Publication No. FHWA-NHI-16-016 

December 2016 

NHI Course No. 130122 

Design and Evaluation of Steel Bridges for 

Fatigue and Fracture

REFERENCE MANUAL
FOREWORD

This Manual covers a full range of topics related to fatigue and fracture in steel bridges, 

including analysis, design, evaluation, repair, and retrofit. The information presented is intended 

to expound and complement the same topics covered in AASHTO’s LRFD Bridge Design 

Specifications and Manual for Bridge Evaluation. The hard and competent work of the Michael 

Baker International and the authors, Francesco M. Russo, Ph.D., P.E., Dennis R. Mertz, Ph.D., 

P.E., Karl H. Frank, Ph.D., P.E., Kenneth E. Wilson, P.E., S.E., in producing this Manual is 

gratefully acknowledged. 

The contributions and constructive review comments received during the preparation of the 

handbook from many bridge engineering professionals across the country are very much 

appreciated. In particular, I would like to recognize the contributions of Matt Farrar of the Idaho 

Transportation Department, Greg Perfetti and David Snoke of the North Carolina Department of 

Transportation and John Hastings of the Tennessee Department of Transportation. 

Finally, I would like to single out and again recognize Dennis Mertz who passed away prior to 

the publication of this Manual. Dennis was a colleague, mentor and friend to many across the 

nation in the bridge design and construction industry. His knowledge, counsel, industry and wit

will be missed. 

Joseph L. Hartmann, Ph.D., P.E. 

Director, Office of Bridges and Structures

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

(USDOT) in the interest of information exchange. The U.S. Government assumes no liability for 

the use of the information contained in this document.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ 

names appear in this report only because they are considered essential to the objective of the 

document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

Technical Report Documentation Page

1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No.

FHWA-NHI-16-016 FHWA-NHI-16-016

4. Title and Subtitle

Design and Evaluation of Steel Bridges for Fatigue and Fracture – Reference

Manual

5. Report Date

December 2016

6. Performing Organization Code

FHWA/DTS-NHI-1

7. Author (s)

Francesco M. Russo, Ph.D., P.E., Dennis R. Mertz, Ph.D., P.E., Karl H. Frank,

Ph.D., P.E., Kenneth E. Wilson, P.E., S.E.

8. Performing Organization Report No.

MBRM143222

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

Michael Baker International

Airside Business Park, 100 Airside Drive 11. Contract or Grant No. 

Moon Township, PA 15108 DTFH61-11-D-00046

12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered

Federal Highway Administration Final Submission

National Highway Institute (HNHI-10) October 2014 – December 2016

1310 North Courthouse Road 14. Sponsoring Agency Code

Arlington, VA 22201 FHWA

15. Supplementary Notes

FHWA Contracting Officer’s Representative: Melonie Barrington, P.E., PMP

FHWA Technical Manager: Brian M. Kozy, Ph.D., P.E.

Michael Baker Principal Investigator: Mary P. Rosick, P.E.

Michael Baker Project Manager: Kenneth E. Wilson, P.E., S.E., PMP

16. Abstract

This Manual explains the relevant issues related to fatigue and fracture in steel bridges, including analysis, design,

evaluation, repair, and retrofit. Chapter 1 provides an introduction to fatigue and fracture, as well as an introduction to

the Reference Manual. Chapter 2 begins with a discussion of cracking in steel structures, including crack behavior,

sources of discontinuities in steel structures, the nature of stresses affecting fatigue and fracture, and brittle and ductile

behavior in steel. Chapter 3 provides the basics of fracture mechanics, covering such topics as fracture control,

evaluation of fatigue cracking, and fracture mechanics as a quantitative tool. Chapter 4 describes fatigue behavior,

including discontinuities and stress concentrations, the influence of production and fabrication on fatigue, testing as the

basis for design limits, and environmental effects. Chapter 5 describes analysis for fatigue, and it provides information

for both approximate and refined analysis methods, including local-stress analysis. Chapter 6 addresses the fatigue

design approach as presented in the AASHTO LRFD Bridge Design Specifications, and it explains the fundamental

fatigue limit state equation, the various AASHTO fatigue detail categories, the differences between finite life and infinite

life, and the computation of fatigue stress range and factored nominal resistance, including a step-by-step design

example for fatigue. Chapter 7 describes fracture control, including design, fabrication, and inspection, and it covers

such topics as redundancy, constraint-induced fracture, and the Total Fracture Control Plan. Chapter 8 addresses the

AASHTO fatigue-evaluation approach, including remaining fatigue life evaluation, estimates of fatigue life based on the

AASHTO Manual for Bridge Evaluation, and remaining fatigue life for “negative remaining life” bridge details. Chapter

9 describes assessment, repair, and retrofit of structures, and it provides a description of several common fatigue details,

general repair and retrofit strategies, as well as constraint-induced fracture, over-height vehicle collisions, and fitnessfor-service analysis. Finally, Chapter 10 covers non-welded components such as built-up members, bolts and rods, and

reinforcement of concrete. In addition, Appendix A describes fatigue calibration based on the SHRP2 Project R19B.

17. Key Words 18. Distribution Statement

Fatigue, Fracture, Cracking, Fracture Control Plan,

Loads, Resistance, Analysis, Design, Evaluation,

Retrofit, Repair, Stress Range, Residual Stress, Cycles,

Brittle, Ductile, Toughness, Discontinuity, Weld,

Fatigue Details, Fatigue Life, Finite Life, Infinite Life

This report is available to the public from the NHI 

Bookstore at 

http://www.nhi.fhwa.dot.gov/training/nhistore.aspx

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price

Unclassified Unclassified 310 

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

SI* (MODERN METRIC) CONVERSION FACTORS 

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 Celsius o

C 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx 

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce 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 o

F 

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 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

TOC.1 

Table of Contents

Chapter 1 Background and Organization of the Manual.................1.1

Section 1.1 Introduction ............................................................................................... 1.1

1.1.1 Historical Perspective ...........................................................................................1.1

1.1.2 Evolution of Fatigue and Fracture Design, Evaluation, and Inspection Approaches

1.4

Section 1.2 Scope of Reference Manual and Presentation of Major Themes......... 1.13

1.2.1 Physical Phenomena of Cracking .......................................................................1.14

1.2.2 Fatigue Stress ....................................................................................................1.14

1.2.3 Fatigue Resistance.............................................................................................1.15

1.2.4 Fatigue and Fracture Control ..............................................................................1.15

1.2.5 Retrofit Strategies...............................................................................................1.16

Chapter 2 Cracking in Steel Structures............................................2.1

Section 2.1 Crack Behavior.......................................................................................... 2.1

2.1.1 Necessary Conditions...........................................................................................2.1

2.1.2 Crack-growth Regimes .........................................................................................2.1

Section 2.2 Sources of Discontinuities in Steel Structures....................................... 2.4

2.2.1 Production ............................................................................................................2.4

2.2.2 Fabrication............................................................................................................2.4

Section 2.3 Stress ......................................................................................................... 2.8

2.3.1 Sustained Stress...................................................................................................2.9

2.3.2 Cyclical Stress ....................................................................................................2.11

2.3.3 Stress Concentrations from Details.....................................................................2.12

Section 2.4 Material Behavior .................................................................................... 2.13

2.4.1 Brittle versus Ductile Behavior ............................................................................2.13

2.4.2 Effects of Temperature and Strain Rates ............................................................2.17

Chapter 3 Theory ...............................................................................3.1

Section 3.1 General....................................................................................................... 3.1

Section 3.2 Accounting for a Crack ............................................................................. 3.1
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Section 3.3 Principles of Fracture Control.................................................................. 3.5

3.3.1 Material Toughness ..............................................................................................3.5

3.3.2 Effect of Critical Crack Size upon Inspection.........................................................3.7

3.3.3 Assurance through CVN Toughness Requirements..............................................3.8

Section 3.4 Paris’ Law and Miner’s Rule ................................................................... 3.10

Section 3.5 Fracture Mechanics as a Quantitative Tool........................................... 3.12

Chapter 4 Fatigue Behavior ..............................................................4.1

Section 4.1 The Influence of Production and Fabrication.......................................... 4.1

4.1.1 Materials and Processing......................................................................................4.1

4.1.2 Discontinuities at Welded Joints ...........................................................................4.3

4.1.3 Weld Residual Stresses........................................................................................4.6

4.1.4 Bolting and Riveting............................................................................................4.12

4.1.5 Cold Bending ......................................................................................................4.13

4.1.6 Hot Bending........................................................................................................4.14

4.1.7 Heat Straightening Repairs.................................................................................4.15

Section 4.2 Stress Parameters Influencing Fatigue ................................................. 4.16

4.2.1 Effect of Minimum Stress ....................................................................................4.17

4.2.2 Effect of Steel Yield Strength ..............................................................................4.18

4.2.3 Consideration of Variable Amplitude Fatigue Loading.........................................4.19

Section 4.3 Testing as the Basis for Design Limits.................................................. 4.23

4.3.1 Development of Design Limits for Finite Life.......................................................4.23

4.3.2 Development of Design Limits for Infinite Life .....................................................4.27

4.3.3 Testing to Establish the Fatigue Resistance of Special Elements .......................4.29

Section 4.4 Environmental Effects............................................................................. 4.29

4.4.1 Weathering Steel ................................................................................................4.30

4.4.2 Corrosion Effects on Fatigue Life........................................................................4.31

Section 4.5 Summary.................................................................................................. 4.35

Chapter 5 Analysis for Fatigue .........................................................5.1

Section 5.1 General....................................................................................................... 5.1

Section 5.2 Load-Induced vs. Distortion-Induced Fatigue......................................... 5.1
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

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Section 5.3 Global Analysis ......................................................................................... 5.2

5.3.1 Approximate Analysis ...........................................................................................5.2

5.3.2 Refined Analysis ...................................................................................................5.9

Section 5.4 Fatigue Stress Analysis .......................................................................... 5.10

5.4.1 Nominal-Stress Approach ...................................................................................5.10

5.4.2 Local-Stress Approach........................................................................................5.11

5.4.3 Fracture-Mechanics Approach............................................................................5.17

Chapter 6 AASHTO Fatigue Design Approach ................................6.1

Section 6.1 General....................................................................................................... 6.1

6.1.1 The Fatigue Limit State.........................................................................................6.1

Section 6.2 Classification of Fatigue ........................................................................... 6.3

Section 6.3 Load-Induced Fatigue ............................................................................... 6.5

6.3.1 General Limit State...............................................................................................6.5

6.3.2 Applicability.........................................................................................................6.15

6.3.3 Infinite Life – The Fatigue I Load Combination....................................................6.15

6.3.4 Finite Life – The Fatigue II Load Combination.....................................................6.18

6.3.5 Calibration of the Fatigue Limit State ..................................................................6.22

6.3.6 Special Details and Provisions for Other Structure Types ...................................6.24

Section 6.4 Distortion-Induced Fatigue..................................................................... 6.46

Section 6.5 Step-by-Step Application of LRFD Fatigue Design............................... 6.50

6.5.1 Determine Locations Requiring Fatigue Limit State Verification (Step 1) ............6.50

6.5.2 Compute Force Effects (Step 2)..........................................................................6.50

6.5.3 Calculate Stress Ranges at Fatigue Details (Step 3) ..........................................6.54

6.5.4 Calculate Fatigue Resistance (Step 4)................................................................6.56

Section 6.6 Example Problem of Fatigue Design...................................................... 6.57

6.6.1 Determine Locations Requiring Fatigue Limit State Verification (Step 1) ............6.58

6.6.2 Compute Force Effects (Step 2)..........................................................................6.58

6.6.3 Calculate Stress Ranges at Fatigue Details (Step 3) ..........................................6.59

6.6.4 Calculate Fatigue Resistance (Step 4)................................................................6.59

Chapter 7 Fracture Control ...............................................................7.1

Section 7.1 Historical Development of Fracture Control Practices........................... 7.1
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

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Section 7.2 Fracture Control by Design ...................................................................... 7.4

7.2.1 Charpy V-Notch Requirements for Primary Members ...........................................7.5

7.2.2 Fracture Critical Members.....................................................................................7.7

7.2.3 Selection of Materials..........................................................................................7.11

7.2.4 Detailing to Avoid Constraint...............................................................................7.15

Section 7.3 Fracture Control By Enhanced Fabrication........................................... 7.29

7.3.1 Fabrication Controls............................................................................................7.31

Section 7.4 Fracture Control By In-Service Inspection............................................ 7.32

Chapter 8 AASHTO Fatigue-Evaluation Approach ..........................8.1

Section 8.1 Identifying the Nature of Cracking........................................................... 8.1

8.1.1 Load-Induced Fatigue...........................................................................................8.1

8.1.2 Distortion-Induced Fatigue....................................................................................8.2

Section 8.2 Remaining Fatigue Life Evaluation .......................................................... 8.2

8.2.1 Estimating the Stress Range.................................................................................8.3

Section 8.3 Estimating Fatigue Life by the MBE......................................................... 8.6

8.3.1 Infinite-Life Check ................................................................................................. 8.6

8.3.2 Finite Life..............................................................................................................8.7

8.3.3 Example ...............................................................................................................8.9

Section 8.4 Remaining Fatigue Life for “Negative Remaining Life” Bridge Details

8.10

8.4.1 General...............................................................................................................8.10

8.4.2 Fatigue Serviceability Index, Q ...........................................................................8.10

8.4.3 Strategies to Increase the Fatigue Serviceability Index.......................................8.12

Chapter 9 Assessment, Repair, and Retrofit of Structures.............9.1

Section 9.1 Common Fatigue Details .......................................................................... 9.1

9.1.1 Web Gaps Associated with Out-of-Plane Bending ................................................9.2

9.1.2 Fatigue Considerations for Welds .........................................................................9.4

9.1.3 Welded Cover Plates ............................................................................................9.9

Section 9.2 Repair Strategies..................................................................................... 9.12

9.2.1 Understand the Source of Cracking ....................................................................9.12

9.2.2 Design Repair Detail...........................................................................................9.14
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9.2.3 Validate Repair Detail .........................................................................................9.16

Section 9.3 Special Topics ......................................................................................... 9.17

9.3.1 Constraint-Induced Fracture ...............................................................................9.17

9.3.2 Over-Height Vehicle Collisions............................................................................9.17

9.3.3 Fitness-for-Service Analysis................................................................................9.19

Chapter 10 Non-Welded Components..............................................10.1

Section 10.1 Built-Up Members ................................................................................ 10.1

10.1.1 Behavior of Riveted and Bolted Connections ..................................................10.1

10.1.2 Bolted Connections with Bolts Loaded in Shear..............................................10.2

10.1.3 Bolted Connections with Bolts Loaded in Tension...........................................10.5

10.1.4 Riveted Members and Connections ................................................................10.7

Section 10.2 Anchor Rods ...................................................................................... 10.10

10.2.1 Fatigue Considerations for Anchor Rods.......................................................10.10

10.2.2 Stress Corrosion Cracking / Hydrogen Embrittlement ...................................10.13

Section 10.3 Reinforcement of Concrete............................................................... 10.14

10.3.1 Reinforcing Bars ...........................................................................................10.15

10.3.2 Prestressing Strands.....................................................................................10.17

10.3.3 Post-Tensioning Tendons and Anchorages...................................................10.20

10.3.4 Stay Cables ..................................................................................................10.21

Appendix A............................................................................................ A.1

Section A.1 General ...................................................................................................A.1

Section A.2 Fatigue Limit State Calibration .............................................................A.2

Section A.3 Components of the Fatigue Limit State ...............................................A.2

A.3.1 Multiple Presence ............................................................................................A.2

A.3.2 Cycle Counting / Cycles Per Passage..............................................................A.3

A.3.3 Selection of Fatigue Load Factors..................................................................A.10

Section A.4 Calibration of the Fatigue Limit State ................................................A.13

Glossary ................................................................................................ G.1

References ............................................................................................ R.1

Figure and Table Credits.......................................................................F.1
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Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.1 

CHAPTER 1 BACKGROUND AND ORGANIZATION OF THE MANUAL 

SECTION 1.1 INTRODUCTION 

This Reference Manual, along with an accompanying training course, is a primary component of 

the Design and Evaluation of Steel Bridges for Fatigue and Fracture training program. Its 

objective is to provide engineers with the necessary technical information to effectively design 

and evaluate steel highway bridge structures for the limit states of fatigue and fracture to 

improve safety, economy, and longevity of infrastructures. An additional objective is to educate 

engineers about the history, scope, methodologies, assumptions, limitations, and application of 

the American Association of State Highway and Transportation Officials (AASHTO) 

Specifications addressing fatigue and fracture. 

The learning outcomes for this Manual and training program are expected to enable students to: 

• Explain the fundamentals of fatigue and fracture on steel highway structures 

• Identify the various analysis methods for determining fatigue and fracture on steel highway 

structures

• Explain the various AASHTO methodologies as it pertains to fatigue and fracture design

• Identify the AASHTO methodology for fatigue and fracture evaluation

• Describe the various strategies for repair and retrofit of steel highway structures

This Manual is intended to be used by State DOT bridge and structures engineers and 

practitioners responsible for steel bridge design and evaluation, as well as engineers at all levels 

including designers, consultants, reviewers, maintenance and management engineers, and load 

raters.

1.1.1 Historical Perspective 

Some of the first reports of fatigue and fracture failures in metal structures are traced back to the 

1800’s (Shank, 1954). With the onset of the industrial age and more widespread use of wrought 

iron and early steels in manufacturing, industrial, and transportation industries, steel began to be 

used in tension members with repeated loads. Examples of failures were reported in elements 

such as mine hoists, railroad bridge members, railroad car axles, as well as pressure vessels and 

storage tanks. Observations of cracks in truss hangers and stringer end connection angles led to 

investigations between the 1930’s and 1960’s. The earliest welded bridge fractures were reported 

in Germany, Belgium, and France in the 1920’s and 1930’s in welded vierendeel truss bridges 

(Barsom and Rolfe, 1999). These early fractures led to prohibitions against welding to the 

tension flange of girders (which we now know from experience is the cause of secondary 

distortion-induced fatigue cracking in structures from that era). It was not until the late 1960’s 

that the beginnings of the modern approach to fatigue and fracture design and evaluation of 

bridges began to take form.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.2 

Figure 1.1.1-1 provides a chronological summary of the important developments presented in 

this chapter. Beginning with 1900 and continuing to the present day, thirteen key events and 

developments related to fatigue and fracture in steel bridges are identified on a timeline. These 

events include significant research findings, development of design provisions, and bridge 

failures, and they have shaped the current practice of design, evaluation, and inspection of steel 

bridges for fatigue and fracture. These key events are described in greater detail in subsequent 

sections of this chapter.

Figure 1.1.1-1 Chronological summary of important developments related to fatigue and 

fracture of steel bridges.

1.1.1.1 Basic Description of Fatigue and Fracture

The modern view of fatigue of welded structures is that fatigue is the process of crack extension 

under the application of repeated loading sufficiently large (above a threshold, which is 

explained later) with initiation assumed present due to some discontinuity introduced in the 

manufacturing of the base metal or as a consequence of fabrication. The process of fatigue crack 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.3 

extension is labeled as sub critical crack growth since the process consists of incremental crack 

extension with each cycle of loading. The meaning of “sub critical” is that the crack can be 

tolerated in the member without unstable propagation and fracture. 

Fracture is characterized by unstable crack extension which occurs when the energy required to 

extend the crack is exceeded by the energy released by an incremental extension of the crack. 

Fracture is the rupture in tension or rapid extension of a discontinuity (which could be a fatigue 

crack), leading to gross deformation, loss of function or serviceability, or complete separation of 

the component. The crack extends over time in a stable manner due to fatigue until it reaches its 

critical size, and fracture becomes the end event of a fatigue crack. This process is shown 

schematically in Figure 1.1.1.1-1. 

Figure 1.1.1.1-1 Fatigue crack extension from repeated load above threshold. 

All structures are assumed to have a crack initiating discontinuity arising from either the 

manufacturing of the steel or as a result of cutting, drilling, welding, or other changes made to 

the member during fabrication. All steel members possess discontinuities due to fabrication and 

manufacturing, but these are benign as long as the stresses are kept sufficiently low. The 

structural engineering approach to fatigue presumes the existence of some discontinuity that 

serves as a potential initiation site for cracking. It acknowledges that all inspection methods have 

detection limits which serve to limit the initial discontinuity size, but also allows for 

discontinuities that cannot be identified. Inspection cannot detect all discontinuities; its purpose 

is to identify and reject those that could cause harm. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.4 

Fatigue details also exhibit what is referred to as threshold fatigue strength. This means that 

applied stress ranges below the threshold stress range theoretically do not cause crack extension. 

The threshold is a function of the geometry of the fatigue detail, a combination of the local stress 

concentration at the detail and the expected initial discontinuity. Most modern highway bridges 

on major roads are designed so that the stress is below the threshold which provides a structure 

which will confidently not exhibit fatigue crack extension.

1.1.1.2 Importance of Fatigue and Fracture in Bridge Engineering

In modern high volume interstate highways, fatigue frequently controls much of the design of 

welded bridge members, including both proportions and details. The large number of fully 

loaded trucks produces millions of cycles of fatigue loading each year. The number of trucks on 

an interstate highway typically exceeds 1,000 trucks per day, which produces over 27 million 

cycles in 75 years. In order for the bridge to survive this repeated loading, the design stress range 

is conservatively kept below the threshold value in most cases. The lower allowable stress ranges 

associated with the threshold causes the design and location of details such as splices, stiffeners, 

and any attachments to be controlled by fatigue. Modern bridge designs utilize weld details 

which have known and acceptable fatigue resistance. Vintage details such as welded cover plates 

are not used due to their low fatigue resistance. The designer must select the proper details based 

upon the expected fatigue stress. 

In a flexural member, the stress range is not constant along its length. Consequently, the designer 

must determine the stress range at every detail that is susceptible to fatigue and assure that it is 

within acceptable limits. The designer needs to specify which parts of a member are subject to 

tension since these portions are subject to more stringent material toughness and weld inspection 

criteria. The goal of the design is to provide a fatigue tolerant structure which will not exhibit

fatigue damage or any fracture during the service life of the structure. 

1.1.2 Evolution of Fatigue and Fracture Design, Evaluation, and Inspection Approaches

1.1.2.1 Evolution of Fatigue Design 

Pre-1950’s steel bridges were mostly connected with rivets, and welding was used for nonstructural connections, if at all. Fatigue of riveted bridges had been a concern of the railroad 

industry, and extensive studies of the fatigue properties of riveted and later bolted and butt 

welded connections were performed by Professor W.M. Wilson at the University of Illinois

starting in the 1930’s (Wilson and Coombe, 1939; Wilson, 1940). This work was continued by 

Munse and Stallmeyer with the inclusion of other welded connections. These tests were done on 

relatively small specimens using mechanical loading equipment.

The fifth edition of the American Association of State Highway Officials (AASHO) Standard 

Specifications for Highway Bridges (AASHO, 1949), published in 1949, contained no mention 

of fatigue, and welding was allowed only on low carbon steel and wrought iron used for 

connection of secondary members, such as stiffeners, railings, and bracing. The welding and 

material to be welded was to conform to Specifications for Welded Highway and Railway 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.5 

Bridges, Design, Construction, and Repair (AWS, 1936), of the American Welding Society, first 

published in 1936. There were no notch toughness requirements for the base metal or weld 

metal, and the inspection requirements were generally visual inspection. 

The seventh edition of the AASHO Standard Specifications for Highway Bridges (AASHO, 

1957), published in 1957, allowed welding of a new steel, ASTM A373, which was the 

forerunner to ASTM A36 steel. However, it also did not contain any mention of fatigue design. 

The first AASHO fatigue design provisions were introduced in 1965. The 1965 ninth edition of 

the AASHO Standard Specifications for Highway Bridges (AASHO, 1965) had extensive fatigue 

design provisions and defined fatigue categories. The fatigue resistance was based largely on the 

University of Illinois work, a summary of which is contained in the Welding Research Council 

publication Fatigue of Welded Steel Structures authored by W.H. Munse (1964). A similar 

approach was employed in mechanical engineering components using base metal data from 

rotating beam specimens and fatigue notch factors. Fatigue life was thought to be dependent 

upon the “R” ratio, the algebraic ratio of the minimum stress (Smin) to the maximum stress (Smax), 

and tied to the use of a Goodman diagram, shown in Figure 1.1.2.1-1, to determine fatigue 

resistance. The Goodman diagram was developed based on research by J. Goodman during the 

early 1900’s but is no longer used today in structural engineering. 

Figure 1.1.2.1-1 Goodman diagram for early determination of fatigue strength. 

The allowable fatigue stress when the maximum stress is tensile was defined as:

Rk

fk F ro

r

2

1

1− =

Equation 1.1.2.1-1
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.6 

where 

Fu is the tensile strength of the material in psi, and α, referred to as alpha, is a coefficient with 

values defined by AASHTO varying from 0 to 1.06, depending on the type and location of 

material, the type of maximum stress, and the number of cycles of maximum stress.

Since the minimum tensile strength of ASTM A36 steel is 58,000 psi, the value for k1 equals 1 

for this steel and increases with higher strength steels, implying a variable fatigue resistance as a 

function of material tensile strength. The coefficients k2 and fro were tabulated for each fatigue 

category and design life with different values if the maximum stress was tensile or compressive. 

A modified formula, which had the yield strength of the material as a variable, was used when 

the maximum stress was compressive. The coefficients were tabulated for three cyclic design 

lives of 100,000, 500,000, and 2,000,000 cycles, which were a function of road type and load 

length. The design life for an AASHTO “H” loading on a major road was 2,000,000 cycles of 

assumed constant amplitude loading, while a lane load on the same bridge would have a design 

life of 100,000 cycles. The allowable fatigue stress for a category, categorized by the Smax

parameter, varied along the length of the girder due to the inclusion of the R-ratio, which is 

related to dead load and live load stresses. The design specification included ASTM A36 steel, as 

well as ASTM A242 (a weathering steel), ASTM A440 (a non-weldable steel), and ASTM A441 

(a weldable steel with yield strength that varied with the thickness of the plate). 

The tenth edition of the AASHO Standard Specifications for Highway Bridges (AASHO, 1969), 

published in 1969, had changes in the fatigue design specification and included ASTM A588, 

ASTM A572, and ASTM A514 steel. ASTM A588 for welded structures required supplemental 

Charpy V-notch (CVN) testing for information only. Although the CVN test was established 

around 1900, this was the first bridge steel to have a toughness requirement, albeit an 

informational one. Along with the variation in allowable fatigue stress due to the inclusion of the 

tensile strength in the coefficient, k1, there were separate fatigue categories for the high strength 

ASTM A514 steel. Some categories, such as Category F, had alpha equals 0 and k2 equals 1, 

which gives a constant stress range independent of material strength and mean stress. This is 

similar to modern design approaches in that it is material-independent. 

It is interesting to compare the tenth edition Category F base metal adjacent to a fillet weld and 

Category K ASTM A514 base metal adjacent to a transverse stiffener with a tensile maximum 

stress to Category C of the current AASHTO LRFD Bridge Design Specifications (AASHTO, 

2015b); these are physically analogous details (AASHO, 1969; AASHTO, 2015b). The 

comparison is shown for a design life of 500,000 cycles in Table 1.1.2.1-1. Category F is much 

more conservative than the present specification, while the upper end of the resistance values for 

Category K are comparable to the present specifications, as might be expected for a fatigue 

specification that is independent of material grade.
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1.7 

Table 1.1.2.1-1 Comparison of fatigue design stress range for a welded stiffener. 

Category Design Stress Range (ksi)

C – LRFD 20.6

F (1969) 12

K (A514) (1969) 12.7 through 21.2 for R>0

The basis for most modern fatigue design in bridges comes from work originally completed 

through NCHRP Project 12-7 conducted from 1966 to 1972. This research resulted in the 

publication of NCHRP Report 102, entitled Effect of Weldments on the Fatigue Strength of Steel 

Beams (Fisher et al., 1970) and NCHRP Report 147, entitled Fatigue Strength of Steel Beams

with Welded Stiffeners and Attachments (Fisher et al., 1974). These studies involved the testing 

of 531 steel beams and girders, each having two or more details, and demonstrated that the stress 

range was the most significant factor in the design for fatigue. This seminal research examined 

rolled shapes, welded beams, groove welded splices, cover plates, and various stiffener details. 

The beams used in the research were small 14 inch deep sections. Later tests included larger 

plate girder specimens. 

The fatigue strength of weldments was eventually defined in the NCHRP Project 12-7 research 

using an exponential relationship between stress range and fatigue life shown below: 

3

r S

A N = Number of FailuretoCycles =

Equation 1.1.2.1-2

where A is a constant for a given category of fatigue details and is computed based on regression 

analysis of test data. 

This equation plots as a linear relationship on a log-log scale, as shown in Figure 1.1.2.1-2. The 

mean stress or minimum stress was found not to be a statistically significant parameter upon the 

fatigue life of the specimens. The beam specimens used in the testing program preserved the 

local tensile residual stress at the weld. The magnitude of the residual stress local to the weld is 

equal to the yield strength of the base metal. The residual stresses in the specimens were 

consistent with those in real details that would be applied to bridge girders. Only full-size 

specimens were able to capture the influence of residual stress. Smaller specimens did not lock in 

the residual stresses, and test results inferred a dependence on mean stress as a factor in fatigue 

life. The tests included steel with specified yield strengths from 36 to 100 ksi, covering the range 

of steels available at the time of the testing. 

Tests at very low applied stress ranges have revealed that at low stress ranges, no cracking 

occurs (Fisher et al., 1983). This level of stress range is called the threshold stress range, SRth, 

and is an important characteristic of the fatigue resistance. If the stress range is below this 

threshold, no crack extension occurs, and the fatigue life is deemed to be infinite. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.8 

Figure 1.1.2.1-2 Fatigue S-N curve. 

It was not until the 1974 interim specifications to the AASHTO Standard Specifications for 

Highway Bridges (AASHTO, 1974a) that the fatigue design concepts still fundamentally in use 

today were introduced to designers. In the 1974 major revisions, AASHTO adopted the stress 

range concept, with the stress range now being the only design variable required for fatigue. 

Variations in strength of materials were deemed to be immaterial to fatigue resistance. Six 

fatigue categories designated A through F of decreasing fatigue resistance were introduced, with 

members and their details grouped to specific categories. The AASHTO specifications added 

figures to explain the details and provided the foundation for over four decades of development 

of the fatigue design and evaluation specifications.

From 1974 to 1994, the AASHTO standard specifications continued to be used for the design of 

bridges. The AASHTO standard specifications relied on the standard design vehicle, known as 

HS 20, for the calculation of live load effects. The live load effects were generally computed 

with the same vehicle weight used for the calculation of force effects for both strength and 

service conditions, without adjustment. They were also computed with the same distribution 

factors used for the design of a bridge for both strength and service conditions (which included 

both single-lane and multi-lane loading, depending on the number of stress cycles). This 

typically resulted in the design of members for fatigue considering multiple loaded lanes on the 

bridge simultaneously. 

Over time, as additional domestic and international data sets became available, the AASHTO 

fatigue design approach was re-examined and fundamentally confirmed. Keating and Fisher 

(Keating and Fisher, 1986) examined 1,500 test data points in addition to the fatigue test data 

points originally collected in the NCHRP Project 12-7 investigation. Their updated study, 

completed in 1986, confirmed the accuracy of the AASHTO fatigue design curves as reasonably 

predicting the lower bound fatigue life of an expanded population of test data. Minor adjustments 

were made to the slopes of the AASHTO fatigue design curves, as well as a slight adjustment in 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.9 

the infinite life maximum stress range for cover-plated beams, but otherwise the original fatigue 

research was confirmed for its accuracy. The larger data set was used to create a new category, 

B’, to cover certain longitudinally loaded group welded attachments. Category E’ was also 

created to represent the fatigue strength of web attachments thicker than 1 inch.

In 1994, the AASHTO LRFD Bridge Design Specifications (AASHTO, 1994) were introduced. 

For the first time, fatigue was defined as its own limit state. The design vehicle was changed 

from the previous HS 20 to a new lighter-weight vehicle, 75 percent of the weight of the prior 

HS 20 vehicle and with an extended wheelbase. Fatigue assessments are now conducted with 

only a single vehicle in a single lane on the bridge and with a lower impact value than is used for 

design at the strength and service limit states. 

In 1995, Clause 12 was added to the Bridge Welding Code (AWS D1.5) (AASHTO/AWS, 1995), 

containing requirements for fabricating fracture critical structures. This essentially replaced the 

Guide Specifications for Fracture Critical Non-Redundant Steel Bridge Members, published in 

1978 by AASHTO (AASHTO, 1978), for welding and fabrication requirements. Clause 12 of the 

AWS D1.5 provides information related to contract documents, base metal requirements, 

welding processes, consumable requirements, Welding Procedure Specification (WPS), 

contractor requirements, thermal cutting, repair of base metal, straightening, curving, cambering, 

tack welds and temporary welds, preheat and interpass temperature control, postweld thermal 

treatments, weld inspection, and repair welding. However, it does not assign responsibility for 

specifying which, if any, steel bridge member or member component falls in the category of 

fracture critical.

In 2009, there were additional changes to the fatigue design provisions with the single fatigue 

load combination being replaced with Fatigue I and Fatigue II load combinations, though these 

effectively are the same as the prior check but stated differently. A section dealing with 

constraint-induced fracture was also introduced at that time. 

1.1.2.2 Evolution of Fracture Control Plans and Fracture Critical Inspections

Control of Steel Construction to Avoid Brittle Failure (Shank, 1957), edited by Shank and 

published by the Welding Research Council in 1957, provides a summary of the understanding 

of brittle fracture in the 1950’s. This publication also coincided with the beginning of the 

interstate highway construction. The monogram concentrates heavily on material properties as 

the cause of structural fractures and discusses fatigue in a single paragraph. It indicates the need 

to reduce stress concentrations for increased fatigue resistance and acknowledges that

improvement in fatigue design will also reduce the risk of a brittle fracture. The coupling of 

fatigue and fracture was stated as:

“Moreover, the beginning of a small fatigue crack may become the focus of a 

brittle fracture crack even though from a strictly fatigue viewpoint the part would 

still have a long life.” 
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This statement does not focus on fatigue cracking as a root cause of subsequent brittle fracture 

but inversely as low toughness reducing the fatigue life. The monograph concludes with the 

sentence: 

“This discussion serves to indicate the present limitations of our knowledge, but 

more important, it is meant to show that the three factors – materials, design and 

fabrication – all may play an important role in the ultimate performance and no 

one of them should be neglected at the expense of others.” 

This last sentence is the heart of the fracture control plan currently used in the design of steel 

bridges and other structures. 

The critical crack size is dependent upon the material’s fracture toughness, which also depends 

upon the temperature and rate of loading. The goal of the fracture control plan is to assure 

material that can tolerate cracks of the order of the material’s thickness at the lowest anticipated 

service temperature under operating stress levels. A 0.4 by 0.4 inch CVN test specimen is used to 

measure the notch toughness of the material, which is correlated with material fracture 

toughness. 

Much of the knowledge of low carbon, lower strength steels and fracture came from studies of 

welded ship hull failures during World War II. The fractures of the all-welded Liberty Ships (see 

Figure 1.1.2.2-1) stimulated a large program to improve their fracture resistance. The changes 

included improved chemistry control and CVN toughness requirements of the base metal, 

improved hatch geometry to reduce stress concentrations, and the addition of a riveted crack 

arrest band around the ship to arrest a running crack. The work on the Liberty Ships was 

followed by extensive fracture testing at the Naval Research Laboratory by Pellini and his 

colleagues (Pellini, 1983). 

The concept of a Nil Ductility Temperature (NDT) as a means of characterizing the fracture 

resistance of steel came from a dynamic test of a specimen containing a brittle weld with a notch. 

The NDT was the temperature above which the test plate could bend plastically without 

propagation of a brittle fracture. Pellini’s approach assumed that the cracking would occur from 

a locally embrittled area of the weld. If the temperature of the plate was above the NDT, the 

crack would not propagate outside of the locally embrittled area of the weld. Hence, the 

approach taken was to rely upon a base metal capable of arresting a dynamic crack. Pellini’s 

approach did not consider that fatigue cracks formed in sound metal could be the cause of the 

fracture. 
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1.11 

Figure 1.1.2.2-1 Liberty Ship fracture. 

The collapse of the Point Pleasant Bridge in 1967 and its subsequent failure investigation marked 

a significant change in design and construction of steel bridges. The collapse was triggered by a 

brittle, unstable crack extension of a small crack in a single eyebar which formed the chain 

suspending the bridge. The bridge was in service for over 40 years with no apparent structural 

distress. The fractured eyebar is shown in Figure 1.1.2.2-2. The eyebar has been assembled with 

the left-hand side matched to show the extent of plastic deformation which occurred on the lefthand segment before it finally fractured. The right-hand fracture in the right side shows no 

evidence of any plasticity. The fracture of this side was triggered by the small cracks, 0.15 inches

deep, shown in Figure 1.1.2.2-3. 

The graphic difference in failure mode of the sides of the eyebar brought to the attention of the 

bridge engineering community that bridge steels needed to be able to tolerate cracks that might 

form under service load so that they may be discovered during an inspection. The smooth 

machined tensile coupons that were relied upon in the mill test of the material verified that 

material would perform in a ductile manner like the left segment of the eyebar but did not 

provide a measure of the material’s resistance to brittle fracture. Materials that could tolerate a 

small crack without failure were clearly needed. This led to the implementation of the CVN 

requirement for bridge steels subjected to tension. The fracture toughness requirement for bridge 

steels was based on work in the nuclear field and verified by low temperature fracture testing of 

large girder specimens.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.12 

Figure 1.1.2.2-2 Fractured eyebar from the failed Point Pleasant Bridge. 

Figure 1.1.2.2-3 Shallow cracks at exterior of the pin hole in the Point Pleasant Bridge. 

The failure of the Point Pleasant Bridge by the fracture of a single member due to lack of 

redundancy, even though there were two eyebars forming the suspension chain, caused a change 

in the design of bridges. Clearly these members needed special consideration. These critical 

members were labeled as fracture critical. The required fracture toughness, fabrication 

inspection, and welding requirements of these members was developed as a result of the failure. 

These requirements, built upon a fracture mechanics understanding as espoused earlier by Shank 

(i.e., with materials, design, and fabrication having important roles), led to a holistic approach to 

providing an increase in reliability of these members. 

The increased fabrication inspection requirements were implemented to reduce the probability of

discontinuities and stress concentrations in these members. The higher toughness was to ensure 

that failure of these members would not be triggered by a small undetectable crack which might 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.13 

develop during the service life of the bridge. The implementation of hands-on inspection of the 

fracture critical members provided further safety to ensure that any crack that developed, even 

with these increased material and fabrication requirements, was discovered before it became 

unstable. 

In addition, supplemental AASHO material specification toughness was required for ASTM 

A588 and ASTM A572 when it was welded but not for the higher strength ASTM A514. The 

10th edition of the AASHO Standard Specifications for Highway Bridges (AASHO, 1969) 

included detailed welding procedures for ASTM A514 and mandatory radiograph testing of all 

tension butt welds. Ultrasonic inspection was not mandated. All ASTM A514 welds were to be 

inspected for more than 48 hours after welding to ensure any delayed cracking could be 

discovered. 

It is also important to note that during the 1970’s, the American Society for Nondestructive 

Testing (ASNT) standards for the various levels of inspectors were implemented. Prior to the 

development of these criteria, the uniformity and quality of nondestructive inspection was not 

controlled and was variable. The American Welding Society (AWS) followed up later with the 

Certified Weld Inspector Certification. These changes in the qualifications for shop inspectors 

greatly increased the reliability and uniformity of weld inspection. These changes ensured that 

weld inspectors were adequately trained and qualified, and they greatly reduced the variability in 

weld quality. 

These requirements have proved to be successful. A national dialogue about fracture control 

strategy evolved during the decade following the collapse of the Point Pleasant Bridge. As a 

result, a Fracture Control Plan (FCP) was developed by AASHTO and AWS, and AASHTO's 

first Guide Specifications for Fracture Critical Non-Redundant Steel Bridge Members

(AASHTO, 1978) was published in 1978. Since that time, no bridge built using the requirements 

of the AASHTO FCP has suffered any fracture. 

Later defined and currently enforced, FCMs require enhanced, arms-length inspections as a 

result of the Mianus Bridge collapse. The AASHTO FCP, along with this more stringent inservice inspection requirement, is referred to as the Total FCP in this Manual.

SECTION 1.2 SCOPE OF REFERENCE MANUAL AND PRESENTATION OF 

MAJOR THEMES

This Manual covers the relevant topics related to fatigue and fracture in steel bridges, including 

analysis, design, evaluation, repair, and retrofit. Chapter 2 begins with a discussion of cracking 

in steel structures, including crack behavior, sources of discontinuities in steel structures, the 

nature of stresses affecting fatigue and fracture, and brittle and ductile behavior in steel. Chapter 

3 provides the basics of fracture mechanics, covering such topics as fracture control, evaluation 

of fatigue cracking, and fracture mechanics as a quantitative tool. Chapter 4 describes fatigue 

behavior, including discontinuities and stress concentrations, the influence of production and 

fabrication on fatigue, testing as the basis for design limits, and environmental effects. Chapter 5 

describes analysis for fatigue, including information for both approximate and refined analysis 

methods. Chapter 6 addresses the fatigue design approach as presented in the AASHTO LRFD 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.14 

Bridge Design Specifications (AASHTO, 2015b), and it explains the fundamental fatigue limit 

state equation, the various AASHTO fatigue detail categories, the differences between finite life 

and infinite life, and the computation of fatigue stress range and factored nominal resistance, 

including a step-by-step design example for fatigue. Chapter 7 describes fracture control, 

including design, fabrication, and inspection, and it covers such topics as redundancy, constraintinduced fracture, and the Total FCP. Chapter 8 addresses the AASHTO fatigue-evaluation 

approach, including remaining fatigue life evaluation, estimates of fatigue life based on the 

AASHTO Manual for Bridge Evaluation (AASHTO, 2015d), and remaining fatigue life for 

“negative remaining life” bridge details. Chapter 9 describes assessment, repair, and retrofit of 

structures, and it provides a description of several common fatigue details, it describes general 

repair and retrofit strategies that are common to virtually all fatigue details, and it covers the 

special topics of constraint-induced fracture, over-height vehicle collisions, and fitness-forservice analysis. Finally, Chapter 10 covers non-welded components such as built-up members, 

bolts and rods, and reinforcement of concrete. In addition, Appendix A describes calibration of 

the Fatigue I and II load combinations based on the SHRP2 Project R19B (Modjeski and 

Masters, 2015). 

Information in this Manual about bridge design for fatigue and fracture is based on the AASHTO 

LRFD Bridge Design Specifications, 7th Edition with 2015 Interim Revisions (referred to in this 

Manual as AASHTO LRFD) (AASHTO, 2015b). However, it should be noted that the fatigue 

load factors presented in this Manual are based on the 2017 edition of the AASHTO LRFD 

Bridge Design Specifications. Information about bridge evaluation for fatigue and fracture is 

based on the AASHTO Manual for Bridge Evaluation, 2nd Edition with 2015 Interim Revisions 

(referred to in this Manual as MBE) (AASHTO, 2015d).

The following sections provide a brief summary of some of the major themes presented in this 

Manual.

1.2.1 Physical Phenomena of Cracking 

Crack growth in steel bridges requires two conditions to occur: existing discontinuities and 

tensile stresses normal to the discontinuities. Cyclical stresses with a tensile component can 

cause fatigue crack growth, while sustained tensile stress or a single stress cycle with a tensile 

stress component can cause fracture. The nature of this relationship is described in Chapter 3. 

Crack growth can be delineated into three distinct regimes: initiation, steady-state propagation, 

and unstable fracture. All three of these regimes, as well as the general behavior of fatigue 

cracking, are described in Chapter 2.

1.2.2 Fatigue Stress

The dominant parameter for fatigue design is stress range, which can be readily computed by the 

design engineer for a specific bridge application. The stress range for the fatigue limit state is the 

algebraic difference between a maximum and minimum live load stress caused by the passage of 

a single fatigue design vehicle occupying a single lane. The most common cause of fatigue 

cracks in bridges is in-service cyclical stress range due to trucks. As such, the fatigue limit state 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.15 

includes only force effects from live load and no other loads. The single truck concept was 

validated as part of the SHRP2 Project R19B research (Modjeski and Masters, 2015), a summary 

of which is provided in Appendix A. 

The fatigue design vehicle is similar to the HL-93 design truck but with a constant spacing of 

30.0 feet between the 32.0-kip axles. In addition to the static force effects, a 15 percent increase 

in the vehicle force effects is applied to account for dynamic load allowance (also known as 

impact). 

Two load combinations, Fatigue I and Fatigue II, are defined in AASHTO LRFD Table 3.4.1-1 

for the fatigue limit state. The Fatigue I load combination is applied to check if the detail under 

investigation will theoretically exhibit infinite life. When a detail cannot exhibit infinite life due 

to excessive stress range, the Fatigue II load combination is applied to ensure that the detail will 

exhibit sufficient finite life based upon the projected average daily truck traffic (ADTT) for 75 

years, the design life specified in AASHTO LRFD. 

The computation of the factored stress range for fatigue is covered in considerable detail in 

Chapter 6, including a step-by-step design example.

1.2.3 Fatigue Resistance

AASHTO LRFD characterizes the fatigue resistance of details based upon the testing and 

conclusions discussed in Chapters 4 and 6. Details are characterized into eight Detail Categories,

A, B, B’, C, C’, D, E, and E’, in order of descending fatigue resistance. Fatigue details and their 

respective detail categories are presented in AASHTO LRFD Table 6.6.1.2.3-1. 

In the log-log resistance curves, the resistance is represented by a sloping line followed by a 

straight horizontal line. The sloping portion represents the finite life nominal resistance. These 

limits are established through testing and represent a 97.5 percent probability of survival in the 

region of finite life. For finite life, the resistance is proportional to the cube root of a detail 

constant, A, divided by the number of design cycles of loading, N, for that particular detail.

The straight horizontal portion of the curve represents the infinite life nominal resistance, and 

these resistance values are based on the constant amplitude fatigue threshold (CAFT). The region 

of infinite life represented by the CAFT is somewhat less certain than the finite life region, given 

a lesser number of long-life tests, though the Fatigue I load combination has been established to 

provide safe behavior for infinite life. 

The computation of fatigue resistance is covered in considerable detail in Chapter 6, including a 

step-by-step design example.

1.2.4 Fatigue and Fracture Control 

Fatigue and fracture in steel bridges must be considered during analysis and design before the 

bridge is constructed, as well as in evaluation for existing bridges. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

1.16 

Analysis is described in considerable depth in Chapter 5. For load-induced fatigue, several 

analysis methods are described, including both approximate analysis and refined analysis

methods, the local-stress approach, and the fracture-mechanics approach.

Design based on AASHTO LRFD for fatigue and fracture is described in Chapters 6 and 7, 

respectively. For the fatigue limit state, the design stress range must not exceed the factored 

nominal resistance. For fracture, a three-legged stool approach is implemented, including design, 

fabrication (including quality control inspection), and in-service inspection as required elements 

of a comprehensive plan, referred to as the Total FCP. 

Evaluation is described in Chapter 8. A fatigue evaluation is not routinely performed with each 

rating of a steel bridge, but only when the remaining fatigue life of an uncracked bridge is 

desired as input into operating decisions. A methodology for fatigue evaluation of steel bridges is 

included in the MBE. 

1.2.5 Retrofit Strategies

If fatigue-related problems are encountered in the field (most commonly on older bridges), then a 

repair or retrofit strategy must be employed to rectify the problem and to help prevent additional 

problems. While the specifics of the repair strategy are dependent upon the nature of the detail 

and problem, there are several general repair and retrofit strategies that are common for virtually 

all fatigue details. These general strategies include understanding the source of cracking, 

designing the repair detail, and validating the repair detail. Although the specifics of these three 

steps are dependent on the unique fatigue characteristics of the bridge, each step is essential for 

any successful repair or retrofit strategy.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

2.1 

CHAPTER 2 CRACKING IN STEEL STRUCTURES

SECTION 2.1 CRACK BEHAVIOR

Cracking in steel structures can manifest as a slow, stable process of growth from repeated 

applications of stress or suddenly when the conditions are right. If crack growth is allowed to 

propagate and continue long enough, total separation/loss of the member can result when the 

uncracked cross section is sufficiently reduced such that the member can no longer resist the 

internal forces and the crack extends in an unstable mode. The unstable growth is typically in the 

form of brittle fracture in steel bridge members. The fatigue process can take place at stress 

levels (calculated on the initial section) that are substantially less than those associated with 

yielding under static loading conditions. The usual condition that produces fatigue cracking is the 

application of a large number (millions) of load cycles, with some above a “threshold.” 

Consequently, the types of structural engineering applications that are susceptible to fatigue 

cracking include dynamically loaded structures such as bridges, highway sign and lighting 

structures, crane-support structures, stacks and masts, and offshore structures. 

2.1.1 Necessary Conditions

Crack growth in metals requires two conditions to occur: existing discontinuities and tensile 

stresses normal to the discontinuities. Cyclical stresses with a tensile component can cause 

fatigue crack growth, while sustained tensile stress or a single stress cycle with a tensile stress 

component can cause sudden and complete fracture. 

A relationship exists between load and resistance for both fatigue and fracture. However, the 

parameters in this relationship vary for fatigue and fracture. For example, the load parameter to 

initiate fatigue is stress range, while that for fracture is total stress. The nature of this relationship 

is discussed further in Chapter 3. 

2.1.2 Crack-growth Regimes

Crack growth can be delineated into three distinct regimes: initiation, steady-state propagation, 

and unstable fracture, as illustrated in Figure 2.1.2-1. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

2.2 

Figure 2.1.2-1 General crack-growth regimes.

2.1.2.1 Initiation

It is inevitable that discontinuities are present in fabricated steel components. These 

discontinuities are byproducts of steel making, as well as the various cutting, drilling, punching, 

and welding operations associated with the fabrication of steel bridge and structural elements. 

They are discussed in greater detail in Section 2.2. Given these preconditions, the engineer is 

responsible to control the stresses to avoid potential fatigue and subsequent brittle fracture 

resulting from growth of these discontinuities. The fatigue behavior of a fabricated steel 

engineering structure is controlled by the size, shape, and location of the discontinuities, and the 

stresses applied. 

The initiation portion of general crack growth in which existing discontinuities are sharpened 

into cracks is essentially non-existent for all fabricated steel structures and can conservatively be 

ignored. Thus, they are assumed to be present at the start. Crack growth in bridges is delineated 

into only two regimes: stable fatigue cracking and unstable fracture. Figure 2.1.2.1-1 graphically 

illustrates crack growth in bridges. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

2.3 

Figure 2.1.2.1-1 Crack-growth regimes for steel bridges with assumed initial discontinuity. 

2.1.2.2 Propagation 

The propagation regime of crack growth represents steady-state fatigue cracking that may occur 

when stresses above the threshold are applied. Fatigue is the propagation of microscopic cracks 

into macro cracks by the repeated application of tensile stress. An existing crack grows a small 

amount in size each time a load is applied. Growth occurs at the crack front, which is initially 

sharp. Even at relatively low loads, there will be a high concentration of stress at the sharp front, 

and plastic deformation (slip on atomic planes) therefore occurs at the crack front. Continued slip 

results in a blunted crack tip, and the crack grows a minute amount during this process. Upon 

unloading, not necessarily to zero, the crack tip again becomes sharp. The process is repeated 

during each load cycle and is described in detail in terms of the fracture mechanics model in 

Chapter 3. The rate of growth of the crack increases exponentially over time and is depicted by 

the nonlinear propagation region of Figure 2.1.2.1-1. 

2.1.2.3 Fracture

When a critical size is achieved, the stable crack fractures in an unstable manner without an 

increase in stress. Fracture may be defined as rupture in tension or rapid extension of a crack, 

leading to gross deformation, loss of load-carrying capacity, or complete separation of the 

component. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

2.4 

Failure occurs in one of two ways. One possibility is that the steel has sufficient toughness and 

the fatigue crack grows to such an extent that the loss of section means the load simply can no 

longer be resisted by the uncracked ligament (for example, overload). In this case, failure occurs 

by yielding of the remaining material, or, exceptionally, by instability if the crack growth 

produces a grossly unsymmetrical section. In the case of yielding and a ductile failure, the 

critical flaw size is proportional to the yield strength. If the steel does not have sufficient 

toughness, the section fails by brittle fracture. In the case of a brittle failure, the critical size is 

proportional to the fracture toughness of the material which varies with rate of application of the 

load and the temperature of the material. The fracture toughness of the bridge steel is 

characterized by the Charpy V-notch (CVN) toughness (ASTM, 2012), discussed in detail in 

Section 2.4.1. Fracture is represented by the rapid extension of the crack with a limited number 

of additional cycles and is depicted qualitatively in Figure 2.1.2.1-1. It should be noted that in 

bridge structures, cracking may not necessarily lead to unstable propagation, since in many cases 

the limited magnitude of stress may allow the cracking to arrest, resulting in the need for either 

no repair or simple repair. 

SECTION 2.2 SOURCES OF DISCONTINUITIES IN STEEL STRUCTURES

The discontinuities that exist in all fabricated steel structures are a consequence of the 

manufacturing process of the steel itself and/or the normal fabrication processes of the 

components. 

2.2.1 Production

Discontinuities in rolled shapes and plates arise from surface and edge imperfections, 

irregularities in mill scale, laminations, seams, and inclusions, as well as from mechanical 

notches due to handling, straightening, cutting, and shearing. These irregularities are controlled 

by product specifications. In a rolled shape or plate away from connections and attachments, 

fatigue crack growth can start from one of these sources. Comparatively, the unaltered rolled 

shape or plate presents the most favorable fatigue life situation. However, there are not many 

practical cases in which a rolled shape or plate does not have some kind of attachment, 

connection, or other alteration, and these details have fatigue resistance less than the unaltered 

shape or plate. As a consequence, fatigue cracking in base metal away from details is rarely 

observed. As will be discussed in Chapter 6, AASHTO characterizes fatigue resistance through 

lettered Detail Categories A through Eʹ, Detail Category A exhibiting the highest fatigue 

resistance and Eʹ the worst (AASHTO, 2015b). Unaltered rolled shapes or plates are categorized 

as Detail Category A.

2.2.2 Fabrication

A simple built-up section is composed of several steel plates joined together by welding. An 

example is a plate girder with the plates joined through fillet welding, the most common practice. 

Though common, there are possible discontinuities introduced. The kinds of discontinuities that 

can occur in a welded detail are shown pictorially in Figure 2.2.2-1. These include partial 

penetration and lack of fusion, porosity and inclusions, undercut or micro discontinuities at the 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

2.5 

weld toe, and cracking or inclusions around a weld repair, at start-stop locations, or at arc strikes. 

Although the fabricator of the structure and those responsible for the fabrication inspection will 

attempt to minimize these discontinuities, it is neither practical nor economically possible to 

eliminate them.

In the case of a typical flange-to-web fillet weld, as shown in Figure 2.2.2-1, partial penetration 

is not a discontinuity and is of no concern as the applied stress is parallel to the weld. Surface 

discontinuities are subject to visual and magnetic-particle inspection, and can be readily 

identified and addressed if established workmanship criteria are not satisfied. The hidden 

discontinuities, such as porosity, are accepted as AASHTO LRFD (AASHTO, 2015b) is based 

upon tests of real welds with porosity discontinuities in them. 

Figure 2.2.2-1 Discontinuities in a welded beam. 

Test data on welded details have demonstrated that all fatigue cracks commence at some initial 

discontinuity in the weldment or at the weld periphery, and grow perpendicular to the applied 

tensile stresses. In a welded beam without attachments (simply two flange plates welded to a 

web), most laboratory fatigue cracks are observed to originate in the web-to-flange fillet welds at 

internal discontinuities such as porosity (trapped gases in the unfused area expanding and 

becoming trapped in the solidifying weld), incomplete fusion, or trapped slag. Figure 2.2.2-2

shows a fatigue crack that has formed from porosity (highlighted by arrow) in longitudinal 

submerged-arc fillet welds. These relatively large discontinuities are always present to some 

degree, irrespective of the welding process and techniques used during fabrication. The effect of 

these internal discontinuities is accounted for in the design fatigue resistance, which eliminates 

the need to identify them by internal inspection or remove them by repair. In other words, these 

internal discontinuities do not govern. Surface discontinuities in stress concentrations propagate 

faster and govern.
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2.6 

Figure 2.2.2-2 Fatigue cracks forming from internal porosity in web-to-flange connection.

Attachments, such as cover plates, gussets, stiffeners, and other components welded to a web or 

flange, introduce a transverse weld toe, thus forming a line of elevated residual tension where 

fatigue cracking can start from small, sharp discontinuities. Figure 2.2.2-3 and Figure 2.2.2-4

show a fatigue crack that has formed at a cover plate fillet weld toe. The crack surface in Figure 

2.2.2-4 shows various stages of crack propagation. The first stage (1) is a surface crack growing 

in the flange as a semi-circle until it penetrates the far side of the flange. The second stage (2) is 

a through crack in the flange growing both to the right and left until it reaches the flange tip on 

the right. Finally, with the flange tip severed, the through crack grows toward the web on the left 

(3), with the rougher texture on the fracture surface suggesting more rapid propagation. 

Figure 2.2.2-3 Fatigue crack at end of cover plate fillet weld toe.
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2.7 

Figure 2.2.2-4 Crack surface showing fatigue crack growth (with stages of crack 

propagation identified). 

In most cases, a discontinuity is an expected result of the type of fabrication process and has no 

effect on the life of the member if designed properly. For instance, the partial penetration shown 

in Figure 2.2.2-1 is a natural consequence of the fillet-welded connection; it is not expected that 

the two fillet welds will fuse in the central region of the connection. Furthermore, since the crack 

represented by the lack of penetration is parallel to the direction of the stress field (assuming a 

girder web-to-flange weld), the crack will not open under the application of stress (because the 

primary stress is from bending) and failure by fatigue will not occur. However, if the web plate 

was pulled away from the flange, then the lack of penetration would be perpendicular to the 

applied stress and this would be a fatigue sensitive detail. 

Consider a detail involving mechanical fasteners—an I-shaped beam with a cover plate fastened 

to the beam flange with bolts. The discontinuity between the flange and the cover plate could be 

described as a discontinuity or crack, but since the discontinuity is parallel to the stress field, the 

"crack" does not grow and therefore its presence does not affect the fatigue performance of the 

member.

Mechanical details, in which holes are drilled or punched and forces are transferred by means of 

rivets or bolts, present a somewhat more severe fatigue resistance situation than the bare rolled 

shape. Drilled or sub-punched and reamed holes yield some reduction in fatigue life as compared 

with an unaltered member, but the difference usually is not very great due to the preloaded highstrength bolts. The disturbing effect of the hole is largely mitigated by the presence of the high 

local compressive stresses introduced by the bolt (Detail Category B). Punched holes give a 

greater reduction in fatigue resistance than do drilled or sub-punched and reamed holes because 

of imperfections at the hole edge arising from the punching process. In this case, the crack 

usually starts at the edge of the hole.

Broadly speaking, any mechanically connected detail has a higher fatigue resistance than does its 

equivalent welded detail. The types of discontinuities associated with weld toes transverse to the 

direction of stress introduced when welding have already been discussed. In addition to the fact 

that more discontinuities will be present when welding is used, inspection for discontinuities is 

more difficult than is the case when mechanically fastened details are used. Repairing 
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2.8 

discontinuities in welded details is also difficult. Prohibiting the use of welded details in fatigue 

situations, however, is usually not a practical option. 

The task of the structural engineer is to be able to proportion those structural members that have 

a potential for failure by fatigue crack growth so that they have a fatigue resistance exceeding the 

applied range of stress. As described in Chapter 6, this is done in the environment that some 

probability of failure must be accepted; in real terms, there is no structure that can be designed 

for zero probability of failure. The design will be carried out in the expectation that 

discontinuities will be present initially in all fabricated steel structures and that all such members 

will contain residual stresses of relatively high magnitude. A concomitant feature is that in the 

design process it is possible to identify the size of discontinuities that are permissible and then to 

use this information as the basis for both initial inspection of the structure as well as periodic 

inspections. This latter feature is not yet well-developed in design specifications, and the usual 

procedure is to accept as permissible discontinuity sizes consistent with the specifications that 

accompany the fabrication processes.

SECTION 2.3 STRESS

Cracking in steel structures can only occur when there are tensile stresses present. Total stress 

governs fracture, and fluctuation in stress, or stress range, governs fatigue. Thus, as introduced in 

Section 1.1.1, sustained stresses are important in the investigation of fracture, while cyclical 

stresses are important in the investigation of both fatigue and fracture. 

Figure 2.3-1 illustrates the stresses applied to details due to dead load and live load. In addition 

to these applied stresses are potential residual stresses embodied within the details.
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2.9 

Figure 2.3-1 Typical stress versus time history for a continuous bridge. 

2.3.1 Sustained Stress

2.3.1.1 Residual Stresses from Production and Fabrication

Steel structures that are fabricated by welding contain residual or "locked-in" stresses that are a 

consequence of the welding process. These have considerable influence on the propagation of 

fatigue cracks. The main effect is to significantly reduce the effects of the mean stress levels. 

This effect is numerically demonstrated in Section 4.2.3.2. For modern codes, this has brought 

about a return to the simple stress range versus cycle life model for fatigue strength suggested by 

Wöhler almost 150 years ago (Wöhler, 1870). Furthermore, independence of steel grade was 

justified by the use of a large database of laboratory results taken from tests of different steel 

grades produced in different countries. Code developers have taken advantage of such 

opportunities and, consequently, fatigue design guidelines have been greatly simplified and 

harmonized internationally.

Consider a weld used to join adjacent plates as shown in Figure 2.3.1.1-1. As the weld cools, it 

tries to contract in width and, more importantly, in length. However, since the plate and the weld 

must maintain compatibility of length, the relatively cooler (and thus less expanded) plate 

restrains the weld during the cooling and contraction process. This puts the weld and a relatively 

small volume of plate adjacent to the weld into tension. Conversely, the main portion of the plate 

is compressed by the contracting weld, thereby placing it into compression. The resulting 
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2.10 

stresses from this process are called residual stresses. Since there are no external forces applied 

during this process, the equilibrium condition of the cross section must be reflected in the 

balance between residual tensile stress and the area over which it acts and the residual 

compressive stress and its associated area. The actual distribution and magnitude of the residual 

stress pattern depends upon such factors as the strength of the steel and the weld metal, the 

sequencing of the welds, the geometry of the connected parts, and the size of the weld relative to 

the connected parts. The important fact, however, is that the magnitude of the tensile residual 

stress can reach the yield strength of the material.

Figure 2.3.1.1-1 Residual stresses in groove-weld connected plates.

It follows, of course, that the rolled shapes or built-up members used in structural applications 

also contain regions of high residual tensile stress. For example, very large residual tensile 

stresses are present at the junction of the flange and web of a beam that has been built up by 

welding the component parts together. This junction is also the location of the discontinuities 

that are a potential source of fatigue crack growth, which means that the discontinuity is under a 

condition of initial stress even before load is applied. For the usual condition wherein this initial 

stress is at or near the yield strength, this means that stress range, rather than the maximum 

applied stress, the stress ratio (ratio of maximum stress to minimum stress), or some other 

parameter of applied stress, is the governing condition describing fatigue crack growth. The 
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2.11 

concept of stress range is thus the fundamental characterizing parameter used to design and 

assess steel structures for fatigue. This is reflected in the AASHTO approach.

To summarize, in large welded structures, there are very high tensile residual stresses near 

potential fatigue crack sites, and their presence significantly reduces the effects of mean stress 

level of the applied stresses and steel grade upon crack propagation for standard weldable 

structural steels. As a result, it is generally agreed that stress range is the dominant stress 

parameter for fatigue design.

2.3.1.2 Dead-Load Stresses from Construction

Sustained dead-load stress accumulates during the construction of a bridge. Since stress due to 

dead load is constant and always present in the member, as illustrated by the horizontal dashed 

line in Figure 2.3-1, the change in stress is always simply equal to the change in stress produced 

by the cyclical loads, as discussed in Section 2.3.2. 

As discussed in Section 2.3.1.1, the dead-load stress is not significant for fatigue as the residual 

tensile stress local to the weld toe is typically at or near the yield strength, making the dead-load 

stress inconsequential. 

2.3.2 Cyclical Stress

2.3.2.1 Transportation and Handling

In a few unique cases, fatigue cracks have been discovered prior to bridges being put into service 

as a result of stresses induced during transportation and handling (Fisher, 1984). In a case study 

of the I-480 Cuyahoga River Bridge in Ohio, longitudinal fatigue cracks were observed in girder 

webs in the gaps at the ends of transverse stiffeners cut short of the bottom flanges, a location 

where cracks would not occur during service. 

All of the cracks were located near the wooden blocks used to support the girders during 

shipment by rail. Similar girders shipped by truck were crack-free. Stiffeners were welded to 

both sides of the flange, and cracks were also observed in each side of the web. Vertical tie-down 

rods used to support the girders offered little resistance to lateral movement of the girders. 

Twisting of the girder flanges resting on the wooden support blocks occurred from the lateral 

sway of the girder due to improper blocking of the gap to prevent the distortion. Fatigue cracks 

were caused by large cyclical web-bending stresses in the short web gap. 

2.3.2.2 In-Service Live Load

Figure 2.3-1 shows the applied stress history at a certain location in a member as a truck crosses 

a bridge. Shown are the maximum live-load stress, the minimum live-load stress, and the deadload stress. In any history of stress versus time, there is one absolute maximum live-load stress 

and one absolute minimum live-load stress. The stress range between these two extremes is 

shown in the figure. (It is noteworthy that the stress range is independent of the dead-load stress, 
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2.12 

and it has already been indicated that stress range is the dominant stress-related feature of 

fatigue-resistance determination.) However, there can be other "local" maximum and minimum 

live-load stresses. This leads to the question: how is the detail under examination for fatigue 

resistance influenced by these other stress variations? A method is presented in Chapter 4 that 

accounts for the fatigue damage that results when the cyclical loading is not applied at a constant 

harmonic amplitude. 

Though fatigue is driven by tensile stresses, the entire stress-range excursion, tensile and 

compressive stress, is considered. Since local to the weld toe, the residual stress is at or near the 

yield strength, the superposition of residual and applied stresses produces an excursion entirely 

in tension. If the stress range is entirely in compression, it is not considered for fatigue, as a 

crack cannot grow beyond the extremely small zone of residual tensile stresses at the weld toe.

2.3.3 Stress Concentrations from Details

All elements of a fabricated steel structure contain production- or fabrication-related 

discontinuities, and most also include stress concentrators, such as weld toes, located at details 

such as attachments or connections.

At the attachment, the nominal stress (i.e., the stress in the member away from any stress 

concentration) becomes amplified from several sources of stress concentration, as illustrated in 

Figure 2.3.3-1. First, the amplification is reflected in the local structural stress (which is also 

commonly referred to as the hot-spot stress). AASHTO defines the local structural stress as the 

stress at a welded detail including all stress raising effects of a structural detail but excluding all 

stress concentrations due to the local weld profile itself. Second, there is the local total stress. 

While the local structural stress is computed using extrapolation methods, the local total stress is 

not based on extrapolation. Rather it is based upon an analysis which includes the weld 

geometry.
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2.13 

Figure 2.3.3-1 Concentration of nominal stress into local structural stress and local total 

stress. 

SECTION 2.4 MATERIAL BEHAVIOR

2.4.1 Brittle versus Ductile Behavior

Structural steels fail in either a ductile or brittle manner, as introduced in Section 2.1.2.3, 

depending upon conditions such as temperature, strain rate, material toughness, and constraint. 

Ductile failures are typically preceded by large amounts of plastic deformation and are 

characterized by a failure surface oriented 45 degrees to the applied stress. Brittle failures 

typically occur with little or no prior plastic deformation and at extremely high speeds, 

approaching 7000 ft/sec in steels (Barsom and Rolfe, 1999). They are characterized by a failure 

surface oriented normal to the applied stress. The fracture of the Caltrans Workers Memorial 

Bridge (originally known as the Bryte Bend Bridge) in Sacramento, California in 1970 is shown 

in Figure 2.4.1-1. The failure is attributed to the low-toughness of ASTM A514 steel at a 

reentrant corner detail (between a transverse brace and the tension flange of the tub girder) in the 

presence of a weld-toe crack from fabrication and/or shipping. Note the characteristic appearance 

of the brittle fracture surface showing chevron marks (highlighted in the figure) in the flange 

pointing back to the fracture initiation site.
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2.14 

Figure 2.4.1-1 Fractured tub-girder flange from the Caltrans Workers Memorial Bridge 

(with chevron marks highlighted). 

Brittle versus ductile behavior is influenced by fracture toughness of the material. An accurate 

determination of the fracture toughness is complicated, especially in most structural engineering 

design situations. Less sophisticated approaches are used for practical problems in structural 

engineering. The most widely used method for approximating the toughness quality of a steel is a 

procedure that was developed over 80 years ago known as the Charpy V-notch (CVN) impact 

test. In brief, this method measures the energy absorbed by the rapid fracture of a small bar 

containing a machined notch. The bar is broken by a swinging pendulum, and the absorbed 

energy is measured by the difference in swing height before and after fracture.

A plot of CVN absorbed energy as a function of temperature is shown in Figure 2.4.1-2. The 

CVN absorbed energies shown in the lower left portion of the figure are characteristic of lower 

levels of notch toughness or brittle behavior at low test temperatures (the lower shelf), while the 

CVN absorbed energies in the upper right portion at higher temperatures (the upper shelf) are 

characteristic of ductile behavior. The region between these two extremes is called the transition 

region. 
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2.15 

Figure 2.4.1-2 Charpy V-notch absorbed energy as a function of temperature.

The fracture surfaces of three of the Charpy V-notch specimens are called out in Figure 2.4.1-2

and shown separately in Figure 2.4.1-3, Figure 2.4.1-4, and Figure 2.4.1-5. The fracture surface 

on the specimen at -60°F (below the transition region) is characterized by flat fracture surfaces 

(brittle behavior) and no noticeable change in width at the notch. The fracture surface at 55°F 

(above the transition region) is characterized by shear lips (ductile behavior) and a noticeable 

change in width at the notch. The specimen at 0°F exemplifies the transition.
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2.16 

Figure 2.4.1-3 Photograph of fracture surface of Charpy V-notch Specimen 2A1 tested at 

lower temperature (see Figure 2.4.1-2).

Figure 2.4.1-4 Photograph of fracture surface of Charpy V-notch Specimen 2E5 tested at 

the transition temperature (see Figure 2.4.1-2).
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2.17 

Figure 2.4.1-5 Photograph of fracture surface of Charpy V-notch Specimen 2I3 tested at 

higher temperature (see Figure 2.4.1-2).

Some materials other than bridge steels do not exhibit a distinct transition behavior. Other 

materials exhibit relatively low notch toughness at all temperatures (such as high-strength 

aluminum), yet others exhibit relatively high notch toughness at all temperatures (such as steels 

with yield strengths greater than bridge steels).

Bridges are designed to preclude fracture based upon proper material selection or, when 

applicable, the use of a Fracture Control Plan (FCP) per the Bridge Welding Code

(AASHTO/AWS, 2010). A transition temperature is established as an indication of the notch 

toughness of a structural material. The designer selects a steel with a fracture-toughness level 

that is sufficiently high above the transition temperature for the intended application, as 

discussed in detail in Chapter 7. Thus the design for fracture is a function of material 

specifications and fabrication control rather than fracture mechanics analysis methods. 

2.4.2 Effects of Temperature and Strain Rates

CVN tests are performed at higher, more easily achieved, temperatures than bridge service 

temperatures. They are also performed at greater, more easily controlled, strain rates than bridge 

service loadings. Fortunately, correlations between test temperature and intermediate and impact 

strain rates are available and are well defined. These correlations allow for the use of this 

common and simple test to characterize the expected in-service performance of bridge steels.

In general, the fracture toughness of steels increases with increasing temperature and decreasing 

strain rate. This behavior is shown schematically in Figure 2.4.2-1. The transition from brittle to 

ductile behavior begins at lower temperatures for specimens tested at slow loading rates, 

compared with specimens tested at impact loading rates used in CVN tests. The shift in transition 

curves between bridge loading (intermediate, with approximately 1.0 second loading to fracture) 

and impact (less than 0.001 second to fracture) is about 75 percent of the shift between static and 

impact curves.
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2.18 

Figure 2.4.2-1 Schematic representation of the shift in temperature and upper shelf due to 

strain rate.

The fracture behavior of bridge steels as a function of the temperature shift based upon loading 

rate in conjunction with the fracture criterion and the AASHTO operating temperature zones 

(AASHTO, 2015b) results in the AASHTO FCP (AASHTO/AWS, 2010), discussed in detail in 

Chapter 7. 
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3.1 

CHAPTER 3 THEORY

SECTION 3.1 GENERAL

Fracture mechanics provides a theoretical basis for understanding many aspects of fatigue and 

fracture behavior in steel structures. The use of the fracture mechanics method of analysis is 

relatively recent. Originally advanced to explain the rupture of glass specimens (Griffith, 1921), 

its introduction into the field of structural engineering practice started when it was used in the 

1940's to help explain the catastrophic failure of welded ship hulls. Currently it is employed to 

assess the behavior of elements used in machinery, pipelines, automotive parts, spacecraft, 

turbine blades, and many other components. 

In this chapter, basic concepts of the fracture mechanics approach are described to assist the 

reader in understanding crack behavior and the basis of the fatigue and fracture design rules. For 

those who might need to design at higher levels of sophistication, it provides the basis for further 

reading and self-instruction. 

Only a basic level of fracture mechanics concepts is employed in this chapter. For simplicity, the 

discussion is limited to cases in which the loads are applied at locations remote from the crack 

locations and normal to the crack surfaces, the so-called Mode 1 configuration. Excellent review 

articles provide more detailed information (for example, see Irwin and de Wit, 1983; Rolfe, 

1983; and Smith, 1978-79), and several reference books are available (Broek, 1984; Barsom and 

Rolfe, 1999; and Pellini, 1983). Detailed fracture mechanics application to the assessment of 

structures can be found in publications on fitness-for-service such as API 579-1/ASME FFS-1 

(API, 2007) and BS 7910 (British Standards Institute, 2015).

SECTION 3.2 ACCOUNTING FOR A CRACK

Five cases of a loaded plate containing a crack are shown in Figure 3.2-1. It requires no 

knowledge of fracture mechanics to appreciate that Cases 1 through 5 are placed in order of 

increasing severity. Taking Case 1 as the basis for comparison, the following important fracture 

mechanics parameters can be identified as elements of the base case are changed: 

• The influence of increasing the crack length (Case 2)

• The influence of crack location (i.e., at the edge of the plate) (Case 3)

• The addition of bending on an edge crack (Case 4)

• The presence of a stress concentration (Case 5)

Of course, the result of any of these parameters in weakening the plate will depend on the actual 

circumstances. The effect can be significant, however. For instance, the consequence of a sharp 

stress concentration in combination with a crack (Case 5) could weaken a plate to less than onehalf of its uncracked strength. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

3.2 

Figure 3.2-1 Five different cases of a plate containing a crack. 

A magnified view of the area around a crack tip in an infinitely wide plate is shown in 

Figure 3.2-2. This resembles closely the conditions of Case 1 in which the crack length is small 

compared with the plate width. When a remote stress, σ, is applied, the crack opens a certain 

distance, d, and the stress that this cross-sectional area would have carried is diverted to the 

uncracked area of the plate. This diversion creates a high concentration of stress in the vicinity of 

the crack tip. For an elastic material, theoretically this stress is infinite at the crack tip which is 

modeled as having a sharp zero radius. In real materials, plastic zones are formed since the strain 

exceeds the ability of the material to behave elastically. 

This process—whereby (1) an applied load causes a crack to open, (2) the crack opening relieves 

crack surfaces of stress, and (3) crack tip plastic straining is created—is the fundamental 

mechanism that weakens structures containing cracks or discontinuities. Fracture mechanics 

focuses on the local behavior at the crack tip. The state of stress at the crack tip controls whether 

the crack will advance under increase in load, producing unstable (brittle) crack extension or 

stable progressive extension under fatigue loading. (It should be noted that in bridge structures, 

cracking may not necessarily lead to unstable propagation, since in many cases the limited 

magnitude of stress may allow the cracking to arrest, resulting in the need for either no repair or 

simple repair.) 
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3.3 

Figure 3.2-2 Crack stress field and crack characteristics in a wide plate.

If plasticity is ignored, a description of the stress field near the crack tip can be obtained. Using 

special stress functions, a solution containing the coordinates r and θ is developed. For the 

particular case of θ = 0 (that is, for the stress in the y-direction), the stress is:

2 yy

a

r

σ π

σ

π =

Equation 3.2-1 

provided that the crack length, a, is much larger than the distance from the crack tip, r, at which 

point the stresses are being evaluated and the crack length “2a” is much smaller than the plate 

dimensions. The numerator in Equation 3.2-1 determines the gradient of the theoretical stresses 

as they rise to infinity when r approaches zero. This numerator is called the stress intensity 

factor, K, a single term characterizing the intensity of the stress at the crack tip. Thus: 

K a =σ π

Equation 3.2-2 
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3.4 

The advantage of this model is that any combination of stress and crack length can be 

characterized by the single parameter K. Analytical solutions are available for other particular 

geometrical configurations and loading conditions; these are summarized in handbooks (Tada et 

al., 1985; Roark et al., 2012). However, many practical cases cannot be solved analytically. In 

such instances, the following expression is used to approximate K: 

K WY a = σ π

Equation 3.2-3 

where Y is an expression that corrects for plate and crack geometry and W corrects for 

nonuniform local stress fields caused by stress concentration due to connection geometry and 

local residual stresses. Usually such correction factors are determined using numerical methods.

However, solutions can also be found in handbooks. 

As an example of the effect of crack geometry upon the stress intensity factor, the edge crack 

present in Cases 3 through 5 in Figure 3.2-1 produces a more severe case than the center crack in 

Cases 1 and 2. The crack length in the center crack is “2a”, while the crack length in the edge 

crack is “a”. The value of Y in Equation 3.2-3 is 1.12 for an edge crack. Consequently, the ratio 

of the stress intensity factor of an edge crack to a center crack with equal crack lengths “c” and 

the same applied stress in a large plate is:

Equation 3.2-4 

A crack at an edge of a flange produces a 58 percent larger stress intensity factor at the crack tip 

than a similar size crack centered on the plate. 

Equation 3.2-1 is based upon linear-elastic material behavior and cannot account for yielding at 

the crack tip. Furthermore, stress redistribution due to plasticity alters the stress field outside the 

crack tip plastic zone. Nevertheless, if the plastic zone is small, say less than 2 percent of the 

plate thickness, of the crack length, and of the uncracked ligament, then the elastic stress 

intensity factor (K) approach is satisfactory.

However, these limitations are violated in many practical situations. For example, an elastic–

plastic analysis may be required when stress concentrations cause localized plasticity. The most 

common analyses either use a parameter named J, which is an expression of the change in 

potential energy with respect to crack length, or use a parameter called the crack tip opening 

displacement (CTOD). Further description of elastic-plastic analyses is available elsewhere 

(Barsom and Rolfe, 1999). In addition, ASTM has produced standards for determining these 

parameters experimentally (e.g., ASTM, 2013). These inelastic parameters can be approximately 

related by Equation 3.2-1. An equivalent elastic K value for plane stress can also be estimated 

using the following equation: 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

3.5 

2

y

K J CTOD

E = =σ

Equation 3.2-5 

where E is Young's modulus and σy is the effective yield strength. When plate thickness is large 

enough to restrict behavior to essentially two-dimensional straining (plane strain conditions), the 

material constant, E, is replaced by E / (1− υ2), where υ is Poisson's ratio. Steels with high 

resistance to fracture (high fracture toughness) can tolerate large inelastic strains at the crack tip 

before crack extension, while steels with low resistance to fracture exhibit little crack tip 

plasticity before fracturing. 

A further restriction on K exists for small crack lengths, where all of the approaches explained 

above lose their validity. When the size of the crack or initial discontinuity is of the order of 

grain size, microstructural properties such as grain orientation influence crack growth (Lankford, 

1985). Microstructural fracture mechanics models may then become necessary. These models are 

not yet well defined, and no generally accepted design rules are available. For the usual situation, 

when the crack length is greater than about five grain diameters, the models that assume an 

isotropic continuum (i.e., those employing K or J) are sufficiently accurate.

SECTION 3.3 PRINCIPLES OF FRACTURE CONTROL 

3.3.1 Material Toughness 

The collapse of the Point Pleasant Bridge from the brittle/unstable extension of a small flaw 

provided the impetus for the bridge engineering community to consider a new fracture control 

strategy which included the probable existence of a crack in a tension member. The realization of 

the possibility for a small crack to cause a complete fracture of a member led to the development 

of a fracture control plan. This plan consisted of revised fabrication, welding, and inspection 

standards, fracture toughness requirements for the steels and weldments, and more stringent 

fatigue design specifications. Later, after the collapse of the Mianus River Bridge, in-service 

inspection of nonredundant tension members also became more stringent. 

An accurate determination of the fracture toughness is complicated, especially in most structural 

engineering design situations. This is primarily due to the fact that, for most designs, plane strain 

conditions do not dominate; conditions of essentially two-dimensional stress (plane stress) have 

an influence, thereby disqualifying K as a model that characterizes combinations of stress and 

crack length. Elastic-plastic models are needed because the stress at fracture produces a plastic 

zone size that exceeds the limitations cited for the validity of K specified in Section 3.2. 

Less sophisticated approaches are used for practical problems in structural engineering. The most 

widely used method for approximating the toughness quality of a steel is a procedure that was 

developed in the early 1900’s, the Charpy impact test, introduced in Chapter 2. 

The Charpy impact test and many other similar procedures (Pellini, 1983) provide only 

qualitative information, because stress and crack length values cannot be assessed directly.

However, correlation with fracture mechanics models is available for certain situations (Barsom 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

3.6 

and Rolfe, 1999). For example, Charpy impact data in the lower region of the energy versus

temperature response curve can be converted into dynamic plane-strain fracture toughness 

values, KId, using an empirical formula. If required, the KId values can then be converted to static 

plane-strain fracture toughness values, KIc. In general, such correlations are valid only for steels 

of low to medium strength which covers typical bridge steels. Moreover, the toughness value 

where conditions change from plane strain to plane stress depends upon the yield strength, crack 

geometry, and thickness of the element. These correlations provide an estimate for the material’s 

resistance to crack propagation; they do not capture the resistance of a crack propagation, 

particularly in materials with high toughness to yield strength ratio. 

At a given temperature, a given material will always exhibit higher fracture toughness for plane 

stress conditions than for plane strain conditions in the elastic-plastic region. Therefore, KIc and 

KId are conservative first estimates of the fracture toughness. Elastic–plastic analyses, which 

result in less conservatism, can be used when the design problem justifies increased complexity 

of work. 

The need for the steel to tolerate a crack which might form by fatigue from the extension of an 

initial small discontinuity (e.g., a tiny slag intrusion at the surface of the fusion line of a fillet 

weld or embedded discontinuity in a butt weld) was provided by including fracture toughness in 

the material specifications for tension members. The fracture toughness requirements are based 

upon the basic fracture mechanics relationship between applied stress, flaw size, and toughness: 

KK WY a 1c => πσ

Equation 3.3.1-1 

where the left side of the inequality is KIc, the material’s fracture toughness, and the right side is 

the stress intensity for the crack in the structure. 

The stability of the crack as a function of the parameters of Equation 3.3.1-1 is shown in Figure 

3.3.1-1. Combinations of crack size and stress level below the upper solid line have a stress 

intensity factor less than the fracture toughness of the material and represent stable cracks that 

can be tolerated in the material. The upper solid line shown in the graph is when KIc equals K, 

and this is the instability line similar to the limit defined by Euler buckling of a column.

Combinations of stress and crack size above this line are unstable and will produce a brittle 

fracture. The fracture control strategy is designed to prevent the crack from reaching its critical 

size during the life of the structure. The level of fracture toughness specified by the Charpy Vnotch energy requirements is designed to ensure that the critical crack size will be easily 

detectable by a close visual inspection of the bridge. 

Higher strength steels require higher toughness to provide the same critical crack as a lower 

strength steel since the stress levels in the high strength steels are likely larger. Consequently, the 

toughness levels are higher for higher strength steel. Thicker components also require higher 

toughness due to the constraint offered by the thicker material, which limits the plasticity at the 

crack tip. In addition, thicker materials have larger crack sizes when the crack is visible on the 

surface of the plate. 
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3.7 

The minimum toughness specified in the material specification provides the means to calculate a 

tension component’s ability to resist brittle fracture. If the toughness is not specified, the 

designer does not have a basis to assure the flaw tolerance of the component. This is similar to 

what would occur if the yield or tensile strength was not specified; the designer would not be 

able to calculate the load resulting in yielding of the member.

Figure 3.3.1-1 Fracture resistance as a function of toughness, stress, and crack size. 

3.3.2 Effect of Critical Crack Size upon Inspection

As depicted in Figure 3.3.1-1, the critical crack size (i.e., the crack size that will trigger unstable 

crack propagation and fracture of the member) is a function of flaw size, applied stress, and 

fracture toughness. The lower dashed line in the figure represents the behavior if the toughness 

of the material is less. Similarly, the critical crack size for a given stress level decreases.

The eyebars in the Point Pleasant Bridge were fabricated with very low toughness steel. The 

critical crack depth was only approximately 1⁄4 inch. Its companion bridge, the St. Mary’s Bridge, 

was inspected after the collapse of the Point Pleasant Bridge to evaluate its safety. It was 

impossible to distinguish between cracks of this size and rust pits formed on the interior of the 

eyebar pin hole. Due to the low toughness or low flaw tolerance of the material, the safety of the 

bridge could not be reliably determined due to the inability to find these small cracks. The bridge 

was subsequently taken out of service and demolished. 

Modern bridge steels used in tension members have toughness requirements to provide tolerable 

crack sizes that exceed the size crack that could frequently be missed in a field inspection. The 

toughness level increases with increase in yield strength since the stress level at failure in the 

member is controlled by the material’s strength. The validity of the toughness requirements was 

verified in full-size girder tests performed at Lehigh University (Roberts et al., 1977c). The tests 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

3.8 

showed that when the maximum design stress is applied to the girders at service loading rate 

with the specimen cooled to the lowest anticipated service temperature, fatigue cracks of the 

order of the plate thickness could be tolerated without producing a brittle fracture. 

For bridges fabricated with toughness requirements, current in-service bridge inspection using 

primarily visual inspection provides adequate reliability. However, older welded bridges 

fabricated without toughness requirements may have much smaller critical flaw sizes and 

therefore may require more sensitive inspection techniques. Riveted bridges are not as critical 

since they do not have fatigue prone details and have inherent member redundancy. 

3.3.3 Assurance through CVN Toughness Requirements

The grades of steels used in bridge structures have a complex fracture toughness behavior. The 

toughness of a given steel varies with the rate of loading and the temperature, as introduced in 

Chapter 2. Extensive tests have shown that the static and dynamic curves have similar shapes and 

that the difference between the two curves can be described in terms of difference in 

temperature, often called the temperature shift. The temperature shift for steels is inversely 

proportional to the yield strength, Fy, of the steel. Very high strength steels (i.e., steels with yield 

strengths of 150 ksi or greater) show no temperature shift; the dynamic and static curves are 

identical. However, for lower strength steels, the temperature shift can be estimated as:

215 1.5 T F

s y = −

Equation 3.3.3-1 

For example, a Grade 50 steel has a temperature shift of 140 °F. The Charpy V-notch (CVN) test 

used to measure the notch toughness of the structural steels is a dynamic test. The service 

loading rate of a bridge is an intermediate loading rate, 101

 seconds. The response of the material 

at this intermediate loading rate is depicted by the curve between the dynamic and static curves. 

The difference in temperature between the dynamic and intermediate curves is approximately 

0.75Ts. 

The test temperature used for the dynamic CVN temperature is the lowest anticipated service 

temperature (often referred to as LAST) of the structure plus 0.75Ts. This methodology is shown 

in Figure 3.3.3-1. The required toughness and LAST define the point on the intermediate loading 

rate toughness curve in Figure 3.3.3-1a. The temperature is shifted up to the dynamic curve using 

the temperature shift concept and finally down to the CVN curve of Figure 3.3.3-1b to define the 

required CVN energy at the shifted temperature.
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3.9 

(a) Controlled load rate test 

(b) CVN test

Figure 3.3.3-1 CVN-toughness development.

A number of correlations have been developed to relate the fracture toughness to the notch 

toughness measured using CVN testing. The most commonly used correlation is of the form: 

12.5 K CVN Id = (in units of ksi√in.)

Equation 3.3.3-2 
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3.10 

where CVN is the impact energy in ft-lbs absorbed by the steel in a dynamic CVN test. 

For example, for a 50-ksi yield strength steel (Ts = 140 °F) to be used in a structure with a LAST 

of -35 °F, the CVN test temperature can be calculated as:

0.75 35 0.75 (140) 70 CVN s T LAST T = + =− + =

Equation 3.3.3-3 

The required toughness for a 1-inch through crack in the center of the plate can be calculated 

using Equation 3.2-2, where “a” is the half-crack length. Assuming the maximum applied stress 

can be up to the yield strength: 

K required y = = = σπ π a 50 0.5 62.7 ksi in

Equation 3.3.3-4 

The required CVN absorbed energy can be calculated using Equation 3.3.3-2: 

2 2

62.7 25.1

12.5 12.5

KId CVN ft lb     = = = −        

Equation 3.3.3-5 

Therefore, the material requirement is that the average of three CVN specimens tested at 70 °F 

must exceed 25 ft-lb. 

Similar calculations were used to develop the toughness requirements in ASTM A709, the bridge 

steel specification. It should be noted that these requirements apply only to tension members. 

Fracture critical members have slightly higher toughness and lower test temperature to provide 

enhanced flaw tolerance. The weld metal toughness requirements in AWS D1.5 are more 

stringent than the base metal requirements, since the weld qualification geometry used to obtain 

the test specimens does not match the production welds. The weld qualification tests are used to 

ensure that the weld metal in the structure has a toughness equal to or greater than the base 

metal.

SECTION 3.4 PARIS’ LAW AND MINER’S RULE

Extension of cracks by fatigue is labeled stable crack propagation since the crack extends a finite 

distance with each load cycle. The first application of fracture mechanics to fatigue crack 

propagation was in the aerospace industry by Paris, Gomez, and Anderson (Paris et al., 1961). 

They reasoned that the extension of a crack by fatigue would be proportional to the range of 

stress at the crack tip. They coined a new parameter to describe this range of stress in terms of 

the local elastic crack tip stress, referred to as Delta (∆) K, as shown below. 

Equation 3.4-1 
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3.11 

They found that the average crack extension per load cycle, (which is also the slope of the 

crack extension curve), could be related to the value of Delta (∆) K by a simple power law, often 

referred to as the Paris power law: 

Equation 3.4-2 

where:

= average crack extension per load cycle

They also found that a value of n equal to 4 best fit their data form studies of fatigue crack 

growth in aluminum aircraft alloys. The value of the coefficient C is a material property. Later 

studies in steels found that a value of n equal to 3 gave the best fit to the data. 

Later studies indicated that as the maximum stress intensity of the crack approached the fracture 

toughness of the material, the crack growth accelerated. The later studies also indicated that if 

the value of Delta (∆) K was small, no crack extension occurred. This limiting value is often 

termed the crack growth threshold and is written as Delta (∆) Kth. 

The fatigue crack growth under random loading similar to that produced by vehicles on a bridge 

was found to be proportional to the effective stress range in place of the constant stress range. 

The effective stress range is calculated using a rainflow cycle counting algorithm and Miner’s 

linear cumulative damage law. 

Miner’s linear rule for variable amplitude fatigue is:

Equation 3.4-3 

where ni is the number of cycles at stress range i and Ni is the constant amplitude fatigue life at 

the stress level i. 

These values can be written as:

Equation 3.4-4 

and nnii = γii TT, where T is the total number of cycles and γi is the fraction of the total cycles 

occurring at stress level i. 

Substituting these values into Miner’s rule yields: 
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3.12 

Equation 3.4-5 

Rewriting the equation, the total number of fatigue cycles to failure, T, becomes: 

Equation 3.4-6 

Equation 3.4-6 has the same form as Equation 3.4-4, the equation for the constant amplitude 

fatigue life. The effective stress range, defined as the constant amplitude stress range that will 

produce the same fatigue life as the variable amplitude stress history, is: 

Equation 3.4-7 

Substituting into Equation 3.4-7 a crack growth exponent of 3 for structural steels yields the 

following: 

Equation 3.4-8 

This relationship was used to relate the typical traffic vehicle spectrum of fatigue stresses into a 

constant level stress range which produces the same fatigue damage, which in turn becomes the 

fatigue design truck.

SECTION 3.5 FRACTURE MECHANICS AS A QUANTITATIVE TOOL

The basic fracture mechanics concepts can provide insight into the resistance of structures under 

fatigue loading. The Paris power law presented in Equation 3.4-2 provides a method to calculate 

the fatigue resistance of a structure. The equation may be rewritten in the following form:

Equation 3.5-1

where:
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3.13 

ai = initial crack length (inches)

ac = critical crack length (inches)

σr = stress range (ksi)

C = crack growth constant for the material = 3.6x10-10 for structural steel with a crack 

growth exponent of n = 3 

If the functions of W and Y are known, the fatigue life can be calculated using this equation.

Normally, due to the complexity of these expressions, the integral must be evaluated 

numerically.

To demonstrate the use of Equation 3.5-1, it will be used to evaluate the fatigue life of a wide 

cracked plate with a crack length of 2a in the center, as shown in Figure 3.5-1. The stress is 

applied remotely from the crack, and the width of the plate is much larger than the crack length, 

2a. Therefore, W and Y both equal 1, allowing the integration to be performed quite simply. 

Figure 3.5-1 Wide cracked plate with a crack length of 2a in the center.

For this example, Equation 3.5-1 results in the following:

Equation 3.5-2 

The term in the parentheses provides a means of evaluating the significance of the initial flaw 

size to the critical flaw size. If ai and ac are of comparable size, the fatigue life becomes very 
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3.14 

short. However, if the initial flaw size is controlled during fabrication through the shop 

inspection requirements and the critical flaw size provided by the material’s fracture toughness is

of the order of the plate thickness, then the term in the parentheses approaches 1 and the critical 

flaw size has minimal effect on the fatigue life. If ai is much smaller than ac, then the estimate of 

the fatigue life becomes:

Equation 3.5-3 

The initial crack size and stress range have been placed under the radical sign to demonstrate the 

relative importance that each has on the fatigue life. A 10 percent reduction in the initial flaw 

size results in a 5 percent increase in fatigue life, while a 10 percent reduction in the stress range 

results in a 37 percent increase in fatigue life. As a consequence, a reduction in the design stress 

range is the most effective method of increasing fatigue resistance of a structure, given that the 

ratio ai to ac is small.

The more general form of the fatigue life equation, Equation 3.5-1, can be helpful in interpreting 

and understanding the AASHTO fatigue categories. The equation is written again as: 

Equation 3.5-4 

The integral shown in brackets is a function of the crack and detail geometry and the initial and 

final crack size. For a given fatigue detail, this would be a constant if the geometry and initial 

flaw size are controlled. However, for practical welded bridge construction, these become 

random variables, although limited by the fabrication standards. Consequently, the fatigue life of 

replicate test specimens typically will not be a single value. The fatigue life categories in 

AASHTO are based upon a lower bound of the fatigue strength that consider the variability of 

these variables upon fatigue resistance. If A is defined as the value of the term in brackets 

divided by the crack growth constant, C, then fatigue life can be defined using the following 

simple expression: 

Equation 3.5-5 

Taking the logarithm of each side of the equation provides a linear log-log relationship:

Log N = Log A – 3 Log σr

Equation 3.5-6 

This is the form of the AASHTO fatigue requirements. AASHTO provides the value of A for 

each fatigue category. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.1 

CHAPTER 4 FATIGUE BEHAVIOR

As introduced in Chapter 2, fatigue in steel structures is the process of growth of cracks under 

the action of repetitive tensile loads. Further, in Chapters 2 and 3, the presence of discontinuities 

is revealed to be one of two conditions necessary for fatigue-crack growth. The fatigue life of a 

component is dependent upon the applied stress range, the initial discontinuity introduced during 

fabrication, and local stress increase due to the joint geometry. The influence of each of these 

variables is discussed in this chapter. 

SECTION 4.1 THE INFLUENCE OF PRODUCTION AND FABRICATION

Discontinuities exist in all fabricated steel structures as a consequence of the manufacturing 

process of the steel itself and/or the normal fabrication processes of the components. 

The term “discontinuity” does not necessarily imply defect. A discontinuity may or may not be 

classified as a defect, depending upon its size and orientation in the member or connection. 

Discontinuities are rejectable only if they exceed the specification requirements for type, size, 

distribution, or location. These acceptance criteria can be found in the AASHTO/AWS D1.5 

Bridge Welding Code for weldments (AASHTO/AWS, 2010), ASTM A6 for base metal (ASTM, 

2014), and the AASHTO LRFD Bridge Construction Specifications (AASHTO, 2015a). All 

cracks detected during the shop inspection are rejectable. The shop inspection serves to ensure 

that any discontinuities that remain in the weld will not reduce the design fatigue resistance.

4.1.1 Materials and Processing

Discontinuities may be found in the base metal of rolled shapes and plates. Figure 4.1.1-1

illustrates representative discontinuities for a rolled beam.
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4.2 

Figure 4.1.1-1 Examples of discontinuities in a rolled beam.

Seams and laps are longitudinal base-metal discontinuities in rolled shapes and plates. When 

located parallel to the applied stress, they are generally not considered critical. When 

perpendicular to the applied stresses, they can propagate as cracks. Seams and laps are surfaceconnected discontinuities that result from cracks in the surface of the slab or mechanical 

deformations caused by the manufacturing process. Rolling blunts the discontinuities such that 

the seam is generally not as sharp as the original slab crack.

Laminations are planar discontinuities elongated during rolling. They generally are parallel to the 

surfaces and are most commonly found near the mid-thickness of rolled shapes or plates. 

Laminations may be completely internal, or they may extend to an edge. Laminations are formed 

when gas voids, nonmetallics, or slab shrinkage cavities are rolled flat.

Inclusions result from nonmetallic, solid material being entrapped in slabs during the steel 

production process and flattened during rolling. These discontinuities sometimes appear after 

flame cutting the plate to size or beveling the plate in preparation for a groove weld. The AWS 

D1.5 specifications (AASHTO/AWS, 2010) limits the size of these planar discontinuities that 

may be left in place. Larger discontinuities must be either ground out or repaired by welding. 

Some joint geometries can produce large through thickness stresses, such as the corner joint 

shown in Figure 4.1.1-2. The stress caused the shrinkage of the welds on each side of the plate 

and produced a tear in the center vertical plate. Figure 4.1.1-3 shows an improved detail with the 

weld preparation on the vertical plate which engages any discontinuities in the plates and limits 

the through thickness stress generated by the weld shrinkage. Other joint improvements are 

shown as well. This topic is further covered in Section 7.1.4.2. 
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4.3 

Figure 4.1.1-2 Lamellar tear due to through thickness stresses from weld shrinkage.

Figure 4.1.1-3 Improved weld details to reduce through thickness stresses.

4.1.2 Discontinuities at Welded Joints 

At welded joints, discontinuities may be found in the weld metal or in the heat-affected zone in 

butt, tee, corner, and lap joint configurations. Figure 4.1.2-1 illustrates representative 

discontinuities for a welded beam. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.4 

Figure 4.1.2-1 Examples of discontinuities in a welded beam.

Porosity is created when solidifying weld metal entraps gas. The discontinuity is generally 

spherical in shape but may be elongated. Undercut generally is the result of the molten weld 

metal not filling the base metal melted at the edge of the weld. It is caused by either improper 

technique and/or excessive weld heat. The AWS Bridge Welding Code requires that undercut 

greater than 0.01 inch must be repaired if the weld is transverse to the direction of applied stress 

(AASHTO/AWS, 2010). For longitudinal welds parallel to the direction of stress, such as webto-flange welds, the allowable undercut depth is 1/32 inches. It is located at the junction of the 

weld and the base metal, at a fillet-weld toe (as shown in Figure 4.1.2-1), or at a groove-weld 

fusion line. The lack of fusion shown in the figure is the result of the fillet welds used in the 

connection. It is of no consequence if the applied stress is parallel with the weld. Fillet welds are 

commonly inspected using magnetic particle inspection which detects surface discontinuities. 

Internal discontinuities such as porosity are accounted for in the Category B fatigue design 

allowable stress ranges. However, if they are big enough, they are rejectable through the 

AASHTO/AWS D1.5 inspection acceptance criteria (AASHTO/AWS, 2010). 

More complete descriptions of common discontinuities present in both weld and base metal can 

be found in AWS Bridge Welding Code (AASHTO/AWS, 2010).

A sample welded detail, as introduced in Figure 2.3.3-1, shows a plate under uniform stress with 

a longitudinal fillet-welded attachment. The nominal stress is the uniform stress away from the 

attachment and can be calculated using simple principles of strength of materials.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.5 

The nominal stress becomes amplified closer to the attachment from two sources of stress 

concentration. First, the effect of global geometry of the connection as the section changes from 

a plate to a tee section produces an elevated stress referred to as the local structural stress. 

Finally, the stress concentration due to the local geometry of the weld toe dependent upon 

random parameters, such as weld profile and ripples in the weld toe, elevates the local structural 

stress further, becoming the local total stress. The local total stress can be accurately 

characterized for a specific weld geometry but not for a category of details.

The effect of a variation in geometry can be understood by visualizing stress flow lines. Consider 

the case of a short fillet welded attachment in a flat plate, as shown in Figure 4.1.2-2. Away from 

the attachment, the flow lines are uniformly distributed across the width of the plate. The 

attachment must elongate with the plate as the plate is loaded, since the attachment is fixed to the 

plate by the weldment. Therefore, the attachment is stressed. As the stress “flows” into the 

attachment, a concentration of stress occurs at the weld toe, as shown in Figure 4.1.2-2. The 

amount of stress flowing into the attachment, and hence the stress concentration, is dependent on 

the attachment length parallel to the stress. As the length increases, more stress can flow into the 

attachment and the stress concentration increases. The AASHTO fatigue specifications recognize 

the effect of attachment length and thickness upon the local stress at the weld toe in their fatigue 

categories. The larger or longer the attachment, the lower the fatigue strength and corresponding 

fatigue category.

Figure 4.1.2-2 Stress flow lines in fillet-welded attachments.

As a general rule, details that involve crack growth from internal discontinuities, such as 

porosity, slag inclusions, cold laps, and other comparable conditions, will have a higher fatigue 

resistance. These discontinuities experience little or no stress concentration. Details that provide

a lower fatigue resistance involve connections that experience fatigue crack growth from initial 

discontinuities in the weld toes and weld ends where there is a high stress concentration due to 

geometric conditions, as shown earlier in Figure 2.3.3-1. 
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4.6 

The relative influence of discontinuities and the stress concentration on detail fatigue resistance

is shown schematically in Figure 4.1.2-3. The fatigue resistance of detail types commonly used 

in bridge construction is characterized as Detail Categories A through E' (AASHTO, 2015b). The 

higher-resistant (greater fatigue life) details, such as Detail Category A (plain plate or rolled 

shape), are dominated by the initial discontinuity size and do not have large stress concentrations 

caused by a change in the cross section. The lower-resistant (lower fatigue life) details, such as 

Detail Category E', are dominated by larger stress concentrations at a weld toe with a much 

smaller initial discontinuity. The initial discontinuity curve peaks around Detail Category B due 

to the upper limit of discontinuity sizes as specified (AASHTO/AWS, 2010) for groove welded 

details and the acceptance of porosity in longitudinal fillet welds. The initial discontinuities in 

Detail Categories C through E' are the same, with small slag intrusions at the fusion line between 

the weld and base metal (Signes et al., 1967). The detail categories and their application in 

bridge design are discussed in detail in Chapter 6. 

Figure 4.1.2-3 Relative influence of initial discontinuity size and stress concentration. 

4.1.3 Weld Residual Stresses

4.1.3.1 Source and Magnitude

As introduced in Section 2.3.1.1, fabricated steel structures contain “residual” or “locked-in” 

stresses that have been introduced as a result of production and fabrication processes which 

cause differential cooling of the steel. 

The results from residual stress measurements on beam specimens of three different steel types 

are plotted in Figure 4.1.3.1-1. These distributions correspond to the measured residual stresses 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.7 

in the flanges of welded beam specimens and are in the longitudinal direction, parallel with the 

longitudinal axis of the web-to-flange fillet weld. As indicated by Figure 4.1.3.1-1, large tensile 

residual stresses were measured in the vicinity of the web-to-flange fillet welds. As the steel

strength increased, the magnitude of the maximum tensile residual stress also increased and was 

near or above the yield strength for the weld metal itself. The residual stress at the tip of the 

flanges is also high. This residual stress at the flange tip is due to the thermal cutting of the 

flanges from wide plates. The quarter points of the flange are in compression. The sums of the 

residual tensile and compressive stresses are equal, and therefore the net internal force on the 

cross section is zero. The metal melted and heated during the welding and thermal cutting 

process will contract as it cools. The contraction of the heated area is resisted by the adjacent 

material which has not been heated. The differential shrinkage causes residual tensile stresses to 

form in the area that has been heated and compressive stresses in the unheated area. 

Figure 4.1.3.1-1 Residual-stress distributions in welded plate girder flanges.

For the typical condition in the vicinity of the welded fatigue detail where this initial residual 

stress is at or near the yield strength, stress range, rather than the maximum applied stress, the 

stress ratio, or some other parameter of applied stress, is the governing parameter characterizing 

fatigue-crack growth. The effect of the level of applied stress, the mean stress, upon fatigue life 

was studied in a factorial experiment using beam specimens and found to be statistically 

insignificant (Fisher et al., 1970). These full-size specimens used in the tests which define the 

fatigue life categories in the specification had the residual stresses at the details. Therefore, the 

effect of residual stress upon fatigue performance is incorporated into the specifications. This 

will be illustrated by the following numerical example.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.8 

Example

Figure 4.1.3.1-2 shows a rectangular plate and its assumed residual stress pattern. (This 

idealization could represent the flange of a welded beam.) This example illustrates how the local 

residual stress inherent in all welded structures influences the cyclic stress at a weld location.

Given:

According to the designer, the plate will be subjected to a maximum tensile stress of 31 ksi and a 

minimum compressive stress of 18 ksi. Calculate the net range of stress that will exist for a 

discontinuity at the center of the plate (cf., the junction of the web and flange of a welded beam). 

Compare this range of stress with the stress range that will be computed by the designer, that is, 

+31 ksi − (−18 ksi) = 49 ksi. The plate has a yield strength of 44 ksi.

Solution: 

Initial conditions: The pattern of residual stress is shown in Figure 4.1.3.1-2(a). It shows that the 

values of the initial residual stress are as high as the yield stress. Since the residual stress does 

not exceed the yield stress, the corresponding strains can be calculated from the elastic 

relationship, σ = E ε, and these strains are shown in Figure 4.1.3.1-2(b). There is no force on the 

member, and it is noted (by inspection) that the condition P = ∫σ dA = 0 is met. (This can be 

verified by calculation.) 

Figure 4.1.3.1-2 Initial stress condition in a welded plate.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.9 

Apply tensile force such that the design stress level is +31 ksi. This is computed as follows: 

P = σ A = (31,000 psi) (1 in x 5 in) = 155,000 pounds = 155 kips 

During application of this force, which is the equivalent of the imposition of a uniform tensile 

strain superimposed over the residual strain of Figure 4.1.3.1-2(b), not all parts of the cross 

section respond in the same way. Specifically, the relationship ε = σ / E will not be valid for 

those regions of the resultant strain diagram where the strain is greater than the yield strain. In 

Figure 4.1.3.1-3, part (a) shows the residual strain (which is simply Figure 4.1.3.1-2(b) repeated), 

part (b) shows the strain imposed by the tensile force, part (c) shows the resultant strain, and part 

(d) shows the corresponding stress diagram assuming elastic – perfect plastic material behavior.

Figure 4.1.3.1-3 Superimposed strain and corresponding stress.

The value of the uniform strain corresponding to the imposition of the applied force, 1.40 x 10−3, 

was determined by trial and error to satisfy the requirement that ∫ σ dA = 155 kips. Iteration is 

required as this is now a plastic, no longer elastic, analysis. That the integral is satisfied can be 

confirmed by first calculating the dimensions of the stress diagram, Figure 4.1.3.1-3(d), and then 

calculating the force volume obtained when the stress diagram is superimposed on the cross 

section.

Next, apply a force producing a nominal stress of 18 ksi compression. This requires that the 155-

kip force be removed and an additional force of (−18,000 psi) (1 in x 5 in) = −90,000 pounds = 

−90 kips be applied. Thus, the change in force is ΔP = 155 kips + 90 kips = 245 kips. As before, 

a uniform strain must be applied of sufficient magnitude such that ∫ σ dA = P = 90 kips. By 

iteration, this has been determined to be a strain of 1.70 x 10−3. 

Figure 4.1.3.1-4(a) shows the strains that existed at the end of the previous step. Figure 4.1.3.1-

4(b) shows the uniform compressive strain that must be applied to satisfy the requirement that a 

compressive force of 90 kips is imposed. The resultant strains are shown in Figure 4.1.3.1-4(c). 
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4.10 

Figure 4.1.3.1-4 Additional superimposed strain and corresponding stress.

The stress values in Figure 4.1.3.1-4(d) can be explained by examining the stresses in the midwidth fiber of the cross section. As shown in Figure 4.1.3.1-5, the stress initially was 44 ksi (i.e., 

the yield strength). Upon initial loading of the 155-kip force, the stress remained at this value, 

even though the strains increased as shown in the figure. The unloading that occurred in the third 

step took the stresses down to 5.8 ksi compression. Thus, the actual change in stress at the midwidth fiber was from +44 ksi down to –5.8 ksi, which results in a total change of 49.8 ksi. The 

result is that the actual change in stress, 49.8 ksi, is nearly equal to the change in stress calculated 

by the designer, 49 ksi. The difference between the two values is attributable to round-off errors 

in the calculations. The reader can verify that the imposition of these stresses on the cross section 

does, in fact, produce the value of 90 kips. 

Figure 4.1.3.1-5 Stress and strain at mid-depth fiber.
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4.11 

Still with reference to Figure 4.1.3.1-5, it should be borne in mind that unrestricted plastic flow 

of the cross section cannot occur. The small zone of weld and plate that is at yield is limited to 

some finite value of strain because the material adjacent to it remains elastic. Hence, the stress 

concentration in a high residual tensile stress region is cycled to a limited strain. The magnitude 

of the applied stress does not change the results. If the applied loads were smaller, the yielding at 

the critical area of tensile residual stress would still occur and the local stress range would be 

elevated with a maximum stress equal to the yield stress of the material. Application of peening 

at the weld toe can introduce a local compressive residual stress which will increase fatigue 

resistance. 

4.1.3.2 Effects

To summarize, in large welded structures, there are very high tensile residual stresses near 

fatigue crack sites, and their presence significantly reduces the effects of applied stress levels and 

steel grade upon crack propagation for standard weldable structural steels. As a result, it is 

generally agreed that stress range is the only dominant stress parameter. However, there has been 

a great deal of discussion regarding the best way to treat the following cases:

• The influence of compressive applied stresses

• The fatigue resistance of non-welded elements

• The fatigue resistance of stress-relieved welded elements

• The difference between results taken from testing small specimens and those taken from 

testing full-scale elements

Some of the differences between various codes can be traced to different interpretations of the 

effect of residual stresses (and other built-in stresses) upon the fatigue resistance of structural 

elements. A selection of approaches to these cases is described below. 

Nearly all fatigue guidelines for steel structures recommend that non-welded elements, stressrelieved welded elements, and welded elements be treated in the same manner when the applied 

stress ranges are tensile. However, when the applied stress ranges are compressive, or partly 

compressive, recommendations vary. According to the AASHTO recommendations (AASHTO, 

2015b), it is possible to ignore all fully compressive stress ranges. However, if a part of the stress 

range is tensile, then the whole stress range must be considered. European recommendations 

suggest that the whole stress range should be employed, regardless of whether it is completely or 

partially compressive, when welded elements are assessed. Eurocode 3 (EC 3) (European 

Committee for Standardisation, 1992) allows a reduction of the compressive stress range to 60 

percent of its magnitude for non-welded and stress-relieved elements. The European Convention 

for Constructional Steelwork (ECCS) recommendations (European Convention for 

Constructional Steelwork, 1985) are the most conservative; they recommend that 100 percent of 

the stress range be used for all elements and all cases. It can be observed that there are no known 

cases of load-induced fatigue cracking in bridge structures when the cyclic stresses are totally in 

compression (Fisher et al., 1974). 
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4.12 

Authors of the AASHTO provisions argue that, even if fatigue cracks start within tensile residual 

stress fields, under fully compressive loading, cracks will eventually stop when they propagate 

beyond the influence of these stresses. The developers of the EC 3 (European Committee for 

Standardisation, 1992) note that a crack growing from an as-welded joint in an element may be 

dangerous when applied stress ranges are fully compressive. Indeed, some test elements have 

failed due to cracks growing under fully compressive applied loading. Also, the EC 3 provisions 

(European Committee for Standardisation, 1992) reflect an attempt to accommodate those cases 

where there are no high tensile residual stresses.

For the ECCS document (European Convention for Constructional Steelwork, 1985), it was 

decided to provide conservative recommendations, because in most complex structures, the 

magnitudes of built-in stresses are unknown. Built-in stresses do not originate only from 

welding-related residual stresses, but they may also be caused by other effects, such as lack of 

fit, settlement of supports, temperature gradients, and ineffective expansion joints. Therefore, it 

was determined that no advantage should be given to cases in which applied stresses are in 

compression or in which elements contain no tensile residual stresses. 

The final point in this section relates to the physical testing of fatigue specimens. Compared with 

elements that have no tensile residual stresses, the presence of tensile residual stress near 

potential crack sites in an element reduces its fatigue resistance, especially at long lives. Small 

test specimens may not contain the same high level of tensile residual stress found in full-scale 

elements. For this reason, most recent research programs have concentrated upon testing of fullscale elements in order to establish code recommendations. Therefore, results taken from tests of 

small specimens should be employed with caution for design assessments. However, small 

specimens are useful when exploring variables such as improvement procedures or use of new 

materials.

Test programs are sometimes used to obtain a more accurate fatigue-resistance relationship than 

is provided in fatigue codes. Whenever possible in these circumstances, it is desirable that the 

test specimen have the same dimensions as the element under consideration for the real structure. 

4.1.4 Bolting and Riveting 

Mechanical connection details, in which holes are drilled or punched and forces are transferred 

by means of rivets or bolts, present a somewhat more severe fatigue resistance situation than the 

bare rolled shape. This is due to the fact that the holes, if drilled or sub-punched and reamed, 

produce a slight reduction in fatigue resistance as compared with an unaltered member. If 

tensioned high-strength bolts are used, the disturbing effect of the hole is largely mitigated by the 

presence of the high local compressive stresses introduced by the bolt. Punched holes give a 

greater reduction in fatigue resistance than do drilled or sub-punched and reamed holes because 

of imperfections at the edge of the hole arising from the punching process. In this case, the crack 

usually starts at the edge of the hole.

Broadly speaking, any mechanical connection detail has a higher fatigue resistance than does its 

equivalent welded detail. The local stress concentration adjacent to an open hole in a large plate 

is 3. However, the small surface irregularities associated with the hole-making process result in 

good fatigue resistance of these connections. The open hole has the poorest fatigue resistance. A 
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4.13 

preloaded connection that is loaded below its slip load will fail not at the hole but in the end of 

the connection where there is relatively little movement between the plates. Consequently, the 

fatigue strength of a connection loaded below its slip load is based upon the stress in the gross 

section of the plate. In a bearing connection, the failure is through the hole and the stress is 

calculated based on the net section. 

Punching can reduce the fatigue resistance of the connection due to the small tears that occur 

adjacent to the hole. Punched holes have a reduced fatigue resistance and are only allowed in 

secondary cross-frame members.

Chapter 10 provides additional background information about the fatigue strength of riveted and 

bolted connections. 

4.1.5 Cold Bending

In bridge construction, it is often necessary to bend structural steel to produce the required detail. 

Some examples include cross-frame gusset plates on skewed bridges, flanges for reduced end 

depth or dapped ends of girders, webs of curved girders, and flanges of cambered girders. When 

the required bending is performed at ambient temperature, it is referred to as cold bending. Hot 

bending, on the other hand, is when the steel is heated to reduce its strength and facilitate 

bending. 

The residual bending deformation of steel is due to the inelastic strains in the steel. If the yield 

strength of the steel is not exceeded, the steel returns to its original shape after bending. In the 

stress-strain curve of Figure 4.1.5-1, the steel is loaded in the elastic region from Point A1 to 

Point B with no permanent deformation or property change. Further loading beyond the yield 

point causes elongation to Point E. If the steel is unloaded, it returns to Point A2, and there is 

some permanent plastic deformation of the steel. 
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4.14 

Figure 4.1.5-1 Cold-bending example.

What happens when the steel is reloaded? It now follows Path A2-E-C-D-F, returning to follow 

the original stress-strain curve at Point E. A slight loss in ductility (percent elongation), 

represented by the cross-hatched area, results due to a shorter yield plateau.

If the steel is loaded along Path A1-B-C-D to cause strain hardening and then unloaded to Point 

A3, what happens when the steel is reloaded? It follows Path A3-D-F. More permanent 

deformation results, along with changes to the steel properties, including elimination of the yield 

plateau, elevation of the yield strength, and greatly reduced ductility, with no effect on tensile 

strength. 

The plastic deformation that occurs in bending increases the strength, reduces the ductility, 

reduces fracture toughness, and can cause surface cracking. The AASHTO LRFD Bridge 

Construction Specifications, Article 11.4.3.3 (AASHTO, 2015a) limits the radius of a bend, 

which limits the plastic strain introduced in the bending operation to prevent significant 

reductions in the steel properties. Research has indicated that cold bending is the preferred 

method of bending since it was found to have the least effect upon the material’s properties. The 

minimum bend radius allowed for a main member is five times the thickness of the plate 

(Keating and Christian, 2012). 

4.1.6 Hot Bending

Hot bending of steel reduces the bending forces but can result in reduction in the material’s 

ductility. The temperature must be below the transformation temperature of the steel and above 

the blue brittle range. In order to maintain the material properties, the maximum temperature is 

limited to 1200 °F in the AASHTO LRFD Bridge Construction Specifications, Article 11.4.3.3

(AASHTO, 2015a) for rolled steel and 1100 °F for higher strength, quenched and tempered 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.15 

steels. The minimum temperature should be 700 °F. Hot bending is allowed with the approval of 

the engineer.

Heat curving is used to bend the flanges for curved steel girders with a large radius. Tighter 

radius girders are fabricated with flanges cut to the desired curve. Cut curving the flanges can 

produce a large quantity of scrap steel, while heat curved flanges can be cut from the rectangular 

plates with little waste of material. The AASHTO LRFD Bridge Construction Specifications

(AASHTO, 2015a) place limits on the girders that can be heat curved. These limits are based 

upon limiting the stress in the girder, particularly the web, to limit distortion and loss of strength. 

Heat curving is done either with V heating patterns or continuous strip heating of one side of the 

flange, as illustrated in Figure 4.1.6-1. The heating causes expansion of the flange on the heated 

side, which is resisted by compression of the flange on the unheated side. Upon cooling, the 

compressed unheated side of the flange forces the heated side to compress, resulting in shrinkage 

of the heated side of the flange and curving of the flange. 

Figure 4.1.6-1 Examples of strip and v-heat curving of girder flanges. 

4.1.7 Heat Straightening Repairs

Research data (Avent et al., 2000) indicate that heat straightening affects the mechanical 

properties of steel. Early researchers used undamaged steel and a small number of heats to 

conclude that property changes after cooling were minimal. However, tests on damaged and 

subsequently heat-straightened plates and beams indicate that some property changes may be of 

significance after repeated straightening or repair of members with large deformations. 

The number of times a girder can be damaged and heat straightened must be considered. 

Changes in all the material properties become more evident with the increasing number of 
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4.16 

damage/repair cycles. Material property changes were usually acceptable after two cycles. Thus, 

a condition that is safe to straighten once is usually safe to straighten a second time. The changes 

become significantly greater after four and eight damage/repair cycles, respectively. Based upon 

Avent et al. (2000), re-damaged members at the same location should not be subjected to heat 

straightening more than twice. NCHRP Report 604 reached the same conclusion in full-scale 

testing to evaluate fatigue and fracture resistance (Connor et al., 2008). 

Additional information about heat straightening is provided in Heat Straightening Repairs of 

Damaged Steel Bridges, A Technical Guide and Manual of Practice (Avent and Mukai, 1998). 

SECTION 4.2 STRESS PARAMETERS INFLUENCING FATIGUE

Prior to the extensive National Cooperative Highway Research Program (NCHRP) studies of 

fatigue resistance at Lehigh University beginning in the late 1960’s, the fatigue stress limits were 

a function of the type of steel, the nominal stress range at the detail, and the exponent of the 

fatigue equation. The results of the NCHRP research (Fisher et al., 1970; Fisher et al., 1974; and 

Fisher et al., 1980b) are discussed in this section. Prior to this extensive research effort, the 

specifications of the American Association of State Highway Officials (AASHO), the precursor 

to AASHTO, the American Welding Society (AWS), and the American Railway Engineering 

Association (AREA), the precursor to AREMA, limited the applied stress to this older approach 

to fatigue, as described in Chapter 1. 

The NCHRP-sponsored testing assessed the resistance of multiple base metal, welded, bolted, 

and riveted details on large scale specimens. The effect of type of loading, member size, 

constraint, material grade, stress range, minimum and maximum test stress levels, and fabrication 

quality were studied experimentally. The results led to the conclusions still used today that 

fatigue life is fundamentally related to the detail type and the applied stress range. 

The initial NCHRP project tested over 500 full-size specimens, each with multiple attachments, 

so that many details could be subjected to differing stress ranges while testing a single specimen. 

Hundreds of additional details have been tested since in follow-up work. A photograph of one of 

the specimens is provided in Figure 4.2-1, and a drawing of a specimen from the NCHRP 354 

long-life studies showing many different attachments is provided in Figure 4.2-2. The tests were 

conducted under constant amplitude test loading, meaning every stress range cycle was equal. 

This of course differs from real bridge loading where each passage is of a vehicle of different 

weight, axle spacing, speed, and lane position. The treatment of variable amplitude loading is 

presented in Section 4.2.3. Several observations from the test programs are presented below. 

These observations relate to the effect of minimum stress as compared to stress range, the effect 

of steel type, and the nature of the stress ranges. 
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4.17 

Figure 4.2-1 Flexural fatigue tests conducted at Lehigh University. 

Figure 4.2-2 Sample test beam from NCHRP 354 long-life tests. 

4.2.1 Effect of Minimum Stress

When a cluster of fatigue data is plotted, the level of minimum stress has very little impact on its 

resulting fatigue life. Details were tested in which the stress range was entirely tensile with a 

large minimum stress, entirely tensile with a near zero minimum stress, and in reversal with 

stress cycles alternating between compression and tension. The data indicate no significant 

difference or relationship to minimum stress and a strong correlation to total stress range when it 

comes to determining fatigue life. 
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4.18 

Figure 4.2.1-1 plots the measured fatigue life for three test scenarios described above: one in 

which the minimum stress was 14 ksi (tensile), one in which the minimum stress was 2 ksi 

(tensile), and one in which the minimum stress was compressive (-10 ksi). No significant 

difference in fatigue life was found. This reinforces the prior discussion regarding the influence 

of residual stress from Section 4.1.3. In addition to the plotted points, three dashed lines are also 

shown in Figure 4.2.1-1. These lines represent the mean and the 95-percent confidence limits for 

the data (i.e., plus and minus two standard deviations from the mean). The mean and 95-percent

confidence interval boundaries are commonly used in fatigue design. The significance of the 

lower bound (i.e., two standard deviations to the left of the mean) is that this boundary signifies 

the typical assumed design life in AASHTO LRFD. 

Figure 4.2.1-1 Effect of minimum stress on fatigue life.

4.2.2 Effect of Steel Yield Strength

The same types of observations were found when fatigue test data were plotted for A36, A441, 

and A514 steel types, as presented in Figure 4.2.2-1. The steels tested were the extreme yield 

strength materials used in structures at the time of the test program and still represent the 

extremes of yield strength for modern steel bridges. These steels have specified yield points 

ranging from 36 to 100 ksi. Testing of welded beams composed of each of these materials 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.19 

indicated that the minimum or maximum expected fatigue life was generally the same for all 

grades of steel. These findings with respect to minimum stress (as presented in Section 4.2.1) and 

grade of steel are important in that they greatly simplify the analysis and design of steel 

structures for fatigue and again emphasize the point that fatigue design and evaluation can be 

strictly related to live load stress range and number of cycles.

Figure 4.2.2-1 Effect of steel grade on fatigue life.

4.2.3 Consideration of Variable Amplitude Fatigue Loading

Constant amplitude fatigue is the term used to describe the behavior of an element subjected to 

cycles of fatigue loading of equal stress range. It is commonly the type of loading applied to 

specimens in a laboratory in order to determine fatigue life, such as the majority of the tests 

described in previous sections. It is the benchmark by which fatigue life is predicted for details, 

although it bears little resemblance to the actual variation of stress to which a detail will be 

subjected in the field. Most experimental results relate to constant amplitude behavior. There 

have been variable amplitude tests performed on steel structures (e.g., NCHRP 267 and 354), and

the results of the constant and variable amplitude loading show that relatively simple rules can be 

used to establish equivalencies between the two. 
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4.20 

Miner’s rule is commonly used to estimate the effect of variable stress range that occurs in 

service with the constant amplitude test data used to develop the fatigue resistance in the 

laboratory (Miner, 1945). It was previously introduced with Equation 3.4-8. It was historically 

used along with truck weight survey data to define the weight of the AASHTO fatigue design 

truck and can also be used to provide a stress range equivalency to design or assess fatigue life 

when the vehicle loading is different than the AASHTO LRFD fatigue design truck. Equation 3.4-

8, repeated herein, computes an equivalent single stress range that over a specified number of 

cycles produces fatigue damage equivalent to the variable amplitude loading but having the same 

number of cycles. In the equation, Sre is the equivalent stress range, Sri is the stress range 

magnitude of an individual cycle, and γi is the percentage of the whole corresponding to each 

stress range magnitude. 

Equation 4.2.3-1 

An example of the application of Miner’s rule to compute an effective stress range is provided, 

along with a presentation of “damage” using the concept that fatigue damage is related to the 

cube of the stress range and the number of occurrences. This same procedure is discussed in 

Chapter 6 as it relates to the development of the fatigue design vehicle specified in AASHTO 

LRFD. 

In Table 4.2.3-1, the characteristics of variable amplitude loading for a detail are presented. In 

first column (1) is an interval, a method used for grouping stress cycles. In this example, each 

interval, sometimes called a “bin,” corresponds to a 1-ksi grouping. In the second column (2), the 

percentage of the total number of cycles corresponding to the given stress range is noted. Note 

that the percentages total 100 percent. In the third column (3) is the stress range measured in 

units of ksi. In the fourth column (4) is the cube of the stress range, as it has been found that 

fatigue life and hence “damage” are proportional to the cube of the stress range for welded steel. 

The fifth column (5) multiplies the percentage of cycles times the cube of the stress range to 

determine the relative damage caused by a specific stress range. Finally column six (6) computes 

the incremental damage from a particular range of stress. The total damage must total 100 

percent. 
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4.21 

Table 4.2.3-1 Application of Miner’s rule to a variable spectrum.

(1) (2) (3) (4) (5) (6)

Stress 

Interval

Percent of 

Vehicles, γi

Sri, ksi Sri

3

, (ksi)3 γi Sri

3

, (ksi)3

(i.e., “relative damage”)

Percent

Damage

1 40 percent 3 27 10.80 9 percent

2 25 percent 4 64 16.00 13 percent

3 15 percent 5 125 18.75 15 percent

4 9 percent 6 216 19.44 16 percent

5 5 percent 7 343 17.15 14 percent

6 3 percent 8 512 15.36 13 percent

7 2 percent 9 729 14.58 12 percent

8 1 percent 10 1000 10.00 8 percent

Ʃ = 100 percent Ʃ = 122.08 Ʃ = 100

percent

Sre = (122.08)

(1/3) = 5 ksi

This example applies the concepts of Miner’s rule to determine the effective stress range, 5 ksi, 

and also provides an assessment of which cycles contribute most and least to the total fatigue 

damage. Of note is that the stress ranges from 3 to 5 ksi constitute 80 percent of the total number 

of cycles but cause only 37 percent of the total damage. The highest three stress ranges, 8 to 10 

ksi, only constitute 6 percent of the total number of cycles but cause an almost equal amount of 

damage (33 percent) as the three lowest stress ranges. This is consistent with life, or damage, 

being related to the cube of the stress ranges, with a small percentage of high stress ranges using 

up a large portion of the detail’s available fatigue life.

Another example of Miner’s rule is the analysis of a bridge for special traffic. Consider the 

design of a bridge for a mining road. The vehicle weight distribution for the loaded and unloaded 

trucks is given in Table 4.2.3-2 and Table 4.2.3-3, respectively. The expected number of round 

trips per day is 192. The calculation was made to determine the effective truck which represents 

the loaded and unloaded truck. The effective truck weight is 133.2 kips for the loaded trucks and 

43.4 kips for the unloaded trucks. 
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4.22 

Table 4.2.3-2 Vehicle weight distribution for loaded trucks.

Weight of Truck, 

W (kips) 

Number of Trips per 

Day

γi (i.e., Number of 

Trips per Total) 

γi W3 

(ksi)3

110 12 0.063 83,187.5

120 35 0.182 315,000.0

130 57 0.297 652,234.4

140 71 0.370 1,014,708.3

150 17 0.089 298,828.1

Total 192 1 2,363,958.3

 Wre = 133.2 

Table 4.2.3-3 Vehicle weight distribution for unloaded trucks.

Weight of Truck, 

W (kips) 

Number of Trips per 

Day

γi (i.e., Number of 

Trips per Total) 

γi W3 

(ksi)3

40 56 0.292 18,666.7

42 45 0.234 17,364.4

44 34 0.177 15,084.7

46 34 0.177 17,236.6

48 23 0.120 13,248.0

Total 192 1 81,600.3

 Wre = 43.4 

The effective stress range for both trucks was calculated using these effective truck weights as 

follows: 

Equation 4.2.3-2 

The effective truck load in conjunction with a dynamic load allowance can be used in the 

analysis of the bridge to estimate the fatigue stress range at the critical locations in the bridge. 

This procedure can be used as long as the number of cycles expected does not exceed the 

intersection of the finite life design equation and threshold stress range. This cycle limit can be 

found for the various details in AASHTO LRFD Table 6.6.1.2.3-2 for a 75-year service life. The 

ADTT in checking the table is the sum of the loaded and unloaded trucks (e.g., 384 in the 

previous example), and this value would be used as the ADTT. If a service life other than 75 

years is being considered, the values in the table can be adjusted as noted in the commentary of 

the specification. If the number of expected cycles exceeds the limit, the design should be based 

on satisfying the infinite life design provisions, and the expected maximum load range of 150 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.23 

kips should be used to calculate the stress at the critical details and the stress compared to the 

threshold stress range. 

SECTION 4.3 TESTING AS THE BASIS FOR DESIGN LIMITS

4.3.1 Development of Design Limits for Finite Life

As described in previous sections, using test data first collected in earnest during the 1960’s and 

1970’s, researchers developed best fit lines through the test data that represented the mean 

behavior. An example of a generic mean regression curve is provided in Figure 4.3.1-1. The

fatigue data is plotted in log-log space, and the regression appears as a line. However, these lines 

are also frequently referred to as “curves,” which is what they look like when plotted on non-log 

axes. 

Figure 4.3.1-1 Fatigue life test data plotted on a log-log scale. 

The meaning of the mean regression line as it relates to fatigue life is that the predicted life from 

this curve has only a 50 percent chance of being a safe prediction. For the design of new 

structures, this is inadequate and different standards were adopted. 

For design, the curves that depict allowable (nominal) stress range versus design loading cycles 

have been offset two standard deviations (i.e., -2σ) to the left of the mean curve. Assuming a 

normal distribution, two standard deviations to each side of the mean encompasses 95 percent of 

the data, and the remaining tail probabilities on each side sum to 5 percent. In design, the upper 

tail is irrelevant because it depicts resistance far in excess of the demand, and only the lower tail 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.24 

that sums to 2.5 percent is important in terms of risk. For this reason, it is said that design fatigue 

curves represent a 97.5-percent confidence that the fatigue life of a detail will not be exceeded 

during the design life of the bridge. This is the fundamental assumption historically used in the 

AASHTO design approach. Safety is provided (in part) through the application of these 

conservative bounds for fatigue life, and the corresponding “allowable” stress ranges. The 

statistical shift of the mean curve to the lower bound AASHTO design curves is depicted in 

Figure 4.3.1-2. The safety inherent in the two standard deviation shift is apparent in the 

difference between the mean and the design life. A more recent calibration of the fatigue limit 

state, which is discussed in further detail in Chapter 6 and in Appendix A, results in a different 

definition of safety, but the fundamental concept remains the same, namely to provide a safe 

lower bound prediction of fatigue life. 

Figure 4.3.1-2 Mean and lower bound fatigue curves.

In Figure 4.3.1-2, the following terms are used: 

N̅ = the mean life corresponding to a specific stress range

Nlb = the lower bound, or design life, for the same stress range 

The shaded area represents the 2.5-percent probability of failure associated with the design life 

estimate. 

Once the fatigue test data in the prior figures were plotted, a linear regression analysis was 

performed. The resulting regression equations are described by the following relationship: 
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4.25 

Equation 4.3.1-1 

which is of the form of a linear equation, y = b - mx. 

Alternatively, the relationship between the stress range, S, and number of cycles, N, is presented 

as:

Equation 4.3.1-2 

For steel, the exponent “B” is approximately 3, and researchers have enforced a common value 

of 3 in all design fatigue equations. This forms the basis of the assertion that fatigue life is 

inversely proportional to the cube of the effective stress range. 

In addition to sloping lines or curves defining the finite fatigue life behavior, an additional 

boundary called the constant amplitude fatigue threshold (CAFT) was established. This is 

discussed in Section 4.3.2. However, prior to moving on from the discussion of finite life, a brief 

discussion of the definition of “life” is provided in the following section. 

4.3.1.1 A Definition of Finite Life 

The fatigue resistance in AASHTO LRFD was developed through the testing of large specimens 

under repeated loading. The specimens were loaded until “failure” occurred, and the 

corresponding life of the detail and stress range were recorded. After hundreds of tests of many 

different types of fatigue details, a family of fatigue design curves was established.

There is no consistent definition of “failure” used by researchers. During the testing of several 

hundred welded and rolled steel beams, Hirt (1971) defined failure as “generally defined in this 

study as an increase in midspan deflection of 0.020 inch due to fatigue cracking of the test 

beam.” He also states that, “This usually occurred when the crack had propagated through 

enough of the flange for net-section yielding to occur. At this stage, most of the fatigue life of the 

beam was exhausted. The crack generally had destroyed 15% to 75% of the flange area.” 

Figure 4.3.1.1-1 and Figure 4.3.1.1-2 are taken from the Hirt report (1971) and depict the large 

number of applied cycles before visible cracks were observed (using magnifying glasses and 

microscopes) and the much shorter duration until the section was deemed to have failed. It 

required 435,000 cycles before a crack that began in the weld metal propagated through the 

bottom flange and only an additional 32,000 before the specimen was deemed to have failed. 
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4.26 

Several other important observations are presented in the Hirt report (Hirt, 1971). The following 

quotes are excerpted:

• “Most of the fatigue life of the welded beams was spent growing a crack from its initial 

size to a visible crack. This corresponded to growth rates below 10-6 in. per cycle where 

little information is available from crack growth studies.” 

• “More than 75% of the life was spent in this region growing a crack from its initial size 

to a visible crack.”

There are several useful pieces of information from these statements that relate to the idea of 

fatigue life and failure:

• The majority of fatigue life is exhausted growing a crack from a small initial 

discontinuity, and crack growth rates are extremely small per cycle.

• When visible fatigue cracking is observed in the field, the majority of fatigue life has 

been expended. 

• Significant cracking is possible with little observable change in overall member behavior, 

and vertical deflection increases that are observable only with instrumentation correspond 

to significant loss of tension flange area. 

Figure 4.3.1.1-1 Crack size and growth versus number of cycles for a welded beam.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.27 

Figure 4.3.1.1-2 Number of cycles leading to failure in a steel girder.

In the NCHRP Project 12-15(5) study, the results of which are published in NCHRP Report 354 

(Fisher et al., 1993), researchers studied the long life behavior of steel beams with welded 

transverse stiffeners, longitudinal attachments, and cover plates. For the definition of life for 

cracks forming at the web stiffeners and attachments, a criteria of a through-thickness crack in

the web or a crack 1 inch long otherwise was established as the definition of life. 

In tests to determine the fatigue performance of composite sections (Daniels and Fisher, 1968), 

strain gauges attached to the underside of the top flange of a composite beam were used to detect 

shear stud failures by examining the relative change in top flange strain over time, indicative of a 

loss of composite action. 

As for other types of tests, additional unique definitions of failure are found. However, it is 

consistent that fatigue tests do not define failure as complete member failure but rather the onset 

of unstable propagation or significant changes in overall member behavior. 

4.3.2 Development of Design Limits for Infinite Life

Research has shown that stress cycles below the constant amplitude fatigue threshold (CAFT) do 

not cause fatigue crack growth under constant amplitude loading. However, it is known that 

bridges are subjected to variable amplitude loading and may have many cycles whose magnitude 

is in excess of the effective stress range. Under variable amplitude loading, the stress cycles 

above the CAFT contribute to crack growth. The higher stress ranges cause crack extension and 

cause a decrease in the CAFT, with eventually all stress cycles contributing to fatigue crack 

growth. It is this knowledge of the decay of the CAFT limit that leads to a need to guard against 
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4.28 

infrequent occurrences of a maximum stress range and thus guard against crack growth. Three 

possible scenarios are explored in Figure 4.3.2-1 to demonstrate the relationship between 

effective stress range, maximum stress range, crack growth, and infinite life. This figure is the 

foundation of the selection of the Fatigue I load factor which is discussed in greater detail in 

Chapter 6. 

Figure 4.3.2-1 Fatigue life versus effective and maximum stress.

In Case 1, a histogram of loading is provided in which the effective stress range is relatively 

large. For a large effective stress range (Sre), the number of cycles to failure is low in a relative 

sense since the stress range is large. The effective stress range significantly exceeds the CAFT, 

and the fatigue life for a scenario such as this one is based on the finite life concepts discussed in 

Section 4.3.1. 

In Case 2, the effective stress range is computed to be less than the CAFT which would imply 

infinite life. However, only when a specimen is subjected to constant amplitude loading with all 

cycles below the CAFT does the CAFT behavior hold true. A limited number of stress cycles 

above the CAFT results in crack extension, cracking will eventually progress, and the CAFT 

limit would be reduced to the point that all cycles, large and small, contribute to crack growth. 

Case 3 is the basis for infinite life design. For infinite life, a designated maximum stress range 

must be below the CAFT in order for infinite life to be ensured under variable amplitude loading. 

Although it is not statistically possible to keep all stress cycles below the CAFT, research found 

that if a very small number of cycles (i.e., 0.01 percent) were in excess of the CAFT, crack 

growth was effectively prevented throughout the expected design life of the structure. 
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4.29 

Examination of the histograms of random loading determined that a doubling of the effective 

stress range would provide this small probability of exceedance. This relationship between the 

load factors for finite life (effective stress) and infinite life (maximum stress) is further discussed 

in Chapter 6, detailing the development of the AASHTO LRFD design approach. Recent studies 

using weigh-in-motion data indicate that the relationship between the effective and maximum 

stress ranges is no longer the historical value of 2, assumed in the past. The maximum stress 

range will now be defined by a factor of approximately 2.2 using the load factors of 1.75 and 0.8 

for the Fatigue I and Fatigue II load combinations, respectively, as adopted by AASHTO in 

2016. 

4.3.3 Testing to Establish the Fatigue Resistance of Special Elements

AASHTO LRFD does not have a codified procedure for defining the fatigue strength of special 

structural elements. However, procedures and test methods have been developed for some bridge 

hardware and components. A method of qualifying modular expansion joints through tests has 

been developed and is used by manufacturers of the joints to qualify them for use on bridges. 

Due to the complexity of these joints and the proprietary nature of their design, these joints are 

tested in accordance with a procedure given in NCHRP Report 402, Appendix A (Dexter et al., 

1997). 

Cable stay anchorage systems and the strand used in the cable stays are tested in accordance with 

the requirements of PTI DC45.1-12: Recommendations for Stay Cable Design, Testing and 

Installation (PTI, 2012). This specification covers other hazards such as corrosion and fire, as 

well as installation specifications for the products. The fatigue requirements are intended to 

provide a stay cable which is not susceptible to fatigue damage due to service loads. Additional 

details on stay cable testing are provided in Chapter 10. 

Other codes have established test procedures for developing a design fatigue resistance for a new 

connection or equipment. Generally in the U.S., if at least 12 replicate specimens at three 

different stress ranges are tested to failure, the test results are evaluated and compared to the 

design categories in specifications. The 95-percent confidence limit for 95-percent survival of 

the test data should be equal to or greater than the design line for the category. 

SECTION 4.4 ENVIRONMENTAL EFFECTS 

In the presence of moisture and air, all steels have a potential to corrode. The rate of corrosion 

depends on the access to oxygen, moisture, and other contaminants, particularly road salt on the 

surface of the metal. As rust formation progresses, the rust forms a barrier and the rate of rusting 

slows down. With many common steels, the rust layers are not well adhered, at some point they 

fall off, and then corrosion re-initiates, this time on a reduced section. 
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4.30 

4.4.1 Weathering Steel

With weathering steel, the oxidation process initiates in the same way, but the specific alloys 

produce a stable patina layer that is well adhered to the base metal and less porous than rust that 

forms on traditional steels. This dense patina develops under conditions of alternating wet and 

dry cycles to produce a protective barrier that impedes the ingress of oxygen, moisture, and 

pollutants. This results in a steel structure that is self-protective over time. The formation of the 

rust patina does result in minor pitting and surface corrosion of the steel that marginally degrades 

its resistance as compared to other base metals. AASHTO recognizes this distinction between the 

surface conditions of weathering and non-weathering steels in its treatment of fatigue categories. 

For plain base metal of non-weathering steels, AASHTO designates this as Category A, the most 

favorable fatigue condition. A similar noncoated weathering steel structure would be assigned 

one lower fatigue category (i.e., Category B), acknowledging the influence of pitting on surface 

roughness and overall fatigue resistance. Although there is a reduction in fatigue category for 

weathering steel from A to B, most steel structures have bolted or welded attachments that

further lower the fatigue category performance of weathering and non-weathering steels alike. 

This is substantiated by physical testing of cruciform joints, a typical Category C detail, and 

comparing those results to weathering steel fatigue data. 

Figure 4.4.1-1 is taken from Fisher, Kulak, and Smith (Fisher et al., 1998) which also has a 

broader discussion of the impacts of corrosion on the resistance of weathering steel. It 

demonstrates that the geometric effect of the cruciform construction, a Category C detail, is more 

significant than the shift in resistance associated with weathering steel pitting.
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4.31 

Figure 4.4.1-1 Fatigue life comparison of weathering steel and Category C cruciform joints. 

4.4.2 Corrosion Effects on Fatigue Life

The effects of corrosion influence fatigue life in several ways. Corrosion, such as may be found 

under a leaking deck joint or at a crevice in built-up sections where debris and moisture can 

accumulate, results in a local reduction in cross section and a jagged or notch-like condition on 

the surface or edge of the member. These local corrosion effects are found frequently on older 

steel structures and are a consequence of many years of service, sometimes in aggressive 

environments. The problem is not unique to highway bridges; many steel railroad bridges have 

similar problems, particularly open deck railroad bridges in which the timber ties bear directly on 

the top flange of the longitudinal beams. Open deck railroad bridges frequently have corrosion 

on and around the top flanges due to the entrapment of debris or contaminants. Fisher, Kulak, 

and Smith (Fisher et al., 1998) comment that localized depressions on the order of 1 to 2 inches 

in diameter and depths on the order of 1/8 to 5/16 inches are commonly found on the top flanges 

of open deck steel railroad bridges. This localized corrosion is a more aggressive form of pitting 

that also influences the fatigue resistance of weathering steel and serves to reduce the fatigue life 

of the structure. Although this localized pitting is not desirable, it has been found to be not 

particularly detrimental since the stress concentration resulting from a pit is not particularly 

severe.

Corrosion may also introduce sharp notches on the surfaces or edges of structural steel members, 

and these notches have been found to have a more significant effect on overall fatigue life. The 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.32 

influence of these notches is analogous to the stress concentration at edge cracks for which 

classic fracture mechanics solutions are available. An illustration of the stress concentration at 

the tip of a corroded edge crack is provided in Figure 4.4.2-1. These shallow cracks typically 

produce fatigue lives comparable to Category C and typically do not control the fatigue life 

estimate of the structure.

Figure 4.4.2-1 Edge notch effects on stress concentration. 

Fisher et al. (1998) report that if corrosion has reduced the thickness of the structural steel 

elements by more than one half, fatigue cracking is likely to initiate at a notch within the 

corroded region rather than at a traditional net section location such as the edge of the rivet or 

bolt hole, even when the overall net section has been reduced in area and inertia for an 

approximate level of corrosion. 

There are also situations in which corrosion is more or less uniform across the entire cross 

section. This is the case when corrosion is due to a more general source, such as high humidity, 

aggressive environment, or some other scenario in which the corrosive impact affects the entire 

member somewhat uniformly. It has been found that when corrosion is uniform throughout the 

cross section, the fatigue life can be reasonably estimated based on the stress ranges computed on 

the reduced cross section. This assumes that there are no notches or other discontinuities that 

would pose a more severe fatigue condition on the structure. Fisher et al. (1998) state that the 

effect of corrosive environment on crack growth and the effect on stress concentration has not 

received much attention for civil engineering applications. However, the available laboratory 

tests did not indicate a significant impact on stress concentration. This does not imply that the 

impact of corrosion on fatigue resistance is negligible, however, since the notch effect and 

overall increase in stress range from general corrosion must still be considered.

The influence of section loss should not be underestimated. Unprotected steel will undergo 

continual reduction in plate thickness over time due to the cyclical formation of corrosion 

products. A study of corrosion rates, as-inspected plate thicknesses, and the influence of 

corrosion on section property reduction was carried out by the Illinois Department of 

Transportation. In their report (Hahin, 1994), they present an example of an in-service bridge in 

the state of Illinois in which the non-weathering steel was left unpainted for 25 years. The 
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4.33 

moment of inertia of the as-installed rolled shape was significantly reduced in that 25-year 

timeframe. Sketches of the as-installed and as-inspected conditions are provided in Figure 4.4.2-

2. 

Figure 4.4.2-2 Influence of corrosion on section properties. 

The computation of remaining fatigue life must recognize that the nominal stresses in the section 

are increased because of the reduction in section modulus, and the engineer must also consider if 

the Category A fatigue resistance still applies as well.

Albrecht and Lenwari (2008) report on the fatigue testing of corroded stringers removed from an 

abandoned streetcar trolley bridge. The bridge was constructed in 1900 and for the next 58 years 

carried mass transit trolleys until operation was suspended in 1958. The bridge remained albeit in 

an abandoned state until 1985 when the stringers were removed from the bridge and transported 

to the laboratory. The bridge was severely corroded at two locations: (1) on the top flange where 

pits formed at the intersection of the railway ties and the top flange and (2) at the top of the 

bottom flange where debris accumulation and trapped moisture resulted in significant corrosion 

over the lower 6 inches of the web and flange. When the stringers were tested in the laboratory, 

nine tests were performed with the stringers in their as-removed condition (i.e., with the 

corrosion pits on the top flange located on a compression flange). An additional 13 tests were 

performed with the stringers tested in the inverted position so that the severe pitting on the top 

flange could be loaded in tension. All of the fatigue cracks that formed during testing initiated at 

rust pits, indentations, mechanical seams from rolling, and notches that were formed by 
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4.34 

corrosion over the years. Of the ten stringers tested in the normal position, six had Category A 

strength, two had Category B strength, and two had Category C strength. For those tested in the 

inverted position with the top flange rust pits now located on the tension face, nine had a 

Category B strength, three had a Category C strength, and one had a Category D strength. The 

results of all of the stringer tests are shown in the graph in Figure 4.4.2-3. 

Figure 4.4.2-3 Influence of long-term corrosion on the fatigue performance of rolled 

shapes. 

The authors conclude that corrosion clearly reduced the fatigue resistance of the trolley bridge 

stringers below that of the non-corroded beams. The reduction was clearly evident in the beams 

tested in the inverted position. The authors comment that the AASHTO S-N curve for Category 

A should not apply to a corroded rolled beam and that methods are available to account for the 

fatigue life loss due to uniform corrosion and pitting. The findings of the Albrecht study support 

the prior findings of Fisher, Kulak, and Smith (Fisher et al., 1998) relative to the greater 

influence of pitting and notch effects on reducing remaining fatigue life as compared to the 

overall section loss of uniform corrosion. 

Although no firm guidance is available based on these studies, engineers should be aware, 

especially when computing the remaining fatigue life of older steel bridges, that the type of 

corrosion found may in fact influence the remaining fatigue life calculations, and some 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

4.35 

consideration to evaluating the base metal as a category less than A should be given. No 

guidance is found in the AASHTO design specifications (AASHTO, 2015b) or in the Manual for 

Bridge Evaluation (AASHTO, 2015d) regarding the influence of corrosion on expected fatigue 

life.

SECTION 4.5 SUMMARY

The statistical analysis of full-scale test results of cover-plated beams, welded beams, rolled 

beams, and groove-welded splices revealed that stress range is the dominant stress parameter 

influencing fatigue resistance (Fisher et al., 1970). The use of stress range was confirmed by a 

minimum notch-producing detail – the rolled beams – which provide an upper boundary for 

fatigue resistance. Similar behavior was observed for a severe notch-producing detail – the 

cover-plated beams – which provide a lower boundary for fatigue resistance. The result of the 

analysis of variance for the three bridge steels of the day – ASTM A36, ASTM A441, and 

ASTM A514 (Grades 36, 50, and 100, respectively) – showed that the dominant variable at the 

95-percent confidence level was stress range for each grade of steel. Minimum stress appeared to 

have little or no influence. Further, it was found that regardless of grade of steel, no 

improvement in the goodness of fit was achieved when minimum or maximum stress was 

included in the analysis. As noted herein, most specifications have adopted a fatigue life 

estimation for welded details that is dependent solely upon the stress range and connection detail. 

The fatigue resistance is independent of the material strength.
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5.1 

CHAPTER 5 ANALYSIS FOR FATIGUE

SECTION 5.1 GENERAL

In all fatigue designs and evaluations, a calculated or measured stress range is compared to some 

permissible stress range. As discussed in detail in previous chapters, stress range is the dominant 

stress parameter for fatigue. The processes by which these stress parameters are established 

ranges from the very simplistic to the extremely complex. 

Three possible analytical approaches, depending on the level of refinement in the stress analysis, 

can be used for assessment of the fatigue limit state of a detail:

• Nominal-stress approach

• Local-stress approach

• Fracture mechanics

The difference in level of analysis is illustrated in Figure 2.3.3-1, which shows a plate under 

uniform stress with a longitudinal fillet-welded attachment. The nominal stress is the uniform 

stress away from the attachment that can be calculated using simple bending and axial load 

equations. 

At the attachment, the nominal stress becomes amplified from several sources of stress 

concentration. First, the amplification is reflected in the local structural stress, or the hot-spot 

stress. AASHTO defines the local structural stress as the stress at a welded detail including all 

stress raising effects of a structural detail but excluding all stress concentrations due to the local 

weld profile itself. 

Second, there is the local total stress. While the local structural stress is computed using 

extrapolation methods, the local total stress is not based on extrapolation. Rather it is dependent 

on random parameters, such as weld profile and ripples in the weld toe, and typically cannot be 

accurately characterized through analysis. Fracture mechanics can be applied to analyze 

qualitative aspects of the problem; however, many assumptions are required to provide 

meaningful quantitative results.

SECTION 5.2 LOAD-INDUCED VS. DISTORTION-INDUCED FATIGUE

Fatigue cracking is classified as either load- or distortion-induced. The assumption has been that 

fatigue stresses can be calculated, usually at an elementary level. The loads used are similar to 

those associated with the in-plane strength design of the members. In many instances, however, 

fatigue crack growth results from the imposition of deformations, not loads. Distortion-induced 

fatigue stresses are not typically quantified by analysis. Although it is possible in some of these 

cases to calculate a stress range, this is usually performed after the fact with very refined analysis 

and requires that comparison field measurements be made. Designers are not likely to be able to 

identify the need for such calculations in the course of their work. As will be seen, this type of 

fatigue crack growth results from the imposition of relatively small deformations, usually out-ofplane, in local regions of a member. These deformations are not anticipated in the design process 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

5.2 

because they are not captured in simple distribution, or grillage analysis. The main defense 

against this source of cracking is proper detailing, and this, in turn, is dependent on experience. 

Distortion-induced cracking is estimated to be the cause of over 90 percent of all fatigue 

cracking (Connor and Fisher, 2006). 

SECTION 5.3 GLOBAL ANALYSIS

The analysis of bridges and structures is a mixture of science and engineering judgment. In most 

cases, simple models with conservative assumptions can be used to arrive at the design forces for 

various elements. From these design forces, specifically moments, nominal stresses are 

determined. For example, for straight beam bridges with small skews, beam line models with 

approximate distribution factors can be used to arrive at the design moments. For more complex 

structures or for situations where refinement offers significant benefits, a more refined analysis 

(e.g., grid or 3-D) might be justified.

AASHTO LRFD (AASHTO, 2015b) provides two methodologies to determine nominal stresses:

• Approximate methods as specified in AASHTO LRFD Article 4.6.2 

• Refined methods as specified in AASHTO LRFD Article 4.6.3 

Design and evaluation seek to estimate the performance of new and existing bridges with the 

least amount of effort. 

Within a given design or evaluation procedure, the engineer has the option of using simplified 

methods that tend to be somewhat conservative or pursue a more refined approach for improved 

accuracy when necessary to achieve better results. It is recommended that wherever feasible, 

simplified analysis procedures should be applied first, before resorting to higher-level analysis 

methods. 

Refined methods, such as finite element analysis, load testing, and site-specific live load factors, 

can be applied to reduce uncertainties in bridge design and evaluation, thereby achieving 

increased load capacities while maintaining the same target reliability level.

5.3.1 Approximate Analysis 

The focus of this section is an introduction to live load distribution analysis for longitudinal and 

transverse members. Since the 1930’s, designers have used simplified distribution factors that 

isolate the transverse design of a bridge from its longitudinal design. Live load distribution 

analysis is an integral component of typical fatigue design and evaluation of bridges. 

Approximate methods of structural analysis suitable for the design and evaluation of bridges can 

be found in Section 4 of AASHTO LRFD (AASHTO, 2015b) and in Section 6A.3 of the MBE

(AASHTO, 2015d). An approximate method of analysis can be utilized to determine the live 

load distribution to individual components of typical highway bridges. Live load distribution 

factors are dependent on multiple characteristics of each bridge.
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5.3 

5.3.1.1 Main Members

The cross-section type of the girders and deck influence their relative stiffnesses and therefore 

the load distribution. The design moment in the girder will vary with girder spacing, span length, 

flexural stiffness, and torsional stiffness. AASHTO LFRD expressions account for many 

parameters that were neglected previously, including skew. 

The different distribution formulas are tied to the member type and load effects. The LRFD load 

distribution formulas are specified for exterior and interior girders, for shear and moment, and 

for one-lane loaded and two-or-more-lane loaded cases. The distribution factors are expressed as 

a fraction of full lanes. 

When the bridge is analyzed for fatigue design or evaluation by approximate load distribution, as 

specified in AASHTO LRFD Article 4.6.2, the distribution factor for moment for one traffic lane 

should be used. As discussed earlier, the AASHTO fatigue methodologies are based upon a 

single truck at a time on the bridge, representing the worst case for accumulating fatigue damage, 

and nominal fatigue stresses are derived from moments. 

The types of superstructures covered by the distribution-factor equations are described in 

AASHTO LRFD Table 4.6.2.2.1-1. The distribution-factor equations for moments in interior and 

exterior girders appear in AASHTO LRFD Tables 4.6.2.2.2b-1 and 4.6.2.2.2d-1, respectively. 

Figure 5.3.1.1-1 illustrates the cross referencing of the superstructure types with the distributionfactor equations for moment in interior girders. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

5.4 

Figure 5.3.1.1-1 Cross referencing of AASHTO LRFD tables. 

A range of applicability is listed for each equation based on the parameters used in the equation. 

When the girder spacing exceeds the listed value in the “range of applicability” column, the 

specifications require the use of the lever rule or refined analysis methods. The lever rule can be 

conservative compared with other available methods of analysis, and the engineer might instead 

consider the use of refined analysis for parameters outside the “range of applicability.” The 

ranges of applicability for the variables involved are seen in the far right column of Figure 

5.3.1.1-1. 

As it turns out, an exponential distribution-factor equation is given in AASHTO LRFD Table 

4.6.2.2.2b-1 for moment in interior girders with one design lane loaded, but AASHTO LRFD

Table 4.6.2.2.2d-1 specifies the lever rule be used to determine moment in exterior girders with 

one design lane loaded. Thus, one lane loading is analyzed using the traditional lever rule to 

determine the fraction of live load carried by the exterior girder. A statical summation of 

moments is performed about one point to calculate the reaction at a second point. That reaction 

as a fraction of the live load is the distribution factor predicted by the lever rule method. The 

lever rule method conservatively predicts live load reaction on exterior beam lines. The lever 

rule only depends on geometry and does not account for the stiffness of the members since the 

assumed structural model is determinate.

The multiple presence factors of AASHTO LRFD Article 3.6.1.1.2 are not applicable for fatigue. 

Thus, the exponential distribution factor equation for interior girders should be divided by 1.2 as 

it is implicitly included in the formulation, and no multiple presence factor should be used with 

the lever rule for exterior girders.
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5.5 

Design Example

The given parameters for an approximate-analysis design example are as follows in Figure 

5.3.1.1-2 through Figure 5.3.1.1-5. 

Figure 5.3.1.1-2 Girder-elevation schematic.

Figure 5.3.1.1-3 Bridge typical section. 
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5.6 

Figure 5.3.1.1-4 Bridge framing plan. 

Figure 5.3.1.1-5 Girder half-elevation. 

For this design example, fatigue will be checked for the fillet-welded connection of the 

transverse intermediate stiffeners to the girder. This detail corresponds to Illustrative Example 

4.1 in AASHTO LRFD Table 6.6.1.2.3-1, and it is classified as Detail Category C' in AASHTO 

LRFD Table 6.6.1.2.3-1. 

For this design example, the fillet-welded connection of the transverse intermediate stiffeners 

will be checked at the location of maximum positive moment. The fatigue detail is located at the 

inner fiber of the tension flange, where the transverse intermediate stiffener is welded to the 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

5.7 

flange. However, for simplicity, the computations will conservatively compute the fatigue stress 

at the outer fiber of the tension flange. 

The live load distribution factors for moment for an interior girder are computed as follows.

First, for interior girders, the longitudinal stiffness parameter, Kg, must be computed: 

Kg = n ⋅ (I + A ⋅ eg

2

) 

At the location of maximum positive moment:

n = 8 

I = 22,196 in4 

A = 48 in2 

eg = 36.5 in 

Therefore,

Kg = 689,150 in4

After the longitudinal stiffness parameter is computed, AASHTO LRFD Table 4.6.2.2.1-1 is used 

to find the letter corresponding with the superstructure cross section. The letter corresponding 

with the superstructure cross section in this design example is "a." 

For one design lane loaded, the distribution of live load per lane for moment in interior beams 

from AASHTO LRFD Table 4.6.2.2.2b-1 is as follows:

where:

S = 9.75 ft 

L = 120 ft 

ts = 8.0 in 

Therefore,

g = 0.47 lanes per interior girder 

As previously described, the exponential distribution factor equation for interior girders should 

be divided by 1.2 as it is implicitly included in the formulation. Therefore, 

g = 0.47/1.2 = 0.39 lanes per interior girder 
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5.8 

At the location of maximum positive moment, the range of live load plus impact moment due to 

the passage of the fatigue truck is given as: 

M = 1198 k-ft per lane

and 

Sb-interior = 1307 in3 

Therefore,

gM = 467 k-ft per interior girder

fb-interior = 4.29 ksi for an interior girder 

For one design lane loaded, the distribution of live load per lane for moment in exterior beams is 

computed using the lever rule, as per AASHTO LRFD Table 4.6.2.2.2d-1, as follows (see Figure 

5.3.1.1-6): 

(0.5)(4.25) (0.5)(10.25)

9.75 g

+ =

g = 0.74 lanes per exterior girder 

Figure 5.3.1.1-6 Schematic of the lever rule.

For the exterior beam,

M = 1198 k-ft per lane 

and

Sb-exterior = 1240 in3 (as the bridge-deck overhang is less than one-half of the 
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5.9 

girder spacing shown in Figure 5.3.1.1-6 above, the 

composite exterior girder is less stiff)

Therefore,

gM = 887 k-ft per exterior girder

fb-exterior = 8.58 ksi for an exterior girder 

Each of these stresses must be compared to the permissible stresses for the AASHTO Fatigue I 

and Fatigue II load combinations, and the appropriate checks must be satisfied. These topics are 

further covered in Chapter 6. 

5.3.1.2 Transverse Members

LRFD distribution formulas cannot be used for transverse members spaced greater than 6 feet on 

center. 

A lever-rule method of analysis is generally used for such members. The loading on longitudinal 

members is converted to live load reactions on a transverse member.

The controlling members for fatigue can include the transverse floorbeams. The current 

specifications assume no lateral load distribution on the floorbeams. If the floorbeam does not 

come into contact with the slab, the lever rule should be used to determine the moment in the 

floorbeam. If the floorbeam does come into contact with the slab, the load is transferred in a 

more complex manner. The percentage of moment taken by the floorbeam and slab will vary 

according to the relative stiffness of the floorbeam and slab. A more refined approach to analysis 

may be used to provide a more realistic assessment of the floorbeam moment.

For cases where floorbeams have been used without stringers on highway bridges, it has 

appeared proper to calculate the live load reaction transmitted to the floorbeam assuming the 

deck slab to act as a continuous beam supported by floorbeams. No transverse distribution of 

wheel loads is allowed unless a refined analysis is used.

5.3.2 Refined Analysis 

Bridges or loading conditions for which accurate live load distribution formulas are not readily 

available in AASHTO LRFD Table 4.6.2.2.1-1 should be analyzed by refined methods of 

analysis. In addition, bridges that fall outside the ranges of applicability of AASHTO LRFD

Tables 4.6.2.2.2b-1 and 4.6.2.2.2d-1 should also be analyzed by refined methods. Refined 

analysis may also be considered and has been used to obtain more accurate and realistic stress 

ranges when assessing existing structures and performing remaining fatigue life analyses.

Horizontally curved bridges should be analyzed using refined methods in order to capture (i.e., 

model) complex force effects (e.g., warping stresses).
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5.10 

A highly deteriorated structure or a structure with extensive structural repairs or retrofits may 

behave differently than the structure as originally designed. Refined analysis procedures may be 

useful for a detailed fatigue investigation of such structures. 

Depending upon the elements used, a refined analysis may yield moments from which nominal 

stresses can be derived, or it may yield nominal stresses directly.

Where the bridge is analyzed for design by any refined method, as specified in AASHTO LRFD

Article 4.6.3, a single design truck should be positioned transversely and longitudinally to 

maximize stress range at the detail under consideration, regardless of the position of traffic or 

design lanes on the deck. 

For diaphragms or cross-frames, the range of load is determined by the passage of the fatigue 

design truck along the length of the bridge but in a single transverse position (i.e., one particular 

lane). While previous versions of the AASHTO specifications allowed for the maximum tension 

load to come from loading in one lane and the compression load to come from another lane, this 

provision is no longer applicable. It should be noted that the single truck in a single lane 

provision is exclusively for diaphragms and cross-frames. For orthotropic decks or box girders, 

no such distinction is made. 

If it were assured that the traffic lanes would remain as they are indicated at the opening of the 

bridge throughout its entire service life, it would be more appropriate to place the truck at the 

center of the traffic lane that produces maximum stress range in the detail under consideration. 

However, because future traffic patterns on the bridge are uncertain and in the interest of 

minimizing the number of required calculations, the position of the truck is made independent of 

the location of both the traffic lanes and the design lanes.

For fatigue evaluation, it may be appropriate to assume the single truck is in a striped lane if 

traffic patterns on the bridge have not changed since its opening.

For detailed information about modeling and analysis using refined methods, see FHWA’s 

Manual of Refined Analysis (Modjeski and Masters, 2016). 

SECTION 5.4 FATIGUE STRESS ANALYSIS

5.4.1 Nominal-Stress Approach

The nominal-stress approach is the simplest way to assess the fatigue limit state at a detail and, 

as such, is included in design specifications from a variety of industries. This approach 

determines fatigue resistance and applied stress based on calculating a nominal stress near the 

detail being considered using simple equations for resolving bending and axial load in the 

member. The local stress concentrations that occur at the detail and at the notch are accounted 

for in the specified fatigue detail category resistance, described in Chapter 6.
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5.4.2 Local-Stress Approach

The local-stress approach is similar to the nominal-stress approach, but the S-N curves in this 

approach are based on the range in the local structural stress, also called the hot-spot stress. To 

produce the S-N curves, full-scale tests are performed and the hot-spot stress ranges are either 

measured (i.e., strain gauges) or calculated (i.e., refined finite element models) and plotted 

against the cycles to failure. In effect, the stress concentration is taken out of the fatigue 

resistance and, instead, is accounted for in the analysis. This has the advantage of collapsing all 

the S-N curves for different categories into a single baseline S-N curve, but it increases the 

complexity of the analysis. The test data and the baseline S-N curve still include the effect of the 

local total stress, which may be impossible to accurately calculate and, therefore, must still be 

treated empirically.

5.4.2.1 Application of Local-Stress Approach

For the limited number of bridge details shown in AASHTO LRFD (AASHTO, 2015b), full-scale 

tests resulted in the characterization of their fatigue resistance. Therefore, the nominal-stress 

approach has been satisfactory for the bridge industry and others as well. However, for tubular 

structures used for ancillary sign structures, the nominal-stress approach breaks down. Fatigue 

resistance of tube-to-tube connections is dependent upon member and plate thickness, tube 

diameter, and for end plate connections, parameters such as bolt circle diameter, anchor-rod 

diameter, and number of anchor rods, resulting in an infinite number of possible connections. 

Not every possible tube-to-tube connection can be tested to define a unique S-N curve for each.

Therefore, the hot-spot stress approach was developed as the only practical alternative for tubular 

structures (AWS, 2010 and Marshall, 1992). For bridges, the hot-spot stress approach is useful in 

understanding the cracking that occurs from in-plane and out-of-plane forces (e.g., orthotropic 

steel decks and sign structures) since out-of-plane forces are not addressed by typical bridge 

analysis.

5.4.2.2 Stress Components

The local-stress (or hot-spot) location is often in high strain gradient fields and, as a result, 

measurement of the local structural stress involves considerable uncertainty. To address this 

problem, guidelines have been established to extrapolate a stress concentration factor (SCF) from 

multiple strain gauge measurements (Zhao et al., 1999). Another simple approach is to define the 

hot-spot stress as the stress measured with a 1/8-inch strain gauge placed as close as practically 

possible to the weld toe (e.g., centered about 1⁄4 inch from the weld toe) (Dexter et al., 1994). 

The baseline curve is sensitive to the definition of the hot-spot stress. British Standard (BS) 7608 

(BSI, 1994) defines a Category T curve, along with a correction factor based on the plate 

thickness, and AWS (AWS, 2010) uses the X2 curve. As it turns out, these curves are similar to 

AASHTO Detail Category C, which is the nominal stress S-N curve associated with butt welds 

with reinforcement (not ground flush) in a flat uniform plate. Therefore, the hot-spot stress is 

equal to the nominal stress in this detail. For assessment of web gap details and other bridge 

details using the hot-spot approach, it is recommended that AASHTO Detail Category C be used 
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5.12 

together with a hot-spot stress range measured or calculated 1⁄4 inch from the weld toe (Dexter et 

al., 1994). 

It should be noted that, although AASHTO does not explicitly classify detail categories for 

distortion-induced fatigue, they limit the development of web-gap stresses through improved 

detailing requirements. While these fatigue issues can be avoided in new bridges through the use 

of proper detailing, there are many thousands of in-service bridges dating back to before the mid1970’s that are susceptible to such cracking (Connor and Fisher, 2006). Research has 

demonstrated that distortion-induced fatigue can be classified as a Category C detail (Connor and 

Fisher, 2006). When the transverse stiffeners serve as diaphragm connection plates, the number 

of cycles to initiate distortional fatigue cracking of the web at the stiffener termination coincides 

with data for the AASHTO S-N curve for Category C details. 

In design, the hot-spot stress approach involves the calculation of the stress concentration factor 

using parametric equations or finite element analysis (FEA) (AASHTO, 2015b; Connor et al., 

2012; IIW, 2007; Zhao et al., 1999). However, FEA results are highly mesh dependent, since the 

local structural stress is often in an area of high strain gradients. 

The disadvantage in the local-stress approach lies mainly in the variability between different hotspot stress definitions and varying baseline S-N curves. Another problem involves the constant 

amplitude fatigue threshold (CAFT). The hot-spot approach implies that all details will have a 

CAFT at the same number of cycles, while full-scale fatigue tests show that the CAFT occurs at 

different orders of magnitude of cycles for different categories. As a result, a conservative 

approach is to ignore the CAFT for the hot-spot stress approach. 

5.4.2.3 Model Discretization and Calibration 

Stress evaluation at weld toes presents technical problems to the analyst who uses FEA, in that 

the angle the weld makes with the base material represents a sharp discontinuity. At that precise 

point, the discontinuity will cause the model to show a sharp increase in stress that is not in any 

way similar to the calculated stresses used to produce the fatigue database that created the widely 

adopted S-N curves. Thus, the concentration part of the stress that is a component of the baseline 

data provided in the AASHTO nominal-stress provisions must be eliminated from the assessment 

of the stress for such data to be of any use. It follows that for any modeling technique, there must 

be associated a calibration method to bring the estimated stress in line with the procedure used to 

evaluate stresses for the production of the database.

Finite element meshing can be accomplished using shell / plate elements or brick elements. It is 

the consensus of the industry at this time that shell / plate elements are adequate to characterize 

structures and local effects that are typically composed of relatively thin material with small 

effects in the through-thickness direction. This does not prohibit analysts from using brick 

element techniques, should they so desire, as calibration techniques are available for both. 

There are two accepted techniques that provide this calibration. Both use databases that are 

dissimilar to that adopted by AASHTO. They are the following: 
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5.13 

• Extrapolation

• The Battelle Structural Stress (Dong and Hong, 2006) 

The extrapolation method is more widely accepted and is discussed further below. 

Figure 5.4.2.3-1 shows diagrams of conceptual connections for the purpose of illustrating 

concentrations at weld toes in abrupt transitions and in continuous fillets. In most cases, shell 

element sizes are standardized for determining weld toe stresses. Brick elements are often 

invoked at abrupt terminations. 

Currently, the AASHTO specifications only apply the shell-element formulation, which is thus 

of interest for highway structures. 

Figure 5.4.2.3-1 Modeling guidance for evaluation of stress concentrations by 

extrapolation.

Figure 5.4.2.3-2 shows that points on the finite element are selected at an appropriate distance 

from the weld toe for Type “a” and Type “b” details illustrated in Figure 5.4.2.3-1 and how the 

stress is extrapolated to the weld toe to obtain the local structural stress.
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5.14 

Figure 5.4.2.3-2 Stress extrapolation.

Table 5.4.2.3-1 provides a summary of appropriate mesh sizes.

Table 5.4.2.3-1 Recommended mesh sizing and extrapolation for fine and coarse meshes for 

analysis of stress concentration.

Type of Model and Weld Toe Relatively Coarse Models Relatively Fine Models

Type a Type b Type a Type b

Element Size

Shells t x t

max t x w/2 (*) 10 x 10 mm ≤ 0.4 t x t or 

≤ 0.4 t x w/2 ≤ 4 x 4 mm

Solids t x t

max t x w 10 x 10 mm ≤ 0.4 t x t or 

≤ 0.4 t x w/2 ≤ 4 x 4 mm

Extrapolation 

Points 

Shells

0.5 t and 1.5 t 

mid-side 

points (**)

5 and 15 

mm midside points 

0.4 t and 1.0 t 

nodal points 

4, 8, and 12 

mm nodal 

points 

Solids 0.5 t and 1.5 t 

surface center

5 and 15 

mm surface 

center

0.4 t and 1.0 t 

nodal points 

4, 8, and 12 

mm nodal 

points 

Legend: 

(*) w = longitudinal attachment thickness + 2 weld leg lengths 

(**) surface center at transverse welds, if the weld below the plate is not modelled

The validity of the locations of the extrapolation points is based on the authors’ affirmations that 

those locations give best fit to the baseline data. Other codes, such as the DNV or the AWS 

fatigue criteria (AWS, 2010), have alternate extrapolation criteria, indicating that for shell 

elements, the weld at the toe be extrapolated to the mid-plane of the shell. This is a more 

conservative approach, but it is accepted practice.
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5.15 

Again, for bridge structures, element meshes are relatively coarse, and the coarse-mesh columns 

of Table 5.4.2.3-1 are of concern to the bridge engineer.

The local-stress approach (or hot-spot stress approach) appears in AASHTO LRFD (AASHTO, 

2015b), where the procedures discussed above are applied by the designer. It also appears in the 

LRFD Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals

(AASHTO, 2015c), where these procedures have been applied for the designer, resulting in a 

more empirical presentation.

5.4.2.4 Example of Application of the Local-Stress Approach

Though the local-stress (or hot-spot analysis) approach is not applied for typical bridge design, 

the following application not only illustrates its application where appropriate (e.g., orthotropic 

steel bridge decks and sign structures) but also reinforces the nominal stress, local structural 

stress, and local total stress concepts originally introduced in Chapter 2. 

In this application, a stress range of 1 ksi is applied to a cruciform specimen, symmetrical about 

the vertical axis, with additional welded attachments as shown in Figure 5.4.2.4-1. 

Figure 5.4.2.4-1 Cruciform specimen with attachments.

The attachments are characterized in Table 5.4.2.4-1 by length, thickness, and end treatment. 
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5.16 

Table 5.4.2.4-1 Detail characterization. 

Detail Description

A Long attachment with non-tapered end

B Relatively long, medium thick attachment

C Relatively long, medium thin attachment

D Relatively short, medium attachment

E Short attachment

F Long attachment with tapered end

The specimen was modeled using the local-stress (hot-spot) approach discussed above using 8-

node brick elements with dimensions of approximately 1/8 inch by 1/8 inch by 1/8 inch in the 

areas of interest (conforming to Type b - Relatively Fine Model requirements).

The results of the analyses in terms of calculated and extrapolated stress ranges are plotted in 

Figure 5.4.2.4-2 for the two longitudinal stiffener ends and Figure 5.4.2.4-3 for the four 

longitudinally-loaded attachments. Recall, the remote stress is a value of 1 ksi so the stress 

located directly at the discontinuity is the extrapolated stress, and in this case is also the stress 

concentration factor. For the four longitudinally-loaded attachments, the extrapolated stress 

increases with thickness and length. For the two longitudinal stiffener ends, the extrapolated 

stress decreases with the radiused end treatment. In each figure, the nominal stress, the 

extrapolated local structural stress, and the stress concentration factor (SCF) are illustrated.

Figure 5.4.2.4-2 Extrapolated stresses at longitudinal stiffener details in Figure 5.4.2.4-1. 
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Figure 5.4.2.4-3 Extrapolated stresses at longitudinally-loaded attachments in Figure 

5.4.2.4-1. 

5.4.3 Fracture-Mechanics Approach

The basic concepts of the fracture-mechanics approach are described in detail in Chapter 3 to 

assist the reader in understanding the fatigue-and-fracture design and evaluation rules. However, 

the complexity of this approach is rarely warranted in design. Nevertheless, the concepts of 

fracture mechanics enable the designer to increase his or her qualitative understanding of 

structures containing sharp discontinuities. Because more parameters are explicit in fracture 

mechanics analyses, designers can identify more easily those parameters that influence the 

strength of the structure. Some examples covering the importance of discontinuities, parametric 

studies, and crack propagation behavior are presented in Chapter 3. 
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6.1 

CHAPTER 6 AASHTO FATIGUE DESIGN APPROACH

SECTION 6.1 GENERAL

Fatigue in steel bridges is addressed in AASHTO LRFD by restrictions on the stress range due to 

live load plus impact produced by the passage of a code-specified fatigue design truck (loadinduced fatigue) and by specific detailing requirements (distortion-induced fatigue). Both loadinduced and distortion-induced fatigue must be considered separately during design, but they are 

addressed in different ways, as described in this chapter. 

6.1.1 The Fatigue Limit State

Previous chapters explained that stress range is the dominant parameter for fatigue, and stress 

range can be readily computed by the design engineer at locations that have possibility of 

cracking. The design for load-induced fatigue requires that the factored stress range due to live 

load plus impact resulting from the passage of the fatigue design truck be less than the factored 

nominal resistance at every detail that is subjected to net tensile stress. The limit state is 

expressed mathematically as:

Equation 6.1.1-1 

The left side of the equation represents the factored stress range and is the product of a load 

factor, γ, and the computed stress range due to live load and impact in the member, Delta (∆) f, at 

a detail of interest. Fatigue load factors are different from strength limit state load factors in that 

they are multipliers that are applied to the design truck to represent either a “maximum” (Fatigue 

I load combination) or “effective” (Fatigue II load combination) loading. AASHTO LRFD

specifies a value of 1.75 for the Fatigue I load combination load factor and 0.8 for the Fatigue II 

load combination load factor. The right side of the equation represents the factored nominal 

resistance. For the fatigue limit state, the resistance factor, φ, is taken as 1.0 and safety is 

provided in the selection of the load factors and the confidence limit in the specified nominal 

resistance. A further discussion of recent studies and calibration of the fatigue limit state is 

provided in Appendix A. 

Fatigue is addressed by two sets of design criteria, or load combinations, in AASHTO LRFD, the 

“Fatigue I” load combination and the “Fatigue II” load combination. These two load 

combinations are based upon the two distinct regimes of fatigue behavior. The Fatigue I load 

combination represents infinite fatigue life regime (i.e., the bridge can safely carry an infinite 

number of truck-load induced fatigue cycles). If this load combination is satisfied, the bridge will 

safely avoid cracking during a 75-year design life no matter how many constant amplitude stress 

cycles are applied. This is typically referred to as “infinite life.” The Fatigue II load combination 

represents finite fatigue life regime in which the resistance is not infinite due to the application of 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

6.2 

higher stress ranges. If the Fatigue I load combination is not satisfied, the Fatigue II load 

combination may still provide adequate resistance for a projected number of stress cycles. 

Both the Fatigue I and II load combinations were statistically calibrated as part of Transportation 

Research Board, Strategic Highway Research Project R19B (Modjeski and Masters, 2015). For 

the calibration of the two fatigue load combinations, the reliability index for the current design 

provisions (AASHTO LRFD) was computed. The term “reliability index” is a measure of safety 

given the statistical distributions of the load and resistance data. The reliability index is given the 

variable name of β. The concepts behind β are explained in Figure 6.1.1-1. 

Figure 6.1.1-1 Definition of β using load and resistance statistical characteristics.

In Figure 6.1.1-1, the loads and resistances are represented by normal distribution curves. The 

figure includes a normal distribution curve for the loads, Q, and the resistance, R, and also 

presents their mean values, (R bar) and (Q bar). The area of overlap where the extremes of 

the load and resistance distributions cross is considered to be failure. If a single curve is created 

by subtracting load from resistance (i.e., R-Q), the figure at the right is produced. When R-Q is 

negative, load exceeds resistance, and the design does not satisfy the limit state objective. In 

order to control the number of failures, the mean of the R-Q curve is offset some distance from 

zero, defined as β times the standard deviation, σ. A β equal to zero (no offset) indicates a 50 

percent chance of failure. A β of 3.5, commonly used as a target for strength limit states, 

corresponds to a probability of failure of 2 in 10,000 times. The recent calibration of the fatigue 

limit state is based on a target β of 1.0, which corresponds well to the β found from assessing 

past LRFD practices. A β of 1.0 is consistent with a probability of failure of approximately 16 

percent, a much larger chance the limit state will be exceeded (i.e. cracks may develop) than the 

accepted failure rate at the strength limit state. 

Calibration of the Fatigue I load combination required that a load factor be chosen so that the 

maximum truck effect could be enveloped with a high degree of confidence. The maximum truck 

is one whose effects must be limited so that crack growth does not occur under infrequent 

passages. The concept of a maximum weight truck (or maximum stress range) is one which 

occurs a maximum of 1 in 10,000 occurrences. A load factor of 2.0, later revised to 1.75 by the 

R19B researchers, was suggested to account for the stress ranges of these infrequently occurring 
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6.3 

vehicles. Similarly, calibration of the Fatigue II load combination was performed to address the 

accumulated damage of many millions of vehicle passages. A load factor of 0.8 was proposed to 

capture the cumulative force effects of millions of average or effective stress cycles. The 

calibration of both load combinations is discussed in this chapter, as well as in greater detail in 

Appendix A. 

The philosophical underpinning of the AASHTO approach to fatigue design is based on the 

following assumptions: 

• The total range of live load plus impact stress is damaging and must be considered.

• Residual stresses need not be considered.

• Only details subjected to net tensile stress need to be designed for fatigue.

• The stresses are generally calculated in composite bridges assuming the slab and girder 

are fully effective for both positive and negative bending moments. 

SECTION 6.2 CLASSIFICATION OF FATIGUE

Two different sources of fatigue are identified in AASHTO LRFD: load-induced and distortioninduced fatigue. 

Load-induced fatigue is defined in AASHTO LRFD as “fatigue effects due to the in-plane stresses 

for which components and details are explicitly designed.” Simply stated, load-induced fatigue is 

related to the in-plane primary stresses that are calculated from analysis. Examples of these inplane stresses include the flexural stress in a flange or web of a steel I-girder, stress ranges in a 

cross-frame that result from a refined analysis, stress ranges at a shear stud to girder flange 

connection when designing a composite girder, stress ranges due to wind in light and sign 

structures, and other similar instances where engineers have results from analysis. 

As described in Chapter 2, all steel structures possess initial discontinuities, stress 

concentrations, and residual stresses due to rolling and/or welding. Load-induced fatigue 

cracking is the growth of cracks from these conditions due to applied stress-range cycles from 

the passage of trucks, such as at the end of a cover plate end weld on the Yellow Mill Pond 

Bridge shown in Figure 6.2-1. This crack was detected in 1970 and is representative of cracking 

that occurred in some older bridges constructed when cover-plating rolled beams was a means of 

increasing their capacity. This type of detail is no longer used in new construction and simply 

illustrates a load-induced fatigue crack, a type which might still be found when inspecting older 

bridges. Details such as this one are not desirable for new bridges because of their poor fatigue 

performance.

Load-induced fatigue is controlled by the Fatigue I and II load combinations by which members 

are proportioned to limit stress ranges to those specified as allowable for each detail type. 
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6.4 

Figure 6.2-1 Cracking of a cover plate on the Yellow Mill Pond Bridge.

Distortion-induced fatigue is the designation given to cracking that arises from local out-of-plane 

secondary stresses not typically calculated in analysis. This type of cracking represents the 

majority of observed fatigue cracks that are discovered in in-service bridges. It occurs in bridges 

at diaphragm / cross-frame connection plates that are not positively attached to the girder 

flanges, at floorbeam connections to main girders, as well as in situations such as floorbeam to 

truss and tie girder connections. Since the mid-1980’s, and dating back to the use of the 

AASHTO Standard Specifications for Highway Bridges, AASHTO has required the engineer to 

design new structures to prevent distortion-induced fatigue, though it remains an ongoing 

problem in many existing bridges (see Chapter 9 for repair and retrofit guidance). Distortioninduced cracking is prevented by providing a positive load path to transmit unintentional and 

intended force effects between transverse and longitudinal members. A schematic of the most 

common mechanism causing distortion-induced fatigue is provided in Figure 6.2-2. 

Distortion-induced cracking is controlled by detailing members and connections to mitigate outof-plane distortions, not by proportioning members to satisfy specific limit states.
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6.5 

Figure 6.2-2 Common mechanism causing distortion-induced fatigue of a web gap and 

resulting web tensile stresses.

AASHTO designates fatigue categories to some design details that have no design nominal stress 

definition. Deck joints (e.g., modular joints) need to be designed by the vendor and then tested to 

define their fatigue acceptance, and AASHTO qualifies these by testing. Orthotropic decks also 

have fatigue design approaches that are codified. 

SECTION 6.3 LOAD-INDUCED FATIGUE

6.3.1 General Limit State

To provide a standard definition of the load-induced fatigue limit state, AASHTO LRFD provides 

the following description in Article 1.3.2.3: 

“The fatigue limit state shall be taken as restrictions on stress range as a result of 

a single design truck occurring at the number of expected stress range cycles.” 

Furthermore, the commentary to the article states:

“The fatigue limit state is intended to limit crack growth under repetitive loads to 

prevent fracture during the design life of the bridge.” 

With these two statements, a concise definition of the nature and intent of the limit state is 

provided. The purpose of the limit state check is to limit crack growth over the design life of the 

structure. The limit state is expressed mathematically as restrictions on cyclical stress ranges 

caused by the passage of a single design truck. It takes the form of Equation 6.1.1-1. 

For the Fatigue I load combination, the load factor, γ, is 1.75, and for the Fatigue II load 

combination, γ is 0.8. For the fatigue limit state, Φ equals 1.0. 
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6.6 

The factored force effect is on the left side of Equation 6.3.1-1, and the factored nominal 

resistance is on the right side, as shown in Equation 6.3.1-2. 

Factored Force Effect ≤ Factored Resistance 

Equation 6.3.1-2 

The force effect and resistance components are explored below.

6.3.1.1 Factored Force Effect

As introduced in Chapter 2 and numerically illustrated in Section 4.1.3, stress range is the 

dominant stress parameter for fatigue design. Further, Section 2.3.2.2 concludes that the most 

common cause of fatigue cracks in bridges is in-service cyclical stress range due to trucks. 

Therefore the fatigue limit state only considers force effects from live load and no other loads. 

The Fatigue I load combination is applied to check if the detail under investigation will safely 

achieve infinite life. When a detail cannot provide infinite life due to the magnitude of the 

repeating stress range, the Fatigue II load combination is applied to ensure that the detail will 

exhibit sufficient finite life based upon the projected average daily truck traffic (ADTT) for 75 

years, the design life specified in AASHTO LRFD. 

The force effect for the fatigue limit state, Δf, is the live load stress range due to the passage of 

the fatigue load. The fatigue design vehicle is similar to the HL-93 design truck but with a 

constant spacing of 30.0 feet between the 32.0-kip axles, as illustrated in Figure 6.3.1.1-1. The 

30-foot axle spacing is used for fatigue stress calculations to better represent the overall force 

effects of four- and five-axle semi-trailers that produce the majority of fatigue damage 

(AASHTO, 1990). 

The single truck in a single lane concept was introduced with AASHTO LRFD. Prior to that, the 

Standard Specifications for Highway Bridges used a multi-lane distribution factor to design for 

fatigue, along with other differences. The single truck concept was validated as part of the 

SHRP2 Project R19B research (Modjeski and Masters, 2015), a summary of which is provided in 

Appendix A. The R19B research team evaluated millions of weigh-in-motion study records and 

determined there was a very small number of similar weight and configuration trucks traveling 

closely in the same lane or adjacent lanes and on that basis validated the prior assumption of a 

single truck in a single lane live load model. 

The passage of the vehicle also produces a dynamic response. In addition to the static force 

effects, a 15 percent increase in the vehicle force effects is applied to account for dynamic load 

allowance, commonly called impact and abbreviated as “IM” in AASHTO LRFD. This is related 

to vehicle suspension characteristics, surface roughness of the approach and bridge pavement, 

and the natural frequency of the bridge. 
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6.7 

Figure 6.3.1.1-1 AASHTO fatigue design vehicle.

6.3.1.2 Factored Resistance

AASHTO LRFD specifies the design resistance of details based upon the testing and conclusions 

thereof discussed in Section 4.3. Details are categorized and organized into eight Detail 

Categories (A, B, B’, C, C’, D, E, and E’) in order of descending fatigue resistance, which is 

shown graphically in Figure 6.3.1.2-1. Each piecewise continuous curve consists of a sloping 

portion of variable resistance followed by a straight horizontal line, representing the constant 

amplitude fatigue threshold (CAFT) as discussed previously in Section 4.3. All the fatigue 

details and their respective detail categories are presented in AASHTO LRFD Table 6.6.1.2.3-1. 

For each detail, a written description of the type of detail and orientation / type of loading is 

provided, along with a sketch illustrating the particular detail or application. Refer to AASHTO 

LRFD for the most current illustrations of each fatigue detail, though several examples are 

provided for common conditions herein. To recall, these resistance limits are established through 

testing and represent a 97.5 percent probability of survival in the region of finite life (sloping 

boundaries). The region of infinite life represented by the threshold is not statistically based, 

given a lesser number of long-life tests, though the Fatigue I load combination has been 

established to provide safe behavior for infinite life. A brief description of the detail categories is 

provided. 
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6.8 

Figure 6.3.1.2-1 Nominal fatigue resistance of the detail categories specified in AASHTO 

LRFD. 

Detail Category A – Detail Category A includes base metal (except for noncoated weathering 

steel) with no changes in geometry (e.g., a cope) and steel with rolled or cleaned surfaces and 

flame-cut edges fabricated with specific surface finish requirements. Detail Category A details 

represent the maximum fatigue resistance and therefore are unlikely to control the design of most 

steel structures since most steel members have details such as mechanical connections, welded 

connections, or welded attachments that reduce fatigue resistance. An example of a Detail 

Category A detail with illustration of potential crack initiation point is shown in Figure 6.3.1.2-2. 
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6.9 

Figure 6.3.1.2-2 Detail Category A – example (base metal at edge of rolled beam). 

Detail Category B – Detail Category B includes a variety of common welded details, such as 

longitudinally loaded built-up sections connected with fillet welds or full penetration groove 

welds that are welded from both sides. A common Detail Category B detail is the connection of a 

web and flange for a typical plate girder. Other examples of Detail Category B welded details 

include the side welds connecting cover plates to rolled shapes as is commonly found on older 

bridges, the welds throughout the length of a typical longitudinal stiffener, and full penetration 

butt splices with the welds ground smooth and weld soundness established by nondestructive 

testing (NDT). The Detail Category B designation also applies to mechanically fastened joints 

such as pretensioned slip critical connections, as well as bearing type connections with 

pretensioned high-strength bolts and standard size holes. Detail Category B also includes the 

base-metal fatigue resistance of noncoated weathering steel. An example of a Detail Category B 

detail is shown in Figure 6.3.1.2-3. 

Figure 6.3.1.2-3 Detail Category B – example (full penetration groove weld). 
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6.10 

Detail Category B’ – Detail Category B’ applies to built-up sections such as box members which 

are commonly constructed with one-sided full penetration welds with backing bars left in place 

after welding. The category also applies to box-shaped members with corners joined by partial 

penetration welds with the welds parallel to the direction of stress.

Detail Category C – Detail Category C applies to both base metal and welded connections. 

Examples of Detail Category C include reentrant corners, copes, cuts, blockouts, and other 

geometrical discontinuities that are commonly found when rolled shapes are modified to fit 

certain connection conditions. Detail Category C also applies to various welded details. This 

includes some longitudinally loaded stiffeners with radiused transitions and welds ground 

smooth at the end of the detail, certain transversely loaded details connected with full penetration 

or fillet welds, and special welds such as those used to construct elements of orthotropic deck 

systems. Details in Detail Category C are generally considered to be the transition between 

details affected primarily by discontinuities and those affected more so by stress concentration. 

An example of a reentrant corner crack for a Detail Category C detail is shown in Figure 6.3.1.2-

4. 

Figure 6.3.1.2-4 Detail Category C – example (reentrant corner). 

Detail Category C’ – Detail Category C’ is a special detail category specifically reserved for 

checking the fatigue stress range effects in base metal at the toe of transverse stiffeners to flange 

fillet welds and transverse stiffener to web fillet welds. This detail category has the same fatigue 

life constant as Detail Category C, but it has a higher threshold stress. A transverse crack from a 

weld toe for a Detail Category C detail is shown in Figure 6.3.1.2-5. 
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6.11 

Figure 6.3.1.2-5 Detail Category C' – example (transverse stiffener). 

Detail Category D – Detail Category D details are a transition between details influenced by 

discontinuities (A, B, B’, C, and C’) and those whose performance is dominated by geometry 

and stress concentration (D, E, and E’) (see Figure 4.1.2-3). It includes both base metal, bolted 

joint details, and welded attachment details. Included are details such as open holes in steel 

sections; certain galvanized and bolted connection details; terminations of longitudinal stiffeners 

and gusset plates used to connect lateral bracing elements where the details have been improved 

by creating radiused end transitions; short longitudinal attachments without end treatment; 

several orthotropic deck details; and other details. Given the number of different types of details 

that fall in this category, Detail Category D is an example of fatigue life being related to stress 

concentration (in a relative sense) since base metal, bolted, and welded details are all addressed. 

All of these are subject to a stress concentration, be it from manufacturing such as punching of 

holes or from the welding of attachments to a steel element. An example of a crack from an open 

hole edge for a Detail Category D detail is shown in Figure 6.3.1.2-6. 
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6.12 

Figure 6.3.1.2-6 Detail Category D – example (open hole edge). 

Detail Categories E and E’ – The description of Detail Categories E and E’ are grouped together 

as they generally apply to the same types of details. The Detail Categories E and E’ details 

include weld and cover plate terminations, longitudinal stiffener terminations, lateral bracing 

connection plates, and miscellaneous welded attachments. Each one of these details is similar in 

that they are oriented parallel to the direction of primary stress in the member and are long 

enough and thick enough to draw stress out of the member with high stress concentrations at the 

ends of the section where the welds terminate (see Section 4.1.2). Detail Categories E and E’ 

details also terminate abruptly, as compared to the Detail Category D details which have more 

gradual terminations and transitions and somewhat enhanced fatigue performance. It is this 

combination of high stress at the abrupt termination and the fact that the elements desire to draw 

load away from the basic member (due to its length and thickness) that gives rise to high local 

stresses and the potential for fatigue cracking. In examining the AASHTO detail categories, the 

engineer will notice that as elements grow longer parallel to the direction of primary stress in the 

member and as they grow thicker in dimension, the fatigue resistance diminishes. This 

observation is consistent with longer and thicker elements causing more severe stress 

concentrations in the base metal of the primary member as more stress is able to flow into them. 

See Section 4.1.2 for additional background discussion on the effect of attachment size on stress 

concentration. An example of cracking at the end of a cover plate for a Detail Category E / E’ 

detail is shown in Figure 6.3.1.2-7. 
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6.13 

Figure 6.3.1.2-7 Detail Category E / E' – example (cover plate termination). 

Regarding the various fatigue categories, it is worth noting that engineers have the freedom to 

modify specific design details in order to meet certain fatigue limit state requirements. An 

example is a longitudinal stiffener used to stiffen the web of an I-beam or box girder bridge. The 

most punitive fatigue category would be Category E’, which is the appropriate fatigue category 

for a longitudinal stiffener equal to or greater than 1 inch thick and welded to the base metal with 

no end transition. The limits of a longitudinal stiffener are first and foremost defined by a 

strength requirement, yet the termination location of the stiffener is frequently related to the 

computed stress ranges where the engineer desires to end the stiffener. If the stress range at a 

desired termination point exceeds the Category E or E’ allowable stresses as specified in 

AASHTO LRFD, the engineer has the opportunity to provide a radiused transition at the end of 

the stiffener or carry the detail longitudinally to a location on the member where it terminates in 

a zone of permanent compression. The effects of attachment thickness and end treatment are 

presented in Table 6.3.1.2-1, taken from the AASHTO LRFD specifications. When the stiffener 

terminates abruptly in a blunt end, the attachment is classified as Category E or E’, depending on 

its thickness. With a more gradual transition, the condition at the end is improved. The 

improvement is without regard to attachment thickness. An example is presented in Figure 

6.3.1.2-8. 
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6.14 

Figure 6.3.1.2-8 Improvement in detail category by end treatment.

Table 6.3.1.2-1 Variation of detail category for longitudinal stiffener terminations. 

Description Detail 

Category

Location of 

Cracking Illustrative Figure

Base metal at the termination of longitudinal stiffener-to-web or longitudinal stiffener-to-box welds:

With the stiffener attached by fillet welds and with no transition radius provided at the termination:

Stiffener thickness 

< 1.0 in. E 

In the primary 

member at the end 

of the weld toe

See Figure 6.3.1.2-9 

Stiffener thickness 

≥ 1.0 in. E’

With the stiffener attached by welds with a transition radius, R, provided at the termination with the termination 

ground smooth:

R ≥ 24 in. B 

In the primary 

member near the 

point of tangency 

of the radius

See Figure 6.3.1.2-10

24 in. > R ≥ 6 in. C 

6 in. > R ≥ 2 in. D 

2 in. > R E 
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6.15 

Figure 6.3.1.2-9 Improvement in detail category by end treatment.

Figure 6.3.1.2-10 Improvement in detail category by end treatment.

6.3.2 Applicability

Load-induced fatigue cracks can only grow at details subjected to a net applied tensile stress. 

AASHTO LRFD Article 6.6.1.2 requires that wherever the maximum tensile live load stress due 

to the Fatigue I load combination exceeds the unfactored permanent compressive stress, details 

shall be evaluated for fatigue. If the tensile stress does not overcome the unfactored permanent 

load stress, net tensile loading is not available to grow a crack beyond the small zone of residual 

stress, even when a source of initiation is present. 

6.3.3 Infinite Life – The Fatigue I Load Combination 

The Fatigue I load combination controls the propagation of cracks that may occur when the 

maximum stress range is applied to a detail. It will control when there are higher numbers of 

applied stress cycles (ADTT). AASHTO LRFD Table 6.6.1.2.3-2 provides a table defining the 

equivalency between the variable amplitude fatigue life and infinite life curves shown previously 

in Figure 6.3.1.2-1. For the Fatigue I load combination, the loading terms are the load factor and 

computed stress range, respectively, and the nominal resistance is defined as the constant 

amplitude fatigue threshold (CAFT). Thus, the limit state equation becomes:

Equation 6.3.3-1 

where: 

 = loading terms

 = nominal resistance as defined in AASHTO LRFD
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6.16 

The load effects and resistance are detailed in the following sections.

6.3.3.1 Factored Force Effect for Infinite Life

The load factor for Fatigue I, meant to preclude crack growth under the maximum stress range, is 

1.75. The premise of the CAFT is that under constant amplitude loading, if all stress ranges are 

less than the threshold resistance, cracks will not propagate from a discontinuity. However 

bridges are not subject to constant amplitude loading but rather random loading with occasional 

large stress cycles. These larger stress cycles, even when limited to very low occurrences, can 

cause crack extension, and subsequent cycles of lesser stress ranges result in crack extension. 

Tests have determined that the number of stress cycles for these maximum stress ranges should 

be kept less than a 1:10,000 occurrence in order for the threshold behavior to be valid. The 

NCHRP 267 and 354 studies examined the long-life behavior under variable amplitude loading 

and tested the existence of the CAFT (Fisher, Mertz, and Zhong, 1983) and (Fisher, Nussbaumer, 

Keating, and Yen, 1993). Even with rates of exceedance as low as 0.05 percent, fatigue crack 

growth was evident in welded longitudinal web attachments and welded cover plates. Several 

transverse stiffeners demonstrated cracking with exceedance rates as low as 0.01 percent. The 

research demonstrated that the CAFT is a valid limit, but under variable amplitude loading, the 

number of cycles of CAFT exceedance must be severely limited. The use of a load factor of 1.75 

for the infinite life check is intended to guard against, or design for, these maximum stress 

ranges. 

In addition to the load factors normally used for fatigue, AASHTO LRFD has also introduced 

additional fatigue load factors for orthotropic decks and box girders. For orthotropic decks, 

because of their unique fatigue response characteristics, AASHTO LRFD provides a special load 

combination that increases the Fatigue I load factor to 2.25 when investigating fatigue at the 

welded rib-to-floorbeam cutout details and at the rib-to-deck welds. For box girders, AASHTO 

LRFD Article 6.11.5 introduces an additional factor of 0.75. 

6.3.3.2 Factored Nominal Resistance

The resistance for an evaluation of infinite life is termed the constant amplitude fatigue threshold 

(CAFT) or alternately the constant amplitude fatigue limit (CAFL), with the terms commonly 

used interchangeably. AASHTO uses the acronym CAFT in its specifications. Unlike finite life 

tests, for which there are many tests and the statistical distribution of resistance is readily 

determined, infinite life tests are time consuming and expensive and more limited in number. 

The statistical properties of the CAFT are not well established. The CAFT is simply a straight 

line drawn to bound the available test data and at which point it is assumed that cracking can be 

prevented under constant amplitude loading. Other CAFT limits could also be drawn at different 

stress levels. They do not have the same precision as the finite life equations for fatigue 

resistance. Nevertheless they are used to design structures so that fatigue cracking is prevented 

over the design life. 

On the resistance side of the equation, AASHTO expresses infinite life resistance as follows: 
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6.17 

Equation 6.3.3.2-1 

with (Delta (∆)F)TH provided in AASHTO LRFD as well as in Table 6.3.3.2-1. The values for the 

CAFT presented by AASHTO represent the horizontal lines in Figure 6.3.1.2-1. 

Table 6.3.3.2-1 AASHTO constant amplitude fatigue threshold (CAFT) values.

Detail Category Threshold (ksi)

A 24

B 16

B’ 12

C 10

C’ 12

D 7

E 4.5

E’ 2.6

A325 Bolts in Axial Tension 31

A490 Bolts in Axial Tension 38

6.3.3.3 Fatigue from Shear Buckling

An additional check is required that involves shear. Because AASHTO allows for the postbuckling response of steel girder webs at the strength limit state, buckling of the web is not 

specifically precluded. However, since the web slenderness and stiffener spacing would allow for 

buckling under some load cases, a concern was expressed that the possible buckling of the web 

at the service and fatigue limit states be restricted. Thus, AASHTO LRFD requires that a check be 

made of web buckling under the combined effects of the unfactored dead load plus the live load 

resulting from the Fatigue I load combination. This check is unique from the checks for flexural 

or axial stress since it also involves the calculation of the accumulated dead load forces. This 

fatigue check is compared to a buckling capacity, and thus the total internal shear forces acting 

on the section are needed.

Equation 6.3.3.3-1 

The factored shear force is equal to the unfactored shears from dead load plus the Fatigue I live 

load plus impact shear.

On the resistance side, the section strength is limited to the shear buckling capacity,

Equation 6.3.3.3-2 
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6.18 

For shear, φ is equal to 1, C is equal to the ratio of the shear buckling capacity to the plastic 

shear strength of the web and depends on web slenderness and transverse stiffener spacing, and 

Vp equals the plastic shear capacity of the web, taken as:

Equation 6.3.3.3-3 

Fy is the yield strength of the web material, and D and tw are the depth and thickness of the web. 

6.3.4 Finite Life – The Fatigue II Load Combination 

The Fatigue II load combination controls the propagation of cracks under repeating load effects 

over the design life of the structure. It allows for higher stress ranges but only for a finite number 

of cycles. It makes use of the concept of stresses produced by an “effective” truck and compares 

them to finite life resistance. For finite life, the limit state is expressed as:

Equation 6.3.4-1 

The term, A, represents the detail constant, and N is the required number of design cycles for the 

detail. Each is described in the following sections. 

6.3.4.1 Factored Force Effect for Finite Life

The load factor for Fatigue II, which was selected to represent the stresses produced by many 

random truck crossings, is specified as 0.8. This factor was chosen to represent the stresses 

produced by an effective truck and is used to assess the bridge’s finite life (i.e., the anticipated 

life of a detail subjected to many cycles of a repeating equal magnitude load). The finite life load 

factor of 0.8 is based on the SHRP2 R19B project, the results of which are described in 

considerable detail in Section 6.3.5 and Appendix A. The stresses produced by the fatigue design 

truck and the load factor, γ, are called the effective stress range. 

6.3.4.2 Factored Resistance

In the region of finite life, the nominal fatigue resistance is a function of the detail category and 

the number of cycles. It is generally accepted that for structural steels, the life is inversely 

proportional to the cube of the applied stress range. 

Equation 6.3.4.2-1 
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6.19 

A doubling of the stress range decreases the life by a factor of 8. Control of the stress range is 

therefore the most important factor in extending the fatigue life of a detail, as was previously 

discussed in Chapter 2. 

AASHTO rearranges this equation into the following form and defines this as the finite life 

nominal resistance of a specific class of details. The allowable stress range is expressed as a 

function of the specific detail and the number of cycles throughout the design life of the bridge, 

as follows: 

Equation 6.3.4.2-2 

with A given as a detail constant and N representing the number of design cycles of loading for a 

particular detail. This equation plots as a straight line when the logarithms of stress and the 

number of cycles are used for the axes. Though plotting as a straight line, this is frequently 

referred to as a “curve” in this document and in the literature. Plotted on standard axes (not 

logarithmic axes), the equation would indeed plot as a curved line. 

The AASHTO detail constants, A, needed to compute the finite life resistance are provided in 

Table 6.3.4.2-1. 

Table 6.3.4.2-1 AASHTO detail constants for finite fatigue life. 

Detail Category Constant, A times 108 (ksi3)

A 250

B 120

B’ 61

C 44

C’ 44

D 22

E 11

E’ 3.9

A325 Bolts in Axial Tension 17.1

A490 Bolts in Axial Tension 31.5

The additional term required to compute the fatigue resistance is the number of design cycles, N, 

to which a detail is subjected. AASHTO specifies that the number of design cycles is: 

Equation 6.3.4.2-3 

This equation computes the number of design cycles associated with the 75-year design life. The 

equation involves the computation of the average daily truck traffic in a single lane, ADTTSL, as 

well as the number of cycles of loading per vehicle passage, n. The ADTTSL is an estimate of the 

number of trucks in a given day that will produce the effective stress range. It is computed in 

AASHTO LRFD as a function of the total truck volume and the assumed percentage of trucks that 

travel in the critical lane location.
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6.20 

The engineer must estimate the average daily truck traffic in a single design lane averaged over 

the life of the structure, ADTTSL. The starting point for this estimate is the current ADTT in one 

direction. This is computed by taking a percentage of the ADTT for one direction of the bridge 

and assigning a portion of the total truck traffic to the most heavily traveled lane using the 

following equation: 

Equation 6.3.4.2-4 

where:

p = the fraction of trucks in the most heavily traveled lane 

ADTT = average daily truck traffic in one direction

To determine the ADTT in a single direction, AASHTO LRFD suggests that if directional split 

information is not available, 55 percent of the total traffic be assumed in one direction. AASHTO 

LRFD stipulates that the traffic percentage in the most heavily traveled lane, p, be taken as 100 

percent for a single lane available to trucks, 85 percent for two lanes available, and 80 percent 

for three or more lanes available, since regardless of the number of lanes, trucks tend to bunch in 

specific driving locations. When determining the ADTT, consultation with the project traffic 

engineers is suggested in order to determine the estimated truck traffic as a percentage of the 

single-direction ADT. If guidance on the percentage of trucks is not available, Table 6.3.4.2-2

may be used as a guide (see AASHTO LRFD Article C3.6.1.4.2).

Table 6.3.4.2-2 Percentage of trucks for roadway types.

Class of Highway Percentage of Trucks in Traffic

Rural Interstate 20 percent

Urban Interstate 15 percent

Other Rural 15 percent

Other Urban 10 percent

The number of cycles per truck passage, n, is also required. In order to understand how the 

number of stress cycles varies for different span arrangements, let us first consider a simple span 

beam with a single moving point load. The stress range at the point of interest is proportional to 

the algebraic difference between the live load bending moment at the point of interest with the 

load placed in the critical location and the live load moment with no vehicle on the bridge, which 

is zero. This is shown graphically in Figure 6.3.4.2-1. 
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6.21 

Figure 6.3.4.2-1 Influence line for bending moment in a simply supported span.

Trucks contain many axles, however, and if each axle is allowed to cross the influence line, 

multiple cycles may be accumulated. Considering the AASHTO fatigue design vehicle, with axle 

spacings of 14 feet and 30 feet, the short span depicted above is loaded and unloaded three times 

during the passage of one truck. For longer spans, this loading / unloading cycle is not as 

pronounced since the stress is more a function of the total truck than individual axle or axle 

grouping effects.

For a continuous span, again with a single moving unit load, the definition of stress range is still 

the same (i.e., the algebraic difference between the maximum and minimum live load stresses). 

Figure 6.3.4.2-2 presents an example of an influence line for bending at a point in the end span 

of a continuous bridge. The ordinates corresponding to three separate unit load placements (not 

three loads at the same time) are plotted as well. An engineer could use such an influence line, or 

more commonly a continuous beam analysis program, to determine these maximum and 

minimum live load moments and hence the stresses. 

Figure 6.3.4.2-2 Influence line for bending moment in the end span of a continuous bridge. 

Example time histories of stress versus time per vehicle passage are shown in Figure 6.3.4.2-3 to 

demonstrate the nature of actual loading histories. Shown are the larger changes in stress that 

correspond to the passage of design vehicles, as well as smaller oscillations that reflect the 

dynamic response of the bridge. 
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6.22 

Figure 6.3.4.2-3 Time histories of stress versus vehicle passage for various bridge types. 

For the short simple span, a series of cycles are produced due to individual axle crossings as 

shown by multiple peaks of stress. For the long simple span, the axle effect is not as pronounced, 

and there is essentially one longer cycle of loading, increasing then decreasing with residual 

vibrations afterwards. The end and center span time histories for a continuous span also follow 

the trend of an influence line with forces increasing or decreasing fairly uniformly with the small 

oscillations being due to vibration characteristics.

Cantilever / suspended (pin-and-hanger) bridges are more unique. A suspended span in a pinand-hanger type bridge is unloaded until the load is between the hangers but vibrates even after 

the truck leaves the span due to the boundary conditions and due to the continued movement of 

the cantilever support point as the truck crosses the anchor spans. An analogous behavior is 

presented for the anchor span. Its behavior reflects the crossing of a truck on the anchor span but 

also the suspended span which it supports. Not until the truck is remote from the anchor and 

suspended spans does this span become fully unloaded, vibrating until the oscillations decay. 

For all of the above time histories, it is the larger cycles of stress that dominate the number of 

equivalent cycles when the cycles are combined using techniques such as Miner’s rule. Many 

cycles of small stress contribute very little to fatigue damage and are frequently neglected.

6.3.5 Calibration of the Fatigue Limit State 

The discussion in Section 6.3.3 and Section 6.3.4 focused on the engineering approach to 

satisfying infinite and finite life design provisions of AASHTO LRFD. Within the calculations are 

various parameters such as load factors, resistance factors, a number of cycles per truck passage, 

and the premise that fatigue loading is caused by a single truck in a single lane. These 

assumptions were never fully calibrated like the strength limit state has been in the past. The 

SHRP2 Project R19B study (Modjeski and Master, 2015) included a statistical calibration of 

each of the fatigue load combinations, and the results are provided herein. The discussion begins 

with the Fatigue II load combination, for which most of the fatigue test data applies, and follows 
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6.23 

with a discussion of the infinite life provisions of the Fatigue I load combination. A more 

detailed presentation of the calibration process is provided in Appendix A. These changes to the 

load factors are being considered for adoption in 2016. 

6.3.5.1 Calibration of the Fatigue II Load Combination 

The load factor for the Fatigue II load combination, the premise of single truck / single lane 

loading, and the “cycles-per-passage” table were studied as part of the SHRP2 Project R19B 

study. Researchers used weigh-in-motion (WIM) data to collect millions of records of actual 

truck crossings. After filtering out inaccurate data, as well as the many “under 20 kip” records, 

over 8 million records remained and were processed during the calibration study.

Using a series of computer models for simple and continuous bridges, the R19B team ran the 

millions of actual trucks over a series of simulated simple-span and two-span continuous bridges 

and recorded the fluctuation in moment (and hence fatigue stress range) over time. Using a cycle 

counting tool known as the rain flow method, they estimated the total number of cycles produced 

by a given number of truck crossings and computed an effective moment using Miner’s rule. 

More cycles than truck crossings were evident, with shorter bridges having significantly more 

cycles per truck than long bridges (those with spans in excess of 100 feet). Based on the bending 

moment simulation data and further statistical analyses by the R19B team, the current “cyclesper-passage” table is presented in Table 6.3.5.1-1. 

Table 6.3.5.1-1 AASHTO cycles-per-passage table. 

Longitudinal Members n 

Simple span girders 1.0

Continuous girders Near interior support 1.5

Elsewhere 1.0

With the new value for n, a component of the finite life resistance equation for the Fatigue II 

load combination was calibrated. A trial load factor of 0.8 was chosen that provides a 95 percent 

confidence that the load factor will envelope the bending moments and hence stresses produced 

by the effective truck. For the resistance data, researchers relied on a large dataset of finite life 

test data collected through several decades. A Monte Carlo simulation was performed to test the 

trial load and assumed resistance factor of 1.0 to determine if the target β of 1.0 was achieved. 

The outcome of the Monte Carlo simulation process validated the choice of a Fatigue II load 

factor of 0.8, an increase of 0.05 from the previous AASHTO LRFD value of 0.75. The R19B 

report recommended that the load factor increase was justified by the calibration process, the 

general upward trend in vehicle weights, and the desire to design structures for a service life 

possibly in excess of 75 years. 

The use of a β of 1.0, consistent with a probability of failure of approximately 16 percent, is 

justified as follows. The target β was calibrated by first assessing the β inherent in the current 

AASHTO LRFD specification fatigue limit state. There is no evidence to believe that the existing 

provisions are unsafe nor unduly conservative. Using existing successful practices is a common 

back sight when performing calibration studies. Additionally, the assumed mean value of the 
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6.24 

load factor used in the simulation is actually the mean plus 1.5 standard deviation value of the 

effective stress range load factor, so a degree of conservatism is provided on the load factor side 

with a design mean that is biased to the true mean. The resistance data set was truncated and only 

the lower tail of the resistance data was used. Data points that suggest long life or high stress 

resistance were purposely excluded from the curve fitting for the resistance data. However the 

traditional μ-2σ offset in the resistance models is no longer used; rather the true mean and 

standard deviation are used for the resistance model. 

The team also used the WIM data to determine the likelihood of similarly configured trucks 

crossing a bridge simultaneously in adjacent lanes or following closely in the same lane. The 

availability of the WIM data on a per-lane basis allowed the research team to search for 

occasions where these side-by-side or following crossings occurred. Their conclusion is that it 

was rare to find two similarly loaded and configured trucks crossing the bridge at the same time. 

The researchers concluded that there was no need to deviate from the AASHTO LRFD single 

truck in a single lane design approach.

6.3.5.2 Calibration of the Fatigue I Load Combination 

Using the same WIM data as for the Fatigue II load combination calibration, the Fatigue I load 

combination was calibrated. The objective of the Fatigue I load combination remains to safely 

provide infinite life. For each of the various WIM sites, the moment that corresponded to a 0.01 

percent probability of exceedance was established as the definition of the maximum effect. This 

envelopes the maximum load / stress effect in order to limit the number of cycles beyond the 

threshold in order to prevent fatigue crack growth under infrequent overloads. This moment was 

then normalized to the AASHTO fatigue truck design moments to provide a ratio between these 

1:10,000 occurrence moments and those predicted from application of the AASHTO design 

vehicle. The load factors were thus chosen to envelope all but the 1:10,000 heaviest vehicles / 

bending moment force effects. Similar to the Fatigue II load combination calibration, a Monte 

Carlo simulation process was carried out for Fatigue I with a target β of 1.0. The calibration 

process concluded that a load factor of 2.0 was most appropriate, a significant change from the 

previous 1.5 value. At the request of the AASHTO T14 subcommittee (responsible for the 

structural steel design provisions), the R19B team took another look at the calibration, and in 

August 2015, recommended moving forward with a reduced load factor of 1.75. As with the 

change to the Fatigue II load factor, this change was adopted based on a vote of approval in 

2016. 

6.3.6 Special Details and Provisions for Other Structure Types

Although the majority of this chapter focuses on main members, the design of other bridge and 

structural elements contain fatigue design provisions as well. This section addresses the fatigue 

design considerations for other important bridge structure components, including cross-frames, 

considerations for skewed and curved bridges, design of shear studs for composite beam bridges, 

fatigue aspects of modular bridge expansion joints, and fatigue design of special structures 

including orthotropic steel decks and highway sign and lighting structures.
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6.25 

6.3.6.1 Cross-Frames

The term “cross-frame” is the name commonly used to describe the truss-type bracing used to 

provide lateral-torsional buckling resistance to rolled and welded girders alike. The design of 

cross-frames must consider the fatigue effects in the members of the cross-frame as well as the 

effects of cross-frame loading on the design of the cross-frame connections. The design of the 

cross-frame and its connections is described in this section. An additional aspect of cross-frame 

design and detailing relates to the prevention of distortion-induced fatigue cracking in the main 

girders. This aspect of cross-frame detailing is addressed later in Section 6.4.

A cross-frame member is commonly welded to a gusset plate; however, end bolted connections 

have been used as well. The connections where the cross-frame members are attached to the 

gusset plates must be designed for fatigue. The accompanying photos in Figure 6.3.6.1-1 depict 

two cross-frames, one which uses rolled WT sections in a K-frame configuration and the other 

using angles in an X-frame configuration. The fatigue design approach is similar for each of 

these variations.

Figure 6.3.6.1-1 K-type and X-type cross-frames.

Where force effects in cross-frames or diaphragms are computed from a refined analysis, such as 

is commonly used in the design of curved and some skewed steel bridges, it is necessary to 

evaluate the fatigue stress ranges in the members and their connections. It is common that the 

load position producing the greatest live load tension in a member, say one of the diagonals in 

the cross-frames shown, is not in the same lane location transverse to the bridge as the load 

position producing the maximum compression load. In such cases, the effect of positioning the 

fatigue truck in two different transverse positions might create the largest possible range of force 

in these bracing members. However the loading and unloading would correspond to two unique 

cycles and is not from the passage of the same truck. For these reasons, in 2015, AASHTO LRFD

clarified that the definition of the load / stress range for cross-frame members is the range of 

stress produced in a member by the passage of the truck in a fixed transverse portion along the 

length of the bridge. This implies that the approach for cross-frame fatigue is like that for main 

member fatigue; a truck traveling the length of the bridge, in a fixed transverse lane, is what is 

used to compute the range of load in the member and its connections. The refined analysis of 
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6.26 

force and stress ranges in cross-frames need not capture the extremes when those are produced 

by different transverse lane locations.

To determine the fatigue stress range and resistance, AASHTO LRFD requires that angle and WT 

sections welded to a gusset plate, a common connection, be treated as a Detail Category E’ weld

(see Figure 6.3.6.1-2). The stress in the base metal of the cross-frame member is computed due 

to the range of axial force in the member. The effect of bending due to eccentricity in the 

connection is to be ignored. However the effect of lack of full attachment and the corresponding 

stress increase is accounted for through the use of a shear lag reduction factor, UU = 1 − xx̅ LL⁄ , 

which is multiplied by the gross area to represent the lack of full effectiveness due to partial 

attachment of members such as angles and WT sections.

Figure 6.3.6.1-2 Shear lag considerations for cross-frame member end connections.

For cases in which the ends of the cross-frame members are bolted, the fatigue stress range is 

also computed. When slip-critical connections are used, no deduction in member area is required 

for the presence of bolt holes and the shear lag reduction factor is applied to the gross member 

cross section. For cases in which slip-critical connections are not used, admittedly an unusual 

occurrence for diaphragm connections, the effective area must be corrected to the net area. 
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6.27 

6.3.6.2 Curved and Skewed Bridges

Curved and skewed bridges are unique from conventional straight and non-skewed steel bridges 

in that they are subject to primary bending moments as well as lateral bending moments arising 

from the effects of torsion and skew. As these bridges are loaded, torsion from curvature and 

unequal deflection due to skew causes the cross-frames to become loaded. Although this unequal 

deflection can also occur in straight non-skewed bridges, the phenomenon of differential 

deflection is exacerbated in curved and moderately to sharply skewed bridges (i.e., those whose 

skew angle exceeds 20 degrees from a square condition). The force transfer from the crossframes to the girders results in lateral forces being exerted on the flanges and therefore lateral 

flange bending moments and stresses. These lateral bending moments and stresses can be 

significant, and their presence reduces the girders’ ability to resist primary bending. Although it 

is likely that the live load placement causing the maximum in-plane stress is not necessarily at 

the same position as that causing the maximum lateral flange bending (unless the results from a 

refined analysis model provide concurrent force effects), it is acceptable and conservative to use 

the envelope values. An example is provided in Figure 6.3.6.2-1 to demonstrate the application 

of AASHTO LRFD to a bottom flange connection plate in a curved bridge. 

Figure 6.3.6.2-1 Bottom flange weld subject to in-plane and lateral flange bending. 

Due to the effects of primary bending, the Fatigue I load combination in-plane bending stress at 

the intersection of the connection plate and the inside of the bottom flange is calculated to be 9 

ksi. In addition, the lateral flange bending stress range from curvature and skew effects must be 

added to this. The detail of the weld connecting the stiffener to the bottom flange is provided, 

and the most highly stressed portion of the weld is located 7.5 inches from the centerline of the 

web. The range of lateral flange bending moments was computed to be 8 ft-kips. The flange 

measures 18 inches wide and 1 inch thick. The calculations for the lateral stress range are as 

follows: 
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6.28 

Equation 6.3.6.2-1 

Equation 6.3.6.2-2 

When added to the primary bending stress of 9 ksi, the combined stress range of 11.2 ksi is 

compared to the Detail Category C’ infinite life resistance of 12 ksi and the detail satisfies the 

infinite life requirement. No further check for finite life is required. 

6.3.6.3 Shear Studs

Headed shear studs are the most common form of providing composite action between concrete 

decks and steel beams. Attached by means of a “stud gun,” the process of welding a stud to a 

beam flange involves establishing an arc between the tip of the stud and the beam flange, 

creating a pool of molten steel, and then forcing the stud into the molten steel. This creates a full 

cross-sectional weld at the end of the stud. 

The design of shear studs must satisfy requirements of the strength and fatigue limit states, and 

the latter are described herein. The design procedure defined in AASHTO LRFD Article 6.10.10 

considers the force effects from straight, skewed, and curved bridges. Figure 6.3.6.3-1 depicts a 

beam cross section indicating the placement of the studs, demonstrates the horizontal shear 

loading to which they are subjected, and includes a photo of several steel beams after attachment 

of the studs. When loaded in fatigue until failure, the failure of a welded stud is characterized by 

one of the three failure surfaces in Figure 6.3.6.3-2. 

Figure 6.3.6.3-1 Shear stud connection to beam flange and force transfer mechanism.
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6.29 

Figure 6.3.6.3-2 Shear stud failure mechanisms.

Since the role of the shear stud is to join the concrete deck to the steel beam, the composite 

action is enforced through resistance to the horizontal shear flow across the slab-to-beam 

interface. The flow of shear comes from two sources, that due to conventional flexure and shear, 

Vfat, as well as a lateral component from skew and curvature, Ffat. 

The horizontal shear flow from applied vertical shear forces in the beam is modeled using a 

traditional equation: 

Equation 6.3.6.3-1 

where:

Vfat = fatigue shear range per unit length (kips/inch) 

Vf = vertical shear force range under the applicable fatigue load combination 

(kips) 

Q = first moment of the transformed short-term area of the concrete deck about 

the neutral axis of the short-term composite section (inches3

) 

I = moment of inertia of the short-term composite section (inches4) 

This is a conventional application of a shear flow equation from strength of materials where the 

force computed by the term Vfat represents the range of longitudinal force per unit inch to resist 

the shear flow between the deck and the top of the steel beam using the fatigue truck to compute 

the range of vertical shear force, Vf. 
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6.30 

In addition, lateral shearing forces due to curvature and skew may also be present.

In the case of curvature, the force on the shear connectors is taken as the larger of an inferred 

force due to curvature, Ffat1, and that due to direct application of cross-frame forces, Ffat2, as 

might be obtained from a refined analysis. 

First, for estimated force effects from curvature, the following equation is provided, as illustrated 

in Figure 6.3.6.3-3. 

 Equation 6.3.6.3-2 

where: 

Abot = area of bottom flange (in2

) 

σflg = range of longitudinal fatigue stress in the bottom flange without 

consideration of flange lateral bending (ksi) 

l = distance between brace points (feet)

w = effective length of deck (inches) takes as 48 inches except at end supports 

where w may be taken as 24 inches

R = minimum girder radius within panel (feet)

Figure 6.3.6.3-3 Analysis model for lateral loading of shear stud groups. 

In the equation for Ffat1, the force in the bottom flange is used as an indicator of the range of 

longitudinal force acting along the interface between the beam and slab. It is important to clarify 

this point since the equation references stresses and forces in a flange which in fact does not have 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

6.31 

studs attached to it. The longitudinal force obtained by multiplying the stress and flange area 

together, σflgAbot, is divided by the radius, R, to create an equivalent radial load. This load, shown 

as q in Figure 6.3.6.3-3, is then accumulated between cross-frames spaced a distance apart equal 

to l. This is the total radial load acting between cross-frames. It is assumed that this entire load 

must be resolved “near” a cross-frame, and the 24- and 48-inch limits for w apply accordingly. 

This method is simply a way of estimating the total radial force demand between cross-frames 

and apportioning the load to a local region surrounding each frame. 

An alternate source of lateral load is the range of force introduced by the cross-frames 

themselves. An analysis model for net range of force at the top flange from cross-frames is 

presented in Figure 6.3.6.3-4. 

Figure 6.3.6.3-4 Analysis model for net range of force at top flange from cross-frames. 

Equation 6.3.6.3-3 

where: 

Frc = net range of cross-frame or diaphragm force at the top flange (kip) 

Using the greater lateral force contribution from considerations of curvature, Ffat1, or from direct 

use of the local cross-frame forces, Ffat2, the resultant shear demand on the stud is computed as a 

vector sum as follows: 

Equation 6.3.6.3-4 

where:

Vsr = horizontal shear range per unit length (kips/inch) 

Having determined the shear flow or force per unit length, Vsr, the designer solves for a 

theoretical pitch for a chosen number of studs per group and performs the layout of the studs. 

Commonly this is done at even intervals along the length of the beam such as tenth points. The 

pitch is found using the strength of an individual stud or groups of studs and is predicted as 

follows: 
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6.32 

Equation 6.3.6.3-5 

where: 

n = number of shear connectors in a cross section

Zr = shear fatigue resistance of an individual shear connector

The resistance of a shear connector, Zr, is, like other fatigue details, a function of the number of 

cycles in the finite life region and also has a constant amplitude fatigue threshold limit for higher 

cycle designs. The resistance of shear connectors in AASHTO LRFD is based on work by Slutter 

and Fisher (1966). Their work included unidirectional and reverse loading push-out tests of shear 

studs embedded in a concrete slab. Both 3⁄4-inch and 7/8-inch diameter studs were tested. A total 

of 35 specimens using 3⁄4-inch diameter studs were tested along with nine additional specimens 

tested with 7/8-inch diameter studs. 

In the region of finite life, the resistance of an individual welded shear stud connector is given in 

AASHTO LRFD Article 6.10.10.2 as 

 Equation 6.3.6.3-6 

where:

α (alpha) = finite life resistance of the shear stud in ksi; is dependent on the 

number of design cycles, N

d = diameter of the shear stud in inches

In Figure 6.3.6.3-5, taken from Slutter and Fisher (1966), the line labeled “Eq. 2” is given as 

log NN = 8.072 − 0.1753SSrr. The variable Sr is the range of horizontal shear stress and is related 

to the value alpha used in AASHTO LRFD by the relationship shown in the equation below. 

Thus the Slutter and Fisher equation can be related to that given in AASHTO LRFD with the 

appropriate substitution. The AASHTO LRFD equation for finite life is unlike other fatigue life 

equations in that it represents the mean strength from laboratory tests. Most fatigue life equations 

are based on the mean minus two standard deviations, or a 97.5 percent confidence that the 

provided life will exceed the predicted life. Slutter and Fisher defend using the mean life since 

their regression analysis neglected test results from studs tested in reversal which demonstrated 

much higher strengths. Also given the redundancy of shear studs with many hundreds applied to 

typical beams, isolated failures of a few studs will not change the overall system behavior and is 

considered acceptable.
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6.33 

Figure 6.3.6.3-5 Shear stud push-out test results.

For infinite life, the strength of the shear stud is specified as 5.5d2. The value of 5.5 used for 

alpha is a derived value. It comes from the CAFT for average shear stress between the slab and 

flange of 7 ksi multiplied by the value of π/4 (i.e., 5.5). The CAFT value of 7 ksi leading to the 

alpha value of 5.5 ksi was somewhat arbitrarily but conservatively chosen since limited data 

existed regarding infinite life at the time. Recent research by Ovuoba and Prinz (2015) includes 

testing six additional push-out test specimens with applied average shear stress ranges between 

30 and 60 MPa (4.35 and 8.7 ksi). These tests were conducted near the current AASHTO CAFT

limit to add additional data points in this area where henceforth there was little information. 

Their work suggests a CAFT value for shear stress of 6.5 ksi, not unlike the implied value of 7 

ksi assumed in the derivation of alpha equals 5.5 in the infinite life AASHTO LRFD equations. 

No changes to the specifications are expected as a result of these slight changes in the CAFT 

values.

6.3.6.4 Expansion Joints 

Of the various types of joints used to accommodate expansion and contraction of bridges (steel 

and concrete), modular bridge expansion joints are among the most complex. They rely on a 

series of interconnected steel elements, welded and bolted, to allow for movements in the bridge 

due to thermal expansion and contraction and from other sources such as creep and shrinkage, 

deflection under high winds, and longitudinal movement due to braking in bridges with flexible 

substructures. 
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6.34 

The design requirements for modular bridge expansion joints are provided in AASHTO LRFD

Article 14.5.6.9 and follow the procedures first outlined in NCHRP Report 402, Fatigue Design 

of Modular Bridge Expansion Joints (Dexter, Connor, and Kaczinksi, 1997). Additionally, 

fatigue and overall durability testing requirements are found in the AASHTO LRFD Bridge 

Construction Specifications (AASHTO, 2015a) and follow the guidance found in NCHRP 

Report 467, Performance Testing for Modular Bridge Joint Systems (Dexter, Mutziger, and 

Osberg, 2002). 

Although the discussion below focuses on the design of Modular Bridge Joint Systems (MBJS), 

it is rare for an engineer involved in the design of a bridge to design the joint components. They 

are typically chosen as engineered systems from vendors who manufacture and market such 

devices. The engineer will typically only size the joint from a movement perspective and detail 

its connection to the structure via a blockout to accommodate the joint as shown in the 

accompanying photographs in Figure 6.3.6.4-1 and Figure 6.3.6.4-2. The design guidance in 

AASHTO LRFD is used to proportion joint elements, but their acceptance is only confirmed after 

passing the acceptance test criteria in the AASHTO LRFD Bridge Construction Specifications. 

Figure 6.3.6.4-1 Modular joint installation. 
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6.35 

Figure 6.3.6.4-2 Underside of modular joint with details shown. 

The design of expansion joint components must meet the requirements of the strength and 

fatigue limit states. Only the fatigue design considerations are discussed herein. The joints are 

proportioned assuming that the conventional 32-kip axle of the fatigue design truck is replaced 

by two 16-kip axles, and these loads are transmitted to the joint as two 8-kip wheel loads. A high 

impact value of 75 percent is used for fatigue design due to the rapid loading and unloading of 

joints. This value represents the downward effects of load application, rebound, and dynamic 

load effects. The 75 percent value was confirmed through field testing of modular joints in 

Europe and in the United States. 

Since joints are subjected to multiple cycles per truck passage over many years, the designs must 

satisfy infinite life requirements of the Fatigue I load combination. Due to the effects of vertical 

grade and braking, a horizontal force component is applied. A common value of 20 percent is 

used for the horizontal force range as a fraction of the vertical force range, assumed to be evenly 

distributed as 10 percent forward and 10 percent backward. This is to be increased for bridges on 

vertical grades in excess of five percent.

The structural members of an MBJS must meet fracture toughness requirements and must be 

designed for infinite life, as mentioned previously. Their design is frequently governed by 

limiting the fatigue stress range at critical details, though numerous strength limit state checks 

are required as well. Multiple fatigue sensitive details may be present, including the connection 
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6.36 

between center beams and support bars. These may be welded or connected through a 

mechanical yoke system. Other fatigue sensitive details include attachments to the center beams 

and support bars such as to support the equidistant springs and shop or field splices that may be 

required for wide joints or joints installed as part of phased construction. 

AASHTO LRFD Article 14.5.6.9.7 outlines the fatigue design approach for MBJS elements. For 

the determination of the stress range in primary load-carrying elements, several simplified 

analytical models are provided for computing forces and stresses in single- and multiple-support 

bar systems. The influence of bolted splices which create hinges and thus higher stress ranges in 

the center beams is discussed. The need to check other details such as welded attachments to the 

support bars and center beams is discussed in the commentary to the design specification. 

Due to the inherent difficulty in predicting the stresses in MBJS assemblies, their performance is 

judged after the static design process by fatigue testing using the Opening Movement Vibration 

Test outlined in the AASHTO LRFD Bridge Construction Specifications (AASHTO, 2015a). The 

test is used to demonstrate the performance of center beam to support bar connections, 

connections of attachments to the center beams, and the performance requirements for shop or 

field splices in the center beams. The design of anchors connecting the joint system to the 

concrete deck (i.e., anchor shear studs and edge beams) may be exempted from testing and 

design, provided certain minimum member size and anchor spacing requirements of the design 

specifications are met.

6.3.6.5 Orthotropic Steel Decks

Orthotropic steel decks represent a deck type used on some long span steel structures to provide 

weight reduction, rapid construction, and long life. They are generally applicable on high 

volume, long span, or otherwise critical structures. Having first been used in Europe in the 

1930’s, these deck types, though infrequently used, have certain advantages as mentioned above. 

Orthotropic steel decks are unique in that the steel deck plate serves to receive the direct loading 

from traffic and at the same time serves as a top flange to the longitudinal main girders, as well 

as the transverse floorbeams (see Figure 6.3.6.5-1). Stiffened by ribs and floorbeams, the deck 

system is subject to a complex stress distribution and the direct effects of local wheel loads, as 

well as global participation in the structural response. Orthotropic steel decks may be made 

integral with “I” and box-shaped girders or may be stand-alone deck systems used in structures 

such as suspension, arch, and other long-span structural forms. They have been used as integral 

parts of new construction, as well as to limit dead load in bridge rehabilitation and redecking 

projects such as the Bronx-Whitestone Bridge reconstruction project. 

Orthotropic decks are characterized by common components. These include the steel deck plate, 

a series of ribs which stiffen the deck plate and themselves span between transverse floorbeams, 

and the transverse floorbeams which span to the main supporting members. Critical welded 

connections exist between the ribs and the deck, at the intersection of the ribs and floorbeams, 

and at the connection of the floorbeams to the main longitudinal spanning elements. 

The FHWA Manual for Design, Construction, and Maintenance of Orthotropic Steel Deck 

Bridges (Connor et al., 2012) is the most recent comprehensive manual covering most aspects of 
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6.37 

steel orthotropic decks. Only a brief description is provided herein, and the reader should consult 

Connor et al. (2012) for many additional details on analysis, design, detailing, and construction 

not addressed in this manual. 

Figure 6.3.6.5-1 Orthotropic deck and I-beam steel bridge. 

A schematic of the fabrication of an orthotropic steel deck is presented in Figure 6.3.6.5-2. 

Shown is an inverted deck as it would be fabricated consisting of a deck plate (the riding surface) 

and the supporting elements – the ribs and floorbeams. The ribs, commonly bent using a press 

break into a U-shaped closed section, are first welded to the underside of the deck plate. This is 

depicted on the left side of the figure. Then floorbeams are fabricated and cutouts are located so 

as to allow for the ribs to pass through each floorbeam and to control the local stresses that arise 

from floorbeam-to-rib interaction. The floorbeam is then fit around the ribs and is welded to the 

ribs and deck plate. A photo of the ribs passing through a floorbeam is provided in Figure 

6.3.6.5-3. Figure 6.3.6.5-1 through Figure 6.3.6.5-3 are taken from Connor et al. (2012). 
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Figure 6.3.6.5-2 Fabrication schematic of orthotropic steel decks. 

Figure 6.3.6.5-3 Orthotropic deck rib and floorbeam intersection. 
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6.39 

AASHTO LRFD categorizes various common details found in orthotropic steel decks and assigns 

the standard AASHTO fatigue categories to those details. Included are fatigue strength 

categories for rib-to-deck welds, bolted and welded rib splices, deck plate splices, rib-tofloorbeam welds, floorbeam cutouts, and rib wall connections. 

Because of the unique fatigue response characteristics of orthotropic decks, AASHTO LRFD

provides a special load combination that increases the Fatigue I load factor to 2.25 when 

investigating fatigue at the welded rib-to-floorbeam cutout details and at the rib-to-deck welds. 

The increased load factor is cited in AASHTO LRFD as a result of prior investigations that found 

the basic load factor for live load is unconservative to provide infinite life for certain orthotropic 

steel deck details. This increased load factor is based on stress monitoring of orthotropic decks. 

The increase of the load factor for infinite life reflects a greater difference between the maximum 

stress range and effective stress range, as compared to standard girder design. Fatigue design of 

orthotropic decks is more highly dependent upon localized wheel loads as opposed to general 

truck weight distributions, and the load distribution and relative movement of orthotropic decks 

is significantly different than the load-induced fatigue behavior of steel girders.

For the evaluation of finite life using the Fatigue II load combination, the effect of local wheel 

crossings must also be considered. For orthotropic deck details connected directly to the deck 

plate (i.e., the rib-to-deck weld), partial cycles are created by the crossing of individual loads or a 

total of five partial cycles from the passage of a single truck. AASHTO suggests that the stress 

range can be conservatively taken as the worst case from the five wheels or that Miner’s rule can 

be used to determine an effective stress range from a group of wheels. Five cycles of loading are 

to be used for every truck passage. This is described in AASHTO LRFD in greater detail.

Figure 6.3.6.5-4 presents a refined loading model whereby the standard fatigue truck axle loads 

are converted into equivalent rectangular patch loads in order to perform the local analysis of 

orthotropic decks. AASHTO LRFD Article 4.6.3.2.4 requires that the refined analysis of 

orthotropic decks be accomplished using a three-dimensional finite element model and describes 

some of the simplifying assumptions that can be used in the creation of the model. 

Figure 6.3.6.5-4 AASHTO orthotropic deck wheel patch loading.
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6.40 

6.3.6.6 Structural Supports for Highway Signs, Luminaires, and Traffic Signals

AASHTO publishes the LRFD Specifications for Structural Supports for Highway Signs, 

Luminaires, and Traffic Signals (AASHTO, 2015c), focusing specifically on the structural 

design aspects of those elements. Unlike a highway traffic bridge where the number of cycles of 

loading can be correlated to design traffic volumes and other structural parameters, the design of 

highway structures, light poles, traffic signals, and other appurtenances must consider the 

completely random nature of loading from wind, interactions with gust loading from vehicles, 

and the harmonic response of traffic structures mounted on bridges. Because of the inability to 

define a design number of cycles, the design of these types of structures is done exclusively with 

the goal of providing infinite life.

Highway traffic and lighting structures are commonly constructed of steel, though aluminum is 

also used. The AASHTO standard provides guidance for the design of both materials, and a 

specific chapter, Section 11, is devoted to fatigue design. The fatigue design for sign and lighting 

structures is based on specific loads that are unique to these types of structures and also includes 

an importance factor related to the risk of structural failure posing a hazard to the motoring 

public. Three importance categories are established, and different importance factors are 

assigned to each. Category 1 applies to long-span cantilever sign structures (greater than 50 ft.), 

high mast towers (greater than 100 ft. tall), large sign structures, and structures located in areas 

where wind-induced vibrations are known to occur. Category 3 applies to structures on roads 

with speed limits of 35 mph or less where structural failure would not affect traffic. Category 2 is 

defined as not falling in either Category 1 or 3, as previously defined. 

Wind loads are provided as equivalent static loads acting on projecting areas of the various 

structures. The wind loads were selected so as to minimize the possibility of objectionable 

vibrations and deformations in service and to minimize the development of fatigue cracks in the 

various unique connections found in sign and lighting structures. The loadings specified are to be 

used to compute stress ranges in the vicinity of fatigue sensitive connection details using either 

standard, nominal stresses computed based on classical structural analysis or alternately by a 

method based on experimental testing or finite element analysis. The types of design loads 

considered for fatigue include:
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6.41 

• Galloping – An aeroelastic instability in which the wind causes an initial vibration of the 

structure, accompanied with continued coupling of the structural vibration, with the wind 

effects resulting in large amplitude vibration. Galloping results from the wind effects on 

attachments (e.g., signs and signal heads), not the structure itself (i.e., a structure with no 

attachments is not generally prone to galloping). AASHTO provides an equivalent 

pressure to be applied vertically to the projected area of the structure, though only over 

the length of the structure where there is an attachment.

• Vortex shedding – Another form of aeroelastic instability where the structure is a bluff 

body in the flow of wind. The flow of wind spins into vortices on the leeward side of the 

structure, and these shed on alternating sides of the structure. Each vortex causes an area 

of low pressure that pulls the cross section across the wind, and since the vortices 

alternate, so does the across-wind motion. However, the nature of the motion can also 

exacerbate the effects of the shedding, which is why it is an aeroelastic phenomenon. 

Vortex shedding occurs only at a critical wind velocity where the vortices are allowed to 

form and match the resonance of the structure itself; generally these are low wind 

velocities (i.e., less than 30 mph). Vortex shedding effects occur on the structure itself 

where there are no attachments, and attachments actually tend to disrupt the formation of 

vortices. Therefore, vortex shedding mostly occurs with high mast lighting structures. 

The AASHTO specification provides an equivalent static pressure based on the mean 

wind velocity at the site, and this is used in the computation of the nominal fatigue 

stresses.

• Natural wind gust – This is meant to capture the along-wind vibratory response of the 

structure from the wind blowing on and past the structure. All structures are susceptible 

to natural wind gust vibrations. 

• Truck-induced gust – Cantilevered and non-cantilevered overhead sign and traffic signal 

support structures are to be designed to resist equivalent static truck gust pressures. 

Passage of trucks beneath the structures may induce vertical gust loads on horizontally 

projecting areas (e.g., variable message signs, the structure itself, and other attachments 

mounted along the horizontal span of the structure). The loads are specified to act in the 

vertical direction to the exposed area of horizontal supports, as well as in the horizontal 

plane of all signs, attachments, and other appurtenances. The pressures are assumed to act 

over a lateral distance of 12 feet, corresponding to the width of the standard traffic lane. 

Figures illustrating galloping and vortex shedding (see Figure 6.3.6.6-1) and truck-induced gust 

(see Figure 6.3.6.6-2) are provided. Each of these is taken from FHWA-NHI-05-036, Guidelines 

for the Installation, Inspection, Maintenance and Repair of Structural Supports for Highway 

Signs, Luminaries, and Traffic Signals (Garlich and Thorkildsen, 2005).

The resistance to fatigue is the application of the CAFT rules for the various details commonly 

encountered in traffic lighting support structures. Covered by the specification are plain 

members, mechanically fastened connections, holes and cutouts, groove welded connections, 

fillet welded connections, and attachments. Guidance is provided for both steel and aluminum 

structures. Various unique details are commonly used in the fabrication and construction of 

lighting and support structures. The AASHTO specification provides sketches illustrating the 
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6.42 

many unique connection types and provides the appropriate fatigue design guidance for each 

(AASHTO, 2015c). Examples of unique connections covered by the specifications include 

multiple examples of the connection of tubular members with the use of welded gusset plates, 

tube-to-plate connections, and the treatment of holes and access openings in structural members. 

Figure 6.3.6.6-3, Figure 6.3.6.6-4, and Figure 6.3.6.6-5 depict finite element solutions and stress 

concentrations for certain common details found in sign and lighting structures, as well as 

representative sketches from the AASHTO specifications (AASHTO, 2015c). The finite element 

analysis models are from a presentation given of findings from NCHRP Project 10-70, CostEffective Connection Details for Highway Sign, Luminaire and Traffic Signal Structures (Roy et 

al., 2009). 

Figure 6.3.6.6-6 and Figure 6.3.6.6-7 are from the State of Illinois, Sign Structures Manual

(Bureau of Bridges and Structures, 2012) and depict a common overhead sign truss, as well as 

common bolted and welded details. 

Figure 6.3.6.6-1 Galloping (left) and vortex shedding (right) behavior of cantilevered signs. 
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Figure 6.3.6.6-2 Truck-induced gust loading of overhead structures. 

Figure 6.3.6.6-3 Fatigue cracking at a stool connection. 
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Figure 6.3.6.6-4 Fatigue cracking around reinforced access holes.

Figure 6.3.6.6-5 Fatigue cracking at tube base plate and stiffeners.
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Figure 6.3.6.6-6 Standard Illinois DOT overhead sign truss schematic.
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Figure 6.3.6.6-7 Welded truss joint details and bolted chord splice.

SECTION 6.4 DISTORTION-INDUCED FATIGUE

Transverse connection plates are used to connect elements such as diaphragms and cross-frames 

to longitudinal beams. Due to the differential displacement of the longitudinal elements, forces 
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6.47 

are transferred between adjacent girders via the diaphragms or cross-frames. When this happens, 

lateral loads are imposed upon the transverse connection plate, the girder web, and the girder 

flanges. In many bridges of the past, engineers were concerned about transverse welds between 

connection plates and the flanges of the primary girders, creating a fracture concern.

For instance, the 1949 version of the AASHO Standard Specifications for Highway Bridges 

specifically precluded transverse welds to a tension flange when the flange stress exceeded 75 

percent of its capacity (AASHO, 1949). So unless a member was purposely overdesigned just to 

allow welding to the tension flange, transverse welds between connection plates and tension 

flanges were omitted as a matter of standard practice. As a result, it was common to leave the 

connection plate unattached to the girder flange. Due to out-of-plane distortion, the resulting 

displacement and out-of-plane forces applied to the connection plate were not able to be resisted 

by the lateral stiffness of the flange but rather were transferred directly into the web and 

secondarily into the flange or slab. This out-of-plane force applied near the top and bottom of the 

web in the transverse direction resulted in displacements concentrated in a small web gap area 

and frequently resulted in cracks at the top or bottom of the stiffener or at the toe of the web-toflange longitudinal weld. This is conceptually illustrated in Figure 6.4-1 and Figure 6.4-2. 

Figure 6.4-1 Distortion-induced fatigue loading of a diaphragm and girder.
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Figure 6.4-2 Web gap displacements in a girder-floorbeam steel bridge. 

When a connection between the connection plate and girder flange is not provided, cracking such 

as that shown in Figure 6.4-3 has been noted. Although skew and curvature exacerbate the 

differential displacement effects, this type of cracking has been found in all bridge types. The 

bridge in Figure 6.4-3 is a non-skewed bridge with regularly spaced cross-frames and has 

significant cracking at many cross-frames throughout the bridge in positive and negative moment 

regions. 

Figure 6.4-3 Distortion-induced fatigue cracking of a steel girder. 
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AASHTO LRFD Article 6.6.1.3.1 requires that, as a minimum, connection plates used to connect 

diaphragms and cross-frames, as well as those used to connect floorbeams, be welded or bolted 

to both the compression and tension flanges of the longitudinal beam. For bridges in which the 

force effects in the diaphragm and cross-frame are not directly computed (e.g., a straight or 

slightly skewed bridge), the specification requires that the connection between the transverse 

connection plate and the flanges be designed to resist a 20-kip transverse load. However, for 

bridges in which diaphragm, cross-frame, or floorbeam effects are computed by analysis, the 

forces resulting from that analysis are required to be transferred through this connection. Minor 

exceptions to these requirements are provided for rolled beam bridges that are straight and have 

composite reinforced concrete decks. The 20-kip provision is simply a rule of thumb that applies 

for straight, non-skewed bridges to detail the size of the weld. The intent of connecting to both 

flanges and providing a minimum strength connection is to provide a sufficient amount of 

stiffness to limit the amount of relative movement between the flange and web and to limit web 

lateral displacements. Because stiffness and not strength is the governing criteria behind the 

potential success of these connections, a welded attachment between the stiffener and flange is 

preferred, although a bolted connection is allowed. A bolted connection having the required 

stiffness of an equivalent welded connection is a more time-consuming, more costly, and less 

proven detail. It also does very little to alleviate the underlying fatigue concerns with welded 

connections because a similar fatigue detail exists where the transverse stiffener is welded to the 

girder web only several inches above or below the flange in question. Providing the bolted 

attachment to the flange does not change the underlying fatigue resistance of the girder as a 

practical matter. The practice is allowed but discouraged since it does not improve the overall 

fatigue resistance of a structure in any meaningful way.

It should be noted that transverse connection plates are distinguished from transverse stiffeners 

whose purpose is only to stiffen the web for shear resistance. A transverse stiffener provided 

simply to improve the shear resistance of the web does not require attachment to both flanges. 

AASHTO LRFD indicates that transverse shear stiffeners need not be in bearing or contact with 

the tension flange. At the compression flange, only a tight fit attachment is required, though a 

positive attachment is certainly permitted. The latitude to only tight fit the stiffener to the 

compression flange and leave it cut short from the tension flange greatly simplifies installation of 

the stiffeners, as they need not be in contact and connected to both flanges of the structure. 

Another source of distortion-induced fatigue cracking is the attachment of lateral bracing 

connection plates to the webs of steel beams. Similar to the transverse connection plate, under 

the action of differential vertical displacement, forces are induced into lateral bracing systems 

that result in the diagonals of the lateral bracing being loaded alternately in tension and 

compression. The lateral bracing members therefore exert a potentially large lateral force on the 

webs of what are commonly plate girders. Given the relatively large forces that are introduced in 

the out-of-plane direction of the web, fatigue cracking has been documented in these connections 

due to the concentrated lateral displacement of the web between the lateral bracing connection 

plate and the nearest flange. The flange serves as a relatively stiff out-of-plane element and 

restrains the bottom of the web, or a concrete slab restrains the top of the web. 

AASHTO LRFD Article 6.6.1.3.2 provides guidance on the attachment of lateral bracing plates to 

steel girders. It indicates that if it is not practical to attach the lateral bracing connection plate 

directly to the flange, then the connection plate may be attached to the web with the gusset plate 
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6.50 

being separated from the flange by a distance of at least one half the width of the closest flange. 

The horizontal bracing connection plates must be at least 6 inches from the nearest flange as 

well. The stipulation of these minimum offset distances is so that the forces that are introduced 

into the lateral bracing connection plate are introduced at a distance far enough away from the 

nearest source of restraint, the nearest flange, so as to reasonably preclude the possibility of 

distortion-induced fatigue cracking. The requirement for locating the lateral connection plate on 

the web does not preclude other types of fatigue cracking that may result. These connection 

plates will still need to be evaluated for the appropriate load-induced fatigue detail used to attach 

them to the web of the beam. 

SECTION 6.5 STEP-BY-STEP APPLICATION OF LRFD FATIGUE DESIGN

This section combines information from prior sections and demonstrates the practical application 

of AASHTO LRFD for fatigue design. A numerical example then follows. The use of the 

AASHTO LRFD specifications for fatigue design involves the application of the following steps: 

Step 1. Determine locations requiring fatigue limit state verification.

Step 2. Compute force effects. This includes both the moving live load analysis and the 

calculation of distribution factors (or use of refined analysis methods) to compute forces 

in the individual members. For all force effects, apply the dynamic load allowance 

(impact), which is a required 15 percent increase in the force effects of the design truck.

Step 3. Calculate stress ranges at fatigue details.

Step 4. Calculate fatigue resistance of the specific details used on the structure and verify 

factored stress ranges are below the computed resistance.

6.5.1 Determine Locations Requiring Fatigue Limit State Verification (Step 1)

Fatigue must only be investigated when the detail is subjected to a net applied tensile stress. This 

is done by comparing the permanent compression, where it exists, to the maximum tensile stress 

produced by the Fatigue I load combination. Only when the tensile stress due to the Fatigue I 

load combination exceeds the unfactored permanent stress does fatigue need to be considered. 

6.5.2 Compute Force Effects (Step 2)

AASHTO LRFD specifies that the loading to be applied is a single fatigue design truck placed in 

a single lane. This approach has been used since the introduction of LRFD, and its 

appropriateness was validated during the SHRP2 R19B research project. Additional information 

about the SHRP2 R19B study is provided in Appendix A. Examples of the determination of 

force effects for a common girder bridge and a more unique structure, a tied arch, are provided 

below. 

6.5.2.1 Case Study – Force Effects for a Common Girder Bridge

Step 2.1 – Position the load longitudinally. 
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Using the principles of influence lines, position the fatigue truck at the longitudinal location 

which maximizes and minimizes the live load bending moment at the particular detail. For the 

common case of a continuous span bridge, this involves determining the peak ordinates of the 

influence line and placing the truck accordingly. Figure 6.5.2.1-1 demonstrates the two locations 

of the fatigue design truck that would be chosen to maximize the range of moments, and hence 

the range of stress, near midspan of Span 1 at a detail to be investigated. The loads are 

individually placed, once in Span 1 and once in Span 2, not simultaneously as the figure might 

suggest, and the moments are computed for each pseudo-static position.

Figure 6.5.2.1-1 Influence line for bending moment for a three-span continuous bridge.

Step 2.2 – Apply impact. 

The dynamic load allowance, commonly referred to as the impact factor, amplifies the static 

force effects due to contributing factors such as pavement roughness and vehicle / bridge 

dynamic characteristics. It is applied at the fatigue limit state as a 15 percent increase in the 

load effects computed from the moving load analysis. 

Step 2.3 – Determine the fraction of bending moment resisted by a particular member. 

For a traditional multi-girder bridge, the live load bending moments are first computed in the 

longitudinal direction and then distributed transversely. AASHTO provides empirical live 

load distribution factor equations to approximate the fraction of the total vehicle force effect 

that must be resisted by the most heavily loaded beam. The use of these empirical equations 

relieves the engineer from the difficulty of determining an exact transverse positioning of the 

vehicle. They are used in lieu of a refined analysis, such as a grid or 3-D finite element 

model, to determine individual member force effects. The concept of live load distribution 

factors is illustrated in Figure 6.5.2.1-2. 
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Figure 6.5.2.1-2 Distribution factor concept.

For a multi-beam steel bridge with a concrete slab, AASHTO LRFD provides the 

following equations for the case of a single lane loaded. It is important to recall that the 

fatigue limit state is based on a single truck in a single lane producing the stress ranges in 

question. 

Equation 6.5.2.1-1 

To determine the moments in the beam, the force effects due to the entire vehicle on a 

per-lane basis (see Figure 6.5.2.1-1) are then multiplied by the distribution factor (DF) to 

determine the fraction of the force assigned to the most heavily loaded beam. The 

equation above must be modified, however, since included in this equation is the 

AASHTO multiple presence factor of 1.2 that was developed during the calibration of the 

strength limit state. The 1.2 multiple presence factor is included in the standard singlelane distribution factor equations to account for possible overloaded vehicles that produce 

force effects greater than those included in the live load calibration process. This 

occasional heavy weight vehicle that is important at the strength limit state is accounted 

for with the Fatigue I load combination instead and thus the additional 20 percent must be 

removed from the DF equations when designing for fatigue. Thus for fatigue, the DF 

equation results must be divided by 1.2 as shown below. 

Equation 6.5.2.1-2 

AASHTO LRFD specifies that fatigue design be carried out using a single design vehicle 

placed in a single lane. The lanes are “design lanes” and do not correspond to the striped 

lane conditions since these are not guaranteed to be permanent. A “design lane” is 

hypothesized to be at any lateral location on the bridge. However, lane placement is not 

required when using the DF equations. For exterior beams, a check of the DF using the 
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“lever rule” model is required, and for that method, the loads are positioned manually by 

the engineer to determine the DF.

6.5.2.2 Case Study – Force Effects for a Tied Arch Bridge

For a more complex structure, the same principles apply to determining the live load effects (i.e., 

live loads must be placed longitudinally and transversely to determine the critical loadings). The 

example shown is the Kentucky Lake tied arch bridge (see Figure 6.5.2.2-1). The bridge was 

analyzed and designed using a three-dimensional finite element model. The influence lines for 

bending moment and axial load at a point of interest in the tie girder are plotted in Figure 6.5.2.2-

2. Unlike the case of a girder bridge, which decouples the determination of bending moments 

and the distribution of forces to specific members, the finite element approach captures the 

effects of longitudinal and transverse positioning simultaneously. It incorporates the concept of 

“influence lines” and “load distribution factors” at the same time through a three-dimensional 

internal distribution of loading effects, commonly called an influence surface. Shown in Figure 

6.5.2.2-2 are the axial load and primary bending moment influence lines for live loads traveling 

in a fixed transverse position (i.e., a longitudinal slice through the influence surface). Similar 

lines can be generated for other design or striped lanes.

Figure 6.5.2.2-1 Kentucky Lake Bridge point of interest.
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Figure 6.5.2.2-2 Kentucky Lake Bridge axial load and bending moment influence lines.

6.5.3 Calculate Stress Ranges at Fatigue Details (Step 3)

Once the detail is found to require investigation and the distributed live load forces are 

determined, the stresses due to the factored and distributed fatigue loads must be computed. For 

axially loaded members (e.g., truss members, the tie girder described previously, or members of 

a cross-frame), the steel section alone is used to resist the stresses. 

For the case of flexural members, when shear connectors are provided over the entire length of 

the girder and the concrete deck slab meets the minimum area of reinforcing steel provisions of 

AASHTO LRFD, it is permitted to compute the flexural stresses using the short-term composite 

section of the steel girder and transformed concrete slab for both the positive and negative 

bending moments. Although the negative live load moments cause some tension in a composite 

concrete slab, the shear connectors and longitudinal slab steel result in a slab with only fine 

cracking, and the full composite section is maintained for the calculation of stresses.

The range of stress, Delta (∆)f, at any detail is computed using the common formula for flexural 

stress:

Equation 6.5.3-1 

where:

 = range of moment 

y = vertical distance from the neutral axis of the short-term composite section to 

the detail being evaluated

In = moment of inertia of the short-term (n) composite section
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Details that are furthest from the neutral axis are subjected to the highest stress range but may 

not be critical since the fatigue resistance of the detail is also important. For instance, in the 

accompanying Figure 6.5.3-1, numerous details were welded to a plate girder and tested.

Figure 6.5.3-1 Multiple fatigue details on a plate girder.

Although the web-to-flange weld is furthest from the neutral axis of the section and is subjected 

to the highest stress range, it likely does not control the design due to the presence of more 

critical details. For instance, the transverse (vertical) stiffeners that are very near the bottom 

flange have essentially the same stress range as the web-to-flange weld but are a more severe 

fatigue detail category (C’) as compared to the longitudinal weld (B), and thus will control. Also 

near the bottom flange are various longitudinal stiffeners, and these are generally more severe 

than the transverse stiffener, so it is likely that their lesser resistance will govern the fatigue 

design in regions of comparable stress range. The intent of this discussion is to demonstrate that 

some judgment can be used when evaluating fatigue in steel structures.

Details from an actual bridge are provided in Figure 6.5.3-2 to further illustrate this point and to 

show details from a composite bridge. The corner chamfer detail illustrates the minimum and 

maximum clearances used to locate the ends of fillet welds in a plate girder. For the two cross 

sections shown in the figure, a continuous fillet weld connects the web and flange but is not 

shown. 
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Figure 6.5.3-2 Common web-to-flange, connection plate, and shear stud welds.

At the elevation of the inside surface of the bottom flange, the web-to-flange weld is present 

along with the weld connecting the transverse stiffener to the flange. The web-to-flange weld (a 

continuous fillet weld) is a Detail Category B weld, while the transverse stiffener weld is a Detail 

Category C’ weld. The Detail Category C’ condition is more restrictive and thus the fatigue 

detail of the web-to-flange weld does not need to be checked. 

At the top flange, several details are also present. These include the web-to-flange weld (again 

not shown in this detail), as well as the shear studs welded to the flange to create the composite 

condition. The shear studs welded to the outside of the flange are a Detail Category C detail, 

while the web-to-flange weld on the inside of the flange, where the stresses are marginally less, 

is a Detail Category B weld. Again, the web-to-flange weld is not the controlling detail. Shear 

studs must also be checked to ensure that their welds to the top flange do not fail in fatigue. This 

is described in AASHTO LRFD Article 6.10.10. 

6.5.4 Calculate Fatigue Resistance (Step 4)

Much time has been spent detailing the development of the finite and infinite life resistance 

models for fatigue in this and other chapters. To apply these models in AASHTO LRFD, the 

following procedure is generally followed: 

Step 4.1 – Categorize the details present on the member being investigated. 

Categorize the details located on the member of interest and their location along its length. 

These include details such as mechanically fastened joints, welds joining components of 

built-up members, and welded attachments. 

Step 4.2 – Classify the details according to AASHTO as Category A, B, B’, C, C’, D, E, or E’.

Step 4.3 – Determine the frequency of loading. 

Step 4.4 – Determine the number of cycles per truck passage.
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The current AASHTO recommended number of cycles per truck passage is presented in 

Table 6.3.4.2-3. However, it is likely that these recommendations will be replaced by the 

simpler approach in Table 6.3.5.1-1. 

Step 4.5 – Determine the number of cycles over the 75-year design life.

For the investigation of the Fatigue II load combination, determine the number of design 

cycles using the equation N = (365)(75)(n)(ADTT)SL. 

Step 4.6 – Compute the infinite life resistance.

For the investigation of the Fatigue I load combination, the resistance is the CAFT value. 

Determine this value from AASHTO LRFD Table 6.6.1.2.5-3 or from Table 6.2.3.2-1 herein.

Step 4.7 – Determine if adequate infinite resistance is provided. 

Compare the infinite life resistance with the fatigue demand. If the stress ranges are less than 

the fatigue resistance, then the design is adequate. However, if they are not, then the detail 

must be revised to comply with the AASHTO LRFD limits or a check of finite life (Step 4.8) 

must be performed. 

Step 4.8 – If infinite life is not provided (see Step 4.7), compute the finite life resistance.

Use the following equation to determine the finite life fatigue resistance.

In cases where adequate infinite or finite life is not provided, in some cases, a detail can be 

relocated to improve its performance. For example, if the resistance is exceeded at a transverse 

stiffener or connection plate, the engineer can explore another arrangement of the connection 

plates so that the detail is located at a region of lower stress range. If the resistance is exceeded 

for a longitudinal stiffener termination, the termination can be moved to a region of lower stress 

range or to a zone of permanent compression, or the end of the detail can be improved by 

providing a radiused transition. In some cases, an increase in section modulus might be required, 

but only after exhausting these simpler and more cost effective changes first.

SECTION 6.6 EXAMPLE PROBLEM OF FATIGUE DESIGN

For the girder shown in Figure 6.6-1, the process described in Section 6.5 will be employed to 

determine the fatigue stresses and check a point 56 feet from the left abutment, the 0.4 point of 

the end span. An assumed cross-frame connection plate is at this location.
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Figure 6.6-1 Girder elevation for sample fatigue calculations. 

6.6.1 Determine Locations Requiring Fatigue Limit State Verification (Step 1)

Because the cross-frame connection being considered is welded to both flanges, and the bottom 

flange in particular is in flexural tension when dead load and live load are considered together, a 

fatigue check of the weld to the bottom flange is required. 

6.6.2 Compute Force Effects (Step 2)

Step 2.1 – Position the load longitudinally.

A continuous beam analysis program was used to determine the maximum positive and 

negative live load moments due to the fatigue truck, prior to applying impact or 

distribution factors, at the point of interest. The results are: 

Positive LL moment = 1,573 ft-kips 

Negative LL moment = -496 ft-kips 

Step 2.2 – Apply impact. 

An additional 15 percent is added to each of the above moments to reflect the impact 

value specified for use in the fatigue limit state.

Positive LL+I moment = 1.15 * 1,573 ft-kips = 1,809 ft-kips 

Negative LL+I moment = 1.15 * -496 ft-kips = -570 ft-kips 

Step 2.3 – Determine the fraction of bending moment resisted by a particular member.

For the girder in question, an exterior beam, the live load distribution factor was 

determined using the lever rule and is 0.75 lanes. Therefore, the moments per girder are 

computed as follows: 
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Positive moment, including impact and distribution, M(+) = 0.75 * 1,809 = 1,357 ft-kips 

Negative moment, including impact and distribution, M(-) = 0.75 * -570 = -428 ft-kips 

6.6.3 Calculate Stress Ranges at Fatigue Details (Step 3)

The range of stress is determined by applying the range of moments from above to the composite 

section of the slab and girder. The bridge being evaluated has shear studs between the girder and 

slab and meets all requirements to be considered fully composite for both signs of the bending 

moment.

The section modulus at the weld between the bottom of the web and flange was computed to be 

2,661 in3

. This value is based on the uncracked composite section (using n).

Therefore the range of stress at the detail is computed as:

For the evaluation of the Fatigue I load combination, a 1.75 load factor is applied, and for the 

Fatigue II load combination, a load factor of 0.8 is applied. Thus, 

Factored stress range, Delta (∆)f, for Fatigue I = 1.75 * 8.05 = 14.09 ksi 

Factored stress range, Delta (∆)f, for Fatigue II = 0.8 * 8.05 = 6.44 ksi 

Now that the stresses have been computed, the resistance of the detail must be determined.

6.6.4 Calculate Fatigue Resistance (Step 4)

Step 4.1 – Categorize the details present on the member being investigated. 

The detail being investigated is a welded connection plate attaching a cross-frame to the 

girder.

Step 4.2 – Classify the details according to AASHTO as Category A, B, B’, C, C’, D, E, or E’.

AASHTO LRFD classifies a welded connection between a connection plate and a girder 

flange as Category C’.

Step 4.3 – Determine the frequency of loading. 

The average daily truck traffic in the most heavily traveled lane is estimated from the 

following equation: 
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ADTTSL = p * ADTT

For this design, the ADTT value was provided by the traffic engineer as 675 trucks per 

day, and three lanes are available for truck traffic on the bridge. Therefore, AASHTO 

requires that the fraction of truck traffic assumed in the most heavily traveled lane be 

taken as 80 percent of the total volume. Thus, 

ADTTSL = 0.80 * 675 = 540 trucks per day 

Step 4.4 – Determine the number of cycles per truck passage.

For a point in the end span of this continuous beam bridge, one cycle per truck passage is 

produced. 

Step 4.5 – Determine the number of cycles over the 75-year design life. 

For the investigation of the Fatigue II load combination, determine the number of design 

cycles using the equation N = (365)(75)(n)(ADTT)SL. 

N = 365 * 75 * 1 * 540 = 14,782,500 cycles 

Step 4.6 – Compute the infinite life resistance.

For the investigation of the Fatigue I load combination, the resistance is the CAFT value. 

For a Category C’ detail, the threshold resistance is 12 ksi. 

Step 4.7 – Determine if adequate infinite resistance is provided. 

The first step is to determine if the design meets the infinite life requirements. The 

factored stress range from the Fatigue I load combination, 14.09 ksi, is compared to the 

constant amplitude fatigue threshold, 12 ksi. Since the computed stress range is greater

than the threshold, infinite life is not provided. Therefore, further evaluation of this detail 

is required. 

If the Fatigue I load combination check is satisfied (i.e., if the Fatigue I stress range is 

less than the CAFT), then the finite life resistance does not need to be compared to the 

Fatigue II load combination stress range to determine if the design is suitable. The second 

check shown below in Step 4.8 is not required for that situation. 
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Step 4.8 – If infinite life is not provided (see Step 4.7), compute the finite life resistance. 

Use the following equation to determine the finite life fatigue resistance.

For a Category C’ detail, the constant, A, is 44 x 108

 ksi3. Therefore, the finite life 

resistance is:

The factored stress range from the Fatigue II load combination, 6.44 ksi, is compared to 

the finite life resistance computed above, 6.68 ksi. Since the computed stress range is less 

than the finite life resistance, finite life is provided. 

In the event that both infinite and finite life resistance are not sufficient, the Engineer 

must modify the design, including such options as moving the connection plate or 

revising the girder dimensions.
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7.1 

CHAPTER 7 FRACTURE CONTROL

SECTION 7.1 HISTORICAL DEVELOPMENT OF FRACTURE CONTROL 

PRACTICES

In the rare instances when the conditions are right for a fracture to occur, it is due to a critical 

combination of crack geometry, applied stress, temperature, and loading rate acting 

simultaneously on a member. The interrelationship of these factors was covered in Chapter 3, 

which describes the theoretical basis of brittle fracture in steel. Also covered in Chapter 3 are the 

background to material toughness requirements, the influence of crack size on element behavior, 

the influence of temperature and loading rate on the toughness requirements for bridge steels, 

and the theoretical use of fracture mechanics as a quantitative design or analysis tool. This 

chapter provides more complete coverage of the development of a comprehensive approach in 

which design, fabrication, and inspection requirements each have an important role in fracture 

control. 

The concept of a bridge-specific approach to fracture control traces its origins to the collapse of 

the Point Pleasant Bridge (also known as the Silver Bridge) in West Virginia in December 1967 

(see Figure 7.1-1). The collapse of the bridge was from the brittle fracture of an eyebar 

originating from a very small crack that was of an undetectable size. This collapse raised 

awareness on two fronts. First, there was no understanding at the time as to how many other 

bridges with similar brittle material were in the nation’s inventory. As it turns out, only one 

bridge with similar eyebar material was located. A hanger detail of the same material was used in 

the Carquinez Truss Bridge, and the applicable eyebars were replaced. This event provided 

impetus for the creation of what are now called the National Bridge Inspection Standards (NBIS) 

and the National Bridge Inventory (NBI) in 1971. Second, it was the beginning of a national 

dialogue about the prevention of brittle fracture and defined bridge inspection procedures, 

frequency, inspector qualifications, and reporting requirements. 

Figure 7.1-1 Point Pleasant Bridge before and after its collapse.

Over the next few years, other significant cracking events occurred on bridge structures. The 

fracture of the Bryte Bend Bridge during construction, which was fabricated with acceptable 
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7.2 

steel, heightened the concern about the need for fracture toughness requirements for bridge 

steels.

Concurrent with some of these notable cracking events, a series of efforts were underway that 

would forever change elements of steel bridge design, fabrication, and inspection. As described 

below, there were numerous incremental changes to AASHTO, American Society for Testing 

and Materials (ASTM), American Welding Society (AWS), Federal Highway Administration 

(FHWA), and State design, fabrication, and inspection practices throughout the 1970’s and 

1980’s. At about the same time, the American Society for Nondestructive Testing (ASNT) was 

developing and refining the requirements to qualify shop inspectors through its Recommended 

Practice No. SNT-TC-1A, Personnel Qualification and Certification in Nondestructive Testing

(ASNT, 1966). 

The first fracture-related provisions for bridges were formalized in 1973 and 1974. Included 

were material-only changes to the ASTM A709 specification and numerous AASHTO “M” 

specifications. The use of Charpy V-notch (CVN) testing was introduced as a supplemental 

requirement. The CVN testing supplemental requirements applied only to base metals, while the 

treatment of weld metals was ambiguous. During this same time, in 1974, AASHTO introduced 

the Standard Specifications for Welding of Structural Steel Highway Bridges as a supplement to 

AWS D1.1 (AASHTO, 1974b). This was a precursor to the AASHTO/AWS D1.5 Bridge 

Welding Code published in 1988. This marked the first time a national welding specification for 

steel bridges was put forth. Some states had developed their own welding specification, but this 

was the first national specification. 

Also in 1974, AASHTO introduced the fatigue design details1 and categories that are still used 

for the most part in the current AASHTO LRFD specifications. Enhancements for nondestructive 

testing were added to the Standard Specifications for Welding of Structural Steel Highway 

Bridges in 1975 (AASHTO, 1975). 

In 1976, the first CVN requirements were added to the AASHTO design specifications, the 

Standard Specifications for Highway Bridges, with the understanding that they were to relate to 

design considerations rather than material specifications. The burden was thus placed on the 

designer to have a role in fracture prevention with the understanding that decreasing the 

possibility of fatigue crack formation and growth is an effective means to fracture prevention. 

With the 1977 interims to the aforementioned design specifications, the first discussion of 

redundancy was added to the bridge design specifications, and nonredundant members were 

treated as more conservatively designed than redundant members by imposing a one category 

shift in the allowable fatigue stresses. The intent again was to discourage the use of fatigue 

sensitive details on nonredundant members through the lessening of the fatigue resistance. Also 

in 1977, AASHTO published the first M270 material standard and toughness testing, and 

minimum standards became a mandatory requirement unless specifically exempted by the owner.

 

1 AASHTO first introduced fatigue design provisions in 1965, though as described in Chapter 1, they were 

fundamentally different than the stress-range concept and detail categories introduced in 1974.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.3 

Therefore, as described above, there were incremental advancements in bridge design, material 

specification, and fabrication requirements throughout much of the 1970’s. The culmination of 

all of this was brought forth in 1978 when AASHTO released the Guide Specifications for 

Fracture Critical Non-Redundant Steel Bridge Members (AASHTO, 1978). This was when the 

term “fracture critical” first became widely used to describe members whose failure would cause 

collapse of the bridge, and this was also when more stringent base metal requirements, 

introduction of weld metal toughness requirements, increased shop inspection requirements, and 

requirements of inspector certification were added to standard practice. In addition, fracture 

critical welds were required to be inspected by both ultrasonic testing (UT) and radiographic 

testing (RT) methods. Those requirements were collectively referred to as the AASHTO Fracture 

Control Plan (AASHTO FCP).

The collapse of the Mianus River Bridge in 1983 (see Figure 7.1-2) led to changes in the federal 

bridge inspection standards. This bridge was designed prior to the establishment of the AASHTO 

FCP, but the collapse did not occur from a brittle fracture that the AASHTO FCP could have 

prevented. Rather it was the result of a pin-and-hanger failure from a combination of corrosion 

and fatigue. This accident highlighted the need for more in-depth inspection requirements for 

Fracture Critical Members (FCM’s), and this was the nexus of changes to the NBIS that now 

require hands-on inspection of FCM’s. Therefore, the nation’s fracture control approach now 

includes the AASHTO FCP requirement that had oversight on the design and fabrication of a 

bridge and a federal oversight component throughout the life of the bridge. 

Figure 7.1-2 Collapse of the Mianus River Bridge. 

Even with the AASHTO FCP and the creation of a combined AWS D1.1 document for buildings 

and bridges in 1972, it was identified that bridge welding had more specialized requirements 

than buildings, and there was a need for a bridge-specific welding code. In 1982, a subcommittee 

was formed with AASHTO and AWS representatives to begin work on such a document. This 

resulted in the creation of AASHTO/AWS D1.5 Bridge Welding Code, first published in 1988 

(AASHTO/AWS, 1988). In 1995, the Bridge Welding Code was amended with Clause 12, 

named the “AASHTO/AWS Fracture Control Plan (FCP) for Nonredundant Members,” 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.4 

containing the various materials and workmanship provisions from the AASHTO FCP. By this 

point, other design and material specific requirements from the AASHTO FCP had been 

integrated into the AASHTO Standard Specifications for Highway Bridges and ASTM 

A709/AASHTO M270, and the Guide Specifications for Fracture Critical Non-Redundant Steel 

Bridge Members were withdrawn in 1989. 

Collectively, the enhancement of design and materials specifications, fabrication and shop 

inspection (AASHTO/AWS FCP), and field inspection requirements (23 CFR 650) form the 

proverbial “three-legged-stool” that is deemed the Total Fracture Control Plan (TFCP) in this 

document (see Figure 7.1-3). This chapter describes each leg of the TFCP, presented in sequence 

of the normal life cycle for a bridge – first material and design, then fabrication and shop 

inspection, and finally field inspection. It is important to note that with the implementation of the 

requirements of the TFCP, there have been no noted brittle fractures of “modern” steel bridges 

(i.e., those designed and fabricated based on the various improvements detailed herein). More 

importantly, bridge collapse from fracture has not occurred. 

Figure 7.1-3 Three legs of the Total Fracture Control Plan (TFCP).

SECTION 7.2 FRACTURE CONTROL BY DESIGN

The first leg of the “three-legged-stool” Total FCP is the actions taken during the type selection 

and design of a steel bridge structure. Throughout design development, the engineer must make a 

series of choices regarding structure type (e.g., girder, truss, arch), member type (e.g., I-beam, 

box beam, welded, mechanically built-up), material selection (e.g., grade and characteristics of 

steel), and detailing that have an influence on fracture resistance. Each of these decisions made 

during the design phase has a subsequent influence on fabrication, inspection, and future 

maintenance.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.5 

AASHTO LRFD Article 1.3.2.3 states that “the fracture limit state shall be taken as a set of 

material toughness requirements of the AASHTO Materials Specifications.” Although the limit 

state is narrowly defined as only a series of material requirements, the various choices described 

above regarding structure type and member type all play a role in determining how fracture 

control will be addressed during design. Unlike the strength, service, extreme event, and fatigue 

limit states which require the computation of forces and stresses and a comparison to a resistance

value, fracture is unique in that this limit state is generally not addressed via calculations but 

rather through the use of well-understood materials, by enforcing workmanship requirements, 

and through the choice of structure and member type. In this chapter, the treatment of fracture as 

a design consideration will focus on: 

• Identifying fracture critical members

• Selecting appropriate materials

• Detailing structures to minimize the possibility of fracture

When fracture is rigorously considered computationally (and it rarely is in the bridge engineering 

profession), the process is complex. A fracture mechanics approach requires input parameters, 

such as material properties, anticipated service temperature, loading rate, plate thickness, and 

crack geometry, in order to compute common crack characterizing parameters (i.e., K or J), 

which are then compared to the expected fracture toughness to determine the susceptibility of a 

particular assumed condition. These calculations are difficult to perform accurately in practice 

because many engineering problems do not fit nicely into cracked section models which presume 

idealized conditions. Thus the use of fracture mechanics analysis methods is not common, and no 

such calculations are required of the bridge design engineer when using LRFD. Instead, 

engineers specify materials with a desired level of toughness and choose details that are known 

to provide good long-term behavior as a means of fracture prevention for new steel structures. A 

background on fracture mechanics for bridge design is presented in Chapter 3. Other references 

that discuss the application of fracture mechanics to bridge design include Barsom and Rolfe 

(1999), Fisher, Kulak, and Smith (1998), and Keating, Kulicki, Mertz, and Hess (1990). 

7.2.1 Charpy V-Notch Requirements for Primary Members

A primary member is defined by AASHTO as “a member designed to carry the loads applied to 

the structure as determined from an analysis.” AASHTO LRFD Article 6.6.2 states that all 

primary longitudinal steel members, their connections, and transverse floorbeams shall meet 

mandatory Charpy V-notch (CVN) requirements when subjected to computed tensile stresses at 

the Strength I load combination. Elements such as the tension chord of a truss, the tie girder of a 

tied arch bridge, or flanges and webs of beams in bending are examples of members or 

components of a member that can experience tension. 

In AASHTO LRFD Article 6.7.4.1, diaphragms and cross-frames in curved steel bridges are 

additionally defined as primary members implying similar CVN requirements as for the main 

girders. Though these members certainly carry computed dead and live load forces, they are not 

generally considered as critical as the main girders. A proposal is pending to AASHTO 

Subcommittee T-14 for 2016 consideration for the primary member designation to be struck 

from cross-frames and diaphragms so as to exempt them from the CVN test requirements. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.6 

However, in all cases it is the responsibility of the engineer to properly identify primary steel 

members subjected to tensile stress so that the CVN requirements can be applied during their 

fabrication. These primary member CVN requirements are the first and most basic requirement 

for fracture control. AASHTO LRFD Article 6.6.2 specifically exempts the following bridge 

items from CVN requirements unless required by the engineer: splice plates and filler plates in 

bolted splices connected in double shear; intermediate transverse web stiffeners not serving as 

connection plates; bearings, sole plates, and masonry plates; expansion dams; and drainage 

material. 

An example that demonstrates the application of the AASHTO requirements for CVN 

designation is provided in Figure 7.2.1-1 and Figure 7.2.1-2. 

Figure 7.2.1-1 Strength I bending moment envelope for a three-span continuous beam (only 

half of diagram shown). 

As previously described, the Strength I load combination is used to define members or regions of 

members for which the mandatory CVN requirements apply. The Strength I load combination 

bending moment envelope (factored dead and live loads are combined) for an example three-
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.7 

span continuous bridge with spans of 140 ft. – 180 ft. – 140 ft. is provided in Figure 7.2.1-1. The 

example girder, for which half the total length is shown in Figure 7.2.1-2 owing to symmetry, is 

made up of various plates whose lengths are shown, connected with full penetration butt splices 

along with two field splices. In regions where the maximum moment envelope is positive, the 

bottom flange will experience tension. Similarly in other regions where the minimum moment 

envelope is negative, the top flange will experience tension. There are significant lengths where 

each of these conditions is met, meaning either flange could be in tension depending on live load 

position. It should be clarified that the designation of “tension zones” must be based on stresses. 

The use of moments in this example will reasonably define the limits of tension for purposes of 

discussion. However in reality, the ratio of non-composite and composite loads will slightly shift 

the true tension zones from those extrapolated solely from the use of bending moments. 

Figure 7.2.1-2 Tension zones and required CVN designation for a three-span continuous 

beam (only half of girder shown). 

Figure 7.2.1-2 presents a common approach for designating the zones of tension on engineering 

plans. It is common to label, point to, or otherwise denote what elements of the girder are subject 

to the mandatory CVN requirements due to the presence of tensile stress. The limits of the 

tension regions correspond to the moment diagram provided in Figure 7.2.1-1. As is commonly 

the case for continuous beams, the majority of the plates in the example bridge can experience 

tension at one time or the other. The number of plates that will always be in compression is 

limited. In many bridges, there may be no plates at all that will be in permanent compression 

based on the way the engineer chooses to lay out the welded plate transitions and bolted field 

splice locations. Fabricators may need to, or choose to, introduce welded butt splices into the 

girder even when the plate size is not changed, perhaps due to plate-length limitations. For these 

reasons, it is useful to define the zones of tension using a linear dimension as in Figure 7.2.1-2 to 

explicitly define the regions of possible tension for each flange.

7.2.2 Fracture Critical Members

In addition to the primary member tension requirements, more stringent requirements apply to a 

special class of members known as Fracture Critical Members (FCM). A FCM is defined by 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.8 

AASHTO as “a steel primary member or portion thereof subject to tension whose failure would 

probably cause a portion of or the entire bridge to collapse.” In other words, it is a nonredundant 

steel member subjected to tension, which will be explained in detail below. These members are 

subjected to specific and more stringent attention during design, fabrication, and both shop and 

in-service inspection. One requirement is that they be designed to satisfy the infinite life 

requirements of the Fatigue I load combination regardless of traffic volume on the bridge. They 

may also be subjected to an elevated design load if the owner decides to invoke the optional 

redundancy load modifiers presented in AASHTO LRFD, though many owners choose not to do 

so. The use of the redundancy load modifier, ηR, increases the total factored load by 5 percent to 

provide an additional margin of safety for nonredundant members. Additional details are 

provided in AASHTO LRFD Article 1.3.4. 

The identification of FCMs revolves around three important questions: 

1. Is the member made of steel?

2. Does the member ever experience tension?

3. Could the failure of the member cause collapse or loss of function of the bridge (i.e., is it 

nonredundant)? 

If all of these conditions are met, then the member is deemed to be fracture critical. In order to 

answer these questions, the engineer must be able to identify members that meet the 

requirements listed above. It should be obvious if a member is made of steel, and somewhat 

obvious if the member experiences tension under loading, but the question of redundancy is 

often somewhat more difficult to answer. 

7.2.2.1 Redundancy

AASHTO defines redundancy as “the quality of a bridge that enables it to perform its design 

function in a damaged state.” Redundancy is therefore related to the ability of a bridge to 

continue to carry dead and live load, without collapse, even in the presence of certain levels of 

damage.

The design of steel bridges today typically involves redundant structural systems. AASHTO 

LRFD Article 1.3.4 states “Multiple-load-path and continuous structures should be used unless 

there are compelling reasons not to use them.” A redundant bridge, such as a multi-beam steel 

bridge, has sufficient transverse and longitudinal load paths to ensure survival even in the 

unlikely loss of a member component or full member. The presence of multiple, parallel primary 

members spanning between supports, diaphragms or cross-frames, a concrete deck, and even the 

barrier rails, all form part of a redundant load path in the unlikely event of the loss of a primary 

member. In the design of redundant bridges, engineers are not required to quantify through 

analysis how load would be transferred in the unlikely event of a member loss. It usually 

amounts to a qualitative assessment of the bridge system based on engineering judgement. 

Nonredundant members do not have alternate, secondary load paths to sustain a member loss and 

remain stable except occasionally only through load paths typically not accounted for in design. 

For instance, a statically determinate truss (without considering transverse members) has exactly 

the minimum number of primary members to be considered stable and determinate when 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.9 

considered in two dimensions. Every primary member is needed to maintain the structure’s 

stability, thus making them all equally critical. A failure of any primary member of a determinate 

truss leads to an unstable structure (on paper), and thus they all would be considered 

nonredundant. A certain number of these members are loaded in tension, making them not only 

nonredundant but fracture critical as well. It is important to be able to distinguish between 

redundant, nonredundant, and fracture critical primary members in a steel bridge. It is 

fundamental to understanding their behavior and identifying potential vulnerabilities, and it also 

impacts fabrication and in-service inspection, as will be discussed later in this chapter.

There are very rare instances in which nonredundant primary members in steel bridges have 

failed resulting in a collapse. The only known examples in the United States are the Silver 

Bridge at Point Pleasant, West Virginia (see Figure 7.1-1), the I-95 Bridge over the Mianus River 

in Connecticut (see Figure 7.1-2), the I-35W Mississippi River Bridge in Minnesota, and the I-5 

Skagit River Bridge in Washington. The Silver Bridge was the only case directly caused by a 

brittle fracture. There are a greater number of cases where a failure of an individual member in 

an apparently nonredundant bridge has not led to the collapse of the structure. Examples where 

fracture occurred but did not cause collapse include the following: 

• The 1976 full-depth fracture of the two-girder US-52 Lafayette Street Bridge over the 

Mississippi River in St. Paul, Minnesota (Fisher, 1984) 

• The 1977 full-depth fracture of the two-girder I-79 bridge at Neville Island in Pittsburgh, 

Pennsylvania (Fisher et al., 1980a) 

• The 2003 fracture of the two-girder US-422 Bridge near Pottstown, Pennsylvania 

(Kaufmann, Connor, and Fisher, 2004) 

• The 2012 simulation of a lower chord fracture of the US-421 truss bridge over the Ohio 

River between Madison, Indiana and Milton, Kentucky (Connor, Digglemann, and 

Sherman, 2013) 

These bridges did not collapse due to their ability to redistribute load in ways that are generally 

not captured by simple analyses. A conventional analysis, such as the planar analysis of a simply 

supported truss, does not capture the load redistribution benefits of elements such as lateral 

bracing systems, floor systems, decks, and barriers that can provide alternate load paths for 

certain primary members. The degree of redundancy of a particular structure is not always 

evident, and a detailed analysis of the load path and structural configuration is required to 

understand the load redistribution characteristics of the structure. However there are no standard 

rules and little guidance for this redundancy analysis. AASHTO LRFD discusses this in Article 

C6.6.2 where it indicates that a standard procedure for using analysis to determine what members 

are fracture critical (i.e., a redundancy analysis) is not yet available. This is due to a lack of 

consensus as to what load cases should be studied, what members should be considered failed, 

how to capture the dynamic effects of fracture, as well as many other issues such as how to 

account for the participation of bracing members and transverse members. The use of refined 

analysis to assess bridges is thus left by AASHTO to the discretion of an engineer and an owner 

to agree upon. This leaves a certain amount of ambiguity when engineers are designing or 

analyzing bridges with fracture critical members. Because of this ambiguity, FHWA instituted a 

policy addressing the design of FCM’s. This policy is described in the following section. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.10 

7.2.2.2 FHWA Policy on Fracture Critical Members 

In order to alleviate some of this ambiguity on how FCM’s are to be identified and treated, 

FHWA issued its “Clarification of Requirements for Fracture Critical Members” in 2012 

(FHWA, 2012b). The memo addresses the FHWA policy for classification of steel bridge 

members for design, fabrication, and inspection. It provides clarification on how various types of 

redundancy may be used during design, evaluation, and inspection. The following are definitions 

of the various types of redundancy discussed in the FHWA memo: 

• Load Path Redundancy is the redundancy inherent to a system because of multiple 

longitudinal load paths between points of permanent support. An example of a bridge 

containing load path redundancy is a common multi-girder steel bridge. The FHWA 

memo does not prescribe the minimum number of required parallel girders such that 

sufficient load path redundancy is provided. There is no consensus among state agencies 

on this matter, with some accepting a three-girder bridge as redundant and others 

requiring four or more beam lines. In the case of the Hoan Bridge, two of the three main 

girders completely fractured, the third was cracked as well, yet the bridge did not collapse 

and carried some live load before the fracture was discovered. Load path redundancy is 

typically determined through qualitative assessment by engineering judgement and not 

calculations. 

• Structural Redundancy is the redundancy in a system provided by structural continuity. In 

a hypothetical multi-span continuous beam or system, the fracture of a member within a 

span may not necessarily cause collapse if the damaged system has alternate load paths to 

carry load back to supports via longitudinal or transverse load redistribution. The 

sufficiency of this alternate load path however requires that the system be analyzed for 

potential failure scenarios to establish the demands on these backup load paths. 

Assessment of structural redundancy will typically require the use of a three-dimensional 

model of the bridge. In the design of a new bridge, structural redundancy may be 

leveraged for exemption from in-service fracture critical inspection requirements, but 

FHWA does not allow engineers to consider this to exempt the member from fracture 

critical fabrication requirements. This is discussed further as part of a new definition 

called a System Redundant Member, defined later in this section. 

• Internal Redundancy is a design approach based on the requirement that the fracture of an 

individual component within a built-up member will not result in complete failure of the 

member. For instance, a member may consist of a section of many elements that are 

bolted or riveted together (e.g., plates and angles connected together to form a box for a 

tension tie or truss, or a built-up plate girder). The analysis typically involves a sectional 

stress check with one plate element removed. The premise of internal redundancy is that 

individual elements are not welded together. There is no continuous path that allows a 

crack in one element to propagate into an adjoining element. Because of questions 

surrounding issues such as energy dissipation during fracture, what constitutes effective 

isolation, how to ensure the capacity of the remaining member, and what load 

combinations should be evaluated for this extreme event scenario, the use of internal 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.11 

redundancy as the only means to achieve redundancy for new bridge design is not 

allowed by FHWA.

Regarding the designation of FCM’s, AASHTO states “The Engineer shall have the 

responsibility for determining which, if any, component is a fracture-critical member (FCM). 

Unless a rigorous analysis with assumed hypothetical cracked components confirms the strength 

and stability of the hypothetically damaged structure, the location of all FCMs shall be clearly 

delineated on the contract plans.” FHWA takes a similar position, but currently limits the 

analysis-based exemption to in-service inspection requirements, and not to fabrication 

requirements. 

If a non-load path redundant member is fabricated to FCM standards and could be shown by 

some analysis to exhibit structural redundancy, the FHWA memo classifies this as a System 

Redundant Member (SRM). A SRM is a member that has been fabricated according to the 

AASHTO/AWS FCP, as one without load path redundancy, but does not need to be considered 

an FCM for purposes of in-service inspection. This is consistent with the aforementioned FHWA 

statement that analysis alone cannot exempt a member from FCM fabrication requirements. 

However, analysis can be used to eliminate certain members from FCM in-service inspection 

requirements. That is the crux of the SRM designation. Internal redundancy, though beneficial, is 

not deemed sufficient to eliminate a member’s fracture critical designation for in-service 

inspection since a fracture could exist for some time undetected, and knowingly operating a 

bridge in this compromised condition is not acceptable to FHWA. 

In summary, the key points of the FHWA policy clarification are as follows: 

• A member is not fracture critical if either load path redundancy or structural redundancy 

is provided. 

• In-service bridges built according to the FCP (post-1978) and new bridges can be 

evaluated using refined analysis to determine their sufficiency of structural redundancy. 

• The FHWA memo introduced the new member classification, a System Redundant 

Member (SRM), which is a non-load path redundant member that gains its redundancy by 

system behavior.

• SRM’s must still be fabricated according to the AASHTO/AWS FCP, but may be 

relieved from fracture critical in-service inspection requirements.

• Internal redundancy is not recognized to exempt the member from fracture critical 

classification. This may change as new research becomes available.

7.2.3 Selection of Materials

When selecting the specific materials for a bridge design, several factors are considered, 

including strength, toughness, weldability, corrosion protection, availability, and cost. 

AASHTO LRFD Article 6.4 provides basic material requirements for steels that are recognized by 

the specifications. Included are various provisions for structural steels used in plates and shapes 

as well as other materials such as: pins and rollers; bolts, nuts, and washers; shear studs; weld 

metal; castings; and cables and strands.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.12 

The material properties for bridge steel are well defined for new structures. Historically many 

different types of steels, with widely varying chemistries and mechanical properties, have been 

used. These material properties influence the inherent tolerance of steels to fracture. AASHTO 

LRFD provides a table of minimum properties for steels commonly used for new bridge 

construction. This table is reproduced herein as Table 7.2.3-1. 

Table 7.2.3-1 Minimum mechanical properties of structural steel by shape, strength, and 

thickness. 

AASHTO

Designation

M 270M/

M 270

Grade 36

M 270M/

M 270

Grade 50

M 270M/

M 270

Grade 50S

M 270M/

M 270

Grade 

50W

M 270M/

M 270

Grade 

HPS 50W

M 270M/

M 270

Grade

HPS 70W

M 270M/

M 270

Grade HPS 100W

Equivalent ASTM

Designation

A709/

A709M

Grade 36

A709/

A709M

Grade 50

A709/

A709M

Grade 50S

A709/

A709M

Grade 

50W

A709/

A709M

Grade 

HPS 50W

A709/

A709M

Grade 

HPS 70W

A709/

A709M

Grade HPS 100W

Thickness of 

Plates (in.) 

Up to 4.0 

incl.

Up to 4.0 

incl.

Not 

applicable

Up to 4.0 

incl.

Up to 4.0 

incl.

Up to 4.0 

incl.

Up to 2.5 

incl.

Over 2.5 

to 4.0 incl.

Shapes All groups All groups All groups All groups Not 

applicable

Not 

applicable

Not 

applicable

Not 

applicable

Minimum Tensile 

Strength, Fu (ksi) 58 65 65 70 70 85 110 100

Specified 

Minimum Yield 

Point or Specified 

Minimum Yield 

Strength, Fy (ksi) 

36 50 50 50 50 70 100 90

By using materials from the AASHTO table of approved steels and the common requirements 

present in state construction specifications, there are multiple levels of control of basic material 

properties. 

The plans and specifications must clearly indicate the grade of steel to be used and the 

temperature zone in which the bridge is to be constructed. The selection of steel for a particular 

application is left to the discretion of the designer and owner. Steels are generally selected for 

design considering the yield strength as the primary factor. Steels with yield points of 36, 50, and 

70 ksi are the most common, and these values have been in use for many decades. Less common, 

though specified for some high demand applications, are steels with a 100 ksi yield strength. In 

Section 4.2.2, the yield strength of the steel was shown to not be a factor in fatigue life, and there 

are no advantages to using higher strength steels to control fatigue or fracture potential. 

In order to provide materials with enhanced toughness, weldability, and enhanced atmospheric 

corrosion properties, high-performance steels (HPS) were introduced in the late 1990’s. These 

plate steels are manufactured as either quenched and tempered (Q&T) or treated by 

thermomechanically controlled processing (TMCP) in order to achieve the higher toughness 

values. Thicker plates, those in the 1.5 inches to 2 inches range and up to a maximum of 4 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.13 

inches, are required to be quenched and tempered in order to achieve the required mechanical 

properties. This Q&T operation effectively limits the plate lengths to 50 feet or less, thus 

increasing the costs of members fabricated with these plate length limits. For plates less than 1.5 

inches to 2 inches thick, and this again depends on the mill, a TMCP plate is available that 

enables the mill to manufacture the plates “in-line” without additional treatment and provide the 

desired mechanical properties. The use of TMCP plates greatly expands the plate length limits 

and also includes wider slabs as well. As these rolling practices have evolved over time and as 

additional mills develop HPS rolling capabilities, no firm value is suggested as to what plates are 

available in HPS 50W, HPS 70W, and HPS 100W grades, and in specific lengths and widths. 

The engineer should check with fabricators at the time of design to determine what materials are 

available, as this might alter certain design decisions as to how long to make field sections and 

which size plates should be used. 

Toughness requirements are achieved through CVN testing of base material as it comes from the 

production mill. The AASHTO requirements vary for fracture critical and non-fracture critical 

members as well as for grade of steel and plate thickness. The temperature zone for a specific 

bridge relates to the minimum service temperature and is usually specified by the owner. The 

CVN requirements from the AASHTO specifications are provided in Table 7.2.3-2. 

Table 7.2.3-2 CVN impact energy requirements.

Grade 

(Y.P./Y.S.)

Thickness

(in.)

Fracture Critical Non-fracture Critical

Min. Test 

Value 

Energy 

(ft·lbs.)

Zone 1

(ft·lbs. @ °F)

Zone 2

(ft·lbs. @ °F)

Zone 3

(ft·lbs. @ °F)

Zone 1

(ft·lbs. @ °F)

Zone 2

(ft·lbs. @ °F)

Zone 3

(ft·lbs. @ °F)

36 t≤4 20 25 @ 70 25 @ 40 25 @ 10 15 @ 70 15 @ 40 15 @ 10

50/50S/50W t≤2 20 25 @ 70 25 @ 40 25 @ 10 15 @ 70 15 @ 40 15 @ 10

2<t≤4 24 30 @ 70 30 @ 40 30 @ 10 20 @ 70 20 @ 40 20 @ 10

HPS 50W t≤4 24 30 @ 10 30 @ 10 30 @ 10 20 @ 10 20 @ 10 20 @ 10

HPS 70W t≤4 28 35 @ -10 35 @ -10 35 @ -10 25 @ -10 25 @ -10 25 @ -10

HPS 100W t≤21⁄2 28 35 @ -30 35 @ -30 35 @ -30 25 @ -30 25 @ -30 25 @ -30

21⁄2<t≤4 36 not permitted not permitted not permitted 35 @ -30 35 @ -30 35 @ -30

The aforementioned table distinguishes between fracture critical and non-fracture critical 

material requirements. AASHTO places the responsibility for determining whether members are 

fracture critical on the design engineer. Fracture critical members are subjected to more stringent 

CVN requirements, a key aspect in designing to prevent fracture in steel bridge members. 

Depending on the minimum service temperature, the corresponding material performance 

requirements vary. AASHTO divides bridges into three zones depending on the minimum 

service temperature. The zones are described in Table 7.2.3-3. The importance of the 

temperature zone is that it defines the CVN requirements for particular grades of steel used in 

different temperature conditions. 
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Table 7.2.3-3 Temperature zone designations for Charpy V-notch requirements. 

Minimum Service Temperature Temperature Zone

0°F and above 1

-1°F to -30°F 2

-31°F to -60°F 3

There is often confusion about the “minimum service temperature” as required to implement the 

requirements of Table 7.2.3-3. AASHTO has no definition, yet a designation of one is needed for 

the specification of materials. In 1978, Hartbower proposed a temperature map for FCM’s that 

defined the lowest anticipated service temperature (LAST) based on an analysis of weather data 

from the period of 1950 through 1970 (see Figure 7.2.3-1). In the footnote to the temperature 

map in the source document is a note indicating that the contours are based on hourly readings 

with a 99 percent chance that the plotted values will not be exceeded (Hartbower, 1978). Though 

not adopted in specification form, this map is useful for engineers trying to understand the 

temperature zone designation and corresponding CVN requirements. 

Figure 7.2.3-1 Lowest anticipated service temperature (LAST). 
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7.2.4 Detailing to Avoid Constraint 

Fractures in steel girders have resulted from either the propagation of fatigue cracks to the point 

of fracture or as the result of large fabrication defects somehow undetected. When fracture 

following fatigue growth occurs, cracks are able to lengthen over time until such point that a 

component or an entire member is lost due to fracture of the remaining section. As mentioned in 

Chapter 4, however, visible cracking occurs very late in the life of a crack and indicates that 

most of the useful life of the detail has been exhausted. Fracture due to unstable crack 

propagation could occur soon after a crack is discovered. There are other instances, however, 

where the crack growth stage is not evident and fracture occurs under routine service conditions. 

It is the responsibility of the design engineer is to choose details that are not susceptible to 

fracture due to excessive constraint. Two sources of constraint in welded steel structures will be 

described herein: that associated with elements joined with intersecting welds, and the constraint 

from thick plates and highly constrained joints. 

7.2.4.1 Constraint-Induced Fracture

Constraint-induced fracture (CIF) is a type of fracture attributed to local constraint conditions in 

steel under tension, which may occur at details of certain geometries. It occurs due to the 

inability of steel to locally yield under a combined state of stress. One undesirable practice that is 

conducive to CIF occurrence is the intersection of multiple welds at a common location, as 

shown in Figure 7.2.4.1-1. Although the figure shows a longitudinal stiffener as the attachment, 

CIF is also possible with other types of attachments (e.g., a lateral bracing gusset plate) and has 

also been noted at bearing stiffener to flange connections as well.
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Figure 7.2.4.1-1 Example of improper stiffener detail with intersecting welds susceptible to 

CIF. 

To understand the phenomenon of CIF in steel structures, an understanding of the behavior of 

steel in tension is important. Under tension, lateral contraction occurs due to Poisson’s effect. 

For instance, in a steel tension test, elongation of the specimen occurs along with contraction in 

the lateral direction. In a steel I-beam, flexure of the section results in longitudinal tensile 

stresses developing in the web as well as in attachments parallel to the direction of loading. As 

the web and attachments elongate, the web contracts in the through thickness direction. This is 

illustrated in Figure 7.2.4.1-2 (Connor et al., 2007). Note that at the end of the longitudinal 

attachment, the web plate is in a state of plane stress and the out-of-plane stresses are zero.
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Figure 7.2.4.1-2 Illustration of local stress condition and natural deformations of girder 

web at stiffener termination when detailed correctly. 

CIF can occur when the web gap area is not allowed to contract due to the proximity of the 

longitudinal and vertical stiffeners and their attaching welds. As flexural tension is applied to the 

girder web, its tendency to contract in the through thickness direction is highly restrained by the 

intersection of the longitudinal attachment, the transverse stiffener, and the multiple intersecting 

welds that all join at a common location. Under the actions of applied stress in the primary 

direction and the resulting restraint stresses in the through thickness direction, a more complex 

triaxial state of stress develops. Considering von Mises’ yield criterion, this results in a combined 

state of stress that exceeds the uniaxial yield stress and greatly reduces the ductility of the 

material under the triaxial stress. The reduction in ductility can make the material behave in a 

brittle fashion. 

An example of the local state of stresses in a highly constrained condition is shown in Figure 

7.2.4.1-3 (Connor et al., 2007). Of note in this figure is how it differs from Figure 7.2.4.1-2. The 

longitudinal attachment, instead of stopping some distance away from the transverse connection 

plate, is now in contact with it, sometimes welded to it, and the longitudinal and vertical welds 

intersect. As a result, instead of the free lateral contraction of the web depicted in Figure 7.2.4.1-

2, the web is now restrained in the through thickness direction and a stress, σ3, develops as a 

result. Due to the presence of the restraining stresses in the secondary direction, the material’s 

ability to resist primary stress in the computed direction is diminished. When the degree of 

restraint is significant enough, constraint-induced fracture is possible. 
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Figure 7.2.4.1-3 Illustration of triaxial stress state created in a highly constrained condition 

with insufficient gap. 

Constraint-induced fractures have occurred on the I-794 Hoan Bridge in Milwaukee, Wisconsin 

(Fisher et al., 2001), the US 422 bridge in Pottstown, Pennsylvania (Kaufmann et al., 2004), the 

Diefenbaker Bridge in Saskatchewan (Ellis et al., 2013), and possibly other cases not identified 

as such at the time. In each of those bridges, premature fracture at a lateral gusset plate 

connection to a steel girder web occurred and is attributed to CIF. The welded details in which 

these fractures occurred are common and exist in many steel structures throughout the nation. In 

no case did the bridge collapse following the fractures, though each required closure for repair. 

In the case of the December 2000 fracture of the I-794 Hoan Bridge, the failure was dramatic. 

The span in which fracture occurred was composed of three main girders with a floorbeam and 

stringer system supporting the deck. Gusset plates connecting the bottom lateral bracing system 

were fabricated with a slot to fit around and center on the transverse stiffener. When the girders 

were fabricated, the slot in the gusset plate was pushed tight against the transverse stiffener, and 

created a triaxial constraint condition that led to the fracture of two of the three main girders 

(Connor et al., 2007). Figure 7.2.4.1-4 depicts the condition of the bridge following the fracture 

along with a close-up of a similar lateral bracing gusset plate detail. There were several 

important findings and outcomes from the Hoan Bridge investigation, including the following 

(FHWA, 2001): 

• The failure was confirmed through laboratory investigation as brittle fracture.

• There was no evidence of fatigue cracking prior to fracture initiation.
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• The narrow gap between the gusset plate and transverse stiffener increased the local 

stiffness and prevented yielding and stress redistribution in the constrained area. 

• Prior similar cracks were found several years earlier and were at the time assumed to be 

fatigue cracks. These prior cracks did not result in the chain reaction fracture of multiple 

elements of the bridge.

• The States were advised through a series of technical advisories and memos from the 

FHWA to identify bridges that might have similar details, conduct inspections, and 

implement selected retrofits as necessary.

In the case of the US 422 bridge, fracture occurred in the web at the intersection of welds 

connecting a lateral bracing gusset plate and a transverse connection plate, with the longitudinal 

and vertical welds intersecting at a common location several inches above the bottom flange. The 

fracture initiated in the web and propagated vertically until it was arrested by an internal 

discontinuity, and propagated downward resulting in fracture of the bottom flange. Figure 

7.2.4.1-5 provides photographs of the bridge and fracture location. This fracture occurred in 

warm weather and was discovered only during a routine inspection in May 2003. There was no 

noticeable deformation of the bridge otherwise. 

CIF cracks found in the Diefenbaker Bridge are also shown in Figure 7.2.4.1-6 to show the 

similar nature and extent of cracking in each of the three bridges.

In both the Hoan and the US 422 bridges, CIF fractures occurred in materials that otherwise met 

current material property requirements. In the case of the US 422 bridge, the tensile and CVN 

properties of the plate were obtained and compared to modern requirements. The yield and 

tensile strength of the web plate exceeded the requirements for ASTM A36. Although mandatory 

CVN testing was not required at the time this bridge was fabricated, the test results proved that 

the flange material met AASHTO Zone 2 fracture critical toughness requirements. The web and 

gusset plate had CVN results marginally less than that of the flange, but all were in general 

conformance with the AASHTO requirements. For the I-794 Hoan Bridge, material tests were 

conducted after the demolition of the approach spans. The complete toughness versus 

temperature transition curve was developed, and these results demonstrated that the fractured 

web plates satisfied the AASHTO Zone 2 requirements for fracture critical materials for the 

minimum service temperatures. For the Diefenbaker Bridge, the steel (ASTM A373-56T) was 

tested and it was determined that the yield, tensile, and CVN values were consistent with steels 

of the bridge’s vintage but that the CVN results did not meet the requirement of ASTM A709. 

However, the below-standard CVN values were found not to be a contributing factor, nor was 

temperature as the fracture occurred in the summer.
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Figure 7.2.4.1-4 Hoan Bridge post-fracture photos and gusset plate detail. 
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Figure 7.2.4.1-5 Fracture of the US 422 Bridge; lateral bracing configuration (top) and 

bottom view of fractured flange and gusset plate (bottom). 
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Figure 7.2.4.1-6 CIF cracks in the Diefenbaker Bridge.
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To guard against CIF, AASHTO provides an approach for engineers to use in the design of new 

steel structures. They state:

“To the extent practical, welded structures shall be detailed to avoid conditions 

that create highly constrained joints and crack-like geometric discontinuities that 

are susceptible to constraint-induced fracture. Welds that are parallel to the 

primary stress but interrupted by intersecting members shall be detailed to allow 

a minimum gap of 1 inch between weld toes.”

This requirement focuses on the need to maintain a 1-inch separation between weld toes as the 

key practice to minimize the potential for CIF. This separation is depicted in Figure 7.2.4.1-7. 

The figure also depicts the preferred practice when longitudinal and transverse elements 

intersect. Depending on the specific location and detail, the preference is generally for the 

longitudinal attachment to be continuous while breaking the transverse stiffener. This provides 

the best flow of stress into and out of the longitudinal attachment. 

Figure 7.2.4.1-7 Weld detail where the longitudinal stiffener is continuous.
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There are other details where CIF is possible. The following six figures (Figure 7.2.4.1-8 through 

Figure 7.2.4.1-13) provide illustrations which are followed by commentary on practices that are 

encouraged and discouraged with respect to CIF. These six figures and their accompanying 

commentary relate to Details A through F. In these six figures, arrows on both ends refers to 

stress reversal, whereas arrows on only one end refers to one-directional stress.

Figure 7.2.4.1-8 Detail A. 

DETAIL A – When vertical and longitudinal stiffeners are required, it is preferred to have them 

on opposite sides of the web to preclude intersecting details. This detail is acceptable for webs in 

tension, compression, or reversal. However, frequently the length of the attachment is such that an 

interference is inevitable. See Detail B in Figure 7.2.4.1-9. 
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Figure 7.2.4.1-9 Detail B.

DETAIL B – When vertical and longitudinal stiffeners will intersect, make the longitudinal 

stiffener continuous and break the transverse stiffener, welding it to the top and bottom of the 

longitudinal stiffener with fillet welds. This detail is acceptable for webs in tension, compression, 

or reversal. Provide a 1-inch gap minimum between all weld toes.

Figure 7.2.4.1-10 Detail C.

DETAIL C – When a longitudinal stiffener will intersect a bearing stiffener, provide full height 

bearing stiffeners and weld the longitudinal stiffener to the bearing stiffener with fillet welds. 

This detail is acceptable for webs in compression, which is where a longitudinal stiffener and 

bearing stiffener would generally intersect (e.g., a zone of flexural compression at the bottom of 

a web over a pier). Provide a 1-inch minimum gap between all weld toes.
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Figure 7.2.4.1-11 Detail D.

DETAIL D – Detail D, like Detail C above, has full height bearing stiffeners and longitudinal 

stiffeners. It is possible to discontinue the longitudinal stiffener near the bearing stiffener, 

leaving a minimum 1-inch gap but only when the web is loaded in compression and cannot 

experience tension at the Fatigue I load combination. This type of detail is discouraged, and 

Detail C is preferred.

Figure 7.2.4.1-12 Detail E.

DETAIL E – When a vertical attachment, such as a diaphragm connection plate or shear 

stiffener, intersects a lateral gusset plate, and the girder web is loaded in tension, compression, or 

reversal, the preferred practice is to have the gusset plate be a continuous element, breaking the 

vertical stiffener and welding it with fillet welds to the gusset plate. Provide 1-inch minimum 

gaps between all weld toes.
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Figure 7.2.4.1-13 Detail F.

DETAIL F – When the web is loaded in compression only and a vertical attachment (e.g., a 

connection plate or shear stiffener) intersects a gusset plate, the preferred practice is to have the 

gusset plate be a continuous element, breaking the vertical stiffener and welding it with fillet 

welds to the gusset plate. The intersection must provide 1-inch minimum gaps between all weld 

toes. However, because the longitudinal stresses are entirely in compression, it is also acceptable

to slot the gusset plate to fit around a continuous bearing stiffener, as shown in Figure 7.2.4.1-13. 

The gusset plate is then welded to the stiffener and the girder web, maintaining a 1-inch 

minimum gap between all weld toes.

Related to the AASHTO 1-inch weld gap requirement, research at Purdue University (DeLong 

and Bowman, 2010) also examined existing structures and the amount of web gap necessary to 

preclude CIF. Their research addressed the existing inventory of thousands of bridges with 

potential intersecting weld problems due to the presence of longitudinal stiffeners, gusset plates, 

and transverse stiffeners connected at common locations. Their concern was that just because a 

constraint-induced fracture occurred on several steel bridges, this should not lead to the general 

conclusion that it is likely on other existing bridges. The Purdue research confirmed the 

recommendations proposed by others (Mahmoud, Connor, and Fisher, 2005) with regard to the 

inspection of existing steel bridges, namely that a minimum observable gap in the field of 1/4 

inch should provide for sufficient yielding and ductility so that CIF is unlikely. The research at 

Purdue also examined the influence of intersecting welds on the fatigue life of small gap details. 

They found that the presence of narrow web gaps did not seem to affect the fatigue life of such 

details, the fatigue life being governed by the toe at the outside end of a gusset plate and not by 

the toe nearer to the transverse connection plate. The test results for narrow web gaps where 

longitudinal stiffeners are terminated near transverse stiffeners was inconclusive. 

7.2.4.2 Thick Plates

For a number of years, it has been known that welding thick components together in highly 

constrained joints can lead to fracture. This has been demonstrated in through thickness and 

lamellar tearing fractures in steel structures in the past. Lamellar tearing failures have been 
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reported where plates are welded at right angles to each other, resulting in through thickness 

stresses in one of the connected plates. Examples of these types of failures have been found in 

connections for rigid frames. 

Brittle fractures have occurred during fabrication, immediately after fabrication, and shortly after 

an element has been placed into service. These early-age failures are not related to fatigue but 

rather to the unique condition present in complex joints or in joints and elements constructed 

with thick plates associated with large restraining forces which develop during differential 

cooling. Although it is generally desirable to avoid the angled connection of multiple thick plates 

and complex details, sometimes it is unavoidable. To minimize the potential for brittle fracture in 

thick joints, special precaution is required during fabrication, including the application of 

preheat, specific welding sequences, and robust nondestructive testing and inspection to provide 

the best possible performance. 

Thick plate failures, known as lamellar tearing failures, have occurred beneath the weld metal in 

rolled steels with poor through-thickness ductility (see Figure 4.1.1-2). It is a failure type that 

occurs in tee and corner joints beneath the fusion boundary of the weld and the parent material. 

Failure is by tearing of the base metal in long parallel fibers at a location of inherently low 

ductility.

Failure is driven by either shrinkage strains at the time of fabrication or by high through 

thickness strains during service, additive to the strains due to residual stress. Thicker plates are 

generally more prone to lamellar tearing. In tee, corner, or other cruciform welds, those 

fabricated with full penetration butt welds are most susceptible.

Joint design and detailing have a significant influence on the susceptibility of lamellar tearing. 

Suggestions to improve the performance of thick joints include: 

• Replacing full penetration welds with balanced fillet welds

• Replacing unbalanced welds with balanced welds

• Replacing large single-sided welds with balanced double-sided welds 

• Beveling the fusion boundary of the susceptible plate to reduce the through thickness 

effects 

These suggested improvements are depicted in Figure 7.2.4.2-1. 
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Figure 7.2.4.2-1 Recommended joint configurations to reduce the risk of lamellar tearing.

SECTION 7.3 FRACTURE CONTROL BY ENHANCED FABRICATION 

The second leg of the “three-legged-stool” Total FCP is implementation of supplemental 

fabrication requirements as defined in Clause 12 of the AASHTO/AWS D1.5 Bridge Welding 

Code (AASHTO/AWS, 2010). Clause 12 provides supplemental requirements for materials, 

workmanship, and fabrication processes to provide structures with limited but acceptable 

discontinuities such that fracture is effectively prevented throughout the expected service life. 

The AASHTO/AWS Clause 12 FCP is structured in such a way that members fabricated to and 

meeting its requirements are not expected to suffer failure due to brittle fracture during their 

operating life.

As described in Section 2.2, there are steel manufacturing and fabrication processes such as 

rolling, cutting, welding, and drilling that result in the creation of discontinuities in all fabricated 

steel structures. Although known cracks are not allowed to remain in a fabricated element, some 

discontinuities are always present. The susceptibility to fatigue and fracture is a function of the 

severity of the discontinuities and their location relative to applied tensile stresses. The FCP 

attempts to limit the size, frequency, and severity of these discontinuities. 

The fundamentals of fracture mechanics, previously discussed in Chapter 3, demonstrate that 

there is an interrelationship between a variety of factors including: material toughness; loading 

rate; in-service temperatures; the size, location, and orientation of discontinuities; and the levels 

of tensile stress that all combine to define regions of safe and unsafe behavior. The FCP 

recognizes this interrelationship and imposes minimum standards for materials and expectations 

on workmanship so that at the limits of each of these variables, a structure with a predictable and 

adequate reliability is provided. 
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The development of a fracture control plan, as well as national bridge inspection standards, can 

be traced to the collapse of the bridge at Point Pleasant, West Virginia (the Silver Bridge) in 

1967 (see Figure 7.1-1). As a result, the 1970’s saw rapid changes to engineering practice, 

including the introduction of CVN testing as a quality control measure for steel bridge 

fabrication and the introduction of modern fatigue design principles. The implementation of 

formal FCP’s began in 1978 with the publication of the Guide Specifications for Fracture 

Critical Non-Redundant Steel Bridge Members (AASHTO, 1978). This formalized the 

requirements for testing of materials in FCM’s as a quality control measure, and provided 

requirements for fabrication and shop inspection of FCM’s as unique and requiring special 

attention as compared to redundant members. The AASHTO requirements are no longer 

maintained in the Guide Specification format; rather they have now been fully incorporated in 

the ASTM A709 standard, the AASHTO LRFD Bridge Design Specifications, and in the 

AASHTO/AWS D1.5 Bridge Welding Code, Clause 12, entitled “AASHTO/AWS Fracture 

Control Plan (FCP) for Nonredundant Members.” The remainder of the D1.5 Bridge Welding 

Code focuses on requirements that apply equally for both fracture critical and non-fracture 

critical elements alike.

The provisions of the AASHTO/AWS FCP address items such as:

• Contract documents 

• Base metal requirements

• Welding processes

• Consumable requirements 

• Welding Procedure Specification (WPS)

• Certification and qualification

• As-received inspection of base metal

• Thermal cutting

• Repair of base metal

• Straightening, curving, and cambering 

• Tack welds and temporary welds 

• Preheat and interpass temperature control 

• Post-weld thermal treatments

• Weld inspection 

• Repair welding

• Attachments to FCM’s

Guidance in these areas is not unique to FCM’s; it applies to all steel structures. The purpose of 

AASHTO/AWS D1.5 Clause 12 is to provide more specific and/or stringent guidance in these 

areas for FCM’s.

The design engineer is responsible to indicate the presence of FCM’s in the contract documents, 

to specify the materials to be used in accordance with the agency policies, and is typically 

involved in the review and approval of shop drawings and associated fabrication procedures. The 

FCP provisions pertaining to material properties, fabrication, shop inspection requirements, and 

qualifications of shop personnel are typically addressed by owner / agency specifications. The 
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engineer must be familiar with these requirements and determine their suitability for a specific 

application. Occasionally, special provisions are required to amend an agency’s typical 

requirements. The combination of agency materials and fabrication specifications, along with the 

input and approval of the engineer during all phases, is essential to control the fabrication of 

FCM’s.

The AASHTO/AWS FCP also requires that FCM’s be noted in the contract documents, most 

typically on the design plans, and that this designation is required prior to bidding. The 

designation of FCM’s alerts all interested parties of the special attention required for certain 

elements of the structure. Prior to fabrication, it is common for shop drawings to be developed 

and reviewed. The shop drawings and supporting information regarding member fabrication will 

define: the materials chosen for member fabrication; specific welding processes; information on 

consumables to be used; and welding procedures. In addition, it may include information 

regarding the certification and qualification of specific individuals responsible for fabricating the 

FCM’s; will identify cutting procedures; and may include pre-approval of repair procedures in 

advance. The obligation of the engineer is to ensure that the various procedures intended for the 

fabrication of the FCM’s designated in the design documents are appropriate and allowed by the 

owner’s policy. 

7.3.1 Fabrication Controls 

Fabrication of FCM’s can only be done by shops possessing an intermediate or advanced 

certification through the AISC Certification Program Requirements for Steel Bridge Fabricators

(AISC, 2011) and possessing the additional fracture critical endorsement. This is done to limit 

the fabrication of FCM’s to those shops with the training and experience in fabricating FCM’s 

and with the ability to meet the AASHTO/AWS D1.5 requirements. 

FCM’s are fabricated from base metals such as those previously referenced in Table 7.2.3-2 that 

adhere to toughness, heat treatment, and other mechanical properties as required by the FCP. An 

inspection of the base metal is required prior to member fabrication. The edges and ends of 

plates are required to be cut by thermal cutting. This includes edges that have previously been 

mechanically rolled or sheared. Inspection of the prepared edges is required. Visual 

discontinuities are to be inspected using magnetic particle testing. Specific repair processes are 

called for when the base metal contains rejectable discontinuities outside the limits of the 

specification. The repair procedures can include rotating the base metal so that the discontinuity 

no longer lies within a joint, by thermal cutting to adjust the length of a specific plate, with 

welding to repair a specific location of damage, or in the extreme case by replacement with equal 

or better material.

FCM’s, like all welded steel members, are welded using only specifically approved welding 

processes, consumables, and in accordance with approved welding procedure specifications. The 

procedures for FCM’s are more stringent than for non-fracture critical members. Quality 

assurance inspection of the fabrication process is required to ensure compliance with the FCP. 

However, this does not relieve the fabricator from the obligation to follow the plan in its entirety. 

Shop quality assurance inspectors are required to be familiar with the nature of work and have 
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the authority to accept or reject materials and workmanship. In addition to visual inspection, 

NDT technicians are also required and subject to the certification requirements of the FCP.

The use of repair welding on FCM’s falls into two categories: noncritical and critical weld 

repairs based on the severity of the defect to be corrected. Repair welding to correct deficiencies 

in base metal or in previously deposited weld metal is permitted. The approval of repair 

procedures in advance is permitted before beginning the work in order to eliminate requiring 

specific approval at the time a particular discontinuity is discovered by inspection. Repair 

welding can also be used to build up previously deposited but insufficiently sized welds; to 

remove discontinuities, rollover, undercut, gouges, and laminar discontinuities; for the repair of 

base metal; and for other defects deemed noncritical. Whether noncritical or critical welding 

repair is performed, all repair welding is subject to inspection. Specific requirements are 

provided for the identification of unacceptable discontinuities, surface preparation, material and 

workmanship requirements, post-welding heat treatment, and final inspection and acceptance.

Procedures are specified for straightening, curving, and cambering fracture critical members. 

Cold bending of fracture critical members is allowed only with specific approval of the engineer. 

SECTION 7.4 FRACTURE CONTROL BY IN-SERVICE INSPECTION 

The third and final leg of the “three-legged-stool” Total FCP is provided by regular in-service 

inspections. Even if the design and fabrication requirements are followed and the bridge is 

performing as intended, there is always a chance that a crack could develop through fatigue or 

another anomalous scenario such as a truck impact or bearing freeze. In this case, we rely on the 

member to survive a short time until the next inspection occurs and the damage can be identified 

and repaired. 

Modern standardized bridge inspection practices trace their origins to the Federal-Aid Highway 

Act of 1968. Following the collapse of the suspension bridge at Point Pleasant, West Virginia in 

1967 (see Figure 7.1-1), the National Bridge Inspection Standards (NBIS) were established, and 

uniform rules for inspection, data collection, and reporting were developed and implemented in 

the coming years. Prior to 1968, there was no uniform standard for collecting and reporting 

bridge inspection data, though state initiated inspections were periodically performed. 

Subsequent legislation clarified what bridges were included in the inventory and have amended 

and made changes to the requirements periodically.

In 1983, the Mianus River Bridge collapsed, again focusing attention on bridges and their safety. 

This failure, related to corrosion and the eventual failure of a pin-and-hanger suspended span 

carrying I-95, triggered the requirement for hands-on inspection of fracture critical bridges as 

part of the Surface Transportation and Uniform Relocation Assistance Act of 1987. 

While some cracks may be detected during routine inspections, fracture critical inspections are 

unique in that they require the inspection team to be close enough to the member for it to qualify 

as “hands-on”; that is, the team must be close enough to the fracture critical components and 

members to touch the elements. The inspection is at a minimum a visual inspection but 
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commonly uses other nondestructive techniques such as dye penetrant, magnetic particle, or 

ultrasonic testing to assess the condition of the members. 

There are several requirements that are key to successfully inspecting bridges with FCM’s. These 

are detailed below. These requirements share many features with the protocols for inspecting 

routine bridges. The requirements for the qualification of inspectors, record-keeping protocols, 

inspection intervals, etc. come from 23 CFR 650 Subpart C. They are additionally detailed in 

publications such as the AASHTO Manual for Bridge Evaluation (AASHTO, 2015d) and the 

FHWA Bridge Inspector’s Reference Manual (FHWA, 2012a).

Understand Resource Requirements – A qualified team is required to administer and conduct the 

inspection. This includes staff working for the owner as a program manager as well as the field 

personnel. The program manager must have a Professional Engineer (PE) license or ten years of 

bridge experience and must have successfully completed a comprehensive bridge inspection 

course such as NHI “Safety Inspection of In-Service Bridges” (FHWA, 2012d) or equivalent. 

Team leaders are the individuals responsible for planning and executing the inspection. There are 

multiple paths to attaining this status, including combinations of education, experience, and 

successful completion of NHI or equivalent inspection training courses. The team leader is 

assisted by qualified inspectors and NDE technicians as required.

The type of access must be considered. In order to meet the hands-on requirements, various types 

of access equipment might be required. These include various types of commercially available 

bucket trucks, ladders, ground mounted access, the use of rope access climbing, and frequently a 

combination of these techniques to access specific elements of a bridge. The type of access 

depends on the geometry of the bridge, the type of available access equipment, cost, impacts to 

traffic for inspection, and local factors that are unique to most bridges. The team leader must 

work with the entire inspection team to plan the inspection in advance, given the complications 

of access.

The need for specialty equipment must also be assessed. Many inspection teams have the ability 

to perform simple nondestructive tests such as dye penetrant or magnetic particle testing. 

However, for more complex testing such as ultrasonic testing or field x-ray (radiography), a subconsultant and specialty testing firm are needed. This adds a level of coordination, cost, and 

complexity, but is sometimes required to determine the condition of certain FCM’s, to verify the 

limits of observed cracks, to conduct pin integrity tests, and for other purposes. 

FCM Identification – A copy of the design plans or as-built drawings should be available in the 

bridge inspection records. It is also helpful to have access to shop drawings to the extent that 

they are available. As part of planning the inspection, the team leader, with assistance from 

others, should review the design drawings, shop drawings, as-built plans, previous inspection 

reports, rehabilitation drawings, and any other pertinent information. All FCM’s should be 

designated prior to inspection. Additionally, for each FCM, the team leader should locate all 

fatigue sensitive details associated with the individual members. For instance, this could include 

noting the presence of welded attachments on certain FCM’s so they are specifically included in 

the field inspection. Specific attention should be paid to details categorized as AASHTO Detail 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.34 

Category D or lower in resistance, since these are most likely to be limiting factors to the 

remaining fatigue life of a steel bridge.

Develop Inspection Procedure – There are various factors that can impact the success of a 

fracture critical inspection. For instance, accurately locating cracks in a heavily deteriorated steel 

member may be difficult. Knowing the expected condition of the materials is therefore critical to 

the potential success of the inspection effort. Bridges frequently carry attached utilities. These 

can interfere with a hands-on inspection of certain elements. Inspectors will frequently encounter 

environmental concerns, such as lead paint and confined spaces, and have to work in all weather 

and element conditions, all of which complicate the inspection process. Bridges are frequently 

dirty, laden with debris near expansion joints, and can contain contaminants, such as bird or 

animal excrement, all of which serve as health and access hazards. Bridges frequently cross other 

roads, railroads, streams, and rivers, which pose a challenge for access and safety that must be 

considered by the inspection team. The complexity of an individual bridge and site conditions 

will dictate the method of access, the time required to complete the inspection, and the relative 

complexity of the work. A pre-inspection meeting with the team leader and the inspection team 

should be held in order to go over safety requirements in advance, to assign staff to the 

individual inspection teams, to document the required tools and procedures to be used, to discuss 

any unique NDE requirements, and to discuss the project in general. 

Prepare Follow-up Procedure – During or immediately following the inspection, the team leader 

should begin to identify any follow-up procedures based on the results of the inspection. These 

follow-up procedures could include a need for additional nondestructive testing, an updated load 

rating analysis, a remaining fatigue life analysis, the preparation of repair and rehabilitation 

plans, and in the most severe condition could result in recommendations to load restrict or 

permanently close a bridge. Any critical findings discovered during the inspection, or any 

inspection, must immediately be brought to the attention of the owner. 

Quality Control/Quality Assurance – The team leader is responsible for quality control (QC) and 

quality assurance (QA) of the inspection. During the actual inspection, the team leader should 

perform routine QC checks on the inspection findings of other inspection team members. The 

team leader should also refine or update the inspection procedures as the field work progresses in 

order to address changed conditions in the field or as it is found that more or less scrutiny is 

required for certain details. It is not uncommon to find details and conditions in the field that 

differ from the plans and even the prior inspection report. The team leader’s responsibility is to 

manage this change and properly document the updated conditions in the inspection report. The 

inspection team should observe and document how the conditions change from prior inspection 

cycles and based on a pattern of change predict the future maintenance and rehabilitation needs 

for the bridge. Examples of changed conditions could include crack growth from a prior cycle, 

new crack observations, assessment of the effectiveness of prior retrofits, and other similar 

observations that are related to the potential future life of the structure. It is not uncommon for 

changes to be made to structures that are not included on the design plans. Examples include 

utility attachments or field modifications that may negatively influence the fatigue or fracture 

characteristics of an existing steel structure. These should be noted in the field notes, 

photographed, sketched, and the bridge inspection and maintenance files updated accordingly. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.35 

Develop a Periodic Inspection Plan – Based on the findings of the inspection, the team leader 

should recommend an inspection interval for the structure. These intervals are frequently 24 

months (the maximum allowed by 23 CFR without exemption), but it is also not uncommon to 

require more frequent inspection intervals, particularly as deterioration or member damage is 

noted on the bridge. Special inspections are sometimes required for specific elements of the 

bridge that require more frequent observation. There are advantages and disadvantages to the 

same inspection team conducting the inspection of a bridge repeatedly. The advantages of course 

are familiarity and first-hand knowledge of how conditions have changed over time. There is 

also a perceived disadvantage as well, that being a potential relaxed attitude toward the structure 

having seen it so many times. Each agency should consider these possible outcomes when 

planning and staffing bridge inspection projects. 

Inspection Report – Following the completion of the inspection, a detailed inspection report is 

required. The inspection report generally contains four main components: a narrative, 

documentation support, an evaluation of the conditions, and recommendations. 

The narrative describes the approach to the inspection, identifies the fracture critical members, 

details the inspection procedures, provides an overall description of the bridge, as well as a 

detailed description of the FCM’s, and contains a summary and conclusions. The narrative 

frequently integrates other elements such as excerpts from the design drawings, photographs 

from the inspection, reports from nondestructive testing, sketches, and other field information or 

logs required to support the discussion in the project narrative. The narrative includes basic 

structure information such as overall photographs, information on the type of structure, the year 

it was built, the types of materials that were used to construct it, and any prior retrofit history. 

The narrative will frequently reference prior inspection reports and rehabilitation efforts. The 

individuals who perform the inspection, and their qualifications, will be detailed. A description 

of the scope of inspection, the means of access, and the types of routine and NDT equipment 

used should be provided. 

Photographs and sketches should be used to highlight the fracture critical members of the bridge 

and to describe the details in the context of AASHTO fatigue categories. Reporting this 

information in a consistent manner over multiple inspection cycles promotes completeness and 

repeatability and allows the owner and future inspection teams to assess changes over time. It is 

important to document the condition of the FCM’s and attached details. This is the fundamental 

reason for the detailed inspection.

An assessment of the overall condition of the structure should be provided with specific attention 

to how existing deficiencies affect the resistance or remaining life of the FCM’s. The inspection 

report should document the impact of existing deficiencies and prioritize these for future 

rehabilitation work. If any critical findings are presented in the inspection report, 

recommendations must be made to minimize the risk. A critical finding is a structural or safety 

deficiency that requires immediate follow-up inspection or action. Based on the observations of 

the inspector, and in consultation with the owner, a critical finding could result in a 

recommendation for additional inspection, an updated load rating, load posting, partial or full 

closure of the bridge, and immediate or long-term repairs. The experience of the inspection team, 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

7.36 

the team leader, and the owner are required to assess the critical finding and to determine an 

appropriate course of action. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.1 

CHAPTER 8 AASHTO FATIGUE-EVALUATION APPROACH

A methodology for fatigue evaluation of steel bridges is included in the MBE (AASHTO, 

2015d). A fatigue evaluation is not routinely performed with each rating of a steel bridge; it is 

generally performed only when the remaining fatigue life of an uncracked bridge is desired as 

input into operating decisions. For example, if redecking of a cover-plated girder bridge is 

planned, a fatigue evaluation may suggest that the cover-plate ends should be retrofitted to match 

the service life extension of the bridge from the redecking. 

The original fatigue-evaluation methodology as presented in the 1st Edition of the MBE included 

several levels of reliability of the evaluation: minimum, evaluation, and mean life. The first 

significant enhancements to this methodology are included in the 2015 Interim Revisions to the 

2nd Edition. A second evaluation life and a methodology for low fatigue-life bridges accounting 

for past successful performance were added based upon NCHRP Report 721 (Bowman et al., 

2012). 

In this chapter, the methodology is examined and illustrated. 

SECTION 8.1 IDENTIFYING THE NATURE OF CRACKING

As introduced in Chapter 4, fatigue damage is categorized as either load-induced or distortioninduced. 

8.1.1 Load-Induced Fatigue

8.1.1.1 General

Load-induced fatigue is that due to the in-plane stresses in the steel plates that comprise bridge 

member cross sections. These in-plane stresses are those typically calculated by designers during 

bridge design or evaluation. 

8.1.1.2 Determining Fatigue-Prone Details

Bridge details are only considered prone to load-induced fatigue damage if they experience a net 

tensile stress. Thus, fatigue damage need only be evaluated if, at the detail under evaluation: 

Equation 8.1.1.2-1 

where:

(Δf)tension = tensile portion of the effective stress range as specified in MBE

Article 7.2.2 (discussed in detail in Section 8.2.1) 

fdead-load compression = unfactored compressive stress at the detail due to dead load
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.2 

8.1.2 Distortion-Induced Fatigue

Fatigue life is not evaluated for distortion-induced fatigue. Distortion-induced fatigue is that due 

to secondary stresses in the steel plates that comprise bridge member cross sections. These 

stresses can only be calculated with very refined methods of analysis, far beyond the scope of a 

typical bridge design or evaluation. These secondary stresses are minimized through proper 

detailing.

A distortion-induced crack propagating from the web gap at a transverse connection plate not 

positively attached to a longitudinal connection plate is illustrated in Figure 8.1.2-1. 

Figure 8.1.2-1 Typical distortion-induced fatigue crack.

In new design, the transverse connection plate should be welded or bolted to the longitudinal 

connection avoiding the web gap. Detailing to minimize the potential for distortion-induced 

fatigue, such as connecting transverse connection plates for diaphragms and floorbeams to both 

the compression and tension flanges of girders, is specified in AASHTO LRFD Article 6.6.1.3 

(AASHTO, 2015b). 

For existing bridges, the transverse connection plate should be connected to the longitudinal 

connection plate by adding connection angles to each side of the plate. (Field welding is an 

option, but bolting is preferred.)

SECTION 8.2 REMAINING FATIGUE LIFE EVALUATION 

The evaluation methodology discussed herein is appropriate for bridges where fatigue cracking 

has not been visually detected. 

If fatigue cracking has already been visually detected, a more complex fracture-mechanics 

approach, as discussed in Chapter 3, is appropriate instead of the methodology presented herein. 

Further, the expense and trouble of a fracture-mechanics analysis may not be warranted. 

Generally, upon visual detection of fatigue cracking, the majority of the fatigue life has been 

exhausted and retrofitting should be initiated. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.3 

8.2.1 Estimating the Stress Range

The stress range, either measured or calculated, is the stress range due to a single truck in a 

single lane on the bridge, as specified in AASHTO LRFD Article 3.6.1.4.3 (AASHTO, 2015b). 

The stress range used for fatigue-life evaluation can be estimated in three ways:

1. Estimated from measured strains,

2. By direct application of AASHTO LRFD (AASHTO, 2015b), or 

3. Estimated from a truck-weight survey.

8.2.1.1 Quantifying Uncertainty: Partial Load Factors 

In determining the fatigue life, the uncertainty associated with the stress range, Rs, has two 

components: 

• Uncertainty associated with analysis, represented by the analysis partial load factor, Rsa

• Uncertainty associated with assumed effective truck weight, represented by the truckweight partial load factor, Rst

The product of these uncertainties is termed the stress-range estimate partial load factor, Rs. 

The partial load factors were adapted from the AASHTO Guide Specifications for Fatigue 

Evaluation of Existing Steel Bridges (AASHTO, 1990) and are summarized in Table 8.2.1.1-1. 

As uncertainty is removed from the evaluation by more refined analysis or site-specific data, the 

increased certainty is reflected in lower partial load factors. Uncertainty decreases as one moves 

down the rows of the table. Simplified and refined analysis are as defined in AASHTO LRFD

Articles 4.6.2 and 4.6.3 (AASHTO, 2015b), respectively. 
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8.4 

Table 8.2.1.1-1 Partial load factors: Rsa, Rst, and Rs. 

Stress-range Estimation

Methods

Analysis Partial Load

Factor, Rsa

Truck-Weight Partial 

Load Factor, Rst

Stress-Range Estimate 

Partial Load Factor, Rs

For Evaluation-1, Evaluation-2, or Minimum Fatigue Life

Section 8.2.1.2 -

simplified analysis, and 

truck weight per AASHTO 

LRFD Article 3.6.1.4

1.0 1.0 1.0 

Section 8.2.1.3 –

simplified analysis, and 

truck weight by truck 

survey or weigh-in-motion 

study

1.0 0.95 0.95 

Section 8.2.1.2 - refined 

analysis, and truck weight 

per AASHTO LRFD

Article 3.6.1.4

0.95 1.0 0.95 

Section 8.2.1.3 - refined 

analysis, and truck weight 

by truck survey or weighin-motion study

0.95 0.95 0.90 

Section 8.2.1.4 - fieldmeasured strains N/A N/A 0.85 

For Mean Fatigue Life

All methods N/A N/A 1.00

8.2.1.2 Application of the AASHTO LRFD Specifications

The effective stress range shall be estimated as: 

Equation 8.2.1.2-1 

where:

Rp = multiple presence factor defined below

Rs = stress-range estimate partial load factor specified in Table 8.2.1.1-1

Δf = factored calculated stress range due to the passage of the fatigue truck as 

specified in AASHTO LRFD Article 3.6.1.4 for the Fatigue II load 

combination of AASHTO LRFD Table 3.4.1-1 (AASHTO, 2015b) 

The multiple presence factor shall be calculated:
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.5 

for longitudinal members, as: 

5 6 0.0107 0.988 6.87 10 4.01 10 ( ) p PRESENT

L

R L ADTT

n

− − = +× +× +

Equation 8.2.1.2-2 

and for transverse members, as:

Rp = 1.0 

where:

L = span length (ft) 

(ADTT)PRESENT = present average daily truck traffic in both directions (trucks/day) 

(see Table 8.2.1.2-1) 

nL = number of striped lanes 

The multiple presence factor was developed as discussed in NCHRP Report 721 (Bowman et al., 

2012) for 2 ≤ nL ≤ 4 and 30 ft ≤ L ≤ 220 ft using the following assumptions. 

Table 8.2.1.2-1 Assumed (ADTT)PRESENT.

nL Assumed (ADTT)PRESENT

2 8,000

3 11,000

4 13,000

The commentary to MBE Article 7.2.2.1 states that the use of the multiple presence factor “may 

be justified outside of these ranges, but are not based on experimental evidence.”

The stress range may be calculated using simplified or refined analysis, as defined in AASHTO 

LRFD Articles 4.6.2 and 4.6.3, respectively; and the fatigue truck is as specified in AASHTO 

LRFD Article 3.6.1.4 factored in accord with the Fatigue II load combination of AASHTO LRFD

Table 3.4.1-1. 

8.2.1.3 Truck-Weight Survey

The effective stress range shall be estimated as: 

() () eff p s survey ∆= ∆ f RR f

Equation 8.2.1.3-1 

where:

Rp = multiple presence factor defined in Section 8.2.1.2

Rs = stress-range estimate partial load factor specified in Table 8.2.1.1-1

(Δf)survey = calculated stress range due to the passage of a fatigue truck determined by 

a truck survey or weigh-in-motion (WIM) study 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.6 

The stress range may be calculated using simplified or refined analysis, as defined in AASHTO 

LRFD Articles 4.6.2 and 4.6.3, respectively; and the fatigue truck is determined by a truck 

survey or WIM study factored in accord with the Fatigue II load combination of AASHTO LRFD

Table 3.4.1-1. 

8.2.1.4 Field-Measured Strains

The effective stress range may be estimated through field measurements of variable-amplitude 

strains at the fatigue-prone detail under consideration under typical traffic conditions. Field 

measurements of strains represent the most accurate means to estimate effective stress ranges at 

fatigue-prone details. Variable-amplitude stress-range behavior was previously discussed in 

Section 4.5.2. 

The effective stress range, (Δf)eff, shall be taken as the cube root of the weighted sum of the 

cubes of the variable-amplitude stress ranges from the measured strains, as given in:

( )

1

3 3 ( )eff s i i ∆ = Σ∆ fR f γ

Equation 8.2.1.4-1 

where:

Rs = the stress-range estimate partial load factor, calculated as RsaRst, unless otherwise 

specified

γi = percentage of cycles at a particular stress range

Δfi = the particular stress range in a field-measured stress-range histogram greater than 

45 percent (= 0.80/1.75) of the constant-amplitude fatigue threshold of the 

fatigue-prone detail

SECTION 8.3 ESTIMATING FATIGUE LIFE BY THE MBE

As introduced in Chapter 6, fatigue life is characterized as infinite or finite. The estimation of an 

existing bridge detail’s fatigue life, infinite or finite, is reviewed in this section.

8.3.1 Infinite-Life Check

Theoretically, a fatigue-prone detail will experience little or no fatigue damage during its 75-year 

design life if all of the stress ranges experienced by the detail are less than the constantamplitude fatigue threshold. Thus, the detail under evaluation is said to have infinite fatigue life. 

If:

max () ( )TH ∆ ≤∆ f F

Equation 8.3.1-1 

then the estimated fatigue life in years, Y, is infinite,
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.7 

where:

(Δf)max = Rp times the factored calculated stress range due to the passage of the 

fatigue truck as specified in AASHTO LRFD Article 3.6.1.4 for the Fatigue 

I load combination of AASHTO LRFD Table 3.4.1-1, or 

= 2.2 (Δf)eff when the effective stress range is calculated using a truck 

survey, WIM study, or measured strains with Rs = 1.0

(ΔF)TH = constant-amplitude fatigue threshold given in AASHTO LRFD Table 

6.6.1.2.5-3 

AASHTO LRFD previously assumed that the maximum stress range was twice the effective 

stress range. Thus, a multiplier of 2.0 was previously used in the equation for (Δf)max above, 

representing the previous Fatigue I load factor of 1.5 divided by the previous Fatigue II load 

factor of 0.75. 

The AASHTO Subcommittee on Bridges and Structures increased the Fatigue I and Fatigue II 

load factors to 1.75 and 0.8, respectively. Thus, the multiplier in the equation for (Δf)max above is 

2.2, which equals 1.75 divided by 0.8. It is unlikely that the maximum stress range during the 

design life of the bridge will be captured during a limited field-testing session; therefore means 

to extrapolate from the measured effective stress range to the maximum stress range must be 

used. When measured values are used to evaluate fatigue life, the multiplier in the equation for 

(Δf)max should be reconsidered based upon the discussion of Section 8.1.1. 

8.3.2 Finite Life

If the infinite-life check is not satisfied, the finite life of the detail may be estimated as described 

in this section.

Much scatter, or uncertainty, exists in experimentally derived fatigue resistance. For design, a 

conservative fatigue resistance is assumed at two standard deviations below the mean fatigue 

resistance or life. This corresponds to the minimum expected finite fatigue life for evaluation. 

Limiting actual usable fatigue life to this design life is very conservative and costly. As such, 

means of estimating evaluation fatigue lives and the mean finite fatigue life are also included in 

the MBE to aid the evaluator in the decision-making. 

Four levels of fatigue life may be estimated:

1. Minimum life (very conservative design life)

2. Evaluation 1 life (a less conservative life)

3. Evaluation 2 life (an even less conservative life)

4. Mean life (most likely life)

The resistance factors for fatigue life, given in Table 8.3.2-1, represent the uncertainty of the 

fatigue life of the various detail categories, A through E′. As the stress-range estimate grows 

closer and closer to the actual value of stress range, the probability of occurrence associated with 

each level of fatigue life approaches the values given in Table 8.3.2-2. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.8 

Table 8.3.2-1 Resistance factor, RR. 

Detail Category 

as defined in 

AASHTO LRFD

Table 6.6.1.2.3-1 

Minimum Life

RR

Evaluation 1 

Life

RR

Evaluation 2 

Life

RR

Mean Life

RR

A 1.0 1.5 2.2 2.9

B 1.0 1.3 1.7 2.0

Bʹ 1.0 1.3 1.6 1.9

C 1.0 1.3 1.7 2.1

Cʹ 1.0 1.3 1.7 2.1

D 1.0 1.3 1.7 2.0

E 1.0 1.2 1.4 1.6

Eʹ 1.0 1.3 1.6 1.9

Table 8.3.2-2 Probabilities of occurrence associated with levels of fatigue life. 

Level of Fatigue Life Probability of Occurrence

Minimum (Design) Life 98 percent

Evaluation 1 Life 84 percent

Evaluation 2 Life 67 percent

Mean Life 50 percent

MBE Article 7.2.5.1 gives an expression for estimating the total finite fatigue life of a fatigueprone detail, in years, based upon the selected level of life:

Equation 8.3.2-1 

where:

RR = resistance factor as given in Table 8.3.2-1

A = detail category constant as specified in AASHTO LRFD Table 

6.6.1.2.5-1 

n = number of stress-range cycles per truck passage

g = estimated annual traffic-volume growth rate in percentage 

a = present age in years

[(ADTT)SL]PRESENT = present ADTT in a single lane 

(Δf)eff = effective stress range

In lieu of better information, AASHTO LRFD Table 6.6.1.2.5-2 may be used to determine the 

number of stress-range cycles, n. Otherwise, it may be determined from influence lines or field 

measurements.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.9 

8.3.3 Example 

Determine the remaining fatigue life of the end weld of the cover plate of MBE Example A1 

(AASHTO, 2015d). Consider the transverse welds connecting the cover plate ends to the flange.

The flange thickness is 0.855 inches. 

The cover plate end weld is Detail Category Eʹ from AASHTO LRFD Table 6.6.1.2.3-1. 

Therefore, fatigue must be considered, as shown in the following computations. 

Therefore, since

the cover plate end weld does not have infinite life. 

Now more data is required. 

Assume g = 2 percent

Rs = 1.0 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.10 

For Detail Category Eʹ and:

RR = 1.0, therefore Minimum Life = 42 years 

RR = 1.3, therefore Evaluation 1 Life = 50 years

RR = 1.6, therefore Evaluation 2 Life = 57 years

RR = 1.9, therefore Mean Life = 63 years

Since the age of the bridge is already 48 years, it appears that retrofit or more evaluation is 

required to assure sufficient remaining life. Such additional evaluation is explored in Section 8.4. 

SECTION 8.4 REMAINING FATIGUE LIFE FOR “NEGATIVE REMAINING 

LIFE” BRIDGE DETAILS

8.4.1 General

Due to the conservative nature of fatigue design and evaluation, many times the calculated 

remaining fatigue life is determined to be negative, suggesting that the detail should have already 

cracked when it has not. The MBE addresses such cases through the Fatigue Serviceability Index, 

introduced with the 2015 interim revisions to the 2nd Edition of the MBE. 

8.4.2 Fatigue Serviceability Index, Q

MBE Article 7.2.6 defines the Fatigue Serviceability Index, Q, as a dimensionless measure of the 

performance of a structural detail, at a particular location in the structure, with respect to the 

overall fatigue resistance of the member, calculated as:

Y a Q GRI N

  − =    

Equation 8.4.2-1 

where:

Y = calculated fatigue life

a = present age of the detail, in years 

N = greater of Y or 100 years 

G = load path factor from Table 8.4.2-1
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.11 

R = redundancy factor from Table 8.4.2-2

I = importance factor from Table 8.4.2-3

Table 8.4.2-1 Load path factor, G. 

Number of Load Path Members G

1 or 2 0.8

3 0.9

4 or more 1.0

Table 8.4.2-2 Redundancy factor, R. 

Type of Span R

Simple 0.9

Continuous 1.0

Table 8.4.2-3 Importance factor, I. 

Structure or Location I

Interstate highways, major arterial state 

routes, or other critical routes 0.9 

Secondary arterials or urban areas 0.95

Rural roads or low ADTT routes 1.0

The load path, redundancy, and importance factors reflect risk and modify the Fatigue 

Serviceability Index much as the load modifiers of AASHTO LRFD Article 1.3.2.1 modify loads. 

MBE Article 7.2.6.2 suggests that the Fatigue Serviceability Index may be used as a guide for 

inspection or preservation actions but provides no guidance as to acceptable index values. The 

commentary to MBE Article 7.2.6 states that Q varies between 1.0 and 0.0. Clearly, a negative 

value of Q, suggesting a negative remaining fatigue life, is not acceptable.

The NCHRP project (Bowman et al., 2012) which originally proposed the Fatigue Serviceability 

Index as a guide for actions suggests the actions in Table 8.4.2-4 as a function of Q. This table 

was proposed to AASHTO, but not adopted. It is provided here only for guidance on acceptable 

index values from the researchers who developed the index, Q. 

Table 8.4.2-4 Fatigue Serviceability Indices and suggested actions. 

Fatigue Serviceability Index, Q Suggested Action

1.0 to 0.2 Continue regular inspection

0.19 to 0.10 Increase inspection frequency 

0.09 to 0.0 Assess frequently

< 0.0 Retrofit, replace, or reassess
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.12 

8.4.3 Strategies to Increase the Fatigue Serviceability Index

8.4.3.1 General

The Fatigue Serviceability Index can be increased by rational modification of the factors 

included in its calculation or through retrofit of the detail. 

8.4.3.2 Refined Calculation

8.4.3.2.1 Accepting Greater Risk

Traditionally, Evaluation 1 Life has been used in determining remaining fatigue life, with a 

probability of occurrence of 84 percent, as discussed in Section 8.3.2. If the detail under 

evaluation has already experienced a long successful fatigue life, bridge-specific factors such as 

a high degree of redundancy and/or a decreased inspection interval may suggest that the 

evaluator accept greater risk in the fatigue assessment. As such, the Evaluation 2 Life or Mean 

Life could be used in the determination of remaining life. 

8.4.3.2.2 Using More Accurate Data

A more accurate estimate of the fatigue life refines the Fatigue-Serviceability-Index calculation. 

Sources of improvement of the fatigue-life estimate include:

• Field measurement of the stress ranges to determine the effective stress as discussed in 

Section 8.2.1.4, 

• More refined analysis to determine the effective stress,

• Weigh-in-motion data to determine the fatigue truck as discussed in Section 8.2.1.3, or 

• Site-specific ADTT counts.

8.4.3.2.3 Using a Truncated Distribution

In MBE Article 7.2.7.2.3, the MBE acknowledges a negative remaining fatigue life or Fatigue 

Serviceability Index. The equation below estimates the mean, evaluation, and minimum fatigue 

lives based upon truncating the distribution when no fatigue cracking is evident. 

( ) 1 0.73 1 0.27 2.19 x PP Y Ye mean

− Φ −+−     ′ =

Equation 8.4.3.2.3-1 

where:

Ymean = mean fatigue life before updating

Φ-1 = inverse of the standard normal variable's cumulative probability function 

x = variable based upon the fatigue life being updated 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

8.13 

= 0.039 for Minimum Life 

0.074 for Evaluation 1 Life

0.12 for Evaluation 2 Life

0.18 for Mean Life

P = probability of fatigue life being shorter than current age before updating 

0.27

2.19

0.73

mean

a Ln

Y

P

        +

  = Φ

 

Equation 8.4.3.2.3-2 

where:

a = present age in years

Φ = standard normal variable's cumulative probability function 

The standard normal variable's cumulative probability function and the inverse of the standard 

normal variable's cumulative probability function are commonly included in commercial 

spreadsheets.

The fatigue life of a structural detail is typically characterized by a lognormal distribution, as 

shown in Figure 8.4.3.2.3-1. When the estimated life using Section 8.3.2 is smaller than the 

present age, the remaining life becomes negative as illustrated. In this situation, if field 

inspection reveals no cracking, the estimated life is overly conservative. 
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8.14 

Figure 8.4.3.2.3-1 Probability density function of fatigue life and estimated life. 

The equation for updated life is based upon: 

• The lower tail of the total life distribution truncated up to the present life 

• The eliminated probability P computed 

• The resulting probability density function divided by (1 – P) to ensure that the total 

probability under the distribution curve remains 1.0 

Then the updated life is determined to maintain the same reliability level for fatigue life 

distribution as illustrated in Figure 8.4.3.2.3-2.
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Figure 8.4.3.2.3-2 Truncated probability density function of fatigue life and updated life.

8.4.3.2.4 Example 

Update the calculated remaining fatigue life of the end weld of the cover plate of the example in 

Section 8.3.3. 

The cover plate end weld is Detail Category Eʹ from AASHTO LRFD Table 6.6.1.2.3-1. 

Ymean = 63 years

a = 48 years

Calculate an updated Evaluation 2 Life. 

x = 0.12 for Evaluation 2 Life
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8.16 

The remaining life is now 64 – 48 = 16 years.

8.4.3.3 Retrofit

If the updated Fatigue Serviceability Index is not acceptable, the fatigue life may be increased by 

retrofitting the critical detail to improve the detail category, as discussed in Chapter 9. This 

strategy increases the Fatigue Serviceability Index when further enhancement of the calculated 

Fatigue Serviceability Index, through more accurate estimates, is no longer possible or practical. 
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9.1 

CHAPTER 9 ASSESSMENT, REPAIR, AND RETROFIT OF STRUCTURES

In addition to analyzing, designing, and evaluating for fatigue and fracture, it is often necessary 

to assess damage and provide repair and retrofit for steel bridge structures. This chapter provides 

a general summary of some common fatigue details (i.e., details for which care and assessment is 

required to ensure that the design satisfies fatigue requirements). It should be noted that more 

detailed information about the repair and retrofit of structures for fatigue and fracture is provided 

in the Manual for Repair and Retrofit of Fatigue Cracks in Steel Bridges (Dexter and Ocel, 

2013). This reference provides a wealth of information that is not repeated in this chapter. 

SECTION 9.1 COMMON FATIGUE DETAILS

Details that may be subject to fatigue cracking may exist on a variety of bridges, such as girder, 

frame, truss, or arch superstructure configurations. In addition, they may also exist on 

substructure components. 

Fatigue details are most commonly encountered on older bridges that were constructed prior to 

the mid-1970’s2

 and/or on bridges that lacked proper quality control (QC) measures. As 

described in Chapters 6 and 7, AASHTO provides design requirements for fatigue and fracture to 

prevent the problems described in this chapter. Therefore, steel bridges constructed in the 

modern era using AASHTO fatigue specifications and using proper QC generally do not exhibit 

these fatigue problems. However, since many pre-1970’s bridges remain in service, the issues 

described in this chapter must still be considered when assessing older bridges. 

The fatigue performance of steel bridges reveals that the majority of cases of fatigue damage 

which have been reported for highway and railway bridges are caused by secondary load effects 

not considered during design. In most cases, unforeseen interaction between different members 

and load-carrying systems in the bridge, often combined with details exhibiting low fatigue 

resistance, have been the cause of fatigue cracking in bridge details. In some cases, a complex 

stress state may also exist in structural details which is neglected in the traditional line-girder 

design method and which may have been considered by the designer. The basic mechanism 

behind most types of fatigue cracking caused by secondary effects is an applied out-of-plane 

distortion generated by the displacement compatibility of adjacent girders as the truck passes

over the bridge, creating a cyclical stress.

A common feature in many details which have experienced fatigue cracking is that they 

incorporate an abrupt change in stiffness, frequently in unstiffened web gaps where the applied 

distortion is concentrated. This often results in high local stresses which might eventually lead to 

fatigue cracking in the detail. The most common types of distortion-induced fatigue damage can 

 

2 The fatigue provisions that are used in design today were largely adopted in 1974 and have been modified little 

since then, so an exact date cannot be defined because there is always a lag between AASHTO adoption and 

implementation by individual states. However, any bridge constructed in 1974 and before will have poor fatigue 

details, and bridges constructed between 1975 and 1979 may or may not have poor fatigue detailing.
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9.2 

be found in the connections between stringers and transverse elements, between transverse 

elements and longitudinal girders, and at the connections of diaphragms and cross-frames.

In addition to the details described above, low fatigue resistance can also be present in elements 

with coped ends (most significantly at copes with small radii) and cut-short flanges, at 

connections between girder welded splices, at repair plates that have been welded perpendicular 

to the primary live load stress, and in riveted structures that employed tack welds to hold plates 

in position during fabrication and erection. Each of these fatigue details is most prevalent in 

bridges constructed prior to the mid-1970’s. 

A few of the more common details and bridge elements requiring careful attention for fatigue are 

described in greater detail in the following sections. It should be noted that problems with these 

details are generally not encountered on bridges constructed in the modern era using proper QC 

measures. 

9.1.1 Web Gaps Associated with Out-of-Plane Bending

Out-of-plane bending occurs when a member is loaded such that it twists about its longitudinal 

axis. Bridge members are normally designed to resist axial tension or compression, shear, or inplane bending. However, when the bridge is loaded unsymmetrically about its longitudinal axis 

(e.g., due to a heavy truck in a curb lane), the girders do not deflect equally, and the bridge twists 

about its longitudinal axis. Local out-of-plane bending can occur at the connection of the crossframes to the girders and at the unsupported web in the gap between the connection plate 

termination and the web-to-flange weld.

A common source of out-of-plane bending is the connection between transverse elements (e.g., 

floorbeams, cross-frames, or diaphragms) and the main longitudinal girders. When the transverse 

elements deflect or rotate, they cause out-of-plane bending and distortion in the main 

superstructure members, as illustrated in Figure 9.1.1-1. Rotation, θ, of the transverse elements 

causes out-of-plane bending in the longitudinal elements, which in turn results in a lateral shift, 

Delta (∆), in the web gap when there is not a positive connection between the plate and the 

flange. 
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Figure 9.1.1-1 Out-of-plane bending at connection between floorbeam and girder.

The web at the end of the gap is restrained from rotating by the connection plate below the gap, 

as well as by the concrete deck holding the top flange in place above the gap. This semi-flexible 

connection is commonly referred to as a “web–gap” detail. As illustrated in Figure 9.1.1-1, the 

web gap is frequently in the range of 3⁄4 to 1 inch between the end of the connection plate and the 

longitudinal element. The resulting out-of-plane bending is distortion-induced rather than loadinduced, and it can occur in welded or riveted members. For a given rotation of the floorbeam, a 

smaller web gap results in larger web stresses.

Out-of-plane, lateral bending of the flanges occurs in skewed bridges with staggered floorbeams, 

diaphragms, and cross-frames due to the differential deflection between the girders, as illustrated 

in Figure 9.1.1-2. When contiguous cross-frames are used, flange deformations are reduced but 

cross-frame forces become greater. If a gap exists at the end of the stiffeners connecting the 

cross-frames to the girders and if the connection plate is not connected as required in the current 

specifications, the large cross-frame forces may introduce cracking in the web gap. 
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9.4 

Figure 9.1.1-2 Out-of-plane bending due to differential deflection in skewed bridges.

Another common location for out-of-plane bending is at lateral bracing. For many years, lateral 

bracing was required by AASHTO and owners as a permanent wind bracing system for the 

bottom flange. Primary live loads from trucks cause the lateral bracing to vibrate up and down at 

its midpoint, as well as to lengthen and shorten as it participates in resisting live load forces. This 

combined movement due to vibration and lengthening bends the gusset plate about its mid-plane 

and alternately “pushes and pulls” on the web plate. 

9.1.2 Fatigue Considerations for Welds 

Welds on bridges that were designed after the mid-1970’s and that employed proper QC 

measures generally do not experience significant fatigue issues. However, older bridges with 

intersecting welds, longitudinal stiffener butt welds, field welds, or intermittent welds may be 

susceptible to fatigue cracking.

Intersecting welds are defined as welds that run through each other, overlap, touch, or have a gap 

between their toes of less than 1⁄4 inch. A common location of intersecting welds is the detail 

where transverse stiffeners and longitudinal stiffeners intersect, as illustrated in Figure 9.1.2-1. 

Any narrow gap between the longitudinal plates and transverse plates is likely to have a high 

stress concentration. The intersections of horizontal and vertical weld attachments are fatigue 

details and can be the source of constraint-induced fracture. 
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Figure 9.1.2-1 Gap in welds at intersection of transverse and longitudinal stiffeners.

A similar detail occurs at gusset plates for lateral bracing framing into the web at a transverse 

stiffener. The gusset plate conforms to the strain in the web and acts like a short flange connected 

to the web. If the gusset plate is interrupted at the transverse stiffener, a crack may form in the 

gap between the gusset plate and the stiffener, as shown in Figure 9.1.2-2. Modern bridge design 

requires that the lateral system is connected directly to the girder flange with bolts. 
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9.6 

Figure 9.1.2-2 Crack at bottom lateral connection plate.

Another common fatigue detail is longitudinal stiffeners extended the full length of the bridge 

into tensile regions where they were not required for strength. These full-length longitudinal 

stiffeners were often butt spliced using welds with no preparation or quality control, often 

resulting in lack of fusion. Fatigue cracks propagated from the lack of fusion, severing the 

longitudinal stiffener and creating an edge crack into the web with a length equal to the stiffener 

width. Although the welded joints were located in regions of relatively low bending stress, large 

cracks developed after the stiffener weld fractured and propagated under relatively low stress 

ranges. Figure 9.1.2-3 shows an example of a fracture emanating from a stiffener butt joint. 
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Figure 9.1.2-3 Fracture from longitudinal stiffener splice.

In addition to intersecting welds and longitudinal stiffener butt welds, field welds on older 

bridges must also be assessed for fatigue. Field welds are often used with patch plates or splice 

plates to repair corroded areas, to add strengthening components (e.g., to repair corrosion 

damage), and to correct fabrication errors. Sometimes steel patch plates or splice plates are field 

welded to those areas of reduced section to increase the total (or static) strength. However, these 

repairs can be ineffective since the welds may be perpendicular to primary stresses, creating 

Category D or E fatigue details with what used to just be base metal (a Category A detail). The 

chemistry of older steels used in riveted construction was often not suitable for welding, and this 

often led to welds and heat-affected zones with low toughness and fracture susceptibility. 

Intermittent welds can also be fatigue details since they contain a series of partial length welds, 

and the start and finish of each partial weld can be considered as a fatigue initiation point. 

Between the late 1950’s and the early 1970’s, intermittent welding, or stitch welding, was often 

used to connect bridge members. Analysis showed that the stitch welds provided the required 

strength and that continuous fillet welds were not required. However, the intermittent weld ends 

resulted in multiple fatigue initiation locations, and the practice of stitch welding of bridge 

members was discontinued by the mid-1970’s. Many bridges with intermittent welds, however, 

are still in service.

In addition to the fatigue cracking in welds described above, Figure 9.1.2-4 shows a fatigue crack 

that initiated at a tack weld in a riveted structure. Tack welds were commonly used to hold 
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9.8 

individual elements of a member together as final riveting was completed. Tack welds are 

common and were widely used for decades in the construction of riveted or bolted built-up 

members. A tack weld would be considered as a Category E detail if the provisions of the 

AASHTO LRFD specifications were used in their evaluation. However, many times tack welds 

are not significant enough to constitute structural welds. Given their widespread use in flexural 

and tension members alike, owners have been faced with the challenge of whether to remove 

what can be thousands of individual tack welds from a large structure in order to alleviate a 

potential crack initiation site. Research at Purdue University determined that tack welded riveted 

members, when tested, performed better than the Category C design curve. Therefore for 

evaluation, tack welds can be considered as a Category C detail. The prior Category E rating was 

considered too severe. Clarifying language has been provided in the MBE. The tack welds 

studied in the NCHRP 721 project varied but were in the range of 1 to 2 inches in total length 

(Bowman et al., 2012). 

Figure 9.1.2-4 Fatigue crack at toe of tack weld. 

Figure 9.1.2-5 shows a fracture that started at an incorrectly located hole that was welded. This 

resulted in a large lack of fusion and the resulting fracture. The modern remedy for this problem 

is to fill the hole with a properly tightened high-strength bolt, resulting in a hole with a fatigue 

resistance comparable to Category B.
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Figure 9.1.2-5 Fracture from welded hole.

9.1.3 Welded Cover Plates

A cover plate is defined as a welded plate generally used in conjunction with a rolled structural 

shape that increases the shape’s flexural resistance by providing additional flange section. Cover 

plates usually extend over a limited length of a beam, as shown in Figure 9.1.3-1. The use of 

welded partial length cover plates on rolled beams was popular with designers in many states 

from 1940 to 1970, but they are seldom used in modern bridge designs. Partial length cover 

plates minimize the amount of structural steel required, since a simply supported steel beam 

experiences higher bending stresses at midspan where the plate is utilized. Partial length cover 

plates are also used in continuous spans in regions of maximum positive moment and maximum 

negative moment. 
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Figure 9.1.3-1 Fatigue crack at end of welded partial length cover plate.

After cover plates were in service and were inspected, it became apparent that the termination 

point of welded cover plates was a fatigue detail where cracks could initiate. The cracks occur 

because of fatigue problems associated with the stress concentration at a sudden change in 

section, combined with the inherent residual stresses at the end of a welded plate. Cover plates 

were fabricated and attached in a variety of styles, all of which have low fatigue resistance. 

To improve this fatigue detail, several attempts were made to lessen the chance of crack 

propagations in partial length cover plates. For example, some cover plates were tapered or 

rounded to reduce stress risers. Others were widened to reduce stress risers. However, each of 

these conditions still resulted in low fatigue resistance. The only successful means of improving 

the fatigue resistance of cover plates was to terminate the cover plate with a bolted connection 

during fabrication. The current AASHTO LRFD specifications recognizes the superior fatigue 

resistance of end-bolted cover plates. 

However, many existing bridges still have welded cover plates rather than end-bolted cover 

plates. On these bridges, fatigue cracks normally initiate at the weld toe and then propagate into 

the flange. The crack front develops a subsurface thumbnail or half penny shape as it propagates 

through the flange until reaching the inside surface. A fatigue crack at the end of a cover plate 

moving into the flange and web is shown in Figure 9.1.3-1 and is illustrated in Figure 9.1.3-2. 

When the fatigue crack has grown to a critical size and stress intensity, then fracture occurs. 
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Figure 9.1.3-2 Crack at end of cover plate propagating through the flange and into the web.

The progression of a fatigue crack at a cover plate without an end weld is shown in Figure 9.1.3-

3. The crack initiates at the termination of the weld and grows into the flange as an ellipticalshaped crack. Once the crack propagates through the flange, it grows as a two-end crack and then 

finally as a single-ended crack when the crack reaches the flange tip. The roughness of the 

fracture surface is an indication of the crack propagation rate. The greater the surface roughness, 

the faster the crack is propagating. After the crack reaches the flange tip and becomes singleended, the stress intensity at the crack tip more than doubles, causing the increase in propagation 

rate.
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9.12 

Figure 9.1.3-3 Crack at end of cover plate without an end weld.

It should be noted that many of the fatigue details described above are no longer commonly used 

in bridge design. However, they may still be present on existing bridges designed prior to the 

mid-1970’s and must therefore be considered when assessing bridges for fatigue issues. 

SECTION 9.2 REPAIR STRATEGIES

If fatigue-related problems are encountered in the field (most commonly on older bridges), then a 

repair strategy must be employed to rectify the problem and to help prevent additional problems. 

While the specifics of the repair strategy are dependent upon the specific nature of the detail and 

problem, there are several general repair and retrofit strategies that are common for most fatigue 

details. These general strategies are described in the following sections.

9.2.1 Understand the Source of Cracking

Before designing any repairs or retrofits, the first step must always be to understand the source of 

the crack. Without such an understanding, the proper repair or retrofit cannot be determined with 

any degree of certainty that it will successfully solve the problem. In addition, without such an 

understanding, any unsuitable repairs or retrofits may result in even worse problems. Therefore, 

it is essential that repairs and retrofits are not pursued until there is an understanding of why, 

how, and when the crack formed. 

9.2.1.1 Assessment of Fatigue-Driven or Fracture-Driven

A first step in understanding the source of cracking is to assess whether the cracks are driven by 

fatigue or fracture. In some cases, this can be accomplished visually based on the detailing and 

crack path. In other situations, however, the crack must be cored to assess the presence of fatigue 

striations or cleavage fracture. A memorandum issued by the Federal Highway Administration 

(FHWA) on July 10, 2001 suggests that, for some details in tension zones that are found to be 

cracked based on inspection, the cracks should not be assumed to be fatigue-related, and cores of 

the fracture surface should be removed and analyzed for evidence of brittle fracture (FHWA, 

2001). 
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9.13 

If the crack is determined to be fracture-driven, then a bolted repair is typically used. All similar 

details that may also be susceptible to cracking must also be assessed. If the cracks are identified 

to be formed in a brittle mode, then an immediate safety evaluation of the structure should be 

performed and the potential need for bridge closure should be assessed. In addition, the urgency 

of this evaluation increases during periods of cold service temperatures. 

If the crack is determined to be fatigue-driven, then the next step is to assess whether the crack is 

load-induced or displacement-induced. Such as assessment is critical in evaluating the suitability 

of drilling a hole in the crack tip. Drilling of holes should not be considered a universal solution 

to repair of fatigue cracks.

9.2.1.2 Assessment of Load-Induced or Displacement-Induced

Several strategies can be employed when seeking to understand if the crack is load-induced or 

displacement-induced. A first step, if it has not already been completed, is to inspect the bridge, 

focusing on fatigue details and locating any fatigue cracks. If one particular detail has cracked, it 

is highly likely that other similar details may have also cracked. A keen eye can be the best tool 

in finding fatigue cracks, looking either for open cracks or for rust staining or discoloration as 

evidence that oxidized material is bleeding from an existing crack. In addition, two common 

nondestructive techniques used to expose cracks are dye penetrant and magnetic particle 

inspection. When fatigue cracks are encountered, the crack should be carefully measured and the 

specific detail should be thoroughly documented. 

In addition, another important step in determining the source of cracking is to understand the 

geometry of the bridge and how it affects system behavior of the bridge. In some cases, a 

computer model of the entire bridge may need to be created to better understand the global 

behavior of the bridge. This is especially applicable for skewed and/or curved steel bridges. 

A common strategy for understanding the source of cracking is to apply instrumentation to 

common details in the bridge. Strain gauges provide an effective way to measure stress ranges on 

steel bridges, and they can be applied to a variety of structural components, including girder 

webs and flanges. Weldable strain gauges are shown in Figure 9.2.1.2-1. These strain 

measurements should be compared with the calculated stresses to evaluate if the analytical model 

can be used to predict further cracking at the measured location and at similar locations on the 

bridge. 
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9.14 

Figure 9.2.1.2-1 Weldable strain gauges applied to a steel bridge member.

As an alternative, displacement measurements can provide a quick and cost-effective strategy in 

many instances, primarily for benchmarking displacements to a computer model, or assessing the 

effectiveness of a stiffening retrofit for distortion-induced cracking. Displacement measurements 

can be obtained using either dial gauges or linear variable differential transformers (LVDT). 

In conjunction with instrumentation, load tests can be performed with heavily loaded trucks of a 

specified weight and axle configuration. The trucks cross the bridge at a slow rate, patterning the 

truck locations to obtain the worst effect, and the resulting stress ranges are documented and 

compared with the fatigue limits for the various details being investigated. It should be noted that 

the fatigue stress ranges and thresholds presented in AASHTO LRFD are based on nominal 

stresses at the detail. If strain gauges are placed near the weld, the local stress concentration will 

increase the stress above the nominal value, leading to a conservative estimate of fatigue 

resistance. 

The assessments described in this section can be used not only to determine the source of 

existing cracks but also to predict the remaining life until cracks may develop at other locations. 

9.2.2 Design Repair Detail

After the source of the fatigue crack has been determined, the repair detail can be designed. The 

selected repair detail is a direct function of the specific fatigue detail, the fatigue crack source, 

and the crack length. 

Various repair and retrofit methods are described in considerable detail in the Manual for Repair 

and Retrofit of Fatigue Cracks in Steel Bridges (Dexter and Ocel, 2013). For guidance in 

determining the most suitable repair detail and understanding the various requirements of each 

repair detail, this reference provides a wealth of information that is not repeated in this chapter.
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9.15 

For example, for surface treatments of weld toes with shallow cracks originating from the 

surface, the following fatigue mitigation methods are available:

• Grinding (disc grinding or burr grinding) 

• Gas tungsten arc (GTA) remelting

• Air hammer peening

• Ultrasonic impact treatment (UIT)

Similarly, for out-of-plane distortion, the following repair methods are available: 

• Hole drilling

• Diaphragm or cross-frame removal

• Diaphragm repositioning 

• Bolt loosening 

• Web-gap stiffening (welded attachment, bolted connections, hybrid connections, 

adhesives, or nails) 

• Web-gap softening (gross material removal or large hole retrofit)

For each repair and retrofit method, it is important to understand the limitations of application, 

the required equipment, the various procedures, and any follow-up recommendations. A work 

plan should be developed for each repair detail, as illustrated in Figure 9.2.2-1, before 

commencing any field work.
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9.16 

Figure 9.2.2-1 Work plan to retrofit tie girder/floorbeam connection cracking.

Depending on the complexity and cost of the specific retrofit, it may be appropriate to apply the 

retrofit method to all similar details with similar loading on a bridge, even if they do not exhibit 

any fatigue cracks. This may prevent future problems with similar details. However, if the 

analytical model indicates the stress ranges at the other locations are below the threshold for 

crack extension, it may be appropriate to do nothing in terms of repair or retrofit. 

9.2.3 Validate Repair Detail

The repair process is not complete until the repair detail has been validated. This step is essential, 

regardless of whether the repair detail is being applied to all similar details on a bridge or 

whether a decision has been made to do nothing in terms of retrofit. Either way, validating that 

the correct action was taken is essential.

Two key components of this final step are ongoing inspections and instrumentation. After the 

work on the bridge has been completed, the details that were repaired or retrofitted should be 

inspected to verify that the work was accomplished successfully and to note any changes in the 
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9.17 

fatigue crack. In addition, a plan should be established for future inspections of the repair or 

retrofit. This plan should include a prescribed frequency of inspection, drawings showing the 

specific locations of the repair details, a detailed procedure for inspecting the repair details, and 

an ongoing log of field measurements associated with the specific fatigue crack or fatigue detail.

In addition, after the work on the bridge has been completed, the instrumentation that was 

performed to assess the most appropriate repair detail should be repeated. The various strain and 

displacement values that were documented before the repair should be documented once again 

after the repair has been completed to help validate the success of the specific repair and to 

establish a benchmark for future documentation of instrumentation findings. A plan should also 

be established for future instrumentation. This plan should include a prescribed frequency of 

instrumentation, drawings showing the specific types and locations of instrumentation, a detailed 

procedure for instrumentation, and an ongoing log of instrumentation findings. Significant 

changes in the instrumentation findings should trigger a more in-depth assessment of the repair 

details. 

SECTION 9.3 SPECIAL TOPICS

9.3.1 Constraint-Induced Fracture

In Section 7.1.4.1, the concept of constraint-induced fracture (CIF) is illustrated, specifically 

with reference to the Hoan Bridge that fractured in 2001. In response to that fracture, FHWA 

issued a memorandum on July 10, 2001 to the states to highlight the problem and to suggest 

some remediation measures (FHWA, 2001). Since this memorandum was published, AASHTO 

has taken action to include CIF as a design consideration in AASHTO LRFD. Specifically, welds 

should be spaced with a minimum 1-inch gap so as not to intersect. While this may be 

appropriate for new design, research after 2001 has found that the critical distance for causing 

CIF is when the welds come within 0.25 inches or less, as described in Section 7.1.4.1. 

Therefore, for the assessment of existing bridges, the 0.25-inch rule may be used, as this is not 

outlined in the 2001 FHWA memorandum nor published in the MBE. 

Possible corrective measures may include grinding or drilling away welds to remove the 

intersecting condition to at least meet the 0.25-inch criterion. Additionally, holes can be drilled 

above and below the intersecting weld that would effectively capture any fracture between the 

holes if it were to form. 

9.3.2 Over-Height Vehicle Collisions

In addition to the fatigue details previously described in Section 9.1, a vehicle or vessel collision 

with a steel girder superstructure could also cause significant damage to a bridge (see Figure 

9.3.2-1). Overpass bridges which cross over an interstate, for example, can be subjected to overheight vehicle collisions. Special loads or oversized loads may exceed the provided vertical 

clearance, and similarly, a bridge over a navigable waterway could also be hit (Chavel and 

Yadlosky, 2011).
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9.18 

Figure 9.3.2-1 Damage to a steel bridge girder due to an over-height vehicle collision.

A common method of repair for over-height vehicle collisions is heat straightening. Repair and 

retrofit using heat straightening is described in considerable detail in Heat Straightening Repairs 

of Damaged Steel Bridges, A Technical Guide and Manual of Practice (Avent and Mukai, 1998). 

As described in this reference, primary keys to a successful repair are: (1) selecting the heating 

patterns and sequences, (2) controlling the heating temperature and rate, and (3) controlling the 

applied restraining forces during repair. 

Similar to the steps described in Section 9.2, repair and retrofit for over-height vehicle damage 

should generally include assessment of the degree of damage (particularly an examination of 

cracking at the collision location and at the toes of adjacent attachments such as cross-frames) 

and review of heating patterns, temperature control, and any jacking plans submitted by the 

repair contractor. In addition, the supervision of repairs should include monitoring the 

temperature, controlling the restraining forces, reviewing the proposed heating patterns, and 

checking geometric tolerances after straightening is completed.

Based on research from NCHRP Report 604 (Connor et al., 2008), it is recommended that the 

number of heat straightening repairs at a specific location be limited to two. Research has 

demonstrated that, after the third damage and repair cycle, there is a substantial decrease in the 

fatigue life at some details, along with a decrease in the base metal fracture toughness where the 

impact occurred.

Lastly, it is often found that impact damage may cause actual brittle fractures in the vicinity of 

the impact location. Generally, this does not mean the base metal is inadequate, but it is due to 

dynamic loading produced during the vehicle impact. Chapter 2 explained that the fracture 

toughness of steel is related to loading rate and temperature. Additionally, the AASHTO Charpy 

V-notch (CVN) requirements were established based on a temperature shift concept that equates 

the results from a dynamic Charpy impact toughness to that of a static fracture toughness at an 

intermediate loading rate since bridges are typically not loaded at true dynamic rates. When a 

bridge is struck by an over-height vehicle, this assumption is no longer valid because the bridge 

is being impacted at a true dynamic rate. Therefore, the AASHTO CVN toughness requirements 

would not be sufficient to prevent brittle fractures from an over-height vehicle impact, and 

finding brittle fractures after these events should not be surprising. 
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9.3.3 Fitness-for-Service Analysis

A fitness-for-service (FFS) analysis is a quantitative engineering evaluation that is performed to 

demonstrate the structural integrity of an in-service component that may contain a flaw or 

damage (API, 2007). More specifically, FFS is a methodology that accounts for actual service 

stresses, flaw or damage zone sizes, as-built material properties, and operating environment to 

determine the actual safety or reliability of a structure in its present condition or its expected 

future state. FFS provides a common sense engineering approach to evaluating the suitability of 

a structure for its intended service. Practical benefits of FFS include a foundation for establishing 

the remaining life of a structure, as well as a basis for making capital-based decisions for repair 

or replacement. 

FFS is applied most extensively to steel structures, since steel is widely used in many different 

types of structures and can be readily fabricated by welding. Welded joints inherently contain 

discontinuities or stress concentrations, and traditional design of steel structures accounts for 

these discontinuities and stress concentrations by conservatively limiting the size of 

discontinuities permitted in fabricated joints and by applying cautious factors of safety to joint 

stresses. In effect, traditional design assumes that no significant discontinuities or serviceinduced damage (e.g., fatigue cracking, corrosion, or distortion from collision) exists in the 

structure. 

In contrast, FFS acknowledges the presence of discontinuities, stress concentrations, and serviceinduced damage and assesses the structure in its existing or anticipated condition. Therefore, FFS 

provides a quantitative assessment that is based on rational evaluation of stresses, material 

properties, nondestructive examination, and fracture mechanics (Vecchio, 2006). 

An FFS assessment generally includes the following procedure: 

• Review original design and operating history – may include required safety margins, test 

results, material certificates, repair records, and remaining fatigue life requirements

• Assess any flaws and/or damage – quantify nature and extent of existing damage 

• Perform stress analyses – strain gauge analyses are most beneficial since they provide 

actual service loading data, but finite element analyses can also be used

• Determine critical damage size and/or remaining life – often the most important part of 

an FFS assessment since it establishes the need for repair or replacement

• Design repairs or replacement, as needed – must address any critical damage size and/or 

remaining life requirements 

• Perform in-service monitoring – regardless of the outcome of the FFS analysis, ongoing 

monitoring is essential to ensure the continual proper functioning of the structure 

FFS is never pursued during design, and it is generally considered only as a last resort for 

evaluation. It requires a very accurate representation of the flaw size and shape, an accurate state 

of stress, and considerable material testing to understand the fracture toughness. Therefore large 

amounts of data and input are needed, and it often requires many assumptions as well. FFS can 

be quite complex and challenging in many cases.
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9.20 

Due to its complexities and its unique application to each situation, FFS cannot be covered 

extensively in this Manual. More information is available in specifications such as Fitness-ForService (API, 2007) and Guide to Methods for Assessing the Acceptability of Flaws in Metallic 

Structures (BS 7910) (British Standards Institute, 2015). 

9.3.3.1 Fitness-for-Service Case Study

A fitness-for-service evaluation was performed on the electro-slag welds (ESW) of the west 

Fremont Bridge approach superstructures in Portland, Oregon, as requested by FHWA. The 

approach superstructure, fabricated in 1970, consists of two trapezoidal steel box girders 

connected by rolled steel crossbeams and a reinforced concrete deck continuously composite 

with the box girder and crossbeam top flanges. A photo of the bridge is presented in Figure 

9.3.3.1-1, and a typical section is shown in Figure 9.3.3.1-2. 

Figure 9.3.3.1-1 Fremont Bridge in Portland, Oregon. 
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9.21 

Figure 9.3.3.1-2 Typical cross section of Fremont Bridge based on original drawings. 

This evaluation required gathering knowledge of the service loads, fabrication stresses, material 

properties, non-destructive testing, and failure analysis pertaining to the weldments in question, 

as described below. The serviceability of the weldments was assessed based on the fatigue and 

fracture performance. This FFS evaluation facilitated the development of repair or inspection 

requirements to assure public safety. A comprehensive report of the FFS findings is presented in 

A Fitness-for-Purpose Evaluation of Fracture Critical Electro-Slag Welds (Lovejoy, 2009). The 

following is a general overview of the primary findings and conclusions. 

SERVICE LOADS – The first FFS evaluation involved service loads. No formal load rating or 

seismic analysis was performed. However, it was determined that the maximum design stress for 

the box girder flange plates was less than or equal to 55 percent of the minimum yield stress of 

the base metal, or 27.5 ksi. In addition, structural load testing concluded that the maximum 

thermal stress range was approximately 3.0 ksi, the maximum single event live load was less 

than 6 ksi, and the root-mean-cube effective stress range was less than 2.0 ksi. 

FABRICATION STRESSES – Residual stresses from the welding process were shown by 

previous studies to have a core of triaxial tension and a compressive outer shell surrounding the 

weld region. The magnitude of these stresses was near the yield strength of the weld metal.

MATERIAL PROPERTIES – The tensile, toughness, and crack growth threshold properties of 

the base heat affected zones (HAZ) and weld metals were quantified. The lowest measured 

fracture toughness, as defined by the small scale yielding criteria applied to ASTM E 1820 test 

data, was found to be 97 ksi-in1⁄2 in the weld metal at 0oF. The minimum fatigue crack growth 

threshold measured, as defined by ASTM E 647, was 8.4 ksi-in1⁄2 in the weld metal and 7.1 ksiin1⁄2 in the base metal. A sample curve showing Charpy V-notch data in a heat affected zone is 

presented in Figure 9.3.3.1-3. 
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9.22 

Figure 9.3.3.1-3 Charpy V-notch data in heat affected zone.

NON-DESTRUCTIVE TESTING – Based on the original fabrication inspection documents and 

previous weld testing, the most likely size of weld defects to escape inspection was found to be 

less than 1⁄4 inch in maximum dimension. The largest flaw anticipated to escape detection is 1⁄2 

inch in minimum dimension. Two of the 20 fracture critical electro-slag welds inspected 

contained rejectable defects based on the AASHTO/AWS D1.5 Bridge Welding Code. One of 

these welds with ultrasonic testing rejectable defect indications was inspected with radiographic 

testing, and no defects were identified. Based on radiographic testing and detailed analysis of the 

ultrasonic testing results, these defect indications were not considered to be problematic. A 

photograph of ultrasonic testing of the electro-slag welds is presented in Figure 9.3.3.1-4, and 

fusion lines in the electro-slag welds are shown in Figure 9.3.3.1-5. 
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9.23 

Figure 9.3.3.1-4 Ultrasonic testing of electro-slag welds. 

Figure 9.3.3.1-5 Fusion lines in electro-slag welds. 

FAILURE ANALYSIS – Based on the quantified data previously described, a failure assessment 

was made considering two modes of failure – brittle and ductile. Based on the strip yield theory 

of combined failure modes, the electro-slag welds were found to be very unlikely to fail under 

even the most extreme combination of service loads and relatively low material crack tolerance. 

Critical crack dimensions were on the order of four inches for an assumed through-thickness 

crack in a finite width plate. Given the maximum crack size to escape non-destructive testing, the 

fatigue crack growth threshold, and the service loads, fatigue crack growth under live load was 

not anticipated for the service life of this structure. From a traditional Stress Life (S-N) approach, 

infinite fatigue life was predicted based on comparison with fatigue testing of similar electro-slag 

welds.
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9.24 

As a direct result of the fitness-for-service evaluations on this bridge, it was concluded that the 

welds have sufficient toughness and fatigue resistance to remain in-service with no retrofitting.

More specifically, the FFS evaluations led to the following conclusions: 

• The electro-slag weld metal had equal strength but slightly less ductility than the base metal.

• The toughness was substantially lower than the base metal, but it was adequate to sustain 

anticipated service conditions. 

• The fatigue crack growth threshold indicated that fatigue crack growth was very unlikely 

under service loads. 

• The fabrication and inspection quality of these welds was very good. A flaw larger than 1⁄2 

inch is unlikely to exist in any of the electro-slag welds, and they are probably less than 1⁄4 

inch. 

• The bottom flange welds experienced higher fatigue stress ranges than the upper flange 

welds.

• From a conventional S-N approach, the electro-slag welds are expected to have an infinite 

fatigue life.

• Retrofitting of the electro-slag welds is not necessary nor is it recommended.

• A rigorous yet reasonable non-destructive testing program can ensure public safety. 
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10.1 

CHAPTER 10 NON-WELDED COMPONENTS 

Although fatigue and fracture are generally associated with welded construction, other structural 

elements can also be subject to the effects of fatigue or fracture, including riveted or bolted 

members, reinforcing or prestressing steel, cable hangers, tendons, and cable stays. This chapter 

focuses on the fatigue and fracture characteristics of non-welded components.

SECTION 10.1 BUILT-UP MEMBERS

10.1.1 Behavior of Riveted and Bolted Connections 

The fatigue behavior of mechanically fastened connections is an important part of the design of 

new high strength bolted connections, as well as the assessment of existing riveted and bolted 

members. Mechanically fastened connections are used in many applications, such as bolted field 

splices of girder and truss members, for the connection of bracing elements, and as part of 

riveted or bolted built-up-member construction. In general, mechanically connected details have 

a better fatigue life than equivalent welded details. They do not introduce the same types of 

internal discontinuities, stress concentrations, or residual stresses associated with welding and 

tend to distribute connection forces over a larger portion of the connected element. 

The introduction of holes into a structural member does however cause its own form of stress 

concentration. The presence of the hole interrupts the uniform flow of stress across the width of 

the element. For the simple case of an infinitely wide plate with a central hole, the stress at the 

edge of the hole, parallel to the stress field, is three times as large as the nominal stress on the net 

section. This is known as the stress concentration factor, as it relates the true stress in the 

presence of the discontinuity to a reference or nominal stress on the gross or net section. Figure 

10.1.1-1 depicts this general case showing the elevated stress condition near the edge of the hole. 
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10.2 

Figure 10.1.1-1 Stress concentration caused by central hole. 

Structures however are not composed of infinitely wide plates but rather elements of finite 

thickness in which the holes generally occupy a portion of the cross-sectional area. Application 

of the load through fasteners in bearing against the edge of the hole increases the stress 

concentration effects as compared to uniform stress applied to the entire width of the plates that 

would be assumed when load is transferred by friction and clamping force. These stress 

concentrations in bearing connections are understood and documented through many full-scale 

tests of bolted and riveted members. The presence of these holes and edge bearing loading 

conditions are accounted for in the AASHTO LRFD specifications through the specific details 

and categories used for mechanically fastened joints. 

Although mechanical connections are not as fatigue sensitive as welded connections, the fatigue 

strength of riveted or bolted built-up sections is a more severe fatigue condition than base metal 

of basic rolled shapes and plates due to the stress concentration effects discussed above. The 

presence of punched or drilled holes provides a reduction in fatigue life compared with the plain 

member. Punched holes create a less desirable fatigue condition because the act of punching 

results in damage and permanent imperfections around the edge of the hole. For holes that are 

drilled full size, sub-punched, or sub-drilled and reamed to the proper size, the edge condition of 

the holes is improved and the fatigue resistance is enhanced. These different hole conditions are 

treated with different fatigue categories in AASHTO LRFD. 

10.1.2 Bolted Connections with Bolts Loaded in Shear

High-strength bolted connections are commonly used in steel structures. Bolts are typically used 

to connect distinct elements of the structure together in the field. The most common use of bolts 

is in shear type connections. These include common connections such as flange butt splices, the 
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10.3 

connection of diaphragms and cross-frames to transverse connection plates, and for the assembly 

of large elements such as truss members, tie girders, and edge girders in long-span structures. 

Most commonly, high-strength bolts are installed in a pretensioned condition, creating a 

clamping force between the elements.

In connections that transmit load by shear, the load transfer can occur by some combination of 

friction between the plies created by the bolt clamping force or by bearing of the bolt against the 

edge of the connected material. It is likely that in a bolted connection, a certain number of bolts 

are in bearing at any one time, so the true nature of load transfer is difficult to ascertain. Kulak, 

Fisher, and Struik (2001) discuss the behavior of high strength bolted friction connections as an 

example of load transfer and fatigue.

In the simple butt splice connection shown in Figure 10.1.2-1, assuming that all of the load 

transfer is by friction, there is a significant discontinuity in strain between the main plate and the 

upper and lower splice connection plates. At one point, the main plate carries 100 percent of the 

applied load and is fully strained. At the same point, the connected plate is clamped to the main 

plate yet carries no load. Under the action of cyclic loading, a small amount of slip occurs at this 

location causing cracks to form from the plates rubbing against each other. This is the cause of 

fretting fatigue. Numerous tests have demonstrated that the cracks initiate in the faying surface 

near the end of the splice plates resulting in gross section failures of the main plate. Because the 

pretensioning forces from bolting do not uniformly compress the lap splice to the main plate, slip 

or fretting can occur in the main plate between the end of the splice plates and the first line of 

bolts. 

Figure 10.1.2-1 Basic failure modes (a) gross section failure and (b) net section failure. 

The other type of fatigue failure that can occur is crack initiation and propagation from the edge 

of the bolt hole. In this type of failure, cracks initiate at the edge of the hole and grow across the 
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10.4 

net section of the member. These types of cracks are more likely to form in structures where the 

slip resistance of the connection has been exceeded, or where the bolts are in bearing against the 

edge of the hole. The “pin type” loading of the bolt against the edge of the hole results in a 

significant stress concentration along the lateral edges of the hole. Eventual failure is by fracture 

of the net section. 

In either case of fretting or net section failures, the fatigue failure is always known to occur in 

the connected material and not in the bolt itself. Results from hundreds of fatigue tests on highstrength pretensioned bolted connections are presented by Kulak, Fisher, and Struik (2001). 

As shown in Figure 10.1.2-2, the test data indicate that Detail Category B is a conservative and 

reliable estimate of the expected fatigue resistance of high-strength bolted splices. Although the 

Detail Category B classification was originally developed from tests conducted on plain welded 

beams, this detail category constituted a reasonable lower bound to the test data for bolted joints. 

The use of this 97.5 percent survival value for evaluating the fatigue resistance of bolted 

connections is expected to be conservative, especially for joints subject to reversal loading, since 

the compression portion of the load cycle is not expected to contribute significantly to crack 

growth. 

Figure 10.1.2-2 Results of fatigue tests on high strength bolts.
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10.5 

When compared to the test data from welded details, the scatter of bolted shear splice test data is 

much greater. This is due to several sources. First, the test data were compiled from a wide 

variety of sources and various different types of details that were tested. This explains some of 

the scatter. In addition, welded details have a pre-existing tensile residual stress that results in the 

entire stress range causing damage during the test. The bolted connections do not include the 

same level of residual stress, and therefore every cycle is not as likely to cause damage 

especially for those details tested in reversal.

For design of bolted connections for fatigue, AASHTO LRFD provides four approaches: 

1. For high strength bolted joints designed as slip-critical and using pretensioned bolts 

installed in holes drilled full size or sub-punched and reamed to full size, stresses are to 

be computed based on the gross section and Detail Category B applies. 

2. For high strength bolted joints designed as bearing connections but with pretensioned 

bolts installed in holes drilled full size or sub-punched and reamed to full size, stresses 

are to be computed based on the net section and Detail Category B applies.

3. For evaluating the gross and net section stress in members with pretensioned bolts 

installed in holes punched full size or for evaluating the net section stress in members 

connected with non-pretensioned bolts, Detail Category D applies. 

4. For connections between angles or tee members to gusset plates, an additional correction 

is required to reduce the member effective area due to the effects of shear lag. The fatigue 

categories remain the same as above, but the member area is reduced.

In Cases 1 and 2 above, the holes are fabricated in such a way that damage is minimized and 

high strength tensioned bolts are used in the connections. This is the most favorable condition. 

The distinction between the gross section (for slip critical connections) and net section (for 

bearing connections with tensioned bolts) reflects the severity of the local stress condition 

around the holes in each type of connection. (It should be noted that each type of connection is 

Category B, but the method of calculating the stress is different. For pretensioned connections, 

the gross section is used, but for bearing connections, the net section is used. Therefore, the 

stress on the net section can be viewed as more severe than the stress on the gross section.) Case 

3 includes a series of less favorable conditions. Holes punched full size contain crack initiation 

sites in the final member. Connections using non-tensioned bolts are prone to slip and stress 

concentration at the hole edges under repeated loading. For each of these conditions, Detail 

Category D applies.

10.1.3 Bolted Connections with Bolts Loaded in Tension

The less commonly used joint configuration in bridges is one in which bolts are loaded in direct 

tension or direct tension and the additional effects of prying action. Prying action effects are 

possible when connected elements try to separate under the application of the applied tensile 

load. These tensile loads can come from direct tension (i.e., the true hanger type connection) or 

as a result of end restraint of moment in deep framed connections. As the connected elements 

separate, the high-strength bolt is subjected to an additional prying force due to the flexibility of 

the outstanding leg of the connected element. The bolt is subjected to tension as well as a certain 
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10.6 

amount of bending, as shown in Figure 10.1.3-1, and the cyclic effects of the prying force can 

cause crack growth in the threaded portion of the bolt with cracks initiating at the thread root. 

Figure 10.1.3-1 Prying forces acting on bolted connection. 

The amount of prying action the bolt will experience in a connection is strongly influenced by 

the amount of preload in the bolt. Properly tensioned bolts in a very stiff connection will 

experience very little prying action under cyclic loading. Conversely, in a flexible connection, 

significant prying forces in the bolt are present, and if the bolt preload is low, separation of the 

connected parts is likely. This leads to large increases in bolt tension, yielding of the bolt is 

possible resulting in even greater elongations, and fatigue failures have occurred. 

AASHTO LRFD requires that high-strength bolts in axial tension satisfy the fatigue requirements 

considering the effects of direct tension plus the effects due to prying action. As a safeguard 

against fatigue failure, the calculated prying forces are limited to 30 percent of the externally 

applied direct tension. The specification also prohibits the use of ASTM A307 bolts in 

connections subjected to fatigue. AASHTO LRFD provides an approach to compute the load 

effects due to prying action and flexible connections. This approach can be universally applied to 

loads of any limit state, including strength, service, and fatigue. 
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10.7 

For mechanically fastened web angle connections, a combination of larger gage length and 

reduced angle thickness (as permitted by the beam end shear design) is required both for 

preventing angle cracking and for preventing fastener failure, and both for repair and for new 

design. 

10.1.4 Riveted Members and Connections

Prior published reports, such as Fisher, Kulak, and Smith (1998) and Kulak, Fisher, and Struik 

(2001), comment that the experimental evidence demonstrates that the fatigue cracking in riveted 

connections and built-up riveted members originates from the connected material and not from a 

failure of the rivet itself. The fatigue resistance is related to the characteristics of the connected 

part such as the size and condition of the hole, the method of hole forming, the bearing 

conditions of the rivet against the edge of the hole, and the clamping force provided in the 

connection. They comment that the influence of clamping force, bearing condition, and method 

of hole formation have not been assessed in a rigorous way. Although these factors may have an 

influence on fatigue resistance, their individual contribution has not been studied. Rather, the 

fatigue resistance of built-up riveted members has been established by tests of full-size or near 

full-size members loaded in tension or bending. The members were frequently removed from inservice bridges and were deemed to be undamaged from a fatigue perspective at the time of 

testing. A plot of the available test data, presented in Figure 10.1.4-1, shows a significant amount 

of scatter in the available fatigue life in the members that were tested. Most of these members 

were made from mild steel, but several tests of wrought iron members are also included in the 

test data. The results primarily include riveted built-up flexural members, with a more limited 

number of direct tension fatigue tests of truss members.
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10.8 

Figure 10.1.4-1 Fatigue performance of riveted built-up members.

Isolated failures of riveted truss members due to fatigue have been reported in the literature. 

These in-service failures typically occurred at the connection between truss members and gusset 

plates. The failures were shown to occur where the member initially connects to the gusset plate, 

through failure of the net section of the member, or occasionally at the end of the member where 

the gusset plate is most heavily loaded. A combination of stress concentration, initial flaw 

conditions at the hole edges, and shear lag or nonuniform loading of the gusset plate are 

responsible for fatigue cracking in all cases. The stress concentration effects from the connection 

of built-up or rolled shape members is expected to be more severe than would be found in the 

butt splices of a flange plate. This is due to a concentration of force effects due to shear lag and 

eccentricity. The fatigue resistance of riveted connections is reduced because the pretensioning 

force is not as great nor as reliable and a greater amount of bearing load transfer occurs. Load 

distribution in riveted truss connections is unequal and can result in a larger portion of the total 

member load being delivered by a smaller fraction of the total number of fasteners in the 

connection. Although this is not likely to affect the static resistance of the connection, the uneven 

distribution may affect the fatigue resistance.
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10.9 

AASHTO LRFD does not specifically address the fatigue category for riveted connections, as 

they are not commonly used in new construction. The closest analogy to the performance of a 

riveted connection is Detail 2.3 in the AASHTO LRFD specifications which references the 

performance of mechanically fastened joints using non-pretensioned fasteners.

When it comes to bridge evaluation, the MBE indicates that the base metal at the net section of 

riveted connections is to be evaluated as a Detail Category C detail. The MBE commentary 

indicates that the Detail Category D classification used for new designs with non-tensioned 

fasteners is used to represent the first cracking of a built-up member. The Detail Category C 

classification better represents the expected life of a detail when the initial discontinuity has 

grown to a critical size. It is deemed to better represent the critical stage of fatigue crack growth 

for members with a high degree of internal redundancy. The MBE goes on to state however that 

once cracks are visually detected, a more complex fracture mechanics approach should be used 

in lieu of the stress range approach. Research at Purdue University suggests that, for riveted 

members in poor condition with loose or missing rivets or with obvious signs of damage from 

hole punching, the engineer should revert back to the standard Category D designation, much 

like an open hole (Bowman et al., 2012). 

Another aspect of fatigue and fracture for riveted members is the treatment of tack welds (see 

Figure 10.1.4-2). Tack welds are generally associated with non-welded components such as 

built-up members. They were commonly used to hold individual elements of a member together 

as final riveting was completed. Tack welds are common and were widely used for decades in 

the construction of riveted or bolted built-up members. 

Figure 10.1.4-2 Tack weld detail. 

A tack weld would be considered as a Category E detail if the provisions of the AASHTO LRFD

specifications were used in their evaluation. However, many times tack welds are not significant 

enough to constitute structural welds. Given their widespread use in flexural and tension 

members alike, owners have been faced with the challenge of whether to remove what can be 

thousands of individual tack welds from a large structure in order to alleviate a potential crack 

initiation site. Research at Purdue determined that tack welded riveted members, when tested, 

performed better than the Category C design curve. Therefore for evaluation, tack welds can be 
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10.10 

considered as a Category C detail. The prior Category E rating was considered too severe. 

Clarifying language has been provided in the MBE. The tack welds studied in the NCHRP 721 

project varied but were in the range of 1 to 2 inches in total length (Bowman et al., 2012). 

SECTION 10.2 ANCHOR RODS

10.2.1 Fatigue Considerations for Anchor Rods 

Anchor rods, or anchor bolts, are the most common means of attaching structures such as 

overhead signs, traffic signals, high mast poles, and other similar structures to concrete 

foundations. They consist of fully threaded bars embedded into the concrete, to which the 

overhead structure is eventually connected with nuts. Due primarily to the action of wind, but 

also due to forces such as gust induced loading on cantilever and overhead sign structures, these 

anchor rods are subjected to high cycles of variable amplitude tensile loading which can make 

them prone to fatigue. 

Two common types of anchor bolt connections are used: single nut and double nut varieties. A 

single nut connection is typically used when the underside of the base plate rests on a leveling 

grout pad. The double nut connection is used when the base plate is otherwise unsupported. 

Illustrations of each of these conditions are provided in Figure 10.2.1-1 and Figure 10.2.1-2. 

Figure 10.2.1-1 Typical double nut connection. 
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10.11 

Figure 10.2.1-2 Typical single nut connection. 

Research conducted at the University of Texas at Austin examined the fatigue behavior of 

steel anchor bolts (Frank, 1978). The study investigated the contribution of various 

parameters including: the strength of steel, thread size and pitch, bolt diameter, the method of 

forming threads (rolled or cut), the influence of galvanizing, and the effect of double nuts. 

Also studied was the stress corrosion behavior of anchor bolts. The report included an 

assessment of the results of testing by others as well. The summary of the fatigue testing 

indicated the type of steel, thread size, diameter, effect of galvanizing, and method of the 

forming of threads were not significant for design. The lower bound fatigue life for anchor 

bolts with single nuts and anchor bolts with loose double nuts was consistent with Detail 

Category E. Pretensioned anchor bolts, those with double nuts tightened one third of a turn 

past snug tight, had improved fatigue lives. Although no evidence of stress corrosion 

cracking was found in the test bolts, Frank recommended that the maximum yield strength 

for anchor bolts be limited to 125 ksi. This is consistent with modern practices that limit the 

yield strength of anchor bolt material.

Fisher, Kulak, and Smith (1998) also discussed and summarized the history of fatigue test 

data for threaded rods. They reported that most threaded rod fatigue tests were conducted 

under constant amplitude fatigue loading and that many of the tests were conducted in a 

double nut configuration in order to pre-stress a short section of the anchor bolt. A small 

amount of vertical misalignment was also included in some tests. The fatigue test data 

included threaded rods tested without preload, rods preloaded to a snug tight level, and rods 

preloaded by one third turn of the nut past the snug tight condition. Figure 10.2.1-3 presents 

results of fatigue tests on threaded rods. 
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10.12 

Figure 10.2.1-3 Results of fatigue tests on threaded rods.

Fisher, Kulak, and Smith (1998) comment that although there is considerable scatter in the 

results, the evidence suggests that anchor bolts loaded in fatigue have poor resistance. Included 

in the test data shown are anchor bolts of various grades, thread sizes, methods of forming, and 

bolt diameters, none of which were statistically significant to the fatigue life. The bolts tested 

with a vertical misalignment, as much as 1:40, did not have a significantly reduced fatigue life. 

Therefore AASHTO LRFD maintains this plumbness requirement for anchor bolts since there is 

insufficient evidence as to the fatigue resistance of anchor bolts with greater misalignments.

NCHRP Report 412 (Kaczinski et al., 1998) provides the most current information on the 

behavior of anchor bolts in fatigue. Although prior research indicated that Detail Category E’ 

was a reasonable lower bound for anchor bolts tested in the finite life region, and Detail 

Category E appeared to be a reasonable design curve for infinite life, no testing of anchor bolts 

below a stress range of 10 ksi was available to verify the existence of a constant amplitude 

fatigue threshold (CAFT). Additionally, the behavior of anchor bolts was thought to potentially 

be different than the E and E’ Detail Categories since these categories were developed for 

welded details with high tensile residual stress distributions and stress concentrations. 

Anchor bolt fatigue originates at the thread root, and the residual stress distribution is possibly 

even compressive in these regions. Given the nature of fatigue design in light and sign structures, 
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10.13 

the behavior in the finite life region is of limited use since the design of new structures is 

predicated on providing an infinite life detail. Thus an accurate determinaton of the CAFT was 

needed. The NCHRP 412 report determined the strength of double-nut anchor bolts tightened to 

a snug tight condition evaluating the effects of mean stress, yield strength, bolt pretension, thread 

forming method, and misalignment. Their conclusions are as follows and form the basis of the 

current AASHTO design approach: 

• In the region of finite life, snug tight bolts should be designed to satisfy the Category E’ 

requirements.

• In the region of infinite life, the CAFT limit for Detail Category D (7 ksi) is applicable to 

both snug tight and fully tensioned anchor bolts. 

• Although no benefit is derived when installing bolts in a fully tightened condition (i.e., 

one third of a turn beyond snug tight), doing so prevents the possibility of a nut becoming 

loose in service.

• Misalignment need not be considered when limited to a maximum value of 1:40. Bending 

from prying action must be controlled through selection of a base plate having adequate 

thickness. 

• The above recommendations assume a maximum total stress of approximately 60 percent 

of the anchor bolt yield stress, as the level of maximum stress strongly influenced the 

fatigue strength (characteristically different than welded details in which only stress 

range is of concern).

Design of anchor bolts for fatigue is covered in the AASHTO LRFD Specifications for Structural 

Supports for Highway Signs, Luminaires, and Traffic Signals (AASHTO, 2015c) and is based on 

satisfying the 7 ksi limit for infinite life. The specification indicates that mandatory Charpy Vnotch testing is not required for anchor bolt material since anchor bolts conforming to the F1554 

specification (ASTM, 2015) have generally been found to have adequate toughness. Due to the 

use of anchor bolts in an environment in which they are subjected to fatigue as well as an 

aggressive environmental exposure, and due to the fact that there have been anchor bolt failures 

in structures in the past, a minimum of eight bolts are required for base connections of high-level 

(pole type) luminaire towers. The commentary (AASHTO, 2015c) indicates as many as 12 

anchor bolts may be required when fatigue governs the design. 

10.2.2 Stress Corrosion Cracking / Hydrogen Embrittlement

Stress corrosion cracking is generally associated with anchor rods or bolts. Stress corrosion is a 

term that has traditionally been used to describe the effects of hydrogen embrittlement. However, 

to aid in the understanding of the mechanisms causing the crack, stress corrosion and hydrogen 

embrittlement must be separated. Both mechanisms produce failure through crack extension 

under static steady loading. Both also normally exhibit a threshold stress which is dependent 

upon the material properties and the environment. Once a threshold stress is exceeded, failure 

may occur within hours or it may take months for the crack to extend to failure. 

The most prevalent form of cracking in the relatively low strength steels used in bridges and in a 

relatively benign environment is hydrogen assisted cracking. The hydrogen atom and ion are 

very small and can migrate through the crystal lattice to locations of high stress. The hydrogen 
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10.14 

causes separation of the material along grain boundaries. The hydrogen can come from internal 

sources such as hydrogen trapped in the steel during the steel-making process or introduced 

during the welding process from contaminated welding consumables. External hydrogen 

embrittlement is typically the result of a cathodic reaction at the surface of the steel, which can 

be exacerbated by a sacrificial zinc coating. A small crack in the coating tends to focus the 

evolution of the hydrogen on the crack surface and tip, leading to hydrogen induced cracking 

(Townsend, 1975; Brahimi, 2007). 

Hydrogen induced cracking in bridge steels occurs due to hydrogen introduced during the 

welding process either from the consumables, surface moisture, or paint. Higher strength steels 

are more sensitive and require more stringent limits on hydrogen. Fluxes and coated welding 

rods are normally supplied in sealed containers which then must be stored after opening at an 

elevated temperature to prevent moisture absorption from the ambient air. The AWS 

specifications spell out the requirements for preheating, as well as diffusible hydrogen limits for 

the electrodes and fluxes. The ultrasonic, magnetic particle, and final visual inspection of 

fracture critical welds cannot be done for at least 24 hours and up to 72 hours for thick high 

strength steels. The intent of the delayed inspection is to ensure delayed cracking caused by 

hydrogen, if it occurs, is found during the inspection. 

High strength bolts are susceptible to delayed hydrogen assisted cracking. A490 bolts are not 

allowed to be zinc coated due to problems first found with the fracture of galvanized A490 bolts 

(Townsend, 1975; Brahimi, 2007). The lower strength A325 bolts are commonly galvanized 

without problems. Both the A490 and the A325 specifications have maximum hardness values to 

ensure the bolts will not exhibit delayed cracking. Bolts which exceed these hardness values 

have failed after installation. The use of galvanized A354 Grade BD bolts should be avoided. 

The hardness of these bolts is allowed to be higher than the A490 limit. Often the A354 bolt has 

been specified for high strength large diameter rods. These large diameter rods are difficult to 

through-harden due to the relatively lean alloys employed by the manufacturer. Due to their large 

cross section, the outer surface of the bolt cools the quickest in the quenching process, producing 

a bolt with high hardness on the outer portion and a lower strength core. The critical root of the 

thread is located in this outer band of high hardness material, though the surface hardness is 

measured at one quarter of the bolt diameter. This is a concern for fracture, and thus the use of 

the A354 Grade BD galvanized bolts is discouraged for tensioned applications. 

SECTION 10.3 REINFORCEMENT OF CONCRETE

Concrete is commonly reinforced by one of two methods: internal mild reinforcing and internal 

prestressed reinforcing. In a conventional reinforced concrete structure, the structure is assumed 

to crack under service with the reinforcing steel being required to carry the tensile forces 

associated with bending and shear. In a prestressed concrete structure, members are most 

commonly designed to remain uncracked under specified service conditions. As such, the entire 

transformed section of the concrete and prestressing steel is effective at resisting the applied 

bending moments. The result of this uncracked condition is that a very large section is available 

to resist the external forces.
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10.15 

It is not common for the fatigue limit state to govern the design of structural concrete. For 

reinforced concrete elements, there are design checks provided in AASHTO LRFD related to 

maximum fatigue stress range allowed in reinforcing steel. AASHTO LRFD also addresses the 

design of prestressed concrete elements, though fatigue rarely governs the design of such 

elements.

10.3.1 Reinforcing Bars

Reinforced concrete, which cracks under the application of service loads, resists the externally 

applied forces through an internal force couple of reinforcing steel tension and concrete 

compression, as illustrated in Figure 10.3.1-1. The concrete portion of the member is used to 

resist the internal compressive forces, and internal reinforcing steel is used to resist the tensile 

forces. Because the internal reinforcing steel is subjected to tension, and this tension fluctuates 

due to the application of live load, fatigue is one of the limit states that must be satisfied in the 

design of a reinforced concrete element. Therefore the passage of routine traffic creates stress 

cycles throughout the life of the bridge, and they in turn load the reinforcing steel in fatigue. 

Figure 10.3.1-1 Resultant forces on beam subject to distributed load. 

The fatigue of reinforcing steel is a possibility in reinforced concrete structures. For instance, 

structures such as a longitudinally reinforced concrete slab bridge, of which there are many 

thousands throughout the United States, are subjected to many fatigue cycles throughout their 

life. Other examples include reinforced concrete caps in substructures which are constantly 

loaded and unloaded as vehicles traverse the bridge and load is transferred to the bearings. 

Because of the many cycles of fatigue loading that can be applied to a cracked reinforced 

concrete section, AASHTO LRFD requires that the computed stress ranges in the reinforcing steel 

be less than the CAFT. The requirement is expressed as:

Equation 10.3.1-1 
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10.16 

with the stress range being taken as that corresponding to the Fatigue I load combination and the 

constant amplitude fatigue threshold provided by an equation presented below. There are no 

provisions in AASHTO LRFD for the finite life evaluation of a reinforcing bar.

The AASHTO LRFD constant amplitude fatigue threshold for straight reinforcement bars is given 

as:

Equation 10.3.1-2 

expressed in units of ksi. The variable fmin is the minimum live load stress resulting from the 

Fatigue I load combination, combined with the more severe stress from either the permanent 

loads or the permanent loads, shrinkage, and creep-induced external loads. In other words, it is a 

total minimum stress including the effects of permanent and transient loads at the same time. The 

AASHTO relationship was established by enveloping the results of many fatigue studies 

considering a range of bar sizes and reinforcing steel grades. Its accuracy as a true constant 

amplitude fatigue threshold was studied and is described later in this section.

The AASHTO equations are derived from an NCHRP research project by Hanson et al. (1976). 

Their study focused primarily on Grade 60, #8 reinforcing bars, though other sizes and grades 

were also tested. Hanson’s equation for fatigue life is the one used in AASHTO LRFD with a 

slight simplification. Hanson’s research comprised 353 concrete beams, most of which were 

tested in the finite life region. The conclusion of the research was that the fatigue limit of 

reinforcing steel was not sensitive to concrete beam dimensions, material properties, reinforcing 

bar size, steel grade, or metallurgy (Amorn et al., 2007). The original work of the NCHRP study 

concluded that the maximum stress and the minimum stress (i.e., the stress range) was a 

dominant parameter along with a factor related to the geometry of the rolled ribs and lugs of the 

reinforcing. These deformations, essential to bond of the reinforcing steel to the concrete, 

influence the fatigue life of the reinforcing steel because they serve as crack initiation sites.

Tilly (1979) provides a thorough synopsis of the various factors that influence the fatigue of 

reinforcing bars. One of the challenges associated with the fatigue analysis of concrete structures 

is determining how to correlate the performance of bars tested in air with those embedded in 

concrete. The difficulty of knowing how to accurately compute the stress in the reinforced 

concrete element poses a fundamental challenge when trying to apply the free length bar test data 

to the performance of bars embedded in concrete and loaded in flexure. 

The simplest types of tests to conduct are of course axial fatigue tests of free length bars. These 

tests can be conducted quickly and without ambiguity as to the magnitude of the stress range and 

the fatigue life of the specimen. These tests are not without their challenges, specifically trying to 

overcome the premature failures that commonly occur where the bars are gripped in the test 

machine. However many years of testing have developed standardized approaches and methods 

of testing in order to develop reliable fatigue test results. 

Somewhat more difficult but of greater similarity to actual in-service conditions are bending tests 

on reinforced concrete beams. Although these tests bear a greater resemblance to actual service 
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10.17 

conditions, they introduce an additional complication and that is the determination of the fatigue 

stress range in the reinforcing steel in a section that is cracked under service load. Tilly 

comments that the results of bending tests have typically shown greater lives than axial “in air” 

loading, but the differences are not very significant. Tilly cites work consistent with findings of 

others that the fatigue life of smaller bars is somewhat better than larger bars. It is hypothesized 

that the lower fatigue life for larger bars is potentially due to the fact that a larger bar is more 

likely to have a defect than is a smaller bar. The influence of corrosion on fatigue life of 

reinforcing steel was also discussed. Tilly comments that corrosion not only reduces the cross 

section of the bar, therefore increasing its stress, but in and of itself creates pitting and as a result 

decreases the remaining fatigue life of the reinforcing steel even further. This is a significant 

observation for bridge evaluation and remaining fatigue life determination.

Equation 10.3.1-2 was recently evaluated as part of the fatigue limit state calibration conducted 

as part of the SHRP2 Project R19B, Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Modjeski and Masters, 2015). Regarding the AASHTO limits, the R19B report 

offers the following: 

ACI Committee report ACI 215R-74(92) and the supporting literature indicate that 

nonprestressed reinforcement exhibits a constant amplitude fatigue threshold, yet it is 

unclear that these equations are in fact the threshold values. ACI 215R-74(92) suggests 

that the resistances are “a conservative lower bound of all available test results.” In 

other words, a horizontal constant amplitude fatigue threshold has been drawn beneath 

all the curves.

Therefore the “limit” was arbitrary, and its reliability was unknown. In the calibration of the 

limit state, an assumed Fatigue I load factor of 2.0 was chosen based on calibration of the limit 

state for steel structures. When this load factor was applied to the evaluation of concrete 

reinforcing bars in tension, it was determined that the AASHTO approach would provide a level 

of reliability substantially higher than for the fatigue of steel structures. An initial suggestion was 

that a resistance factor, φ, could be taken as 1.25. This is unusual and inconsistent with other 

fatigue design approaches. In lieu of the higher load factor, the R19B researchers instead 

suggested simply raising the nominal resistance equation to the following value:

Equation 10.3.1-3 

As discussed in Chapter 6, the Fatigue I load factor is currently 1.75. This results in a change of 

the nominal resistance equation by the ratio of 1.75/2.0. 

10.3.2 Prestressing Strands

The fatigue behavior of prestressing strands and the fatigue behavior of prestressed concrete 

elements has been a focus of research since the material was first widely introduced into practice 

in the 1950’s. At the time, researchers were wrestling with not only the determination of strand 

fatigue properties but also with the basic problems of how to develop test methods and fixtures to 
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10.18 

accurately determine the characteristics of strands. Data on the fatigue performance of 

prestressing strand has been gathered by numerous investigators through the years, as well as by 

various industry groups including manufacturers. The results of prestressing strand fatigue data 

testing have not always been presented in a consistent manner nor do they reflect tests that have 

been conducted under similar conditions. The fatigue performance of strands has been assessed 

both by flexural testing of small-scale and full-size elements, as well as by many tests of strands 

in air. The conclusions of these two types of testing have also not always been consistent. 

In a study for the Texas Department of Transportation (Paulson et al., 1983), researchers 

synthesized several decades of prestressing strand fatigue behavior and supplemented historical 

information with additional testing. Their findings were corroborated by others including Heller 

(2003). The 1983 report by Paulson et al reviews the results of over 700 individual specimens of 

seven-wire prestressing strand tested in fatigue. This included test results from the United States 

as well as Europe. The early researchers noted a clear trend: beams that remained uncracked 

performed well, whereas beams that cracked during loading were susceptible to fatigue failure 

with little to no impending warning. Paulson reviewed the results of the various tests and 

performed a regression analysis on the fatigue test data. In Figure 10.3.2-1, the solid line 

represents the mean result and the dashed line represents the 97.5 percent survival limit. It is 

notable that the performance of prestressing strand tested in air follows the same logarithmic 

behavior as for other structural steel elements discussed previously. 

Figure 10.3.2-1 Results of prestressing strand tests.

Although prestressing strand obeys the same general behaviors as other steel elements when 

subjected to fatigue loading, the design process for prestressed concrete is characteristically 

different than for steel structures. For a prestressed concrete structure, the designer is not 
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10.19 

concerned with fatigue life estimation but rather the design approach is generally to take steps to 

avoid the chance of fatigue failure. The Paulson research suggested a fatigue limit of 20 ksi as a 

reasonable endurance limit for strands. 

One fundamental problem with the fatigue behavior of cracked sections is coming up with a 

model that consistently predicts the range of stress in the strands in the vicinity of the crack. 

Until an accurate estimate of the stress range can be made, there is no reasonable way to create a 

reliable fatigue model. Paulson suggests that the fatigue test data summarized in his report is also 

applicable for elements such as hangers, stay cables, and other elements where the loading in 

direct tension most directly corresponds to the nature of most laboratory fatigue tests. Regarding 

pretensioned concrete girders, they divided their recommendations into two cases: uncracked 

girders and cracked girders. Paulson suggests that for uncracked girders, the behavior of the 

strand in fatigue is very similar to the fatigue of strand when treated as an isolated element. 

However for cracked girders, the situation is more complex. At the time of Paulson’s work, no 

code recommendations were available related to fatigue of prestressing strand. Their work 

suggested a logarithmic fatigue life equation similar to those used currently for structural steel. 

Modern practice has replaced their suggested equations with a series of limiting stress values for 

uncracked and cracked sections alike.

Heller states, in follow-up work to the original Paulson study, that “The published literature 

does not include a single case of a strand fatigue failure in an uncracked prestressed concrete 

beam. It is not considered possible to design a prestressed concrete beam such that the stress 

range in the strand is sufficiently large to cause a fatigue failure without cracking the concrete 

first. With this in mind, it is rational to specify that the fatigue capacity of the pretensioned 

concrete beam is satisfactory if the extreme concrete tensile stress is limited such that no 

cracking can occur.” This is fundamentally the approach taken in AASHTO LRFD. 

AASHTO LRFD defines a constant amplitude fatigue threshold for prestressing tendons. For 

tendons having a radius of curvature in excess of 30 feet, the limit is 18 ksi. For tendons having a 

radius of curvature less than 12 feet, the limit is 10 ksi. Engineers are allowed to interpolate 

linearly between the two radii. In post-tensioning applications, tendons are frequently deviated 

vertically and laterally using curved tendon profiles. The geometry of these ducts is related to the 

constant amplitude fatigue threshold value to be used in a particular design. In pretensioned 

applications, strands are also frequently held down, or deviated, in order to control stresses near 

the end of the beam, as well as to provide enhanced shear strength in the harped region. At the 

locations of the hold-down anchors, strands are bent sharply around a mechanical device, and 

this change in profile would also be considered a location of sharp curvature. 

From a practical standpoint, the evaluation of prestressing strands for fatigue is not frequently 

performed. AASHTO LRFD states that fatigue of the reinforcement need not be checked for fully 

prestressed components designed to meet the tensile stress limitations of the Service III load 

combination. The vast majority of prestressed concrete structures are designed to satisfy this load 

combination and by default would be exempt from any fatigue checks. In the rare instances in 

which an owner would allow the computed tensile stresses to exceed the permissible values of 

AASHTO LRFD, the section should be assumed to be cracked under service load conditions, 

subjecting the reinforcing steel to a stress range that would need to be computed and checked 

against the fatigue resistance.
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10.20 

10.3.3 Post-Tensioning Tendons and Anchorages

Tendon anchorages are a critical component of any post-tensioning system and are usually based 

on proprietary designs by specialty hardware suppliers. The purpose of the anchor is to provide a 

common location at which post-tensioning tendons are terminated and their tensile force 

converted into compression acting on the concrete member. The performance of post-tensioning 

anchorage systems is typically established through a combination of detailed analysis and 

experimental testing. This testing includes static and fatigue testing in order to assess the 

performance of the complex anchoring system under static and fatigue loading.

Post-tensioning anchors can take several forms. These include an older style basic bearing plate 

and trumpet configuration, used for smaller tendons, as shown in Figure 10.3.3-1. 

Figure 10.3.3-1 Post-tensioning anchor detail. 

More commonly used are special cast anchors, known as multi-plane anchors, which deliver the 

high compression load they must resist into the concrete in a specially reinforced local zone at 

the end of the element. These areas require special reinforcement and confinement in order to 

resist the high static loads associated with anchorage of the tendon, as well as to resist the 

fluctuating loads associated with transient load effects. Figure 10.3.3-2 shows a multi-plane 

anchorage system.
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10.21 

Figure 10.3.3-2 Multi-plane anchorage system. 

The design and performance of these anchorages, as it relates to fatigue, is not something that the 

engineer of record is typically responsible for. Post-tensioning anchors and systems in general 

are typically subjected to prequalification testing by agencies and manufacturers in order to 

determine their suitability. Testing of anchorages usually involves static tests that determine the 

reliable anchorage of prestressing steel, tests to ensure the anchor can adequately deliver its force 

to the surrounding concrete, and special fatigue tests which assess the performance of the system 

under varying stress in the tendons. Other elements of the design of a post-tensioning anchor 

include the geometry of the trumpet and the ductwork. By providing a smooth transition from the 

wedge anchors into the duct, fatigue life performance and anchorage efficiency are increased.

10.3.4 Stay Cables 

The requirements for the fatigue design of stay cables described herein come largely from the 

Post-Tensioning Institute Recommendations for Stay Cable Design, Testing, and Installation

(PTI, 2012). The AASHTO specifications are largely silent in this area.

Within the PTI recommendations are guidance on quality control testing of stay cable materials 

as well as recommendations concerning the design of stay cable systems. The requirements for 

testing relate to the obligations of manufacturers and system vendors related to quality assurance 

and control in the manufacturing of strands, bars, wires, and couplers. Given that only isolated 

elements are generally tested, the acceptance standard for an element does not imply that a 

system should be designed to the same level. Rather the design limit of stress range for a given 

number of cycles is significantly less for an in-service structure as compared to the acceptance 

criteria for isolated elements. This is shown schematically in Figure 10.3.4-1. 
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10.22 

Figure 10.3.4-1 Fatigue safety philosophy. 

Due to the unique characteristics of many stay cable systems, system qualification tests are 

required to demonstrate adequate performance. This includes both fatigue and static strength 

criteria. The PTI criteria define the acceptance testing of stay cables. The fatigue acceptance test 

criteria include specified test stress ranges, as well as an upper limit on the maximum cable 

stress. During testing of a completed cable mock-up, the failure of individual wires is limited to 2 

percent of the total stay cross section. Any failure of a bar in a bar-type system will result in 

rejection of the test. Failures are not permitted in any component of the anchorage during testing. 

Failures of any anchor components constitute automatic rejection of the test.

The PTI commentary indicates that stay cable acceptance tests are to ensure that stay cable 

systems have uniform and high levels of quality and reliability. They also acknowledge that the 

fatigue loading ranges for stay cables computed by designers are subject to a high degree of 

uncertainty. The test criteria in the PTI recommendations are knowingly conservative to 

envelope the uncertainties of stay cable behavior and due to the importance of the stays 

themselves. Additionally, the acceptance test duration is very short and in no way mimics the 

time and environmental exposure of a real cable. Therefore a high standard for acceptance is 

required. At the conclusion of the fatigue testing, the specimens must be reloaded to a load of 95 

percent of the minimum ultimate tensile strength of the cable to demonstrate adequate strength 

performance after the conclusion of the fatigue test. At the conclusion of the fatigue and static 

tests, test cable is required to be dissected and its components examined. 
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The fatigue design vehicle for cable-stayed bridges is the same as that used for the design of 

ordinary structures, the AASHTO fatigue loading placed in a single lane. However the computed 

load effect is multiplied by 1.4 in order to capture the effects of heavy trucks on longer spans 

placed in adjacent lanes. The standard dynamic load allowance of 15 percent is applied. 

An additional fatigue concern for stay cables is the dynamic effects of wind loading and cable 

vibration. Some cable-stayed bridges have been subjected to undesirable wind-induced 

vibrations in the main cables. This cable vibration can be caused by turbulence present in the 

airflow (buffeting), vortex shedding, galloping, fluid structure interaction, wind and rain acting 

in combination, and a combination of these factors. Failures in cables and cable attachments due 

to each of these factors have occurred in the past. Recently the failure of a stay cable anchor in 

Minneapolis was attributed to cable vibration resulting in a connection plate between the cable 

and supporting tower exceeding its fatigue strength, breaking loose, and the cable falling onto the 

bridge deck (Wiss, Janney, Elstner Associates, Inc., 2012). The PTI recommendations provide 

guidance to help engineers develop a preliminary assessment of the susceptibility of cables to 

rain-wind induced vibrations, cable galloping, damping, the use of stabilizing cables, and the 

detailing of connections to minimize fatigue susceptibility of these critical elements.

For design at the fatigue limit state, both finite and infinite life design criteria are presented. The 

detail constants for finite life and the constant amplitude fatigue threshold limit for infinite life 

are provided. When comparing the computed stress to the fatigue limit, the computed stress 

range must be increased by 140 percent (a factor of 1.4) in order to account for the fatigue effects 

of long span, multi-lane loading. The suggested design life of 75 years is recommended for cable 

design, although the expected life of the bridge could be significantly longer. 

An additional concern for stay cables is the interaction of the stay cable and the cable saddle. 

Minimum saddle radii are suggested for strands and bundled stays so that the effects of curvature 

and fretting on fatigue can be avoided. 

The construction of cable-stayed bridges also involves operations that are fatigue and fracture 

sensitive. The PTI recommendations have various provisions that cover construction items such 

as the welding of steel pipe and weld inspection. 
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A.1 

APPENDIX A

CALIBRATION OF THE FATIGUE I AND II LOAD COMBINATIONS

SECTION A.1 GENERAL

AASHTO LRFD introduced the concept of calibrated limit states to the practice of bridge 

engineering in the United States. Following their introduction in 1994, the design of structures 

has been based on satisfying the design requirements of the strength, service, extreme event, and 

fatigue and fracture limit states. One significant enhancement introduced with AASHTO LRFD

was the introduction of calibrated loads, load factors, and load combinations to provide a more 

uniform level of safety and risk to various designs. Calibration is a process of selecting load and 

resistance factors and creating load combinations so that a targeted level of safety can be 

achieved. It requires that the uncertainties in the various inputs (i.e., the parameters on the load 

and resistance side) be known or able to be confidently estimated. The calibration of the 

AASHTO LRFD specifications was initially performed only to satisfy strength limit state criteria. 

The strength limit state statistics were produced through the NCHRP 12–33 project, documented 

in NCHRP Report 368 (Nowak, 1999) and in NCHRP 20-07/186 (Kulicki et al., 2007). 

Fatigue, however, had been an uncalibrated limit state with an unknown, though deemed safe, 

level of safety. The limit state was based on testing to define safe design resistance values (see 

Section 4.4) and vehicle weight studies to establish load factors, but a statistical definition of 

safety was never fully established. The SHRP2 Project R19B – Bridges for Service Life Beyond 

100 Years: Service Limit State Design (Modjeski and Masters, 2015) studied various aspects of 

the load and resistance models for the service and fatigue limit states in order to calibrate them. 

Unlike the current fatigue design principles which base their design vehicle, load factors, and 

distribution factor approach on studies from the 1960’s and 1970’s, the recent SHRP2 study 

relies on modern weigh-in-motion (WIM) data to investigate these various inputs. The R19B 

project relied on approximately 65 million individual vehicle records in a nationwide WIM 

database. Approximately 10 million of those vehicles were removed from the database because 

of perceived errors or lack of usefulness of the data. Additionally, for the calibration of the 

fatigue limit state, vehicles whose gross weight was less than 20 kips were also excluded since 

these cause no measurable fatigue damage. 

After several rounds of filtering, approximately 8.7 million records remained and were used in 

the calibration of the fatigue limit state. As would be expected with data from many WIM sites 

throughout the United States, there is a significant scatter in the findings. For the 15 sets of WIM 

data provided by FHWA, the mean truck weight ranged from 20 to 65 kips with a maximum 

gross vehicle weight of approximately 202 kips. Because of the geographic diversity of the WIM 

sites, traffic volumes varied greatly. The lowest truck traffic volume expressed as the ADTT 

value was a site in Arizona with less than 100 trucks per day, while for a site in Arkansas, the 

ADTT was nearly 4,600 trucks per day. 
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A.2 

SECTION A.2 FATIGUE LIMIT STATE CALIBRATION

The AASHTO formulation for the fatigue limit state requires that the stress range be less than the 

nominal resistance, expressed as follows: 

Equation A.2-1 

In the finite life region, the factored design stress must be below the finite life resistance:

Equation A.2-2 

where the number of design cycles is given by the following equation: 

Equation A.2-3 

For the infinite life region, the factored design stress must be below the constant amplitude 

fatigue threshold (CAFT): 

Equation A.2-4 

In order to calibrate the fatigue limit state, various inputs to this approach must be investigated. 

These include the load factors, γ, the number of cycles of loading per passage of the design truck, 

n, and the premise that the stress range, Delta (∆)f, is related to the stresses produced by the 

design truck in a single lane only. These variables were investigated by the R19B team. Their 

findings and recommendations follow. 

SECTION A.3 COMPONENTS OF THE FATIGUE LIMIT STATE

A.3.1 Multiple Presence

One of the assumptions of the AASHTO fatigue limit state is that structures need only be 

designed for the passage of the fatigue truck in a single lane. That is, there is no need to consider 

the simultaneous presence of trucks in adjacent lanes or trucks following each other in the same 

lane. The R19B team investigated the validity of this single truck, single lane design concept. 

The availability of the WIM data allowed researchers to filter the records and find times and 

speeds for occasions where similar weight trucks, with similar axle spacings, were crossing the 

bridge in the same lane or in adjacent lanes with the headway limited to less than 200 feet, as 

illustrated in Figure A.3.1-1. 
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A.3 

Figure A.3.1-1 Headway distance. 

Using data from WIM sites in Florida and New York, the researchers concluded that there was a 

very low percentage of similar weight and configuration trucks traveling in adjacent lanes or 

trucks following one another in the same lane. On this basis, the researchers concluded that 

based on the low number of observed side-by-side and following occurrences, it is acceptable to 

consider only a single truck in a single lane for fatigue design. This confirms that a single lane 

live load model, as has been used in the past editions of AASHTO LRFD, is applicable for the 

load side of the limit state equations.

A.3.2 Cycle Counting / Cycles Per Passage 

The calculation of an estimated number of design cycles is required for design for finite life. This 

is expressed by Equation A.2-3 and includes the effects of 75 years of truck traffic in the most 

heavily traveled lane. It is assumed to produce a certain number of cycles per truck passage, n. 

The AASHTO LRFD recommendations for the number of cycles per crossing are provided in 

Table A.3.2-1. 

Table A.3.2-1 AASHTO cycles-per-passage. 

Longitudinal Members n

Span Length > 40 ft. Span Length ≤ 40 ft.

Simple span girders 1.0 2.0

Continuous girders Near interior support 1.5 2.0

Elsewhere 1.0 2.0
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A.4 

The R19B team investigated the validity of these requirements using the WIM data. The WIM 

data was used to compute midspan moments for simply supported bridges, moments at the 

interior support of two-span continuous bridges, and moments at 0.4 of the end span of two-span 

continuous bridges for bridges of various lengths. To do this, measured vehicles were run as a 

simulated traffic stream across bridges from 30 ft. to 200 ft. in length (per span) to determine the 

number of cycles and magnitude of moment for various span lengths. A time history of bending 

moment was developed, as presented in Figure A.3.2-1. 

Figure A.3.2-1 Bending moment time history for a single truck passage on simplesupported bridges at midspan.

Figure A.3.2-1 demonstrates the variation in midspan bending moment for simply-supported 

bridges loaded by a particular vehicle chosen from the WIM data. It is useful to compare the 

behavior of the shortest span, 30 feet, and the longest span, 200 feet. For the longer span, a 

gradual increase-decrease in bending moment is apparent, and effectively one large cycle of 

moment is produced. For the shorter spans, the loading and unloading response of individual 

axles or axle groupings causes a greater number of smaller cycles for a single vehicle passage.

Figure A.3.2-2 shows a similar bending moment versus time plot for a family of two-span 

continuous bridges. The negative moment at the interior support is plotted. Again examining the 

longest bridge, the behavior is similar to what would be expected from the passage of a single 

point load. Moments increase to a peak, decrease as the vehicle crosses the pier, and follow a 

similar pattern in the second span. However, examining shorter spans, it is obvious that the 

moment at the pier fluctuates significantly due to the peak responses generated by multiple axles 

combining or interfering with each other. Using these time histories as an indication of the 
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A.5 

fluctuation of stress, it is apparent that the definition of a cycle is more complex for the shorter 

spans. 

Figure A.3.2-2 Bending moment time history for a single truck passage on two-span 

continuous bridges at the pier support.

The rain flow counting algorithm is a method that accounts for the numerous partial cycles in the 

time history and was used by the R19B team to investigate the AASHTO approach to cycles-perpassage for the standard fatigue truck loading. In the rain flow method, time is plotted on the 

vertical axis with the origin being the earliest time. Stress is plotted on the horizontal axis, with 

tensile portions of stress (positive) being on the right and compressive stresses (negative) being 

plotted on the left. The rain flow method was envisioned to look like rain falling on the roof of a 

Japanese pagoda and falling from the tips of the roof either to the ground or to lower levels 

(Dowling, 1972). 

Figure A.3.2-3 depicts the rain flow method of cycle counting for a portion of a stress time 

history. The rules for rain flow counting are as follows (Downing and Socie, 1982): 

1. Rain begins at the beginning of the time history and at the inside of every peak. 

2. Analysis of rain flow is first done by considering all of the flows that begin at a tensile 

peak (i.e., Points 2, 4, 6, etc.). 

3. A half cycle is produced when rain terminates at a compressive peak opposite a more 

tensile peak than the point of origin (i.e., rain beginning at Point 2, flows to Point 3, and 

terminates since Point 3 is opposite (across the axis from) a “more tensile” Point 4 than 

the point of origin). 
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4. A half cycle is produced when rain falls off the time history (i.e., Path 4-5-7-9-11). 

5. A half cycle is produced when rain merges with a flow that began at an earlier tensile 

peak (i.e., Path 6-6’ or 8-8’ or 10-10’) or when it flows in the opposite direction of a 

tensile peak of greater magnitude (i.e., such as Path 5-6).

6. The process is then repeated for all rain that begins at the compressive peaks.

7. Each path is assigned a magnitude based on the value of stress at the start and end of the 

flow and these are deemed half cycles.

8. The number of half cycles of equal magnitude are added as a way of accounting for 

complete cycles. There are commonly some residual half cycles.

Figure A.3.2-3 Rain flow counting example.

Considering the time history shown in Figure A.3.2-3, the rain flow method would produce the 

half cycles and stress ranges presented in Table A.3.2-2. 
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Table A.3.2-2 Rain flow stress cycles for the example time history.

Positive Direction Half Cycles Negative Direction Half Cycles

Path Amplitude Path Amplitude

1-2 2 2-3 3 

3-4 4 4-5-7-9-11 6 

5-6 1 6-6’ 1 

7-8 1 8-8’ 1 

9-10 4 10-10’ 4 

11-12 5 12-13 4 

13-14 2 

The path from 4 to 11 involves three instances where the rain falls onto a lower roof and 

continues to flow until it leaves the time history at Point 11. Thus when rain is introduced to the 

roof at Point 6, 8, or 10, it encounters rain that was previously introduced at Point 4 and is 

therefore interrupted, creating a series of truncated cycles (i.e., 6-6’, 8-8’, and 10-10’, as noted in 

Table A.3.2-2 and Figure A.3.2-3). The cycles are then grouped based on their common 

amplitudes, and the cycles are counted. This is shown in Table A.3.2-3. 

Table A.3.2-3 Amplitude and cycle count for rain flow example.

Amplitude of Cycles Number of Cycles and Paths 

1 2 (4 – 1/2 cycles = Paths 5-6, 7-8, 6-6’, 8-8’)

2 1 (Paths 1-2, 13-14) 

3 0.5 (Path 2-3) 

4 2 (4 – 1/2 cycles = Paths 3-4, 9-10, 10-10’, 

12-13) 

5 0.5 (Path 11-12) 

6 0.5 (Path 4-11) 

In a similar way that stress time histories can be counted, so can fluctuations in moment. After 

completing the truck crossing simulations, the total number of moment cycles found through the 

rain flow process was divided by the number of trucks processed in the database to compute an 

average number of cycles per truck passage. For simply-supported bridges, the number of cycles 

at midspan varied from 2 to 2.5 cycles per passage for short spans and decreased to one cycle per 

passage for spans of 100 feet or greater. For positive moment in the end spans of a continuous 

bridge, the number of cycles varied from 2.3 to 3.5 for short spans and dropped to 1 to 1.5 cycles 

for span lengths of 100 feet or greater. Finally, for negative moment over the interior support of a 

continuous bridge, there were 2.5 to 3.5 cycles per passage for short spans and about 2.5 cycles 

per passage for longer spans. As discussed previously, the greater number of cycles for short 

span bridges is attributed to the axle grouping effects as opposed to the effect of an entire 

vehicle.

Section 3.3 of this Manual, specifically Equation 3.3-8, discusses the development of an 

equivalent stress range concept, Miner’s rule, which expresses an equivalency between a variable 

amplitude stress spectrum and one of constant amplitude and having the same life. The R19B 

research team extended this concept to the idea of an equivalent moment since the bridges being 

studied were those whose stress ranges were directly proportional to live load moment. In order 
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A.8 

to develop an equivalent moment, the probability density functions for moment were developed 

for each WIM site and for various bridge lengths (simple and continuous), and thus an equivalent 

moment could be developed. An example of the moment probability for various simple spans is 

provided for one specific WIM site in Figure A.3.2-4. 

Figure A.3.2-4 Effective bending moment versus probability of occurrence.

Given the probability of certain moments being produced by the WIM trucks for various spans, 

the equivalent moments were computed using Miner’s rule with the exponent, n, taken as 3, 

known as a root mean cube function. 

Equation A.3.2-1 

These equivalent moments were compared to the AASHTO LRFD fatigue truck moments to 

determine how the measured trucks (producing simulated moments) compared to those expected 

from the LRFD fatigue truck loading. 

Figure A.3.2-5 depicts the ratio of the equivalent moment compared to that predicted by the 

AASHTO fatigue truck. The ratio of the equivalent moment to the AASHTO moment is 

consistently lower for shorter spans. Although only the midspan, simple span plot is shown, the 

trend is similar for continuous spans as well. 
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Figure A.3.2-5 Equivalent moment divided by AASHTO fatigue truck for 15 WIM sites.

The use of the equivalent moment was then extended to the computation of fatigue damage 

produced by the equivalent vehicles and that produced by the AASHTO vehicles as a means of 

also studying the influence of the cycles of loading term, n. 

The boundary of actual fatigue damage is represented by the following equation: 

Equation A.3.2-2 

Similarly, the boundary of code fatigue damage is represented by the following equation: 

Equation A.3.2-3 

where:

Meq = equivalent moment found by Miner’s rule 

M = AASHTO fatigue truck moment 

A = AASHTO detail constant
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NR = actual number of cycles

N = AASHTO design number of cycles, (365)(75)(n)(ADTT)SL, using the AASHTO 

“n” values

A parameter, λ, was developed to express the ratio of fatigue damage caused by the actual (WIM 

based) loads divided by the predicted damage caused by the AASHTO model.

Equation A.3.2-4 

The ratio demonstrated that if the current AASHTO model is used, the damage was biased with 

shorter spans having less cumulative damage relative to the LRFD approach than longer spans. 

Although the short spans have a higher number of cycles than longer spans, the equivalent 

moments were also less than predicted by the standard AASHTO design vehicle. The bias in the 

λ values was proposed by the R19B researchers to be corrected by changing the cycles-perpassage approach and eliminating the under / over 40 foot span length distinction. The changes 

presented in Table A.3.2-4 were proposed to provide an equal bias to all span lengths and for 

simple and continuous span bridges. 

Table A.3.2-4 Suggested cycles-per-passage factors. 

Longitudinal Members n 

Simple span girders 1.0

Continuous girders Near interior support 1.5

Elsewhere 1.0

A.3.3 Selection of Fatigue Load Factors

Calibration of the Fatigue I load combination is based on continuing the philosophy that the limit 

state should have a probability of exceedance no more than 1:10,000. In terms of the bending 

moment (and hence stress) statistics, this exceedance can be determined by examining the 

cumulative distribution functions (CDF’s) for a data set. The R19B report presents an example of 

the use of the CDF’s to determine the 1:10,000 exceedance moment (see Figure A.3.3-1). For 

this particular WIM site, the simulated truck moments for 1:10,000 exceedance criteria are 

approximately 2,500 kip-ft. This exceedance moment was compared to the AASHTO design 

truck moments to normalize them for various bridges. 
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Figure A.3.3-1 1:10,000 probability of exceedance moments from a single WIM site. 

The CDF’s for the maximum moment ratios (Fatigue I) and the cumulative damage ratios 

(Fatigue II) were plotted and analyzed in order to calibrate the load factors for the fatigue load 

combinations (see Figure A.3.3-2 and Figure A.3.3-3). A straight line corresponding to a normal 

distribution was superimposed on the data plots, and from this, the mean, standard deviation, and 

variance were determined so that load factors could be determined. The research team 

determined that, for design, the mean design load should be taken as equal to the mean of the 

WIM data plus 1.5 standard deviations (i.e., μ+1.5σ), which corresponds to a mean design value 

with an approximate 5 percent probability of exceedance. 

Using the μ+1.5σ design mean to set the load factors, the range of load factors for the Fatigue I 

load combination was found to be between approximately 1.6 and 2.5. The R19B researchers 

recommended a value of 2.0 for the Fatigue I load combination. This was a change from the 

AASHTO value at the time of the research of 1.5. For the Fatigue II load combination, the range 

of calibrated load factors was found to be between approximately 0.75 and 0.87. The R19B 

researchers recommended a value of 0.8. This was a change from the AASHTO value at the time 

of the research of 0.75. Subsequent to the publication of the R19B report, and at the request of 

the AASHTO T14 Subcommittee, members of the R19B research team examined the statistical 

data for the Fatigue I load combination again, since this large change from 1.5 to 2.0 was 

perceived to be a major change for the fatigue design of steel bridges and one that could 

negatively impact the assessment of newer steel bridges designed using the previous 1.5 load 

factors. In August 2015, the R19B team presented revised recommendations to AASHTO to 

change the Fatigue I load factor to 1.75 while maintaining the recommended 0.8 value for the 

Fatigue II load combination. These changes were subsequently adopted by AASHTO. 
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Figure A.3.3-2 Load factor versus standard normal variable curves for Fatigue I, simple 

span bridges.
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Figure A.3.3-3 Load factor versus standard normal variable curves for Fatigue II, simple 

span bridges.

SECTION A.4 CALIBRATION OF THE FATIGUE LIMIT STATE

In order to calibrate a limit state, the uncertainties on both the load and resistance side must first 

be quantified. Trial load factors were chosen as described previously. Calibration also requires 

characterization of the uncertainty of resistance as well as testing the trial load and resistance 

factors to determine if they provide the required degree of safety. The researchers made use of 

existing test data that have been used to develop the S-N curves found in the AASHTO LRFD

specifications. These S-N curves, which follow a log-log relationship, or in exponential form as 

N = ASR

-B, present a relationship between stress range and fatigue life in the finite life region. 

The regression analysis found values clustered around 3 for the term “B” in the exponential 

equation, so a coefficient of 3 was imposed for design purposes. 

Similar to the approach taken in the investigation of load factors, the investigation of resistance 

required that the statistical parameters of the fatigue life test data be determined. For each of the 

eight detail categories in the AASHTO LRFD specifications, the available test data were plotted, 
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A.14 

and the mean, standard deviation, and variance were computed. Having thus established the 

statistical characteristics of the resistance data and having previously chosen trial load factors, 

the research team performed a reliability analysis using a Monte Carlo simulation to verify the 

chosen load and resistance factors that would achieve a reliability close to the target value. 

Selection of the target reliability index was performed by first determining the current reliability 

index for the Fatigue I and Fatigue II load combinations. The reliability index, called β, for the 

Fatigue I load combination varies from 0.9 for Category E to 2.0 for Category D. Both of these 

values are the extreme reliability indices. The other reliability indices lie between 1.1 and 1.5. 

For the Fatigue II load combination, the reliability index is in the range of 0.9 to 1.3, with 

extreme values of 0.7 for Category E and 1.4 for Category E’. The researchers settled on a 

proposed target reliability index, β, of 1.0, not unlike the existing level of reliability. Using the 

proposed load factors, the statistical characteristics of the resistance data, and an inherent 

resistance factor of 1.0, they computed β for the various AASHTO detail categories. The β for 

both the Fatigue I and Fatigue II load combinations vary from 0.9 to 1.2 and are tightly clustered 

around the target value of 1.0. This validates that the load factors chosen and the inherent 

resistance factor of 1.0, along with the suggested changes in the number of cycles to failure 

included in the finite life assessment, will produce the desired reliability. 

A β of 1 suggests an 84 percent confidence in predicting that the detail will survive at least as 

long as the required design life. This chosen value of β is not significantly different than that 

inherent in structures designed using AASHTO LRFD, and researchers did not feel that there was 

excessive risk or conservatism in these older designs. As a comparison, the reliability index, β, 

chosen for the calibration of the strength limit state was 3.5. This implies that a structure 

designed to satisfy the strength limit state has an approximate 1:10,000 probability that the 

strength of the structure will be exceeded over the life of the bridge. 

This last step, validating that the calibrated β is consistent with the target β, validates that the 

chosen load and resistance factors result in the desired level of safety being achieved and the 

fatigue limit state is deemed to be calibrated. Other subtle changes to the fatigue specifications 

were suggested by the R19B team, such as some adjustments to the detail constants, A, and 

minor adjustments to the constant amplitude fatigue threshold (CAFT) for certain details. These 

possible changes have already been evaluated by AASHTO, and it was determined that they will 

not be included in any update to the AASHTO LRFD specifications at this time.
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GLOSSARY

The following terms are commonly used when considering design and evaluation of steel bridges 

for fatigue and fracture. (Many of the definitions presented below are as per AASHTO or 

FHWA.)

AASHTO—American Association of State Highway and Transportation Officials. AASHTO sets 

standards and publishes specifications, test protocols, and guidelines which are used in highway 

and bridge design and construction throughout the United States.

ADTT—Average Daily Truck Traffic. This value is used to compute the number of stress cycles 

to which a detail is subjected.

AWS—American Welding Society. AWS seeks to advance the science, technology, and 

application of welding and allied joining and cutting processes.

Brittle—Structural behavior that leads to sudden loss of load-carrying capacity immediately 

when the elastic limit is exceeded.

CAFT—Constant amplitude fatigue threshold. 

Charpy V-Notch Impact Requirement—The minimum energy required to be absorbed in a 

Charpy V-notch test conducted at a specified temperature.

Charpy V-Notch Test—An impact test complying with AASHTO T 243M/T 243 (ASTM 

A673/A673M). 

Constant Amplitude Fatigue Threshold—The nominal stress range below which a particular 

detail can withstand an infinite number of repetitions without fatigue failure.

Constraint-Induced Fracture—A form of brittle fracture that can occur at details characterized 

by highly constrained joints without any perceptible fatigue crack growth and, more importantly, 

without any warning.

CVN—Charpy V-notch. 

Cyclical Stress—Stress that is not constant but rather is applied in cycles due to repeated loading, 

unloading, and subsequent reloading.

Design Cycles—The number of cycles of stress range for which a bridge component is designed. 

Detail Category—A grouping of components and details having essentially the same fatigue 

resistance.

Discontinuity—An internal defect that is not observable by visual inspection. Discontinuities can 

generally be described as either volumetric defects that are three-dimensional (e.g., slag 
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G.2 

inclusions and porosity) or planar defects that are essentially two-dimensional (e.g., cracks or 

lack of fusion). Discontinuities are inevitable byproducts of steel-making but must be controlled.

Distortion-Induced Fatigue—Fatigue effects due to secondary stresses not normally quantified in 

the typical analysis and design of a bridge.

Ductile—Structural behavior characterized by significant inelastic deformations before any loss 

of load-carrying capacity occurs. Ductile behavior provides warning of structural failure by large 

inelastic deformations.

Effective Stress Range—The assumed constant amplitude stress range produced by the Fatigue II 

load combination and used to determine if adequate finite life is provided. 

Effective Truck—An assumed effective or statistically average weight truck that produces the 

stresses calculated using the Fatigue II load combination. 

Evaluation—An assessment of the performance of an existing bridge. 

Evaluation Fatigue Life—A level of fatigue life specified by AASHTO which equals a 

conservative fatigue life for evaluation (greater than the minimum fatigue life but less than the 

mean fatigue life).

Fatigue—The initiation and/or propagation of cracks due to a repeated variation of normal stress 

with a tensile component. 

Fatigue Design Life—The number of years that a detail is expected to resist the assumed traffic 

loads without fatigue cracking. In the development of the AASHTO LRFD Bridge Design 

Specifications, it has been taken as 75 years. 

Fatigue I Load Combination—A fatigue and fracture load combination related to infinite loadinduced fatigue life.

Fatigue II Load Combination—A fatigue and fracture load combination related to finite loadinduced fatigue life.

Fatigue Life—The number of repeated stress cycles that results in fatigue failure of a detail.

Fatigue Resistance—The maximum stress range that can be sustained without failure of the 

detail for a specified number of cycles.

FCM—Fracture-critical member.

FHWA—Federal Highway Administration. FHWA is an agency within the U.S. Department of 

Transportation that supports State and local governments in the design, construction, and 

maintenance of the Nation’s highway system and various federally and tribal owned lands. 

Finite Fatigue Life—The number of cycles to failure of a detail when the maximum probable 

stress range exceeds the constant amplitude fatigue threshold.
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Fitness-for-Service Analysis—A quantitative engineering evaluation that is performed to 

demonstrate the structural integrity of an in-service component that may contain a flaw or 

damage.

Fracture—Rupture in tension or rapid extension of the fatigue crack, leading to gross 

deformation, loss of function or serviceability, or complete separation of the component.

Fracture Control Plan—A plan for non-redundant structures intended to provide a higher level 

of safety based on specific requirements for control of cracks (through detailing and enhanced 

fabrication inspection protocols) and specification of minimum material properties for steel and 

weld metal measured by CVN testing.

Fracture Critical Inspection—A FCM inspection must be at least a hands-on inspection of the 

fracture critical member or member component. The term hands-on means that the inspector 

must be close enough to place their hands on the fracture critical member or member component 

(tension area) being inspected. The inspection may also include non-destructive evaluation or 

non-destructive testing methods as determined by the Program Manager and outlined in the FCM 

inspection procedures.

Fracture-Critical Member—A steel primary member or portion thereof subject to tension whose 

failure would probably cause a portion of or the entire bridge to collapse. 

Fracture Mechanics—The field of mechanics concerned with the study of the propagation of 

cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force 

on a crack and those of experimental solid mechanics to characterize the material's resistance to 

fracture.

Fracture Toughness—A measure of the ability of a structural material or element to absorb 

energy without fracture. It is generally determined by the Charpy V-notch test. 

Heat Straightening—A repair technique applied to bends and distortions in steel elements in 

order to restore them to their original shape.

Infinite Fatigue Life—The condition when the design stress range calculated using the Fatigue I 

load combination is less than the constant amplitude fatigue threshold. 

Initiation—The portion of general crack growth in which existing discontinuities are sharpened 

into cracks.

Internal Redundancy—A form of redundancy that can be provided by built-up member detailing 

that provides mechanical separation of elements in an effort to limit fracture propagation across 

the entire member cross section. Internal redundancy is generally not considered for the purpose 

of identifying FCMs.

Limit State—A condition in which a component or structure becomes unfit for service and is 

judged either to be no longer useful for its intended function or to be unsafe. Limits of structural 

usefulness include brittle fracture and fatigue. 
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Load-Induced Fatigue—Fatigue effects due to the in-plane stresses for which components and 

details are explicitly designed.

Load Path Redundancy—A form of redundancy that is based on the number of main supporting 

members between points of support, usually parallel, such as girders or trusses. For the purpose 

of identifying FCMs, redundancy has been defined primarily based on conservative 

consideration of load path redundancy alone. 

Maximum Stress Range—The assumed constant amplitude stress range produced by the Fatigue I 

load combination and used to determine if infinite life is provided. 

Maximum Truck—An assumed maximum weight truck that produces the stresses calculated 

using the Fatigue I load combination.

Mean Fatigue Life—A level of fatigue life specified by AASHTO which equals the most likely 

fatigue life. 

Minimum Fatigue Life—A level of fatigue life specified by AASHTO which equals the 

conservative design fatigue life.

National Bridge Inspection Standards—Federal regulations establishing requirements for 

inspection procedures, frequency of inspections, a bridge inspection organization, qualifications 

of personnel, inspection reports, and preparation and maintenance of bridge inventory records. 

The NBIS apply to all structures defined as highway bridges located on or over all public roads. 

NBIS—National Bridge Inspection Standards.

Negative Remaining Life—The condition in which the calculated remaining fatigue life is 

determined to be negative, suggesting that the detail should have already cracked when it has 

not.

Nominal Resistance—Resistance of a component or connection to load effects, based on its 

geometry, permissible stresses, or specified strength of materials.

Out-of-Plane Distortion—Distortion arising from secondary stresses induced in bridge girders 

from displacement compatibility between the girders and the bracing elements.

Propagation—The portion of general crack growth that represents steady-state fatigue cracking 

that may occur when stresses above the threshold are applied. 

Rain Flow Counting—A method of analysis of fatigue data used to reduce a spectrum of varying 

stress into a set of simple stress reversals.

Redundancy—The quality of a bridge that enables it to perform its design function in a damaged 

state.

Redundant Member—A member whose failure does not cause failure of the bridge.
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Required Fatigue Life—A product of the single-lane average daily truck traffic, the number of 

cycles per truck passage, and the design life in days. 

Residual Stress—The stresses that remain in an unloaded member or component after it has been 

formed into a finished product by cold bending, and/or cooling after rolling or welding.

Resistance Factor—A resistance multiplier accounting for the variability of material properties, 

structural dimensions and workmanship, and the uncertainty in the prediction of resistance. 

Stress Concentration—A location in a bridge member where stress is concentrated. A steel 

member can fail, via a propagating crack, when a concentrated stress exceeds the material’s 

resistance. Fatigue cracks generally begin at stress concentrations.

Stress Range—The algebraic difference between extreme stresses resulting from the passage of a 

load. 

Structural Redundancy—A form of redundancy that can be provided by continuity in main 

members over interior supports or other three-dimensional mechanisms. Structural redundancy is 

generally not considered for the purpose of identifying FCMs.

System Redundant Members (SRM)—Members that are not designated as FCMs and do not 

necessarily require fracture critical inspection but that must be fabricated in accordance with 

AWS D1.5 Clause 12. The criteria, assumptions, and refined analysis used to determine the 

system redundancy condition must be retained to account for changes over the life of the 

structure.

Total Fracture Control Plan—A fracture control plan that incorporates specific fracture control 

requirements set forth by AASHTO, AWS, and FHWA.

Truncated Distribution—A conditional distribution used in statistics that results from restricting 

the domain of some other probability distribution. Truncated distribution can be used to estimate 

the fatigue life when the calculated remaining fatigue life is determined to be negative but no 

fatigue cracking is evident.

Web Gap—A small, unstiffened segment of a steel girder web created when a connection plate is 

not attached to the tension flange. Web gaps are often subjected to out-of-plane distortion when 

there is differential deflection between adjacent girders, leading to the creation of fatigue cracks.
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FIGURE AND TABLE CREDITS

Figure 2.3-1 From A Fatigue Primer for Structural Engineers, by J.W. Fisher, G.L. 

Kulak, and I.F.C. Smith, 1998, Chicago, IL: National Steel Bridge Alliance. 

Copyright 1998 by the National Steel Bridge Alliance. Reprinted with 

permission. 

Figure 2.3.3-1 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Figure 9.8.3.4.4-1), by the American Association of 

State Highway and Transportation Officials, 2015, Washington, DC: 

AASHTO. Copyright 2015 by AASHTO. Reprinted with permission. 

Figure 2.4.2-1 Adapted from Fracture and Fatigue Control in Structures: Applications of 

Fracture Mechanics, by J.M. Barsom and S.T. Rolfe, 1999, West 

Conshohocken, PA: American Society for Testing and Materials. Copyright 

2008 by the American Society for Testing and Materials. Adapted with 

permission. 

Figure 3.2-1 From A Fatigue Primer for Structural Engineers, by J.W. Fisher, G.L. 

Kulak, and I.F.C. Smith, 1998, Chicago, IL: National Steel Bridge Alliance. 

Copyright 1998 by the National Steel Bridge Alliance. Reprinted with 

permission. 

Figure 3.2-2 From A Fatigue Primer for Structural Engineers, by J.W. Fisher, G.L. 

Kulak, and I.F.C. Smith, 1998, Chicago, IL: National Steel Bridge Alliance. 

Copyright 1998 by the National Steel Bridge Alliance. Reprinted with 

permission. 

Figure 4.2-2 From Resistance of Welded Details Under Variable Amplitude Long-Life 

Fatigue Loading, NCHRP Report 354 (Figure 1), by J.W. Fisher, et. al., 

1993, Washington, DC: Transportation Research Board. Copyright 1993 by 

the Transportation Research Board. Reprinted with permission. 

Figure 4.2.1-1 Adapted from Effect of Weldments on the Fatigue Strength of Steel Beams, 

NCHRP Report 102 (Figure 33, pg. 25), by J.W. Fisher, et. al., 1970, 

Washington, DC: Transportation Research Board. Copyright 1970 by the 

Transportation Research Board. Adapted with permission. 

Figure 4.2.2-1 Adapted from Effect of Weldments on the Fatigue Strength of Steel Beams, 

NCHRP Report 102 (Figure 36, pg. 28), by J.W. Fisher, et. al., 1970, 

Washington, DC: Transportation Research Board. Copyright 1970 by the 

Transportation Research Board. Adapted with permission. 

Figure 4.3.1-2 Adapted from “Fatigue Design: Its Past and What It Is Today” (PDF pg. 21), 

by John W. Fisher, Ph.D., [n.d.], 

(http://www.mceer.buffalo.edu/education/Bridge_Speaker_Series/2010-

2011/presentations/Fisher_presentation.pdf). Copyright by John W. Fisher, 

Ph.D. Adapted with permission. 

Figure 4.3.1.1-1 From Effects of Weldments on the Fatigue Strength of Steel Beams, Fritz 

Engineering Laboratory Report 325, by M.A. Hirt, 1971, Bethlehem, PA: 

Fritz Engineering Laboratory, Lehigh University. Copyright 1971 by M.A. 

Hirt. Reprinted with permission.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

F.2 

Figure 4.3.1.1-2 From Effects of Weldments on the Fatigue Strength of Steel Beams, Fritz 

Engineering Laboratory Report 325, by M.A. Hirt, 1971, Bethlehem, PA: 

Fritz Engineering Laboratory, Lehigh University. Copyright 1971 by M.A. 

Hirt. Reprinted with permission.

Figure 4.4.1-1 From A Fatigue Primer for Structural Engineers, by J.W. Fisher, G.L. 

Kulak, and I.F.C. Smith, 1998, Chicago, IL: National Steel Bridge Alliance. 

Copyright 1998 by the National Steel Bridge Alliance. Reprinted with 

permission. 

Figure 4.4.2-3 From "Fatigue Strength of Trolley Bridge Stringers Made of ASTM A7 

Steel,” by P. Albrecht and A. Lenwari, 2008, Journal of Bridge 

Engineering, 13(1), p. 73. Copyright 2008 by the American Society of Civil 

Engineers. Reprinted with permission. 

Figure 5.3.1.1-1 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Table 4.6.2.2.1-1), by the American Association of State 

Highway and Transportation Officials, 2015, Washington, DC: AASHTO. 

Copyright 2015 by AASHTO. Reprinted with permission. 

Figure 5.4.2.3-1 Adapted from Recommendations for Fatigue Design of Welded Joints and 

Components, by A. Hobbacher, 2007, Shaker Heights, OH: Welding 

Research Council. Copyright 2007 by the Welding Research Council. 

Adapted with permission. 

Figure 5.4.2.3-2 Adapted from Recommendations for Fatigue Design of Welded Joints and 

Components, by A. Hobbacher, 2007, Shaker Heights, OH: Welding 

Research Council. Copyright 2007 by the Welding Research Council. 

Adapted with permission. 

Table 5.4.2.3-1 Adapted from Recommendations for Fatigue Design of Welded Joints and 

Components, by A. Hobbacher, 2007, Shaker Heights, OH: Welding 

Research Council. Copyright 2007 by the Welding Research Council. 

Adapted with permission. 

Table 6.3.1.2-1 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Table 6.6.1.2.3-1), by the American Association of State 

Highway and Transportation Officials, 2015, Washington, DC: AASHTO. 

Copyright 2015 by AASHTO. Reprinted with permission. 

Table 6.3.3.2-1 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Table 6.6.1.2.5-3), by the American Association of State 

Highway and Transportation Officials, 2015, Washington, DC: AASHTO. 

Copyright 2015 by AASHTO. Reprinted with permission. 

Table 6.3.4.2-1 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Table 6.6.1.2.5-1), by the American Association of State 

Highway and Transportation Officials, 2015, Washington, DC: AASHTO. 

Copyright 2015 by AASHTO. Reprinted with permission. 

Table 6.3.4.2-2 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Table C3.6.1.4.2-1), by the American Association of 

State Highway and Transportation Officials, 2015, Washington, DC: 

AASHTO. Copyright 2015 by AASHTO. Reprinted with permission. 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

F.3 

Table 6.3.5.1-1 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Table 6.6.1.2.5-2), by the American Association of State 

Highway and Transportation Officials, 2015, Washington, DC: AASHTO. 

Copyright 2015 by AASHTO. Reprinted with permission. 

Figure 6.3.6.3-1 From On the Fatigue Capacity of Headed Shear Studs in Composite Bridge 

Girders (Figure 1), by B. Ovuoba and G.S. Prinz, 2015, Fayetteville, AR: 

Steel Structures Research Laboratory, University of Arkansas. Copyright 

2015 by the Steel Structures Research Laboratory, University of Arkansas. 

Reprinted with permission. 

Figure 6.3.6.3-2 From On the Fatigue Capacity of Headed Shear Studs in Composite Bridge 

Girders (Figure A-1), by B. Ovuoba and G.S. Prinz, 2015, Fayetteville, AR: 

Steel Structures Research Laboratory, University of Arkansas. Copyright 

2015 by the Steel Structures Research Laboratory, University of Arkansas. 

Reprinted with permission. 

Figure 6.3.6.3-5 From Fatigue Strength of Shear Connectors, by R.G. Slutter and J.W. 

Fisher, 1966, Bethlehem, PA: Lehigh University. Copyright 1966 by J.W. 

Fisher. Reprinted with permission. 

Figure 6.3.6.4-1 From TechStar Inc., [n.d.], TechStar Inc.: Findlay, OH. Copyright by 

TechStar Inc. Reprinted with permission. 

Figure 6.3.6.4-2 Adapted from TechStar Inc., [n.d.], (https://www.techstarinc.com/projects/benicia-martinez/dscf0049.jpg), TechStar Inc.: Findlay, 

OH. Copyright by TechStar Inc. Adapted with permission. 

Figure 6.3.6.5-4 From AASHTO LRFD Bridge Design Specifications, 7th Edition (with 2015 

Interim Revisions) (Figure 3.6.1.4.1-1), by the American Association of 

State Highway and Transportation Officials, 2015, Washington, DC: 

AASHTO. Copyright 2015 by AASHTO. Reprinted with permission. 

Figure 6.3.6.6-3 From Cost-Effective Connection Details for Highway Sign, Luminaire and 

Traffic Signal Structures, by S. Roy, et. al., 2009, Bethlehem, PA: Lehigh 

University. Copyright 2009 by J.W. Fisher. Reprinted with permission. 

Figure 6.3.6.6-4 From Cost-Effective Connection Details for Highway Sign, Luminaire and 

Traffic Signal Structures, by S. Roy, et. al., 2009, Bethlehem, PA: Lehigh 

University. Copyright 2009 by J.W. Fisher. Reprinted with permission. 

Figure 6.3.6.6-5 From Cost-Effective Connection Details for Highway Sign, Luminaire and 

Traffic Signal Structures, by S. Roy, et. al., 2009, Bethlehem, PA: Lehigh 

University. Copyright 2009 by J.W. Fisher. Reprinted with permission. 

Figure 6.3.6.6-6 From Sign Structures Manual (OS-A-1), by Bureau of Bridges and 

Structures, 2012, Springfield, IL: Illinois Department of Transportation. 

Copyright 2012 by the Illinois Department of Transportation. Reprinted 

with permission.

Figure 6.3.6.6-7 From Sign Structures Manual (OS-A-2 and OS4-A-2), by Bureau of Bridges 

and Structures, 2012, Springfield, IL: Illinois Department of Transportation. 

Copyright 2012 by the Illinois Department of Transportation. Reprinted 

with permission.
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

F.4 

Table 7.2.3-1 Adapted from AASHTO LRFD Bridge Design Specifications, 7th Edition 

(with 2015 Interim Revisions) (Table 6.4.1-1), by the American Association 

of State Highway and Transportation Officials, 2015, Washington, DC: 

AASHTO. Copyright 2015 by AASHTO. Adapted with permission. 

Table 7.2.3-2 Adapted from AASHTO LRFD Bridge Design Specifications, 7th Edition 

(with 2015 Interim Revisions) (Table 6.6.2-2), by the American Association 

of State Highway and Transportation Officials, 2015, Washington, DC: 

AASHTO. Copyright 2015 by AASHTO. Adapted with permission. 

Table 7.2.3-3 Adapted from AASHTO LRFD Bridge Design Specifications, 7th Edition 

(with 2015 Interim Revisions) (Table 6.6.2-1), by the American Association 

of State Highway and Transportation Officials, 2015, Washington, DC: 

AASHTO. Copyright 2015 by AASHTO. Adapted with permission. 

Figure 7.2.4.1-5 From Robert Connor, Ph.D., [n.d.], Copyright by Robert Connor, Ph.D. 

Reprinted with permission. 

Figure 7.2.4.1-6 From “Investigation and Repair of the Diefenbaker Bridge Failure” by R.M. 

Ellis, 2013, 2013 Conference of the Transportation Association of Canada. 

Copyright 2013 by the Transportation Association of Canada. Reprinted 

with Permission.

Table 8.2.1.1-1 From Manual for Bridge Evaluation, 2nd Edition (with 2015 Interim 

Revisions) (Table 7.2.2.1-1), by the American Association of State Highway 

and Transportation Officials, 2015, Washington, DC: AASHTO. Copyright 

2015 by AASHTO. Reprinted with permission. 

Table 8.2.1.2-1 Adapted from Fatigue Evaluation of Steel Bridges, NCHRP Report 721

(pgs. E-4, E-23), by M.D. Bowman, et. al., 2012, Washington, DC: 

Transportation Research Board. Copyright 2012 by the National Academies 

Press. Adapted with permission. 

Table 8.3.2-1 From Manual for Bridge Evaluation, 2nd Edition (with 2015 Interim 

Revisions) (Table 7.2.5.1-1), by the American Association of State Highway 

and Transportation Officials, 2015, Washington, DC: AASHTO. Copyright 

2015 by AASHTO. Reprinted with permission. 

Table 8.4.2-1 From Manual for Bridge Evaluation, 2nd Edition (with 2015 Interim 

Revisions) (Table 7.2.6.1-1), by the American Association of State Highway 

and Transportation Officials, 2015, Washington, DC: AASHTO. Copyright 

2015 by AASHTO. Reprinted with permission. 

Table 8.4.2-2 From Manual for Bridge Evaluation, 2nd Edition (with 2015 Interim 

Revisions) (Table 7.2.6.1-2), by the American Association of State Highway 

and Transportation Officials, 2015, Washington, DC: AASHTO. Copyright 

2015 by AASHTO. Reprinted with permission. 

Table 8.4.2-3 From Manual for Bridge Evaluation, 2nd Edition (with 2015 Interim 

Revisions) (Table 7.2.6.1-3), by the American Association of State Highway 

and Transportation Officials, 2015, Washington, DC: AASHTO. Copyright 

2015 by AASHTO. Reprinted with permission. 

Table 8.4.2-4 Adapted from Fatigue Evaluation of Steel Bridges, NCHRP Report 721

(Table 13, pg. 35), by M.D. Bowman, et. al., 2012, Washington, DC: 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

F.5 

Transportation Research Board. Copyright 2012 by the National Academies 

Press. Adapted with permission. 

Figure 8.4.3.2.3-1 Adapted from Fatigue Evaluation of Steel Bridges, NCHRP Report 721

(Figure C7.2.7.2.3-1, pgs. E-15, E-30), by M.D. Bowman, et. al., 2012, 

Washington, DC: Transportation Research Board. Copyright 2012 by the 

National Academies Press. Adapted with permission.

Figure 8.4.3.2.3-2 From Fatigue Evaluation of Steel Bridges, NCHRP Report 721 (Figure 

C7.2.7.2.3-1, pgs. E-15, E-30), by M.D. Bowman, et. al., 2012, Washington, 

DC: Transportation Research Board. Copyright 2012 by the National 

Academies Press. Reprinted with permission.

Figure 10.1.2-2 Adapted from Guide to Design Criteria for Bolted and Riveted Joints 

(Figure 5.46), by Kulak, G.L., J.W. Fisher, and J.H.A. Struik, 2001. 

Chicago: American Institute of Steel Construction. Copyright 2001 by the 

Research Council on Structural Connections. Adapted with permission. 

Figure 10.1.4-1 From Steel Design Guide 17: High Strength Bolts, a Primer for Structural 

Engineers (Figure 7.1), by the American Institute of Steel Construction, 

2002. Chicago: American Institute of Steel Construction. Copyright 2002 by 

the American Institute of Steel Construction. Reprinted with permission.

Figure 10.2.1-3 Adapted from A Fatigue Primer for Structural Engineers, by J.W. Fisher, 

G.L. Kulak, and I.F.C. Smith, 1998, Chicago, IL: National Steel Bridge 

Alliance. Copyright 1998 by the National Steel Bridge Alliance. Adapted 

with permission.

Figure 10.3.2-1 From A Fatigue Study of Prestressing Strand, by C. Paulson, K.H. Frank, 

and J.E. Breen, 1983, Austin, TX: Texas State Department of Highways and 

Public Transportation, Transportation Planning Division. Copyright 1983 by 

the Texas Department of Transportation. Reprinted with permission.

Figure 10.3.3-2 From DYWIDAG-Systems International USA Inc., [n.d.], DYWIDAGSystems International USA Inc.: Freedom, PA. Copyright by DYWIDAGSystems International USA Inc. Reprinted with permission. 

Figure 10.3.4-1 From Recommendations for Stay Cable Design, Testing, and Installation. 

PTI DC45.1-12, by the Post-Tensioning Institute, 2012, Farmington Hills, 

MI: Post-Tensioning Institute. Copyright 2012 by the Post-Tensioning 

Institute. Reprinted with permission.

Figure A.3.1-1 From Bridges for Service Life Beyond 100 Years: Service Limit State Design

(Figure 5.17), by Modjeski and Masters, 2015, Washington, DC: 

Transportation Research Board. Copyright 2015 by the National Academies 

Press. Reprinted with permission. 

Table A.3.2-1 Adapted from AASHTO LRFD Bridge Design Specifications, 7th Edition 

(with 2015 Interim Revisions) (Table 6.6.1.2.5-2), by the American 

Association of State Highway and Transportation Officials, 2015, 

Washington, DC: AASHTO. Copyright 2015 by AASHTO. Adapted with 

permission. 

Figure A.3.2-1 From Bridges for Service Life Beyond 100 Years: Service Limit State Design

(Figure 5.26), by Modjeski and Masters, 2015, Washington, DC: 
Design and Evaluation of Steel Bridges for Fatigue and Fracture Reference Manual

F.6 

Transportation Research Board. Copyright 2015 by the National Academies 

Press. Reprinted with permission.

Figure A.3.2-2 From Bridges for Service Life Beyond 100 Years: Service Limit State Design

(Figure 5.27), by Modjeski and Masters, 2015, Washington, DC: 

Transportation Research Board. Copyright 2015 by the National Academies 

Press. Reprinted with permission. 

Figure A.3.2-3 Adapted from Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Figure 5.30), by Modjeski and Masters, 2015, Washington, 

DC: Transportation Research Board. Copyright 2015 by the National 

Academies Press. Adapted with permission. 

Table A.3.2-2 Adapted from Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Table 5.17), by Modjeski and Masters, 2015, Washington, 

DC: Transportation Research Board. Copyright 2015 by the National 

Academies Press. Adapted with permission. 

Table A.3.2-3 Adapted from Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Table 5.18), by Modjeski and Masters, 2015, Washington, 

DC: Transportation Research Board. Copyright 2015 by the National 

Academies Press. Adapted with permission. 

Figure A.3.2-4 From Bridges for Service Life Beyond 100 Years: Service Limit State Design

(Figure 5.33), by Modjeski and Masters, 2015, Washington, DC: 

Transportation Research Board. Copyright 2015 by the National Academies 

Press. Reprinted with permission. 

Figure A.3.2-5 Adapted from Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Table 5.22), by Modjeski and Masters, 2015, Washington, 

DC: Transportation Research Board. Copyright 2015 by the National 

Academies Press. Adapted with permission. 

Table A.3.2-4 Adapted from Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Table 6.6.1.2.5-2), by Modjeski and Masters, 2015, 

Washington, DC: Transportation Research Board. Copyright 2015 by the 

National Academies Press. Adapted with permission.

Figure A.3.3-1 From Bridges for Service Life Beyond 100 Years: Service Limit State Design

(Figure 5.35), by Modjeski and Masters, 2015, Washington, DC: 

Transportation Research Board. Copyright 2015 by the National Academies 

Press. Reprinted with permission. 

Figure A.3.3-2 From Bridges for Service Life Beyond 100 Years: Service Limit State Design

(Figure 5.36), by Modjeski and Masters, 2015, Washington, DC: 

Transportation Research Board. Copyright 2015 by the National Academies 

Press. Reprinted with permission. 

Figure A.3.3-3 Adapted from Bridges for Service Life Beyond 100 Years: Service Limit 

State Design (Figure 5.37), by Modjeski and Masters, 2015, Washington, 

DC: Transportation Research Board. Copyright 2015 by the National 

Academies Press. Adapted with permission.