporting calculations, the design of 

temporary bracing components, sharing systems and similar components are based on 

specific materials’ properties, and may utilize used materials. The contractor/erector 

must assure that the actual materials used in the field satisfy all requirements on which 

the design was based, and are in good condition. Where material properties cannot be 

documented, material testing may be required.

When the project includes work to an existing bridge, the erection plans and procedures 

must account for the effects of the work on the existing structure. This assessment 

should be based on as-built conditions of the existing structure, including any 

deterioration of bridge components. A complete structural assessment report for the 

existing structure may be required by some agencies (IDOT, 2004). 

Erection plans prepared by an erector that is a subcontractor to the general contractor 

should be reviewed by the general contractor prior to submittal to the owner or 

reviewing agency. The general contractor should assure that all work activities on the 

project site are coordinated, work schedules are compatible, and overall site access and 

traffic control are accounted for.

SECTION 3. ERECTION PLANS

8.3.1 General

As noted previously, the extent of the information contained in the erection plans will 

vary with the bridge size and complexity and the site constraints. A sample set of 

erection plans for a steel girder bridge may be found in the AASHTO/NSBA Steel Bridge 

Collaboration, “Steel Bridge Erection Guide Specification,” which may be downloaded 

from the AASHTO/NSBA website. Figures 8-1 through 8-6 and Figures 8-7 through 8-10 

beginning on the following page show example erection plans for a skewed steel Igirder and a precast concrete girder bridge, respectively, taken from actual projects.
8.3

Figure 8-1 Steel Girder Erection Drawings 1 – Plan Stages 1 and 2
8.4

Figure 8-2 Steel Girder Erection Drawings 2 – Plan Stages 3-5 and 6
8.5

Figure 8-3 Steel Girder Erection Drawings 3 – Plan Stages 7-10
8.6

Figure 8-4 Steel Girder Erection Drawings 4 – Shoring Elevations
8.7

Figure 8-5 Steel Girder Erection Drawings 5 – Shoring Towers
8.8

Figure 8-6 Steel Girder Erection Drawings 6 – Lifting and Local Bracing Details
8.9

Figure 8-7 Concrete Girder Erection Plan 1 – South Span Girders Plan and Clearances
8.10

Figure 8-8 Concrete Girder Erection Plan 2 – South Span Girders Plan
8.11

Figure 8-9 Concrete Girder Erection Plan 3 – North Span Girders Plan and Clearances
8.12

Figure 8-10 Concrete Girder Erection Plan 4 – North Span Girders Plan
Engineering for Structural Stability in Bridge Construction Reference Manual

8.13

8.3.2 General Plan

An overall plan of the project site including all existing conditions, topography, and the 

new structure should be provided (Figures 8-1 and 8-7). Any railroad tracks, waterways, 

and roads should be located, as well as any existing structures, and horizontal and 

vertical clearances shown. The general plan can be used to show girder delivery and 

lay-down locations. Girder delivery methods and piece weights should be coordinated 

with the fabricator or precaster. This drawing should also show equipment locations 

referenced to the bridge centerline and any substructures. 

The general plan should also show the location of any buried or overhead utilities. 

Protection of underground utilities, if required, should be indicated. Operating 

clearances between crane booms, aerial lifts, and similar equipment and power/utility 

lines should be shown. In cases where utilities must be de-energized or temporarily 

relocated, the limits of the site associated with this action should be included.

General site topography should be included so that the location of site leveling for 

cranes or girder storage, or access road construction can be referenced to existing 

grades. When girder erection will be from barges operating on the waterway adjacent to 

the proposed bridge, the plan should include the waterway channel limits referenced to 

a given water elevation, waterway cross-sections showing channel profiles, and the 

expected water level during erection activities as well as water level variations. Barge 

mooring locations along with equipment locations on the barges should be provided.

8.3.3 Erection Sequencing

The erection plan should show the erection sequence for all members, both girders and 

bracing for the permanent structure, as well as any temporary bracing and shoring. 

Sequencing starts with the member delivery and is only completed for a member when 

it is placed and supported or braced as required to assure adequate strength and 

stability while controlling deformation within the limits that will allow fit-up of connections 

and provide a finished structure of proper alignment and elevation. The “Stages 1 and 2 

Construction Plan” notes on Figure 8-1 provide an example of a step-by-step sequence 

from delivery to crane release.

The installation of all required temporary bracing and shoring must be specifically 

identified for each stage of setting girders; as may be seen in Figure 8-2. The “Stage 6 

Construction Plan” notes in Figure 8-2, for instance, call for bracing of the beam to the 

south abutment and the temporary bent prior to releasing the crane. Member reference 

designations on the erection plans should be the same as those shown on the shop 

detail drawings. When holding cranes are used, the holding crane position, girder hold 

location and required holding load must be provided.

A contingency plan should be developed to supplement the erection sequence. The 

erection plan is based upon anticipated conditions during erection determined from local 

weather conditions, seasonal considerations, project staffing, material availability/supply 
Engineering for Structural Stability in Bridge Construction Reference Manual

8.14

and other factors. Actual conditions or events, however, may differ and the contingency 

plan provides predetermined responses and identifies required resources to respond to 

unexpected events. As examples, an approaching storm may produce wind speeds in 

excess of those used in designing certain stage of erection, requiring installation of 

additional temporary bracing, or heavier than normal rains may increase river flows, 

increasing loads to temporary bents located in the river as well as delaying erection 

activities.

8.3.4 Calculations

Some bridge owners may prequalify engineers for erection engineering, require the 

erection engineering to be undertaken by a firm that is prequalified by the owner for 

design of the bridge category to be erected, or require the engineer’s credentials be 

submitted by the erector along with his bid. These calculations are normally the general 

contractor’s responsibility and may be prepared by someone other than the erection 

engineer. Computer generated calculations should be verified for selected conditions by 

hand methods.

Design calculations should address all critical stages of the erection sequence and 

substantiate the structural capacity and stability of the girders at each stage. 

Calculations should be referenced to the erection stage they address and use the 

member reference designations shown on the erection drawings. Girder capacity must 

be calculated using the spacing between bracing that matches the erection stage. This 

is particularly important where not all cross-frames or diaphragms are in place for an 

intermediate erection stage. Calculations must demonstrate the structural adequacy of 

any partially bolted primary splices after release from cranes or other external support.

The design calculations should also determine member deformations, particularly for 

curved or highly skewed (over 30 degrees) girders. Deformations must be limited such 

that connection fit-up of girder segments and bracing systems can be made without 

excessive forcing of members into alignment. In curved and skewed girder bridges, the 

differential displacements may cause difficulties with cross-frame installation. Girder 

elevations should be provided at splice locations and any shoring towers.

The determination of shoring loads must be based on maximum loads at the given 

location, which may vary for different erection stages. Tower design should conform to 

the AASHTO Specifications for Bridge Temporary Works. Shoring towers must be 

designed for wind loads as well as the girder and lateral brace reactions. When a 

deadman is used for guy cable or bracing anchorage, the design should consider worst 

case soil conditions, based on best available data in evaluating dead man resistance to 

uplift or sliding. In addition, provisions for cable tensioning should be determined 

considering cable elongation. Shoring design should consider the effect of tower 

shortening and settlement as well as lateral deflections on structure performance. 

An assessment of the site soil’s ability to support cranes and other equipment loads 

should be included, and when required, designs for crane pads should be provided. 

Crane, or other equipment, load effects on abutments, retaining walls, and underground 
Engineering for Structural Stability in Bridge Construction Reference Manual

8.15

utilities must also be considered. This may require field investigations to verify structure 

or utility location, depths, and structural conditions. Site investigation data should be 

included with the calculations.

Calculations should also be provided to verify the capacity of contractor-fabricated 

rigging, such as lifting and spreader beams and lifting lugs. Catalog data should be 

included for manufactured items such as slings, clevises, chain-falls, concrete anchors, 

jacks, chain-binders, come alongs, etc. A comparison of available capacity for the 

manufactured item versus required capacity should be provided in the calculations. 

When girders are to be erected from barge mounted cranes, calculations for barge 

stability and barge deck capacity should be provided. These are often prepared by a 

marine engineer/architect consultant. The calculations should clearly define any 

ballasting or deck modifications needed and define operating limits based on wind, 

wave, and current conditions.

If the contractor alters the bridge deck placing sequence, calculations verifying the 

adequacy of the bridge girders for the revised sequence must be prepared. While this 

work is not part of the true erection work, the associated calculations may be required 

along with the erection submittals. In addition to verifying the strength and stability of the 

bridge framing, these calculations should address any alterations to the concrete mix, 

such as the use of set retarding or other admixtures. Girder elevations and fillet height 

drawings or tables also should be prepared.

SECTION 4. GIRDER SETTING

Provisions in the erection plans for setting girders should include delivery locations and 

girder orientations. Crane locations for unloading, travel with load (if required), and 

setting are then developed and shown in the plans. Crane selection is normally 

performed by the erector, and while cranes must have adequate lift capacity and reach, 

availability and cost are often significant factors in final equipment selection. 

The erection plans should include the lifting weight of each girder or girder segment and 

the location of lift points. Calculations for the center of gravity should be included, 

particularly for curved girders or if girders are to be set with cross-frames attached, and 

this should be clearly called out along with the resulting total assembly weight. The 

tabulated pick weights must include the weight of the hook block and all required belowthe-hook rigging. The lifting radius and maximum radius for setting the girder should be 

shown in the erection drawings. This information is often presented in a table on the 

drawings.

Crane capacity charts for each crane to be used should be provided and clearly labeled 

to indicate the specific make and model of the crane, the counterweight configuration, 

boom length and type, and track or outrigger positions. For unusual lifting conditions, a 

trial lift may be made to verify equipment selection and rigging configurations. 

Equipment data and lifting charts are often submitted as attachments in the erection 
Engineering for Structural Stability in Bridge Construction Reference Manual

8.16

procedure submittal and should include data for all rigging and below-the-hook devices. 

Crane locations on plan drawings show the center of rotation of the crane along with 

maximum lifting radius. 

Loads on tracks or outriggers can be large. Figure 8-11 shows a typical ground 

pressure output for a crawler mounted crane with ground pressures exceeding 10,000 

pounds per square foot for several lifting positions. Erection plans should state the 

required allowable soil bearing capacity and maximum applied loads. Crane mats, 

bearing pads under outriggers, as shown in Figure 8-12, and compacted crushed stone 

pads are often required to distribute crane, or other equipment, loads and must be 

shown on the drawings and detailed if used. Allowable soil pressures can be developed 

in accordance with the AASHTO Specifications, recognizing the short term nature and 

localized effects of the maximum crane loads. 

For picks of single members using multiple cranes, the load distribution between cranes 

should be shown along with the method to monitor and control the distribution during 

lifting. The erection plans should include details of lifting and spreader beams, eveners, 

beam clamps, lifting slings, sling angles, and other lifting aids.

When girder erection will take place using barge mounted cranes, the erection plans 

should show barge/crane locations as well as any supply barges. Barge sizes, 

configurations and any deck modifications should be shown along with the method of 

maintaining barge position (spuds, anchors, combinations). If anchors are to be used, 

their location must also be indicated. The plans should include navigation channel limits, 

when applicable, and water depths. Barge stability requirements, such as which 

compartments are to be flooded, should be consistent with the calculations. Notes 

should include operational limits for wind, waves, and currents. A sample plan for a 

crane operating from a barge is shown in Figure 8-13, and the accompanying notes are 

shown in Figure 8-14. Note that in Figure 8-13 the front barge ballast tanks are required 

to be flooded for the crane position and usage shown. The notes in Figure 8-14 provide 

specific crane operating limits based on the barge stability calculations. Requirements 

and positions for tugs, pushers, or other support vessels should be shown along with 

locations of docks or moorings. Documentation that all required authorizations and 

permits have been obtained from the Coast Guard, US Army Corps of Engineers, and 

local agencies should be provided as part of the submittals.
Engineering for Structural Stability in Bridge Construction Reference Manual

8.17

Figure 8-11 Crane Track Pressures for Crawler Crane
Engineering for Structural Stability in Bridge Construction Reference Manual

8.18

Figure 8-12 Truck Crane on Outriggers Supported on Timber Mats
Engineering for Structural Stability in Bridge Construction Reference Manual

8.19

Figure 8-13 Plan for Crane Operating from Barge
Engineering for Structural Stability in Bridge Construction Reference Manual

8.20

Figure 8-14 Plan Notes for Crane on Barge
Engineering for Structural Stability in Bridge Construction Reference Manual

8.21

SECTION 5. GIRDER STABILIZATION

Prior to release of the girder load by the lifting equipment, all provisions for temporary 

bracing and support must be in place. These stabilization provisions should be included 

in the erection plans, along with the sequence of installation. Figure 8-6 includes details 

for a temporary beam brace to restrain girder rotation, while Figure 8-5 shows a 

temporary shoring tower design, including support elevations. 

Details of blocking required to temporarily limit movement of expansion bearings and 

multi-rotational bearings should be shown along with the specific bearing locations 

where they are to be installed. While the exact timing of this within the overall erection 

sequence may vary, the work must be completed prior to placing the girders. 

Locations and details of all temporary support must be shown with the specific erection 

stage or sequence to which it applies. When holding cranes are used, the crane type, 

location and the required holding load need to be included, along with the lift point 

locations along the girder. The locations, required load capacity, and design details for 

any strongbacks, such as shown in Figure 8-15, should be provided, as well as the 

location of temporary shoring towers, as shown on the steel girder erection drawing 

plans, Figures 8-1 through 8-3. 

Design drawings for any custom built shoring, Figure 8-5, should be included and show 

all details such as stiffeners, bracing connections and temporary bearings. When 

commercial shoring towers are used, the drawings should show the tower arrangement 

and overall dimensions, the configuration and details for header beams and associated 

framing, and required leg capacity along with manufacturer’s product data. Tower 

foundation type (e.g., timber mats, precast concrete slabs, cast-in-place footings, and 

piles) along with required soil bearing capacity and foundation design details should be 

shown. 

Figure 8-4 shows an example of steel H-piling used to construct a shoring tower. Tower 

heights and top of tower elevations are typically provided in tables. Methods for 

adjusting elevations and tower release procedures should be provided, and for 

commercial shoring, limits on the extension of screw height adjusters should be 

included as they can significantly affect tower leg capacity. The procedure for tower 

release must not result in uneven load distribution or deformations to the erected 

structure. Provisions for protecting towers from impact by construction operations or 

traffic should be shown on the drawings as well.
Engineering for Structural Stability in Bridge Construction Reference Manual

8.22

Figure 8-15 Precast Concrete Girder Supported on Strongback

Bolting requirements for girder splices and diaphragms or cross-frames are normally 

controlled by owner standard specifications. Any deviation from this practice (with owner 

approval) needs to be called out in detail, including connection location and specific 

bolting and pinning requirements, to include the number of bolts and/or pins in the 

connection as well as their location within the connection. Details must be shown for 

temporary girder end bracing or tie-downs. This includes product data and installation 

details for concrete anchorages. When these connections are made to permanent 

structures, methods for their removal and local repair details, if needed, should be

provided.

SECTION 6. SUBMITTALS

The bridge erector or general contractor should submit the erection plans with 

supporting calculations and documentation to the bridge owner for review. Where third 

party review is required, for instance along some railroads, this review should be 

completed prior to submittal to the owner unless other procedures are agreed upon. 

Most bridges built are composed of straight girders of steel or concrete with spans 
Engineering for Structural Stability in Bridge Construction Reference Manual

8.23

under 100 feet and on straight or slightly skewed alignments. While problems may occur 

with these “smaller” structures, erection submittal requirements should not be overly 

complex for the contractor, or require extensive review efforts by the owner. As an 

example, the Kansas Department of Transportation has three categories of bridge 

erection, based on bridge complexity, and each has an associated set of submittal 

requirements. Factors such as adjacent railroads, larger skew angles, or erection over 

in-service roadways might require more detailed submittals, even for smaller structures.

Recognizing differences in bridge complexity, two bridge classifications, Class A and 

Class B, each with its own submittal requirements, are discussed in this Manual. The 

two submittal classifications, that are presented in the following paragraphs, allow 

balancing submittal requirements with bridge complexity. Class A bridges are those 

meeting all of the following criteria:

• Span length less than 140 feet for steel girders or 120 feet for concrete girders 

(longest span)

• Maximum of one field splice in any span

• Girder radius of curvature is greater than 20 times the span length

• Skew angle less than 30 degrees

• Structure does not cross traffic lanes or railroad tracks

• No multi-crane lifts or erection from floating equipment (except standard twocrane PPC lifts)

• Shoring towers or strongbacks or hold cranes are not used

Bridges that do not meet the Class A criteria are considered Class B bridges. In 

addition, the owner may elevate a bridge to Class B based upon engineering judgment 

or unique girder erection conditions. While permits and approvals from railroads, Coast 

Guard, U.S. Army Corps of Engineers, etc. are listed under Type B bridges, all 

applicable permits must be provided to the owner regardless of the erection scheme, 

and may be provided separately from the erection procedures. Permits may have 

expiration dates and require periodic renewal. The minimum submittal requirements for 

each bridge class are as follows:

Class A bridge:

• Erection plans showing site conditions, crane positions, and girder splice 

locations

• Girder transportation plan

• List of all equipment to be used

• List of members/parts with weights

• Crane locations and lift weights
Engineering for Structural Stability in Bridge Construction Reference Manual

8.24

• Crane configuration and lifting charts

• Erection sequence

• Temporary bracing requirements (provide sketches as a minimum)

• Timing of bracing installation

• Bolting sequence and minimum number of bolts and pins for each splice

• Name and credentials of the erection superintendent who will be in charge of the 

field activities

• Erection schedule

• Traffic control plan

• Contingency plan

Class B bridge: All information for a Class A bridge, plus:

• Drawings of all girder or girder assembly placements with rigging requirements 

and lift calculations

• Drawings for all shoring towers, strongbacks and temporary bracing including, 

foundations, mats, etc.

• Details for any bearing restraints or blocking

• Removal procedures and any repairs for any temporary bracing, anchorage, 

bearing restraints, etc. 

• Manufacturer’s data sheets for all rigging devices, hooks, blocks, pre-engineered 

shoring, anchorage devices

• Methods of protecting shoring towers against accidental impact

• Copies of permits and approvals from railroads, Coast Guard, U.S. Army Corps 

of Engineers, property owners, etc.

• Calculations substantiating structural integrity and stability of members at each 

stage of erection. Compilation of all design loads and associated deflections.

• When drop-in girders are used, calculations for temperature effects for fit-up and 

stresses due to any required jacking forces. Include details for jacking and 

applied load tables. 

• Calculations substantiating structural integrity of partially bolted connections

• Calculations substantiating the structural integrity of all bridge abutments, 

retaining walls, and underground utilities affected by crane or other equipment 

loads

• Calculations and revised girder elevation and fillet height drawings in the event 

an alternate deck placing sequence is proposed. If concrete is modified with 

retarders or other admixtures, mix design data should be included.
Engineering for Structural Stability in Bridge Construction Reference Manual

8.25

• When jacking is used, provide tables of load, jack pressure, and associated 

movement/jack elongations.

• Stressing procedures, loads, elongations, and sequencing for post-tensioning. 

• Manufacturer’s data and load calibration data for jacks used for stressing or 

lifting/pushing.

• Drawings should include general notes for materials and erection operations. 

Design wind, live, and dead loads should be listed as well as design soil bearing 

capacities.

Erection plans and calculations should be prepared under direction of a Licensed 

Professional (or Structural) Engineer and should be sealed prior to submittal. Preferably 

for all projects, but certainly for Class B bridges, a meeting of the parties involved 

should be held to review erection procedures. 

Submittals of erection plans and supporting documents should be reviewed by the 

bridge owner or an engineering firm, generally the bridge design consultant under 

contract to the owner. Review requirements and schedules are normally stipulated in 

the standard specifications, which may sometimes be modified for larger or more 

complex projects by special contract provisions. 

The review should be performed by staff, or owner’s consultant, with experience in 

bridge design and construction practices. The Engineer of Record may perform the 

review since he/she will be aware of the design requirements of the project. Normally, 

the review does not include a complete check of drawings or calculations. The review 

may address areas affecting public safety, assure that proper Quality Assurance/Quality 

Control procedures have been followed, and identify conditions that have caused 

problems in past projects. 

There may be situations where project design criteria or constraints that are not 

apparent to the erector or the erector’s engineer may have significantly influenced 

project design and require modification of erection plans. All review comments should 

be provided to the erector/contractor for resolution. Upon resolution, a final erection 

submittal should be made, and serve to control erection. Any changes to the accepted 

erection sequence require developing supporting documentation as well as resubmittal 

and review prior to undertaking further erection activities. 
Engineering for Structural Stability in Bridge Construction Reference Manual

8.26

SECTION 7. ERECTION CHECKISTS

The following checklist may be used as an aid in reviewing bridge erection submittals 

and assuring completeness. The applicability of the specific items will vary based on the 

bridge complexity and owner requirements.

Item Included N/A

• Topography  

• Structure framing plan with members labeled  

• Field splice locations  

• Member delivery location and orientation  

• Adjacent structures  

• Underground utilities/structures  

• Overhead utilities  

• Roads, railroads, waterways

o Locations

o Clearances

o Traffic Control

















• Crane locations

o Crane type

o Lift radius

o Capacity

o Work pads, foundations

o Travel paths

























• Temporary support locations

o Design load

o Required capacity

o Elevations

















• Holding cranes

o Crane type

o Location

o Hold load and radius

















Figure 8-16 Checklist: Plan Drawings (to Scale) for Each Erection Stage
Engineering for Structural Stability in Bridge Construction Reference Manual

8.27

Item Included N/A

• Member rigging

o Load capacity

o Arrangement and component sizes

o Weights

o Center of gravity of lifted piece





















• Crane lifts at each stage

o Lift load including rigging

o Lift radius

o Crane configuration/boom length

















• Falsework

o Location

o Applied loads/required capacity

o Tower design details

o Foundation requirements

o Elevations

o Method for release





























• Temporary bracing

o Location

o Member sizes

o Connection details

o When installed/removed

o Bearing blocking details

























Figure 8-17 Checklist: Detail Drawings
Engineering for Structural Stability in Bridge Construction Reference Manual

8.28

Item Included N/A

• Erection sequence for each member

o Primary members

o Secondary members













• Temporary tie-down  

• Time requirements for bracing installation  

• Temporary bracing installation/removal  

• Splice and connection bolting data

o Number of bolts/pins

o Location of bolts/pins













• Contingency bracing/wind speed limits  

• Temporary bracing

o Location

o Member sizes

o Connection details

o When installed/removed

o Bearing blocking details

























• Barges

o Configuration, barge data

o Applied loads

o Crane locations and lift data

o Spuds/anchoring arrangements

o Storage areas and capacities

























• Temporary jacking

o Location

o Jack data

o Maximum applied loads

















Figure 8-18 Checklist: Written Procedures and/or Drawing Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

8.29

Item Included N/A

• Design criteria provided  

• Level of analysis is appropriate  

• Stage-by-stage analysis used  

• Support conditions used in modeling match erection 

conditions

 

• Correct loads utilized  

• Member strength verified for each erection stage  

• Member/system stability verified for each erection stage  

• Second-order amplification effects addressed  

• Girder support reactions computed for worst case load 

configurations

 

• Bearings verified for load capacity and rotation  

• Center of gravity and lifting loads computed for each 

piece/assembly

 

• Temporary bracing and hold down design included

o Strength

o Stiffness

o Connection details

















• Temporary shoring system design

o Loads

o Settlement/deflection

o Foundation

















• Calculations for integrity of existing/adjacent structures 

due to crane and equipment loads

o Abutments

o Wingwalls / retaining walls

o Slopes

o Underground utilities/structures





















• Barge stability calculations  

• Calculations for the deck placement if altered from the 

Contract Documents

o Member capacity verifications

o Member stability verifications

o Bearing reactions; uplift

o Girder deflections

o Deck fillet heights

























Figure 8-19 Checklist: Calculations at all Stages of Erection
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8.30

Item Included N/A

• Project superintendent’s name and experience  

• Documents sealed by Professional Engineer  

• Manufacturer’s data for all supplied devices and 

equipment

o Crane load charts

o Beam clamps

o Slings, shackles, turnbuckles, chain, straps, etc.

o Jacks

o Spreader and lifting beams

o Pre-engineered shoring systems





























• Documentation for third party reviews / coordination

o Railroads

o Utilities

o Coast Guard

o Corp of Engineers

o Other regulatory / governmental agencies

























• Girder transportation and shipping plan and supporting 

calculations

 

Figure 8-20 Checklist: Additional Submittal Data
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8.31

SECTION 8. BRIDGE REMOVAL PLANS

Plans and procedures for bridge removal projects should be generally consistent with those 

discussed for erection. The extent of information to be included will vary with the project type 

and extent. For instance, requirements for a project for concrete deck removal and widening 

need to assure that the existing girders, as well as the new girders, possess adequate strength 

and stability in the conditions with the deck removed, once compression flange lateral restraint 

is removed. While girder rotations at connections during erection need evaluation to assure 

member fit-up, this is not a concern when girders are removed.

Dividing removal projects into the same categories as shown in Section 7 is recommended, and 

the Erection Checklist may also be used, noting that the erection supervisor would now be the 

demolition supervisor. Among items that may not be included in the erection checklist that 

would apply to demolition are the following:

Item Included N/A

• Measures to protect existing facilities from falling debris  

• Equipment and method of debris removal  

• Location for debris disposal  

• Disposal and transportation permits  

• Protection of waterways

o Pre-demolition and post-demolition surveys

o Erosion and contamination













• Noise pollution  

• Effects of equipment operating from structure during 

demolition

 

• Impact loads to the structure from removal activities  

• Dust control  

• Water/runoff control  

Figure 8-21 Checklist: Demolition Checklist

SECTION 9. SUMMARY

The erection plans and procedures describe the means and methods to be used by the 

contractor in erecting or demolishing the bridge superstructure. They must assure that sufficient 

strength and stability is maintained at each stage of erection and also provide contingencies for 

unexpected events. They not only guide the contractor, but also provide information for the 

Owner’s review. The documents must be complete and include supporting engineering 

calculations.

In order to match erection document requirements to bridge complexity, two bridge submittal 

classifications, A and B, are presented. Owners may, of course, have other requirements. 

Checklists are included in Chapter 8 which can assist in assuring complete documents 

preparation as well as their review.
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9.1

CHAPTER 9

MAJOR AND UNUSUAL BRIDGE CONSTRUCTION

SECTION 1. INTRODUCTION

While girder bridges are the predominant type of bridge constructed, other bridge types 

are used where economic or aesthetic considerations make them advantageous. 

Stability during erection must be considered for all bridge types, and this chapter 

discusses some of the erection related stability issues for several of these. The in-depth 

evaluation of major and unusual bridges for erection conditions is beyond the scope of 

this Manual. However, many of the guidelines and practices outlined in this Manual will 

also be applicable to them. Loads and load combinations may follow those for girder 

bridges. Also, many of the other bridge types still utilize girders and bracing within the 

overall structure, and the stability of these members must be addressed for construction 

conditions. Unlike many girder bridges, provision for bridge erection is normally part of 

the initial bridge design for more complex structures, and for bridges such as cable stay 

configurations may often control bridge design.

SECTION 2. ARCH BRIDGES

Arch bridge structures have evolved greatly from the masonry construction still in 

existence from as early as 1300 BC to the state of the art structures seen today for 

many medium to long span applications. Today, arch bridges are predominantly 

constructed of steel, reinforced concrete and pre-stressed/post-tensioned concrete, and 

are erected in two primary configurations: tied arches and true arches, as shown in 

Figure 9-1.

Figure 9-1 Arch Bridges – Tied and True Types
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9.2

In a tied-arch bridge, the bottom chord member “ties” the two ends of the arch rib 

together to resist the outward thrust at the base of the arch through tension and keeps 

the arch element in compression. In a true arch, the thrust at the base of the arch is 

resisted by the mass of the bridge’s foundations at the abutments or piers to keep the 

arch in compression. In addition to the AASHTO Specifications, guidance on arch 

design is contained in publication FHWA-NHI-11-023, Design Guidelines for Arch and 

Cable-Supported Signature Bridges.

9.2.1 Steel 

Steel is a popular and economical component for arch bridges and can be used in either 

a trussed or solid-ribbed arch configuration. The trussed arch uses an arch rib that is 

built-up in the form of a truss.

In some instances, particularly for short spans, a tied arch bridge can be erected in one 

piece under the proper conditions. In most instances, tied-arch bridges are constructed 

in place through a sequence of carefully designed and planned erection stages. Figure 

9-2 illustrates the erection stages for an arch where the tie girder is supported on 

falsework. 

Figure 9-2 Arch Bridge Erection Staging on Falsework
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9.3

Figure 9-3 Erection of Tied Arch Bridge Using Falsework

Tied arch bridge erection begins by setting the tie girder sections and end cross girder 

to which the arch ribs attach. The bearings must be blocked both for rotation and to 

provide thrust restraint, unless the tie girder is fully installed prior to starting the arch. 

Since the tie girder is designed primarily as a tension member, it must be temporarily 

supported until the hangers are installed, and must be investigated for biaxial bending 

due to dead loads, any construction loads, and wind. 

Arch segments and tie girders can be supported from below by falsework (Figure 9-2), 

or suspended from cable stays running from temporary towers. In either case, once the 

arch section is positioned, it acts like a vertically curved beam spanning between 

temporary supports under both self-weight and lateral wind loads. The lateral wind loads 

must be transferred into the temporary support towers or through angled stay cables. 

Methods of adjusting the sections vertically at support towers through jacking are 

usually provided, and local buckling effects at support points must be examined. Figure 

9-3 shows an arch being erected utilizing falsework for tie-girder and arch temporary 

support. Arches are built from both abutments toward the crown and a closure arch 

segment completes the arch. Sufficient gap must exist to allow inserting this segment, 

and provisions are often included to jack open the gap to aid in fit-up. Local bucking of 

members due to jacking should be investigated and the effect on the overall arch 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.4

considered; though this is normally not a problem as the required arch spread is very 

small compared to its span. For short arches though, the stresses should be 

investigated.

Prior to releasing any shoring, the arch lateral bracing must be in place. Floor beam 

camber can cause the arches to rotate slightly outward prior to the deck placement, 

making it necessary to pull the crown of the arches together in order to make the top 

strut connections.

In placing and tensioning hangers, the loads to the arch must be kept symmetrical. Arch 

stability is reduced when non-symmetric moments are applied. Local stresses in the 

arch as well as the tie girder webs and flanges due to tensioning need to be evaluated 

for the specific jack stands to be used as these may differ from that assumed during the 

original design. 

A deck arch is a true arch with a deck built above the arch. Construction is carried out in 

much the same manner as a true arch except no tie girder is present. Setting of 

columns and deck framing should progress in a manner that produces symmetrical 

moments in the arch. Temporary bracing of the columns for wind and general stability 

will be required until the deck and permanent lateral bracing is in place. 

Erection of precast arch bridges is performed in a manner similar to steel arches of the 

same configuration. It is critical that field connections achieve adequate strength at each 

stage of construction. 

Cast-in-place concrete arches, and any cast-in-place portions of precast arch bridges, 

are supported by falsework designed in accordance with the AASHTO Specifications for 

Bridge Temporary Works.

SECTION 3. TRUSSES

Truss bridges have been used throughout history. The development of railroads 

increased truss construction, starting with timber truss bridges in the early 1800’s and 

continuing with steel in the late 1800’s.

A truss is a system of members comprising a series of triangles. A truss distributes the

load by creating tension and compression in the members rather than bending. Trusses 

can be advantageous due to their high strength-to-weight ratio, ability to be 

prefabricated, and ability to create long spans.

Truss floor systems consist of rolled beams or built-up girders. Their stability during 

deck placement should be verified based on flange bracing locations as discussed 

elsewhere in this Manual. 

There have been many types of truss configurations used and patented over the years. 

The most common truss type seen in modern bridge construction is the Warren Truss 
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9.5

patented by James Warren in 1848. The Warren Truss consists of equilateral triangles 

between a top and bottom chord and is often seen with and without vertical members. 

Other typical truss types include Howe Truss, Pratt Truss, and Lattice Truss. Figure 9-4

provides schematic representations of the Warren, Howe, Pratt, and Lattice trusses.

Figure 9-4 Typical Truss Configurations

The erection methods commonly used in the construction of truss bridges include ‘stick 

building’ the truss in its final position or pre-assembly of the truss on-site and lifting or 

sliding the truss into its final position. The erection method utilized is typically

determined by the structure’s size, weight, and geometry, construction cost, and site 

conditions. 

9.3.1 Stick Built Truss Erection Analysis

When a truss is erected one piece at a time, it is called stick built. Typically, lower 

chords are set on substructure units or falsework, and vertical, diagonal, and upper 

chord members are installed piece by piece to complete sections of the truss. After 

sections of the truss have been completed between panel points to allow for truss action 

within the members, piece by piece erection of the truss continues by cantilevering the 

truss past the substructure units and falsework. Depending on the length of the 

cantilever, falsework or temporary suspension cables may be required to support the 

truss at intermediate panel points during erection. Generally, a stick built truss will 

involve erecting multiple portions of the truss simultaneously until they meet and the 

truss can be closed. 

As with any structure type, ensuring the strength and stability of the components while 

in an incomplete stage of erection is essential, and truss bridges require significant 

investigation to determine the best erection sequence. The truss structure must be 

analyzed during each stage of construction for the dead load of the truss members, 

construction live loads, and environmental loads such as wind and thermal forces. 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.6

When analyzing the structure during each erection stage, the following items should be 

investigated to ensure the strength and stability of the individual truss members and the 

structure as a whole:

• Analyze truss members and ensure demand does not exceed capacity

• Analyze the structure for lateral loading

• Analyze truss members for concentrated loads

• Analyze bearing capacity

• Verify deflection is controlled to allow proper fit-up for subsequent stages of 

erection

Often times, the loads induced during erection may create tension or compression 

forces in the members that are greater than or opposite to the forces anticipated during 

design for the completed structure. If a compression member is overstressed during 

erection, temporary bracing can be installed to reduce the member’s effective length 

and increase capacity. For overstressed tension members or when bracing is not a 

viable solution for compression members, the cross-sectional properties of the member 

can be increased or the erection sequence can be revised. For diagonal members that 

cantilever from the completed portion of the truss prior to erection of the upper chord, 

temporary cable supports can be installed to support the cantilevered end of the 

diagonal member. Falsework or temporary suspension cables can also be provided 

during erection to support the truss at intermediate points during erection and reduce 

demand on the truss members (Figure 9-5).

During each stage of erection, the structure should be analyzed for lateral loading 

including wind, thermal and/or seismic forces. Temporary bracing may be required 

during the first stages of erection before permanent lateral bracing, struts, floor beams, 

and portals are installed and can adequately brace the structure against lateral loads. 

Additionally, consideration should be given to the amount of the truss structure that is 

erected beyond the lateral bracing, struts, floor beams, and portals that have been 

installed. Typical practice is to install these secondary members as soon as sections of 

the truss have been completed and prior to additional erection of the primary truss 

members.

Jacks are typically located at falsework locations to allow for vertical adjustment of the 

truss lower chord to ease erection fit-up. At jacking locations and at falsework bearing 

locations, concentrated forces are applied directly to truss members and these 

members must be analyzed for local buckling, yielding, and crippling. To reduce the 

localized loading on the truss members, it is recommended that the falsework and jacks 

be located directly beneath panel points of the truss, which will distribute the 

concentrated loads to the vertical and diagonal members framing into the panel point.
Engineering for Structural Stability in Bridge Construction Reference Manual

9.7

Figure 9-5 Temporary Kingpost Supporting 

Cantilever Construction of Bridge 

Truss Over the Mississippi River 

Permanent truss bearings should be analyzed during each erection stage to ensure 

both the strength and rotational capacity of the bearings are not exceeded. Often times, 

vertical loads during erection are substantially less than design loading. However, 

lateral capacity and rotational capacity of the bearing can be critical and should be 

investigated. Additionally, consideration should be given to whether permanent 

expansion bearings need to be temporarily blocked prior to truss closure to ensure 

lateral stability of the structure.

As the partially completed truss structure cantilevers from the substructure units and 

falsework, the existing structure should be analyzed for potential uplift at the support 

locations. It is important to investigate the effects of wind and thermal loading during the 

analysis. If uplift does occur at the supports, counter-weighting of the structure or tiedowns should be designed and installed, which will also assist in the control of 

deflection during erection.

During all stages of erection, the deflection of the individual truss members and the 

structure as a whole should be investigated. It is important to minimize deflections at 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.8

each stage of construction to ease fit-up of the truss elements and reduce the time 

required to fit-up truss member connections. Where required, temporary bracing or 

cable supports can be installed to minimize deflection.

9.3.2 Pre-Assembly Erection Analysis

Depending on the size and weight of the truss and the site conditions, the entire truss 

structure or portions of the truss structure can be pre-assembled on-site and lifted or 

slid into their final position. Examples of this method include pre-assembling portions of 

a truss structure over a waterway on barges and lifting the truss vertically into final 

position and pre-assembling portions of the truss on structure approaches and 

launching the truss horizontally. Ensuring the strength and stability of the components 

while in an incomplete stage of erection is essential. The truss structure must be 

analyzed during each stage of construction for the dead load of the members in place, 

construction live loads, and environmental loads such as wind and thermal forces. 

When analyzing the structure, the following items should be investigated to ensure the 

strength and stability of the individual truss members and the structure as a whole:

• Analyze truss members and ensure demand does not exceed capacity

• Analyze the structure for lateral strength and stability

• Analyze truss members for concentrated loads

In some cases, only a portion of the structure is pre-assembled and lifted or slid into 

place. Additionally, the support or falsework locations are typically not located in the 

same positions as the truss support in the final design. Therefore, the loads induced 

during erection may create tension or compression forces in the truss members that are 

greater than or opposite to the forces analyzed for the completed structure during 

design. If it is determined that truss members are overstressed during erection, 

temporary bracing can be installed, the cross-sectional properties of the member can be 

increased, or the erection plan can be revised.

During lifting or sliding of the truss, it is important to analyze the structure for lateral 

loading. Temporary bracing or tie-downs of the truss and falsework may be required to 

stabilize the structure as a whole. 

At jacking locations, concentrated forces are applied directly to the truss members, 

which must be analyzed for local buckling, yielding, and crippling. Where possible, it is 

recommended that the jacks be located at panel points of the truss, which will distribute 

the concentrated loads to the vertical and diagonal members or floor beams framing into 

the panel point and significantly reduce the localized loading on the truss members.

SECTION 4. CABLE-STAYED BRIDGES

The cable-stayed bridge has emerged as one of the more dominant mid to long span 

bridge types used today. The structure type is defined by having at least one tower, or 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.9

pylon, extending from the bridges foundation and from which cables are attached to 

support the bridge deck. They are commonly used to accommodate clear span needs of 

anywhere from 400 feet to 2000 feet. 

Design considerations for cable-stayed bridges are included in the FHWA-NHI-11-023 

publication, previously referenced. Construction practices for these bridges are 

presented in the Construction Practices Handbook for Concrete Segmented and CableSupported Bridges, which was developed by the American Segmental Bridge Institute 

(ASBI).

SECTION 5. BRIDGE LIFTING AND MOVING

Lifting and moving of bridge structures may involve partially, as well as fully, completed

bridges. General stability concerns for girders are similar to those during normal 

erection, and when the deck is in place during the lifting or moving operation, a laterally 

stiff structure is developed. 

Overall effects of lifting and moving are generally related to changes in support 

locations from those for the bridge in its final position. This change in support location 

can cause stress reversals in primary members, and as a result, distances between 

temporary and permanent support locations should be the minimum consistent with 

clearances and access for moving. 

Local stresses at jacking or lifting locations must be examined, particularly for web 

buckling or crippling. Stiffeners are often added even when not required for member 

capacity in order to accommodate tolerances in jack location. Jacking systems must be 

designed to ensure controlled lift pressures among all locations and provide for read-out 

of loads and pressures during jacking. When a structure is moved after vertical jacking, 

blocking should be used to support the loads rather than the jacks, or locking jacks 

secured against lateral movement must be used. When structures are moved laterally 

by jacks or pullers, guides should be used to control lateral movement and provisions 

for lateral load distribution between components considered. The capacity of 

diaphragms or cross-frames may be insufficient if placed under lateral load. 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.10

Figure 9-6 New Truss on Temporary Trestle for Slide-In

Structure lifting must not induce differential vertical deflection, or overall structure 

misalignment, as it will cause stress redistributions. When bridges are moved 

longitudinally (Figure 9-6), axial loads may be induced into girders, which increase 

compressive stresses. Though slide plates and rollers minimize these forces, a 

conservative estimate of their value should be used to account for uncertainties in field 

operations. Temporary bents used to support structures during lifting or sliding 

operations should be designed for worst case vertical and lateral loads. 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.11

SECTION 6. MOVABLE BRIDGE STABILITY

Figure 9-7 Initial Balancing of the Congress 

Avenue Bridge over the Chicago 

River

Movable bridges are essentially very large machine structures that rely on balance to 

safely operate. The most common types of movable bridges are vertical lift bridges 

(bridges where the movable span moves up and down vertically much like an elevator) 

and bascule type bridges (bridges where the movable leaf rotates either about a fixed 

point or rolls back on itself). Maintenance and construction on a movable bridge can 

alter the balance of a movable bridge which can greatly affect the safe operation of the 

bridge. 

Safe construction and maintenance for a movable bridge requires the contractor’s 

construction procedures to be engineered to ensure the safety and stability of the bridge 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.12

through all steps of the construction. Even small changes in the weight of the movable 

leaf or counterweight can cause the movable span or leaf to become uncontrollable, 

resulting in serious damage to the bridge and possible injury to those working on the 

bridge. 

Because of the complex interactions of machinery, operating systems and weight, 

owners often specify that the contractor hire a Movable Bridge Systems Coordinator 

(MBSC) to oversee the work. The MBSC’s role is to ensure that all systems are fully 

integrated and coordinated to verify the safe performance of the work and operation of 

the bridge upon completion of the work. The MBSC should be an experienced Licensed 

Professional or Structural Engineer knowledgeable in the design and rehabilitation of 

movable bridges.

The individual structural components of the bridge include girders or truss members that 

must be analyzed to ensure strength and stability of the members before and during 

deck placement. In reconstruction, deck removal may produce long unbraced flange 

lengths. As seen in Figure 9-8, construction and rehabilitation may take place with the 

bridge in its “up” position, resulting in increased wind loads to the open structure. 

Key elements to ensure movable bridge stability during construction include the 

following:

• Bridge Lockout. The safest means to work on a movable bridge is to lock the 

bridge leaf in the open position. For bascule type bridges, this is accomplished 

through the use of steel struts to wedge the leaf in the open position. The struts 

are typically designed to resist wind forces on the leaf, other construction loads, 

and the horizontal component of the weight of the span. For vertical lift bridges, 

typically additional weight is added to the counterweight block to ensure that the 

counterweight is always heavier than the span being worked on. Where it is not 

possible to lock the movable leaf or span in the open position due to traffic or 

other constraints, other means of stabilizing the movable span must be employed 

to prevent movement during the construction work. For bascule type bridges, this 

often means the installation of shoring towers to support the counterweight 

during construction. These shoring towers are designed to carry all or a portion of 

the weight of the counterweight. If river traffic prevents shoring of the movable 

leaf or span, then strictly maintaining the balance of the movable leaf is essential 

for the safe completion of the work. Motors and bridge controls are also positively 

locked out to prevent operation during conditions of unbalance or when work is 

occurring on the bridge. This is typically accomplished through the lock out of the 

knife switches or incoming power. Additional measures may also include lashing 

and blocking of the gear train to prevent movement. 

• Bridge Balance. Determining the initial state of balance is a critical first step for 

working on a movable bridge. Often, the state of balance is unknown. Older 

bridges may not have had balance calculations performed. For direct current 

drive bridges, motor amp readings can provide a simple means of determining 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.13

balance. Motor amperage (amp) readings should be nearly the same during 

opening and closing when the bridge is in balance. Higher amp readings during 

opening indicate a span heavy condition. Higher amp readings during closing 

indicate a counterweight heavy condition. Amp readings for alternating current 

bridge drives, particularly the more sophisticated Programmable Logic Circuitry 

(PLC) drives, cannot be relied upon to determine balance. In these cases, strain 

gage testing of the bridge operating machinery is often the only reliable means of 

determining the state of balance of the bridge.

Regardless of the bridge type or position of the movable leaf during work, it is 

essential that accurate records be kept of the weight and location of the material 

being removed and added to the movable span and counterweight. After 

determining the initial balance of the bridge, a spread sheet is usually prepared 

that documents the weight and location of the materials removed and added to 

the bridge. The center of gravity of each member is determined and measured in 

the horizontal, vertical, and transverse direction in order to develop moments 

about a fixed point. A movable leaf is considered in balance when the sum of the 

moments of the movable leaf and counterweight is zero.

• Structural Modeling. Special care must be taken when performing work on the 

main load carrying members of a movable bridge. Main truss chord members 

and diagonals can have significantly different loadings depending upon whether 

or not the movable leaf is in the open or closed position. Developing a computer 

model of the bridge to allow analysis of various stress states during construction 

will assist in assuring the stability of the bridge leaf and avoid overstressing 

members. On older bridges with built-up members, the model will allow the 

engineer to assess how much of a member may be safely taken apart for 

rehabilitation or replacement. Typically, jacking struts or tension rods are used to 

transfer loads around a component being rehabilitated. Major repairs to principal 

members should be avoided under live load conditions or when the bridge is 

being moved since the member loads may increase significantly under these 

conditions. 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.14

Figure 9-8 Intermediate Balancing of the Congress Avenue 

Bridge over the Chicago River
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9.15

Figure 9-9 Late Stage Balancing of Congress Ave Bridge over the 

Chicago River

• Placing the bridge into service. No matter how accurately records are 

maintained on the removal and installation of materials during rehabilitation, it is 

impossible to account for all of the materials or weights removed and added to 

the bridge. One of the safest approaches to placing a rehabilitated movable span 

into service is to ensure that the movable leaf or span can always be controlled. 

For spans or leaves rehabilitated in the open position, this typically means 

ensuring that the span or leaf is counterweight heavy when initially moved. For 

spans or leaves rehabilitated in the closed position, this typically means ensuring 

that the movable span or leaf is span or leaf heavy. Additional weight is added to 

the counterweight or leaf to create this arrangement. A procedure should be 

developed by the contractor’s engineer to incrementally raise or lower the 

movable span or leaf, stopping the movement, setting the brakes and then 

releasing the brakes the see if the span or leaf moves on its own. Using an 

incremental approach, Figure 9-7 and Figure 9-8, to placing the bridge in service 
Engineering for Structural Stability in Bridge Construction Reference Manual

9.16

means that the span or leaf is never brought fully open or closed before a 

thorough understanding of the balance is known. Moving the span or leaf in small 

increments means that there is never enough momentum to prevent the leaf from 

being controlled and stopped should an unbalance condition develop. 

Adjustments can be made to the additional weight added to the bridge in order to 

maintain safe control at all times. Occasionally, an owner will specify that the 

span or leaf cannot be powered open or closed during the initial movement. In 

these cases, air winches and pulleys are required to control the leaf or span until 

the full movement is accomplished.

SECTION 7. SUMMARY

While this Manual focuses on stability of girder bridges, as can be seen from this 

chapter there are many other bridge types. Much of what has been presented in this 

Manual is applicable to the erection of larger and more complex bridges as well; 

construction loads and their effects on strength and stability of both individual members 

and member assemblies must be addressed for all bridges. Particularly for unusual or 

complex bridges, the method of erection is an integral part of the bridge design and 

detailed erection procedures should be included with the contract documents.
APPENDIX A

REFERENCES 
Engineering for Structural Stability in Bridge Construction Reference Manual

A.1

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American Association of State High Transportation Officials. AASHTO LRFD Bridge 

Construction Specifications. Washington, D.C.: American Association of State 

Highway and Transportation Officials, 2010.

American Association of State Highway Transportation Officials. AASHTO LRFD Bridge 

Design Specifications, Customary U.S. Units. Washington, DC: American 

Association of State Highway and Transportation Officials, 2012.

American Association of State Highway Transportation Officials/National Steel Bridge 

Alliance. Steel Bridge Erection Guide Specification S10.1. 2007. AASHTO/NSBA 

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American Institute of Steel Construction. AISC Certification Program for Steel Bridge 

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Benitez, Luis and Michael Haas. “Placing Curves Overhead – A Simplified Analysis of 

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Engineering for Structural Stability in Bridge Construction Reference Manual

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Coffelt, Sean Justin. 2010. Stability Analysis of Single and Double Steel Girders during 

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APPENDIX B

DESIGN EXAMPLES

This appendix contains four design examples analyzed with the UT Bridge, UT Lift, 

UTrAp or STAAD computer program. These four example problems are not 

comprehensive but serve to illustrate various important constructability checks; girder 

lifting, girder erection staging, buckling analysis, concrete deck pour sequence analysis, 

for different bridge types. 

The first two examples focus on traditional steel plate girders in continuous multi-span, 

multi-girder systems. The first example features straight steel plate girders in a skewed 

2-span bridge; the second example features curved steel plate girders in a 3-span 

bridge. 

The third example looks at prestressed concrete bulb tee construction. This example 

features a concrete spliced girder bridge, in which the 3 continuous spans are 

composed of end girder segments, haunched girder segments at the piers, and a dropin girder segment at the middle span; the segments are held in place during 

construction with temporary shoring towers and steel strongbacks prior to cast-in-place 

concrete pours at the splice locations. 

The fourth focuses on a steel bridge similar to that used in example #2; however, 

instead of multiple curved I-shape plate girders, this 3-span continuous bridge features 

curved steel tub girders (i.e., open trapezoidal box girders). Although not a 

consideration during the design, this bridge would be classified as fracture-critical for 

inspection purposes, as there are only two tub girders.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.1

Example Problem #1: 2-Span Multi-Girder Skewed Steel Bridge

This example problem illustrates many of the critical engineering checks associated with verification of

an erection / construction plan. It is not intended to be fully comprehensive, as not all bridge elements

and all limit states are being checked at all locations for all forces generated from all relevant load

combinations for every stage of the steel erection and concrete deck pour. Rather, it serves to

illustrate the level of engineering effort required and to show application of the guidelines and criteria

defined in this Manual. In this example, a symmetric 2-span steel plate girder bridge is considered; the

multi-stringer bridge has straight steel girders and skewed abutments and pier. The bridge site is

located in Illinois.

For simplicity, the analysis / calculation cases in this example are numbered from 0 

(crane pick of girder piece) to 5 (start of deck pour). These cases should not be confused with

erection stages or deck pour sequence stages. Although the analysis / calculation cases are

presented chronologically, there are many more stages than cases; only a handful of cases, 

representing a snapshot of the erection or deck pour completed up through a certain stage, are being 

shown here.

Often the unpresented intermediate stages would not govern as an analysis / calculation case (e.g.

four-girder set erected up to splice #2 vs. two-girder set erected up to splice #2; the latter is more

prone to a system buckling mode). And sometimes a given case, although presented and analyzed,

does not need to be checked by inspection (e.g., positive span moment in Case 4 with the completely

erected steel will never govern vs. Case 5 with the additional positive span moment induced by the wet

concrete of the deck pour).

Some force effects are consistently ignored (e.g., shear in the steel girders) because it is obvious that,

although the shear resistance will remain unchanged, the shear demand in the girders due to the final

bridge condition of supporting the steel and concrete selfweight and design live load will far

exceed the temporary shear demand in the girders due to the steel selfweight during erection or due

to the steel selfweight and the wet concrete selfweight during the deck pour. Also, it is assumed that

constructability has been verified in the design by Engineer of Record.

Some design locations are consistently ignored (e.g., the steel girders over the pier) because it is

obvious that, although the negative moment resistance will remain unchanged, the negative moment

demand in the girders due to the final bridge condition of supporting the steel and concrete selfweight

and traffic live load will far exceed the temporary negative moment demand in the girders due to the

steel selfweight during erection or due to the steel selfweight and the wet concrete selfweight during the 

deck pour.

Some analysis / calculation cases should be checked but are, for the interest of brevity, not

checked here (e.g., the next step after Case 3, in which the last piece of girder line G1 is added, such

that G1 is completely assembled and carries its steel selfweight from abutment to abutment, but it is

only discretely braced by cross-frames to the adjacent girders up through splice #2, and unbraced

beyond that).

Some items that this example does not cover, but which may be required in most cases for complete

evaluation, are:

• Recheck of Constructability provisions of AASHTO LRFD BDS

• Deck Pour Sequence Analysis

• Displacements/Cambers/Fit-up forces

• Bearing loads/rotations and temporary blocking details

• Temporary restraints and/or bracing design
Engineering for Structural Stability in Bridge Construction Reference Manual

B.2

• Overturning/uplift checks

• Bolting requirements at splices and connections

• Hardware design (Lifting beams, clamps, jacks, etc.)

• Crane loads/capacity analysis during lifting.

While most of the calculations in the following sections are self-explanatory, commentary are added

where appropriate regarding assumptions, alternate methodology, caveats, omitted calculations,

derivations, etc.

The general plan, elevation, and cross-section of the bridge are presented in the following figures, along 

with the framing plan and basic detailing of plate sizes, etc. Additional figures will appear later in the 

example problem, as needed, just prior to where the relevant calculations are performed.

Getting started

To begin, a meeting is convened with the bridge Erector to understand the means and methods that

will be utilized, and the level of experience that exists on bridges of similar proportions and

slenderness. It is determined that the Erector will lift all pieces using spreader beams and that all

splices and cross-frame connections will be 100% filled with bolts and tensioned “in air” prior to release

from cranes. No erection or pouring of deck concrete will be done when wind speeds in excess of

20mph is forecast. Partially completed steelwork may be left overnight or over weekends, but if wind

speeds in excess of 20mph are forecast, then additional bracing measures will be installed. The

completed steelwork may be exposed for up to 6 months before the deck is completed. For

stabilization of the first erected girder, temporary bracing by guy-cables is desired, to avoid need of a 

third holding crane.

The Erector has experience with erection of bridges with similar proportions: span length = 164 ft,

cross-frame spacing = 25ft, flange width = 16”, skew = 20 degrees. However, there are concerns about

the slenderness of the two-girder stage since the girder spacing is relatively small (4’-11”). Also, the

skewed supports will increase the loads to the cross-frames, which need to be checked.

Analysis

Due to limited Erector experience with a bridge such as this, a refined staged erection analysis is

conducted to better understand the behavior and the force effects in the individual components. The 

structure is modeled using 3D finite element analysis with frame elements. Link elements are

utilized to represent the depth of the cross-frame to girder connections. Fixed bearing locations

modeled with pin supports and expansion bearings are modeled as rollers. The wind, deck pour,

construction dead load, and construction live load forces are simplified to linear loads acting along the

centerline of the girders.

To investigate global stability for the first two stages of erection, an Eigenvalue buckling analysis is

also conducted using the software tool UT Bridge.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.3

Figure B1-1: Example 1 General Plan and Elevation
Engineering for Structural Stability in Bridge Construction Reference Manual

B.4

Figure B1-2: Example 1 Framing Plan
Engineering for Structural Stability in Bridge Construction Reference Manual

B.5

Figure B1-3: Example 1 Cross-section
Engineering for Structural Stability in Bridge Construction Reference Manual

B.6

Figure B1-4: Example 1 Girder Elevation
Engineering for Structural Stability in Bridge Construction Reference Manual

B.7

The following table of contents illustrates the general categories into which this

example problem is subdivided, and the relevant page number at which the start of

each category, and its specific component analysis or calculation tasks, may be

found.

General Category / Description Specific Analysis / Calculation Task Appendix

Page

Table of Contents N/A B.7 

Bridge Data N/A B.8 

Applied Forces Wind Load B.8 

Applied Forces Wind Forces on Girders B.9 

Structural Analysis Erection Analysis B.10

Structural Analysis Deck Pour Analysis & Evaluation of Stages B.13

Figure Single Girder Pick B.14

Figure Girder Clamp Loading B.15

Case 0 (Girder Lift for Splicing) Section Properties & Applied Forces B.16

Case 0 (Girder Lift for Splicing) Applied Stresses B.17

Case 0 (Girder Lift for Splicing) Local Buckling Resistance & lateral Torsional Buckling B.18 

Case 0 (Girder Lift for Splicing) Controlling Resistance & Lateral Bending Stress B.19

Case 0 (Girder Lift for Splicing) Overall Flexural Check & Constructibility Check B.20

Case 0 (Girder Lift for Splicing) Local Flange Stresses at Girder Clamps B.20

Case 1 (Single Girder Unbraced) Section Properties, Applied Forces & Applied Stresses B.21

Case 1 (Single Girder Unbraced) Local Buckling Resistance B.22

Case 1 (Single Girder Unbraced) Lateral Torsional Buckling & Controlling Resistance B.23

Case 1 (Single Girder Braced) Lateral Torsional Buckling & Controlling Resistance B.24

Case 1 (Single Girder Braced) Lateral Bending Stress & Overall Flexural Check B.25

Case 1 (Single Girder Braced) Constructibility Check B.26

Case 2 (Twin Girder System) Global Buckling Resistance B.27

Case 2 (Twin Girder System) Lateral Bending & Interaction with Lateral Bending B.28

Case 3 (Cross-Frame Bracing) Axial Tension & Axial Compression Resistance B.30

Case 3 (Cross-Frame Bracing) Required Strength of Brace B.32

Case 3 (Cross-Frame Bracing) Required & Provided Bracing System Stiffness B.33

Figure Overhang Bracket Loading B.34

Case 5 (Concrete Deck Pour) Section Properties, Applied Forces & Applied Stresses B.35

Case 5 (Concrete Deck Pour) Local Buckling Resistance B.36

Case 5 (Concrete Deck Pour) Lateral Torsional Buckling & Controlling Resistance B.37

Case 5 (Concrete Deck Pour) Lateral Bending Stress & Overall Flexural Check B.38

Case 5 (Concrete Deck Pour) Constructibility Check & Overhang Bracket Forces B.39

Case 1 (Single Girder Unbraced) Eigenvalue Buckling Analysis in UT Bridge B.40

Case 2 (Twin Girder System) Eigenvalue Buckling Analysis in UT Bridge B.41
Engineering for Structural Stability in Bridge Construction Reference Manual

B.8

Bridge Data:

Continuous 2-span steel plate girder bridge, 6 girders total. Out-to-out deck width is 29'-2". Girder

spacing is 4'-11" for a total of 24'-7" between fascia girders. Structural deck slab thickness is 8 in.

Cross-slope of deck is 5%. The two spans are symmetric at 164 ft long each, with a 96 ft long splice

piece over the pier. Abutments and Pier are at 20 degree skew.

Use Illinois as example location; assume height under 30 feet.

Wind Load:

Use Figure 26.5-1A in ASCE 7-10 to determine basic wind speed for Risk Category II.

V := 115 miles per hour

Use Manual Appendix D Table D-3.2 to determine design wind speed reduction based on construction

duration.

Wind Velocity Modification Factor

Vm := 0.75 Assume 6 weeks to 1 year as duration for steel erection.

Design Wind Speed

DWS := Vm·V DWS = 86.2 mph

Incorporate modified Design Wind Speed into pressure equation

Velocity Pressure Exposure Coefficient (ASCE 7-10, Sect 26.7.3)

Assume Surface Roughness C - Open terrain with scattered obstructions having

heights generally less than 30 feet. Therefore, Exposure Category C 

Manual Table D-3.1, for Height = 30 feet, Kz = 0.98. Say Kz = 1.0.

Take wind directionality factor as 0.85 and topographic factor as 1.0.

Kz :=1 Kzt :=1 Kd := 0.85

Velocity Pressure (Manual Eq.D-3.4b)

q := 0.00256҄·Kz·Kzt·Kd·DWS2 qz = 16.2 psf

Gust Effect Factor G := 0.85

Net Force Coefficient (Assuming deck forms not in place) Cf := 2.2 since ratio of girder spacing

to depth, S/d < 2
Engineering for Structural Stability in Bridge Construction Reference Manual

B.9

Wind Load, continued:

Net Pressure

Qz := G·Cf·qz Qz = 30.3 psf

One Day / Girder Setting Design Wind Speed (Assuming minimum wind speed per D-3.4)

V := 20 mph

Use 1.0 Wind Velocity Modification Factor (built in to minimum wind speed)

Vm := 1.0

Design Wind Speed: 

DWS := Vm·V DWS = 20 mph

One Day Girder Setting Velocity Pressure (Manual Eq. D-3.4b)

qzset := 0.00256·K·K·Kd·DWS2 qzset = 0.9 psf

One Day Girder Setting Net Pressure

Qzset := G·Cf

·qzset Qzset = 1.6 psf

1.6 psf is negligible and can be ignored for short-duration events like girder picks which would not be

occurring unless the wind is minimal anyway. However, use 5 psf as a minimum pressure for stability

checks for pieces that are already set to account for accidental loading, etc. (per D-3.3).

Qzset := 5 psf

Wind Forces on Girders:

Exposed height for girder group = 5.33 feet (worst-case) + 24’-7” bridge width * 5% cross-slope

h := 5.33 + 24.58·0.05 h = 6.56 ft

Exposed height for single girder being set = 5.33 feet (worst-case) hset := 5.33 ft

Force to girder group during partially-erected or fully-erected condition (6+ weeks)

W1 := Qz·h 1 = lb W 198.5

ft

Force to 1st girder during its setting (one day)

Wset := Qzset·hset set = lb W 26.6

ft
Engineering for Structural Stability in Bridge Construction Reference Manual

B.10

Wind Forces on Girders, continued:

Figure B1-5: Wind Load to Girder Group During Partially-Erected or Fully-Erected

Condition

Figure B1-6: Wind Load to 1st Girder During Its Setting (One Day)

Erection Analysis For Case 1 to Case 4:

Figure B1-7: Bridge Modeled in 3D Finite Element Analysis Software to

Determine Forces to Girders (Note Skew is Present But Difficult to See Due to

Perspective)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.11

Erection Analysis, continued:

For the purpose of this example, 4 erection stages will be analyzed for forces in the

girders:

Case 1: One girder set, Span 1 segment and Pier segment with

cantilever into Span 2 up to field splice.

Case 2: Two girder set, Span 1 segment and Pier segment with

cantilever into Span 2 up to field splice.

Case 3: Six girder set, Span 1 segment and Pier segment with

cantilever into Span 2 up to field splice.

Case 4: All Span 1, Span 2, and Pier segments set.

Figure B1-8: Case 1 (Dead = Selfweight, Wind = 26.6 lb/ft)

Figure B1-9: Case 2 (Dead = Selfweight, Wind = 198.5 lb/ft)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.12

Erection Analysis, continued:

Figure B1-10: Case 3 (Dead = Selfweight, Wind = 198.5 lb/ft)

Figure B1-11: Case 4 (Dead = Selfweight, Wind = 198.5 lb/ft)

Other erection cases should also be checked, but are omitted here for brevity. For example, between

Case 3 and Case 4 is the condition with the remainder of the 1st girder line installed from the splice

to abutment with the one day wind pressure of 26.6 lb/ft. And after this is another intermediate case

where the remainder of the 2nd girder line is installed in Span 2 with the cross-frames connected and

the 198.5 lb/ft wind load applied to the girder group.

The worst case strong axis and weak axis bending moments as well as worst case compression 

forces for each segment type of girder for each case is summarized in the table below. The factored

results are shown for the Strength III: 1.25 DC + 1.0 CW load combination.

CASE SEGMENT Mux (k*ft) Muy (k*ft) Pu (k)

1 Span 762 76 0 

1 Pier -579 54 0 

2 Span 900 109 64

2 Pier -623 320 49

3 Span 805 31 14

3 Pier -590 93 10

4 Span 466 37 16

4 Pier -1430 114 11

Table B1-9 Erection Analysis Output Summary
Engineering for Structural Stability in Bridge Construction Reference Manual

B.13

Deck Pour Analysis:

For this example, it is assumed the deck pour will run continuously from abutment to abutment, based

on the Contractor's requested alteration of the original deck pour sequence on the design drawings

(which had the first pours in positive moment regions and then over the pier). The worst case stage for 

the Span girder segments is when the deck has been poured over Span 1 up to the pier. This stage will 

be examined for girder adequacy. The concrete weight is taken as 150 pcf and will be treated as

permanent dead load. The removable formwork is taken as 10 psf and will be treated as construction

dead load. The construction live load is taken as 20 psf in Span 2, but only for computing maximum

negative moment at the pier. The factored results are shown for the Strength I: 1.25 DC + 1.50 CDL + 

1.50 CLL load combination and the Strength VI: 1.40 DC + 1.40 CDL + 1.40 CLL load combination. No

wind load combination (Strength III) is considered, since the deck pour will not be completed in winds

above 20 mph.

Figure B1-12: Case 5

CASE COMB. SEGMENT Mux (k*ft) Muy (k*ft) Pu (k)

5 I Span 1992 1 1 

5 I Pier -3643 1 1 

5 VI Span 2227 1 1 

5 VI Pier -3922 1 1 

Table B1-10 Deck Pour Analysis Output Summary

Evaluation of Stages:

For the purpose of this example, calculations will be displayed for specific erection stages. The 

girders will be checked for adequacy in flexure, axial, and combined stresses according to 

AASHTO 2012 LRFD Specifications, supplemented by Appendix D of the Manual. The first 

girder span segment during the crane pick, prior to field splicing, will be checked (Case 0). The 

first girder, after field splicing, will also be checked for bending resistance (Case 1) with an 

unbraced length from support to support. The two-girder case (Case 2) will be analyzed for 

buckling of a set of girders with an unbraced length of the set from support to support. The 

maximum cross-frame force from the analysis of the six-girder case (Case 3) will be used to 

size a brace member. By inspection, Case 4 will not govern since the girder forces in this case 

will be exceeded by the deck pour case. Finally, the span girder (i.e., positive moment) 

segments will be checked for the deck pour loading (Case 5). While these cases may not 

represent the critical loading for each girder segment, they serve as an example to check for 

adequacy.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.14

Figure B1-13: Example 1 Single Girder Pick
Engineering for Structural Stability in Bridge Construction Reference Manual

B.15

First Field Section During Lift (Case 0)

The first field section (span portion) of the 1st girder line must be lifted with a crane. It is possible to

splice the first field section on the ground with the second field section (pier portion) of the 1st girder

line, provided that a crane with adequate capacity can be found to lift the combined span / pier piece

of the 1st girder line. However, it is more likely that the contractor will use two smaller cranes (as

assumed here), and lift the span portion and pier portion separately, and then splice them in mid-air.

The combined piece will then be set on the abutment and pier bearings.

The cranes can be released if the girder is adequate to span from abutment to pier on its own. If not,

additional cranes can be used to lift the 2nd girder line so that it can be connected to the 1st with the

cross-frames (to reduce the unbraced length from the span length to the cross-frame spacing). Or 

guy-cables can be installed at the needed intervals in the span to provide brace points, after which

the cranes can release the 1st girder line. Then the 2nd girder line can be erected and cross-frames

installed between the two lines.

Section Properties:

Es := 29000ksi Fy := 50ksi = lift

10 L 116 ft + ft

12

L 116.8 ft lift =

Flanges:

ttf := 0.75in btf := 16in tbf := 0.875in bbf := 18in 

Web: Overall Depth:

tw := 0.5in D :=60in d := D + ttf +tbf d = 61.6 in

Calculated Properties: (Note that the steps involved in calculating these properties are

omitted)

Stx := 1051.8in3 Sbx := 1192.2 in3 Yt := 32.74 in Yb := 28.89 in Sy := 75.8 in3 Zx := 1288.4 in3 

Ag := 57.75 in2 rx := 24.42 in ry := 3.44 in Ix :=34436.1 in4 Iy := 681.9 in4 Zy : 124.5 in3

Girder selfweight WDC := Ag·0.490 3

kip

ft ·1.1 = 0.216 

kip

ft with 10% weight allowance for connections, etc.

Applied Factored Forces: (Assume no cross-frames are attached) 

Total piece length: Llift = 116.8 ft

Assume girder clamps are located at quarter points, where max. moment occurs: 

Llift L := 29.2 ft

4 =

Lateral Bending: Muy := 0 kip ft (No appreciable wind during pick, < 2 psf)

Major-axis Bending for Applicable Strength I & III Load Combination: 2

ux DC

L M :=1.25 W 115.3 kip ft 2 ⋅ ⋅=
Engineering for Structural Stability in Bridge Construction Reference Manual

B.16

First Field Section During Lift (Case 0), continued

Flexural Resistance:

Bottom flange is in compression: bfc := bbf tfc := tbf

Top flange is in tension: bft := btf tft := ttf

Applied Stresses:

Bottom flange is in compression: 2

fc fc

yc

t b S :

6

⋅ = Syc = 47.3 in3

Top flange is in tension: − =

2

ft ft

yt

t b S :

6

 Syt = 32 in3

Stress in compression flange without

consideration of lateral bending: ux

buc

bx

M f

S = fbuc = 1.2 ksi

First-order stress due to lateral bending

in compression flange: ⋅( ) = uy ft

L1c

y

M 0.5b

f :

I

 fL1c = 0 ksi

Stress in tension flange without

consideration of lateral bending: ux

but

tx

M f :

S = fbut = 1.3 ksi

First-order stress due to lateral bending in tension flange: uy ( ) ft

Lt

y

M 0.5b

f :

I

⋅ = fLt = 0 ksi

Flange Strength Reduction Factors:

Hybrid Factor (AASHTO 6.10.1.10.1)

Since the flexural member is a homogenous built-up section, the hybrid factor shall be taken

as unity

Rh := 1

Web Load Shedding Factor (AASHTO 6.10.1.10.2)

Depth of web in compression Dc := Yb -tbf

s

rw

y

E : 5.7

F

 

λ= ⋅  

 

= 137.3 λrw c

w

2 D 112.1

t

⋅ =

c w

wc

fc fc

2D t

a :

b t

⋅ = ⋅

c

rw

w

b

wc c

rw

wc w

2 D 1.0 if 

t

R :

a 2D 1.0 otherwise

1200 300 a t

⋅ ≤ λ

=       ⋅   −  ⋅  − λ

+ ⋅      

Web is non-compact, so Eq. 6.10.3.2.1-3 need not be checked per AASHTO 6.10.3.2.1
Engineering for Structural Stability in Bridge Construction Reference Manual

B.17

First Field Section During Lift (Case 0), continued

Local Buckling Resistance (AASHTO 6.10.8.2.2):

Slenderness ratio of the compression flange

s

p t

y

E L:r

F = ⋅ λf = 10.3 (Eq. 6.10.8.2.2-3)

s

pf

y

E : 0.38

F

λ = ⋅ λpf = 9.2 (Eq. 6.10.8.2.2-4)

s

rf

y

E : 0.56

0.7F

λ = ⋅ λrf = 16.1 (Eq. 6.10.8.2.2-5)

Local Buckling Resistance

(Eq. 6.10.8.2.2-1)

( ) b h y f pf

nc1 y f pf

b hy

h y rf pf

nc1

R R F if 

F : 0.7F

1 1 R R F otherwise

R F

F 47.6 ksi

⋅ ⋅ λ ≤λ

=       λ −λ     −− ⋅ ⋅ ⋅ ⋅     ⋅ λ −λ      

=

(Eq. 6.10.8.2.2-2)

Lateral Torsional Buckling Resistance (AASHTO 6.10.8.2.3)

Unbraced length Lb := Llift (Entire piece length) Lb = 116.8 ft.

Effective Radius

of Gyration

fc

t

c w

fc fc

b

r :

1 D t 12 1

3b t

=

  ⋅ ⋅ +⋅   ⋅   rt = 4.6 in. (Eq. 6.10.8.2.3-9)

Limiting Unbraced Length Calculations:

s

p t

y

E L:r

F = ⋅ Lp = 9.2 ft. (Eq. 6.10.8.2.3-4)

s

r t

y

E L: r

0.7F =π ⋅ Lr = 34.4 ft. (Eq. 6.10.8.2.3-5)

Per D-4, Moment gradient modifier ____

Lift

C : 6.0 fo b = r 2 L /L = 0. 5 (quarter points)

Lateral Torsional Buckling Resistance (conservatively used in lieu of AASHTO Appendix 

D6.4.2)

( ) ⋅⋅ ≤

        − = ⋅−− ⋅ ⋅ ⋅ ⋅ ≤             ⋅ −        

⋅⋅⋅

     

=

b hy b p

y b p

nc2 b b h y p b r

hy r p

2

bb s

2

b

t

nc2

R R F if L L

0.7F L L

F : C 1 1 R R F if L <L L

RF L L

CR E otherwise

L

r

F 18.2 ksi

p

(Eq. 6.10.8.2.3-1, 6.10.8.2.3-2, 6.10.8.2.3-3)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.18

First Field Section During Lift (Case 0), continued

Controlling Nominal Flexural Resistance:

Fnc := min(Fnc1,Fnc2) Fnc = 18.2 ksi

Resistance factor φf :=1.0 (AASHTO 6.5.4.2)

Φf·Fnc = 18.2 ksi

Mrx = Φf·Fnc·Sbx Mrx = 1807.7 kip ft

ux

rx

M 0.06

M = Adequate resistance for lateral-torsional buckling

Note that no impact factor is necessary for the crane pick (20% impact only for demolition, not 

erection).

Determine Stress due to Lateral Bending:

First-order lateral bending stress (from previous) fL1c = 0 ksi

Limiting unbraced length for first-order lateral bending stress

b b

p

buc

y

C R 1.2 L 176.7 ft f

F

⋅ ⋅⋅ = (Eq. 6.10.1.6-2)

Lateral bending stress:

elastic lateral torsional buckling stress

2

bb s

cr 2

b

t

CR E F :

L

r

⋅ ⋅π ⋅ =

     

 Fcr = 18.2 ksi (Eq. 6.10.8.2.3-8)

Check if the first-order stress needs to be amplified: Approximated second-order lateral bending stress 

⋅ = ≤ ⋅⋅

   

  ⋅   −    

b b

Lc Lc1 b p

buc

y

L1c

buc

cr

C R f : f if L 1.2 L f

F

0.85 f otherwise f 1

F

 

fLc = 0 ksi

(Eq. 6.10.1.6-4)

Lateral bending check:

Lateral_Bending_Resistance:= “Lateral Bending Requirements Satisfied” if fLc≤0.6Fy

Girder is NOT Adequate in Lateral Flexure” otherwise

Lateral_Bending_Resistance= “Lateral Bending Requirements Satisfied”
Engineering for Structural Stability in Bridge Construction Reference Manual

B.19

First Field Section During Lift (Case 0), continued

Overall Flexural Resistance Check:

The following must be satisfied:

+ ⋅ ≤φ ⋅ = buc Lc φ nc

1 φφ F 18.2 ksi

3

(Eq. 6.10.3.2.1-2)

buc Lc

1 f f 1.2 ksi

3

+⋅ = φf·Fnc =18.2 ksi

Resistance_Check := “Girder Meets AASHTO Flexural Requirements” if + ⋅ ≤φ ⋅ buc Lc φ nc

1 φφ F

3 

“Girder is NOT Adequate in Lateral Flexure” otherwise

Resistance_Check = “Girder Meets AASHTO Flexural Requirements”

Constructability Check:

The following must be satisfied:

fbuc + fLc ≤ Φf·Rh·Fy (Eq. 6.10.3.2.2-1)

fbuc + fLc = 1.2 ksi < Φf·Rh·Fy = 50 ksi

Adequate resistance in compression flange

The following must be satisfied:

Fbut + fLt ≤ Φf·Rh·Fy (Eq. 6.10.3.2.2-1)

fbuc + fLt = 1.3 ksi < Φf·Rh·Fy = 50 ksi

Adequate resistance in tension flange

Local Flange Stresses Check:

In lieu of the simplistic method outlined in Manual Sect. D-6, use the AISC Steel Manual 

13th Edition resistance equation to check for flange local ending at the girder clamps 

(Section J10.1).

The total clamp force at each of the two girder clamps = P

lift

DC

L P : 1.25 W

2 = ⋅⋅ for Strength Load Combination P = 15.8 kip

The tensile concentrated force at each side of the top flange under the girder clamp = P/2

The following must be satisfied:

2

tf y

P 6.25 t F

2

≤ f ⋅ ⋅ ⋅ (AISC Eq. J10-1) where Φ := 0.9

2

tf y

P 7.9 kip 6.25 t F 158.2 kip 2

= < f ⋅ ⋅ ⋅ =

Adequate resistance in top flange for concentrated tensile forces
Engineering for Structural Stability in Bridge Construction Reference Manual

B.20

Figure B1-14: Example 1 Girder Clamp Loading
Engineering for Structural Stability in Bridge Construction Reference Manual

B.21

Resistance of a Single Girder for Case 1 Loading (Span 1 with Cantilever, 1st Line Erected)

Span Segment Controls Case 1 Loading

Section Properties: Es := 29000 ksi Fy = 50 ksi

Flanges:

ttf := 0.75 in btf := 16 in tbf := 0.875 in bbf := 18 in

Web: Overall Depth:

tw := 0.5 in D := 60 in d := D + ttf+ tbf d = 61.6 in

Calculated Properties: (Note that the steps involved in calculating these properties are omitted, as 

they may be easily generated by spreadsheets, analysis software, etc.)

Stx := 1051.8 in3

 Sbx := 1192.2 in3 Yt := 32.74 in Yb := 28.89 in Sy:= 75.8 in3 Zx := 1288.4 in3 

Ag:= 57.75 in2 rx := 24.42 in ry := 3.44 in Ix := 34436.1 in4 Iy := 681.9 in4 Zy:= 124.5 in3

Applied Factored Forces (From Erection Analysis Output Summary):

Major-axis Bending: Mux:= 762 kip Lateral Bending Muy := 76 kip ft

 

Figure B1-15: Major-Axis Bending Moment Diagram

Applied Stresses:

Top flange is in compression: bfc := btf tfc := ttf

Bottom flange is in tension: bft := bbf tft := tbf

Stress in compression flange without

consideration of lateral bending: ux

buc

tx

M f :

S = fbuc = 8.7 ksi

First-order stress due to lateral bending in compression flange: ( ) uy fc

L1c

y

M 0.5 b

f :

I

⋅ ⋅ = fL1c = 10.7 ksi

Stress in tension flange without consideration of lateral bending: ux

but

bx

M f :

S = fbut := 7.7 ksi

First-order stress due to lateral bending in tension flange: ( ) uy ft

Lt

y

M 0.5 b

f :

I

⋅ ⋅ = flt = 12 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.22

Resistance of a Single Girder for Case 1 Loading (Span 1 with Cantilever, 1st Line 

Erected), cont.

Flexural Resistance:

Flange Strength Reduction Factors:

Hybrid Factor (AASHTO 6.10.1.10.1)

Since the flexural member is a homogenous built-up section, the hybrid factor shall be taken as 

unity

 Rh := 1

Web Load Shedding Factor (AASHTO 6.10.1.10.2)

Depth of web in compression Dc := Yt - ttf

s

rw

y

E : 5.7

F

 

λ= ⋅  

 

λ = rw 137.3 c

w

2 D 128

t

⋅ =

c w

wc

fc fc

2D t

a :

b t

⋅ = ⋅

c

rw b

w

b

wc c

rw

wc w

2 D 1.0 if R 1 t

R :

a 2D 1.0 otherwise 

1200 300 a t

⋅ ≤ λ =

=       ⋅   −  ⋅ −λ   + ⋅      

Web is non-compact, so Eq. 6.10.3.2.1-3 need not be checked per AASHTO 6.10.3.2.1.

Local Buckling Resistance (AASHTO 6.10.8.2.2):

Slenderness ratio of the compression flange

fc

f

fc

b

:

2 t

λ = ⋅ λ =f 10.7 (Eq. 6.10.8.2.2-3)

s

pf

y

E : 0.38

F

λ = λ = pf 9.2 (Eq. 6.10.8.2.2-4)

s

pf

y

E : 0.56

0.7F

λ= ⋅ λ = rf 16.1 (Eq. 6.10.8.2.2-5)

Local Buckling Resistance (Eq. 6.10.8.2.2-1 & Eq. 6.10.8.2.2-2)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.23

( ) b h y f pf

nc1 y f pf

b hy

h y rf pf

nc1

R R F if 

F : 0.7F

1 1 R R F otherwise

R F

F 46.7 ksi

λ λ

λ λ

λ λ

⋅⋅ ≤

=       −     −− ⋅ ⋅ ⋅ ⋅     ⋅ −      

=
Engineering for Structural Stability in Bridge Construction Reference Manual

B.24

Resistance of a Single Girder for Case 1 Loading (Span 1 with Cantilever, 1st Line

Erected), cont.

Lateral Torsional Buckling Resistance (AASHTO 6.10.8.2.3):

Unbraced length Lb := 164 ft Taken as span length of 164 ft

Effective Radius

of Gyration fc

t

c w

fc fc

b

r :

1 D t 12 1

3b t

=

  ⋅ ⋅ +⋅   ⋅  

 rt = 3.8 in (Eq. 6.10.8.2.3-9)

Limiting Unbraced Length Calculations:

s

p t

y

E L:r

F = ⋅ Lp = 7.7 ft (Eq. 6.10.8.2.3-4)

s

r t

y

E L: r

0.7F =π ⋅ Lr = 29 ft (Eq. 6.10.8.2.3-5)

Moment gradient modifier Cb := 1 since, f2 := 0 

(See 4th sample in AASHTO LRFD C6.4.10, corresponding to moment in main span of beam 

with cantilever overhang present

Lateral Torsional Buckling Resistance

( ) ⋅⋅ ≤

        − = ⋅−− ⋅ ⋅ ⋅ ⋅ ≤             ⋅ −        

⋅ ⋅π ⋅

     

=

b hy b π

y b π

nc2 b b h y π b r

h y r π

2

b b s

2

b

t

nc2

R R F if L L

0.7F L L

F : C 1 1 R R F if L <L L

RF L L

CR E otherwise

L

r

F 1.1 ksi

(Eq. 6.10.8.2.3-1)

(Eq. 6.10.8.2.3-2)

(Eq. 6.10.8.2.3-3)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.25

Resistance of a Single Girder for Case 1 Loading (Span 1 with Cantilever, 1st Line Erected),

cont.

Controlling Nominal Flexural Resistance:

Fnc := min (Fnc1,Fnc2) Fnc = 1.1 ksi

Resistance factor Φf := 1.0 (AASHTO 6.5.4.2)

Φf·Fnc = 1.1 ksi

Mrx := Φf·Fnc·Stx Mrx = 95.7 kip ft < Mux= 762 kip ft

Single girder is inadequate in flexure. The girder must be held in place (supported) by crane or bracing 

until the second adjacent girder is set and all the diaphragm connections are installed. Guy-cables will 

be used at the contractor’s preference to support the girder.

Lateral Torsional Buckling Resistance (AASHTO 6.10.8.2.3):

Unbraced length Lb := 41 ft Assuming tie-downs at 1⁄4 points of 164 ft span length

Effective Radius of Gyration

fc

t

c w

fc fc

b

r :

1 D t 12 1

3b t

=

  ⋅ ⋅ +⋅   ⋅  

rt = 3.8 in (Eq. 6.10.8.2.3-9)

Limiting Unbraced Length Calculations:

s

p t

y

E L:r

F = ⋅ Lp = 7.7 ft (Eq. 6.10.8.2.3-4)

s

r t

y

E L: r

0.7F =π ⋅ Lr = 29 ft (Eq. 6.10.8.2.3-5)

Moment gradient modifier Cb := 1 since, mid

2

f 1

f

> (See 3rd sample in AASHTO LRFD C6.4.10)

Lateral Torsional Buckling Resistance

( ) ⋅⋅ ≤

        − = ⋅−− ⋅ ⋅ ⋅ ⋅ ≤             ⋅ −        

⋅ ⋅π ⋅

     

=

b hy b π

y b π

nc2 b b h y π b r

hy r π

2

bb s

2

b

t

nc2

R R F if L L

0.7F L L

F : C 1 1 R R F if L <L L

RF L L

CR E otherwise

L

r

F 17.5 ksi

(Eq. 6.10.8.2.3-1)

(Eq. 6.10.8.2.3-2)

(Eq. 6.10.8.2.3-3)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.26

Resistance of a Single Girder for Case 1 Loading (Span 1 with Cantilever, 1st Line Erected),

cont.

Controlling Nominal Flexural Resistance:

Fnc := min(Fnc1,Fnc2) Fnc = 17.5 ksi

Resistance factor Φf := 1.0 (AASHTO 6.5.4.2)

Φf·Fnc = 17.5 ksi

Mrx := Φf·Fnc·Stx Mrx = 1530.8 kip ft > Mux = 762 kip ft

The temporary guy-cables selected by the contractor will be used to prevent lateral translation of the 

cross-section. Guy-cables are an acceptable solution here provided that the unbraced length is limited to 

1⁄4 of the span or less (say 41 ft). Now check lateral bending and flexural interaction to ensure that 

unbraced length is OK.

Determine Stress due to Lateral Bending:

First-order lateral bending stress (from previous): fL1c = 10.7 ksi

Limiting unbraced length for first-order lateral bending stress

b b

p

buc

y

C R 1.2 L 22.2 ft f

F

⋅ ⋅⋅ = (Eq. 6.10.1.6-2)

Lateral bending stress:

elastic lateral torsional buckling stress 2

bb s

cr 2

b

t

CR E F :

L

r

⋅ ⋅π ⋅ =

     

 Fcr = 17.5 ksi (Eq. 6.10.8.2.3-8)

Check if the first-order stress needs to be amplified: Approximated second-order lateral bending 

stress:

b b

buc

L1c b p

y

Lc

L1c

buc

cr

C R

f f if L 1.2 L

F

f :

0.85 f otherwise f 1

F

⋅

≤ ⋅⋅

=    

  ⋅   −    

fLc = 18.1 ksi

(Eq. 6.10.1.6-4)

Lateral bending check:

Lateral_Bending_Resistance := “Lateral Bending Requirements Satisfied” if fLc≤0.6Fy

“Girder is NOT Adequate in Lateral Flexure” otherwise

Lateral_Bending_Resistance = “Lateral Bending Requirements Satisfied”
Engineering for Structural Stability in Bridge Construction Reference Manual

B.27

Resistance of a Single Girder for Case 1 Loading (Span 1 with Cantilever, 1st Line

Erected), cont. 

Overall Flexural Resistance Check:

The following must be satisfied:

+ ⋅ ≤φ ⋅ buc Lc φ nc

1 φφ F

3

(Eq. 6.10.3.2.1-2)

buc Lc

1 f f 14.7 ksi

3

+⋅ = φf·Fnc =17.5 ksi

Resistance_Check := “Girder Meets AASHTO Flexural Requirements” if buc Lc f nc

1 ffF

3

+ ⋅ ≤ f ⋅ 

“Girder is NOT Adequate in Lateral Flexure” otherwise

Resistance_Check = “Girder Meets AASHTO Flexural Requirements”

Constructability Check:

The following must be satisified:

 fbuc + fLc ≤ Φf·Rh·Fy (Eq. 6.10.3.2.1-1)

 fbuc + fLc = 26.8 ksi < Φf·Rh·Fy = 50 ksi

 Adequate resistance in compression flange

The following must be satisified:

 fbut + fLt ≤ Φf·Rh·Fy (Eq. 6.10.3.2.2-1)

 fbut + fLt = 19.7 ksi < Φf·Rh·Fy = 50 ksi

 Adequate resistance in tension flange

Also note the following: among other assumptions, the above Case 1 calculations were 

predicted on the supports (pier and abutment) acting as brace points. For a single girder line, 

cross-frames are not yet present, so this bracing assumption is only valid if the detailing is done 

properly to prevent flange rotation / translation (i.e., tie-downs or other temporary girder end 

bracing).
Engineering for Structural Stability in Bridge Construction Reference Manual

B.28

Two Girders After Release (Case 2)

As explained for Cases 0 and 1, the 1st girder line combined segment (Span 1 piece spliced to 

pier piece) must be temporarily supported or braced so that the 2nd girder line segment (Span 1 

piece spliced to pier piece) can be erected and then attached via the cross-frames to the 1st 

girder line. This could be accomplished via the use of the original picking cranes, or the 

installation of shoring towers in Span 1, or the installation of cable tie-downs in Span 1. It will be 

required to connect all cross-frames (100% bolts) between the two girder lines before releasing 

the temporary braces or removing the temporary supports. At this point, the unbraced length for 

both girder lines will be equal to the cross-frame spacing. By inspection, lateral-torsional 

buckling between cross-frames will not control the resistance. However, global buckling of the 

two-girder system is possible and must be checked.

Ls:= 164 ft Length of main span, not cantilever span

11 S : 4 ft

12 = Spacing between girders

Recall that steel elastic modulus Es= 29000000 psi

Recall from Case 1 that strong-axis moment of inertia Ix= 34436.1 in4

Recall from Case 1 that weak-axis moment of inertia Iy = 681.9 in4

Recall from Case 1 that centroidal distance to top fiber Yt =32.74 in 

Recall from Case 1 that centroidal distance to bottom fiber Yb = 28.89 in

Recall from Case 1 that top flange dimensions are btf = 16 in and ttf = 0.75 in

Recall from Case 1 that bottom flange dimensions are bbf = 18 in and tbf = 0.875 in

Thus centroidal distance to extreme tension fiber t := Yb = 28.89 in

Thus centroidal distance to extreme compression fiber c := Yt = 32.74 in

Thus weak-axis moment of inertia about tension flange

Thus weak-axis moment of inertia about compression flange

Thus the effective weak-axis moment of inertia

Global Buckling Resistance:

Mgs = 1694 kip ft for the system

for each girder in the twin-girder system

Recall, the maximum factored moment in Case 2 is Mux := 900 kip ft for one girder.

Φfx·Mgo = 762.3 kip ft < Mux = 900 kip ft Flexural stability of two girders is not adequate.

At the contractor’s preference, top and bottom flange lateral bracing will be installed in the two 

panels at each end of Span 1. If the owner allows it, this lateral flange bracing can be 

permanent (i.e., drill holes in flanges and install angle iron). Or, if the owner prefers, this lateral 

flange bracing can be temporary and mechanically connected (beam clamps, cables and 

turnbuckles, adjustable straps, etc.)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.29

Two girders After Release (Case 2), continued

The effect of the top and bottom flange lateral bracing will be to stiffen the ends of the span. 

Ultimately this changes the buckled shape K factor so that the twin girders buckle more like a 

column with fixed-ends rather than a pin-ended column. Conservatively this can be modeled 

with a global buckling mode effective span length Leff which is equal to the clear span distance 

of the unstiffened panels. The new global buckling mode resistance Mgs_eff will be computed

based on this effective span.

Leff := 3·25 ft = 75 ft with 2 end panels stiffened at the abutment and at the pier (out of 7 panels 

total)

Mgs_eff = 8100.1 kip ft for the system

for each girder in the twin-girder system

Φfx·Mgo_eff = 3645 kip ft > <Mux = 900 kip ft Flexural stability of two stiffened girders is adequate.

Lateral Bending from wind:

Recall, the maximum factored moment for Case 2 is Muy:= 109 kip ft for one girder at midspan.

Recall, the maximum factored axial load for Case 2 is Pu := 64 kip for one girder.

Ag= 57.8 in2 so axial stress

By inspection, the axial stress is small enough that it can be ignored, so the moment-only 

interaction or strong-axis bending and weak-axis bending will be computed.

Interaction of strong-axis bending (system buckling) and weak-axis bending (yielding):

Unbraced length Lb := 25 ft with cross-frame spacing of 25 ft

Recall from Case 1 that web load shedding factor Rb = 1

Recall from Case 1 that effective radius of gyration rt = 3.8 in

Recall form Case1 that limiting unbraced length Lp = 7.7 ft

Recall from Case 1 that moment gradient modifier Cb = 1

Recall from Case 1 that compression flange width btf = 16 in 

Recall form Case 1 that weak-axis moment of inertia Iy = 681.9 in4

Recall from Case 1 strong-axis section modulus to compression flange Sxc := Stx = 1051.8 in3

Recall that weak-axis factored moment Muy := 109 kip ft 

Recall that strong-axis factored moment Mux := 900 kip ft 

Stress in compression flange without consideration of lateral bending

First-order lateral bending stress in compression flange
Engineering for Structural Stability in Bridge Construction Reference Manual

B.30

Two Girders After Release (Case 2), continued

Limiting unbraced length for first-order lateral bending stress

(Eq. 6.10.1.6-2)

Lateral bending stress:

elastic lateral torsional buckling stress

Fcr = 47 ksi (Eq. 6.10.8.2.3-8)

Check if first-order stress needs to be amplified: Approximated second-order lateral 

bending stress

b b

buc

L1c b p

y

Lc

L1c

buc

cr

C R

f f if L 1.2 L

F

f :

0.85 f otherwise f 1

F

⋅

≤ ⋅⋅

=    

  ⋅   −    

fLc = 16.7 ksi 

(Eq. 6.10.1.6-4) 

Lateral bending check:

Lateral_Bending_Resistance := “Lateral Bending Requirements Satisfied” if fLc≤0.6Fy

“Girder is NOT Adequate in Lateral Flexure” otherwise

Lateral_Bending_Resistance = “Lateral Bending Requirements Satisfied”

The following must be satisfied: (Modified Eq. A6.1.1-1)

Therefore interaction OK.

As an additional check an Eigenvalue analysis is included on Page B-41 of this example. This can utilized 

to provide a more detailed buckling analysis.

Note that if the designer lacked sufficient engineering judgement to recognize that the negative moment 

utilization would not govern for the Case 2 cantilever (because, with the same unbraced length of 19 ft, 

the negative moment, both in Case 5 and under traffic, is much higher), then the negative moment 

resistance could be calculated in the same fashion as the positive moment resistance was in Case 1 (but 

using the section properties of the pier girder segment). Also note that the moment gradient modifier Cb 

would be calculated per C6.4.10 as follows:

f0 := 259 kip ft at brace

f2 := 623 kip ft at pier

f1 := f0 (concave moment)

where Lb := 19 ft and Mux := f2 = 623 kip ft
Engineering for Structural Stability in Bridge Construction Reference Manual

B.31

Adequacy of the Cross-Frame Bracing Member for Case 3 Loading

Cross-frame members act to transfer lateral winds to adjacent girders and their bearings during steel 

erection stages. The cross-frames also provide stability of the girder flanges during erection and 

placement of the deck. In skewed structures the cross-frames experience greater loading than nonskewed structures because the load in a girder will transfer through the cross-frame to an adjacent girder 

due to the closer proximately of the support on that adjacent girder. While deck pour loads may control 

the cross-frame design, for this example Case 3 will be examined with wind load acting on the fully 

erected steel superstructure.

Axial Tension Resistance of the Brace L4x4x3/8 (AASHTO 6.8.2):

Put := 18.2kip Maximum tension force in any brace member from Case 3 analysis model.

Material / Section Properties (Taken from AISC manual) Fy := 36 ksi Fu := 58 ksi Ag:= 2.86 in2 

Note that A36 is still the preferred material specification for angles. Per AISC, availability of angles in 

other grades should be confirmed prior to their specification.

From Figure B1-3, it appears that the brace is welded rather than bolted to the conn. plate, so An := Ag

For shear lag reduction factor, lacking weld details, assume U := 0.60 (0.5 is worst case per 6.8.2.2)

Resistance factors φy := 0.95 φu := 0.80 (AASHTO 6.5.4.2)

Tension resistance for yielding Pry := φy·Fy·Ag = 97.8 kip (Eq. 6.8.2.1-1)

Tension resistance for fracture Pru := φu·Fu·An·U = 79.6 kip (Eq. 6.8.2.1-2)

Axial Resistance Check Put = 18.2 kip < Prt := min(Pry,Pru) = 79.6 kip Tension resistance is adequate

Axial Compression Resistance of the Brace L4x4x3/8 (AASHTO 6.9.4):

Puc := 4.4 kip Maximum compression force in any brace member from Case 3 analysis model.

Material / Section Properties (Taken from AISC manual) Es := 29000ksi Fy := 36ksi Ag := 2.86 in2

Check Slenderness of the Member (Sect. 6.9.4.2)

Following requirement needs to be satisfied for the element to qualify as nonslender:

y

b E k

t F

≤ ⋅ (Eq. 6.9.4.2.1-1) k := 0.45 from Table 6.9.4.2.1-1 

angle leg:

b:= 4 in t := 0.375 in b 10.7

t

= s

y

E k 12.8

F ⋅ =

leg check:

Find Q if element is slender:

y s

s y

s s

2

y

b b F E 1.34 0.76 if 0.91

tEt F

Q : 0.53 E otherwise

b F

t

  − ⋅ ≤⋅    

= ⋅

 

⋅   

(Eq. 6.9.4.2.2-5)

(Eq. 6.9.4.2.2-6)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.32

Adequacy of the Cross-Frame Bracing Member for Case 3 Loading, continued

s

s

s y

s

 Q 1.1

b E 1.0 if 0.45

Q : t F

Q otherwise

 Q 1

=

≤ ⋅ =

=

Determine Effective Slenderness Ratio (KL/r)eff = λeff (Sect. 6.9.4.4)

Recall S = 59 in

S 2 L : max S, 2

  ⋅ =  

  S governs the brace length, so L = 59 in

rx := 1.23 in so 

x

L 48

r =

x x

eff

x

eff

L L 72 0.75 if 80

r r

:

L 32 1.25 otherwise

r

108

    + ≤

  λ =     +

 

λ =

(Eq. 6.9.4.4-1)

(Eq. 6.9.4.4-2)

Limiting KL/r for secondary compression members λlimit:= 140 (Sect. 6.9.3)

Maximum actual slenderness corresponds to minor principal axis buckling rz := 0.779 in K := 1

limit

z

K L 75.7 140

r

⋅ = < l = Therefore, actual maximum slenderness ratio is adequate

Flexural Buckling Resistance

( )

2

s

e g 2

eff

E P: A π ⋅ = ⋅ λ

 Pe = 70.2 kip (Eq. 6.9.4.1.2-1)

Since the various conditions for single-angle members are satisfied as enumerated in AASHTO LRFD 

Sect. 6.9.4.4, the effective slenderness ratio can be calculated per that section; therefore, only flexural 

bucking resistance will be used to determine nominal compressive resistance of the brace. The effect of 

the eccentricities can be neglected when evaluated in this manner. 

Equivalent Nominal Yield Resistance

Po := Q·Fy·Ag Po = 103 kip (Sect. 6.9.4.1.1)

e

o

P 0.7

P =

Nominal Compressive Resistance

( )

o

e

P

P e

o

n o

e

n

P 0.658 P if 0.44

P : P

0.877P otherwise

P 55.7 kip

     

 

  ⋅ ≥ =    

=

(Eq. 6.9.4.1.1-1)

(Eq. 6.9.4.1.1-2)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.33

Adequacy of the Cross-Frame Bracing Member for Case 3 Loading, continued

Resistance factor φc := 0.9 (AASHTO 6.5.4.2) 

Factored Axial Resistance

Prc := φc·Pn Prc = 50.2 kip (Eq. 6.9.2.1-1)

Axial Resistance Check

Puc = 4.4 kip < Prc = 50.2 kip Compression resistance is adequate

Verify Bracing Strength to Provide Girder Stability

Unbraced length Lb := 25 ft = 300 in with cross-frame spacing of 25 ft

Span length L := 164 ft =1968 in

Maximum moment within span Mf := 805 kip ft = 9660 kip in

Height of cross-frame hb := S = 59 in 

Number of braces in span, excluding supports n := 6

Modulus of elasticity Es = 29000 ksi

Moment modification factor Cb := 1

Distance between flange centroids tf bf

o

t t h : d 60.8in

2 2 =− − =

Recall girder cross-sectional properties Yb = 28.89 in Yt = 32.74 in ttf = 0.75 in tbf= 0.875 in

Calculate effective minor axis moment of inertia

t := Yb = 28.39 in c := Yt = 32.74 in 3

tf tf 4

yc

t b I : 256 in

12

⋅ = =

3

bf bf 4

yt

t b I : 425.3 in

12

⋅ = =

4

eff yc yt

t I : I I 631.2 in

c

  = + ⋅=    

(Manual Eq. D-5.2j)

Recall Iy = 681.9 in4 Therefore eff

y

I 0.926

I =

Required strength 2

b f

br 2

b s eff b o

0.005L L M F : 0.7 kip h nE I C h

⋅ ⋅ = = ⋅⋅ ⋅ ⋅

(Manual Eq. D-5.2a)

Length of diagonal member c L : S 2 83.44 in =⋅ =

Required strength of compression brace Fbrc:= Fbr = 0.7 kip (Manual Fig. 5-7, Tension System)

Required strength of tension brace br c

brt

2F L F : 1.98 kip S⋅ = = (Manual Fig 5-7, Tension System)

Available strength of tension brace to resist stability force Prt - Put = 61.42 > Fbrt = 1.98 kip

Available strength of compression brace to resist stability force Prc - Puc = 45.76 kip > Fbrc = 0.7 kip

Therefore, bracing is adequate for strength
Engineering for Structural Stability in Bridge Construction Reference Manual

B.34

Adequacy of the Cross-Frame Bracing Member for Case 3 Loading, continued

Check Required Stiffness of Bracing System βT,reqd

Resistance factor φbr := 0.75

Required stiffness (Manual Eq. D-5.2b)

Calculate Attached Brace Stiffness βb

Area of diagonal member Ac := Ag = 2.86 in2

Area of horizontal member Ah := Ag= 2.86 in2 

Attached brace stiffness 

2 2

s b

b 3 3

c

c h

ESh

: 735101 kip in

2 L S

A A

⋅ ⋅ b = =   ⋅   +

  (Manual Fig. 5-7, Eq. for Tension System)

Calculate Web Distortional Stiffness βsec

Recall web thickness tw = 0.5 in

Intermediate stiffener plate thickness ts := 0.5 in

Intermediate stiffener plate width bs := 7 in

Web distortional stiffness (Manual Eq. D5.2h)

However, for a full depth cross-frame, βsec := 999999999999kip in (infinity)

Calculate In-Plane Girder System Stiffness βg

Number of girders ng := 6

Recall major axis moment of inertia Ix = 34436.1 in4

Girder system stiffness ( )2 2 g s x

g 3

g

24 n 1 SEI

: 45608 kip in n L

⋅ − ⋅ ⋅ β = = (Manual Eq. D5.2i) 

Calculate Total Provided System Stiffness βT and Compare with Required System Stiffness βT,reqd 

Total provided system stiffness

T

b sec g

1

: 42943.6 kip in

111

b = =     + +

bbb   (Rearranged Manual Eq. D5.2g)

ΒT = 42943.6 kip in > βTreqd = 5350.4 kip in Therefore, stiffness of bracing system is 

adequate. 

Note that the controlling case would be the deck pour (Case 5) when moment in the girder is greatest.

Thus Therefore, still OK.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.35

Fascia Girder During Deck Pour (Case 5)

Note: Case 4 was analyzed but does not govern, so capacity calculations for that case are not performed 

in this example. For Case 5 loading, the girder span segment controls, rather than the pier segment.

Section Properties:

 Es := 29000 ksi Fy := 50 ksi

Flanges: ttf := 0.75 in btf = 16 in tbf:= 0.875 in bbf := 18 in

Web: tw := 0.5 in D := 60 in Overall Depth: d := D + ttf + tbf d = 61.6 in

Calculated Properties: (Note that the steps involved in calculating these properties are omitted)

Stx := 1051.8 in3

 Sbx := 1192.2 in3 Yt := 32.74 in Yb := 28.89 in Sy := 75.8 in3 Zx := 1288.4 in3 

Ag := 57.75 in2 rx := 24.42 in ry := 3.44 in Ix := 34436.1 in4 Iy := 681.9 in4 Zx := 124.5 in3

Applied Factored Forces (From Deck Pour Analysis Output Summary):

Major-axis Bending Mux := 2227 kip ft (Strength VI)

Lateral Bending: Muy := 1 kip ft (Strength VI)

Unbraced Length: Lb := 25 ft with cross-frame spacing of 25 ft

Lateral Force on Ea. Flange from Overhang Bracket at Fascia Girder: FL := 0.150 klf (Assumed, see Page 

B-39 for verification)

Lateral Moment in Each Flange from Overhang Bracket at Fascia Girder: 

2

L b

L

F L M :

12

⋅ = (Eq. C6.10.3.4-2)

Factored Lat. Moment in Ea. Flange from Overhang Bracket at Fascia Girder: MLu := 1.50 ML = 11.7 kip ft 

(conservatively assume highest load factor corresponding to all construction dead load)

Flexural Resistance

Top flange in compression: bfc:= btf tfc := ttf

Bottom flange is in tension: bft := bbf tft := tbf

Applied Stresses:

Top flange is in compression: 2

fc fc

yc

t b S :

6

⋅ = 3 S : 32 in yc =

Bottom flange is in tension: 2

ft ft

yt

t b S :

6

⋅ = 3 S : 47.3 in yt =

Stress in compression flange without 

consideration of lateral bending: ux

buc

tx

M f :

S = fbuc = 25.4 ksi

First-order-stress due to lateral bending 

in compression flange: ( ) uy fc Lu

L1c

y yc

M 0.5 b M f :

I S

⋅ ⋅ = + fL1c = 4.5 ksi

Stress in tension flange without 

consideration of lateral bending: ux

but

bx

M f :

S = fbut= 22.4 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.36

First-order stress due to lateral bending 

in tension flange: ( ) uy ft Lu

Lt

y yt

M 0.5 b M f :

I S

⋅ ⋅ = + fLt = 3.1 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.37

Figure B1-16: Example 1 Overhang Bracket Loading
Engineering for Structural Stability in Bridge Construction Reference Manual

B.38

Fascia Girder During Deck Pour (Case 5), continued

Flange Strength Reduction Factors:

Hybrid Factor (AASHTO 6.10.1.10.1)

Since the flexural member is a homogenous built-up section, the hybrid factor shall be taken as 

unity

Rh := 1

Web Load Shedding Factor (AASHTO 6.10.1.10.2)

Depth of web in compression Dc := Yt - ttf

s

rw

y

E : 5.7

F

 

λ= ⋅  

 

λrw= 137.3 c

w

2 D 128

t

⋅ =

c w

wc

fc fc

2D t

a :

b t

⋅ = ⋅

c

rw

w

b

wc c

rw

wc w

2 D 1.0 if 

t

R :

a 2D 1.0 otherwise

1200 300 a t

⋅ ≤ λ

=       ⋅   −  ⋅ −λ   + ⋅      

 Rb = 1

Web is non-compact, so Eq. 6.10.3.2.1-3 need not be checked per AASHTO 6.10.3.2.1.

Local Buckling Resistance (AASHTO 6.10.8.2.2): 

Slenderness ratio of the compression flange

fc

f

fc

b

:

2 t

λ = ⋅

λf = 10.7 (Eq. 6.10.8.2.2-3)

s

pf

y

E : 0.38

F

λ= ⋅ λpf = 9.2 (Eq. 6.10.8.2.2-4)

s

rf

y

E : 0.56

0.7F

λ= ⋅ λrf = 16.1 (Eq. 6.10.8.2.2-5)

Local Buckling Resistance

( ) b h y f pf

nc1 y f pf

b hy

h y rf pf

nc1

R R F if 

F : 0.7F

1 1 R R F otherwise

R F

F 46.7 ksi

⋅ ⋅ λ ≤λ

=       λ −λ     −− ⋅ ⋅ ⋅ ⋅     ⋅ λ −λ      

=

(Eq. 6.10.8.2.2-1)

(Eq. 6.10.8.2.2-2)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.39

Fascia Girder During Deck Pour (Case 5), continued

Lateral Torsional Buckling Resistance (AASHTO 6.10.8.2.3):

Unbraced length Lb := 25 ft with cross-frame spacing of 25 ft

Effective Radius

of Gyration fc

t

c w

fc fc

b

r :

1 D t 12 1

3b t

=

  ⋅ ⋅ +⋅   ⋅  

 rt = 3.8 (Eq. 6.10.8.2.3-9)

Limiting Unbraced Length Calculations:

s

p t

y

E L:r

F = ⋅ Lp = 7.7 ft (Eq. 6.10.8.2.3-4)

s

r t

y

E L: r

0.7F =π ⋅ Lr= 29 ft (Eq. 6.10.8.2.3-5)

Moment gradient modifier Cb := 1 since, mid

2

f 1

f

>

Lateral Torsional Buckling Resistance

( ) ⋅⋅ ≤

        − = ⋅−− ⋅ ⋅ ⋅ ⋅ ≤             ⋅ −        

⋅ ⋅π ⋅

     

=

b hy b π

y b π

nc2 b b h y π b r

h y r π

2

b b s

2

b

t

nc2

R R F if L L

0.7F L L

F : C 1 1 R R F if L <L L

RF L L

CR E otherwise

L

r

F 37.8 ksi

(Eq. 6.10.8.2.3-1)

(Eq. 6.10.8.2.3-2)

(Eq. 6.10.8.2.3-3)

Controlling Nominal Flexural Resistance: 

Fnc := min(Fnc1, Fnc2) Fnc = 37.8 ksi

Resistance factor Φf := 1.0 (AASHTO 6.5.4.2)

Φf·Fnc = 37.8 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.40

Fascia Girder During Deck Pour (Case 5), continued

Determine Stress due to Lateral Bending:

First-order lateral bending stress (from previous): fL1c = 4.5 ksi

Limiting unbraced length for first-order lateral bending stress

b b

buc

p

y

C R

f 1.2 L 13 ft

F

⋅

⋅⋅ = (Eq. 6.10.1.6-2)

Lateral bending stress:

elastic lateral torsional buckling stress

2

bb s

cr 2

b

t

CR E F :

L

r

⋅ ⋅π ⋅ =

     

Fcr = 47 ksi (Eq. 6.10.8.2.3-8)

Check if the first-order stress needs to be amplified: Approximated second-order lateral bending stress:

b b

buc

L1c b p

y

Lc

L1c

buc

cr

C R

f f if L 1.2 L

F

f :

0.85 f otherwise f 1

F

⋅

≤ ⋅⋅

=    

  ⋅   −    

fLc = 8.4 ksi

(Eq. 6.10.1.6-4)

Lateral bending check:

Lateral_Bending_Resistance :=“Lateral Bending Requirements Satisfied” if fLc≤0.6Fy

“Girder is NOT Adequate in Lateral Flexure” otherwise

Lateral_Bending_Resistance = “Lateral Bending Requirements Satisfied”

Overall Flexural Resistance Check:

The following must be satisfied:

buc Lc f nc

1 ffF

3

+ ⋅ ≤ f ⋅ (Eq. 6.10.3.2.1-2)

buc Lc

1 f f 28.2 ksi

3

+⋅ = φf·Fnc =37.8 ksi

Resistance_Check := “Girder Meets AASHTO Flexural Requirements” if buc Lc f nc

1 ffF

3

+ ⋅ ≤ f ⋅ 

“Girder is NOT Adequate in Lateral Flexure” otherwise

Resistance_Check = “Girder Meets AASHTO Flexural Requirements”
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B.41

Fascia Girder During Deck Pour (Case 5), continued

Constructability Check:

The following must be satisified:

 fbuc + fLc ≤ Φf·Rh·Fy (Eq. 6.10.3.2.1-1)

 fbuc + fLc = 33.8 ksi < Φf·Rh·Fy = 50 ksi

 Adequate resistance in compression flange

The following must be satisified:

 fbut + fLt ≤ Φf·Rh·Fy (Eq. 6.10.3.2.2-1)

 fbut + fLt = 25.6 ksi < Φf·Rh·Fy = 50 ksi

 Adequate resistance in tension flange

Overhang Bracket Forces:

Assume 2” edge distance at parapets. Therefore 2 22 deck _ width : 29 ft ft ft 12 12 12

    = + −−        

7 deck width 24 ft

12 overhang : 2

  + −+     = overhang = 2.125 ft Recall D = 60 in

Assume 10” thick deck at fascia overhang; 1⁄2 of weight goes to bracket and 1⁄2 directly to girder

Wfascia := 0.5 overhang 10 in 150 pcf Wfascia = 132.8 plf Concrete weight to bracket

Assume 200 plf for screed rail at fascia overhang Wrail := 200 plf Rail weight to bracket

Assume 10 psf for forms and another 5 psf for bracket components and miscellaneous at fascia 

overhang; 1⁄2 of weight goes to bracket and 1⁄2 directly to girder

Wforms := 0.5 overhang (10 psf + 5 psf) Wforms = 15.9 plf Form weight to bracket

Wbracket := Wfascia + Wrail + Wforms Wbracket = 348.7 plf Total uniform load to bracket

overhang : atan

D

 

a =    

α = 23.03 deg Angle of bracket relative to fascia girder web

FL := Wbracket·tan(α) FL = 148.2 plf Lateral force on flange from bracket

Recall that 150 plf was assumed for lateral force on each flange from bracket in computing 

lateral moments and flange stresses. Therefore, previous calculations are valid.
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B.42

Comparison of Results for Eigenvalue Buckling Analysis from UT Bridge (Case 1)

Recall, for a single girder (Case 1), the factored moment demand Mux := 762 kip ft

This included a load factor of 1.25 for Dead Load.

So, the applied unfactored moment ux

x

M M : 609.6 kip ft 1.25 = =

Per the UT Bridge analysis (unfactored), the Eigenvalue for Case 1 is 0.8941.

This is equivalent to a load factor, meaning that the ultimate resistance φMn := 0.8941Mx = 545 kip ft

Recall, for a single girder (Case 1), the lateral-torsional buckling resistance Mrx := 95.7 kip ft

n

rx

M 5.695

M

φ = (off by 470%)

It appears that the calculated design strength does not reasonably approximate the Eigenvalue 

analysis shown below for this buckling mode. For the reasons behind this, see the discussion in 

Manual Section 6.6. Note that the Eigenvalue is less than 1, which indicates that the single 

girder case is unstable under its own selfweight. The computed AASHTO design strength for 

lateral-torsional buckling also leads to this conclusion since Mrx << Mux. 

Figure B1-17: Case 1 Eigenvalue Analysis
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B.43

Comparison of Results for Eigenvalue Buckling Analysis from UT Bridge (Case 2)

Recall, for a two-girder system (Case 2), the factored moment demand Mux := 900kip ft

This included a load factor of 1.25 for Dead Load.

So, the applied unfactored moment ux

x

M M : 720 kip ft 1.25 = =

Per the UT Bridge analysis (unfactored), the Eigenvalue for Case 2 is 2.1489.

This is equivalent to a load factor, meaning that the ultimate resistance: 

ΦMn := 2.1489 Mx = 1547.2 kip ft per girder

Recall, for a two-girder system (Case 2), the system buckling resistance: 

Mrx:= 762.3 kip ft

φ = n

rx

M 2.03

M

 (off by 103%)

It appears that the calculated design strength does not reasonably approximate 

the Eigenvalue analysis shown below for this buckling mode. This is likely due to 

the omission of the Cb factor in the calculation for global buckling resistance (i.e., 

implied Cb = 1.0). By contrast, the Eigenvalue analysis automatically takes into 

account the moment gradient. Note that the Eigenvalue here is greater than 1.75, 

which should still provide an adequate margin of safety against buckling. However, 

as discussed previously, based on the calculated system buckling resistance, the 

contractor chose to install top and bottom flange lateral bracing in the end panels 

of the span to avoid any potential problems.

Figure B1-18: Case 2 Eigenvalue Analysis
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B.44

Summary

This example has illustrated many of the required checks to verify the adequacy of the

erection and construction plan. While this example selected specific cases as a 

summary of required checks, the erection engineer will be required to provide the

necessary checks are all critical stages of the construction. As in this example, the

first girder is often inadequate to support itself on bearings without additional

temporary supports. In some cases, two girders set on bearings do not meet buckling

criteria and it is important to always include the two girder buckling analysis.

The construction contractor and resident engineer are responsible to observe the

structure during erection. If any unusual deflections in the field are observed, work

should stop immediately and the erection engineer should be consulted.
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Engineering for Structural Stability in Bridge Construction Reference Manual

B.46

Reader 

Notes
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B.47

Reader Notes
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B.48

Reader Notes
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B.49

Reader Notes
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B.50

Reader Notes

 
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B.51

Reader Notes
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B.52

Reader Notes
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B.53

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

General Category / Description Specific Analysis / Calculation Task Appendix Page

Table of Contents N/A B.51

Bridge Data N/A B.52

Framing Plan Details N/A B.54

Applied Forces Wind Load B.59

Lifting Analysis Single Girder Pick with Interior Cross-frames B.61

Figure UT Lift Output B.62

Lifting Analysis Single Girder Pick without Cross-frames B.68

Figure UT Lift Output B.69

Lifting Analysis Single

frames

Girder Pick with Exterior Cross- B.75

Figure UT Lift Output B.76

Lifting Analysis Single Girder Pick without Cross-frames B.82

Figure UT Lift Output B.83

Lifting Analysis Single Girder Pick without Cross-frames B.89

Figure UT Lift Output B.90

Erection Analysis Two Girder System B.96

Erection Analysis Four Girder System B.101

Erection Analysis Multi-Span Girder System B.104

Erection Analysis Bearing Capacity B.105

Deck Pour Analysis UT Bridge Output B.106

Deck Pour Analysis AASHTO Resistance Calculations B.109

Deck Pour Analysis Cross-Frame Capacity B.117

Erection Analysis Splice Capacity with 50% Bolts B.121

Erection Analysis Holding Crane B.125

B.54

EXAMPLE PROBLEM #2: 3-SPAN MULTI-GIRDER CURVED STEEL

STRUCTURE

This example problem expands upon Example Problem #1 to examine the effects

of the curvature in the plate girders during steel bridge construction. While

Example Problem #1 incorporated the use of a commercial 3D finite element

analysis program which are typically utilized in engineering offices, this problem

focuses on analysis using UT Lift and UT Bridge. These free bridge erection

analysis programs were developed by the University of Texas. This problem is not

intended to be comprehensive, but instead a look at the analysis and output

capabilities of UT Lift and UT Bridge focusing on the effects of curvature.

The following table of contents illustrates the general categories into which this

example problem is subdivided, and the relevant page number at which the start

of each category, and its specific component analysis or calculation tasks, may

be found.
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B.55

Bridge Data:

Continuous 3 span curved steel plate girder bridge, 4 girders total. Radius of

curvature is 700 ft at centerline of roadway. Out-to-out deck width is 40.5 ft. 

Girder spacing is 11 ft for a total of 33 ft between fascia girders. Structural deck

slab thickness is 9 in. with 0.5 in. integral wearing surface.

The spans are symmetric, with Spans 1 and 3 at 160 ft long and Span 2 at 210 ft

long measured along the centerline of structure. 

The field splices are also symmetric, with Field Section 1 at 120 ft long in Spans 1 

and 3 (at Abutments 1 and 2), Field Section 2 at approximately 78.15 ft long

(centered on Piers 1 and 2), and Field Section 3 at approximately 133.65 ft long in

the middle of Span 2. Since these measurements are taken at the centerline of

structure, where there is no physical girder, the actual field section lengths vary

depending on which girder is considered.

Erection Analysis:

A single curved girder pick is modeled with UT Lift 1.3 to determine lift point

locations and resulting forces in girder. For this example, Field Section 3 (136.8 ft

long) of the exterior girder G4 is chosen for the lifting analysis. 10% additional

weight is assumed to account for connection material, stiffeners, etc. In computing

the weight of the attached cross-frames, an L8x6x9/16 is assumed.

Therefore,

Ag := 7.56 in2 for L8x6x9/16

( ) ( ) 2 2

X g 3

lb W : 2 490 A 11 ft + 11 ft 7 ft 1236.8 lb

ft

  =⋅ ⋅ + =    

per cross-frame (2 horizontals & 2 diagonals)

Several stages of the bridge erection are examined utilizing UT Bridge to determine

the adequacy of the steel system under self weight and wind loads. A two girder, four

girder, and multi-span system are analyzed during different stages of the erection

sequence.

The capacity of the splice with 50% bolts is examined during steel erection. Bearing

capacities during erection and deck pour in cases of high rotation is also discussed,

however specific bearing details are not included in this example.
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B.56

Deck Pour Analysis:

For this example, it is assumed the deck pour will run in four casts. The first cast is in Span 3 

starting at Abutment 2 and ending at the field splice. The second cast is in Span 2 between 

field splices. The third cast is in Span 1 from the field splice to Abutment 1. The fourth cast is 

over Piers 1 and 2. The worst case stage for the Span 3 girder segment is when the deck has 

been poured over Span 3 up to the splice (first cast). This stage will be examined for girder 

adequacy. The concrete weight should be taken as 150 pcf and treated as permanent dead 

load, while construction dead load, the weight of the forms, should be taken at 10 psf. 

Construction live load should be taken as 20 psf in Spans 2 and 3.

The pour sequence is modeled in UT Bridge, which does not allow for the form weight or 

construction live load, so those are ignored. Wind load is assumed to be negligible during the 

pour and is also ignored. The factored results used in the calculations are from the Strength I: 

1.25 DC + 1.50 CDL + 1.50 CLL load combination. The Strength VI: 1.40 DC + 1.40 CDL + 

1.40 CLL load combination should also be analyzed; however, it can be seen from the Strength 

I results that the design will still be adequate for Strength VI, since at most there will be a 12% 

increase in applied stresses (1.40/1.25), and all the allowable stresses are significantly higher 

than the applied stresses.

Evaluation of Stages:

The girders will be checked for adequacy according to AASHTO 2012 LRFD Specifications. The 

G4 girder (Field Section 3) will be checked for stability as well as bending capacity during the 

pick. The G4 girder (Field Section 1) will be checked for the deck pour loading. While these 

cases may not represent the critical loading for each girder segment, they serve as an example 

to check for adequacy. The erection stages will be checked for displacements and buckling 

eigenvalues utilizing UT Bridge. Note that many necessary checks are not performed here as 

they are conceptually similar to the calculations shown in Example 1 for straight plate girders.
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B.57

Figure B2-1: Example 2 Cross-section
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B.58

Figure B2-2: Example 2 Framing Plan
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B.59

Figure B2-3: Example 2 Field Section 1
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B.60

Figure B2-4: Example 2 Field Section 2 
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B.61

Figure B2-5: Example 2 Field Section 3
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B.62

Wind Load:

Use Figure 26.5-1A in ASCE 7-10 to determine basic wind speed for Risk Category II.

V := 115 miles per hour

Use Manual Appendix D Table D-3.2 to determine design wind speed reduction based on 

construction duration.

Wind Velocity Modification Factor

Vm := 0.75 Assume 6 weeks to 1 year as duration for steel erection.

Design Wind Speed

DWS := Vm·V DWS = 86.3 mph

Incorporate modified Design Wind Speed into pressure equation

Velocity Pressure Exposure Coefficient (ASCE 7-10, Sect 26.7.3)

Assume Surface Roughness C - Open terrain with scattered obstructions having heights 

generally less than 30 feet. Therefore, Exposure Category C

Manual Table D-3-1, for Height = 30 feet, Kz = 0.98. Say Kz = 1.0.

Take wind directionality factor as 0.85 and topographic factor as 1.0.

Kz := 1 Kzt := 1 Kd := 0.85

Velocity Pressure (Manual Eq. D-3.4b)

qz := 0.00256·Kz·Kzt·Kd·DWS2 qz = 16.2 psf

Gust Effect Factor G := 0.85

Net Force Coefficient (Assuming deck forms not in place) Cf := 2.2 since ratio of girder 

spacing to depth, S/d < 2

Net Pressure

Qz := G·Cf·qz Qz := 30.3 psf
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B.63

Wind Load, continued:

One Day / Girder Setting Design Wind Speed (Assuming minimum wind speed per D-3.4)

V := 20 mph

Use 1.0 Wind Velocity Modification Factor (built in to minimum wind speed)

 Vm := 1.0

Design Wind Speed:

DWS := Vm·V DWS = 20 mph

One Day Girder Setting Velocity Pressure (Manual Eq. D-3.4b)

 qzset := 0.00256·Kz·Kzt·Kd·DWS2 qzset = 0.9 psf

One Day Girder Setting Net Pressure

 Qzset := G·Cf·qzset Qzset = 1.6 psf

1.6 psf is negligible and can be ignored for short-duration events like girder picks which would 

not be occurring unless the wind is minimal anyway. However, use 5 psf as a minimum pressure 

for stability checks for pieces that are already set to account for accidental loading, etc. (per D3.3).

 Qzset := 5 psf

Wind Forces on Girders:

Exposed height for girder group = 7.5 feet (worst-case) + 33'-0" bridge width * 5% cross-slope

h := 7.5 + 33.0·0.05 h = 9.15 ft

Exposed height for single girder being set = 7.5 feet (worst case) hset := 7.5 ft

Force to girder group during partially-erected or fully-erected condition (6+ weeks)

 W1 := Qz·h W1 = 277 lb

ft

Force to 1st girder during its setting (one day)

 Wset := Qzset·hset Wset = 37.5 lb

ft
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B.64

Single Girder Pick of G4, Field Section 3 (with inside cross-frames attached)

See the following pages for the UT Lift 1.3 output (Excel spreadsheet). The chosen lift point is 

15'-10 1/4" from the end of the girder with a chord length of 105'-0" between lift points. The 

reaction at each point is approximately 33 kips, which must not exceed the allowable capacity of 

the lift clamps.

Also note that the calculated moment in the lifted curved girder is less than the buckling 

resistance (793.21 kip-ft vs. 2370.09 kip-ft).

The maximum twist at the end of the girder θtotal := 3.023 deg

Since the twist is much more than 1.5 degrees, an alternate lift scheme should be considered. 

Try a lift of the girder G4 without the cross-frames attached. This will induce much less torsion 

of the lifted piece. The remaining Field Section 3 girders will also have to be analyzed (G3, G2, 

and G1) in order to determine a viable lift sequence that includes the placement of the crossframes.
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B.65

Figure B2-6: Page 1 of UT Lift Output for Girder G4 Field Section 3, with CrossFrames
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B.66

Figure B2-7: Page 2 of UT Lift Output for Girder G4 Field Section 3, with CrossFrames
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B.67

Figure B2-8: Page 3 of UT Lift Output for Girder G4 Field Section 3, with CrossFrames
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B.68

Figure B2-9: Page 4 of UT Lift Output for Girder G4 Field Section 3, with Cross-Frames
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B.69

Figure B2-10: Page 5 of UT Lift Output for Girder G4 Field Section 3, with CrossFrames
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B.70

Figure B2-11: Page 6 of UT Lift Output for Girder G4 Field Section 3, with CrossFrames
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B.71

Single Girder Pick of G4, Field Section 3 (without inside cross-frames attached)

See the following pages for the UT Lift 1.3 output (Excel spreadsheet). The chosen lift point is 

28'-4 1/2" from the end of the girder with a chord length of 80'-0" between lift points. The 

reaction at each point is approximately 28 kips, which must not exceed the allowable capacity of 

the lift clamps.

Also note that the calculated moment in the lifted curved girder is less than the buckling 

resistance (224.27 kip-ft vs. 2370.09 kip-ft).

The maximum twist at the end of the girder θtotal := 0.274deg

Since the twist is much less than 1.5 degrees, this should be adequate for fit-up. Since the 

cross-frames will not be attached to G4 during its lift, they will have to be lifted with G3 instead. 

To avoid excessive torsion on the G3 piece, both the inside and outside cross-frames will be 

attached to that girder prior to lifting.
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B.72

Figure B2-12: Page 1 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames
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B.73

Figure B2-13: Page 2 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames
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B.74

Figure B2-14: Page 3 of UT Lift Output for Girder G4 Field Section 3, without CrossFrames
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B.75

Figure B2-15: Page 4 of UT Lift Output for Girder G4 Field Section 3, without

Cross-Frames
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B.76

Figure B2-16: Page 5 of UT Lift Output for Girder G4 Field Section 3, without

Cross-Frames
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B.77

Figure B2-17: Page 6 of UT Lift Output for Girder G4 Field Section 3, without

Cross-Frames
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B.78

Single Girder Pick of G3, Field Section 3 (with both inside and outside cross-frames 

attached)

See the following pages for the UT Lift 1.3 output (Excel spreadsheet). The chosen lift point is 

27'-4" from the end of the girder with a chord length of 80'-0" between lift points. The reaction at 

each point is approximately 31 kips, which must not exceed the allowable capacity of the lift 

clamps.

Also note that the calculated moment in the lifted curved girder is less than the buckling 

resistance (283.54 kip-ft vs. 894.84 kip-ft).

The maximum twist at the end of the girder θtotal := 1.454 deg

Since the twist is less than 1.5 degrees, this should be adequate for fit-up.
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B.79

Figure B2-18: Page 1 of UT Lift Output for Girder G3 Field Section 3
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B.80

Figure B2-19: Page 2 of UT Lift Output for Girder G3 Field Section 3
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B.81

Figure B2-20: Page 3 of UT Lift Output for Girder G3 Field Section 3
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Figure B2-21: Page 4 of UT Lift Output for Girder G3 Field Section 3
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Figure B2-22: Page 5 of UT Lift Output for Girder G3 Field Section 3
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B.84

Figure B2-23: Page 6 of UT Lift Output for Girder G3 Field Section 3 
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B.85

Single Girder Pick of G2, Field Section 3 (without either inside or outside

cross-frames attached)

See the following pages for the UT Lift 1.3 output (Excel spreadsheet). The chosen lift point is 

28'-9 1/2" from the end of the girder with a chord length of 75'-0" between lift points. The 

reaction at each point is approximately 20 kips, which must not exceed the allowable capacity of 

the lift clamps.

Also note that the calculated moment in the lifted curved girder is less than the buckling 

resistance (171.81 kip-ft vs. 739.49 kip-ft).

The maximum twist at the end of the girder θtotal := 1.045deg

Since the twist is less than 1.5 degrees, this should be adequate for fit-up.
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B.86

Figure B2-24: Page 1 of UT Lift Output for Girder G2 Field Section 3
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B.87

Figure B2-25: Page 3 of UT Lift Output for Girder G2 Field Section 3
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Figure B2-26: Page 3 of UT Lift Output for Girder G2 Field Section 3
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Figure B2-27: Page 4 of UT Lift Output for Girder G2 Field Section 3
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Figure B2-28: Page 5 of UT Lift Output for Girder G2 Field Section 3
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B.91

Figure B2-29: Page 6 of UT Lift Output for Girder G2 Field Section 3 
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B.92

Single Girder Pick of G1, Field Section 3 (without outside cross-frames attached)

See the following pages for the UT Lift 1.3 output (Excel spreadsheet). The chosen lift point is 

27'-8 3/4" from the end of the girder with a chord length of 75'-0" between lift points. The 

reaction at each point is approximately 20 kips, which must not exceed the allowable capacity of 

the lift clamps.

Also note that the calculated moment in the lifted curved girder is less than the buckling 

resistance (161.68 kip-ft vs. 814.21 kip-ft).

The maximum twist at the end of the girder θtotal := 0.768 deg

Since the twist is less than 1.5 degrees, this should be adequate for fit-up. A separate run (not 

included here) showed that excessive twists would result from a pick of G1 with the outside 

cross-frames attached. Thus, girder G1 must be picked bare and the cross-frames then 

installed between G2 and G1 after both girders are in place.
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B.93

Figure B2-30: Page 1 of UT Lift Output for Girder G1 Field Section 3
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Figure B2-31: Page 2 of UT Lift Output for Girder G1 Field Section 3
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Figure B2-32: Page 3 of UT Lift Output for Girder G1 Field Section 3
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Figure B2-33: Page 4 of UT Lift Output for Girder G1 Field Section 3
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Figure B2-34: Page 5 of UT Lift Output for Girder G1 Field Section 3
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Figure B2-35: Page 6 of UT Lift Output for Girder G1 Field Section 3
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B.99

Erection of G3 and G4 in Span 3 (with all cross-frames and no shoring)

The entire structure was analyzed for the erection sequence step by step in UT Bridge. Several 

critical erection steps were selected to show as part of this example. The structure was erected 

from Abutment 2 to Abutment 1. The first critical case analyzed consists of the first two girders 

of Span 3 erected with all the cross-frames installed between the girders. See Figures B2-37 

and B2-38 for output of this case.

The minimum vertical positive reaction at the interior girder at the Abutment is 11.2 kips. 

Therefore, the two girder system would not require temporary shoring or tie-downs at the 

bearings due to uplift concerns. The lateral displacement of the two girder system is 27 inches 

which is equal to L/70 for the 160 feet long span. This does not meet the deflection criteria of 

L/150 presented in Section D-7. In addition, the Eigenvalue for the two girder system is 0.5, 

which is not adequate and indicates the girder system would buckle spanning from the 

abutment to the pier with no additional supports. 

Note that this analysis and subsequent erection sequence analyses in this example problem 

use the Strength III: 1.25 DC + 1.0 CW load combination, so the presented Eigenvalues, 

deflections, and span ratios are actually factored (conservative). If more exact results are 

desired, the designer could rerun the analyses with service loads to get the true service level 

deflections, as well as the unfactored Eigenvalues.

Figure B2-36: Analysis of Fully Erected Bridge
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B.100

Figure B2-37: Girder Deflection During Two Girder Erection

Figure B2-38: Girder Stresses and Eigenvalue Analysis During Two Girder 

Erection
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B.101

Erection of G3 and G4 in Span 3 (with all cross-frames and shoring)

Based on the previous analysis, temporary shoring or a hold crane is required to support the 

two girder system during erection of Span 3. Temporary shoring supports were added to the UT 

Bridge analysis model at the midspan of Span 3. See Figures B2-39 and B2-40 for output of the 

two girder system with shoring.

The maximum lateral deflection of a girder in the system is 2.9 inches, which equates to L/660. 

The Eigenvalue has increased to 12.1 indicating an adequate factor of safety against buckling. 

The maximum girders stresses are at 11.1 ksi. These stresses were found to be adequate per 

AASHTO constructability criteria but for brevity the calculations for girder resistance are only 

included in the deck pour analysis located at the end of this example.
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B.102

Figure B2-39: Girder Deflection During Two Girder Erection with Shoring

Figure B2-40: Girder Stresses and Eigenvalue Analysis, Two Girders with Shoring
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B.103

Erection of G3 and G4 in Span 3 (with half of the cross-frames and shoring)

Based on the previous analysis, the two girder system is adequate with temporary shoring at 

midspan. The contractor would like to erect the girders with only half of the cross-frames 

installed to speed up total erection time. The remaining cross-frames would then be installed 

once the bridge is fully erected prior to the deck pour. The two girder system was analyzed 

with every other cross-frame removed in UT Bridge as shown in Figure B2-41. The Eigenvalue 

of 0.29 indicates the girder would buckle due to the increased unbraced length from removing 

cross-frames. Therefore, the contractor will erect the bridge with all cross-frames installed.

Figure B2-41: Girder Stresses and Eigenvalue Analysis, Two Girders with 

Shoring, Half of the Cross-Frames
Engineering for Structural Stability in Bridge Construction Reference Manual

B.104

Erection of G1 through G4 in Span 3 (with all cross-frames and no shoring)

The contractor would prefer to remove the shoring in Span 3 once all four girders in Span 1 are 

erected. Figures B2-42 and B2-43 examine the fully erected Span 3 with no shoring. The 

Eigenvalue of 5.9 represents an adequate factor of safety against buckling of the system. 

However, the maximum lateral displacement of the system is 11.8 inches which equates to 

L/160. While this is within criteria of L/150 presented in Section D-7, the contractor has been 

advised and agreed to keep the Span 3 midspan shoring in place until the erection of Span 2 is 

complete. The lateral deflection of approximately 12 inches is significant and may cause fit-up 

issues with the Span 2 erection.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.105

Figure B2-42: Girder Stresses and Eigenvalue Analysis, Four Girders with no 

Shoring

Figure B2-43: Girder Deflection During Four Girder Erection with no Shoring
Engineering for Structural Stability in Bridge Construction Reference Manual

B.106

Erection of G1 through G4 in Span 3 (with all cross-frames and shoring)

The lateral deflection for the four girder system is reduced to 1.1 inches with the midspan 

shoring in place as shown in Figure B2-44. This is adequate and will allow for proper fit-up 

during the Span 2 erection.

Figure B2-44: Girder Deflection During Four Girder Erection with Shoring
Engineering for Structural Stability in Bridge Construction Reference Manual

B.107

Erection of G1 and G2 in Span 1 (with all cross-frames and no shoring)

The completed structure in Span 3 and 2 provides additional stability for the erection of Girders 

1 and 2 in Span 1. The Girders in Span 1 are adequate to span from pier to abutment without 

additional shoring. The worst case girder deflection at this stage occurs in Span 3 with a lateral 

deflection of 7.0 inches. This is equivalent to L/275 and is adequate based on Section D-7. The 

Eigenvalue of 3.7 for this stage provides adequate safety against buckling.

Figure B2-45: Girder Deflection During Span 1 Erection

Figure B2-46: Girder Stresses and Eigenvalue Analysis During Span 1 Erection
Engineering for Structural Stability in Bridge Construction Reference Manual

B.108

Adequacy of the Bearings During Erection

Depending on the bearing type and possible blocking setup, it may be important to check the 

bearings for rotations and reactions during stages of the bridge construction. The reactions and 

rotations can be output from UT Bridge at each bearing during the various stages of erection 

and deck pour. For this example, the bearing loads and rotations will be examined for one of the 

critical stages. Abutment 2 bearings experience greater than normal service level rotations and 

less than normal service level dead load reactions during the erection of Span 1. This situation 

of high rotation and low vertical reaction could compromise some types of bearings. The vertical 

reactions (16.7 kips for Girder 1 in this example) and rotations at the bearing (0.08 degrees for 

Girder 1 in this example) should be checked against the limits of the bearings. Often times in 

curved bridges, bearings are specially detailed by a fabricator for the specific loading conditions 

of the bridge and the bearing fabricator should be contacted to determine the adequacy of the 

bearings during the construction stages.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.109

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour

Analysis and Methodology:

The entire deck pour is modeled in UT Bridge via four analysis cases. The first cast,

which occurs in Span 3, corresponds to Analysis Case 1. Refer to Figure B2-47 for

the reactions from this analysis.

Figure B2-47: Reactions During Case 1 (1st Deck Pour)

Refer to Figure B2-48 for the normal stresses in the girders from this analysis.

Figure B2-48: Normal Stresses During Case 1 (1st Deck Pour)

Note that in the UT Bridge model, the span numbering is reversed relative to the framing plan of 

Figure B2-2. Since the bridge is symmetric, this makes no difference to the analysis.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.110

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Because this is a continuous bridge, the maximum positive moment in the end span should 

occur at approximately 0.4L into that span, where L is the length of the end span. Refer to 

Exhibits B2-49, B2-50, B2-51, and B2-52, which offer visual proof of this by plotting normal 

stresses in the four girders (one exhibit per each flange tip) throughout the length of the bridge.

Figure B2-49: Girder G4 Normal Stresses at Left Tip of Bottom Flange for 

Analysis Case 1 (1st Deck Pour)

Figure B2-50: Girder G4 Normal Stresses at Right Tip of Bottom Flange for 

Analysis Case 1 (1st Deck Pour)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.111

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour,

continued

Figure B2-51: Girder G4 Normal Stresses at Left Tip of Top Flange for Analysis

Case 1 (1st Deck Pour)

Figure B2-52: Girder G4 Normal Stresses at Right Tip of Top Flange for Analysis Case 1 (1st

Deck Pour)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.112

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour,

continued

The AASHTO equations require the stresses in the flanges to be broken up into components (due

only to lateral bending, as well as without lateral bending), but most analysis programs do not

provide output in this fashion. Therefore, it is necessary to either make some assumptions or

otherwise manipulate the data. One approach would be to look at the normal stresses at the

location where the maximum positive moment in Span 1 occurs (approximately at 0.4L) and

average the sum of the flange tip stresses (from Figures B2-49 through B2-52 above) to compute

the bending stress component. This approach is adopted in this example below. The warping

stresses due to lateral bending could be computed by taking the average of the difference of the

flange tip stresses; refer to Figure B2-53 for a diagram illustrating the decomposition of stresses

into normal and warping.

Another approach for the warping stresses, adopted in this example below, is to use approximations to

account for lateral bending due to the curvature and the deck overhang brackets.

Figure B2-53: Normal and Warping Stresses in Curved I-Girders
Engineering for Structural Stability in Bridge Construction Reference Manual

B.113

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, continued

Section Properties:

Es := 29000 ksi Fy := 50 ksi

Flanges:

ttf := 1 in btf := 20in tbf := 1.5in bbf := 21in

Web: Overall Depth:

w

9 t : in

16 = D := 84 in d := D + ttf + tbf d = 86.5 in

Calculated Properties:

Abf := tbf·bbf = 31.5 in2

 ybf := 0.5·tbf = 0.75 in

Aw := tw·D = 47.25 in2

 yw := tbf + 0.5·D = 43.5 in

Atf := ttf·btf = 20 in2 ytf := tbf + D + 0.5·ttf = 86 in

Ag := Abf+ Aw+ Atf = 98.75 in2 Area of girder

bf bf w w tf tf

b

bf w tf

Ay Ay Ay Y : 38.47 in

AA A

⋅+ ⋅+⋅ = = ⋅ + Centroid measured 

from bottom

Yt := d - Yb = 48.03 in Centroid measured 

from top

( ) ( ) ( ) 3 3 3 2 22 bf bf w tf tf 4

x bf b bf w b w tf b tr

bt bt t D I : A Y y A Y y A Y Y 118986.2 in 12 12 12

⋅ ⋅ ⋅ = + + +⋅− +⋅− + − = Major axis moment

of inertia

x 3

bx

b

I S : 3092.9 in

Y = = Major axis elastic section 

modulus to bottom

x 3

tx

t

I S : 2477.4 in

Y = = Major axis elastic section

modulus to top

3 3 3

bf bf w tf tf 4

y

tb tb D t I : 1825.5 in

12 12 12

⋅ ⋅ ⋅ = ++ = Major axis moment 

of inertia

( )

y 3

y

bf tf

I

S : 173.9 in

0.5 max b ,b = ⋅ Minimum minor axis 

elastic

section modulus
Engineering for Structural Stability in Bridge Construction Reference Manual

B.114

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, continued

Applied Factored Forces: Note: Major-axis moment is based on average flange tip stresses at 0.4L

Major-axis Bending: ( ) ( ) ux tx bx

21.20 ksi + 28.60 ksi 19.83 ksi + 22.60 ksi M : max S , S 5468 kip ft 2 2

  =   ⋅ ⋅ =

 

Unbraced Length: b

123 ft L : 20.5 ft

6 = = with cross-frame spacing approximately 20 ft

Lateral Flange Bending: Note: Lat. Bending could also be based on average flange tip stress difference

Radius of curvature 33 ft R : 700 ft + 716.5 ft

2 = = at Girder G4 Constant N:= 10

Moment in each flange due to lateral bending from curvature 2

ux b

lat

M L M :

NRD

⋅ = ⋅ ⋅

(Eq. C4.6.1.2.4b-1)

Mlat = 45.8 kip ft Note that this value is already factored since the major-axis moment was factored

Minor-axis Bending: Muy := 0 kip ft Assume wind load on girders in negligible during deck pour

Overhang Bracket Forces at Fascia Girder:

Assume bracket loads are applied uniformly along girder although actual bracket spacing = 3 ft

40.5ft - 33 ft overhang : 2 = overhang = 3.75 ft at fascia

Assume 10” thick deck at fascia overhang; 1⁄2 of weight goes to bracket and 1⁄2 directly to girder

wfascia := 0.5 overhang 10 in 150 pcf wfascia = 234.4 plf Concrete weight to bracket

Assume 200 plf for screed rail at fascia overhang

wrail := 200 plf Rail weight to bracket

Assume 10 psf for forms and another 5 psf for bracket components and miscellaneous at fascia 

overhang; 1⁄2 of weight goes to bracket and 1⁄2 directly to girder

wforms := 0.5·overhang·(10 psf + 5 psf) wforms = 28.1·plf Form weight to bracket

wbracket := wfascia + wrail + wforms wbracket = 462.5 plf Total uniform load to bracket

overhang : atan 28.2 deg D

 

a = =    

Angle of bracket relative to fascia girder web

FL := wbracket tan(α) = 247.8 plf Lateral force on ea. flange from bracket

Lateral Moment in Each Flange from Overhang Bracket at Fascia Girder: 2

L b

L

F L M :

12

⋅ = (Eq. C6.10.3.4-2)

Factored Lat. Moment in Ea. Flange from Overhang Bracket at Fascia Girder: MLu := 1.50 ML = 13 kip ft 

(conservatively assume highest load factor corresponding to all construction dead load)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.115

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, continued

Flexural Resistance:

Top flange is in compression: bfc := btf tfc := ttf

Bottom flange is in tension: bft := bbf tft := tbf

Applied Stresses: 

Top flange is in compression: 2

fc fc

yc

t b S :

6

⋅ = 3 S 66.7 in yc =

Bottom flange is in tension: 2

ft ft

yt

t b S :

6

⋅ = 3 S 110.2 in yt =

Stress in compression flange without

consideration of lateral bending: ux

buc

tx

M f :

S = buc f 26.5 ksi =

First-order stress due to lateral bending

in compression flange: uy lat Lu

L1c

yc

0.5M M M

f :

S

+ + = L1c f 10.6 ksi =

Stress in tension flange without

consideration of lateral bending: ux

but

bx

M f :

S = but f 21.2 ksi =

First-order stress due to lateral bending

in tension flange: uy lat Lu

Lt

yt

0.5M M M

f :

S

+ + = Lt f 6.4 ksi =

Flange Strength Reduction Factors:

Hybrid Factor (AASHTO 6.10.1.10.1) 

Since the flexural member is a homogenous built-up section, the hybrid factor shall be taken as unity

 Rh := 1

Web Load Shedding Factor (AASHTO 6.10.1.10.2)

Depth of web in compression Dc := Yt - ttf

s

rw

y

E : 5.7

F

 

λ= ⋅  

 

λrw= 137.3 c

w

2 D 167.2

t

⋅ =

c w

wc

fc fc

2D t

a :

b t

⋅ = ⋅

c

rw

w

b

wc c

rw

wc w

2 D 1.0 if 

t

R :

a 2D 1.0 otherwise

1200 300 a t

⋅ ≤ λ

=       ⋅   −  ⋅  − λ

+ ⋅      

Rb = 0.96

Web is slender, so Eq. 6.10.3.2.1-3 (web bend-buckling) must be checked per AASHTO 6.10.3.2.1. For 

constructability checks, per AASHTO 6.10.3.2.1, use Rb = 1
Engineering for Structural Stability in Bridge Construction Reference Manual

B.116

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Local Buckling Resistance (AASHTO 6.10.8.2.2):

Slenderness ratio of the compression flange

fc

f

fc

b

:

2 t

λ = ⋅ λ =f 10 (Eq. 6.10.8.2.2-3)

s

pf

y

E : 0.38

F

λ= ⋅ λ = pf 9.2 (Eq. 6.10.8.2.2-4)

s

rf

y

E : 0.56

0.7F

λ= ⋅ λ = rf 16.1 (Eq. 6.10.8.2.2-5)

( ) b h y f pf

nc1 y f pf

b hy

h y rf pf

nc1

R R F if 

F : 0.7F

1 1 R R F otherwise

R F

F 48.2 ksi

⋅ ⋅ λ ≤λ

=       λ −λ     −− ⋅ ⋅ ⋅ ⋅     ⋅ λ −λ      

=

(Eq. 6.10.8.2.2-1)

(Eq. 6.10.8.2.2-2)

Lateral Torsional Buckling Resistance (AASHTO 6.10.8.2.3):

Unbraced length Lb = 20.5 ft with cross-frame spacing of approximately 20 ft

Effective Radius

of Gyration fc

t

c w

fc fc

b

r :

1 D t 12 1

3b t

=

  ⋅ ⋅ +⋅   ⋅  

 rt = 4.8 in. (Eq. 6.10.8.2.3-9)

Limiting Unbraced Length Calculations:

s

p t

y

E L:r

F = ⋅ Lp = 9.7 ft. (Eq. 6.10.8.2.3-4)

s

r t

y

E L: r

0.7F =π ⋅ Lr = 36.2 ft. (Eq. 6.10.8.2.3-5)

Moment gradient modifier Cb := 1 since, mid

2

f 1

f

>
Engineering for Structural Stability in Bridge Construction Reference Manual

B.117

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Lateral Torsional Buckling Resistance

( ) ⋅⋅ ≤

        − = ⋅−− ⋅ ⋅ ⋅ ⋅ ≤             ⋅ −        

⋅ ⋅π ⋅

     

=

b hy b π

y b π

nc2 b b h y π b r

hy r π

2

bb s

2

b

t

nc2

R R F if L L

0.7F L L

F : C 1 1 R R F if L <L L

RF L L

CR E otherwise

L

r

F 43.9 ksi

(Eq. 6.10.8.2.3-1)

(Eq. 6.10.8.2.3-2)

(Eq. 6.10.8.2.3-3)

Controlling Nominal Flexural Resistance:

Fnc := min(Fnc1, Fnc2) Fnc = 43.9 ksi

Resistance factor Φf := 1.0 (AASHTO 6.5.4.2)

Φf·Fnc = 43.9 ksi

Mrx := Φf·Fnc·Stx Mrx = 9059.3 kip ft

ux

rx

M 0.6

M = Adequate resistance for lateral-torsional buckling

Determine Stress due to Lateral Bending:

First-order lateral bending stress (from previous): fL1c = 10.6 ksi

Limiting unbraced length for first-order lateral bending stress

b b

p

buc

y

C R 1.2 L 15.9 ft f

F

⋅ ⋅⋅ = (Eq. 6.10.1.6-2)

Lateral bending stress:

elastic lateral torsional buckling stress
Engineering for Structural Stability in Bridge Construction Reference Manual

B.118

2

bb s

cr 2

b

t

CR E F :

L

r

⋅ ⋅π ⋅ =

     

 Fcr = 109.4 ksi (Eq. 6.10.8.2.3-8)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.119

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour,

continued

Check if the first-order stress needs to be amplified: Approximated second-order

lateral bending stress:

⋅ ≤ ⋅⋅

=    

  ⋅   −    

b b

L1c b p

buc

y

Lc

L1c

buc

cr

C R f if L 1.2 L f

F

f :

0.85 f otherwise f 1

F

fLc = 11.9 ksi

(Eq. 6.10.1.6-4)

Lateral bending check:

Lateral_Bending_Resistance := “Lateral Bending Requirements Satisfied” if fLc≤0.6Fy

 “Girder is NOT Adequate in Lateral Flexure” otherwise

Lateral_Bending_Resistance = “Lateral Bending Requirements Satisfied”

Overall Flexural Resistance Check:

The following must be satisified:

buc Lc f nc

1 ffF

3

+ ⋅ ≤ f ⋅ (Eq. 6.10.3.2.1-2)

+⋅ = buc Lc

1 f f 30.4 ksi

3

 φf·Fnc =43.9 ksi

Resistance_Check := “Girder Meets AASHTO Flexural Requirements” if buc Lc f nc

1 ffF

3

+ ⋅ ≤ f ⋅ 

“Girder is NOT Adequate in Lateral Flexure” otherwise

Resistance_Check = “Girder Meets AASHTO Flexural Requirements”
Engineering for Structural Stability in Bridge Construction Reference Manual

B.120

Resistance of Girder G4, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Constructability Check:

The following must be satisfied:

The following must be satisfied: 

fbuc + fLc ≤ Φf·Rh·Fy (Eq. 6.10.3.2.1-1)

fbuc + fLc = 38.4 ksi < Φf·Rh·Fy = 50 ksi

Adequate resistance in compression flange

The following must be satisified:

fbut + fLt ≤ Φf·Rh·Fy (Eq. 6.10.3.2.2-1)

fbut + fLt = 27.6 ksi < Φf·Rh·Fy = 50 ksi

Adequate resistance in tension flange

Web Bend-Buckling Resistance without Longitudinal Stiffeners (AASHTO 6.10.1.9.1):

2

c

9 k : 28.71

D

D

= =

     

(Eq. 6.10.1.9.1-2)

s

crw 2

w

0.9 E k F : 33.6 ksi

D

t

⋅ ⋅ = =

     

(Eq. 6.10.1.9.1-1)

y

crw crw h y

F

F : min F ,R F , 33.6 ksi 0.7

  = ⋅=    

Constructability Check:

Fbuc ≤ Φf·Fcrw (Eq. 6.10.3.2.1-3)

Fbuc = 26.5 ksi < Φf·Fcrw = 33.6 ksi

Adequate resistance in web
Engineering for Structural Stability in Bridge Construction Reference Manual

B.121

Adequacy of the Cross-Frame Bracing Member for Deck Pour Loading

The cross-frames provide stability of the girder flanges during erection and placement of

the deck. Deck pour loads often control the cross-frame design. For this example a 

cross-frame member will be examined for maximum loading during the deck pour.

L8x6x9/16 Single Angle Cross-frame Member.

Axial Tension Resistance of the Brace L8x6x9/16 (AASHTO 6.8.2):

Put := 50.5 kip Maximum tension force in any brace member from UT Bridge analysis model.

Material / Section Properties (Taken from AISC manual) Fy := 36 ksi Fu := 58 ksi Ag := 7.56 in2

Note that A36 is still the preferred material specification for angles. Per AISC, availability of angles in 

other grades should be confirmed prior to their specification.

From Figure B2-1 it appears that the brace is welded rather than bolted to the conn. plate, so An := Ag

For shear lag reduction factor, lacking weld details, assume U := 0.60 (0.5 is worst case per 6.8.2.2)

Resistance factors Φy := 0.95 Φu := 0.80 (AASHTO 6.5.4.2)

Tension resistance for yielding Pry := Φy·Fy·Ag = 258.6 kip (Eq. 6.8.2.1-1)

Tension resistance for fracture Pru := Φu·Fu·An·U = 210.5 kip (Eq. 6.8.2.1-2)

Axial Resistance Check Put 50.5 kip < Prt := min (Pry, Pru) = 210.5 kip Tension resistance is adequate

Axial Compression Resistance of the Brace L8x6x9/16 (AASHTO 6.9.4):

Puc := 18.2 kip Maximum compression force in any brace member from UT Bridge analysis model.

Material / Section Properties (Taken from AISC manual) 

Es := 29000 ksi Fy := 36 ksi Ag := 7.56 in2

Check Slenderness of the Member (Sect. 6.9.4.2)

Following requirement needs to be satisfied for the element to qualify as nonslender:

y

b E k

t F

≤ ⋅ (Eq. 6.9.4.2.1-1) k := 0.45 from Table 6.9.4.2.1-1 

angle leg:

b:= 8 in t := 0.8625 in = b 14.2

t s

y

E k 12.8

F ⋅ =

leg check:

Find Q if element is slender:
Engineering for Structural Stability in Bridge Construction Reference Manual

B.122

y s

s y

s s

2

y

b b F E 1.34 0.76 if 0.91

tEt F

Q : 0.53 E otherwise

b F

t

  − ⋅ ≤⋅    

= ⋅

 

⋅   

(Eq. 6.9.4.2.2-5)

(Eq. 6.9.4.2.2-6)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.123

Adequacy of the Cross-Frame Bracing Member for Deck Pour Loading, continued

=

≤ ⋅ =

=

s

s

s y

s

 Q 1

b E 1.0 if 0.45

Q : t F

Q otherwise

 Q 1

Determine Effective Slenderness Ratio (KL/r)eff = λeff (Sect. 6.9.4.4)

Recall S := 11 ft 2 2 S D L : max S, 2

  + =  

 

S governs the brace length, so L = 132 in

rx := 2.55 in so 

x

L 51.8

r =

x x

eff

x

eff

L L 72 0.75 if 80

r r

:

L 32 1.25 otherwise

r

110.8

    + ≤

  λ =     +

 

λ = (Eq. 6.9.4.4-1)

(Eq. 6.9.4.4-2)

Limiting KL/r for secondary compression members λlimit:= 140 (Sect. 6.9.3)

Maximum actual slenderness corresponds to minor principal axis buckling rz := 1.30 in K := 1

limit

z

K L 101.5 140

r

⋅ = < l = Therefore, actual maximum slenderness ratio is adequate

Flexural Buckling Resistance

( )

2

s

e g 2

eff

E P: A π ⋅ = ⋅ λ

 Pe = 176.2 kip (Eq. 6.9.4.1.2-1)

Since the various conditions for single-angle members are satisfied as enumerated in AASHTO 

LRFD Sect. 6.9.4.4, the effective slenderness ratio can be calculated per that section; 

therefore, only flexural bucking resistance will be used to determine nominal compressive 

resistance of the brace. The effect of the eccentricities can be neglected when evaluated in this 

manner. Equivalent Nominal Yield Resistance

Po := Q·Fy·Ag Po = 261 kip (Sect. 6.9.4.1.1)

e

o

P 0.7

P =

Nominal Compressive Resistance

( )

     

 

  ⋅ ≥ =    

=

o

e

P

P e

o

n o

e

n

P 0.658 P if 0.44

P : P

0.877P otherwise

P 140.4 kip

(Eq. 6.9.4.1.1-1)

(Eq. 6.9.4.1.1-2)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.124

Adequacy of the Cross-Frame Bracing Member for Deck Pour Loading, continued

Resistance factor Φc := 0.9 (AASHTO 6.5.4.2)

Factored Axial Resistance

Prc := Φc·Pn Prc = 126.4 kip (Eq. 6.9.2.1-1)

Axial Resistance Check

Puc 18.2 kip < Prc = 126.4 kip Compression resistance is adequate

Verify Bracing Strength to Provide Girder Stability

Unbraced length Lb := 20 ft = 240 inwith cross-frame spacing of 20 ft

Span length L := 160 ft = 1920 in

Maximum moment with span Mf := 5468 kip ft = 65616 kip in

Height of cross-frame hb := D = 84 in

Number of braces in span, excluding supports n := 7

Modulus of elasticity Es = 29000 ksi

Moment modification factor Cb := 1

Distance between flange centroids tf bf

o

t t h : d 85.2 in

2 2 =− − =

Recall girder cross-sectional properties Yb = 38.47 in Yt = 48.03 in ttf = 1 in tbf = 1.5 in

Calculate effective minor axis moment of inertia

t := Yb= 38.47 in c := Yt = 48.03 in 3

tf tf 4

yc

t b I : 666.7 in

12

⋅ = =

3

bf bf 4

yt

t b I : 1157.6 in

12

⋅ = =

4

eff yc yt

t I : I I 1593.9in

c

  = + ⋅=    

(Manual Eq. D-5.2j)

Recall Iy =1825.5 in4 Therefore eff

y

I 0.873

I =

Required strength 2

b f

br 2

b s eff b o

0.005L L M F : 4.28 kip h nE I C h⋅ ⋅ = = ⋅⋅ ⋅ ⋅

(Manual Eq. D-2.1a)

Length of diagonal member ( ) 2 2 L : D S 156.46 in c = +=

Required strength of compression brace Fbrc:= Fbr = 4.28 kip (Manual Fig. 5-7,

Tension System)

Required strength of tension brace br c

brt

2F L F : 10.15 kip S⋅ = = (Manual Fig 5-7, 

Tension System)

Available strength of tension brace to resist stability force Prt – Put = 159.97 > Fbrt = 10.15 kip

Available strength of compression brace to resist stability force

Prc – Puc = 108.16 kip > Fbrc = 4.28 kip

Therefore, bracing is adequate for strength
Engineering for Structural Stability in Bridge Construction Reference Manual

B.125

Adequacy of the Cross-Frame Bracing Member for Deck Pour Loading, continued

Check Required Stiffness of Bracing System βT,reqd

Resistance factor Φbr := 0.75

Required stiffness ⋅ ⋅ β = = φ⋅⋅ ⋅ ⋅

2

φ

Treqd 2

βr s eφφβ

2.4 L M

: 81754.2 kip in

nE I C

(Manual Eq. D5.2b)

Calculate Attached Brace Stiffness βb

Area of diagonal member Ac := Ag = 7.56 in2

Area of horizontal member Ah := Ag = 7.56 in2

Attached brace stiffness 2 2

s b

b 3 3

c

c h

ESh : 2706164.4 kip in 2 L S

A A

⋅ ⋅ b = =   ⋅   +

 

(Manual Fig. 5-7, Eq. for Tension System)

Calculate Web Distortional Stiffness βsec

Recall web thickness tw = 0.5625 in

Intermediate stiffener plate thickness ts := 0.625 in

Intermediate stiffener plate width bs := 6.75 in

Web distortional stiffness ( ) 3 3

s o w s s

sec

o

E 1.5 h t t b : 3.3 20110.6 kip in

h 12 12

  ⋅ ⋅ ⋅ b = ⋅   + =

 

(Manual Eq. D-5.2h)

However, for a full depth cross-frame, ßsec := 999999999999 kip·in (infinity)

Calculate In-Plane Girder System Stiffness βg

Number of girders ng := 4

Recall major axis moment of inertia Ix = 118986.2 in4

Girder system stiffness ( )2 2 g s x

g 3

g

24 n 1 SEI

: 458704 kip in n L

⋅ − ⋅ ⋅ β = = (Manual Eq. D-5.2i) 

Calculate Total Provided System Stiffness βT and Compare with Required System 

Stiffness βT,reqd

Total provided system stiffness 

β = = ⋅     + +

ββ β  

T

β sec g

1

: 392221.1 kip in

111

(Rearranged Manual Eq. D-5.2g)

βT = 392221.1 kip in > βTreqd = 81754.2 kip in Therefore, stiffness of bracing system is adequate
Engineering for Structural Stability in Bridge Construction Reference Manual

B.126

Adequacy of Splice During Erection with 50% Bolt Installed

It is standard industry practice for the steel erectors to install 50% of the bolts in

splice connections while erection progresses to ease fit-up complications. Once the

steel is fully erected, the splice connections are completed prior to the deck pour.

This is example will examine one stage of the erection sequence for forces on a 

splice with 50% of the bolts installed. The bolts will be analyzed as bearing bolts

since the bolts have not yet be torqued. Figures B2-54 and B2-55 show the details of

the top flange and web splice bolt configurations. The bottom flange and web will

not be examined in this example for brevity, but will be solved similarly as shown for

the top flange.

Figure B2-54: Top Flange Splice Bolt Configuration
Engineering for Structural Stability in Bridge Construction Reference Manual

B.127

Adequacy of Splice During Erection with 50% Bolt Installed, continued

Figure B2-55: Web Splice Bolt Configuration
Engineering for Structural Stability in Bridge Construction Reference Manual

B.128

Adequacy of Splice During Erection with 50% Bolt Installed continued 

Splice Forces

Since UT Bridge does not give moments directly as output, the design forces must be

back-calculated using the flange tip stresses. For this example, the splices in Span 2 for Girder

G4 are checked (with the steel fully erected but prior to the deck pour).

(210 ft - 133.65 ft) x : 38.175 ft

2 = = Approximate Location of Splice in Span 2

Thus x 0.18

210 ft = of span length L

bf := 17 in Top flange width and tf := 1 in Top flange thickness for G4 Field Section 3

2

f 3

f f

b S : t 48.2 in

6 = = Lateral Bending Section Modulus at Top Flange

Af := tf·bf = 17 in2 Cross-sectional Area of Top Flange

σL1 := 6.55 ksi from UT Bridge, Left Tip Stress at Top Flange at 0.2L into Span 2

σR1 := -2.66 ksi from UT Bridge, Right Tip Stress at Top Flange at 0.2L into Span 2

σL2 := 2.51 ksi from UT Bridge, Left Tip Stress at Top Flange at 0.8L into Span 2

σR2 := 1.25 ksi from UT Bridge, Right Tip Stress at Top Flange at 0.8L into Span 2

( L1 R1 L2 R2 ) diff

max ,

: 4.6 ksi

2

s −s s −s s = = Lateral Bending (Warping) Stress in Top Flange

(σ + σσ + σ ) σ = = L1 R1 L2 R2

σum

max ,

: 1.9 kσi

2

Average Vertical Bending Stress in Top Flange

Mfl := Sf·σdiff = 18.5 kip ft Factored Lateral Flange Moment at Splice

ftop := Af·σsum = 33.1 kip Factored Flange Force from Strong Axis Moment at Splice

Bolt Shear Resistance

7/8” dia. A325 Bolts Ab := 0.60 in2 Fub := 120 ksi Ns := 2 (Double Shear)

Nfb := 8 No. Flange Bolts Nwb := 12 No. Web Bolts

Rn := 0.48·Ab·Fub·Ns Rn = 69.1 kip (Eq. 6.13.2.7-1)

Resistance factor Φ := 0.8 (6.5.4.2)

Rr := Φ·Rn Rr =55.3 kip

( ) ( ) 2 2 2 22 4

p b I : A 2 2 3.5 6.5 2 2 1.5 4.5 in 184.8 in = ⋅ ⋅⋅ + +⋅⋅ + ⋅ =    
Engineering for Structural Stability in Bridge Construction Reference Manual

B.129

Adequacy of Splice During Erection with 50% Bolt Installed, continued

Longitudinal Force in Bolt from Vertical Bending Stress

top

longvert

fb

f

F : 4.1 kip N= =

Longitudinal Force in Critical Bolt from Flange Lateral Bending Stress

fl

longlat

p

b

M 6.5 in F : 4.7 kip I

A

⋅ = =

Total Longitudinal Force in Critical Bolt

Flongtotal := Flongvert + Flonglat = 8.8 kip

Transverse Force in Critical Bolt from Flange Lateral Bending Stress

fl

trans

p

b

M 4.5 in F : 3.2 kip I

A

⋅ = =

Total Force in Critical Bolt

2 2 R : F F 9.4 kip u longtotal trans = +=

Rr = 55.3 kip > Ru = 9.4 kip Therefore, Flange Bolts are Adequate with 50% Installed.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.130

Erection of G3 and G4 in Span 3 (with all cross-frames and holding crane supporting top 

flange)

Recall that temporary shoring or a hold crane is required to support the two girder system during 

erection of Span 3. Temporary shoring supports were added to the UT Bridge analysis model at 

the midspan of Span 3. These are now revised to hold crane supports at the girder top flange, 

as the contractor is interested in utilizing this option in lieu of shoring towers. See Figures B2-56 

and B2-57 for output of the two girder system with a hold crane at the top flange.

The maximum lateral deflection of a girder in the system is 0.01 inches, which equates to 

L/192000. The Eigenvalue has increased to 36.1 indicating an adequate factor of safety against 

buckling. The maximum girders stresses are at 20.2 ksi. These stresses were found to be 

adequate per AASHTO constructability criteria but for brevity the calculations for girder 

resistance are only included in the deck pour analysis.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.131

Figure B2-56: Girder Deflection During Two Girder Erection with Holding Crane at

Top Flange

Figure B2-56: Girder Stresses and Eigenvalue Analysis, Two Girders with Holding

Crane at Top Flange
Engineering for Structural Stability in Bridge Construction Reference Manual

B.132

Erection of G3 and G4 in Span 3 (with all cross-frames and holding crane supporting 

bottom flange)

Recall that temporary shoring or a hold crane is required to support the two girder system during 

erection of Span 3. Temporary shoring supports were added to the UT Bridge analysis model at 

the midspan of Span 3. These are now revised to hold crane supports at the girder bottom 

flange, as the contractor is interested in utilizing this option in lieu of shoring towers. See 

Figures B2-58 and B2-59 for output of the two girder system with a hold crane at the bottom 

flange.

The maximum lateral deflection of a girder in the system is 0.04 inches, which equates to 

L/48000. The Eigenvalue has decreased to 8.4 indicating the factor of safety against buckling is 

still adequate. The maximum girders stresses are at 20.2 ksi. These stresses were found to be 

adequate per AASHTO constructability criteria but for brevity the calculations for girder 

resistance are only included in the deck pour analysis.

Although the behavior of the two-girder system is still acceptable with the holding crane 

supporting the bottom flange, it is obvious that the top flange scenario is preferable (improved 

Eigenvalue and deflection).
Engineering for Structural Stability in Bridge Construction Reference Manual

B.133

Figure B2-57: Girder Deflection During Two Girder Erection with Holding Crane at

Bottom Flange

Figure B2-58: Girder Stresses and Eigenvalue Analysis, Two Girders with Holding

Crane at Bottom Flange
Engineering for Structural Stability in Bridge Construction Reference Manual

B.134

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.135
Engineering for Structural Stability in Bridge Construction Reference Manual

B.136

Reader 

Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.137
Engineering for Structural Stability in Bridge Construction Reference Manual

B.138

Example Problem #3: Concrete Spliced Girder

The following table of contents illustrates the general categories into which this example

problem is subdivided, and the relevant page number at which the start of each category, and

its specific component analysis or calculation tasks, may be found.

General

Description

Category / Specific Analysis / Calculation Task Appendix

Page

Table of Contents N/A B.131

Bridge Data N/A B.132

Structural Analysis Girder Stability During Lifting B.132

Figure Section

Web

Properties of FL 78" Bulb Tee w/ Variable B.132

Figure Example 3 Plan B.133

Figure Example 3 Elevation B.134

Figure Example 3 Sections for Constant Depth Girders B.135

Figure Example 3 Sections at Critical Locations B.136

Figure Example 3 Stages of Construction B.137

Material Data Concrete Properties B.138

Drop-In Segment Girder Check Drop-In Segment Girder for Lifting Stability B.138

Pier Segment Girder Check Pier Segment Girder for Lifting Stability B.140

End Segment Girder Wind Load B.142

End Segment Girder Check Girder End Segment for Beam Rollover B.143

Strongback System Design Hanger

Segment

Beams Between Drop-In & Pier B.145

Strongback System Design

Segment

Hanger Bars Between Drop-In & Pier B.146

Strongback System Design

Segment

Strongback Between Drop-In & Pier B.148

Figure Typical Strongback System B.149

Figure Minor Axis Moment of Inertia Calculation for BT-78 B.150

Figure Minor Axis Moment of Inertia Calculation for BT-90 B.152

Figure Minor Axis Moment of Inertia Calculation for BT-180 B.154

Figure Prestress Layout for End Girder Segments B.156

Figure Prestress Layout for Girder Segments at Splices B.156

Figure Prestress Layout for Pier Girder Segments B.157

Figure Prestress Layout for Drop-In Girder Segments B.158
Engineering for Structural Stability in Bridge Construction Reference Manual

B.139

Bridge Data:

Continuous 3 span concrete spliced girder bridge, 5 girders total. Out-to-out deck width is 47

ft. Girder spacing is 9.5 ft for a total of 38 ft between fascia girders. Structural deck slab

thickness is 8.5 in. The spans are symmetric, with Spans 1 and 3 at 210 ft long and Span

2 at 280 ft long. Location is northern Florida, using PPC beams based on a 78" Florida

Modified Bulb Tee with variable web depth.

Cast-in-place splices are 2 ft long at each end of the pier segments. The end span girder

segments are 146 ft long, 78" bulb tees; the 90" bulb tee drop-in segment at Span 2 is 152

ft long. The 124 ft long girder segments at the piers are haunched, varying from a 78" bulb

tee shape in the end spans to a depth of 180" over the piers to a 90" bulb tee shape in

Span 2.

Girder Stability During Lifting:

The process of lifting the girders into place requires certain considerations. While being

lifted the sweep of the girder causes the center of gravity to have some eccentricity. This

causes a small amount of rotation that results in some of the self-weight being applied about

the weak axis of the girder. The girders will be checked for rollover stability based on

Chapter 7. The pier segment girder and drop-in segment girder will be checked.

The general plan and elevation, cross-sections, and construction stages are presented in the

following figures.

The table immediately below presents cross-sectional properties for various PPC bulb tee

girder shapes. The computation of the minor axis moments of inertia, not included in the

table, may be found at the end of this example problem. 

Section Depth

(in.)

Area

(in2

) 

Moment 

of Inertia

(in4

) 

Yb

(in.)

Yt

(in.)

Sb

(in3

) 

St

(in3

) 

BT-78 78 1,261 1,014,899 40.21 37.79 25,237 26,859

BT-84 84 1,315 1,223,135 43.19 40.81 28,317 29,974

BT-90 90 1,369 1,455,041 46.18 43.82 31,511 33,201

BT-96 96 1,423 1,711,587 49.16 46.84 34,818 36,540

BT-102 102 1,477 1,993,747 52.14 49.86 38,237 39,989

BT-108 108 1,531 2,302,492 55.13 52.87 41,767 43,5,48

BT-114 114 1,585 2,638,794 58.11 55.89 45,407 47,217

BT-120 120 1,639 3,003,626 61.10 58.90 49,159 50,996

BT-126 126 1,693 3,397,960 64.09 61.91 53,020 54,884

BT-132 132 1,747 3,822,766 67.08 64.92 56,990 58,882

BT-138 138 1,801 4,279,019 70.07 67.93 61,071 62,989

BT-144 144 1,855 4,767,689 73.06 70.94 65,260 67,204

BT-150 150 1,909 5,289,749 76.05 73.95 69,559 71,529

BT-156 156 1,963 5,846,170 79.04 76.96 73,966 75,962

BT-162 162 2,017 6,437,925 82.03 79.97 78,483 80,504

BT-168 168 2,071 7,065,986 85.02 82.98 83,108 85,155

BT-174 174 2,125 7,731,324 88.01 85.99 87,842 89,914

BT-180 180 2,179 8,434,913 91.01 88.99 92,684 94,782

Table B3-11 Section Properties of Florida 78" Bulb Tee with Variable Web Depth
Engineering for Structural Stability in Bridge Construction Reference Manual

B.140

Figure B3-1: Example 3 Plan
Engineering for Structural Stability in Bridge Construction Reference Manual

B.141

Figure B3-2: Example 3 Elevation
Engineering for Structural Stability in Bridge Construction Reference Manual

B.142

Figure B3-3: Example 3 Sections for Constant Depth Girders
Engineering for Structural Stability in Bridge Construction Reference Manual

B.143

Figure B3-4: Example 3 Sections at Critical Locations
Engineering for Structural Stability in Bridge Construction Reference Manual

B.144

Figure B3-5: Example 3 Stages of Construction
Engineering for Structural Stability in Bridge Construction Reference Manual

B.145

Concrete Properties:

Strength of concrete (assume 28-day strength has already been reached)

 fc := 8500 psi

Modulus of rupture

c

r

f f : 0.24 ksi 0.7 ksi

1000 psi =⋅ = (AASHTO 5.4.2.6)

Concrete modulus of elasticity

c

c

f E : 1820 ksi 5306 psi 1000psi = = ⋅ (AASHTO 5.4.2.4-1)

Check Drop-In Segment Girder for Lifting Stability

Length between lifting points Ldi := 142 ft

Girder properties (uses BT-90)

Gross area of concrete Ag_di := 1369 in2

Girder length Lg_di := 152 ft

Minor axis moment of inertia ly_di := 115887 in4

Distance from centroid to bottom fiber yb_di := 46.18 in

Distance from centroid to top fiber yt_di := 43.82 in

Major axis moment of inertia lx_di := 1455041 in4

Width of top flange bt_di := 62 in

Height of roll axis above centroid* yr_di := yt_di = 43.82 in

*Note: This should be modified to include camber, but ignored here for simplicity (< 1% difference)

Initial lateral eccentricity (based on 1⁄4 inch plus half of PCI sweep tolerance of 1/8” per 10 ft)

Cantilever overhang during lift

( ) g _ di di

di

L L

a : 5 ft

2

− = =

Weight of beam per unit length

di g _ di

kip w : A 150 pcf = 1.426 ft = ⋅

Lateral deflection of center of gravity of girder with full dead weight applied laterally

5 23 4 5

di di di di di di

o _ di di

c y _ di g _ di

0.1 L a L 3 a L 1.2 a

z : w 12.53 in

12 E l L

  ⋅ − ⋅ +⋅ ⋅ + ⋅ = ⋅ =   ⋅⋅ ⋅  

Assuming straight strands, xdi := 0.5·Lg_di – adi = 71 ft measured from lift point to midspan
Engineering for Structural Stability in Bridge Construction Reference Manual

B.146

Check Drop-In Segment Girder for Lifting Stability, continued:

Gravity moment at midspan

( ) ( ) ⋅ ⋅⋅− ( ) = ⋅ − −⋅ − = ⋅ ⋅

2

di di 2 2 di di di di

g _ di di di di di

di di

w x wa L x M : L a x L 3576.51 kip ft 2 L 2 L

Prestress Pdi := 1300 kip (approximate)

Eccentricity of strands edi := yb_di – 3 in – 2 in = 41.18 in (below centroid)

Compressive stress in top flange from gravity load and prestress 

g _ di t _ di di di di t _ di

t _ di

x _ di g _ di x _ di

M y P Pe y f : 629.89 psi

l A l

⋅ ⋅ ⋅ = +− =

Lateral moment capacity

( ) r t _ di y _ di

lat _ di

t _ di

ff l

M : 414.2 kip ft b

2

+ = =      

Initial roll angle

Assuming a small angle, Θ = sin Θ = tan Θ

Equilibrium roll angle

Maximum roll angle for cracking lat _ di

max_ di

g _ di

M

: 0.116 rad

M

Θ= =

Maximum roll angle for failure 

Lateral deflection of center of gravity of girder including rotation effects

Factor of safety for cracking (Manual Eq. D-4.3b)

Factor of safety for failure (Manual Eq. D-4.3a)

Since factor of safety for cracking is above the recommended 1.0 minimum, girder is adequate.

Since factor of safety for failure is above the recommended 1.5 minimum, girder is adequate.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.147

Check Pier Segment Girder for Lifting Stability:

Length between lifting points Lps:= 114 ft

Girder properties (use weighted average of BT-78 and BT-180 and BT-90 to represent 

haunched section)

Girder length Lg_ps := 124 ft

Minor axis moment of inertia

( ) 4 44

4

y _ ps

115158 in 2 136679 in 115887in

l : 126100.75 in

4

+⋅ + = =

Distance from centroid to bottom fiber ( )

b _ ps

40.21 in + 2 91.01 in +46.18 in

y : 67.1 in

4

⋅ = =

Distance from centroid to top fiber ( )

t _ ps

37.79 in + 2 88.99 in +43.82 in

y : 64.9 in

4

⋅ = =

Major axis moment of inertia

( ) 4 44

4

x _ ps

1014889 in 2 8434913 in 1455041 in

l : 4834939 in

4

+⋅ + = =

Width of bottom flange bb_ps := 30 in

Initial lateral eccentricity (based on 1⁄4 inch plus half of PCI sweep tolerance of 1/8” per 10 ft)

Cantilever overhang during lift

( ) g _ ps ps

ps

L L

a : 5 ft

2

− = =

Weight of beam per unit length (use weighted average of BT-78 and BT-180 and BT-90 to 

represent haunched section)

Gross area of concrete 2 22

2

g _ ps

1261 in 2 2179 in 1369 in A : 1747 in

4

+ ⋅ + = =

ps g _ ps

kip w : A 150 pcf = 1.82 ft = ⋅

Lateral deflection of center of gravity of girder with full dead weight applied laterally

5 23 4 5

ps ps ps ps ps ps

o _ ps ps

c y _ ps g _ ps

0.1 L a L 3 a L 1.2 a

z : w 5.96 in

12 E l L

  ⋅ − ⋅ +⋅ ⋅ + ⋅ = ⋅ =   ⋅⋅ ⋅  

Assuming straight strands, xps := 0.5·Lg_ps – aps = 57 ft measured from lift point to midspan

Prestress Pps := 1600 kip(approximate)

Eccentricity of strands ( )

ps t _ ps

16 2 in + 10 78 in - 3 in - 2 in - 2 in

e : y 44.11 in

38

  ⋅ ⋅   = - = (above centroid)

Gravity moment at midspan

( ) ( ) ( ) 2

ps ps 2 2 ps ps ps ps

g _ ps ps ps ps ps

ps ps

w x wa L x

M : L a x L 2933.5 kip ft 2 L 2 L

⋅ ⋅⋅− = ⋅ − − ⋅ − = ⋅ ⋅
Engineering for Structural Stability in Bridge Construction Reference Manual

B.148

Check Pier Segment Girder for Lifting Stability, continued: 

Compressive stress in bottom flange from gravity load and prestress

g _ ps b _ ps ps ps ps b _ ps

b _ ps

x _ ps g _ ps x _ ps

M y P Pe y f : 552.16 psi lAl− ⋅ ⋅ ⋅ = + − =−

Note: Value is negative, so stress is actually tensile, but still less than modulus of rupture fr = 699.71 psi

Lateral moment capacity ( ) r b _ ps y _ ps

lat _ ps

b _ ps

ff l

M : 103.37 kip ft b

2

+ = =      

Midspan radius of curvature

(note prestress, acting above ( ) c x _ ps 5

ps

ps ps g _ ps

E I

R : 2.43 10 in

P e M

⋅ = = − × −⋅ −

centroid, causes downward deflection) 

Camber with respect to beam ends: 

2

g _ ps

ps

ps

L

: 1.14in

8R

∆ = =− . 

Height of roll axis above centroid

modified to include camber

2

ps

r _ ps t _ ps ps

g _ ps

L 1

y : y 65.48 in

L 3

   

= −∆ − =            

Initial roll angle

Assuming a small angle, Θ = sin Θ = tan Θ

Equilibrium roll angle

Maximum roll angle for cracking lat _ps

max_ps

g _ ps

M

: 0.035 rad

M

Θ= =

Maximum roll angle for failure

Theoretical lateral deflection of center of gravity of girder including rotation effect

Factor of safety for cracking c _ ps

o _ ps i _ ps

r _ ps max_ ps

1 FS : 1.84

z

y

= = Θ

+

Θ

(Manual Eq. D-4.3b)

Factor of safety for failure r _ ps max p _ ps

f _ ps

o.p _ ps max p _ ps i _ ps

y FS : 4.73

z e

⋅

⋅

⋅Θ = = ⋅Θ + (Manual Eq. D-4.3a)

Since factor of safety for cracking is above the recommended 1.0 minimum, girder is adequate.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.149

Since factor of safety for failure is above the recommended 1.5 minimum, girder is adequate.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.150

Check Girder End Segment for Beam Rollover:

The standard sized BT-78 girder will be used. Therefore exposed height h := 78 in

Use Figure 26.5-1A in ASCE 7-10 to determine basic wind speed for Risk Category II.

V := 120 miles per hour

Use Manual Appendix D Table D-3.2 to determine design wind speed reduction based on construction 

duration.

Wind Velocity Modification Factor

 Vm := 0.65 Assume less than 6 weeks duration for casting concrete splices.

Design Wind Speed

DWS := Vm·V DWS = 78 mph

Incorporate modified Design Wind Speed into pressure equation

Velocity Pressure Exposure Coefficient (ASCE 7-10, Sect. 26.7.3)

Assume Surface Roughness B – Wooded and/or suburban areas with numerous closely spaced 

obstructions. Therefore, Exposure Category B

Manual Table D-3.1, for Height = 30 feet, Kz= 0.70

Take wind directionality factor as 0.85 and topographic factor as 1.0.

 Kz := 0.7 Kzt := 1 Kd := 0.85

Velocity Pressure (Manual Eq. D-3.4b)

 qz := 0.00256 psf·Kz·Kzt·Kd·DWS2

 qz = 9.3 psf

Gust Effect Factor G := 0.85

Net Force Coefficient (Assuming deck forms not in place) Cf := 2.2 since ratio of girder 

spacing to depth, S/d < 2

Net Pressure

Qz := G·Cf·qz Qz := 17.3 psf

Line Load from Wind ww := Qz·h = 112.64 plf

Length between supports (from abutment to first splice) Ls := 146 ft

Moment of inertia about minor axis Iy := 115158 in4

Lateral deflection at midspan due to wind on uncracked section 4

w s

w

c y

5w L

: 1.88 in

384E l

⋅ ∆= = ⋅

Wind overturning moment acting on girder end segment o ws

h M : w L 53.45 kip ft 2 = ⋅ ⋅=

Applied wind moment at midspan of girder end segment 2

w s

w

w L M : 300.14 kip ft 8⋅ = =
Engineering for Structural Stability in Bridge Construction Reference Manual

B.151

Check Girder End Segment for Beam Rollover:

The standard sized BT-78 girder will be used. Calculate factor of safety for girder cracking and rollover.

Note that wind load assumes a short exposure duration (< 6 weeks) prior to casting of splices.

Gross area of concrete Ag := 1261 in2

Weight per length of girder w := Ag·150 pcf = 1.314 klf

Total weight of girder W := w·Ls = 191.78 kip

Eccentricity from wind overturning moments 

Initial eccentricity of center of gravity of girder (Based on 1 inch plus PCI 

sweep tolerance of 1/8” per 10 ft)

s

i ww

1 1 L e : e 1 in in 1 7.45 in

8 10 ft 3

     =∆ + + + ⋅ ⋅ − =          

(includes wind effects)

Sum of rotational spring constants at supports KΘ := 100000in kip per radian (conservatively assumed)

Note that per the figures in Hurff (2010, a lower bound on the bearing pad rotational stiffness might be 

around 100000 in-kip/rad for a 24 in wide pad and around 50000 in-kip/rad for an 18 in wide pad. The 

bottom flange in this example is 30 in wide, so 100000 in-kip/rad should be conservative. Lateral restraint 

(friction) from strongback system is conservatively ignored. A creep reduction factor should also be 

applied to the rotational stiffness if bracing is not installed immediately after crane release (ignored for 

simplicity due to other conservatisms).

Applied gravity moment 2

s

g

w L M : 3499.93 kip ft 8⋅ = =

Distance from centroid to bottom fiber yb := 40.21 in

Distance from centroid to top fiber yt := 37.79 in

Prestress P := 700 kip (approximate)

Eccentricity of strands (below centroid)

Gross moment of inertia about the x-axis Igx := 1014899 in4

Width of top flange bt := 62 in

Width of bottom flange bb:= 30 in 

Compressive stress at top fiber due to gravity

 

⋅  ⋅ ⋅ ⋅   = +− − =

t

w

g t s t

t

gx g gx y

b M M y P Pe y 2 f : 199.11 psi

IA I I

load and prestress and wind

Modulus of rupture; recall fr = 0.7 ksi, so Lateral moment capacity ( ) r ty

lat

t

ffl

M : 278.24 kip ft

b

2

+ ⋅ = =      

Midspan radius of curvature

( ) c gx 5

s g

E I

R : 3.27 10 in

P e M

⋅ = =− × ⋅ −

Camber with respect to beam ends 

(note gravity deflection not overcome by prestress):

2

s

ps

L : 1.17in

8 R

∆ = =− ⋅ . 

Height of the center of gravity above roll axis

modified to include camber 

(assuming roll axis at bearing pad mid-depth) b

1 y : y 1.5 in + 1 40.93 in 3

  = + ∆⋅ − =    
Engineering for Structural Stability in Bridge Construction Reference Manual

B.152

Check Girder End Segment for Beam Rollover, continued:

Tilt angle at which cracking begins lat

max

g

M : 0.079 rad

M

Θ= =

Superelevation, or tilted angle of support (Based on PCI flatness tolerance of 1/16” over bearing pad 

width bottom flange width and DOT flatness tolerance of 1/16” over bearing seat width

Lateral deflection of center of gravity of girder ( )

( )

4

s

o.bar

c y

1 w L

z : 14.07 in

120 E l

  ⋅   =⋅ =        ⋅  

Radius of stability K r : 521.44 in

W

Θ = =

Width of bottom flange bb:= 30 in

Maximum resisting moment arm b

max

b z : 15 in

2 = = from edge of bottom flange

Height of roll center hr := 1.5 in above bearing pad mid-depth (3 inch elastomeric bearing assumed)

Roll angle of major axis with respect to vertical

Title angle at maximum factor of safety against failure

Lateral deflection of center of gravity of girder including rotation effects

Factor of safety for cracking

(Manual Eq. D-5.3b)

Minimum factor of safety = 1.0, therefore OK.

Factor of safety for rollover

(Manual Eq. D-5.3a)

Minimum factor of safety = 1.5, therefore OK.

Note that buckling of the long span PPC girder at the end segment (simply supported prior to the splice 

pour) is not checked. This is because the inelastic lateral-torsional buckling failure mode and 

corresponding equations are not applicable for PPC bridge girders, as they do not crack under selfweight 

for normal designs.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.153

Design Hanger Beams at Strongback Between Drop-In Girder Segment and Pier 

Segment:

Design load shall be one half of the weight of the drop-in girder segment with load factor of 1.25.

Pdi := 1.25·0.5·0.5·wdi·Lg_di = 67.74 kip (load per channel)

Check pair of MC12x35 hanger beams on underside of drop-in segment

Unbraced length

 Lb := 3.5 ft (assumed)

Max moment

( ) di b

u _mc

P L

M : 59.27 kip ft 4

⋅ = =

Steel yield strength

 Fy := 36 ksi

Steel modulus of elasticity

Es := 290000000 psi

Section modulus

 Zx := 43.2 in3

Radius of gyration about y-axis

 Ry := 1.11 in

Flexural resistance based on yielding

 Mp := Fy·Zx = 129.6 kip ft

s

p y

y

E L : 1.76 r 4.62 ft

F

  = ⋅⋅ =      

(AASHTO 6.12.2.2.5-7)

Since Lp is greater than Lb than there is no need to check for lateral torsional buckling.

Factored flexural resistance

 Mr := 1.0·Mp=129.6 kip ft

Since Mr is greater than Mu, section is satisfactory in flexure

Mr = 129.6 kip ft > Mu_mc = 59.27 kip ft

Max. shear

 Vu_mc := 0.5·Pdi = 33.87 kip

Depth of web

Dweb := 12 in
Engineering for Structural Stability in Bridge Construction Reference Manual

B.154

Design Hanger Beams at Strongback Between Drop-In Girder Segment and Pier 

Segment, cont.:

Thickness of web

 tweb := 0.465 in

Plastic shear force

 Vp:= 0.58·Fy·Dweb·tweb = 116.51 kip (AASHTO 6.10.9.2-2)

web

web

D Ratio1: 25.81

t = =

Transverse stiffener spacing

 do := Lb = 42 in (assumed)

Shear buckling coefficient

 

 

  =+ =              

2

o

web

5 k : 5 5.41

d

D

(AASHTO 6.10.9.3.2-7)

( ) s

y

E k

Ratio2 : 1.12 73.92

F

⋅ =⋅ =

Ratio of shear buckling resistance to yield strength

Cmc := 1.0 (AASHTO 6.10.9.3.2-4)

Nominal shear resistance

 Vn := Cmc·Vp = 116.51 kip

factored shear resistance

vr :-= 1.0 Vn = 116.51 kip

Since Vr is greater than Vu, section is satisfactory in shear

 Vn = 116.51 kip > Vu_mc = 33.87 kip

Design Hanger Bars at Strongback Between Drop-In Girder Segment and Pier Segment

Check pair of 1 5/8” diameter steel threaded bars (AASHTO 6.8.2.1)

Tension in bar (one at each end of the pair of channels)

Tbar:= 2·Vu_mc =67.74 kip
Engineering for Structural Stability in Bridge Construction Reference Manual

B.155

Design Hanger Bars at Strongback Between Drop-In Girder Segment and Pier Segment, 

cont.:

Gross and net area of bar

Yield strength of bar

 Fy.bar := 36 ksi

Ultimate strength of bar

 Fu.bar := 58 ksi

Reduction factor for holes

 Rp := 1.0

Reduction factor to account for shear lag

U := 1.0

Resistance factor for yielding

 Φy := 0.95

Resistance factor for fracture

 Φu := 0.80

Tensile resistance based on yielding

 Pr.y := Φy·Ag·Fy.bar= 70.93 kip

Tensile resistance based on fracture

 Pr.u := Φu·Fu.bar·An·Rp·U = 74.54 kip

Since Pr is greater than Tbar, section is satisfactory in tension.

Pr := min (Pr.y, Pr.u) = 70.93 kip > Tbar = 67.74 kip

Design Strongback Between Drop-In Girder Segment and Pier Segment:

Try twin W14x120 strongback girders (this example uses AISC 13th ed. Flexure section F2 for 

simplicity).

Unbraced Length

 Lb.w14 := 10.5 ft(assumed)

Max. moment

 Mu_w14 := Pdi·Lb.w14 = 711.24 kip ft

Steel yield strength

Fy.w14:= 50 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.156

Design Strongback Between Drop-In Girder Segment and Pier Segment, continued:

Section modulus

 Zx.w14:= 212in3

Flexural resistance based on yielding

 Mp.w14:= Fy.w14·Zx.w14 = 883.33 kip ft

Flexural resistance using lateral torsional buckling

 Lp.w14 := 13.2ft

 Lr.w14 := 52.0ft

Since Lbw14 is less than Lpw14 lateral torsional buckling does not need to be checked.

Flexural resistance

phi_Mn.w14:= 0.9·Mp.w14 = 795 kip ft

Since phi_Mn is greater than Mu, section is satisfactory to flexure.

phi_Mn.w14 = 795 kip ft > Mu_w14 = 711.24 kip ft

Max. shear

 Vu_w14 := Pdi = 67.74 kip

Depth of web

 Dweb.w14 := 14.5 in

Thickness of web

 tweb.w14:= 0.590 in

Plastic shear force

 Vp.w14:= 0.58·Fy.w14·Dweb.w14·tweb.w14 = 249.09 kip (AASHTO 6.10.9.2-2)

web.w14

w14

web.w14

D Ratio1 : 24.58

t = =

Transverse stiffener spacing

 do.w14:= Lb.w14 = 126 in
Engineering for Structural Stability in Bridge Construction Reference Manual

B.157

Design Strongback Between Drop-In Girder Segment and Pier Segment, continued:

Shear buckling coefficient

w14 2

o.w14

web.w14

5 k : 5 5.07

d

D

 

 

  = + =              

(AASHTO 6.10.9.3.2-7)

( ) s w14

w14

y.w14

E k

Ratio2 : 1.12 60.71

F

⋅ = =

Ratio of shear buckling resistance to yield strength

 Cw14 := 1.0 (AASHTO 6.10.9.3.2-4)

Nominal shear resistance

 Vn.w14 := Cw14·Vp.w14 = 248.09 kip

Since Vn is greater than Vu, section is satisfactory in shear.

 Vn.w14= 248.09 kip > Vu_w14 = 67.74 kip

See below for a schematic of the complete strongback / hanger bar / hanger beam system.

Figure B3-6: Typical Strongback System
Engineering for Structural Stability in Bridge Construction Reference Manual

B.158

Figure B3-7: Minor Axis Moment of Inertia Calculation for BT-78
Engineering for Structural Stability in Bridge Construction Reference Manual

B.159

Figure B3-8: Minor Axis Moment of Inertia Calculation for BT-78, continued
Engineering for Structural Stability in Bridge Construction Reference Manual

B.160

Figure B3-9: Minor Axis Moment of Inertia Calculation for BT-90
Engineering for Structural Stability in Bridge Construction Reference Manual

B.161

Figure B3-10: Minor Axis Moment of Inertia Calculation for BT-90, continued
Engineering for Structural Stability in Bridge Construction Reference Manual

B.162

Figure B3-11: Minor Axis Moment of Inertia Calculation for BT-180
Engineering for Structural Stability in Bridge Construction Reference Manual

B.163

Figure B3-12: Minor Axis Moment of Inertia Calculation for BT-180, continued
Engineering for Structural Stability in Bridge Construction Reference Manual

B.164

Figure B3-13: Prestress Layout for End Girder Segments

Figure B3-14: Prestress Layout for Girder Segments at Splices in Spans 1 & 3
Engineering for Structural Stability in Bridge Construction Reference Manual

B.165

Figure B3-15: Prestress Layout for Pier Girder Segments
Engineering for Structural Stability in Bridge Construction Reference Manual

B.166

Figure B3-16: Prestress Layout for Drop-In Girder Segments
Engineering for Structural Stability in Bridge Construction Reference Manual

B.167

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.168
Engineering for Structural Stability in Bridge Construction Reference Manual

B.169

Reader 

Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.170
Engineering for Structural Stability in Bridge Construction Reference Manual

Example Problem #4: 3-Span Box Girder Curved Steel Structure

The following table of contents illustrates the general categories into which this

example problem is subdivided, and the relevant page number at which the start of

each category, and its specific component analysis or calculation tasks, may be

found.

B.171

General Category / Specific Analysis / Calculation Task Appendix

Description Page

Table of Contents N/A B.161

Bridge Data N/A B.162

Structural Analysis Deck Pour Analysis & Evaluation of Stages B.162

Figure Example 4 Cross-section B.163

Figure Example 4 Framing Plan B.164

Figure Example 4 Composite Box Cross-section for Girder 2 B.165

Girder G2 (Concrete Deck Pour) Analysis and Methodology B.166

Figure Problem Setup B.166

Figure Problem Input B.166

Figure Pour Sequence Loads (Analysis Case 1) B.167

Figure Pour Sequence Loads (Analysis Cases 2 and 3) B.167

Figure Maximum Positive Moment Magnitude and Location B.168

Figure Maximum External Brace Axial Stress B.168

Figure Normal

Location

Stresses Before Max. Positive Moment B.169

Figure Normal

Location

Stresses Beyond Max. Positive Moment B.169

Girder G2 (Concrete Deck Pour) Section Properties & Applied Forces B.171

Girder G2 (Concrete Deck Pour) Overhang Bracket Forces & Applied Stresses B.172

Girder G2 (Concrete Deck Pour) Local Buckling Resistance B.173

Girder G2 (Concrete Deck Pour) Lateral Torsional Buckling & Controlling Resistance B.174

Girder G2 (Concrete Deck Pour) Lateral Bending Stress & Overall Flexural Check B.175

Girder G2 (Concrete Deck Pour) Constructability Check B.176

Internal K-Frame Brace Axial Tension & Axial Compression Resistance B.177

Top Flange Lateral Brace Axial Tension & Axial Compression Resistance B.179

Figure Loading Calc. for Steel Dead Load in Field Section 1 B.183

Figure Loading Calc. for Steel Dead Load in Field Section 2a B.184

Figure Loading Calc. for Steel Dead Load in Field Section 2b B.185

Figure Loading Calc. for Steel Dead Load in Field Section 2 B.186

Figure Loading Calc. for Steel Dead Load in Field Section 3 B.187

Figure Loading Calc. for Conc. and Temp. Forms Dead Load B.188

Figure Loading Calculation for Construction Live Load B.189

Analysis with All Bracing Present Eigenvalue Buckling Analysis in UTrAp B.190

Analysis with Missing Bracing Eigenvalue Buckling Analysis in UTrAp B.191
Engineering for Structural Stability in Bridge Construction Reference Manual

B.172

Bridge Data:

Continuous 3 span curved steel box girder bridge, 2 girders total. Radius of curvature is 700 ft at

centerline of roadway. Out-to-out deck width is 40.5 ft. Girders are spaced at 22.5 ft on centers.

Structural deck slab thickness is 9.5 in. with no integral wearing surface.

The spans are symmetric, with Spans 1 and 3 at 160 ft long and Span 2 at 210 ft long measured

along the centerline of structure.

The field splices are also symmetric, with Field Section 1 at 96 ft long in Spans 1 and 3 (at

Abutments 1 and 2), Field Section 2 at 109 ft long (centered on Piers 1 and 2), and Field Section 3 

at 120 ft long in the middle of Span 2. Since these measurements are taken at the centerline of

structure, where there is no physical girder, the actual field section lengths vary depending on

which girder is considered.

The general plan, cross-section, and various details are presented in the following figures.

Deck Pour Analysis:

For this example, it is assumed the deck pour will run in four casts. The first cast is in Span 1 

starting at Abutment 1 and ending at the field splice. The second cast is in Span 2 between field

splices. The third cast is in Span 3 from the field splice to Abutment 2. The fourth cast is over

Piers 1 and 2. The worst case stage for the Span 1 girder segment is when the deck has

been poured over Span 1 up to the splice (first cast). This stage will be examined for girder

adequacy. The concrete weight is taken as 150 pcf and treated as permanent dead load, while

construction dead load, the weight of the forms, is taken at 10 psf. Construction live load is taken

as 20 psf in Spans 2 and 3. The pour sequence is modeled in the 3D finite element program

UTrAp. Wind load is assumed to be negligible during the pour and is ignored; thus the Strength III

load combination is not considered. The factored results used in the calculations are from the

Strength I: 1.25 DC + 1.50 CDL + 1.50 CLL load combination. The Strength VI: 1.40 DC + 1.40

CDL + 1.40 CLL load combination should also be analyzed; however, it can be seen from the

Strength I results that the design will still be adequate for Strength VI, since at most there will be a 

12% increase in applied stresses (1.40 / 1.25) and all the allowable stresses are significantly

greater than the applied stresses.

Evaluation of Stages:

The girders will be checked for adequacy according to AASHTO 2012 LRFD Specifications. The

G2 girder (Field Section 1) will be checked for the deck pour loading. Note that many other checks

(e.g., erection staging) are not performed here as they are conceptually similar to the calculations

shown in Example 1 for straight plate girders. Only the first cast of the deck pour is analyzed here;

if the entire cast sequence were analyzed, all of the girder field sections would have to be checked

for both positive and negative moment. For example, in the negative moment regions, the welded

bottom flange longitudinal T-stiffener, which is located over the piers and terminated at the splices,

would need a design check, along with the box girder itself.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.173

Figure B4-1: Example 4 Cross-section
Engineering for Structural Stability in Bridge Construction Reference Manual

B.174

Figure B4-2: Example 4 Framing Plan
Engineering for Structural Stability in Bridge Construction Reference Manual

B.175

Figure B4-3: Example 4 Composite Box Cross-section, Girder 2
Engineering for Structural Stability in Bridge Construction Reference Manual

B.176

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour

Analysis and Methodology:

Refer to Figure B4-4, which shows the UTrAp setup for this problem, with the girder plate sizes 

along the three spans in elevation view, a plan view of the three spans with the cross-frames 

and top lateral bracing, and the concrete deck pour strips in plan view.

Figure B4-4: Problem Setup

Refer to Figure B4-5 for some of the input for the analysis program UTrAp.

Figure B4-5: Problem Input
Engineering for Structural Stability in Bridge Construction Reference Manual

B.177

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck

Pour, continued 

The first cast of the deck pour is modeled in UTrAp via three incremental analysis

cases. The permanent dead load (steel bridge elements in all spans) corresponds to 

Analysis Case 1. The permanent dead load (wet concrete in Span 1) and construction 

dead load (formwork in all spans) correspond to Analysis Case 2.

The construction live load in Spans 2 and 3 corresponds to Analysis Case 3. Refer

to Figures B4-6 and B4-7 below for the loading data for these three analysis cases. 

The computation of the factored line loads (DC, CDL, and CLL) input into UTrAp for

each analysis case may be found at the end of this example problem.

Figure B4-6: Pour Sequence Loads (Analysis Case 1)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.178

Figure B4-7: Pour Sequence Loads (Analysis Cases 2 and 3)

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour,

continued

Figure B4-8 shows the magnitude and location of the maximum total positive

moment during the first concrete cast, which occurs for the cumulative Analysis

Case 2 (i.e., Analysis Case 1 + Analysis Case 2) at 60 feet into Span 1.

Figure B4-8: Maximum Positive Moment Magnitude and Location for Cumulative

Analysis Case 2 
Engineering for Structural Stability in Bridge Construction Reference Manual

B.179

Refer to Figure B4-9 below, which shows that the maximum axial stress in the

exterior cross-frames is a fraction of 1 ksi. Although a design check of the interior

cross-frames and the top flange lateral bracing is included in this example problem,

a check of the exterior cross-frames would be superfluous. 

.

Figure B4-9: Max. External Brace Axial Stress for Cumulative Analysis Case 2
Engineering for Structural Stability in Bridge Construction Reference Manual

B.180

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour,

continued

Refer to Figures B4-10 and B4-11, which visually represent the normal stresses

adjacent to the location in Span 1 where the maximum positive moment occurs. 

Note that for this case no construction live load is present.

Figure B4-10: Normal Stresses Before Location of Maximum Positive Moment for

Cumulative Analysis Case 2 

Figure B4-11: Normal Stresses Beyond Location of Maximum Positive Moment

for Cumulative Analysis Case 2
Engineering for Structural Stability in Bridge Construction Reference Manual

B.181

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour, continued

The AASHTO equations require the stresses in the flanges to be broken up into components (due

only to lateral bending, as well as without lateral bending), but most analysis programs do not

provide output in this fashion. Therefore, it is necessary to either make some assumptions or

otherwise manipulate the data. One approach would be to look at the normal stresses adjacent to

the location where the maximum positive moment in Span 1 occurs and average the sum of the

flange tip stresses (from Figures B4-10 and B4-11 above) to compute the bending stress

component. This approach was adopted in Example #2 for the curved girder bridge analyzed in UT

Bridge. Another approach, which is adopted in this example, would be to take the bending moment

for the bridge, divide by two to get an average bending moment for the tub girders and thus (with the

major axis section modulus) an average bending stress in the flanges. Based on comparing the

stresses in the two girders (see Figure B4-10 for stresses at 59 feet in Span 1 or Figure B4-11 for

stresses at 61 feet in Span 1), this appears to be fairly reasonable as the stress at any given location

in one girder is only about 1 ksi different at the corresponding location in the other girder.

The warping stresses due to lateral bending could be computed by taking the average of the

difference of the flange tip stresses; refer to Figure B4-12 for a diagram illustrating the decomposition

of stresses into normal and warping. Another approach for the warping stresses, adopted in this

example below, is to use approximations to account for lateral bending due to the curvature and the

deck overhang brackets (this approach was also adopted for Example #2).

Figure B4-12: Normal And Warping Stresses In Curved I-Girders
Engineering for Structural Stability in Bridge Construction Reference Manual

B.182

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour, continued

Section Properties:

Es := 29000 ksi Fy := 50 ksi

Flanges:

ttf := 1 in btf := 16 in bf

5 t : in

8 = bbf := 81 in a := 10 ft center-to-center of top flanges

Webs: Overall depth:

w

9 t : in

16 = D := 78 in 0.5 a b ( ) bf : atan 14.04 deg inclined D

  − θ =   =

 

d := D + ttf + tbf = 79.6 in

Calculated properties: Note that web inclination is not used in all inertia calculations (error is 

minor)

Abf := tbf·bbf = 50.63 in2

 ybf := 0.5·tbf = 0.31 in Note: Ignore 1” lip on ea. side of bot. flange

( ) 2

w w

D A : t 45.23 in

cos = = θ

 yw := tbf + 0.5·D = 39.63 in

Atf := ttf·btf = 16 in2

 ytf := tbf + D + 0.5·ttf = 79.13 in

Ag := Abf + 2Aw + 2Atf = 173.08 in2 Area of girder

bf bf w w tf tf

b

bf w tf

A y 2A y 2A y Y : 35.43 in

A 2A 2A

⋅+ ⋅+ ⋅ = = + +

Centroid measured from bottom

Yt := d - Yb = 44.2 in Centroid measured from top

Major axis moment of inertia:

( ) ( ) ( ) 3 3 3 2 22 bf bf w tf tf 4

x bf b bf w b w tf b tf

b t 2t D 2b t I : A Y y 2A Y y 2A Y y 169614.1 in 12 12 12⋅ ⋅ ⋅ = + + +⋅− + ⋅− + ⋅− =

x 3

bx

b

I S : 4787.4 in

Y = = Major axis elastic section modulus to bottom

x 3

tx

t

I S : 3837.8 in

Y = = Major axis elastic section modulus to top

( ) 2 3 3 3 2

bf bf w tf tf bf 4

y w tf

t b 2D t 2t b 0.5 a b a I : 2A 2A 371957.7 in

12 12 12 2 2

⋅ ⋅ ⋅   +   =++ +   + =      

Minor axis moment of inertia

( )

y 3

y

bf tf

I

S : 5470 in

0.5 max b ,a b = = ⋅ +

Minimum minor axis elastic section modulus

Applied Factored Forces:

Major-axis Bending: ux

15471.4 kip ft M : 7735.7 kip ft 2 = = per tub girder

Unbraced Length: b

162.57 ft L : 16.257 ft

10 = = with cross-frame spacing of approximately 16 ft

Lateral Flange Bending:

Radius of curvature 22.5 ft a R : 700 ft + 706.25 ft

2 2 = − = at Girder G2 top flange Constant N := 10

Moment in each top flange due to lateral bending from curvature ( ) 2

ux b

lat

0.5M L M :

NRD

⋅ = ⋅ ⋅

(Eq. C4.6.1.2.4b-1)

Note: moment in bot. flange will be approx. twice this value (R is more)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.183

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour, continued

Mlat = 22.3 kip ft Note that this value is already factored since the major-axis moment was factored

Minor-axis Bending: Muy := 0 kip ft Assume wind load on girders is negligible during deck pour

Overhang Bracket Forces at Fascia Side of Girder:

Assume bracket loads are applied uniformly along girder although actual bracket spacing = 3 ft

40.5 ft - 22.5 ft - a overhang : 4 ft

2 = = at top flange fascia ( ) a bbf x : 19.5 in

2

− = = more at bot. flange

Assume 10” thick deck at fascia overhang; 1⁄2 of weight goes to bracket and 1⁄2 directly to girder

wfascia := 0.5 overhang 10 in·150 pcf wfascia = 250 plf Concrete weight to bracket

Assume 200 plf for screed rail at fascia overhang wrail := 200 plf Rail weight to bracket

Assume 10 psf for forms and another 5 psf for bracket components and miscellaneous at fascia 

overhang; 1⁄2 of weight goes to bracket and 1⁄2 directly to girder

wforms := 0.5·overhang·(10 psf + 5 psf) wforms= 30 plf Form weight to bracket

wbracket := wfascia + wrail + wforms wbracket = 480 plf Total uniform load to bracket

D : atan 

overhang + x

  a =    

α = 49.13 deg Angle of bracket relative to horizontal

( )

bracket

L

W F : 415.4 plf tan = = a

Lateral force on each flange from bracket

Lat. Moment in Ea. Flange from Overhang Bracket at Fascia Side of Girder: 2

L b

L

F L M :

12

⋅ = (Eq. C6.10.3.4-2)

Factored Lat. Moment in Ea. Girder Flange from Overhang Bracket at Fascia: MLu := 1.50ML = 13.7 kip ft 

(conservatively assume highest load factor corresponding to all construction dead load)

Flexural Resistance

Top flange is in compression bfc := btf tfc := ttf

Bottom flange is in tension bft := bbf tft := tbf

Applied Stresses:

Top flange is in compression: 2

fc fc

yc

t b S :

6

⋅ = Syc = 42.7 in3

Bottom flange is in tension: 2

ft ft

yt

t b S :

6

⋅ = Syt = 683.4 in3

Stress in compression flange without

consideration of lateral bending: ux

buc

tx

M f :

S = fbuc = 24.2 ksi

First-order stress due to lateral bending

in compression flange:

uy

lat Lu

L1c

yc

M

0.5 M M

2 f :

S

    + +

  = fL1c = 10.1 ksi

Stress in tension flange without

consideration of lateral bending: ux

but

bx

M f :

S = fbut= 19.4 ksi

First-order stress due to lateral bending

in tension flange: uy lat Lu

Lt

yt

0.5M 2M M

f :

S

+ + = fLt = 1 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.184

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Flange Strength Reduction Factors:

Hybrid Factor (AASHTO 6.10.1.10.1)

Since the flexural member is a homogenous built-up section, the hybrid factor shall be taken as 

unity

 Rh = 1

Web Load Shedding Factor (AASHTO 6.10.1.10.2)

Depth of web in compression ( )

[ ]

t tf

c

Y t

D : 44.53 in

cos

− = = θ

measured along incline

s

rw

y

E : 5.7

F

 

λ= ⋅  

 

λrw= 137.3 c

w

2 D 158.3

t

⋅ =

c w

wc

fc fc

2D t

a :

b t

⋅ = ⋅

c

rw

w

b

wc c

rw

wc w

2 D 1.0 if 

t

R :

a 2D 1.0 otherwise

1200 300 a t

⋅ ≤ λ

=       ⋅   −  ⋅ −λ   + ⋅      

Rb = 0.97

Web is slender, so Eq. 6.10.3.2.1-3 (web bend-buckling) must be checked per AASHTO 

6.10.3.2.1. For constructability checks, per AASHTO 6.10.3.2.1, use Rb:= 1

Local Buckling Resistance (AASHTO 6.10.8.2.2):

Slenderness ratio of the compression flange

fc

f

fc

b

:

2 t

λ = ⋅

λf = 8 (Eq. 6.10.8.2.2-3)

s

pf

y

E : 0.38

F

λ= ⋅ λpf = 9.2 (Eq. 6.10.8.2.2-4)

s

rf

y

E : 0.56

0.7F

λ= ⋅ λrf = 16.1 (Eq. 6.10.8.2.2-5)

Local Buckling Resistance

( ) b h y f pf

nc1 y f pf

b hy

h y rf pf

nc1

R R F if 

F : 0.7F

1 1 R R F otherwise

R F

F 50 ksi

⋅ ⋅ λ ≤λ

=       λ −λ     −− ⋅ ⋅ ⋅ ⋅     ⋅ λ −λ      

=

(Eq. 6.10.8.2.2-1)

(Eq. 6.10.8.2.2-2)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.185

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Lateral Torsional Buckling Resistance (AASHTO 6.10.8.2.3):

Unbraced length Lb = 16.257 ft with cross-framing spacing of approximately 16 ft

Effective Radius

of Gyration fc

t

c w

fc fc

b

r :

1 D t 12 1

3b t

=

  ⋅ ⋅ +⋅   ⋅  

 rt = 3.7 in. (Eq. 6.10.8.2.3-9)

Limiting Unbraced Length Calculations:

s

p t

y

E L:r

F = ⋅ Lp = 7.5 ft. (Eq. 6.10.8.2.3-4)

s

r t

y

E L: r

0.7F =π ⋅ Lr = 28.2 ft. (Eq. 6.10.8.2.3-5)

Per D-4, Moment gradient modifier Cb := 1 since, mid

2

f 1

f

>

Lateral Torsional Buckling Resistance

( ) ⋅⋅ ≤

        − = ⋅−− ⋅ ⋅ ⋅ ⋅ ≤             ⋅ −        

⋅⋅⋅

     

=

b hy b p

y b p

nc2 b b h y p b r

hy r p

2

bb s

2

b

t

nc2

R R F if L L

0.7F L L

F : C 1 1 R R F if L <L L

RF L L

CR E otherwise

L

r

F 43.7 ksi

p

(Eq. 6.10.8.2.3-1)

(Eq. 6.10.8.2.3-2)

(Eq. 6.10.8.2.3-3)

Controlling Nominal Flexure Resistance:

Fnc := min(Fnc1,Fnc2) Fnc = 43.7 ksi

Resistance factor Φf := 1.0 (AASHTO 6.5.4.2)

Φf·Fnc = 43.7 ksi

Mrx := Φf·Fnc·Stx Mrx = 13964.8 kip ft

ux

rx

M 0.55

M = Adequate resistance for lateral-torsional buckling
Engineering for Structural Stability in Bridge Construction Reference Manual

B.186

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck 

Pour, continued

Determine Stress due to Lateral Bending:

First-order lateral bending stress (from previous): fL1c = 10.1 ksi 

Limiting unbraced length for first-order lateral bending stress

b b

p

buc

y

C R 1.2 L 13 ft f

F

⋅ ⋅⋅ = (Eq. 6.10.1.6-2)

Lateral bending stress:

elastic lateral torsional buckling stress

2

bb s

cr 2

b

t

CR E F :

L

r

⋅ ⋅π ⋅ =

     

 Fcr = 105.4 ksi (Eq. 6.10.8.2.3-8)

Check if the first-order stress needs to be amplified: Approximated second-order

lateral bending stress= 

fLc = 11.2 ksi 

b b

Lc Lc1 b p

buc

y

L1c

buc

cr

C R f : f if L 1.2 L f

F

0.85 f otherwise f 1

F

⋅ = ≤ ⋅⋅

   

  ⋅   −    

 (Eq. 6.10.1.6-4)

Lateral bending check:

Lateral_Bending_Resistance := “Lateral Bending Requirements Satisfied” if fLc≤0.6Fy

“Girder is NOT Adequate in Lateral Flexure” otherwise

Lateral_Bending_Resistance = “Lateral Bending Requirements Satisfied”

Overall Flexural Resistance Check

The following must be satisfied:

+ ⋅ ≤φ ⋅ buc Lc φ nc

1 φφ F

3

(Eq. 6.10.3.2.1-2)

+⋅ = buc Lc

1 f f 27.9 ksi

3

 φf·Fnc =43.7 ksi

Resistance_Check := “Girder Meets AASHTO Flexural Requirements” if + ⋅ ≤φ ⋅ buc Lc φ nc

1 φφ F

3 

“Girder is NOT Adequate in Lateral Flexure” otherwise

Resistance_Check = “Girder Meets AASHTO Flexural Requirements”
Engineering for Structural Stability in Bridge Construction Reference Manual

B.187

Resistance of Girder G2, Field Section 1 for First Cast During Concrete Deck Pour, 

continued

Constructibility Check:

The following must be satisfied:

 fbuc + fLc ≤ Φf·Rh·Fy (Eq. 6.10.3.2.1-1)

 fbuc + fLc = 35.4 ksi < Φf·Rh·Fy = 50 ksi

Adequate resistance in compression flange

The following must be satisfied:

 fbut + fLt ≤ Φf·Rh·Fy (Eq. 6.10.3.2.2-1)

 fbut + fLt = 20.4 ksi < Φf·Rh·Fy = 50 ksi

Adequate resistance in tension flange

Web Bend-Buckling Resistance without Longitudinal Stiffeners (AASHTO 6.10.1.9.1):

Web Depth measured along incline

2

c

9 k : 29.35

D

D

= =

     

(Eq. 6.10.1.9.1-2)

s

crw 2

w

0.9 E k F : 37.5 ksi

D

t

⋅ ⋅ = =

     

(Eq. 6.10.1.9.1-1)

y

crw crw h y

F

F : min F ,R F , 37.5 ksi 0.7

  = ⋅=    

Constructability Check:

Fbuc ≤ Φf·Fcrw (Eq. 6.10.3.2.1-3)

Fbuc = 24.2 ksi < Φf·Fcrw = 37.5 ksi

Adequate resistance in web
Engineering for Structural Stability in Bridge Construction Reference Manual

B.188

Resistance of the Brace for Internal K-Frame

Axial Tension Resistance of the Brace L6x6x7/16 (AASHTO 6.8.2):

Put := 46.66 kip Maximum tension force in any internal brace member from analysis 

model.

Section Properties (Taken from AISC manual) Fy := 36 ksi Fu := 58 ksi Ag := 5.08 in2

From Figure B2-19, it appears that the brace is welded rather than bolted to the conn. Plate, so 

An := Ag

For shear lag reduction factor U, lacking weld details, assume U := 0.60 (0.5 is worst case per 

6.8.2.2)

Resistance factors Φy := 0.95 Φu := 0.80 (AASHTO 6.5.4.2)

Tension resistance for yielding Pry := Φy·Fy·Ag = 173.7 kip (Eq. 6.8.2.1-1)

Tension resistance for fracture Pru := Φu·Fu·An·U = 141.4 kip (Eq. 6.8.2.1-2)

Axial Resistance Check Put = 46.7 kip < Prt := min(Pry, Pru) = 141.4 kip Tension 

resistance is 

adequate

Axial Compression Resistance of the Brace L6x6x7/16 (AASHTO 6.9.4):

Puc:= 46.66 kip Maximum compression force in any internal brace member from analysis model.

Section Properties (Taken from AISC manual) Es:= 29000 ksi Fy := 36 ksi Ag := 5.08 in2

Check Slenderness of the Member (Sect. 6.9.4.2)

Following requirements needs to be satisfied for the element to qualify as nonslender:

y

b E k

t F

≤ (Eq. 6.9.4.2.1-1) k := 0.45 from Table 6.9.4.2.1-1 

angle leg:

b := 6 in 7 t : in

16 = b 13.7t

= s

y

E k 12.8

F =

leg check:

Find Q if element is slender: 

y s

s y

s s

2

y

b b F E 1.34 0.76 if 0.91

tEt F

Q : 0.53 E otherwise

b F

t

  − ⋅ ≤⋅    

= ⋅

 

⋅   

(Eq. 6.9.4.2.2-5)

(Eq. 6.9.4.2.2-6)

 Qs= 0.97

s

s y

s

b E 1.0 if 0.45

Q : t F

Q otherwise

 Q 0.97

≤ ⋅ =

=
Engineering for Structural Stability in Bridge Construction Reference Manual

B.189

Resistance of the Brace for Internal K-Frame, continued

Determine Effective Slenderness Ratio (KL/r)eff = λeff (Sect. 6.9.4.4)

Recall a = 120 in and bbf= 81 in and D = 78 in 2

bbf 2 L : max a, D 2

    =   +        

Strut rather than diagonal governs the brace length, so L = 120 in

Rx := 1.86 in so

x

L 64.5

r =

x x

eff

x

eff

L L 72 0.75 if 80 r r : L 32 1.25 otherwise r

120.4

    + ≤

  λ =     +

 

λ =

(Eq. 6.9.4.4-1)

(Eq. 6.9.4.4-2)

Limiting KL/r for secondary compression members λlimit:= 120 (Sect. 6.9.3)

Maximum actual slenderness corresponds to minor principal axis buckling rz := 1.18 in 

K := 1 for single angles (Sect 4.6.2.5)

limit

z

K L 101.7 120

r

⋅ = < l = Therefore, actual maximum slenderness ratio is adequate

Flexural Buckling Resistance

( )

2

s

e g 2

eff

E P: A π ⋅ = ⋅ λ

 Pe = 100.3 kip (Eq. 6.9.4.1.2-1)

Since the various conditions for single-angle members are satisfied as enumerated in AASHTO LRFD 

Sect. 6.9.4.4, the effective slenderness ratio can be calculated per that section; therefore, only flexural 

bucking resistance will be used to determine nominal compressive resistance of the brace. The effect of 

the eccentricities can be neglected when evaluated in this manner. 

Equivalent Nominal Yield Resistance

Po := Q·Fy·Ag Po = 177.9 kip (Sect. 6.9.4.1.1)

e

o

P 0.56

P =

Nominal Compressive Resistance

( )

     

 

  ⋅ ≥ =    

=

o

e

P

P e

o

n o

e

n

P 0.658 P if 0.44

P : P

0.877P otherwise

P 84.7 kip

(Eq. 6.9.4.1.1-1)

(Eq. 6.9.4.1.1-2)

Resistance factor Φc := 0.9 (AASHTO 6.5.4.2)

Factored Axial Resistance

Prc := Φc·Pn Prc = 76.2 kip (Eq. 6.9.2.1-1)

Axial Resistance Check

Puc = 46.7 kip < Prc = 76.2 kip Compression resistance is adequate
Engineering for Structural Stability in Bridge Construction Reference Manual

B.190

Resistance of the Brace for Top Flange Laterals

Axial Tension Resistance of the Brace WT9x48.5 (AASHTO 6.8.2):

Put := 80.30 kip Maximum tension force in any top flange lateral brace member from analysis model.

Section Properties (Taken from AISC manual) Fy := 50 ksi Fu := 65 ksi Ag := 14.3 in2

 bf := 11.1 in

Assume that the brace is bolted rather than welded to the girder top flange, so assume An := 0.85 Ag

For shear lag reduction factor U, assume WT flange has 3+ fasteners, so U := 0.9 (Table 6.8.2.2-1)

Resistance factors Φy := 0.95 Φu := 0.80 (AASHTO 6.5.4.2)

Tension resistance for yielding Pry := Φy·Fy·Ag = 679.3 kip (Eq. 6.8.2.1-1)

Tension resistance for fracture Pru := Φu·Fu·An·U = 568.9 kip (Eq. 6.8.2.1-2)

Axial Resistance Check Put = 80.3 kip < Prt := min (Pry, Pru) = 568.9 kip Tension resistance is adequate

Axial Compression Resistance of the Brace WT9x48.5 (AASHTO 6.9.4):

Puc := 103.12 kip Max. compression force in any top flange lateral brace member from analysis 

model.

Section Properties (Taken from AISC manual)

Es := 29000 ksi Fy := 50 ksi Ag := 14.3 in2 d:= 9.3 in

Check Slenderness of the Member (Sect 6.9.4.2)

Following requirement needs to be satisfied for the element to qualify as nonslender:

y

b E k

t F

≤ (Eq. 6.9.4.2.1-1) flange: kflange := 0.56 from Table 6.9.4.2.1-1 

stem: kstem := 0.75 from Table 6.9.4.2.1-1 

flange: f

flange

b b : 5.6 in

2 = = tflange := 0.870 flange

flange

b

6.4

t = s

flange

y

E k 13.5

F ⋅ =

stem: bstem := d = 9.3 in tstem := 0.535 in stem

stem

b 17.4

t = s

stem

y

E k 18.1

F ⋅ =

flange check:

Find Q if element is slender:

flange y flange s

flange s flange y

s _ flange s

2

flange

y

flange

b Fb E 1.415 0.74 if 1.03

t E t F

Q : 0.69 E otherwise

b

F

t

      − ⋅ ≤⋅        

= ⋅

 

⋅     

(Eq. 6.9.4.2.2-1)

Qs_flange = 1.22 (Eq. 6.9.4.2.2-2)

flange s

flange flange y

s _ flange

b E 1.0 if 0.56

Q : t F

Q otherwise

≤ ⋅ =

Qflange = 1
Engineering for Structural Stability in Bridge Construction Reference Manual

B.191

Resistance of the Brace for Top Flange Laterals, continued

stem y stem s

stem s stem y

s _ stem s

2

stem

y

stem

b bE F

1.908 1.22 if 1.03

t Et F

Q : 0.69 E otherwise

b F

t

      − ⋅ ≤⋅      

= ⋅

 

⋅   

(Eq. 6.9.4.2.2-3)

(Eq. 6.9.4.2.2-4)

Qs_stem = 1.03

stem s

stem stem y

stem

b E 1.0 if 0.75

Q : t F

Q otherwise

≤ ⋅ =

Qstem = 1

Q := min (Qflange, Qstem) = 1 (Sect. 6.9.4.2.2)

Determine Slenderness Ratio (KL/r) = λ

Recall Lb = 195.1 in and a = 120 in Therefore 2 2 L : a L 229 in = += b

rx := 2.56 in and ry := 2.65 in

K := 0.75 for bolted or welded ends (Sect. 4.6.2.5)

( ) x y

K L

: 67.1

min r ,r

⋅ λ= =

Limiting KL/r for primary compression members λlimit := 120 (Sect. 6.9.3)

λ = 67.1 < λlimit = 120 Therefore, maximum slenderness ratio is adequate

 

( )

2

s

e _ FB 2 g

E P: A π ⋅ = ⋅ λ

 Pe_FB = 909 kip (Eq.6.9.4.1.2-1)

Flexural Torsional Buckling Resistance

KZ := 1 for torsional buckling (Commentary Sect. C6.9.4.1.3)

LZ := L = 229 in for torsional buckling (Commentary Sect. C6.9.4.1.3) 

Ky := 0.75 for bolted or welded ends (Sect. 4.6.2.5)

Ly := L = 229 in

Shear modulus of elasticity G := 0.385·Es = 11165 ksi
Engineering for Structural Stability in Bridge Construction Reference Manual

B.192

Resistance of the Brace for Top Flange Laterals, continued

Additional Cross-Sectional Properties (Taken from AISC manual) 

Major axis moment of inertia Ix := 93.8 in4

Minor axis moment of inertia Iy:= 100 in4

Warping torsional constant Cw := 9.29 in6

St. Venant torsional constant J := 2.92 in4

Distance along y-axis between shear center and centroid

flange

o

t

y : 1.91 in - 1.475 in 2 = =

Polar radius of gyration about shear center 

2 x y

o o

g

I I

r : y 3.97 in

A

+

=+ = (Eq. 6.9.4.1.3-6)

2

o

2

o

y H: 1 0.86

r =− = (Eq. 6.9.4.1.3-3)

2

s

ey 2 g

y y

y

E P : A 974.1 kip

K L

r

p ⋅ = ⋅=

  ⋅  

 

(Eq. 6.9.4.1.3-4)

( )

2

s w

ez 2 2

o z z

E C 1 P : G J 2076.1 kip

K L r

  p ⋅ ⋅ =  + ⋅ ⋅ =

  ⋅  

(Eq. 6.9.4.1.3-5)

( )

ey ez ey ez

e _ FTB 2

ey ez

P P 4P P H

P : 1 1 883.5 kip 2H P P

    + ⋅⋅⋅   = ⋅− −   =

  +  

(Eq. 6.9.4.1.3-2)

Governing Elastic Critical Buckling Resistance

Pe:= min(Pe_FB,Pe_FTB) = 883.5 kip

Equivalent Nominal Yield Resistance

Po:= Q·Fy·Ag Po = 715 kip (Sect. 6.9.4.1.1)

e

o

P 1.24

P =

Nominal Compressive Resistance

( )

     

 

  ⋅ ≥ =    

=

o

e

P

P e

o

n o

e

n

P 0.658 P if 0.44

P : P

0.877P otherwise

P 509.6 kip

(Eq. 6.9.4.1.1-1)

(Eq. 6.9.4.1.1-2)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.193

Resistance of the Brace for Top Flange Laterals, continued

Resistance factor Φc := 0.9 (AASHTO 6.5.4.2)

Factored Axial Resistance

Prc := Φc·Pn Prc = 458.6 kip (Eq. 6.9.2.1-1)

Axial Resistance Check

Puc = 103.1 kip < Prc = 458.6 kip Compression resistance is adequate
Engineering for Structural Stability in Bridge Construction Reference Manual

B.194

Figure B4-13: Loading Computation For Steel Dead Load (Dc) In Field 

Section 1
Engineering for Structural Stability in Bridge Construction Reference Manual

B.195

Figure B4-14: Loading Computation for Steel Dead Load (DC) in Field Section 2a
Engineering for Structural Stability in Bridge Construction Reference Manual

B.196

Figure B4-15: Loading Computation for Steel Dead Load (DC) in Field Section 2b
Engineering for Structural Stability in Bridge Construction Reference Manual

B.197

Figure B4-16: Loading Computation for Average Steel Dead Load (DC) in Field

Section 2
Engineering for Structural Stability in Bridge Construction Reference Manual

B.198

Figure B4-17: Loading Computation for Steel Dead Load (DC) in Field Section 3 
Engineering for Structural Stability in Bridge Construction Reference Manual

B.199

Figure B4-18: Loading Computation for Concrete Dead Load (DC) and

Temporary Forms Dead Load (CDL)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.200

Figure B4-19: Loading Computation for Construction Live Load (CLL)
Engineering for Structural Stability in Bridge Construction Reference Manual

B.201

Eigenvalue Analysis for Cumulative Analysis Case 2

Figure B4-20: First Buckling Mode for Cumulative Analysis Case 2

As stated previously, the governing positive moment occurs at 60 feet into Span 1 and 

corresponds to cumulative Analysis Case 2, or the permanent dead load plus the construction 

dead load (Analysis Case 1 + Analysis Case 2). UTrAp can analyze up to 5 buckling modes. 

Figure B4-20 above shows the buckled shape for the first of the 5 modes, which occurs at an 

Eigenvalue of 2.456. As can be seen, it is a local web buckling phenomenon. Note that the 

cumulative Analysis Case 2 loads are factored, so the true buckling factor, relative to actual 

loads, is much higher: 2.456(1.25 DC + 1.50 CDL).

The other 4 modes are not shown in the interest of brevity. However, they are all very similar. 

Modes 2 through 4 are also local web buckling, occurring at the other three girder webs. The 

Eigenvalue on the fifth mode is 2.636; it occurs at the same web as the first buckling mode and 

is a local web buckling in the opposite direction (mirror image) to that shown. No global 

buckling modes (e.g., girder lateral torsional buckling) are captured in the UTrAp buckling 

analysis for this example, meaning that they are higher modes than the first five (factored 

Eigenvalue must be greater than 2.636). Since post-buckling strength of the webs is 

incorporated in most design specifications, the local web buckling found here is not particularly 

noteworthy. At any rate, the factored design loads are far below the loads associated with these 

(or any other) buckling modes.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.202

Eigenvalue Analysis for Cumulative Analysis Case 2 Without Bracing at Span

1 Splice

Sometime bracing is temporarily omitted to facilitate field splicing of the box girders. The

UTrAp model was modified to reflect this by deleting the top flange bracing on either side of

the first splice (starting and terminating at 96 ft in Span 1). The buckling analysis was rerun

for this bridge to simulate the worst-case condition in which the deck pour was begun without

this bracing in place (i.e., the contractor forgot to complete the brace installation after field

splicing the girders). See Figure B4-21 for the UTrAp plan view of the revised model,

illustrating the missing bracing in Span 1.

Figure B4-21: Problem Setup for Missing Brace Scenario

Again, at 60 feet into Span 1 the buckled shapes for cumulative Analysis Case 2, or the

permanent dead load plus the construction dead load (Analysis Case 1 + Analysis Case 2),

are examined. Figure B4-22 below shows the buckled shape for the first of the 5 modes

analyzed by UTrAp, which occurs at an Eigenvalue of 2.416. As can be seen, it is still a 

local web buckling phenomenon. So the missing braces have, not surprisingly, weakened

the bridge, but only minimally. The first buckling mode occurs at a slightly smaller

Eigenvalue than before (2.416 vs. 2.456). Note that the cumulative Analysis Case 2 loads

are factored, so the true buckling factor, relative to actual loads, is much higher: 2.416(1.25

DC + 1.50 CDL).
Engineering for Structural Stability in Bridge Construction Reference Manual

B.203

Eigenvalue Analysis for Cumulative Analysis Case 2 Without Bracing at Span 1 Splice, 

continued

Figure B4-22: First Buckling Mode for Cumulative Analysis Case 2 with Missing Brace

The other 4 modes are not shown in the interest of brevity. However, they are all very

similar to modes seen before. Modes 2 through 5 are local web buckling, occurring at

various girder webs. The Eigenvalue on the fifth mode is 2.587.

Additionally, instead of contractor error, the much more common situation of the top braces

temporarily being omitted to facilitate splicing can be examined. In this case, only Analysis

Case 1 (steel permanent dead load) would be applicable for the temporary condition, postsplicing, where the box girders are temporarily supporting their own self-weight with some of

the top bracing not yet installed. The Eigenvalue for Analysis Case 1, mode 1, is 12.21,

corresponding to local web buckling at 60 feet into Span 1 (not shown here). With all

bracing in place, the Eigenvalue for Analysis Case 1, mode 1, is 12.47 (not shown here). 

Thus, the impact of the omitted bracing is minimal. Furthermore, the Eigenvalue is more than

twelve times the factored design loads, indicating a reasonable level of safety.
Engineering for Structural Stability in Bridge Construction Reference Manual

B.204

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.205

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.206

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.207

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.208

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.209

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.210

Reader Notes
Engineering for Structural Stability in Bridge Construction Reference Manual

B.211
Engineering for Structural Stability in Bridge Construction Reference Manual

B.212

Reader 

Notes
APPENDIX C

SURVEY ON ENGINEERING FOR STRUCTURAL SAFETY

In an effort to better understand the past experiences in bridge superstructure erection in 

individual states, and their requirement as they relate to superstructure erection, a survey was 

sent to all states that are AASHTO members The survey included 18 questions, starting with 

any past problems related to girder erection (either steel or concrete), but concentrating on 

erection standards, erection design criteria, and submittal and review practices utilized. A 

summary of the survey answers is provided in Part 2 of Chapter 1. The entire survey is provided 

in this appendix.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.1

STATES RESPONDING TO THE SURVEY

1. Arizona Department of Transportation

2. Arkansas Department of Transportation 

3. CA Department of Transportation 

4. CDOT, Colorado Department of Transportation, Staff Bridge Branch

5. Delaware DOT

6. Georgia Department of Transportation

7. Illinois Department of Transportation

8. Iowa Department of Transportation

9. Kansas department of Transportation

10.Maryland SHA, Office of Structures

11.MassDOT, Massachusetts Department of Transportation

12.Michigan Department of Transportation

13.Minnesota Department of Transportation 

14.Missouri Department of Transportation 

15.Nevada Department of Transportation

16.New Jersey Department of Transportation

17.New Mexico Department of Transportation 

18.North Carolina Department of Transportation 

19.North Dakota Department of Transportation 

20.NYSDOT, New York State Department of Transportation

21.Ohio Department of Transportation

22.Oklahoma Department of Transportation (ODOT)

23.Oregon Department of Transportation

24.Pennsylvania Department of Transportation

25.SDDOT, South Dakota Department of Transportation

26.State of Florida Department of Transportation 

27.Texas Department of Transportation 

28.Utah Department of Transportation 

29.Vermont Agency of Transportation 

30.Virginia Department of Transportation 

31.Washington State Department of Transportation

32.Wisconsin DOT 

33.WYDOT, Wyoming Department of Transportation.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.2

1. How often have you experienced any collapses or near-miss events due to 

lifting, handling, or other temporary conditions due to construction of bridge 

superstructure members? Description of the problem(s) and lesson(s) learner or 

a contact person

Responding 

Agency

Frequency Response

Arizona 

Department of 

Transportation

Rarely

Arkansas 

Department of 

Transportation 

CA Department of 

Transportation 

Occasionally Falsework reduces clearance over traffic therefore truck without

permit hit the falsework stringer or backhoe boom not ties 

properly hit the falsework stringer 

CDOT, Staff 

Bridge Branch

Rarely May of 2004 we had a girder collapse mostly due to not being 

able to erect a pair of girders as planned by the contractor, 

consequently only one girder was erected with inadequate 

bracings. Since then we have revised procedures for all Bridge 

Girder Erections specifications. 

Delaware DOT Rarely

Georgia 

Department of 

Transportation

Rarely Beams are occasionally dropped on construction

Illinois Department 

of Transportation

Often On average, about twice a year we have new girders drop 

during erection or existing girders fail or collapse under 

construction loads

Iowa Department 

of Transportation

Rarely Typically this was a result of a crane tipping and releasing the 

girder to save the crane. Crane tipping was the result of picks 

outside the recommended range, erection of girder during high 

wind, and coordination issues between two cranes walking a 

beam. One other situation involved a steel girder which was 

not adequately secured at a splice location (out of 

specifications) as a temporary situation.

Kansas 

Department of 

Transportation

Rarely Contact: Travis Malone at 785.296.2066 or 

Malone@KSdot.org

Maryland SHA, 

Office of 

Structures

Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.3

Responding 

Agency

Frequency Response

MassDOT Rarely Chelsea Street Bridge, the erection of the lift span truss. The 

truss span was being launched and the whole as had been 

assembled up to that time started to slide backwards and 

came off the temporary supports. The lesson learned was 

that restraints had not been installed to prevent the 

backwards slide.

Contact: Rich DeSantis, D4 Construction

Michigan 

Department of 

Transportation

Rarely In 2007, we had a pedestrian bridge approach slab pour fail the 

temporary shoring towers, resulting in collapse of the forms, 

and loss of the pour. This was a small pour of approximately 20 

feet long by 14 feet wide; however, the falsework was over 

loaded, and failed halfway through the pour. Lessons learned 

were to further enforce our specifications which require all 

falsework to be designed and stamped by a registered 

professional engineer. This is not a failure; however, in 2005 we 

had a fascia beam rotate out of plane due to the wet load of the 

concrete during a deck pour. This was a deck replacement 

project for a ramp bridge on a superelevation. The previous 

superelevated shape was a rotated parabola, and our new 

design called for a straight line superelelvation. The haunch 

depth this produced along with the additional overhang width to 

achieve standard shoulders added significant load to the fascia 

beam. Lessons learned were to consider bolstering beam in the 

future to avoid excessive haunch depths, or to transition the 

deck thickness back to our minimum of 9” on the outside of the 

fascia beam, as opposed to running the depth of the haunch 

out to the deck fascia.

Minnesota 

Department of 

Transportation 

Rarely This is very rare with 5-10 years between occurrences. 

Contact information for any of these questions is listed 

above.

Missouri 

Department of 

Transportation 

Rarely

Nevada Dept of 

Transportation

Never

New Jersey 

Department of 

Transportation

Rarely Prestressed Concrete Haunched Girder dropped during 

erection. Crane angle was not appropriate. Welded Steel girder 

Plate and Girders lifted in pairs dropped during erection. Only 

one crane and pick points not far enough apart and too much 

wind.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.4

Responding 

Agency

Frequency Response

New Mexico 

Department of 

Transportation 

Rarely NMDOT had an exterior rolled steel girder fall over due to light 

wind during erection. The girder fell into the channel below. The 

Contractor failed to anchor the girder immediately after 

placement onto the substructure. Lesson learned: anchor 

girders (no matter what type) immediately after placing on 

substructure. NMDOT had a prestressed girder fall off the truck 

during transportation. The transporting truck drove up to the 

bridge site on an approximate slope of 10%. The truck and 

girder tipped over with the prestressed girder imploding. Lesson 

learned: be careful on steep slopes.

North Carolina 

Department of 

Transportation 

Rarely Lenoir County, Kinston: Left Lane Bridge on Crescent Road 

over NC Railroad A temporary shoring tower collapsed during 

erection of continuous plate girders, resulting in significant 

damage to all six lines of girders in the end span – August 

2011. (See attached photos) The shoring towers legs were 

observed to be bowing or not vertical shortly before the 

collapse, and the contractor was making adjustments. The 

cause of the failure is undetermined. Brunswick County, Bridge 

on SR 1105 (North Middleton Avenue) over Intracoastal 

Waterway at Oak Island A strongback rod failed during 

erection of post-tensioned girders, resulting in a girder dropping 

to the ground – December 2008. The Department believes that 

welding of locknuts on high strength bars and reverse 

orientation of temporary cross-frames during their installation 

contributed to the collapse. Guilford County, Bridges on Left & 

Right Lanes Greensboro Western Urban Loop over West 

Friendly Avenue. When a shoring tower was removed, the two 

310-ft. plate girders on that tower tilted over. The girder load 

was put back on the tower until the Department and Contractor 

could decide what to do. The Contractor’s revised plan added 

four shoring towers. The size of the girder’s top flange and the 

lack of top lateral bracing may have contributed to this 

behavior.

North Dakota 

Department of 

Transportation 

Never

NYSDOT Rarely Ensure adequacy of foundations of temporary bents. Follow 

erection plans

Ohio Department 

of Transportation

Never ODOT is not aware of an incident involving near misses or 

collapses in any of its projects over the last decade. There was 

an accident involving a local agency project (Cuyahoga County) 

replacing a CSX railroad bridge (Eastland Road Overpass) on 

September 18, 2010 where the structural steel collapsed during 

erection of the floor bean units. One worker sustained non-life 

threatening injuries and no other injuries were reported. 
Engineering for Structural Stability in Bridge Construction Reference Manual

C.5

Responding 

Agency

Frequency Response

Oklahoma 

Department of 

Transportation 

(ODOT)

Rarely Aware of one case where the Contractor bolted two spans 

together and tried to lift the girder, the girder twisted, and we 

required flame straightening to correct it.

Oregon 

Department of 

Transportation

Rarely 1- Loss of prestressed girder due to lack of proper support.

2- Loss of prestressed girder during hauling to the project site 

from casting plant.

Pennsylvania 

Department of 

Transportation

Occasionally Recently, a steel beam failed during removal due to lateral 

torsional buckling. The position of the lifting points resulted in 

an unbraced compression flange stress limit of 1.85 ksi. The 

applied bending stress was 7.8 ksi, and the beam failed. 

Lessons learned:

• Gravity, Bending, and Stability are related. Recognize 

and understand the stress state.

• As a part of the failure investigation, obtain witness 

statements, capture videos and pictures, and 

coordinate with Central Office Bridge and 

Construction Staff.

• Expect the contractor to revise the procedure.

• For demolition, do not reduce the Factor of Safety to 

below 1.5.

Contact: Tom Macioce at 717.787.2881 or tmacioce@pa.gov

SDDOT Rarely There was a slab bridge falsework collapse on an urban project 

where the end support transverse beams were hung from the 

bridge piers/abutments. The hanger rod/bolt diameter was 

changed (decreased) during construction and approved by the 

falsework designer but the larger hole diameter was left in the 

support beams without additional plate washers added. The 

standard washers covered the holes but were not sufficient to 

prevent them from being pulled through the oversize hole when 

concrete placement overloaded the detail. 

State of Florida 

Department of 

Transportation 

Rarely During the placement of long span Bulb-T superstructure, 

temporary bracing was not adequate and 7 beams that were 

placed and were waiting for deck form placement, collapsed 

because of high winds. Six beams were in place when the 7th 

and last beam was set after which a high wind gust caused the 

7th beam to topple into the 6th beam and so on until all 

collapsed (see photo). There were no injuries or loss of life. 

During a hurricane like event concrete beams that were placed 

but not decked collapsed due to high winds. The reason for the 

collapse was inadequate temporary bracing. There were no 

injuries or loss of life. Because of these mishaps and other near 

miss events, the temporary bracing requirements for FDOT 

projects were strengthened dramatically. The following are links 

to FDOT Standard drawings covering bracing requirements.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.6

Responding 

Agency

Frequency Response

Texas Department 

of Transportation 

Occasionally In most cases the cause has been equipment failures rather 

than a procedural issue. This occurs with both structural steel 

and prestressed girders. TxDOT has had long-standing design 

guidance for proportioning plate girders to avoid local instability 

or buckling issues. The old rule of thumb was that flanges 

widths needed to be 1/3 of the web depth. That has relaxed 

some due to recent research at UT-Austin but we are still much 

more conservative than the LRFD design code.

Utah Department 

of Transportation 

Rarely

Vermont Agency 

of Transportation 

Rarely Last year VTrans had a project to rehabilitate a historic metal 

through truss. While replacing steel on a built-up section of the 

top chord, there was a buckling failure when too many bolts 

were removed. For more information please contact Wayne 

Symonds. 

Virginia 

Department of 

Transportation 

Rarely Superstructure/girder removal of highly skewed continuous 

bridge collapsed during removal. Problem was due to cutting 

/removal of most of the intermediate diaphragms prior to 

removing each segments/girders as was proposed/reviewed on 

the demolition plan.

Washington State 

Department of 

Transportation

Never

Wisconsin DOT Never

WYDOT Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.7

2. How often have you experienced member deformation/stability/alignment 

problems during deck placement? Description of the problem(s) and lesson(s) 

learner or a contact person. 

Responding 

Agency

Frequency Response

Arizona 

Department of 

Transportation

Never

Arkansas 

Department of 

Transportation 

Rarely

CA Department 

of 

Transportation 

Occasionally Falsework reduces clearance over traffic therefore truck without 

permit hit the falsework stringer or backhoe boom not ties properly 

hit the falsework stringer 

CDOT, Staff 

Bridge Branch

Rarely Steel Girders on one construction job showed some excess 

deformation, deflection under wet non-composite concrete loads. 

The pour sequence was revised and concrete was allowed to cure 

before other deck sections were placed. The lesson learned is to 

be more aware of these situations during design and use thicker 

web plates or adjust section areas and camber cuttings 

accordingly.

Delaware DOT Never

Georgia 

Department of 

Transportation

Rarely For steel beams on bad skews, we have occasionally had the 

exterior beam twist while placing concrete. (The diaphragms are 

not fully welded until after deck placement for highly skewed 

bridges)

Illinois 

Department of 

Transportation

Often About two or three times a year, fascia girders during the deck 

pour are not properly braced and cause thin decks to be poured. 

Sometimes girder defection at staged construction joints behave 

abnormally causing the girders to not act identically.

Iowa 

Department of 

Transportation

Occasionally Rotation of the exterior girder. We pay more attention to the 

cantilever overhang and securing the top flange. Loss of support 

of the beam at the abutment. The heavier beams required us to 

modify the bearing we were using.

Kansas 

Department of 

Transportation

Rarely Contact: Travis Malone at 785-296-2066 or Malone@KSdot.org 

Maryland SHA, 

Office of 

Structures

Rarely During staged construction, there have been issues with installing 

diaphragms as one side of the bridge is completely loaded and the 

other is not resulting in misalignment of the bolt holes. Deflection 

of bridge deck slabs under traffic loads during stage construction 

has required changes in deck formwork design details to achieve 

a smooth riding surface. 

MassDOT Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.8

Responding 

Agency

Frequency Response

Michigan 

Department of 

Transportation

Occasionally Staged or part width construction on skewed or curved structures 

often results in geometry or alignment issues on finished 

structures. We have had instances of the crown point not 

matching during the second stage of part width construction, or 

diaphragm rotation causing differential deflections on skewed deck 

pours.

Minnesota 

Department of 

Transportation

Rarely This is extremely rare with more than 10 years between 

occurrences. 

Missouri 

Department of 

Transportation 

Rarely

Nevada Dept of 

Transportation

Never

New Jersey 

Department of 

Transportation

Rarely Bearings shifted longitudinally after deck pour on a long-spancurve bridge with high camber. Reinforced elastomeric bearings 

deformed on steel girder bridge with high camber prior to pouring 

deck and secondary loads.

New Mexico 

Department of 

Transportation 

Never

North Carolina 

Department of 

Transportation 

Often Lateral girder deflections/rotations are often observed on bridges 

with skewed supports. Exacerbating factors include vertical curve 

grades, skew and superelevation (cross-slope).

North Dakota 

Department of 

Transportation 

Rarely Once. Rotation of exterior beam during deck placement.

NYSDOT Occasionally Inadequate shop assembly. Foundation location out of tolerance. 

Cumulative tolerances exceed practical limits

Ohio 

Department of 

Transportation

Rarely ODOT has experienced excessive beam rotation on two steel 

girder projects within the past 10 years that required corrective 

action. In both instances, the lateral bracing was connected with 

bolts that were only snug tightened in slotted holes during the 

deck placement operation. The beans rotated until the bolts 

bottomed out in the slotted holes resulting in exaggerated beam 

rotations. This issue has been addressed from two fronts. First the 

Department prohibited the use of slotted holes and snug-tight 

connections in bracing members. Second, the Department 

construction specifications require all connections to be fully 

tightened before beginning deck placement operations.

Oklahoma 

Department of 

Transportation 

(ODOT)

Occasionally Due to not using proper bracing, there have been some cases 

where we have twisted the outside beam. 

Oregon 

Department of 

Transportation

Rarely Overestimated camber in a steel plate girder superstructure 

resulted in a hump and not meeting the designed finished grade 

profile.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.9

Responding 

Agency

Frequency Response

Pennsylvania 

Department of 

Transportation

Occasionally For steel girders, the deck placement is a critical condition. 

Every few years we experience an issue with distortion of the 

structural members or ride quality of the deck due to the 

deflection of the structural steel during deck placement. The 

issues occur most frequently on skewed steel bridges.

SDDOT Rarely There have been some instances of exterior beam rotation from 

overhang bracket (cantilever) loading that caused some 

separation of the exterior top flange and formwork. In one case 

this separation nearly caused the ends of transverse form joists to 

lose bearing and drop off the beam edge. An exterior beam 

torsional analysis is now typically performed to ensure adequate 

ties are placed to limit the top flange lateral deflection to a 

minimum and prevent future occurrences of this problem. There 

have also been some issues with expandable type joists deflecting 

excessively and not being of good condition/quality for the 

purpose intended.

State of Florida 

Department of 

Transportation 

Rarely A prestressed concrete fascia beam had positive camber 

(downward sag) after full dead load was applied. The beam was 

load tested and found to have acceptable load carrying capacity 

but there was no explanation for why it sagged.

Texas 

Department of 

Transportation 

Rarely The only issue in recent memory was uplift and rotation of a long 

single box girder HOV lane bridge. The designer did not include 

the potential for uplift in the plans. We now put required deck 

placing sequences in the plans if there is a potential for uplift.

Utah 

Department of 

Transportation 

Occasionally

Vermont 

Agency of 

Transportation 

Rarely A couple of years ago a girder bridge experienced significant 

rotation and lateral deflection of exterior girders during concrete 

replacement. This was due to insufficient temporary bracing by the 

Contractor. For more information contact Wayne Symonds. 

Virginia 

Department of 

Transportation 

Rarely Multi- span continuous steel girders where some uplift was 

anticipated/noticed during stage concrete deck pouring. Sequence 

of pouring had to be changed or more stage pouring to be 

considered.

Washington 

State 

Department of 

Transportation

Rarely Concrete girders on a precast simple span bridge rotated outward 

(1⁄2” to 3⁄4”) during deck placement. The Contractor had not 

installed temporary deck bracing details (tension tie member at 

top, compression struts on bottom flange) to ensure girders did not 

rotate. The Contractor assumed the intermediate diaphragms 

were adequate to keep girders from rotating outward.

Wisconsin DOT Rarely

WYDOT Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.10

3. How often have you experienced problems in the final geometry/alignment of 

superstructures during or at the end of erection? Description of the problem(s) 

and lesson(s) learner or a contact person. 

Responding 

Agency

FrequencyResponse

Arizona 

Department of 

Transportation

Never

Arkansas 

Department of 

Transportation 

Rarely

CA Department 

of 

Transportation 

Rarely Bridges (P/S CIP) girder with multiple frame has hinges in them. 

Due to post tensioning girder dead load and prestressing load are 

redistributed to falsework under the long span and combined with 

hinge curl the alignment is invariable. Contact: Rod Simmons.

CDOT, Staff 

Bridge Branch

Rarely Pier cap was a bit shorter or a bit taller than elevation specified. 

The problem was corrected by shimming or shaving the concrete 

surface area and adjusting it for the right elevation. The lesson 

learned is to measure twice and cut once. We recommend to 

survey elevations more carefully.

Delaware DOT Never

Georgia 

Department of 

Transportation

Rarely This occasionally happens but it is usually due to surveying errors.

Illinois 

Department of 

Transportation

Often Problems cited in question 2 above cause thin decks making 

vertical grade changes necessary.

Iowa Department 

of 

Transportation

Never

Kansas 

Department of 

Transportation

Rarely

Maryland SHA, 

Office of 

Structures

Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.11

Responding 

Agency

FrequencyResponse

MassDOT Rarely Wellesley, Route 16 over Route 9. When second stage beam erection 

began, it was found that the first stage beams were not erected 

according to the plans. Paul Maloy, D4 Construction

Palmer, US 20 over Route 67 and CSX RR. Same problem as above. 

The details are still being investigated, but it may be that the 

substructures were not constructed as located on the plans. D2 

Construction

As it happens, both bridges were being built by the same contractor 

who was going out of business during the construction. It would 

appear that the problems encountered were associated with the 

contractor.

Michigan 

Department of 

Transportation

Occasionally As discussed above, staged or part width construction projects 

sometimes experience these issues. We have a skew policy that 

requires refined analysis on curved or severely skewed bridges (> 

30o).

Minnesota 

Department of 

Transportation

Never This essentially never happens

Missouri 

Department of 

Transportation 

Rarely

Nevada Dept of 

Transportation

Rarely On curved structures, we have experienced alignment problems or 

instances where the field splice gap was wider than deigned. 

These have occurred despite shop assembly of the sections in 

question. In some cases, geometric errors of the substructures 

may have contributed to the problems encountered. In one 

instance, field splice connections we redesigned to accommodate 

the additional gap.

New Jersey 

Department of 

Transportation

Rarely Contractor could not attach end diaphragms after erection of 

bridge with severe skew. Construction documents should specified 

plumb at erection or at final position after application of dead load.

New Mexico 

Department of 

Transportation 

Rarely We had a contractor pour a deck onto BT-54 prestressed girders. 

The exterior girders came out of plumb about 5° during the deck 

pour but were not noticed until after forms were stripped for the 

pier and abutment diaphragms. Lesson learned: better anchorage 

of intermediate diaphragms and temporary anchorage or crossframes are needed near girder ends to keep girders plumb.

North Carolina 

Department of 

Transportation 

Rarely Occasionally diaphragms that are a welded frame, as opposed to 

individual angles or WT members, are difficult to install on curved 

structures.

North Dakota 

Department of 

Transportation 

Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.12

Responding 

Agency

FrequencyResponse

NYSDOT Rarely

Ohio 

Department of 

Transportation

Never

Oklahoma 

Department of 

Transportation 

(ODOT)

Rarely

Oregon 

Department of 

Transportation 

Rarely - End bent of an eight span curved single cell post-tensioned 

box girder rotated and lifted off from bearing after posttensioning. Fix required shimming the bearings and plating the 

finger plate joint at end bent. 

- End bent of a three span post-tension box girder were lifted 

from bearing not well adjusted post-tension path.

Pennsylvania 

Department of 

Transportation

Rarely This has occurred with skewed steel bridges. One issue 

occurred because some of the end cross-frame bays were 

installed in the wrong bay location. This resulted in the lateral 

shift of the girders and difficult fit-up.

SDDOT Rarely There have been issues with bearing/anchor bolt alignment in the 

past. Plans now typically call for field welding of the sole plate to 

the bottom flange and block outs in the pier cap to allow for 

casting of anchor bolts after bearing placement. On a recent 

bridge widening project with a skewed and curved superstructure 

there were some alignment differences between old and new 

where the diaphragms had to be field adjusted

State of Florida 

Department of 

Transportation 

Often This is only a common occurrence during the erection of precast 

concrete segmental box girder superstructures where it happens 

on occasion during erection of almost every bridge

Texas 

Department of 

Transportation 

Occasionally This is more common than one might think but is usually the result 

of surveying errors in the field. The fabrication surveying has 

almost always been correct. The issue is usually bents that are out 

of place, at the wrong elevation, or at the wrong skew angle. 

We’ve noticed a general decline in the quality of field surveying 

with the increased use of GPS/Total Station surveying

Utah Department 

of 

Transportation 

Often

Vermont Agency 

of 

Transportation 

Never

Virginia 

Department of 

Transportation 

Rarely Wide width of bridge superstructure steel frames under stage 

construction, where some misalignment occurred on the exterior 

girders. Lateral bracing/diaphragms attachment/connections were 

made unevenly within the frame structure. 
Engineering for Structural Stability in Bridge Construction Reference Manual

C.13

Responding 

Agency

FrequencyResponse

Washington 

State 

Department of 

Transportation

Never

Wisconsin DOT Rarely

WYDOT Never
Engineering for Structural Stability in Bridge Construction Reference Manual

C.14

4. When checking a girder for stability during handling and erection do you 

require AASHTO LRFD be used? If no, what other standard(s) are allowed? 

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

No AASHTO Guide specifications for Temporary Works

Arkansas Department 

of Transportation 

No Contractor is responsible

CA Department of 

Transportation 

No Falsework is checked using ASD.

CDOT, Staff Bridge 

Branch

Yes

Delaware DOT Yes

Georgia Department of 

Transportation

No AASHTO 17th edition or other acceptable analysis methods.

Illinois Department of 

Transportation

Yes

Iowa Department of 

Transportation

No This is the contractor’s responsibility to assure stability using 

means and methods.

Kansas Department of 

Transportation

Yes

Maryland SHA, Office 

of Structures

Yes

MassDOT No AASHTO Standard Specifications

Michigan Department 

of Transportation

Yes

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No MoDOT specifications are typically “end result”. It is the 

contractor’s responsibility to develop a plan for erection of 

structures, with assistance from the fabricator and/or the 

contractor’s engineer.

Nevada Dept of 

Transportation

Yes

New Jersey 

Department of 

Transportation

Yes

New Mexico 

Department of 

Transportation 

Yes

North Carolina 

Department of 

Transportation 

Yes Bridge designers are advised to follow NCDOT’s 

“Constructability Guidelines for Steel Plate Girder Bridges” 

(see attachment labeled “constructability guidelines”)

North Dakota 

Department of 

Transportation 

Yes
Engineering for Structural Stability in Bridge Construction Reference Manual

C.15

Responding 

Agency

Y/N Response

NYSDOT Yes

Ohio Department of 

Transportation

No The Department requires the design for erection procedures 

in accordance with either the AASHTO Standard 

Specifications for Highway Bridges or the AASHTO LRFD 

Bridge Design Specifications. 

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

No The contractor’s engineer often uses AISC construction 

manual.

Pennsylvania 

Department of 

Transportation

No

SDDOT Yes

State of Florida 

Department of 

Transportation 

No AASHTO LRFD, AASHTO Guide Design Specifications for 

temporary works, FDOT Structures Manual/Structures 

Design Guidelines (4.3.4)

Texas Department of 

Transportation 

No The University of Texas developed software (UTBridge and 

UTLift) that we use for both design and erection analyses. 

This is not currently a requirement but will likely become a 

required check when we re-write our specs for 2014.

Utah Department of 

Transportation 

Yes

Vermont Agency of 

Transportation 

Yes

Virginia Department of 

Transportation 

Yes

Washington State 

Department of 

Transportation

Yes We also have a Standard Specification for Temporary 

Bracing:

Wisconsin DOT Yes

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.16

5. Do you require an erection procedure to be submitted by the bridge erector?

Responding 

Agency

Y/N

Arizona Department of 

Transportation

Yes

Arkansas Department 

of Transportation 

Yes

CA Department of 

Transportation 

Yes

CDOT, Staff Bridge 

Branch

Yes

Delaware DOT Yes

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

Yes

Iowa Department of 

Transportation

Yes

Kansas Department of 

Transportation

Yes

Maryland SHA, Office 

of Structures

Yes

MassDOT Yes

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

Yes

Missouri Department 

of Transportation 

No

Nevada Dept of 

Transportation

Yes

New Jersey 

Department of 

Transportation

Yes

New Mexico 

Department of 

Transportation 

Yes

North Carolina 

Department of 

Transportation 

Yes

North Dakota 

Department of 

Transportation 

No

NYSDOT Yes

Ohio Department of 

Transportation

Yes

Oklahoma Department 

of Transportation 

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.17

Responding 

Agency

Y/N

(ODOT)

Oregon Department of 

Transportation

Yes

Pennsylvania 

Department of 

Transportation

Yes

SDDOT Yes

State of Florida 

Department of 

Transportation 

Yes

Texas Department of 

Transportation 

Yes

Utah Department of 

Transportation 

Yes

Vermont Agency of 

Transportation 

Yes

Virginia Department of 

Transportation 

Yes

Washington State 

Department of 

Transportation

Yes

Wisconsin DOT No

WYDOT Yes
Engineering for Structural Stability in Bridge Construction Reference Manual

C.18

6. If the answer to 5 is yes, are they required for all bridges? 

Responding 

Agency

Y/N

Arizona Department of 

Transportation

Yes

Arkansas Department 

of Transportation 

Yes

CA Department of 

Transportation 

No

CDOT, Staff Bridge 

Branch

Yes

Delaware DOT Yes

Georgia Department of 

Transportation

Illinois Department of 

Transportation

No

Iowa Department of 

Transportation

No

Kansas Department of 

Transportation

Yes

Maryland SHA, Office 

of Structures

Yes

MassDOT Yes

Michigan Department 

of Transportation

N/A

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

Nevada Dept of 

Transportation

Yes

New Jersey 

Department of 

Transportation

Yes

New Mexico 

Department of 

Transportation 

No

North Carolina 

Department of 

Transportation 

No

North Dakota 

Department of 

Transportation 

NYSDOT Yes

Ohio Department of 

Transportation

Yes

Oklahoma Department 

of Transportation 

N/A
Engineering for Structural Stability in Bridge Construction Reference Manual

C.19

Responding 

Agency

Y/N

(ODOT)

Oregon Department of 

Transportation

No

Pennsylvania 

Department of 

Transportation

Yes

SDDOT No

State of Florida 

Department of 

Transportation 

Yes

Texas Department of 

Transportation 

No

Utah Department of 

Transportation 

Yes

Vermont Agency of 

Transportation 

Yes

Virginia Department of 

Transportation 

No

Washington State 

Department of 

Transportation

Yes 

Wisconsin DOT N/A 

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.20

7. If the answer to question 6 is no, is there a size, span length, geometry feature 

or other threshold consideration that triggers the requirement? If yes, what size 

threshold or other consideration that triggers submittal of a procedure?

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

Arkansas Department 

of Transportation 

CA Department of 

Transportation 

Yes All steel girder & precast girder. 

CDOT, Staff Bridge 

Branch

No Some actions with in specs only apply when there is traffic below 

the structure.

Delaware DOT N/A

Georgia Department of 

Transportation

Yes For bridges over railroads, erection procedures are required by 

the railroads now.

Illinois Department of 

Transportation

Yes Steel girders only.

Iowa Department of 

Transportation

Yes This is required when the design engineer determines the 

complexity of the erection dictates an erection plan

Kansas Department of 

Transportation

N/A

Maryland SHA, Office 

of Structures

MassDOT

Michigan Department 

of Transportation

Yes As discussed above, staged or part width construction projects 

sometimes experience these issues. We have a skew policy that 

requires refined analysis on curved or severely skewed bridges 

(> 30o). Type of construction (segmental, deck cast with beams, 

etc.), fracture critical, deep curved steel plate girders, girders with 

a field splice, cantilever construction

Minnesota Department 

of Transportation

No Engineering judgment is used to determine which bridges 

require an erection plan. 

Missouri Department of 

Transportation 

Nevada Dept of 

Transportation

N/A
Engineering for Structural Stability in Bridge Construction Reference Manual

C.21

Responding 

Agency

Y/N Response

New Jersey 

Department of 

Transportation

New Mexico 

Department of 

Transportation 

Yes We require erection plans, design calculations and procedures for 

steel girder bridges in accordance with AASHTO/NSBA Steel 

Bridge Erection Guide Specification. We do not require it for 

prestressed girders.

North Carolina 

Department of 

Transportation 

Yes See NCDOT’s “Constructability Guidelines for Steel Plate Girder 

Bridges”.

North Dakota 

Department of 

Transportation 

NYSDOT 

Ohio Department of 

Transportation

N/A Erection plans are required by ODOT Construction and Materials 

Specification (C&MS) Item 501.05 for every project that requires 

erection of steel or precast concrete structural members. 

Oklahoma Department 

of Transportation 

(ODOT)

Yes Curved girder or over traffic

Oregon Department of 

Transportation

No

Pennsylvania 

Department of 

Transportation

N/A

SDDOT Yes There is no set policy on erection plan submittal requirement. It is 

typically based on engineering judgment considering span 

lengths, girder depths, curvature, skew, etc.

State of Florida 

Department of 

Transportation 

Texas Department of 

Transportation 

Yes Our specs say "railroad underpasses, trusses, field-spliced 

(welded or bolted) girders, arches, or other members for which 

erection drawings are required on the plans. “Submit an 

additional copy of the drawings for railroad underpasses. Erection 

drawings are not required for rolled I-beam units unless otherwise 

noted on the plans

Utah Department of 

Transportation 

All bridges require submittal, but only bridges specifically 

designated by the EOR require erection drawing approval. 

Vermont Agency of 

Transportation 

N/A
Engineering for Structural Stability in Bridge Construction Reference Manual

C.22

Responding 

Agency

Y/N Response

Virginia Department of 

Transportation 

Yes Depends on the type of structure given consideration to its span 

length, beam/girder types, bridge geometry (straight, high 

skewed, curved) simple or multi-span, and its behavior to type of 

substructure (i.e. boxed pier caps, prestressed/ post-tensioned)

Washington State 

Department of 

Transportation

Wisconsin DOT No

WYDOT Yes Complexity of bridge (curved, span length < 200’, large skews < 

40 degrees), and bridge type [currently have an deck arch under 

construction, required an erection plan] 
Engineering for Structural Stability in Bridge Construction Reference Manual

C.23

8. Do you have requirements for the erection procedure contents and format? If 

yes, provide a copy or link.

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

No

Arkansas Department 

of Transportation 

No 

CA Department of 

Transportation 

Yes Standard Specification 2010: Section 55-1.03C, "Erection"

CDOT, Staff Bridge 

Branch

Yes See Link on last page

Delaware DOT Yes http://deldot.gov/information/pubs_forms/manuals/standard_speci

fications/index.shtml

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

Yes For Curved Steel Girders

http://www.dot.il.gov/bridges/GBSP55.pdf

Iowa Department of 

Transportation

No

Kansas Department of 

Transportation

Yes Special Provision 08-07004-R03

http://www.ksdot.org/burconsmain/specprov/2007/pdf/07-07004-

r03.pdf

Maryland SHA, Office 

of Structures

No

MassDOT Yes http://www.massdot.state.ma.us/Portals/8/docs/manuals/SSP0

22510MetEng.pdf

Starting on page SUPPLEMENT C2010 - 141

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

Yes
Engineering for Structural Stability in Bridge Construction Reference Manual

C.24

Responding 

Agency

Y/N Response

New Jersey 

Department of 

Transportation

Yes www.nj.gov/transportation/eng/specs/2007/spec500.shtm

New Mexico 

Department of 

Transportation 

Yes ftp://ftp.mdt.mt.gov/research/LIBRARY/NSBASBEGS-1-OLSTEEL_BRIDGE-AASHTO.PDF

North Carolina 

Department of 

Transportation 

Yes http://www.ncdot.org/doh/preconstruct/highway/structur/psp/PSP

2012/PSP033.pdf

http://www.ncdot.org/doh/preconstruct/highway/structur/psp/PSP

2012/PSP006.pdf

North Dakota 

Department of 

Transportation 

No

NYSDOT Yes https://www.dot.ny.gov/divisions/engineering/structures/manuals/

scm 

Ohio Department of 

Transportation

Yes As mentioned above, C&MS 501.05 governs the requirements. 

The ODOT C&MS may be accessed at: 

http://www.dot.state.oh.us/Divisions/ConstructionMgt/OnlineDocs/

Specifications/2013CMS/500/501.htm#A_501_05

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

Yes Web and bearing stiffener at end bents should be plumb at final 

condition.

Pennsylvania 

Department of 

Transportation

Yes The erection drawings and calculations must be signed and sealed by 

a PE registered in Pennsylvania.

SDDOT No The erection procedure submittal information requirements are 

intended to be referenced to those found in the AASHTO/NSBA 

Steel Bridge Erection Guide Specification.

State of Florida 

Department of 

Transportation 

Yes ftp://ftp.dot.state.fl.us/LTS/CO/Specifications/SpecBook/2010Boo

k/460.pdf and see spec 460-7.1.3

ftp://ftp.dot.state.fl.us/LTS/CO/Specifications/WorkBook/Jan2012/

SS4520000.pdf and see spec 452-8.1

Texas Department of 

Transportation 

Yes Clearly indicate at least: procedures, sequence of work, 

equipment to be used, location of falsework, erection cranes and 

holding cranes, falsework design details, girder lifting points, 

adjacent structures loaded and requirements for releasing cranes 

during erection 

Utah Department of 

Transportation 

Yes http://www.udot.utah.gov/main/uconowner.gf?n=7602520459537

371
Engineering for Structural Stability in Bridge Construction Reference Manual

C.25

Responding 

Agency

Y/N Response

Vermont Agency of 

Transportation 

Yes http://vtranscontracts.vermont.gov/sites/aot_contract_administrati

on/files/documents/2011specbook/2011Division500.pdf

Virginia Department of 

Transportation 

No

Washington State 

Department of 

Transportation

Yes Copy Provided

Wisconsin DOT No

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.26

9. Do you specify criteria for erectors for design wind load considerations during 

erection? If yes, what is the wind load or provide a copy or link.

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

No

Arkansas Department 

of Transportation 

No

CA Department of 

Transportation

Yes Specifications for Precast Prestressed Concrete Bridge 

members require that bracing resist the following lateral 

pressures: (see Figure C-10) 

CDOT, Staff Bridge 

Branch

No

Delaware DOT No

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

No

Iowa Department of 

Transportation

No

Kansas Department of 

Transportation

No

Maryland SHA, Office 

of Structures

No

MassDOT Yes See link above

Michigan Department 

of Transportation

No This is done on a project by project basis depending on 

complexity. For example, for jacking loads for bearing 

replacement on a segmental bridge, the design specifies the 

wind load intensity, and the duration the jacks must with stand 

the load.

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.27

Responding 

Agency

Y/N Response

New Jersey 

Department of 

Transportation

No

New Mexico 

Department of 

Transportation 

No We do not specify criteria but we do require all girders to be 

stabilized with falsework, temporary bracing, and/or holding 

cranes until a sufficient number of adjacent girders are erected 

with diaphragms and/or cross-frames connected to provide the 

necessary lateral stability and to make the structure selfsupporting.

North Carolina 

Department of 

Transportation 

Yes AASHTO Guide Specification for Bridge Temporary Works, and 

as amended by NCDOT Special Provision entitled “Falsework 

and Formwork” (see attachment by that same name)

North Dakota 

Department of 

Transportation 

No

NYSDOT No

Ohio Department of 

Transportation

No

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

No

Pennsylvania 

Department of 

Transportation

Yes ftp://ftp.dot.state.pa.us/public/Bureaus/BOPD/Bridge/2013/bd/

bd620m.pdf

SDDOT No

State of Florida 

Department of 

Transportation 

Yes FDOT requires Contractors to comply with the AASHTO Guide 

Design Specifications for Bridge Temporary Works and 

Construction Handbook for Bridge Temporary Works

Texas Department of 

Transportation 

No

Utah Department of 

Transportation 

No

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.28

Responding 

Agency

Y/N Response

Washington State 

Department of 

Transportation

No

Wisconsin DOT No

WYDOT No

Structure Height H (ft) Lateral Pressure (psf)

0 < H ≤30 15

30 < H ≤ 50 20

50 < H ≤ 100 25

H > 100 30

Figure C-23 Lateral Pressure and Structure Height
Engineering for Structural Stability in Bridge Construction Reference Manual

C.29

10. Do you specify criteria to erectors for maximum lateral deflection of girders 

subjected to wind load during erection? If yes, what is the deflection criteria or 

provide a copy or link.

Responding Agency Y/N Response

Arizona Department of 

Transportation

No

Arkansas Department of 

Transportation 

No

CA Department of 

Transportation 

No

CDOT, Staff Bridge Branch No

Delaware DOT No 

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

No

Iowa Department of 

Transportation

No

Kansas Department of 

Transportation

No

Maryland SHA, Office of 

Structures

No

MassDOT No

Michigan Department of 

Transportation

No We follow the provision of the AASHTO LRFD Bridge Design 

Specification.

Minnesota Department of 

Transportation

No

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

No

New Jersey Department of 

Transportation

No

New Mexico Department of 

Transportation 

No

North Carolina Department 

of Transportation 

No

North Dakota Department of 

Transportation 

No

NYSDOT No

Ohio Department of 

Transportation

No

Oklahoma Department of 

Transportation (ODOT)

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.30

Responding Agency Y/N Response

Oregon Department of 

Transportation

No

Pennsylvania Department of 

Transportation

No Pennsylvania does require the contractor to evaluate the 

effects of the deflections.

SDDOT No

State of Florida Department 

of Transportation 

Yes Deflection criteria are probably covered in the AASHTO Guide 

Design Specifications for Bridge Temporary Works and 

Construction Handbook for Bridge Temporary Works

Texas Department of 

Transportation 

No

Utah Department of 

Transportation 

No

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

No

Washington State 

Department of 

Transportation

No

Wisconsin DOT No

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.31

11. Do you specify a minimum safety factor with regard to global stability of a 

partially erected or demolished structure for global structural stability?

Responding 

Agency

Y/N

Arizona Department of 

Transportation

No

Arkansas Department 

of Transportation 

No

CA Department of 

Transportation 

No

CDOT, Staff Bridge 

Branch

No

Delaware DOT No

Department of 

Transportation

No

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

No

Iowa Department of 

Transportation

No

Maryland SHA, Office 

of Structures

No

MassDOT No

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

No

New Jersey 

Department of 

Transportation

No

New Mexico 

Department of 

Transportation 

No

North Carolina 

Department of 

Transportation 

No

North Dakota 

Department of 

Transportation 

No

NYSDOT No

Ohio Department of 

Transportation

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.32

Responding 

Agency

Y/N

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

No

Pennsylvania 

Department of 

Transportation

No

SDDOT No

State of Florida 

Department of 

Transportation 

No

Texas Department of 

Transportation 

No

Utah Department of 

Transportation 

No

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

No

Washington State 

Department of 

Transportation

No

Wisconsin DOT No

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.33

12. Do you provide guidance or design criteria for the strength and stability 

checks for cantilever girder sections during lifting and placement?

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

No

Arkansas Department 

of Transportation 

No

CA Department of 

Transportation 

No

CDOT, Staff Bridge 

Branch

No

Delaware DOT No

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

No

Iowa Department of 

Transportation

No

Kansas Department of 

Transportation

Yes KDOT Design Manual. L/D ≤ 85

Maryland SHA, Office 

of Structures

No

MassDOT No

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

No

New Jersey 

Department of 

Transportation

No

New Mexico 

Department of 

Transportation 

No

North Carolina 

Department of 

Transportation 

No

North Dakota 

Department of 

Transportation 

No

NYSDOT No

Ohio Department of 

Transportation

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.34

Responding 

Agency

Y/N Response

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

No

Pennsylvania 

Department of 

Transportation

No

SDDOT No

State of Florida 

Department of 

Transportation 

No

Texas Department of 

Transportation 

No

Utah Department of 

Transportation 

No

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

Yes

Washington State 

Department of 

Transportation

No

Wisconsin DOT No

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.35

13. Do you require a bridge demolition procedure to be submitted for bridge 

removal?

Responding 

Agency

Y/N

Arizona Department of 

Transportation

Yes

Arkansas Department 

of Transportation 

Yes

CA Department of 

Transportation 

Yes

CDOT, Staff Bridge 

Branch

Yes

Delaware DOT Yes

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

Yes

Iowa Department of 

Transportation

Yes

Kansas Department of 

Transportation

Yes

Maryland SHA, Office 

of Structures

Yes

MassDOT Yes

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

Yes

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

Yes

New Jersey 

Department of 

Transportation

Yes

New Mexico 

Department of 

Transportation 

Yes

North Carolina 

Department of 

Transportation 

Yes

North Dakota 

Department of 

Transportation 

Yes

NYSDOT Yes

Ohio Department of 

Transportation

Yes

Oklahoma Department 

of Transportation 

(ODOT)

Yes
Engineering for Structural Stability in Bridge Construction Reference Manual

C.36

Responding 

Agency

Y/N

Oregon Department of 

Transportation

Yes

Pennsylvania 

Department of 

Transportation

Yes

SDDOT No

State of Florida 

Department of 

Transportation 

Yes

Texas Department of 

Transportation 

Yes

Utah Department of 

Transportation 

Yes

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

Yes

Washington State 

Department of 

Transportation

Yes

Wisconsin DOT No

WYDOT Yes
Engineering for Structural Stability in Bridge Construction Reference Manual

C.37

14. If the answer to question 12 is yes, is there a size, span 

length, geometry feature or other threshold consideration 

that triggers the requirement?

Responding 

Agency

Response

Arizona Department of 

Transportation

Arkansas Department 

of Transportation 

CA Department of 

Transportation 

All bridge demolition requires demolition plan and procedure.

CDOT, Staff Bridge 

Branch

n/a

Delaware DOT No. We make that determination based on the complexity of the structure 

and the conditions surrounding the bridge being removed.

Georgia Department of 

Transportation

Illinois Department of 

Transportation

No but for certain structures we require a Structural Assessment Report 

(see link). http://www.idot.illinois.gov/Assets/uploads/files/DoingBusiness/Manuals-Guides-&-Handbooks/Highways/Bridges/BridgeSpecial-Provisions/gbsp67.pdf

Iowa Department of 

Transportation

Only for special cases as determined by the Engineer.

Kansas Department of 

Transportation 

Yes. See Figure 736-1 in 07-070004-R03

http://www.ksdot.org/burconsmain/specprov/2007/pdf/07-07004-r03.pdf

Maryland SHA, Office 

of Structures

All bridge reconstruction and deck replacement contractions require a 

demolition plan

MassDOT No

Michigan Department 

of Transportation

This would be on a case by case basis depending on the project, and if 

stability were an issue during lifting and placement, procedures would be 

shown in the plans.

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

n/a

Nevada Dept of 

Transportation

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.38

Responding 

Agency

Response

New Jersey 

Department of 

Transportation

Information unknown – job to job basis. 

New Mexico 

Department of 

Transportation 

For existing steel girder bridges that are fracture critical and/or have 

fatigue cracks. We had a bridge collapse on a contractor during deck 

removal. The pin & hanger connections on the steel girders snapped and 

the bridge came down. Because of this, we now require a bridge removal 

plan for these types of bridges. 

North Carolina 

Department of 

Transportation 

Required when work is over the railway right-of-way

North Dakota 

Department of 

Transportation 

If only a portion of the existing bridge is to be removed and traffic will be 

carried by the remaining portion.

NYSDOT Designer specifies need 

Ohio Department of 

Transportation

A plan submission is required when the demolition is over or adjacent to 

active traffic. 

Oklahoma Department 

of Transportation 

(ODOT)

n/a

Oregon Department of 

Transportation

Pennsylvania 

Department of 

Transportation

Any bridge with a span over 80 feet long and any bridge over live traffic.

SDDOT n/a

State of Florida 

Department of 

Transportation 

n/a

Texas Department of 

Transportation 

Demolition plans are not normally required but can be for more complex 

structures (trusses, etc.).

Utah Department of 

Transportation 

Vermont Agency of 

Transportation 

n/a

Virginia Department of 

Transportation 

Depends on the type of structure given consideration to its span length, 

beam/girder types, bridge geometry (straight, high skewed, curved) 

simple or multi-span, and its behavior to type of substructure (i.e. boxed 

pier caps, prestressed/ post-tensioned

Washington State 

Department of 

Transportation

No, we review and approve all demolition plans, including overhangs, rail 

and damaged girder replacements

Wisconsin DOT n/a
Engineering for Structural Stability in Bridge Construction Reference Manual

C.39

Responding 

Agency

Response

WYDOT No, case by case depending on structure type, what it crosses and for 

deck removal/replacement

15. Do you have requirements as to the qualifications of 

those who prepare the erection plan? If so, please provide.

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

Yes PE civil or structural

Arkansas Department 

of Transportation 

No

CA Department of 

Transportation 

Yes An engineer who is registered as a civil engineer in the 

State.

CDOT, Staff Bridge 

Branch

Yes See link on last page

Delaware DOT Yes Must be stamped by profession engineer registered in the state 

of Delaware

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

Yes In Illinois, all require a Structural Engineer’s seal and for certain 

bridges we require IDOT Prequalified Engineers (see link in 

Question 8 above).

Iowa Department of 

Transportation

Yes Licensed Engineer

Kansas Department of 

Transportation

Yes Contractor’s Engineer

Maryland SHA, Office 

of Structures

Yes When calculations and other information are deemed necessary 

to backup erection plans, they shall be signed and sealed by a 

Md. PE.

MassDOT Yes The method and all submissions shall be prepared under the 

supervision of a professional engineer, registered in 

Massachusetts, who is familiar with these Specifications, 

AASHTO, the work, and experienced in this technical field.

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

Yes Preparation of the erection plan needs to be done by a 

registered Professional Engineer in the state of Minnesota.

Missouri Department of 

Transportation 

Yes We require the falsework to be approved by a Registered 

Professional Engineer. Any erection plans needed are provided 

by the fabricator. Fabricators provide the shop drawings, which 

are reviewed by MoDOT.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.40

Responding 

Agency

Y/N Response

Nevada Dept of 

Transportation 

No

New Jersey 

Department of 

Transportation

Yes P.E. Required

New Mexico 

Department of 

Transportation 

Yes Section 1 of 

ftp://ftp.mdt.mt.gov/research/LIBRARY/NSBASBEGS-1-OLSTEEL_BRIDGE-AASHTO.PDF. We also require the erector to 

have 5 years’ experience and have completed construction of a 

minimum 2 bridges with high skew or curved steel within the last 

5 years.

North Carolina 

Department of 

Transportation 

Yes Professional Engineer licensed by the State of North Carolina.

North Dakota 

Department of 

Transportation 

No

NYSDOT Yes

Ohio Department of 

Transportation

Yes Plans shall be prepared, signed, sealed, and dated by an Ohio 

registered Professional Engineer and shall be checked, signed, 

sealed and dated by a second Ohio registered Professional 

Engineer.

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

Yes The drawings and specifications shall be provided by a 

registered professional engineer licensed in the State of 

Oregon.

Pennsylvania 

Department of 

Transportation

Yes The plans must be signed by a PE registered in Pennsylvania.

SDDOT Yes P.E.

State of Florida 

Department of 

Transportation 

Yes Must be prepared by a Professional Engineer Licensed in 

Florida

Texas Department of 

Transportation 

Yes Must be a P.E.

Utah Department of 

Transportation 

Yes PE or SE is required

Vermont Agency of 

Transportation 

Yes PE.

Virginia Department of 

Transportation 

Yes Given structure type, we may/will enforce Engineer in 

performing the task per VDOT Road and Bridge Specifications
Engineering for Structural Stability in Bridge Construction Reference Manual

C.41

Responding 

Agency

Y/N Response

Washington State 

Department of 

Transportation

Yes Licensed Professional Engineer in the State of Washington

Wisconsin DOT No

WYDOT Yes WY PE with experience in the type of work
Engineering for Structural Stability in Bridge Construction Reference Manual

C.42

16. Do you have requirements as to the qualifications of 

those who prepare the demolition plan? If so, please provide.

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

No

Arkansas Department 

of Transportation 

No

CA Department of 

Transportation 

Yes An engineer who is registered as a civil engineer in the 

State.

CDOT, Staff Bridge 

Branch

Yes

Delaware DOT Yes Must be stamped by profession engineer registered in the 

state of Delaware

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

Yes In Illinois, we require a Structural Engineer’s seal.

Iowa Department of 

Transportation

Yes Licensed Engineer

Kansas Department of 

Transportation

Yes Contractor’s Engineer

Maryland SHA, Office 

of Structures

Yes When calculations and other information are deemed 

necessary to backup erection plans, they shall be signed 

and sealed by a Md. PE.

MassDOT Yes

Same as for 15.

Michigan Department 

of Transportation

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No

Nevada Dept of 

Transportation

No

New Jersey 

Department of 

Transportation

Yes P.E. Required
Engineering for Structural Stability in Bridge Construction Reference Manual

C.43

Responding 

Agency

Y/N Response

New Mexico 

Department of 

Transportation 

Yes Must be a plan stamped by a Professional Engineer in 

NM. The P.E. must have a minimum 5 years’ experience 

in this type of work and have done a minimum of 2 

projects within the last 5 years.

North Carolina 

Department of 

Transportation 

Yes Professional Engineer licensed by the State of North 

Carolina. This requirement is only for activities that have 

the capacity to affect travel ways- vehicular or navigable

North Dakota 

Department of 

Transportation 

No

NYSDOT Yes See Comment

Ohio Department of 

Transportation

Yes Plans shall be prepared, signed, sealed, and dated by an 

Ohio registered Professional Engineer and shall be 

checked, signed, sealed and dated by a second Ohio 

registered Professional Engineer.

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

Yes Depend on size, type and location of the bridge 

requirement may vary however an engineer registered in 

the State of Oregon needs to sign and stamp the 

demolition drawings and specifications.

Pennsylvania 

Department of 

Transportation

Yes The plans must be signed by a PE registered in 

Pennsylvania.

SDDOT No

State of Florida 

Department of 

Transportation 

Yes Qualifications are only required for highly sophisticated 

demolition projects (particularly if explosive demolition is 

permitted) and then FDOT requires a Professional 

Engineer Licensed in Florida to develop the plan and this 

is determined on a project by project basis.

Texas Department of 

Transportation 

Yes Must be a P.E.

Utah Department of 

Transportation 

Yes PE or SE is required

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

Yes Given structure type, we may/will enforce Engineer in 

performing the task per VDOT Road and Bridge 

Specifications

Washington State 

Department of 

Transportation

Yes Licensed Professional Engineer in the State of 

Washington

Wisconsin DOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.44

Responding 

Agency

Y/N Response

WYDOT Yes WY PE 
Engineering for Structural Stability in Bridge Construction Reference Manual

C.45

17. Do you have requirements as to the level/degree of 

engineering analysis that is performed by the erector? If yes, 

please provide a copy or link.

Responding 

Agency

Y/N Response

Arizona Department of 

Transportation

No

Arkansas Department 

of Transportation 

No

CA Department of 

Transportation 

No

CDOT, Staff Bridge 

Branch

Yes To some degree, it is based on the requirement of the 

specification for Girder Erection, See link on last page

Delaware DOT No

Georgia Department of 

Transportation

No

Illinois Department of 

Transportation

No

Iowa Department of 

Transportation

No

Kansas Department of 

Transportation

Yes Special Provision 07-07004-R03

http://www.ksdot.org/burconsmain/specprov/2007/pdf/07

-07004-r03.pdf

Maryland SHA, Office 

of Structures

No

MassDOT Yes See link for 8

Michigan Department 

of Transportation

No

Minnesota Department 

of Transportation

No

Missouri Department of 

Transportation 

No Registered Professional Engineer

Nevada Dept of 

Transportation

No

New Jersey 

Department of 

Transportation

Yes P.E. Required 

New Mexico 

Department of 

Transportation 

Yes Section 2 of 

ftp://ftp.mdt.mt.gov/research/LIBRARY/NSBASBEGS-1-

OL-STEEL_BRIDGE-AASHTO.PDF. 

North Carolina 

Department of 

Transportation 

No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.46

Responding 

Agency

Y/N Response

North Dakota 

Department of 

Transportation 

No

NYSDOT No

Ohio Department of 

Transportation

Yes See the response to Question #8 above.

Oklahoma Department 

of Transportation 

(ODOT)

No

Oregon Department of 

Transportation

No

Pennsylvania 

Department of 

Transportation

No

SDDOT No

State of Florida 

Department of 

Transportation 

Yes For beam and girder temporary bracing, the erector 

must comply with the AASHTO Guide Design 

Specifications for Bridge Temporary Works and 

Construction Handbook for Bridge Temporary Works.

Texas Department of 

Transportation 

No Not at this time but we are working on a list of checks to 

be performed for a future specs

Utah Department of 

Transportation 

Yes http://www.udot.utah.gov/main/uconowner.gf?n=760252

0459537371

Vermont Agency of 

Transportation 

No

Virginia Department of 

Transportation 

No But, in certain projects due to structure erection 

complexities, the contract plans will show and determine 

the necessary requirements as needed

Washington State 

Department of 

Transportation

Yes Same as question 8

Wisconsin DOT No

WYDOT No
Engineering for Structural Stability in Bridge Construction Reference Manual

C.47

18. Who reviews erector supplied erection plans? 

Responding 

Agency

Response

Arizona Department of 

Transportation

Resident Engineer

Arkansas Department 

of Transportation 

Bridge Construction Engineer

CA Department of 

Transportation 

Resident Engineer with the assistance of Maintenance Engineer if crane 

loads the existing bridge.

CDOT, Staff Bridge 

Branch

Participants of the Pre Girder Erection meeting review the plan and 

comment. 

Delaware DOT Design engineer of record

Georgia Department of 

Transportation

The Design Group responsible for the bridge plans.

Illinois Department of 

Transportation

Our Bridge design and Construction Review Unit.

Iowa Department of 

Transportation

Design Engineer

Kansas Department of 

Transportation

This depends on the category of the erection.

Maryland SHA, Office 

of Structures

A Transportation Engineer with a bachelor’s degree in engineering from 

an accredited college and a minimum of two years experience in 

professional engineering.

MassDOT The designer of record of the bridge project on behalf of the DOT

Michigan Department 

of Transportation

The design engineer of record.

Minnesota Department 

of Transportation

The design engineer (engineer of record) and fabrication engineer (shop 

plan reviewer).

Missouri Department of 

Transportation 

The fabricator or the contractor is responsible for erection plans. 

Nevada Dept of 

Transportation

Department personnel, or a design consultant hired for construction 

support

New Jersey 

Department of 

Transportation

Design Consultants or in-house design.

New Mexico 

Department of 

Transportation 

NMDOT Bridge Bureau P. E. or a Consultant P.E. hired by NMDOT.
Engineering for Structural Stability in Bridge Construction Reference Manual

C.48

Responding 

Agency

Response

North Carolina 

Department of 

Transportation 

NCDOT Structures Management Unit has a designated Working Drawing 

Review & Approval Section. For the railway projects the General 

Engineering Consultant for the railway.

North Dakota 

Department of 

Transportation 

NYSDOT Main Office Metals Engineering Unit (steel structures) or Region Bridge 

Design (concrete structures)

Ohio Department of 

Transportation

For projects with railroad involvement, the plans require railroad approval 

which is typically performed by an independent consultant retained by 

the railroad. For projects without railroad involvement, the plans require 

design and checking by two different Ohio Registered Professional 

Engineers. Department review and approval is not required. 

Oklahoma Department 

of Transportation 

(ODOT)

ODOT Bridge Division

Oregon Department of 

Transportation

The EOR of the designed bridge.

Pennsylvania 

Department of 

Transportation

For most bridges, the reviews are conducted by the DOT construction 

personnel. For larger projects, consultants are utilized to review 

erection procedures.

SDDOT Bridge Construction Engineer

State of Florida 

Department of 

Transportation 

Usually the construction management staff (FDOT employees or 

Construction Engineering and Inspection Consultants hired by FDOT) 

and for some situations the Engineer of Record, FDOT State 

Construction Office, FDOT State Structures Design Office or FDOT 

District Structures Design Office. 

Texas Department of 

Transportation 

Bridge Division, Bridge Construction & Maintenance Branch (90%) 

Utah Department of 

Transportation 

Engineer of Record

Vermont Agency of 

Transportation 

VTrans construction personnel typically with additional review by 

Structures Design as requested. 

Virginia Department of 

Transportation 

VDOT Engineer or Agents of VDOT

Washington State 

Department of 

Transportation

The Bridge Construction Support Team, within the Bridge & Structures 

Offices, composed of experienced Professional Engineers familiar with 

all types of temporary construction submittals. 
Engineering for Structural Stability in Bridge Construction Reference Manual

C.49

Responding 

Agency

Response

Wisconsin DOT Staff in our fabrication unit sometimes review erection plans but they do 

not approve them.

WYDOT Design Engineer
APPENDIX D

RECOMMENDED ENGINEERING CRITERIA 

The plans and procedures for bridge construction shall be in conformance with 

applicable provisions of the AASHTO LRFD Bridge Construction Specifications, the 

supplementary criteria presented herein, and any other additional requirements 

provided by the Owner. Further discussion of these engineering criteria is contained in 

the referenced sections of the Manual that are indicated in parenthesis.

The term Engineer as used herein refers to the Contractor’s Engineer charged with the 

development of the Contractor’s construction plan and/or the Engineer charged with 

performing a detailed investigation of the anticipated erection sequence for the bridge 

superstructure. 
Engineering for Structural Stability in Bridge Construction Reference Manual

D.1

D-1. MEMBER AND COMPONENT EVALUATION

D-1.1 GENERAL

Girder-bridge superstructures shall be constructed in such a way that strength and 

stability is maintained at all intermediate stages until completion. All members shall be 

lifted, supported, connected, and braced in such a way that no limit states are violated 

at any time and damage such as yielding, buckling and/or concrete cracking is avoided. 

Stability shall include local, member, system and rigid body (rollover) stability. 

The calculations supporting the plans and procedures shall be in accordance with the 

AASHTO LRFD Bridge Design Specifications (referred to herein as the AASHTO LRFD 

BDS), AASHTO LRFD Bridge Construction Specifications, AASHTO Guide 

Specifications for Temporary Works, and the following supplementary provisions. 

Nominal yielding or reliance on post-buckling resistance shall not be permitted for main 

steel load-carrying members for all construction conditions, except for potential local 

yielding of the web in hybrid sections.

Sections in the Manual that provide additional information and commentary related to 

the provisions in this Criteria are referenced throughout.

As a minimum, bridge members and partially completed structures shall be evaluated at 

all of the following stages of construction (ref. Manual 7.2.2):

1. Girder lifting

2. Placement of the initial girder and any associated temporary bracing used to hold 

the girder in place

3. First pair of girders set with permanent bracing installed; and subsequent stages 

of girder erection which the Engineer deems critical

4. All girders and bracing installed prior to deck placement

The effects of wind on the behavior shall be considered during all of the above stages.

Stability during the following stages also shall be evaluated where the Contractor’s 

construction plan related to these stages differs from what is shown in the Contract 

Documents: 

• Deck placement with bracing fully installed between all girders

• Application of the deck overhang bracket loads to the fascia girders during the 

deck placement
Engineering for Structural Stability in Bridge Construction Reference Manual

D.2

Wind loads may be neglected in evaluating the fully erected system of girders for 

concrete loads due to deck placement if Contractor is precluded from work when winds 

in excess of 20 mph are forecast.

D-1.2 ANALYSIS

Analysis methods used (ref. Manual 7.2) shall be sufficiently refined to accurately 

evaluate the applicable force effects and limit states for each stage of girder erection 

and deck placement. For lifting/setting of a single girder, a line girder analysis may be 

satisfactory. Refined grid or 3D analysis methods shall be utilized for the evaluation of 

multi-girder systems, unless it is determined that girder system interaction effects can 

be neglected.

A global stability analysis shall be conducted to verify adequate stability when any 

procedures are being utilized for which the stability condition is not known, by either 

engineering judgment or documented experience on bridges of similar span, 

slenderness, lateral stiffness and bracing.

In cases where the force effects approach the elastic critical buckling limit, the effects of 

a potential second-order amplification of the response shall be considered. This may be 

addressed by a second-order analysis, or by supplemental bracing measures.

The boundary conditions assumed in the analysis model shall be representative of 

those specified in the erection plans, and provided in the field. The boundary conditions 

shall recognize the absence of any vertical restraint in the investigation of uplift 

scenarios. Girder twist shall be restrained at all support locations at all stages. This may 

induce fit-up forces for some detailing provisions.

D-2. LOAD COMBINATIONS AND LOAD FACTORS 

The totaled factored force effect (ref. Manual 7.3) at each stage of construction shall be 

taken as:

Q YQ = ∑ i i (D-2)

where:

Yi = Load factors specified in Table D-1 

Qi = Force effects from the construction design loads specified in Section D-3
Engineering for Structural Stability in Bridge Construction Reference Manual

D.3

DC CDL CLL(d) CW

Strength I 1.25 1.50 1.50 — 

Strength III 1.25 1.25 — 1.0(b)

Strength VI(a) 1.40 1.40 1.40 — 

Service 1.00 1.00 1.00 0.7(b)

Uplift(c)/Overturning 0.90/1.35 0.90/1.35 — 1.0(b)

a) Steel structures for only the case of placing the deck on the fully erected steel. Use Strength I or III for 

intermediate steel conditions, as applicable.

b) The specified load factor of 1.0 for wind load force effects for the strength load combinations is based 

on basic wind speed maps wherein an appropriate safety margin is built into the maps. Wind 

loads may be computed using a wind velocity based on the Wind Velocity Modification Factor 

specified in Table D-3.2 for the construction phase duration under investigation. Note that the 

wind load factor is less than 1.0 for the service load combination.

c) Where a construction design load produces uplift/overturning at the location being investigated, the 

maximum specified load factor shall be applied to the load force effect and where the load resists 

uplift/overturning, the force effect shall be multiplied by the minimum specified load factor.

d) An appropriate dynamic load allowance shall be considered for CLL where applicable.

Resistance factors, φφ, for the strength limit state shall be taken in accordance with the 

AASHTO LRFD BDS, Articles 6.5.4.2 and 5.5.4.2, as applicable. Additional resistance 

factors applied herein include:

, resistance factor for lateral torsional buckling = 0.90

, resistance factor for steel girder bracing stiffness = 0.75

, resistance factor for girder system buckling = 0.90

Safety margins on lifting accessories, jacks, and other manufactured items shall be in 

accordance with manufacturer’s recommendations.

For evaluation of ancillary items, lifting devices, and other conditions for which LRFD 

specifications do not exist, the resistance factors used shall be documented and 

submitted to the Owner for approval.

Table D-1 Load Combinations and Load Factors
Engineering for Structural Stability in Bridge Construction Reference Manual

D.4

D-3. LOADS

D-3.1 PERMANENT DEAD LOADS (DC) 

Permanent Dead Loads (ref. Manual 7.4.2) include the weight of all permanent in-place 

components of the partially completed structure as computed in accordance with the 

AASHTO LRFD BDS design specifications, including the weight of the deck concrete 

during placement and any stay-in-place forms. In the absence of more precise 

information, material unit weights used in the computation of permanent dead loads 

may be taken from Table 3.5.1-1 of the AASHTO LRFD BDS. The weight of stiffeners, 

splices, studs, bolts, paint and other miscellaneous items may be taken as an 

equivalent uniformly distributed weight along the girder, or accounted for using an 

increased material density. In lieu of a project-specific value, the following may be 

assumed for the weight of stay-in-place formwork.

Stay-in-place corrugated metal formwork = 20 psf

Stay-in-place concrete plank formwork = as calculated

D-3.2 CONSTRUCTION DEAD LOADS (CDL) 

Construction Dead Loads (ref. Manual 7.4.3) include the weight of removable temporary 

construction supported by the partially completed structure.

Removable Formwork = 10 psf

Cantilever Formwork = as calculated

Protective Shielding = as calculated

Other = as calculated

D-3.3 CONSTRUCTION LIVE LOADS (CLL)

Construction live loads (ref. Manual 7.4.3.1) include the weight of workers, 

miscellaneous tools and supplies, materials and equipment that are only on the bridge 

during construction. Suggested construction live loads that might be considered include 

the following: 

Workers and light tools a = 20 psf

Overhang live load b = 75 plf
Engineering for Structural Stability in Bridge Construction Reference Manual

D.5

Materials = actual weight

Additional uniform live load (when motorized

buggies are used to place concrete) a = 25 psf

a = applied to concrete deck area

b = applied to outside edge of each concrete deck overhang

Screed machine = per manufacturer’s data

Other equipment = per manufacturer’s data

Dynamic Load Allowance 

Moving and stationary equipment

= minimum 10% of equipment weight for moving equipment 

(except screed machine)

= minimum 10% of equipment operating load for stationary 

equipment

Crane lift as a part of member removal (demolition)

= minimum 20% of the calculated member weight

Accidental release for segmental concrete girders shall be considered as specified in 

AASHTO LRFD BDS Article 5.14.2.3.2. 

Incidental loads = 5 psf lateral load (minimum) over the vertical face of the girder 

applied at the centroid of the loaded area. Load factor for Cw shall apply.

D-3.4 WIND LOADS (CW)

The construction horizontal wind load (ref. Manual 7.4.4), Cw, shall be applied at the 

centroid of the exposed projected area of the windward girder/truss and shall be 

computed as follows: 

Cw = qz G Cf Af (D-3.4a)

where:

qz = velocity pressure at height z above grade (Equation D-3.4b) (psf)

G = gust effect factor, use 0.85

Cf = wind net force coefficient (Tables D-3.3 or D-3.4, as applicable)

Af = exposed projected area of girder or truss (ft2)

The effects of superelevation and horizontal curvature shall be considered in 

determining the exposed projected area.
Engineering for Structural Stability in Bridge Construction Reference Manual

D.6

Velocity pressure, qz, evaluated at height z shall be taken as:

qz = 0.00256 Kz Kzt Kd (VmV)2 (D-3.4b)

Note: VmV = 20 mph minimum

where:

Kz = wind velocity pressure exposure coefficient (Table D-3.1) 

Kzt = topographic factor, use 1.0

Kd = wind directionality factor, use 0.85

V = basic wind speed (mph)

Vm = wind velocity modification factor (Table D-3.2)

z = height of the top of the bridge deck above grade/water (ft)

Height above ground level, z Exposure Category

Height above ground level, z Exposure Category

Ft (m) B C D 

0-15 (0-4.6) 0.57 0.85 1.03

20 (6.1) 0.62 0.90 1.08

25 (7.6) 0.66 0.94 1.12

30 (9.1) 0.70 0.98 1.16

40 (12.2) 0.76 1.04 1.22

50 (15.2) 0.81 1.09 1.27

60 (18) 0.85 1.13 1.31

70 (21.3) 0.89 1.17 1.34

80 (24.4) 0.93 1.21 1.38

90 (27.4) 0.96 1.24 1.40

100 (30.5) 0.99 1.26 1.43

120 (36.6) 1.04 1.31 1.48

140 (42.7) 1.09 1.36 1.52

160 (48.8) 1.13 1.39 1.55

180 (54.9) 1.17 1.43 1.58

200 (61.0) 1.20 1.46 1.61

250 (76.2) 1.28 1.53 1.68

300 (91.4) 1.35 1.59 1.73

350 (106.7) 1.41 1.64 1.78

400 (121.9) 1.47 1.69 1.82

450 (137.2) 1.52 1.73 1.86

500 (152.4) 1.56 1.77 1.89

*For exposure Category descriptions, see Reference Manual 7.4.4) 

Table D-3.1 Velocity Pressure Exposure Coefficient, Kz 
Engineering for Structural Stability in Bridge Construction Reference Manual

D.7

Construction Duration Velocity Modification Factor

0 – 6 weeks 0.65

6 weeks – 1 year 0.75

1 year – 2 years 0.80

2 years – 5 years 0.85

Note: wind load may be neglected during girder lifting and during deck casting if Contractor is precluded from work 

when winds in excess of 20 mph are forecast.

Component Type Construction Condition Force Coefficient

I-Shaped Girder Superstructure Deck forms not in place 2.2*

Deck forms in place 1.1

U-Shaped and Box-Girder 

Superstructure

Deck forms not in place 1.5

Deck forms in place 1.1

Flat Slab or Segmental BoxGirder SuperstructureAny 1.1

*When s/d is greater than 2.0, Cf = 2(1 + 0.05 s/d) ≤ 4

Where 

s = girder spacing

d = girder height

ε Cf

<0.1 2

0.1 to 0.29 1.8

0.29 to 0.7 1.7

Where 

ε = Solid Area of Truss Members

Gross Area of Truss

D-3.5 SEISMIC LOADS

Seismic Loads (ref. Manual 7.4.5) shall not be considered unless required by the bridge 

Owner. If required, the loads shall comply with the Owner’s requirements.

Table D-3.2 Wind Velocity Modification Factors, Vm

Table D-3.3 Wind Net Force Coefficient, Cf, (For Girder Bridges During 

Construction)

Table D-3.4 Wind Net Force Coefficient, Cf (For Truss Bridges During 

Construction)
Engineering for Structural Stability in Bridge Construction Reference Manual

D.8

D-4. GIRDER LIFTING

D-4.1 GENERAL

Lifting procedures (ref. Manual 7.5) shall be developed to ensure that the girder has 

adequate strength and buckling resistance during lifting operations. Girder weight shall 

be based on shop drawing weight or computed from member dimensions accounting for 

fabrication tolerances in finished dimensions. Steel girders should be lifted near their 

quarter points whenever possible. Where a spreader beam is employed, the line of 

support, or line running through the girder lifting points, should pass through the center 

of gravity of the member, and the lifting reactions at each pick point should be equal. 

Cross-frames attached to the girders prior to lifting, and any other variations to the 

girder configuration shall be considered in determining the center of gravity.

The girder bending moments shall be determined treating the girder as simply 

supported at the lift points. Lift points shall not be assumed to provide any lateraltorsional restraint. 

D-4.2 STEEL GIRDERS

Straight steel I-girders, or horizontally curved steel I-girders (ref. Manual 7.5.2) where 

the central angle subtended by the girder length is less than 3 degrees, that are doubly 

symmetric and lifted at two points, shall satisfy the following:

2

2 M M C EI GJ E I C u b cr b bL y y w 2 L L

π π  <φ =φ +    

(D-4.2a)

in which:

CbL = Moment gradient magnifier during lifting

2.0 for 0.225 Lift

bL

L

C

L = ≤ 

6.0 for 0.225 0.3 Lift

bL

L

C

L

= <<

4.0 for 0.3 Lift

bL

L

C

L = ≥
Engineering for Structural Stability in Bridge Construction Reference Manual

D.9

where:

Mu = Factored maximum moment from static analysis (kip-in)

Mcr = Nominal lateral-torsional buckling resistance (kip-in.)

φφb = Resistance factor for lateral torsional buckling = 0.9

L = Unbraced length = (total length of girder segment) (in)

Iy = Moment of inertia of the girder about the vertical axis in the plane of the web (in4) 

Lift L = Average length from the lift points to the ends of the girder (in)

G = Shear modulus, 11,200 (ksi)

J = Torsional constant (in4) 

Cw = Warping constant (in6) 

For singly symmetric sections the flexural resistance based on lateral torsional buckling 

shall be computed in accordance with AASHTO LRFD BDS Appendix D-6.4.2, where 

CbL as computed above shall replace the Cb term. 

D-4.3 CONCRETE GIRDERS

Concrete girders shall be stable and not crack during lifting. The roll stability (ref. 

Manual 7.5) of concrete I-girders shall satisfy Equation D-4.3a and the cracking shall 

satisfy Equation D-4.3b.

Rollover:   θ′ ≤   ′ ′ θ +  

max

max

1.5 r

o i

y

z e (D-4.3a)

 

Cracking: 

max

1.0 1 o i

r

z

y

  θ ≤÷ +   θ  

(D-4.3b)

in which:

max 2.5

i

o

e

z

θ = ′ (D-4.3c)

max

lat

g

M

M

θ =

 (D-4.3d)

i

i

r

e

y

θ =

 (D-4.3e)
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D.10

where:

θi = initial roll angle of rigid beam (rad)

ei = the initial lateral eccentricity of the center of gravity with respect to the roll axis 

(rad).

yr = the height of the roll axis above the center of gravity of the beam (in).

zo = the theoretical lateral deflection of the center of gravity of the beam, computed with 

the full weight applied as a lateral load, measured to the center of gravity for the 

deflected arc of the beam (in).

max θ = tilt angle at which cracking begins, based on tension at the top corner equal to the 

modulus of rupture (rad)

max θ′ = tilt angle at rollover (rad)

Mg = service level strong-axis moment in girder due to selfweight (kip-in)

Mlat = service level weak-axis moment that would cause cracking in top flange of girder 

(kip-in)

The assumed initial eccentricity, ei, shall be taken as a minimum of 1⁄4 inch plus 1/8 inch 

for each 10 feet of beam length or fraction thereof.

For a beam with overall length, l, and equal overhangs beyond the lifting points of 

length, a, at each end: 

( ) ( ) ( ) ( ) 5 3 24 5 0.1 11 1 3 1.2

12 o

y

w

z l al al a

EI l

= −+ +     (D-4.3f)

 

where:

l1 = l – 2a (in)

 Iy = moment of inertia of beam about weak axis (in4

) 

w = girder weight per unit length (kip/in)

o z′ = lateral deflection of girder center of gravity including rotation effects (in) = o z (1 + 

2.5 θ′

max ) 

D-5. GIRDER STABILITY 

D-5.1 GENERAL

The Contractor shall ensure that girders are stable throughout the erection process. 

Prior to release of a girder from its lifting line, adequate bracing shall be installed, as 

necessary, to provide girder stability. Bracing shall be designed for vertical and lateral 

load effects and girder stability forces. Bracing shall be evaluated for both strength and 
Engineering for Structural Stability in Bridge Construction Reference Manual

D.11

stiffness as specified herein. Girder twist shall be restrained at all support locations at all 

stages. 

Steel girders shall be evaluated for local, member, and global stability as specified 

herein and the bracing details shall be defined at each construction stage under 

investigation. The stage of completeness of all bolted connections shall be considered 

when evaluating the strength and stability of the steel during erection.

The Contractor shall ensure that sufficient internal cross-frames or diaphragms are 

provided to control cross-sectional distortion throughout construction. Top lateral 

bracing of tub girders should be installed in the girders prior to shipping and erection of 

the field pieces.

Steel I-girder compression flanges and top flanges of tub girders subject to compression 

shall be evaluated for flange local buckling and for lateral-torsional buckling in-between 

brace points according to Eq. 6.10.3.2.1-2 of the AASHTO LRFD BDS.

Yielding of I-girder compression and tension flanges and top flanges of tub girders 

subject to compression and tension shall be evaluated according to Eqs. 6.10.3.2.1-1 

and 6.10.3.2.2-1, respectively, of the AASHTO LRFD BDS, as applicable. Tub-girder 

bottom flanges subject to compression shall be evaluated for flange local buckling 

according to Eq. 6.11.3.2-1 of the AASHTO LRFD BDS.

Yielding of tub-girder bottom flanges subject to tension shall be evaluated according to 

Eq. 6.11.3.2-3 of the AASHTO LRFD BDS. Web bend-buckling shall be evaluated for Iand tub girders according to Eqs. 6.10.3.2.1-3 and 6.11.3.2-2, respectively, of the 

AASHTO LRFD BDS, as applicable.

D-5.2 STEEL GIRDER BRACING

Bracing members for steel girders (ref. Manual 5.3) shall be evaluated for the applicable 

provisions of Articles 6.8 and 6.9 of the AASHTO LRFD BDS. In addition to resisting all 

applied force effects, bracing members and systems for steel I-girders shall also satisfy 

the applicable stiffness and strength requirements specified below for a discrete 

torsional nodal, relative lateral or nodal bracing system.

For Torsional Nodal Bracing Provided by Cross-frames or Diaphragms:

2

2

0.005 b u

br br b

eff b o

L LM M Fh

nEI C h

= > (D-5.2a)
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D.12

2

2

T 2.4 u

T

br eff b

L LM

n nEI C

b b = >

f

 (D-5.2b)

For Relative Lateral Bracing Provided by a Lateral Truss on the Compression Flange:

0.008 u d

br

o

M C P

h

 

≥    

(D-5.2c)

1 4 u d

br

br b o

M C

L h

  b ≥   φ  

(D-5.2d)

For Nodal Lateral Bracing Provided by Laterally Bracing the Girders from a Rigid 

Structure such as an Adjacent Bridge:

0.2 u d

br

o

M C P

h

 

≥    

(D-5.2e)

1 10 u d

br

br b o

M C

L h

  b ≥   φ  

(D-5.2f)

in which:

sec

11 1 1

Tb g

=+ +

bbbb (D-5.2g)

( ) 3 3

sec

1.5 3.3

12 12

o s s

o

E h t t b

h

 

b =   +

 

 (D-5.2h)

( )2

2

3

24 1 g x

g

g

n S EI

n L

− β = (D-5.2i)

( ) / eff yc yt I I t cI = + (D-5.2j)
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D.13

where:

βT = torsional stiffness of the bracing system (k-in/rad)

βb = stiffness of the cross-frame or diaphragm (k-in/rad)(ref. Manual Fig. 5-6 and 5-7)

βsec = web distortional stiffness (k-in/rad)

βg = in-plane girder system stiffness (k-in/rad)

βT = continuous bracing stiffness (k-in/rad-in)

βbr = the required lateral bracing stiffness (k/in)

E = modulus of elasticity (29000 ksi for steel)

tw = web thickness (in)

bs = width of transverse web stiffener plates (in), (=total combined width for doublesided stiffeners and width of single plate for single sided stiffeners, ref. Manual Fig 

5-8)

ng = number of girders across the width of the bridge

S = girder spacing (in)

Ix = moment of inertia about the strong axis (in4) 

L = span of the girders (in)

Mbr = In-plane flexural resistance of cross-frame or diaphragm (k-in)

Mu = maximum factored girder moment within the unbraced length (k-in)

L = span length (in)

Lb = unbraced length (in)

ho = distance between girder flange centroids (in)

hb = vertical distance between cross-frame bracing chords (or work points) (in)

n = number of cross-frames or diaphragms in the span under consideration

= effective moment of inertia (in4)

= moment of inertia of the compression and tension flange, respectively, of 

the steel section about a vertical axis through the plane of the web (in.4) 

c, t = distance from the centroid of the steel-girder cross-section to the centroid of the 

compression and tension flanges, respectively (in)

Cb =moment magnification factor (use Cb = 1.0 or AISC Chapter F to calculate alternate 

values)

Fbr = required force couple in cross-frame or diaphragm (kip)

Pbr = the required lateral bracing strength (kip)

For the lateral braces closest to the inflection point for a girder in reverse curvature:

Cd = 2.0 

Otherwise:

Cd = 1.0 

Φbr resistance factor for steel girder bracing = 0.75

For all girder geometries except cantilevers, lateral braces shall be positioned as close 

to the compression flange as possible. For cantilever sections, lateral braces shall be 

positioned as close to the tension flange as possible (considering gravity loading, this 

will be the top flange).
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D.14

D-5.3 CONCRETE GIRDER BRACING

Concrete girders (ref. Manual 7.7) shall be braced to satisfy the following (after setting 

the girder on the bearing pads):

Rollover: ( ) max

max max

1.5

o i

r

z ey

θ −a ′ ≤ ′′ ′ θ + +θ (D-5.3a)

Cracking: ( ) max

max max

1.0

o i

r

z ey

θ −a

≤

θ + +θ (D-5.3b)

in which:

4 1

120 o

c y

wL

z

E I = (D-5.3c)

max

lat

g

M

M

θ = (D-5.3d)

K

r

W

θ = (D-5.3e)

( ) max

max

r z h

r

− a

θ = ′ + a (D-5.3f)

max (1 2.5 ) o z′ ′ =+ θ (D-5.3g)

where:

initial lateral eccentricity of center of gravity with respect to roll axis (in) (min. of 1 

inch + 1/8 inch for each 10 feet of girder length or fraction thereof)

hr = distance from bottom of girder to roll axis (use one half of bearing pad thickness)(in)

0 z = the theoretical lateral deflection of the center of gravity of the beam, computed with 

the full weight applied as a lateral load, measured to the center of gravity for the 

deflected arc of the beam (in)
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D.15

tilt angle at which cracking begins, based on tension at the top corner equal to 

the modulus of rupture (rad)

Mlat = service level weak-axis moment that would cause cracking in top flange of girder 

(k-in)

Mg = service level strong-axis moment in girder due to and selfweight (k-in)

w = girder weight per unit length (k/in)

Ec = modulus of elasticity of concrete (ksi)

= moment of inertia of beam about weak axis (in4) 

L = girder span (in)

zmax = maximum resisting moment arm (typically half of bottom flange width) (in) 

Kθ = sum of rotational spring constants of supports (k-in/rad)

W = total weight of beam (k)

y = height of center of gravity of beam above roll axis (in)

α = tilt angle of support (rad)

maximum roll angle at failure (rad)

r = radius of stability (in)

z 0

′ = lateral deflection including rotation effects (in)

In evaluating girder rollover, effects of camber, bearing pad skew, and cross slope shall 

be considered. For wind loading effects, the initial eccentricity, ei, shall be increased by 

a value equal to the lateral deflection at midspan due to wind on the uncracked section, 

plus an eccentricity equal to the wind overturning moment divided by the girder 

selfweight.
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D.16

D-5.4 STEEL GIRDERS GLOBAL STABILITY

Noncomposite steel I-girder systems consisting of two to four girders interconnected by 

cross-frames or diaphragms such that each of the girders interacts in developing the 

global lateral-torsional buckling resistance of the unit as a structural system shall also 

be evaluated to ensure that elastic lateral-torsional buckling of the system does not 

occur (ref. Manual 5.4). For elastic system buckling, singly and doubly symmetric girder 

systems shall satisfy the following:

φ   π ≤ =φ    

2

2 / bk gs

u bk y x

M SE M II n

n L (D-5.4a)

where:

n = number of girders in the system

Mu = maximum factored applied moment in a single girder (k-in)

Mgs = nominal buckling resistance of the single girder system, (k-in)

S = girder spacing (in)

L = span length (in)

Iy, Ix = moments of inertia of a single girder about its weak and strong axis, respectively. 

(in4

) 

Φbk = resistance factor for system buckling = 0.9

E = modulus of elasticity of steel

For singly-symmetric girders, shall be replaced with as follows:

eff yc yt

t II I

c

= + (D-5.4b)

where: 

Iyc and Iyt = moment of inertia of the compression and tension flange, respectively, of the 

steel section about a vertical axis through the plane of the web (in)4

c, t = distances from the centroid of the steel-girder cross-section to the centroid of the 

compression and tension flange, respectively (in)

For three-girder systems:

Iyc = 1.5Iyc (D-5.4c)

S = 2S

For four-girder systems:
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D.17

Iyc = 2Iyc (D-5.4d)

S = 3S

Lateral load effects when combined with the system global buckling resistance 

calculated in D-5.4a through D-5.4d shall satisfy the AASHTO LRFD BDS Eq. A6.1.1-1 

where the global buckling capacity, φφbkMgs/n from Equation D-5.4a, replaces the term 

φφfMnc on the right hand side of the equation.

The Yura equation: has recently been incorporated into AASHTO 

LRFD as Eq. 6.10.3.4.2-1 for checking system buckling during deck pour. The approach 

presented above is applicable for intermediate steel checks prior to the deck pour 

( ), but the AASHTO approach omits the φφ factor and limits the total sum of 

the factored positive girder moments to 50% Mgs during the deck pour (Strength VI load 

combination). Should the sum of the moments exceed 50%, the design can add flange 

level lateral bracing, revise the girder spans/sizes to increase system stiffness, or 

evaluate the amplified girder second-order displacements and verify that they are within 

owner tolerances. Note that amplification can also occur under steel-only dead load as 

the buckling limit is approached, but the recommended system buckling φφ factor and 

Strength I/III load factors should provide an adequate level of safety for most narrow 

systems subject to buckling in the steel-only condition.

D-6. CONCENTRATED LOADS EFFECTS 

At bearing locations and at other locations on steel girders (ref. manual 7.8) subjected 

to concentrated loads, where the loads are not transmitted through a deck or deck 

system, webs without bearing stiffeners shall be investigated for the limit states of local 

web yielding, and local web crippling according to the provisions of Appendix D6.5 – 

Concentrated Loads Applied to Webs without Bearing Stiffeners of the AASHTO LRFD 

BDS. Web sidesway buckling, if applicable, shall be investigated according to AISC 

Specifications J10.4.

The local effect of lifting clamp loads on girder flanges shall be investigated. In lieu of a 

more refined local analysis, the local transverse flange bending stress may be 

computed as follows: 

( ) ( )2 0.75

/ 6

c

yf

f Lf

R k F

bCt

≤

+ (D-6)

where:

Rc = service level concentrated force at each flange edge (kip)

Fyf = specified minimum flange yield stress (ksi)
Engineering for Structural Stability in Bridge Construction Reference Manual

D.18

bf = flange width (in)

tf = flange thickness (in)

CL = length of clamp along flange (in)

k = distance from outer face of flange to web toe of fillet (in)

D-7. DEFLECTION CONTROL 

Girder deflections and rotations (ref. Manual 7.9) shall be controlled such that members 

fit-up can be achieved at each erection stage, and the finished bridge geometry 

conforms with the design plans. Deflections shall be investigated for service loads. 

Deflection and rotation limits for erection shall be established in consultation with the 

erector. Where no job specific criteria are provided, a maximum girder lateral deflection 

limit of the span divided by 150, and maximum girder torsional misalignments (twist) at 

field splice locations of 1.5 degrees shall be used.

D-8. STEEL CONNECTIONS

Connections between permanent and temporary components (ref. Manual 7.10.1) 

required as part of the erection operations shall be evaluated in accordance with the 

applicable provisions of Article 6.13 of the AASHTO LRFD BDS. Any proposed changes 

to the Owner’s standard specified bolting procedures shall be supported by engineering 

calculations and be submitted to the Owner for acceptance. Existing connections and 

splices shall be evaluated for each stage of construction under consideration according 

to the same provisions, as applicable. Reaming of bolt holes during erection shall be 

permitted only with the approval of the Engineer. 

D-9. CONCRETE CONNECTIONS

Anchorage and other connections (ref. Manual 7.10.2) to concrete structures or 

components required as part of the erection operations shall be designed in accordance 

with Appendix D of ACI 318, Building Code Requirements for Structural Concrete. 

Existing anchorages and connections shall be evaluated for each stage of construction 

under consideration according to the same provisions, as applicable.

D-10. TEMPORARY SUPPORTS (FALSEWORK)

Temporary supports and their associated components (ref. Manual 7.11) shall be 

designed to carry vertical and lateral loads due to self-weight and wind and any loads 
Engineering for Structural Stability in Bridge Construction Reference Manual

D.19

that are applied to the temporary supports as the erection progresses. The design of 

temporary towers and falsework shall conform to the AASHTO Guide Specifications for 

Temporary Works. The effects of any longitudinal jacking during the erection shall also 

be investigated. The elevation of the temporary supports shall be such as to support the 

girders at their cambered no-load elevation. The use of temporary supports shall not 

result in any overstressing of the girders. Jacks used in conjunction with the temporary 

supports shall have a stroke adequate to permit full unloading. Unloading of temporary 

supports should be performed such that all temporary supports at each cross-section 

are unloaded uniformly. The deflections of the erected girders at the temporary supports 

when they are removed shall be evaluated, and stability of the girders shall be ensured 

prior to removal of the temporary supports. Where appropriate, holding cranes may be 

substituted for temporary supports.
Engineering for Structural Stability in Bridge Construction Reference Manual

D.20

D-11. BEARINGS

Computed bearing rotations (ref. Manual 7.12) during each stage of construction under 

investigation shall not exceed the rotational capacity of the bearing. Bearings shall be 

installed such that, after dead load has been applied, sufficient rotation capacity shall be 

available to accommodate rotations due to environmental loads and live loads. 

Expansion bearings shall be installed so that they will be in the center of the permitted 

travel at an ambient temperature of 60°F, unless otherwise specified by the Owner. 

Temporary blocking or restraints shall be provided as may be required to control 

bearing movement and assure stability at all construction stages. Note that for skewed 

supports out-of-plane rotations need to be considered in addition to in-plane rotations.

D-12. DECK

D-12.1 FORMS

Plywood, permanent metal forms or concrete panels may be used as deck forms, as 

approved by the Owner (ref. Manual 7.13). Proprietary forms shall be placed in 

accordance with the manufacturer’s specifications incorporating any modifications to 

those specifications approved by the Engineer. Formwork shall be supported by the 

superstructure.

D-12.2 OVERHANGS

Overhang forms (ref. Manual 5.6) shall be removed after the deck has cured. Wherever 

practical, overhang brackets should bear near the bottom flange of the girder and be 

attached to the top flange of the girder. If overhangs bear against the girder web, 

particularly the compression zone of the web, the Engineer shall ensure that 

precautions have been taken to prevent permanent deformation of the web and 

excessive deflection of the wet slab and forms. 

If the loads or their application are to be different than those provided for in the contract 

documents, an additional analysis shall be made by the Engineer. Loads applied on the 

overhang brackets shall be considered in determining and evaluating the lateral force 

on the top flange and the associated lateral flange bending stresses, cross-frame forces 
Engineering for Structural Stability in Bridge Construction Reference Manual

D.21

and web and top flange deformations. The effects of the forces from deck overhang 

brackets acting on the fascia girders of steel-girder bridges shall be evaluated as 

specified in Article 6.10.3.4 of the AASHTO LFRD BDS. 

D-12.3 DECK PLACEMENT

Concrete placements (ref. Manual 5.4) shall either be made in the sequence specified in 

the contract documents, or based on a sequence developed entirely by the Contractor, 

in which case the Engineer shall evaluate the effects of the desired placement 

sequence according to the criteria specified in Article 6.10.3.4 of the AASHTO LFRD 

BDS. 

The duration of each placement shall be specified in the construction plan. The time 

between placements shall be such that the concrete in prior pours had reached an age 

or strength specified in the construction plan. Placements that include both negative and 

positive dead load moment regions should be placed such that the positive moment 

region is poured first. Any accelerating or retarding agents to be used in the concrete 

mix shall be specified.
Engineering for Structural Stability in Bridge Construction Reference Manual

G.1

GLOSSARY

Accepted Method of Analysis – a method of analysis that requires no further verification 

and that has become a regular part of structural engineering practice

Anchorage Zone – the portion of the structure in which the prestressing force is 

transferred from the anchorage device onto the local zone of the concrete, and then 

distributed more widely into the general zone of the structure

At Transfer – immediately after the transfer of prestressing force to the concrete

Axial – in line with the longitudinal axis of a member

Bascule bridge – a bridge over a waterway with one or two leaves which rotate from a 

horizontal to a near vertical position, providing unlimited overhead clearance

Base plate – steel plate, whether cast, rolled or forged, connected to a column, bearing, 

or other member to transmit and distribute its load to the superstructure

Beam – a structural member whose primary function is to transmit loads to the support 

primarily through flexure and shear. Generally this term is used when the component is 

made of rolled shapes.

Beam Column – a structural member whose primary function is to resist both axial loads 

and bending moments

Bearing – A structural device that transmits loads while facilitating translation and/or 

rotation

Bearing Capacity – the load per unit area which a structural material, rock or soil can 

safely carry

Bearing Failure – crushing of material under extreme compressive load

Bearing Plate – a steel plate, which transfers loads from the superstructure to the 

substructure.

Bend-Buckling Resistance – the maximum load that can be carried by a web plate 

without experiencing theoretical elastic local buckling due to bending

Bending Moment – the internal force within a beam resulting from transverse loading.

Biaxial Bending – simultaneous bending of a member or component about two 

perpendicular axes.
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G.2

Bifurcation – the phenomenon whereby an ideally straight or flat member or component 

under compression may either assume a deflected position or may remain undeflected, 

or an ideally straight member under flexure may either deflect and twist out-of-plane or 

remain in its in-plane deflected position

Box Flange – a flange that is connected to two webs. The flange may be a flat 

unstiffened plate, a stiffened plate or a flat plate with reinforced concrete attached to the 

plate with shear connectors.

Box Girder – a hollow rectangular or trapezoidal shaped girder, a primary member along 

the longitudinal axis of the bridge, which provides good torsional rigidity

Bracing Member – a member intended to brace a main member or part thereof against 

lateral movement

Bracket – a projecting support fixed upon two intersecting members to strengthen and 

provide rigidity to the connection

Buckling Load – the load at which an ideally straight member or component under 

compression assumes a deflected position

Built-Up Member – a column or beam composed of plates and angles and other 

structural shapes united by bolting, riveting or welding to enhance section properties

Bulb T-Girder – a t-shaped concrete girder with a bulb shape at the bottom of the girder 

cross-section 

Cable-Stayed Bridge – a bridge in which the superstructure is directly supported by 

cables, or stays, passing over or attached to towers located at the main piers.

Camber – the slightly arched or convex curvature provided in beams to compensate for 

dead load deflection

Cantilever – a structural member that has a free end projecting beyond a support; 

length of span overhanging the support

Cantilever Span – a superstructure span composed of two cantilever arms, or a

suspended span supported by one or two cantilever arms

Cast-In-Place Concrete – concrete placed in its final location in the structure while still in 

a plastic state

Center of Gravity – the point at which the entire mass of a body acts; the balancing 

point of an object

Chord – a generally horizontal member of a truss or cross-frame
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G.3

Closed-Box Section – a cross-section composed of two vertical or inclined webs which 

has at least one completely enclosed cell – a closed-section member is effective in 

resisting applied torsion by developing shear flow in the webs and flanges

Column – a general term applying to a vertical member resisting compressive stresses 

and having, in general, a considerable length in comparison with its transverse 

dimensions

Compact Flange – for a composite section in negative flexure or a noncomposite 

section, a discretely braced compression flange with a slenderness at or below which 

the flange can sustain sufficient strains such that the maximum potential flexural 

resistance is achieved prior to flange local buckling having a statistically significant 

influence on the response, provided that sufficient lateral bracing requirements are 

satisfied to develop the maximum potential flexural resistance

Compact Unbraced Length – for a composite section in negative flexure or a 

noncomposite section, the limiting unbraced length of a discretely braced compression 

flange at or below which the maximum potential flexural resistance can be achieved 

prior to lateral torsional buckling having a statistically significant influence on the 

response, provided that sufficient flange slenderness requirements are satisfied to 

develop the maximum potential flexural resistance

Complex Bridge – movable, suspension, cable stayed, and other bridges with unusual 

characteristics 

Component – a constituent part of a structure

Composite Action – the contribution of a concrete deck to the moment resisting capacity 

of the superstructure beam when the superstructure beams are not the same material 

as the deck.

Composite Beam – a steel beam connected to a deck so that they respond to force 

effects as a unit

Composite Construction – concrete components or concrete and steel components 

interconnected to respond to force effects as a unit

Composite Girder – a steel flexural member connected to a concrete slab so that the 

steel element and the concrete slab, or the longitudinal reinforcement within the slab, 

respond to force effects as a unit

Compression – a type of stress involving pressing together; tends to shorten a member; 

opposite of tension

Compression Failure - buckling, crushing, or collapse cause by compression stress
Engineering for Structural Stability in Bridge Construction Reference Manual

G.4

Compression Flange – the part of a beam that is compressed due to a bending 

moment.

Concentrated Load – a force applied over a small contact area; also known as a point 

load

Connection Angle – a piece of angle serving to connect two elements of a member or 

two members of a structure; also known as a clip angle

Construction Joint – a pair of adjacent surfaces in reinforced concrete where two pours 

meet; reinforcement steel extends through this joint

Continuous Beam – a general term applied to a beam that spans uninterrupted over one 

or more intermediate supports

Continuous Bridge – a bridge designed to extend without joints over one or more interior 

supports

Continuous Span – spans designed to extend without joints over one or more 

intermediate supports

Continuously Braced Flange – a flange encased in concrete or anchored by shear 

connectors for which flange lateral bending effects need not be considered. A 

continuously braced flange in compression is also assumed not to be subject to local or 

lateral torsional buckling.

Cracked Section – a composite section in which the concrete is assumed to carry no 

tensile strength

Creep – time-dependent deformation of concrete under permanent load

Cross-Frame – a transverse truss framework connecting adjacent longitudinal flexural 

components or inside a tub section or closed box used to transfer and distribute vertical 

and lateral loads and provide stability to the compression flanges. Sometimes 

synonymous with the term diaphragm.

Cross-Section - the shape of an object cut transversely to its length

Cross-Section Distortion – change in shape of the cross-section profile due to torsional 

loading

Cross-Sectional Area - the area of a cross-section 

Curved Girder – an I-, closed-box or tub girder that is curved in a horizontal plane

Deck – a component, with or without wearing surface, directly supporting wheel loads
Engineering for Structural Stability in Bridge Construction Reference Manual

G.5

Deformation – a change in structural geometry due to force effects, including axial 

displacement, shear displacement and rotations

Degree-of-Freedom – one of a number of translations or rotations required to define the 

movement of a node. The displaced shape of components and/or the entire structure 

may be defined by a number of degrees-of-freedom

Design Load - the force for which a structure is designed; the most severe combination 

of loads

Diagonal - a sloping structural member of a truss or bracing system

Diagonal Stay - a cable support in a suspension bridge extending diagonally from the 

tower to the roadway to add stiffness to the structure and diminish the deformations and 

undulations resulting from traffic service

Diagonal Tension - the tensile force due to horizontal and vertical shear in a beam

Diaphragm - a vertically oriented solid transverse member connecting adjacent 

longitudinal flexural components or inside a closed box or tub section to transfer and 

distribute vertical and lateral loads and to provide stability to the compression flanges

Disc Bearing – A bearing that accommodates rotation by deformation of a single 

elastomeric disc molded from a urethane compound. It may be movable, guided, 

unguided, or fixed. Movement is accommodated by sliding of polished stainless steel or 

PFTE

Differential Deflection - Non-uniform deflection of adjacent girders; i.e., when one girder 

deflects a greater amount than an adjacent girder

Differential Settlement - uneven settlement of individual or independent elements of a 

substructure; tilting in the longitudinal or transverse direction due to deformation or loss 

of foundation material

Discretely Braced Flange – a flange supported at discrete intervals by bracing sufficient 

to restrain lateral deflection of the flange and twisting of the entire cross-section at the 

brace points

Drift Bolt - a short length of metal bar used to connect and hold in position wooden 

members placed in contact; similar to a dowel

Drift Pin - tapered steel rod used by ironworkers to align bolt holes

Ductile - capable of being molded or shaped without breaking; plastic

Ductile Fracture - a fracture characterized by plastic deformation
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Effective Depth – the depth of a component effective in resisting flexural or shear forces

Effective Length – the equivalent length KL used in compression formulas and 

determined by a bifurcation analysis.

Effective Prestress – the stress or force remaining in the prestressing steel after all 

losses have occurred

Effective Width – the reduced width of a plate or concrete slab which, with an assumed 

uniform stress distribution, produces the same effect on the behavior of a structural 

member as the actual plate width with its nonuniform stress distribution

Eigenvalue – a value used to represent the factor that is applied to the reference load to 

determine the critical buckling load

Elastic - capable of sustaining deformation without permanent loss of shape

Elastic Analysis – determination of load effects on members and connections based on 

the assumption that the material stress-strain response is linear and the material 

deformation disappears on removal of the force that produced it

Elastic Deformation - non-permanent deformation; when the stress is removed, the 

material returns to its original shape

Elastic Limit – the point at which the structural member will begin to permanently deform 

under load

Elasticity - the property whereby a material changes its shape under the action of loads 

but recovers its original shape when the loads are removed

Elongation - the elastic or plastic extension of a member

Embedment Length – the length of reinforcement or anchor provided beyond a critical 

section over which transfer of force between concrete and reinforcement may occur

End Post - the end compression member of a truss, either vertical or inclined in position 

and extending from top chord to bottom chord

End Span - a span adjacent to an abutment

Engineer of Record – registered licensed professional responsible for the design of the 

structure

Equilibrium – a state where the sum of forces and moments about any point in space is 

0.0
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Equivalent Uniform Load - a load having a constant intensity per unit of its length 

producing an effect equal to that of a live load consisting of vehicle axle or wheel 

concentrations spaced at varying distances

Failure - a condition at which a structure reaches a limit state such as cracking or 

deflection where it is no longer able to perform its usual function; collapse; fracture

Falsework - a temporary wooden or metal framework built to support the weight of a 

structure during the period of its construction and until it becomes self-supporting

Fascia - an outside, covering member designed on the basis of architectural effect 

rather than strength and rigidity, although its function may involve both

Fascia Girder - an exposed outermost girder of a span sometimes treated architecturally 

or otherwise to provide an attractive appearance

Filler - a piece used primarily to fill a space beneath a batten, splice plate, gusset, 

connection angle, stiffener or other element; also known as filler plate

Finite Element Method – a method of analysis in which a structure is discretized into 

elements connected at nodes, the shape of the element displacement field is assumed, 

partial or complete compatibility is maintained among the element interfaces, and nodal 

displacements are determined by using energy variational principles or equilibrium 

methods

First-Order Analysis – analysis in which equilibrium conditions are formulated on the 

undeformed structure; that is, the effect of deflections is not considered in writing 

equations of equilibrium

Fixed Bearing – a bearing that prevents differential longitudinal translation of abutting 

structural elements. It may or may not provide for differential lateral translation or 

rotation

Flange Lateral Bending – bending of a flange about an axis perpendicular to the flange 

plane due to lateral loads applied to the flange and/or non-uniform torsion in the 

member.

Flange Lateral Bending Stress – the normal stress caused by flange lateral bending

Flexural Buckling – a buckling mode in which a compression member deflects laterally 

without twist or change in cross-sectional shape

Flexural-Torsional Buckling – a buckling mode in which a compression member bends 

and twists simultaneously without a change in cross-sectional shape
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Floorbeam – a primary horizontal member located transversely to the general bridge 

alignment

Floor System - the complete framework of members supporting the bridge deck and the 

traffic loading

Forms - the molds that hold concrete in place while it is hardening; also known as form 

work

Fracture Critical Member (FCM) - a steel member in tension, or with a tension element, 

whose failure would probably cause a portion of or the entire bridge to collapse

Frame - a structure which transmits bending moments from the horizontal beam 

member through rigid joints to vertical or inclined supporting members

Framing - the arrangement and connection of the component members of a bridge 

superstructure

Free End - movement is not restrained

Girder Radius – the radius of the circumferential centerline of a segment of a curved 

girder

Global Analysis – analysis of a structure as a whole

Global Stability – the stability of an entire structural system in terms of resistance to 

buckling (as opposed to the stability of an individual girder or other element within a 

structural system in terms of resistance to local buckling of that girder or element)

Grillage Analogy Method – a method of analysis in which all or part of the 

superstructure is discretized into orthotropic components that represent the 

characteristics of the structure

Gusset Plate – plate material used to interconnect vertical, diagonal and horizontal truss 

members at a panel point

Hanger - a tension member serving to suspend an attached member; allows for 

expansion between a cantilevered and suspended span

Haunch - an increase in the depth of a member usually at points of support; the outside 

areas of a pipe between the spring line and the bottom of the pipe

Haunched Girder - a horizontal beam whose cross-sectional depth varies along its 

length
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H-Beam - a rolled steel member having an H-shaped cross-section (flange width equals 

beam depth) commonly used for piling; also H-pile

Hinge - a point in a structure at which a member is free to rotate

Hinged Joint – a joint constructed with a pin, cylinder segment, spherical segment or 

other device permitting rotational movement

Holding Crane – a crane used to provide a temporary vertical support to a girder during 

erection

Horizontal Alignment - a roadway's centerline or baseline alignment in the horizontal 

plane

Horizontal Curve - a roadway baseline or centerline alignment defined by a radius in the 

horizontal plane

I-Beam - a structural member with a cross-sectional shape similar to the capital letter "I"

Inelastic – any structural behavior in which the ratio of stress and stain is not constant, 

and part of the deformation remains after load removal

Inelastic Redistribution – the redistribution of internal force effects in a component or 

structure caused by inelastic deformations at one or more sections

Instability – a condition reached in the loading of a component or structure in which 

continued deformation results in a decrease of load-resisting capacity

Integral Bridge - a bridge without deck joints

Interior Girder - any girder between exterior or fascia girders

Jacking - the lifting of elements using a type of jack (e.g., hydraulic), sometimes acts as 

a temporary support system

Jacking Force – the force exerted by the device that introduces tension into the tendons

Knee Brace - a short member engaging at its ends two other members that are joined to 

form a right angle or a near-right angle to strengthen and stiffen the connecting joint

Large Deflection Theory – any method of analysis in which the effects of deformation 

upon force effects is taken into account

Lateral Bending Stress – the normal stress caused by flange lateral bending
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Lateral Bracing – a truss placed in a horizontal plane between two I-girders or two 

flanges of a tub girder to maintain cross-sectional geometry and provide additional 

stiffness and stability to the bridge system

Lateral Torsional Buckling – buckling of a component subject to compression involving 

lateral deflection and twist

Leaf - the movable portion of a bascule bridge that forms the span of the structure

Lightweight Concrete – concrete containing lightweight aggregate and having an air-dry 

unit weight not exceeding 0.120 kcf, as determined by ASTM C567. Lightweight 

concrete without natural sand is termed “all-lightweight concrete” and lightweight 

concrete in which all of the fine aggregate consists of normal weight sand is termed 

“sand-lightweight concrete.”

Linear Response – structural behavior in which deflections are directly proportional to 

loads

Load Buckling – the buckling of a plate element in compression

Load Factor Design - a design method used by AASHTO, based on limit states of 

material and arbitrarily increased loads

Load And Resistance Factor Design (LRFD) - design method used by AASHTO, based 

on limit states of material with increased loads and reduced member capacity based on 

statistical probabilities

Local Buckling - localized buckling of a component subject to compression

Loss of Prestress - loss of prestressing force due to a variety of factors, including 

shrinkage and creep of the concrete, creep of the prestressing tendons, and loss of 

bond

Member - an individual angle, beam, plate, or built component piece intended ultimately 

to become an integral part of an assembled frame or structure

Metal Rocker or Roller Bearing - a bearing that carries vertical load by direct contact 

between two metal surfaces and that accommodates movement by rocking or rolling of 

one surface with respect to the other

Moment of Inertia - the sum of each area in a section times the distance between the 

centroid of that area and the axis under consideration squared

Movable Bridge - a bridge having one or more spans capable of being raised, turned, 

lifted, or slid from its normal service location to provide a clear navigation passage
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Movable Span - a general term applied to a superstructure span designed to be swung, 

lifted or otherwise moved longitudinally, horizontally or vertically, usually to provide 

increased navigational clearance

Multirotational Bearing - a bearing consisting of a rotational element of the pot type, disc 

type, or spherical type when used as a fixed bearing and that may, in addition, have 

sliding surfaces to accommodate translation when used as an expansion bearing. 

Translation may be constrained to a specified direction by guide bars

Negative Moment – moment producing tension at the top of a flexural element

Noncompact Flange – for a composite section in negative flexure or a noncomposite 

section, a discretely braced compression flange with a slenderness at or below the limit 

at which localized yielding within the member cross-section associated with a hybrid 

web, residual stresses and/or cross-section monosymmetry has a statistically significant 

effect on the nominal flexural resistance

Noncompact Section – a composite section in positive flexure for which the nominal 

resistance is not permitted to exceed the moment at first yield

Noncompact Unbraced Length – for a composite section in negative flexure or a 

noncomposite section, the limiting unbraced length of a discretely braced compression 

flange at or below the limit at which the onset of yielding in either flange of the crosssection with consideration of compression-flange residual stress effects has a 

statistically significant effect on the nominal flexural resistance.

Nonlinear Response – structural behavior in which the deflections are not directly 

proportional to the loads due to stresses in the inelastic range, or deflections causing 

significant changes in force effects, or by a combination thereof

Nonuniform Torsion – an internal resisting torsion in thin-walled sections, also known as 

warping torsion, producing shear stress and normal stresses, and under which crosssections do not remain plane. Members resist the externally applied torsion by warping 

torsion and St. Venant torsion. Each of these components of internal resisting torsions 

varies along the member length, although the externally applied concentrated torque 

may be uniform along the member between two adjacent points of torsional restraint. 

Warping torsion is dominant over St. Venant torsion in members having open crosssections, whereas St. Venant torsion is dominant over warping torsion in members 

having closed cross-sections. 

Normal Weight Concrete – concrete having a weight between 0.135 and 0.155 kcf.

Pier - a substructure unit that supports the spans of a multi-span superstructure at an 

intermediate location between its abutments
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Pier Cap - the topmost horizontal portion of a pier that distributes loads from the 

superstructure to the vertical pier elements

Pile - a shaft-like linear member which carries loads to underlying rock or soil strata

Pile Bent - a row of driven or placed piles extending above the ground surface 

supporting a pile cap

Pile Cap - a slab or beam which acts to secure the piles in position laterally and 

provides a bridge seat to receive and distribute superstructure loads

Pin - a cylindrical bar used to connect elements of a structure

Pin-Connected Truss - a general term applied to a truss of any type having its chord 

and web members connected at each panel point by a single pin

Pin and Hanger - a hinged connection detail designed to allow for expansion and 

rotation between a cantilevered and suspended span at a point between supports.

Pintle - a relatively small steel pin engaging the rocker of an expansion bearing, in a 

sole plate or masonry plate, thereby preventing sliding of the rocker

Plate Girder - a large I-shaped beam composed of a solid web plate with flange plates 

attached to the web plate by flange angles or fillet welds

Point of Contraflexure – the point where the sense of the flexural moment changes; 

synonymous with point of inflection

Positive Moment – moment producing tension at the bottom of a flexural element

Post-Tensioning – a method of prestressing in which the tendons are tensioned after 

the concrete has reached a predetermined strength

Post-Tensioning Duct – a form device used to provide a path for post-tensioning 

tendons or bars in hardened concrete

Pot Bearing - a bearing type that allows for multi-dimensional rotation by using a piston 

supported on an elastomer contained on a cylinder, the pot, or spherical bearing 

element

Precast Concrete - concrete members that are cast and cured before being placed into 

their final positions on a construction site

Prestressed Concrete – concrete components in which stresses and deformations are 

introduced by application of prestressing force
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Prestressing - applying forces to a structure to deform it in such a way that it will 

withstand its working loads more effectively

Pretensioning - a method of prestressing concrete in which the strands are stressed 

before the concrete is placed; strands are released after the concrete has hardened, 

inducing internal compression into the concrete

Primary Member - a member designed to resist flexure and distribute primary live loads 

and dead loads

Professional Engineer (PE) - an individual, who has fulfilled education and experience 

requirements and passed rigorous exams that, under State licensure laws, permits them 

to offer engineering services directly to the public. Engineering licensure laws vary from 

State to State, but, in general, to become a PE an individual must be a graduate of an 

engineering program accredited by the Accreditation Board for Engineering and 

Technology, pass the Fundamentals of Engineering exam, gain four years of 

experience working under a PE, and pass the Principles of Practice of Engineering 

exam

Redistribution of Moments – a process that results from formation of inelastic 

deformations in continuous structures

Refined Methods of Analysis – methods of structural analysis that consider the entire 

superstructure as an integral unit and provide the required deflections and actions.

Reinforced Concrete - concrete with steel reinforcing bars embedded in it to supply 

increased tensile strength and durability

Reinforcing Bar - a steel bar, plain or with a deformed surface, which bonds to the 

concrete and supplies tensile strength to the concrete

Residual Stresses – stresses locked into the cross-section typically caused during 

manufacturing or fabrication 

Rocker Bearing - a bridge support that accommodates expansion and contraction of the 

superstructure through a tilting action

Rolled Shape - forms of rolled steel having I, H, C, Z or other cross-sectional shapes

Roller Bearing - a single roller or a group of rollers so installed as to permit longitudinal 

movement of a structure

Safety Factor - the difference between the ultimate strength of a member and the 

maximum load it is expected to carry

Sag - to sink or bend downward due to weight or pressure
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Seat - a base on which an object or member is placed

Seat Angle - a piece of angle attached to the side of a member to provide support for a 

connecting member either temporarily during its erection or permanently; also known as 

a shelf angle

Second-Order Analysis – analysis in which equilibrium conditions are formulated on the 

deformed structure; that is, in which the deflected position of the structure is used in 

writing the equations of equilibrium

Secondary Member - a member that does not carry calculated loads; bracing members

Settlement - the movement of substructure elements due to changes in the soil 

properties

Shear - the load acting across a beam near its support

Shear Connectors - devices that extend from the top flange of a beam and are 

embedded in the above concrete slab, forcing the beam and the concrete to act as a 

single unit

Shear Stress - the shear force per unit of cross-sectional area

Shop Drawings - detailed drawings developed from the more general design drawings 

used in the manufacture or fabrication of bridge components

Skew Angle - the angle produced when the longitudinal members of a bridge are not 

perpendicular to the substructure; the skew angle is the acute angle between the 

alignment of the bridge and a line perpendicular to the centerline of the substructure 

units

Slab - a wide beam, usually of reinforced concrete, which supports load by flexure

Slab Bridge - a bridge having a superstructure composed of a reinforced concrete slab 

constructed either as a single unit or as a series of narrow slabs placed parallel with the 

roadway alignment and spanning the space between the supporting substructure units

Slenderness Ratio – the ratio of the effective length of a member to the radius of 

gyration of member cross-section, both with the respect to the same axis of bending, or 

the full or partial width or depth of a component divided by its thickness

Small Deflection Theory – a basis for methods of analysis where the effects of 

deformation upon force effects in the structure is neglected

Sole Plate - a plate attached to the bottom flange of a beam that distributes the reaction 

of the bearing to the beam
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Span - the distance between the supports of a beam; the distance between the faces of 

the substructure elements; the complete superstructure of a single span bridge or a 

corresponding integral unit of a multiple span structure

Specifications - a detailed description of requirements, materials, tolerances, etc., for 

construction which are not shown on the drawings; also known as specs

Splice – a group of bolted connections, or a welded connection, sufficient to transfer the 

moment, shear, axial force, or torque between two structural elements joined at their 

ends to form a single, longer element

Spliced Precast Girder – a type of superstructure in which precast concrete beam-type 

elements are joined longitudinally, typically using post-tensioning, to form the completed 

girder. The bridge cross-section is typically a conventional structure consisting of 

multiple precast girders. This type of construction is not considered to be segmental 

construction.

St. Venant Torsion – that portion of the internal resisting torsion in a member producing 

only pure shear stresses on a cross-section; also referred to as pure torsion or uniform 

torsion

Stability Limit States – the limit states that often control the design of members subject 

to compression in steel structures. These limit states include local buckling, lateral 

torsional buckling and global buckling 

Staged Construction - construction performed in phases, usually to permit the flow of 

traffic

Stay-In-Place Formwork – permanent metal or precast concrete forms that remain in 

place after construction is finished

Steel-Reinforced Elastomeric Bearing – A bearing made from alternate laminates of 

steel and elastomer bonded together during vulcanization. Vertical loads are carried by 

compression of the elastomer. Movements parallel to the reinforcing layers and 

rotations are accommodated by deformation of the elastomer

Stiffener – a member, usually an angle or plate, attached to a plate or web of a beam or 

girder to distribute load, to transfer shear, or to prevent buckling of the member to which 

it is attached

Stiffening Girder - a girder incorporated in a suspension bridge to distribute the traffic 

loads uniformly among the suspenders and reduce local deflections

Stiffening Truss - a truss used to increase the stability of a girder during lifting
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Stirrup - U-shaped bar used as a connection device in timber and metal bridges; Ushaped bar placed in concrete to resist diagonal tension (shear) stresses

Strain - the change in length of a body produced by the application of external forces, 

measured in units of length; this is the proportional relation of the amount of change in 

length divided by the original length

Stress - the force acting across a unit area in a solid material

Stress Concentration - local increases in stress caused by a sudden change of crosssection in a member

State Transportation Department - that department, commission, board, or official of any 

State charged by its laws with the responsibility for highway construction

Stringer - a longitudinal beam spanning between transverse floorbeams and supporting 

a bridge deck

Strongback – a structural element, usually located above the supported member, that 

provides supplemental support to the structure

Structural Member - an individual piece, such as a beam or strut, which is an integral 

part of a structure

Structural Stability - the ability of a structure to maintain its normal configuration, not 

collapse or tip in any way, under existing and expected loads

Strut - a member acting to resist axial compressive stress; usually a secondary member

Substructure - the abutments and piers built to support the span of a bridge 

superstructure

Superelevation - the difference in elevation between the inside and outside edges of a 

roadway in a horizontal curve; required to counteract the effects of centrifugal force

Superimposed Dead Load - dead load that is applied to a compositely designed bridge 

after the concrete deck has cured; for example, the weight of parapets or railings placed 

after the concrete deck has cured

Superstructure - the entire portion of a bridge structure that primarily receives and 

supports traffic loads and in turn transfers these loads to the bridge substructure 

Suspended Span - a simple span supported from the free ends of cantilevers

Suspension Bridge - a bridge in which the floor system is supported by catenary cables 

that are supported upon towers and are anchored at their extreme ends
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Sway Bracing – transverse vertical bracing between truss members

Sweep – an out of plane imperfection from a member’s perfect geometry

Tee Beam - a rolled steel section shaped like a T; reinforced concrete beam shaped like 

the letter T

Temperature Steel - reinforcement in a concrete member to prevent cracks due to 

stresses caused by temperature changes

Tendon - a prestressing cable, strand, or bar

Tensile Force - a force caused by pulling at the ends of a member

Tensile Strength - the maximum tensile stress at which a material fails

Tension - stress that tends to pull apart material

Thermal Movement - contraction and expansion of a structure due to a change in 

temperature

Tie - a member carrying tension

Tie Plate - relatively short, flat member carrying tension forces across a transverse 

member; for example, the plate connecting a floor beam cantilever to the main floor 

beam on the opposite side of a longitudinal girder

Tie Rod - a rod-like member in a frame functioning to transmit tensile stress; also known 

as tie bar

Tied Arch – an arch in which the horizontal thrust of the arch rib is resisted by a 

horizontal tie

Torque - the angular force causing rotation

Torsion - twisting about the longitudinal axis of a member

Torsional Buckling – a buckling mode in which a compression member twists about its 

shear center

Torsional Rigidity - a beam's capacity to resist a twisting force along the longitudinal 

axis

Torsional Shear Stress – shear stress induced by St. Venant torsion
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Transverse Bracing - the bracing assemblage engaging the columns of bents and 

towers in planes transverse to the bridge alignment that resists the transverse forces 

tending to produce lateral movement and deformation of the columns

True Arch – an arch in which the horizontal component of the force in the arch rib is 

resisted by an external force supplied by its foundation

Truss – a system of members comprising a series of triangles that distribute the load by 

creating tension and compression in the members rather than bending 

Tub Section – an open-topped section which is composed of a bottom flange, two 

inclined or vertical webs and top flanges

Tubular Sections - structural steel tubes, rectangular, square or circular; also known as 

hollow sections

Turnbuckle - a long, cylindrical, internally threaded nut with opposite hand threads at 

either end used to connect the elements of adjustable rod and bar members

U-Bolt - a bar bent in the shape of the letter "U" and fitted with threads and nuts at its 

ends

Ultimate Strength - the highest stress that a material can withstand before breaking

Unbraced Length – distance between brace points resisting the mode of buckling or 

distortion under consideration; generally, the distance between panel points or brace 

locations

Uncracked Section – a section in which the concrete is assumed to be fully effective in 

tension and compression

Uniform Load - a load of constant magnitude along the length of a member

Uplift - a negative reaction or a force tending to lift a beam, truss, pile, or any other 

bridge element upwards off of a bearing or support

Upper Chord - the top longitudinal member of a truss

Vertical - describes the axis of a bridge perpendicular to the underpass surface

Vertical Alignment - a roadway's centerline or baseline alignment in the vertical plane

Warping – distortion of the cross-section from torsion

Warping Stress – normal stress induced in the cross-section by warping torsion and/or 

by distortion of the cross-section 
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Warping Torsion – that portion of the total resistance to torsion in a member producing 

shear and normal stresses that is provided by resistance to out-of-plane warping of the 

cross-section 

Web Crippling – the local failure of a web plate in the immediate vicinity of a 

concentrated load or bearing reaction due to the transverse compression introduced by 

this load

Web Members - the intermediate members of a truss, not including the end posts, 

usually vertical or inclined

Web Plate - the plate forming the web element of a plate girder, built-up beam or 

column

Wide Flange - a rolled I-shaped member having flange plates of rectangular crosssection, differentiated from an S-beam (American Standard) in that the flanges are not 

tapered

Working Stress - the unit stress in a member under service or design load

Working Stress Design - a method of design using the yield stress of a material and a 

factor of safety that determine the maximum allowable stresses

Yield Strength – the stress at which a material exhibits a specified limiting deviation 

from the proportionality of stress to strain

Yield Stress - the stress at which noticeable, suddenly increased deformation occurs 

under slowly increasing load