NIST Technical Note 1886

An Experimental and Computational

Study of Precast Concrete Moment Frames 

under a Column Removal Scenario

Joseph A. Main

Yihai Bao

H.S. Lew

Fahim Sadek

Vincent P. Chiarito

Stephen D. Robert

Jorge O. Torres

NIST Technical Note 1886 

An Experimental and Computational

Study of Precast Concrete Moment Frames

under a Column Removal Scenario 

Joseph A. Main

Yihai Bao

H.S. Lew

Fahim Sadek

Engineering Laboratory

National Institute of Standards and Technology

Vincent P. Chiarito

Stephen D. Robert

Jorge O. Torres

Engineer Research and Development Center

U.S. Army Corps of Engineers

Vicksburg, MS

http://dx.doi.org/10.6028/NIST.TN.1886

September 2015

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie E. May, Under Secretary of Commerce for Standards and Technology and Director 
The policy of the National Institute of Standards and Technology is to use metric 

units in all its published materials. Because this report is intended for the U.S. 

building construction industry, which uses inch-pound units, it is more practical and 

less confusing to use inch-pound units, in some cases, rather than metric units.

However, in most cases, units are presented in both metric and the inch-pound system.

Certain commercial entities, equipment, products, or materials are identified in this 

document in order to describe a procedure or concept adequately. Such identification 

is not intended to imply recommendation or endorsement by the National Institute of 

Standards and Technology, nor is it intended to imply that the entities, products, 

materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Technical Note 1886

Natl. Inst. Stand. Technol. Tech. Note 1886, 102 pages (September 2015)

http://dx.doi.org/10.6028/NIST.TN.1886

CODEN: NTNOEF
iii

ABSTRACT

This report presents an experimental and computational study of two precast concrete moment-frame 

assemblies under a column removal scenario. The main objectives of the study were to (1) characterize 

the behavior and failure modes of the assemblies through full-scale testing and (2) develop computational 

models that could adequately capture the experimental observations and provide additional insights into

the influence of key factors on the responses of the assemblies. The two moment-frame assemblies

represented portions of the perimeter moment frames of two 10-story precast concrete frame buildings. 

One assembly was part of an ordinary moment frame (OMF) from a building designed for Atlanta, 

Georgia (Seismic Design Category B), and the other assembly was part of a special moment frame (SMF)

from a building designed for Seattle, Washington (Seismic Design Category D). The assemblies, each 

comprising three columns and two beams, were subjected to monotonically increasing vertical 

displacement of the unsupported center column. The tests were continued beyond the ultimate capacities

of the assemblies to characterize the failure modes and collapse mechanisms that were developed. 

Experimental measurements included the vertical load, vertical and horizontal displacements at specific 

locations, rotations at beam ends, and strains in reinforcing bars and other steel components. In addition, 

video cameras recorded the progression of damage, including surface cracking, spalling, and component 

failure in the regions surrounding each moment connection. The failure of both the OMF and the SMF 

specimens was characterized by (1) fracture of the bottom anchorage bars at the welded connection to the 

center column and (2) diagonal cracking and shear deformation of the end columns under outward forces 

generated by arching action in the beams. Other failure modes that were observed included shear stud 

failure for the OMF specimen and bond failure of anchorage bars for the SMF specimen.

Computational analyses of the moment-frame assembly tests were carried out using detailed finite 

element models, in which solid elements were used to represent the concrete, steel plates, and steel 

angles, while beam elements were used to represent the longitudinal and transverse reinforcing bars in the 

beams and columns. The models were able to capture the primary response characteristics of the test 

specimens, and the analyses provided additional insights into the overall behavior and failure modes. The 

analyses revealed that out-of-plane bending moments, resulting from eccentricities in the forces 

transferred through the welded beam-to-column connections, contributed to the fracture of the anchorage 

bars in the moment-frame assemblies. Reductions in ductility resulting from welding also contributed to 

the fracture of the anchorage bars, as evidenced by component-level testing of a welded anchorage bar, 

which enabled calibration of the fracture criterion in the finite element modeling. The analyses confirmed 

that the vertical loads were resisted initially through flexural action and subsequently through arching 

action, after closure of the initial gaps between the beams and columns. An energy-based analysis of 

sudden column loss revealed that the ultimate capacities of the moment frames slightly exceeded the 

applicable gravity loads, by 2 % - 11 %. However, the analyses revealed that the responses of the 

assemblies were quite sensitive to uncertain factors such as anchorage bar ductility and the initial gap 

width between the beams and columns, and variations in these factors could result in specimens that 

would not sustain the applicable gravity loads under sudden column loss.

Keywords: buildings; computational model; design standards; disproportionate collapse; finite element 

analysis; moment resisting connections; progressive collapse; precast concrete structures; structural 

robustness; testing.
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v

PREFACE

The experimental and computational study reported herein is part of a comprehensive research program 

being carried out by the National Institute of Standards and Technology (NIST) on prevention of 

disproportionate collapse of building structures. To meet the critical need for experimental data, NIST 

developed a plan to test a series of full-scale structural assemblies of common building types. 

This report presents the results from an experimental and computational study of two precast concrete 

moment-frame assemblies. The specimens represent portions of the perimeter moment frames of two 

precast concrete buildings designed for Seismic Design Categories B and D and incorporating ordinary 

moment frames and special moment frames, respectively. Detailed design of the buildings was carried out 

by S. K. Ghosh and Associates. The design was guided by a panel of experts who reviewed the design

and provided valuable comments. The following experts served on the panel: David R. Bonneville 

(Degenkolb Engineers, San Francisco, CA), Donald O. Dusenberry (Simpson, Gumpertz & Heger, 

Waltham, MA), Ramon Gisanz (Gilsanz, Murray, Steficek, LLP, New York, NY), Thomas A. Sabol

(Englekirk & Sabol, Los Angeles, CA), and Andrew W. Taylor (KPFF Consulting Engineers, Seattle, 

WA).

This research was carried out by NIST in partnership with the U.S. Army Engineer Research and 

Development Center (ERDC) in Vicksburg, Mississippi. ERDC erected the test specimens, deployed the 

instruments, performed the tests, and collected the test data. NIST developed the test plan and designed 

the specimens, developed finite-element models of the test specimens and performed pre-test analyses to 

guide the development of the test plan, analyzed the experimental data to characterize the responses of the 

specimens and compared the data with computational results, performed post-test analyses to investigate 

the sensitivity of the response to various factors, and wrote the report. Zhiyu Zong contributed to the 

finite element model development and experimental data analysis while a Guest Researcher at NIST. 

Isaiah Sampson contributed to the analysis and plotting of experimental data during a Summer 

Undergraduate Research Fellowship at NIST. Financial support for the full-scale tests was provided by 

NIST and the Precast/Prestressed Concrete Institute (PCI). The test specimens were fabricated and 

contributed by the Metromont Corporation.

The authors gratefully acknowledge the thorough review of this report by Jonathan M. Weigand of NIST 

and David J. Stevens of Protection Engineering Consultants.
vi

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vii

TABLE OF CONTENTS

Abstract........................................................................................................................................................iii

Preface .......................................................................................................................................................... v

Table of Contents........................................................................................................................................vii

List of Figures.............................................................................................................................................. ix

List of Tables.............................................................................................................................................xiii

List of Acronyms and Abbreviations......................................................................................................... xiv

Chapter 1 Introduction.................................................................................................................1

1.1 Background...................................................................................................................................... 1

1.2 Scope of Study................................................................................................................................. 2

1.3 Report Outline.................................................................................................................................. 2

Chapter 2 Prototype Buildings....................................................................................................3

2.1 Design of Prototype Buildings......................................................................................................... 3

2.2 Design of Moment Frames............................................................................................................... 4

Chapter 3 Experimental Program................................................................................................7

3.1 Test Specimens................................................................................................................................ 7

3.2 Experimental Configuration........................................................................................................... 10

3.3 Instrumentation .............................................................................................................................. 12

3.3.1 OMF Specimen................................................................................................................... 13

3.3.2 SMF Specimen ................................................................................................................... 15

Chapter 4 Experimental Results ...............................................................................................19

4.1 OMF Specimen .............................................................................................................................. 19

4.1.1 Observed Behavior and Failure Modes.............................................................................. 19

4.1.2 Displacement and Rotation Measurements........................................................................ 24

4.1.3 Strain Measurements.......................................................................................................... 27

4.2 SMF Specimen............................................................................................................................... 35

4.2.1 Observed Behavior and Failure Modes.............................................................................. 35

4.2.2 Displacement and Rotation Measurements........................................................................ 40

4.2.3 Strain Measurements.......................................................................................................... 43

4.3 Summary and Discussion............................................................................................................... 49
Table of Contents

viii

Chapter 5 Computational Modeling and Analysis ...................................................................53

5.1 Pre-Test Modeling and Model Sensitivities................................................................................... 53

5.2 Finite Element Models................................................................................................................... 56

5.3 Material Modeling ......................................................................................................................... 58

5.3.1 Concrete.............................................................................................................................. 58

5.3.2 Steel Plates and Angles ...................................................................................................... 59

5.3.3 Reinforcing Bars................................................................................................................. 60

5.3.4 Torsion Bars....................................................................................................................... 61

5.3.5 Shear Studs......................................................................................................................... 61

5.4 Welded Anchorage Bar Modeling ................................................................................................. 62

5.4.1 Interaction of Bending Moment and Axial Force............................................................... 63

5.4.2 Reduction of Ductility in Heat-Affected Zone ................................................................... 67

5.5 Analysis of Test Specimens........................................................................................................... 70

5.5.1 OMF Specimen................................................................................................................... 70

5.5.2 SMF Specimen ................................................................................................................... 74

5.6 Influence of Span Length............................................................................................................... 78

5.7 Summary and Discussion............................................................................................................... 79

Chapter 6 Evaluation of Structural Robustness ......................................................................81

6.1 Gravity Loads ................................................................................................................................ 81

6.2 Energy-Based Analysis.................................................................................................................. 81

6.3 Results............................................................................................................................................ 82

6.4 Discussion and Limitations............................................................................................................ 84

Chapter 7 Summary and Conclusions......................................................................................85

References ..............................................................................................................................87
ix

LIST OF FIGURES

Figure 2–1. (a) Plan layout and (b) elevation view of prototype buildings..................................................3

Figure 2–2. Perspective illustration of a perimeter moment frame showing link-plate connections and 

placement of spandrel beams within pockets in the columns. ..............................................................5

Figure 2–3. Ordinary moment frame (OMF) connection details. ................................................................5

Figure 2–4. Special moment frame (SMF) connection details.....................................................................6

Figure 3–1. Details of OMF specimen.........................................................................................................8

Figure 3–2. Details of SMF specimen..........................................................................................................9

Figure 3–3. Precast concrete beams and columns prior to assembly. ..........................................................9

Figure 3–4. Front and top views of experimental configuration................................................................11

Figure 3–5. Oblique view of experimental configuration including reaction frame..................................11

Figure 3–6. Assembled specimens prior to testing: (a) OMF specimen; (b) SMF specimen. ...................12

Figure 3–7. Instrumentation: (a) load cell; (b) string potentiometer; (c) LVDT; (d) inclinometer............13

Figure 3–8. Displacement and rotation transducers (OMF specimen).......................................................14

Figure 3–9. Strain gauges on anchorage bars (OMF specimen). ...............................................................14

Figure 3–10. Strain gauges on flexural reinforcing bars (OMF specimen)................................................14

Figure 3–11. Strain gauges on link plates and brace beam (OMF specimen)............................................15

Figure 3–12. Displacement and rotation transducers (SMF specimen). ....................................................16

Figure 3–13. Strain gauges on flexural reinforcing bars (SMF specimen). ...............................................16

Figure 3–14. Strain gauges on shear studs (SMF specimen). ....................................................................16

Figure 3–15. Strain gauges on link plates and brace beams (SMF specimen)...........................................17

Figure 4–1. Applied vertical load vs. vertical displacement of center column for OMF specimen (labeled 

points correspond to images in Figure 4–2)........................................................................................20

Figure 4–2. Progression of damage for OMF specimen (images correspond to labeled points in Figure 4–

1). ........................................................................................................................................................21

Figure 4–3. Detachment of upper column plate from left end column (OMF specimen)..........................23

Figure 4–4. Fractured anchorage bars from lower left connection to center column (OMF specimen). ...23

Figure 4–5. Final damage to right end column viewed from several angles (OMF specimen). ................23

Figure 4–6. Final damage to left end column viewed from several angles (OMF specimen). ..................23

Figure 4–7. Detachment of upper column plate from right end column (OMF specimen)........................24

Figure 4–8. Out-of-plane bending of link plates at right end column: (a) upper link plate; (b) lower link 

plate (OMF specimen). .......................................................................................................................24

Figure 4–9. Applied vertical load vs. vertical displacements at (a) center column and (b) midspan of 

beams (OMF specimen)......................................................................................................................25
List of Figures

x

Figure 4–10. Vertical displacement profile of beams corresponding to indicated vertical loads (OMF 

specimen; displacements magnified). .................................................................................................25

Figure 4–11. Beam end rotations (OMF specimen)...................................................................................26

Figure 4–12. Horizontal displacement of end columns at beam mid-height (OMF specimen). ................27

Figure 4–13. Strain in upper anchorage bars at end columns (OMF specimen)........................................27

Figure 4–14. Strain in lower anchorage bars at center column (OMF specimen)......................................28

Figure 4–15. Deformation and strain profile in anchorage bar and link plate of OMF specimen: (a) 

tension in anchorage bar; (b) compression in anchorage bar..............................................................28

Figure 4–16. Axial force in anchorage bars (OMF specimen)...................................................................30

Figure 4–17. Bending moment in anchorage bars (OMF specimen). ........................................................30

Figure 4–18. Interaction diagrams for axial force and bending moment in anchorage bars 

(OMF specimen). ................................................................................................................................30

Figure 4–19. Axial strain in link plates at end columns (OMF specimen). ...............................................31

Figure 4–20. Axial strain in link plates at center column (OMF specimen)..............................................31

Figure 4–21. Strain in flexural reinforcing bars at midspan of beams (OMF specimen)...........................33

Figure 4–22. Average strain in flexural reinforcing bars at midspan of beams (OMF specimen).............33

Figure 4–23. Axial strain at midspan of front brace beam (OMF specimen). ...........................................34

Figure 4–24. Axial force in front brace beam (OMF specimen)................................................................34

Figure 4–25. Applied vertical load vs. vertical displacement of center column for SMF specimen (labeled 

points correspond to images in Figure 4–26)......................................................................................35

Figure 4–26. Progression of damage for SMF specimen (images correspond to labeled points in Figure 

4–25). ..................................................................................................................................................37

Figure 4–27. Fractured anchorage bars from lower left connection to center column (SMF specimen)...39

Figure 4–28. Progression of splitting failure and concrete spalling at upper anchorage bars at right end 

column (SMF specimen).....................................................................................................................39

Figure 4–29. Final damage to right end column viewed from several angles (SMF specimen)................39

Figure 4–30. Final damage to left end column viewed from several angles (SMF specimen). .................40

Figure 4–31. Applied vertical load vs. vertical displacements at (a) center column, (b) 3/4 span of beams, 

(c) midspan of beams, and (b) 1/4 span of beams (SMF specimen). ..................................................41

Figure 4–32. Vertical displacement profile of beams corresponding to indicated vertical loads (SMF 

specimen; displacements magnified). .................................................................................................41

Figure 4–33. Beam end rotations (SMF specimen)....................................................................................42

Figure 4–34. Horizontal displacement of end columns (SMF specimen)..................................................42

Figure 4–35. Axial strain in link plates at end columns (SMF specimen). ................................................44

Figure 4–36. Axial strain in link plates at center column (SMF specimen)...............................................44

Figure 4–37. Deformation and strain profiles in anchorage bar and link plate of SMF specimen: (a) 

tension in anchorage bar; (b) compression in anchorage bar..............................................................45
List of Figures

xi

Figure 4–38. Strain in shear studs on upper column plate on left end column (SMF specimen)...............45

Figure 4–39. Strain in flexural reinforcing bars at midspan of beams (SMF specimen). ..........................47

Figure 4–40. Average strain in flexural reinforcing bars at midspan of beams (SMF specimen). ............47

Figure 4–41. Strain in brace beams at midspan (SMF specimen)..............................................................48

Figure 4–42. Axial force in brace beams (SMF specimen)........................................................................48

Figure 4–43. Three stages in the response of the precast concrete specimens...........................................50

Figure 4–44. Top view of link plate connection showing (a) eccentricity in force transfer and (b) resulting 

out-of-plane bending...........................................................................................................................50

Figure 5–1. Influence of key factors on computed response of OMF specimen........................................55

Figure 5–2. Influence of key factors on computed response of SMF specimen. .......................................55

Figure 5–3. Finite element models: (a) OMF specimen; (b) SMF specimen.............................................57

Figure 5–4. Solid-element mesh in connection region (SMF specimen)...................................................57

Figure 5–5. Modeling details at moment connection (top view). ..............................................................58

Figure 5–6. Stress-strain response of concrete material model: (a) compression; (b) tension...................59

Figure 5–7. Stress-strain curves used to model steel components. ............................................................60

Figure 5–8. Normalized shear force vs. slip relationship used for shear studs. .........................................61

Figure 5–9. Finite element models of a welded anchorage bar under eccentric loading: (a) detailed model; 

(b) reduced model. ..............................................................................................................................63

Figure 5–10. Calibrated detailed model analysis of reinforcing bar tensile test. .......................................65

Figure 5–11. Detailed model analysis of welded anchorage bar under eccentric loading. ........................65

Figure 5–12. Bending moment in welded anchorage bar vs. distance along bar. ......................................66

Figure 5–13. Interaction of axial force and bending moment for welded anchorage bars under eccentric 

loading: (a) #10 bar, (b) #11 bar. ........................................................................................................67

Figure 5–14. Component test setup for welded anchorage bar. .................................................................68

Figure 5–15. Results of welded anchorage bar component test: (a) stress-strain curve; (b) fractured 

anchorage bar......................................................................................................................................68

Figure 5–16. Calibrated detailed model of welded anchorage bar component test. ..................................69

Figure 5–17. Interaction of axial force and bending moment for welded #11 anchorage bar with reduced 

ductility under eccentric loading.........................................................................................................70

Figure 5–18. Comparison of experimental and computed results for (a) vertical load and (b) horizontal 

reaction from front brace beam at end column tops (OMF specimen). ..............................................71

Figure 5–19. Section views of OMF model near the peak vertical load....................................................72

Figure 5–20. Deflected shape of OMF specimen prior to anchorage bar fracture.....................................72

Figure 5–21. Concrete damage for OMF specimen prior to anchorage bar fracture. ................................72

Figure 5–22. Concrete damage near top of center column for OMF specimen after anchorage bar fracture: 

(a) photograph; (b) contours of computed damage index. ..................................................................73
List of Figures

xii

Figure 5–23. Anchorage bar fracture in OMF model: (a) perspective view; (b) section through bottom 

anchorage bars on bottom link plates..................................................................................................73

Figure 5–24. Bending moment and axial force interaction for anchorage bar of OMF model..................74

Figure 5–25. Comparison of experimental and computed results for (a) vertical load and (b) horizontal 

reaction from brace beams at end column tops (SMF specimen). ......................................................75

Figure 5–26. Anchorage bar fracture in SMF model: (a) perspective view; (b) section through bottom 

anchorage bars on bottom link plates..................................................................................................76

Figure 5–27. Bending moment and axial force interaction for anchorage bars of SMF specimen............76

Figure 5–28. Deflected shape of SMF specimen prior to anchorage bar fracture......................................77

Figure 5–29. Concrete damage for SMF specimen prior to anchorage bar fracture. .................................77

Figure 5–30. Section views of SMF model at the peak vertical load.........................................................77

Figure 5–31. Concrete damage on right end column of SMF specimen: (a) photograph; (b) contours of 

computed damage index......................................................................................................................77

Figure 5–32. Influence of span length on computed vertical load-displacement response: 

(a) OMF specimen and (b) SMF specimen.........................................................................................79

Figure 6–1. Energy-based analysis of sudden column loss........................................................................82

Figure 6–2. Load-displacement relationships for static loading and sudden column loss compared with 

applicable gravity loading: (a) OMF specimen; (b) SMF specimen...................................................83
xiii

LIST OF TABLES

Table 3–1. Average material properties of reinforcing bars.......................................................................10

Table 5–1. Finite element models used to illustrate the influence of key factors on the computed 

responses.............................................................................................................................................54

Table 6–1. Normalized ultimate capacities and dynamic increase factors for OMF and SMF specimens 

with prototype span lengths. ...............................................................................................................83
xiv

LIST OF ACRONYMS AND ABBREVIATIONS

Acronyms

ACI American Concrete Institute

AISC American Institute of Steel Construction

ASCE American Society of Civil Engineers

ERDC U.S. Army Engineer Research and Development Center

NIST National Institute of Standards and Technology

OMF Ordinary Moment Frame

PCI Precast/Prestressed Concrete Institute

SDC Seismic Design Category

SMF Special Moment Frame

Unit Abbreviations

ft foot

in inch

kip 1000 lbf

kN kilonewton

ksi kip per square inch

lbf pound-force

m meter

mm millimeter

MPa megapascal

psf pound-force per square foot 

psi pound-force per square inch
1

Chapter 1

INTRODUCTION

1.1 BACKGROUND

In May of 1968, a gas explosion blew out a load bearing wall on the 18th floor of the Ronan Point tower 

block in London, causing a progression of failures that resulted in the collapse of an entire corner of the

22-story precast concrete building (Griffiths et al. 1968; Delatte 2009). This event provided an impetus 

for the development of design approaches to prevent such cases of disproportionate collapse. Elliott and 

Jolly (2013, Chapter 9) present a summary of design approaches for disproportionate collapse mitigation, 

with application to multi-story precast concrete structures. One such approach is the tie force method, an 

indirect design approach that requires minimum levels of strength and continuity in the connections 

between the various components of a structure. However, this approach does not consider the ductility of 

the ties, and thus does not ensure that the loads can actually be redistributed as large deformations 

develop following a local failure. The alternative load path method is a direct design approach that 

requires structural analysis to demonstrate explicitly the adequacy of the structural system to redistribute 

loads following a local failure. This approach requires characterization of the nonlinear behavior and 

ductility of structural components and connections, which can involve mechanisms such as arching action 

and catenary action. 

Experimental data from structural assemblies and systems under local failure scenarios, such as column 

removal, are indispensable in characterizing the complex nonlinear behaviors whereby alternative load 

paths can be developed. Experimental data are also critical for validation of models used to represent such 

behaviors in analysis of structural systems. To address the need for such experimental data and associated 

modeling capabilities, the National Institute of Standards and Technology (NIST) is carrying out a 

comprehensive analytical and experimental research program to study the vulnerability of multi-story 

building structures to disproportionate collapse. As part of this research, ten-story prototype buildings 

have been designed with various structural systems, including steel frame, cast-in-place concrete frame, 

and precast concrete frame buildings. Moment-frame assemblies representing portions of these structural 

systems have been tested at full scale under simulated column removal. Sadek et al. (2010) described

testing and analysis of steel moment-frame assemblies, while Lew et al. (2011) described testing and 

analysis of cast-in-place concrete moment-frame assemblies. This report focuses on precast concrete 

moment-frame assemblies.

Experimental data on the disproportionate collapse resistance of precast concrete structures have been 

quite limited. As summarized by Elliott and Jolly (2015), several experimental studies have investigated 

the effectiveness of tie forces in precast concrete floor slabs at redistributing loads through catenary 

action (e.g., Regan 1974, Schultz et al. 1977, Engström 1990). Recently, Nimse et al. (2014, 2015) tested 

one-third scale precast concrete frame assemblies under a column removal scenario, comparing the 

performance of monolithic connections, cast-in-place (“wet”) connections, and field-bolted (“dry”) 

connections. Kang and Tan (2015) performed testing of half-scale precast concrete frame assemblies with 

cast-in-place connections under simulated column removal, comparing the performance of specimens 

with different reinforcement details in the joints. These recent reduced-scale assembly tests (Nimse et al. 
Chapter 1

2

2014, 2015; Kang and Tan 2015) considered rectangular beams with clear span to depth ratios of 

approximately nine, which is comparable to the clear span to depth ratio of beams in the cast-in-place 

concrete assemblies tested previously by Lew et al. (2011). However, much deeper spandrel beams are 

common for exterior frames in precast concrete construction. The focus of this study is on spandrel beams 

designed as part of an exterior moment frame, with moment connections formed by field-welding of steel 

link plates between embedded plates in the columns and embedded angles in the beams. Experimental 

data on the performance of such systems under column removal scenarios were previously unavailable.

1.2 SCOPE OF STUDY

The study reported herein included both full-scale testing and finite-element analysis of two precast 

concrete moment-frame assemblies, which represented portions of the third-floor framing of prototype

ten-story buildings. Each test specimen comprised three columns and two beams. While both specimens 

had moment-resisting beam-to-column connections, one specimen was designed as part of an ordinary

moment frame, and the other was designed as part of special moment frame. The specimens were

subjected to monotonically increasing vertical displacement of the unsupported center column to observe 

their behavior under a simulated column removal scenario, which included the development of flexural 

action and arching action. Each test was continued beyond the ultimate capacity of the assembly, to 

characterize the failure modes and collapse mechanisms that developed. Detailed finite element models of 

the test specimens were developed, and the models were able to capture the primary response 

characteristics of the assemblies, providing insight into their behavior and failure modes.

1.3 REPORT OUTLINE

The report describes the experimental and computational approaches used in this study and presents and 

compares the experimental and computational results for the two moment-frame assemblies. Chapter 2

describes the design of the two ten-story prototype precast concrete buildings, with special emphasis on 

the moment connections considered in this study. The section dimensions, reinforcing details, and 

connection details of the test specimens were taken directly from the prototype buildings. Chapter 3

describes the experimental program, including the experimental configuration, the loading procedure, and 

the instrumentation used for both specimens. Chapter 4 summarizes the test results, including the 

observed behavior and failure modes of each specimen, and presents the measured responses, including 

displacements, rotations, strains, and loads. Chapter 5 describes the finite element models used in the 

analysis of the test specimens and presents the results of these analyses, including comparisons with the

experimental data. Chapter 6 presents an evaluation of the structural robustness of the moment-frame 

assemblies, comparing the loads sustained by the assemblies with the applicable gravity loading and 

analyzing the effect of sudden column loss using an energy-based procedure. Chapter 7 summarizes the 

results of this study and lists the main conclusions.
3

Chapter 2

PROTOTYPE BUILDINGS

2.1 DESIGN OF PROTOTYPE BUILDINGS

The National Institute of Standards and Technology (NIST), working with a panel of practicing structural 

engineers, developed the overall configuration and dimensions of two prototype 10-story precast concrete 

buildings for office occupancy. To examine the effectiveness of seismic design and detailing in resisting 

disproportionate collapse, alternative designs were developed for Seismic Design Category B (SDC B) 

and SDC D. A square plan layout was chosen for both prototype buildings, as shown in Figure 2–1(a), 

with plan dimensions of 150 ft × 150 ft (45.7 m × 45.7 m). As shown in Figure 2–1(b), the height of the 

first story is 15 ft (4.6 m), and the height of each upper story is 13 ft (4.0 m). The detailed design of the 

buildings was carried out by a consulting engineering firm (Kim et al. 2009a,b).

Figure 2–1. (a) Plan layout and (b) elevation view of prototype buildings.

Both buildings have perimeter moment frames designed to resist lateral loads, while the interior framing 

is designed for gravity loads only. The building designed for SDC B incorporates ordinary moment 

frames (OMFs), while the building designed for SDC D incorporates special moment frames (SMFs). The 

perimeter moment frames consist of spandrel beams connected to columns by steel link plates welded to 

embedded plates and angles (see Section 2.2). The interior gravity framing consists of simply supported 

inverted-T beams spanning between columns in the east-west direction. The floor system consists of 

cambered double-T members spanning in the north-south direction, with a concrete topping that varies in 

thickness from 3.5 in (89 mm) over the inverted-T beams to 2.5 in (64 mm) at midspan of the double-T 

members. The moment-frame assemblies considered in this study were extracted from perimeter moment 

frames in the north-south direction at the third-story level, as indicated in Figure 2–1.

9 stories @ 13 ft 15 ft

9 stories @ 4.0 m 4.6 m

A B C D E F

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

extracted moment-frame assembly

Gravity frame Seismic moment frame

A

B

C

D

E

F

1 2

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

30 ft

9.1 m

N

3 4 5 6

extracted moment-frame assembly

(a)

(b)
Chapter 2

4

The prototype buildings were designed according to ASCE 7-05 (ASCE 2005) for occupancy category II. 

A superimposed dead load of 10 psf (0.48 kN/m2) was considered in addition to the self-weight of the 

structure. Typical floors were designed for a live load of 100 psf (4.79 kN/m2), which was reduced in 

accordance with section 4.8 of ASCE 7-05 (ASCE 2005). The roof was designed for a live load of 25 psf 

(1.20 kN/m2). Seismic design of the OMF building was based on a location in Atlanta, Georgia, on Site 

Class C. Seismic design of the SMF building was based on a location in Seattle, Washington, on Site 

Class D. The design of the structural members was based on the requirements of the ACI 318-05 code 

(ACI 2005). The design of the beam ledges was based on the PCI Design Handbook (PCI 2004). Both the 

precast structural members and the concrete topping were designed using normal-weight concrete, with a 

specific weight of 150 lbf/ft3(23.6 kN/m3). A compressive strength of 6000 psi (41.4 MPa) was specified 

for the precast structural members, and a compressive strength of 4000 psi (27.6 MPa) was specified for 

the concrete topping. A minimum yield strength of fy = 60 ksi (414 MPa) was specified for the reinforcing 

bars.

Design of the structure was based on three-dimensional analyses of the buildings using a commercially 

available computer program for linear elastic analysis. All structural members except for the double-T 

floor members were included in the structural model, while lateral resistance was provided by the exterior 

columns and spandrel beams only. The floor system was modeled as a rigid diaphragm, and gravity loads 

on the floor system were applied directly to the supporting beams. To represent the construction 

sequence, in which welding of moment connections does not occur until after the self-weight loads are in 

place, the structure was analyzed in two steps. In the first analysis, dead loads were applied to a model 

without rigid frame connections between the beams and columns, with lateral restraints included to 

represent the erection bracing during construction. In the second analysis, the remaining load cases were 

applied to a model that included the rigid frame connections, without the lateral restraints. Final member 

and connection forces for design were obtained by combining the results from the two analyses, with 

appropriate load factors according to the applicable load combinations.

2.2 DESIGN OF MOMENT FRAMES

The exterior framing of the prototype buildings consists of columns and spandrel beams and is designed 

to provide the lateral load resisting system for the buildings. The spandrel beams are placed inside 

pockets in the exterior columns (Figure 2–2), and moment connections are established by welding steel 

link plates to steel angles embedded in the beams and to steel plates embedded in the columns. Moment 

connection details are shown in Figure 2–3 and Figure 2–4 for OMF connections and SMF connections, 

respectively. The steel column plates are embedded in the column concrete using AWS D1.1 Type B 

headed studs (AWS 2010). Anchorage reinforcing bars in the spandrel beams are welded to the steel 

angles embedded at the top and bottom of the beams. For both the OMF and SMF connections, class B 

splices are provided between the anchorage bars and the beam flexural reinforcement, to maintain 

continuity of the beam reinforcement through the connection, as required for precast concrete SMFs by 

Section 21.6.2 of ACI 318-05 (ACI 2005). The beam moment is transferred to the column by the coupling 

forces generated in the top and the bottom link plates. Torsional restraint for the spandrel beams is 

provided by torsion rods installed through sleeves in the beams and columns. 

The precast concrete SMFs were designed in accordance with Sections 21.2 through 21.6 of ACI 318-05

(ACI 2005). As noted in the PCI Design Handbook (PCI 2004, Section 3.6.4), these provisions aim to 

produce structures with strong column, weak beam behavior. Section 21.3 of ACI 318-05 specifically 
Prototype Buildings

5

requires that flexural members of SMFs shall have a clear span not less than four times the effective 

depth. To comply with this requirement, the SMF spandrel beams have a reduced depth relative to the 

OMF spandrel beams. The clear span to depth ratio is 2.7 for the OMF spandrel beams and 4.2 for the 

SMF spandrel beams. Further details on the moment-frame assemblies considered in this study, including

the member dimensions and reinforcement details, are provided in section 3.1.

Figure 2–2. Perspective illustration of a perimeter moment frame showing link-plate connections and 

placement of spandrel beams within pockets in the columns.

Figure 2–3. Ordinary moment frame (OMF) connection details.

TOP VIEW

A A

B B

C

C

SECTION A-A SECTION B-B

SECTION C-C

tw = 0.2db

8 5.5

Fillet welding: 5⁄8 in

Fillet welding: 5⁄8 in

L8x6x1

Link plate:

PL 5.5x12x1

Column plate:

PL 22x12x1

L8x6x1

Flare-bevel-groove 

weld (length = 5 in)

Torsion rod (⌀1⁄2) 

and sleeve

Anchorage bar: #10

Reinforcing bar: #10

Dimensions in inches

(1 in = 25.4 mm)

Hoop: #4 @ 12

Shear studs: ⌀1 4

(three rows of three studs)

Torsion rods

(⌀1⁄2) and

sleeves

86

66

Anchorage

bars: #10 L8x6x1

(hoops omitted

for clarity)
Chapter 2

6

Figure 2–4. Special moment frame (SMF) connection details.

Reinforcing bar: #9 Hoop: #4 @ 8

A A

Torsion rod (⌀5⁄8) 

and sleeve

B B

C

C

tw = 0.2db

L8x6x1

Flare-bevel-groove 

weld (length = 6 in)

Anchorage bar: #11

SECTION C-C

L8x6x1

Link plate:

PL 8x12x1

Column plate:

PL 22x20x1

TOP VIEW

Fillet welding: 7⁄8 in

Fillet welding: 7⁄8 in

SECTION B-B

Dimensions in inches

(1 in = 25.4 mm)

11 8

72

57

Torsion rods

(⌀5⁄8) and

sleeves

Anchorage

bars: #11 L8x6x1

SECTION A-A

Shear studs: ⌀1 4

(five rows of three studs)

(hoops omitted

for clarity)
7

Chapter 3

EXPERIMENTAL PROGRAM

This chapter describes the overall experimental program, which includes the design of the test specimens, 

the experimental configuration, the loading procedure, and the instrumentation. The primary objectives 

of these tests were (1) to characterize the response of the precast concrete moment frames under a column 

removal scenario, particularly the capacity of the moment connections to transfer loads through flexural 

action and other mechanisms; and (2) to provide experimental data for validation of finite-element models 

to be used in evaluating the robustness of precast concrete structural systems. The test specimens were 

two-span moment-frame assemblies extracted from the third-floor framing system in the north-south 

direction (C1~E1) of the ten-story buildings described in Chapter 2 (see Figure 2–1). The specimen from 

the SDC B building was part of an ordinary moment frame (OMF), while the specimen from the SDC D 

building was part of a special moment frame (SMF). Throughout the remainder of this report, these two 

specimens are referred to as the OMF specimen and the SMF specimen, respectively. Section 3.1

describes the test specimens, including measured material properties. Section 3.2 describes the 

experimental configuration for both specimens, including boundary conditions and loading procedure. 

Section 3.3 presents the instrumentation for each of the two tests.

3.1 TEST SPECIMENS

Figure 3–1 and Figure 3–2 show member sizes and reinforcement details for the OMF specimen and the 

SMF specimen, respectively. The testing was conducted at the U.S. Army Engineer Research and 

Development Center (ERDC) in Vicksburg, Mississippi, and the span length of the test specimens was 

reduced from 30 ft (9.1 m) to 25 ft (7.6 m) to fit within the testing facility. Reducing the span length in 

this manner would be expected to cause the capacity of the specimens to increase. The effect of the 

shortened span length was evaluated using computational modeling and is discussed subsequently in 

Section 5.6.

The columns had a rectangular cross section (section A-A in Figure 3–1 and Figure 3–2), which was 

reduced to a T-shape in the connection regions to form pockets for the spandrel beams (section B-B in 

Figure 3–1 and Figure 3–2). Column longitudinal reinforcing bars were welded to 1 in (25 mm) thick 

steel plates at the bases of the end columns. The beams and columns were prefabricated off-site, and 

assembly of the test specimens, including welding of the link plates, took place at the ERDC testing 

facility. Figure 3–3 shows the precast concrete beams and columns prior to assembly.

The OMF specimen incorporated the OMF connection details shown in Figure 2–3, and the SMF 

specimen incorporated the SMF connection details shown in Figure 2–4. In this report, the front of each 

specimen denotes the surface on which the link plates were welded when making the moment 

connections, and the designations left beam and right beam correspond to the orientation of the beams 

when viewing the specimen from the front. As indicated in Figure 3–1 and Figure 3–2, the left beam was 

on the east side of the testing facility, and the right beam was on the west side.
Chapter 3

8

The beams of the SMF specimen were inadvertently installed in an inverted orientation so that the longer 

anchorage bars were at the bottom of the beams rather than at the top as designed (see Figure 2–4). A 

slight misalignment of the torsion rod sleeves in the beams and columns also prevented installation of the 

torsion rods for the SMF specimen. As discussed in Section 5.1, the implications of these errors were 

investigated using computational modeling and were found to have only a slight influence on the response 

of the SMF specimen. The experimental results obtained for the SMF specimen are therefore believed to 

quite closely represent the behavior of the specimen as designed. 

Figure 3–1. Details of OMF specimen.

300 300

B B

C

C

A A

Left beam

(East)

Right beam

(West)

Dimensions in inches 

(1 in = 25.4 mm)

161

Steel base plate (24 40 1) 

SECTION C-C (rotated 90 clockwise) 

#10 (flexural) #4

96

9

#4 @ 12 #10 (anchorage)

SECTION A-A SECTION B-B

24

40 9 22 9

9.5

14.5

FRONT VIEW

#4 @ 4

18 #8 14 #8

#4 @ 4
Experimental Program

9

Figure 3–2. Details of SMF specimen.

Figure 3–3. Precast concrete beams and columns prior to assembly.

All precast beams and columns were designed with concrete having a specified compressive strength of 

6000 psi (41.4 MPa) and with ASTM A706 Grade 60 reinforcing bars having a minimum specified yield 

strength of 60 ksi (413.7 MPa). The average measured 28-day compressive strength of concrete was 

5785 psi (40 MPa) and the average 28-day splitting tensile strength of concrete was 469 psi (3.2 MPa).

Table 3.1 shows average values of the measured mechanical properties of the reinforcing bars used to 

fabricate the specimens. All plates and angles were made of ASTM A36 steel with a minimum yield 

strength of 36 ksi (250 MPa). The torsion rods were ASTM A193 Grade B7 bolts with a minimum tensile

strength of 125 ksi (862 MPa).

300 300

B B

C

C

A

Left beam

(East)

Right beam

(West)

A

161

Dimensions in inches 

(1 in = 25.4 mm) Steel base plate (28 40 1)

SECTION A-A SECTION B-B

28

40 9 22 9

12.5

15.5

SECTION C-C (rotated 90 clockwise)

#9 (flexural)

#4

62

12 #4 @ 12

#11 (anchorage)

#5@4

16 #9

#5@4

12 #9

FRONT VIEW
Chapter 3

10

Table 3–1. Average material properties of reinforcing bars.

Bar Size Yield Strength, fy

ksi (MPa)

Tensile Strength, fu

ksi (MPa) Fracture Strain

No. 4†74 (510) 106 (731) 26 %

1

No. 8†73 (503) 108 (745) 24 %

2

No. 9†71 (490) 109 (752) 21 %

2

No. 10†69 (476) 103 (710) 24 %

2

No. 11†70 (483) 105 (724) 22 %

2

No. 10‡64 (441) 90 (621) 15 %

3

No. 11‡68 (469) 95 (655) 15 %

3

† Data from coupon test

‡ Data from rebar test

1 Gage length: 1 in (25 mm)

2 Gage length: 2 in (51 mm)

3 Gage length: 8 in (203 mm)

3.2 EXPERIMENTAL CONFIGURATION

The experimental configuration, which was essentially the same for both specimens, is illustrated in 

Figure 3–4 and Figure 3–5. The base plates of the end columns were welded to 2 in (51 mm) thick steel 

plates atop concrete footings. Each footing was clamped down to the strong floor using post-tensioning 

bars. The tops of the end columns were restrained by a steel frame to simulate the bracing effect provided 

by the upper stories in a multi-story building. This frame consisted of two W16x67 beams spanning 

between the end columns, with W14x82 cross beams at the inside and outside face of each end column. 

The W16x67 beams rested on support beams bolted to a reaction frame, as shown in Figure 3–5. Round 

steel bars between steel plates were used to provide contact between the cross beams and the column 

faces, thus restraining horizontal movements of the end column tops. 

Vertical load was applied to the unsupported center column using a hydraulic actuator with a capacity of 

400 kip (1779 kN) and a stroke of 20 in (508 mm). The actuator was mounted to a reaction frame as 

shown in Figure 3–5. The load was applied under displacement control at a rate of 1 in/min (25 mm/min)

through a steel loading plate, and horizontal movements of the steel loading plate were restrained by four 

columns positioned at the corners of the plate as shown in Figure 3–4. These columns were welded to 

base plates, which were bolted to the strong floor of the laboratory. A special roller bearing support 

arrangement at the four corners of the plate allowed free vertical displacement of the plate along the four 

columns. A collar on the underside of the loading plate fit over the top of the center column and restrained 

its horizontal movement, thereby keeping the applied load in the vertical direction and limiting 

eccentrically applied loading. A pair of steel plates on the front and back sides of the center column 

restrained out-of-plane motion at the lower end of the center column (see Figure 3–4). Round steel rods 

were used to provide contact between these steel plates and the column faces. A pair of columns 

straddling each beam at midspan provided lateral bracing for the beams. Figure 3–6 shows photographs of 

both specimens assembled in the experimental configuration prior to testing.
Experimental Program

11

Figure 3–4. Front and top views of experimental configuration.

Figure 3–5. Oblique view of experimental configuration including reaction frame.

Steel loading plate Hydraulic actuator

Steel 

loading 

plate

Plates (2) for 

lateral bracing of 

center column

Columns (4) for lateral 

bracing of center column

Columns (2) for lateral 

bracing of beam

FRONT VIEW

TOP VIEW

Post-tensioning bars

Plates (2) for 

lateral bracing of 

center column

Footing Strong floor

Steel plate

W16x67 beams (2) 

for restraint of end 

column tops

W16x67 beams (2) 

for restraint of end 

column tops

24

78

78

300 300

Steel 

bars

Steel bars

56

W14x82 

cross beams

W14x82 cross beams

Hydraulic 

actuator W16x67 beams for restraint 

of end column tops

Footing

Reaction frame

Columns (4) for lateral bracing 

of center stub column 

Support beams for 

W16x67 brace beams

Strong floor
Chapter 3

12

Figure 3–6. Assembled specimens prior to testing: (a) OMF specimen; (b) SMF specimen.

3.3 INSTRUMENTATION

Figure 3–7 shows photographs of selected instrumentation as installed on the test specimens. The vertical 

load applied by the hydraulic actuator was measured using a load cell with a capacity of 400 kip 

(1779 kN), shown in Figure 3–7(a). Displacement measurements included vertical displacements of the 

center column and the beams and horizontal displacements of the end columns. Two types of transducers 

were used to measure displacements: spring-loaded, string-type displacement potentiometers, as shown in 

Figure 3–7(b), with a range of 72 in (1830 mm) and an accuracy of 0.001 in (0.025 mm), and LVDTs 

(linear variable differential transformers, also known as linear variable displacement transducers), as 

shown in Figure 3–7(c), with a range of 6 in (152 mm) and an accuracy of 0.005 in (0.127 mm). LVDTs 

were used only to measure horizontal displacements of the end columns for the OMF specimen, while all 

other displacements were measured using string potentiometers. To measure the rotation of the beam

ends, digital inclinometers were attached to the top surface of the beams, as shown in Figure 3–7(d). 

In addition to the types of instruments shown in Figure 3–7, both specimens were extensively 

instrumented with electrical resistance strain gauges attached to the surfaces of selected steel components. 

Uniaxial strain gauges were attached to the reinforcing bars and anchorage bars in the beams, to the link 

plates connecting the beams and columns, and to the W16x67 beams used to brace the tops of the end 

columns. For the SMF specimen uniaxial strain gauges were also attached to shear studs welded to a 

column plate and embedded in the column concrete. For the OMF specimen, surface strains on some of 

the link plates were measured with 45° strain rosettes, which are assemblies of three strain gauges 

differing in orientation by 45° to enable determination of horizontal, vertical, and shear strains. Strain 

gauges on reinforcing bars and shear studs were installed at the precasting plant prior to concrete 

placement, while surface-mounted strain gauges on the link plates and brace beams were installed at the 

testing facility. The SMF specimen was tested first, and differences between the instrumentation layouts 

for the OMF specimen and the SMF specimen reflect changes made as a result of experience gained from 

testing of the SMF specimen. A total of 67 channels of data were recorded for the OMF specimen, and 77 

channels of data were recorded for the SMF specimen.

(a) (b)
Experimental Program

13

The location and designation of specific instrumentation for each specimen are provided in the following 

subsections. In the designation of instrumentation, the prefix “D” is used to denote displacement gauges 

(both string potentiometers and LVDTs), the prefix “R” is used to denote rotation gauges (inclinometers), 

and the prefix “S” is used to denote strain gauges. The estimated uncertainty in the measured load, 

displacement, rotation, and strain data is ±1 %. In addition to these measurements, three digital video

cameras were used to record each test. A camera was aligned with each of the three columns to capture 

deformations, surface cracking, spalling, and component failure in the region surrounding each moment 

connection.

Figure 3–7. Instrumentation: (a) load cell; (b) string potentiometer; (c) LVDT; (d) inclinometer.

3.3.1 OMF Specimen

Figure 3–8 shows the transducers used to measure displacement and rotation for the OMF specimen. 

String potentiometers measured the vertical displacement of the center column (D85 and D86) and the 

vertical displacement near midspan of each beam (D83 and D88), while two LVDTs (D81 and D90) 

measured the horizontal displacement of the end columns at beam mid-height. Four inclinometers (R91–

R94) measured the rotation at each end of the two beams.

Figure 3–9 shows the strain gauges installed on the anchorage bars of the OMF specimen. Strain gauges 

were installed at locations where tensile forces were expected in the anchorage bars, and the gauges were 

installed in pairs on opposite sides of the bars, to enable measurement of flexure as well as axial strains in 

the bars. Parentheses indicate strain gauges installed on the back side of the bars (i.e., the side further 

from the link plates), as is shown more clearly in the section views. Figure 3–10 shows the strain gauges 

installed on flexural reinforcing bars of the OMF specimen at midspan of each beam. These gauges were 

also installed in pairs on opposite sides of the bars as shown in the section views. Figure 3–11 shows the 

strain gauges installed on the link plates of the OMF specimen and at midspan of the front brace beam 

that spans between the tops of the end columns. Strain rosettes on the link plates are shown as groups of 

three strain gauges differing in orientation by 45° (e.g., gauges S112–S114 on the upper right link plate of 

the left beam). 

Center column

Right

beam

Center column

Left beam

Inclinometer

String 

potentiometer

Left

beam

LVDT

Left end column

Center

column

Loading plate

Hydraulic

ram

Load cell

(a) (b) (c)

(d)
Chapter 3

14

Figure 3–8. Displacement and rotation transducers (OMF specimen).

Figure 3–9. Strain gauges on anchorage bars (OMF specimen).

Figure 3–10. Strain gauges on flexural reinforcing bars (OMF specimen).

D81

D88

D90

D83 D85 D86

R91 R92 R93 R94

12

130

12 12

78

12

130 78

Dimensions in inches 

(1 in = 25.4 mm)

S42(S41)

S46(S45)

S41 S42 11.5 11.5 11.5

S48(S47)

S45 S46

LE

SECTION LE

LC

SECTION LC

RC 11.5RE

S44(S43)

S47 S48

SECTION RC

S43 S44

SECTION RE

Dimensions in inches 

(1 in = 25.4 mm) LM

138.5 138.5

S56(S55)

S50(S49)

S55 S56

SECTION LM

S50 S49

RM

138.5 138.5

S64(S63)

S58(S57)

S63 S64

SECTION RM

S57 S58

Dimensions in inches 

(1 in = 25.4 mm)
Experimental Program

15

Figure 3–11. Strain gauges on link plates and brace beam (OMF specimen).

3.3.2 SMF Specimen

Figure 3–12 shows the transducers used to measure displacement and rotation for the SMF specimen. 

String potentiometers were used for all displacement measurements. Vertical displacements were 

measured at the center column (D85 and D86) and along the two beams near 1⁄4 span (D82 and D89), 

midspan (D83 and D88), and 3⁄4 span (D84 and D87). Horizontal displacements of the end columns were 

measured at beam mid-height (D81 and D90) and at the footings (D109 and D110). Four inclinometers 

(R91–R94) measured the rotation at each end of the two beams.

Strain gauges were installed on the anchorage bars of the SMF specimen in a similar configuration as 

shown for the OMF specimen in Figure 3–9. However, because the beams of the SMF specimen were 

inadvertently installed in an inverted orientation (see Section 3.1), the strain gauges were not at the 

intended locations, and no meaningful data was obtained from these gauges. Figure 3–13 shows strain 

gauges installed on the flexural reinforcing bars of the SMF specimen near midspan of each beam. These 

gauges were installed in pairs on opposite sides of the bars as shown in the section views. Additional 

strain gauges on flexural reinforcing bars at section RM (midspan of right beam) either malfunctioned or 

provided inconsistent data and are not presented in this report. Figure 3–14 shows strain gauges installed 

on shear studs welded to the upper column plate at the left end column. Four shear studs were 

instrumented, each with a pair of strain gauges on opposite sides to capture flexure in the studs. Figure 3–

15 shows the uniaxial strain gauges installed on the link plates of the SMF specimen and at midspan of 

the two brace beams that span between the tops of the end columns. Strain gauges were installed on both 

brace beams for the SMF specimen, while only the front brace beam was instrumented for the OMF 

specimen because of limitations on the number of data acquisitions channels available. 

S76 S123

S122

S65

S67

S66 S110

S109 S111

S115

S113 S114

S112 S79 S125S124 S73

S74

S104 S127

S126 S117

S120

S118

S116

S107 S129

S128

S121

S119

S97

S99

S98

BM

S97

S99

S98

SECTION BM

brace beams

(W16x67)
Chapter 3

16

Figure 3–12. Displacement and rotation transducers (SMF specimen).

Figure 3–13. Strain gauges on flexural reinforcing bars (SMF specimen).

Figure 3–14. Strain gauges on shear studs (SMF specimen).

D81

D88

D90

D83 D85 D86

R91 R92 R93 R94

18

81

18 18

D82 D84 D87 D89

D109 D110

6

72

136

201

18

83

136

201

6

81

Dimensions in inches 

(1 in = 25.4 mm)

LM

138.5 138.5

S21(S22)

S23 S24

SECTION LM

S17 S18

RM

138.5

SECTION RM

Dimensions in inches 

(1 in = 25.4 mm)

S23(S24)

S17(S18)

S19(S20)

138.5

S32(S31)

S26(S25)

S21 S22

S19 S20

S31 S32

S25 S26

A S35 A

SECTION A-A

S36 S40S39

S33 S34 S38S37

S35

(S33)

S36

(S34)

S40

(S38)

S39

(S37)
Experimental Program

17

Figure 3–15. Strain gauges on link plates and brace beams (SMF specimen).

(S100)

(S102)

(S101)

BM

S97

S99

S98

SECTION BM

brace beams

(W16x67)

S100

S102

S97 S101

S99

S98

S103

S105

S104

S65

S67

S66

S70

S72

S71

S68

S69

S75

S77

S76

S73

S74

S106

S108

S107

S78

S80

S79
18

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19

Chapter 4

EXPERIMENTAL RESULTS

This chapter presents experimental results for both the OMF and SMF specimens, tested under a column 

removal scenario as described in Chapter 3. These results include the observed behavior and failure 

modes of each specimen, along with measurements recorded during the experiments. Such measurements 

include the applied vertical load, vertical displacements of the center column and beams, horizontal 

displacements of the end columns, rotations at the beam ends, and strains in reinforcing bars, anchorage 

bars, link plates, and other steel components. Both the observed behavior and the measured data provide 

insights into the performance of the specimens under the column removal scenario. Sections 4.1 and 4.2

present experimental results obtained from the OMF and SMF specimens, respectively. Finally, Section 

4.3 presents a summary and discussion of the key experimental findings.

4.1 OMF SPECIMEN

4.1.1 Observed Behavior and Failure Modes

Figure 4–1 shows a plot of the applied vertical load versus the vertical displacement of the center column 

for the OMF specimen. The vertical displacement of the center column, denoted by , was obtained as an 

average of the displacements measured on each side of the center column (D85 and D86 in Figure 3–8). 

Displacement measurements are further discussed subsequently in Section 4.1.2. The labeled points in 

Figure 4–1 correspond to images in Figure 4–2 that show the progression of damage with increasing . 

The images in Figure 4–2 were obtained from the three video cameras that recorded the test, one camera 

aligned with each of the three columns. Each row of three images in Figure 4–2 corresponds to the same 

value of , which was estimated by tracking and scaling of vertical displacements in the central image. 

The uncertainty in the displacement estimates in Figure 4–2 is approximately 0.2 in (5.1 mm). 

The vertical load vs. displacement response of the specimen was essentially linear up to point a in Figure 

4–1, when concrete cracking occurred in the beams around the upper link plates, as shown Figure 4–2(a), 

and the stiffness of the specimen decreased. Further reductions in stiffness occurred as concrete cracks 

formed in the end columns at the lower column plates, as shown in Figure 4–2(b) and (c). The load 

reached an initial peak of 133 kip (592 kN) at a displacement of  = 2.87 in (73 mm) and then began to 

decrease. A drop in the load at point d was associated with detachment of the upper column plate from the 

left end column. The column plate was attached to the column by shear studs (see Figure 2–3), and 

detachment of the column plate was associated with concrete cracking on the left end column, as 

indicated in Figure 4–2(d). This is shown more clearly in Figure 4–3, which shows the opening of cracks 

and spalling of concrete around the detached column plate under continued loading. 
Chapter 4

20

Figure 4–1. Applied vertical load vs. vertical displacement of center column for OMF specimen (labeled 

points correspond to images in Figure 4–2).

After the drop in load at point d in Figure 4–1, the load began to increase steeply again up to point e, 

reaching an ultimate peak of 166 kip (738 kN) at a displacement of  = 5.66 in (144 mm). Between points 

d and e, the specimen developed additional capacity through arching action, with the top corner of each 

beam bearing against the center column and the bottom corner of each beam bearing against the end 

columns. Such bearing was evidenced by narrowing of the gaps between the beams and columns, with 

associated cracking and spalling of concrete in regions where bearing forces were developed, as indicated 

for the center column and the right end column in Figure 4–2(d). Bearing of the left beam against the left 

end column occurred somewhat later than at the other locations and is indicated in Figure 4–2(e).

After reaching the ultimate load at point e, the load dropped sharply to only 25 % of its peak value. This 

drop in load was associated with fracture of the #10 anchorage bars welded to the bottom connecting 

angle on the left side of the center column (see connection detail in Figure 2–3). Fracture of the anchorage 

bars was evidenced by widening of the gap between the left beam and the center column, as indicated in 

Figure 4–2(e). The anchorage bars fractured at the end of the flare-bevel-groove weld on the connecting 

angle, as is evident in Figure 4–4, which shows the connecting angle and welded anchorage bars 

recovered from the specimen after the test.

After fracture of the anchorage bars, the load increased steeply as the specimen developed additional 

resistance through arching action, reaching 70 % of the ultimate load at point f. A drop in load at point f

was associated with fracture of the lower torsion bar at the right end column, accompanied by diagonal 

cracking and shear deformation of the right end column below beam level. Shear deformation of the right 

end column continued throughout the remainder of the test, and Figure 4–5 shows the final state of 

damage viewed from several angles. Another drop in load at point g was associated with fracture of the 

lower torsion bar at the left end column, accompanied by shear deformation of the left end column below 

beam level, which continued throughout the remainder of the test. Shear deformation of the left end 

column occurred with extensive concrete spalling, and Figure 4–6 shows the final state of damage viewed 

from several angles.

0

222

445

667

890

0 127 254 381 508

0

50

100

150

200

0 5 10 15 20 Vertical Load (kN)

Vertical Displacement of Center Column,  (mm) Vertical Load (kip)

Vertical Displacement of Center Column,  (in)

a

d

e

f g

h

b

c
Experimental Results

21

Figure 4–2. Progression of damage for OMF specimen (images correspond to labeled points in Figure 4–

1).

concrete

cracking

detachment of upper 

column plate from 

left end column, 

with associated 

concrete cracking

Left End Column

(a)

(d)

concrete 

cracking

concrete 

cracking

concrete 

spalling

 ≈ 0.4 in (10 mm)

 ≈ 3.9 in (99 mm)

concrete cracking at 

lower column plate 

on right end column

concrete cracking at 

lower column plate on 

left end column

 ≈ 1.3 in (33 mm)

 ≈ 1.6 in (41 mm)

(b)

(c)

Center Column Right End Column

bearing of beam against column

(indicated by reduced gap)

bearing of beams against column

(indicated by reduced gaps)
Chapter 4

22

Figure 4–2 (continued). Progression of damage for OMF specimen (images correspond to labeled points 

in Figure 4–1).

diagonal cracking and 

shear deformation of 

right end column 

below beam level

concrete spalling and 

shear deformation of 

left end column below 

beam level

concrete 

cracking

Left End Column Center Column Right End Column

(f)

(g)

(h)

fracture of 

lower torsion 

bar at right 

end column

detachment of upper 

column plate from 

right end column, 

with associated 

concrete cracking 

and spalling

fracture of lower 

torsion bar at left 

end column

 ≈ 7.7 in (196 mm)

 ≈ 11.0 in (279 mm)

 ≈ 14.4 in (366 mm)

fracture of lower anchorage bars 

on left side of center column 

concrete (indicated by increased gap)

spalling

concrete 

spalling

concrete 

spalling

concrete 

spalling

(e)  ≈ 5.5 in (140 mm)

bearing of beam against column 

(indicated by reduced gap)
Experimental Results

23

Figure 4–3. Detachment of upper column plate from left end column (OMF specimen).

Figure 4–4. Fractured anchorage bars from lower left connection to center column (OMF specimen).

Figure 4–5. Final damage to right end column viewed from several angles (OMF specimen).

Figure 4–6. Final damage to left end column viewed from several angles (OMF specimen).

center

center
Chapter 4

24

At point h in Figure 4–1, the upper column plate detached from the right end column, similar to the 

failure observed previously on the left end column at point d. As indicated in Figure 4–2(h), this failure 

was accompanied by cracking and spalling of concrete on the right end column, which is shown more 

clearly in Figure 4–7. Large deformations of the link plates were observed, as shown in Figure 4–8, which 

were indicative of extensive yielding,. Concave out-of-plane bending occurred at the upper link plate 

[Figure 4–8(a)], where tensile forces caused the beam to pull away from the column, and convex out-ofplane bending occurred at the lower link plate [Figure 4–8(b)], where compressive forces caused the beam 

to bear against the column. Finally, as the load continued to decrease and large chunks of concrete spalled 

from the specimen, the test was terminated at a center column displacement of  = 17.8 in (452 mm).

Figure 4–7. Detachment of upper column plate from right end column (OMF specimen).

Figure 4–8. Out-of-plane bending of link plates at right end column: (a) upper link plate; (b) lower link 

plate (OMF specimen).

4.1.2 Displacement and Rotation Measurements

Figure 4–9 shows the vertical load plotted against the vertical displacements at (a) the center column and 

(b) midspan of the beams. Figure 4–10 shows the corresponding displacement profile of the beams at 

selected values of the center column displacement , where  is an average of the two displacement 

measurements on each side of the center column (D85 and D86). Figure 4–10 was obtained by plotting 

displacements from Figure 4–9 at the transducer locations shown in Figure 3–8. Figure 4–9 and Figure 4–

10 show good agreement between the measurements of symmetrically placed displacement transducers up 

(a) (b)
Experimental Results

25

to the ultimate load at  = 5.66 in (144 mm), indicating that symmetry was largely maintained to this 

point. Some asymmetry of the displacement profile is evident after the ultimate load, with larger 

displacements on the left side of the center column than on the right side. This asymmetry is a result of 

the anchorage bar fractures on the lower left side of the center column, which permitted in-plane rotations 

of the center column, as is evident in Figure 4–2(e) – (h).

Figure 4–9. Applied vertical load vs. vertical displacements at (a) center column and (b) midspan of 

beams (OMF specimen).

Figure 4–10. Vertical displacement profile of beams corresponding to indicated vertical loads (OMF 

specimen; displacements magnified).

Figure 4–11 shows the measured rotation at both ends of the right beam (R93 and R94, see Figure 3–8) 

plotted against the vertical displacement of the center column. Rotation measurements from the left beam 

(R91 and R92) are not presented because these inclinometers appeared to have malfunctioned. Figure 4–

11 shows the measured rotations plotted with the beam chord rotation, calculated as  = tan−1(/L), where 

L = 300 in (7620 mm) is the centerline-to-centerline beam span. This plot shows that the measured 

rotations were essentially linearly proportional to the vertical displacement of the center column, . The 

measured rotations at the two ends of the beam span differed from the calculated beam chord rotation by 

0

222

445

667

890

0 127 254 381 508

0

50

100

150

200

0 5 10 15 20 Vertical Load (kN)

Vertical Displacement (mm) Vertical Load (kip)

Vertical Displacement (in)

D83 D88

0

222

445

667

890

0 127 254 381 508

0

50

100

150

200

0 5 10 15 20 Vertical Load (kN)

Vertical Displacement (mm) Vertical Load (kip)

Vertical Displacement (in)

D85 D86

(a) (b)

Center column Midspan of beams

-508

-381

-254

-127

0

-7620 -3810 0 3810 7620

-20

-15

-10

-5

0

-300 -150 0 150 300 Vertical Displacement (mm)

Spanwise Distance (mm) Vertical Displacement (in)

Spanwise Distance (in)

17.8 in

10.6 in

 = 5.7 in

 = 1.1 in

 =

 =
Chapter 4

26

less than 0.20° (0.0035 rad) for most of the test, with the rotation at the center column being slightly 

greater and the rotation at the end column being slightly less. This implies that the beam essentially 

rotated as a rigid body, with most of the deformations localized at the beam-to-column connections.

Figure 4–11. Beam end rotations (OMF specimen).

Figure 4–12 shows the horizontal displacement of the end columns at beam mid-height, with positive 

values signifying outward displacement, plotted against the vertical displacement of the center column. 

The average of the two measurements, which cancels out rigid-body motions, is also plotted for 

comparison. Initially, both end columns displaced slightly inward, reaching an average inward 

displacement of 0.044 in (1.1 mm) prior to the onset of arching action. After the onset of arching action at

a center column displacement of  ≈ 4.0 in (100 mm) (point d Figure 4–1), both end columns displaced to 

the left by about 0.17 in (4.4 mm), indicating a slight rigid-body rotation of the end columns, which were 

linked at their tops by brace beams (see Figure 3–4). During this rigid-body rotation, the average inward 

displacement decreased slightly as a result of arching action. After fracture of anchorage bars at a center 

column displacement of  = 5.66 in (144 mm) (point e in Figure 4–1), the motion of the right column 

changed directions, and both end columns moved outward. The measured displacement from both gauges 

froze at an outward displacement of about 0.15 in (3.8 mm) and did not provide meaningful data after this 

point. Horizontal displacements after this point were estimated from the video images in Figure 4–2, with 

an estimated uncertainty of ±0.1 in (±2.5 mm) determined by comparing displacements obtained from the 

video images with the those measured by the displacement gauges. The displacements estimated from the 

video images are shown as solid circles in Figure 4–12 and indicate that both end columns continued to 

displace outward as a result of arching action. An average outward displacement of 0.75 in (19 mm) was

estimated at a center column displacement of  = 14.4 in (366 mm), which corresponds to point h in 

Figure 4–1.

0.0000

0.0175

0.0349

0.0524

0.0698

0 127 254 381 508

0

1

2

3

4

0 5 10 15 20 Rotation (rad)

Vertical Displacement of Center Column (mm) Rotation ( )

Vertical Displacement of Center Column (in)

R93 (at center column)

R94 (at right end column)

beam chord rotation
Experimental Results

27

Figure 4–12. Horizontal displacement of end columns at beam mid-height (OMF specimen).

4.1.3 Strain Measurements

Strain measurements in the anchorage bars of the OMF specimen are presented in Figure 4–13 and Figure 

4–14, where Figure 4–13 shows measured strains in the upper anchorage bars at the end columns and 

Figure 4–14 shows measured strains in the lower anchorage bars at the center column. Locations of the 

strain gauges, which were installed in pairs on opposite sides of each bar, were shown in Figure 3–9,

along with the section designations (LE, RE, LC, and RC) referenced in Figure 4–13 and Figure 4–14. All 

gauges on the anchorage bars recorded tensile strains (positive values), which was expected, since gauges 

were installed on the upper bars at the end columns, where negative bending moments developed in the 

beams, and on the lower bars at the center column, where positive bending moments developed. 

Figure 4–13. Strain in upper anchorage bars at end columns (OMF specimen).

-7.6

0.0

7.6

15.2

22.9

0 127 254 381 508

-0.3

0

0.3

0.6

0.9

0 5 10 15 20 Horizontal Displacement (mm)

Vertical Displacement of Center Column (mm) Horizontal Displacement (in)

Vertical Displacement of Center Column (in)

D81 (left end column)

D90 (right end column)

Average

Solid circles indicate

displacements estimated

from video images

0 127 254 381 508

0

4000

8000

12000

16000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S43 (back)

S44 (front)

0 127 254 381 508

0

4000

8000

12000

16000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6⁬)

Vertical Displacement of Center Column (in)

S41 (back)

S42 (front)

(a) (b)

Upper anchorage bar: Section LE

(at left end column)

Upper anchorage bar: Section RE

(at right end column)
Chapter 4

28

Figure 4–14. Strain in lower anchorage bars at center column (OMF specimen).

Figure 4–15. Deformation and strain profile in anchorage bar and link plate of OMF specimen: (a) 

tension in anchorage bar; (b) compression in anchorage bar.

Larger tensile strains were observed on the front side of each anchorage bar, at least initially, indicating 

out-of-plane bending of the bars with curvature away from the front of the specimen, as illustrated in 

Figure 4–15(a). This out-of-plane bending resulted from the eccentricity between the tensile force in the 

anchorage bar and the equilibrating tensile force developed in the link plate. At locations where the 

anchorage bars were subjected to compression, bending occurred in the opposite direction, as illustrated 

in Figure 4–15(b). The deformation and strain profiles in Figure 4–15 are further discussed subsequently 

in relation to strain measurements on the link plates.

Figure 4–16 and Figure 4–17 present the axial force and the out-of-plane bending moment in the 

anchorage bars, respectively, calculated from the measured strains in Figure 4–13 and Figure 4–14.

Figure 4–18 presents corresponding interaction diagrams of axial force plotted against bending moment. 

These axial force and bending moment values were calculated by assuming a linear strain profile across 

the bar (illustrated in Figure 4–15), using the measured stress-strain curve for a #10 bar (from tensile 

testing reported in Table 3–1) to calculate the corresponding stress profile, and numerically integrating 

0 127 254 381 508

0

5000

10000

15000

20000

25000

30000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S47 (back)

S48 (front)

0 127 254 381 508

0

5000

10000

15000

20000

25000

30000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S45 (back)

S46 (front)

(a) (b)

Lower anchorage bar: Section LC

(at center column, left side)

Lower anchorage bar: Section RC

(at center column, right side)

column plate

link plate

2

2

column plate

link plate

Strain profile: section 1 Strain profile: section 2:

+

+

-

Strain profile: section 1 Strain profile: section 2

-

-

+

(a)

(b)
Experimental Results

29

the stress profile over the cross section of the bar. Open circles on the curves of calculated bending 

moment and axial force indicate the point at which yielding first occurred on either side of the bar. The 

curves terminate when significant reductions in strain were observed, because the basic stress-strain 

relationship cannot be applied after unloading occurs, since unloading and reloading occur elastically, 

rather than along the original stress-strain curve.

Figure 4–16 through Figure 4–18 show that out-of-plane bending moments resulting from connection 

eccentricities played an important role in the behavior of the anchorage bars. Figure 4–18(a) shows that 

yielding of the upper anchorage bars at the end columns occurred primarily as a result of bending, at axial 

force values well below the yield capacity of 81.3 kip (362 kN), calculated based on a nominal area of 

1.27 in2(819 mm2) for a #10 bar and a yield strength of fy = 64 ksi (441 MPa) listed in Table 3–1. The 

calculated bending moments are larger at the end columns than at the center column, probably as a result 

of unbalanced forces in the column plates, which permitted more extensive out-of-plane bending and 

eventually led to detachment of the column plates (see Figure 4–3 and Figure 4–7). Figure 4–16(a) shows 

that the upper anchorage bar at the left end column (Section LE) reached a peak axial force at a center 

column displacement of  = 3.5 in (89 mm), close to the displacement at which detachment of the upper 

column plate on the left end column was noted in Figure 4–2(d). Figure 4–16(a) also shows that the upper 

anchorage bar at the right end column (Section RE) reached a peak axial force at a much larger center 

column displacement of  = 11.9 in (302 mm), close to the displacement at which detachment of the 

upper column plate on the right end column was noted in Figure 4–2(h). The strain measurements thus 

corroborate the failure modes identified previously from the video images.

Anchorage bar fracture occurred on the left side of the center column, near Section LC, and Figure 4–

14(a) shows that strain gauges S45 and S46 at Section LC both exhibited drops in strain at  = 5.7 in 

(145 mm), close to the displacement at which anchorage bar fracture was noted in Figure 4–2(d). An

earlier drop in strain measurement S45, at  = 2.5 in (133 mm), prevented calculation of the axial force

and bending moment at Section LC at the point of fracture using the procedure described above.

However, Figure 4–16(b) shows that the lower anchorage bar on the opposite side of the center column 

(at Section RC) reached a peak axial force of 97.7 kip (435 kN) with a bending moment of almost zero 

when fracture occurred. Note that strain gauges on the anchorage bars were attached 3.5 in (89 mm) from 

the end of the connecting angles (see Figure 3–9). Because of steep gradients in bending moment near the 

welded ends of the anchorage bars, bending moments at the end of the weld, where fracture occurred, 

could be significantly greater than those calculated at the location of the gauges. The interaction of 

bending moment and axial force in the welded anchorage bars is further discussed in Section 5.4.1 in the 

context of computational modeling.

Figure 4–19 and Figure 4–20 present measured axial strains in the link plates (see Figure 3–11 for gauge 

locations), where Figure 4–19 shows strains in the link plates at the end columns and Figure 4–20 shows 

strains in the link plates at the center column. Strain rosettes were located at a number of locations on the 

link plates, and strain transformations were applied to the rosette data to obtain vertical and shear strains 

in addition to axial strains. However, these transformations are applicable only for elastic behavior, and 

yielding of the link plates occurred very early in the response, at  ≈ 1 in (25 mm) or earlier. The shear 

and vertical strain values in this early stage of the response were not found to provide significant insights 

into the behavior of the assembly, so only axial strain values are presented in this report.
Chapter 4

30

Figure 4–16. Axial force in anchorage bars (OMF specimen).

Figure 4–17. Bending moment in anchorage bars (OMF specimen).

Figure 4–18. Interaction diagrams for axial force and bending moment in anchorage bars 

(OMF specimen).

0.00

111.21

222.41

333.62

444.82

0 127 254 381 508

0

25

50

75

100

0 5 10 15 20 Axial Force (kN)

Vertical Displacement of Center Column (mm) Axial Force (kip)

Vertical Displacement of Center Column (in)

Section LC

Section RC

0.00

111.21

222.41

333.62

444.82

0 127 254 381 508

0

25

50

75

100

0 5 10 15 20 Axial Force (kN)

Vertical Displacement of Center Column (mm) Axial Force (kip)

Vertical Displacement of Center Column (in)

Section LE

Section RE

(a) (b)

Upper anchorage bars

at end columns

Lower anchorage bars

at center column

Yield point

Yield point

-0.23

0.00

0.23

0.45

0.68

0.90

0 127 254 381 508

-2

0

2

4

6

8

0 5 10 15 20

Bending Moment (kN·m)

Vertical Displacement of Center Column (mm)

Bending Moment (kip∙in)

Vertical Displacement of Center Column (in)

Section LC

Section RC

-0.23

0.00

0.23

0.45

0.68

0.90

0 127 254 381 508

-2

0

2

4

6

8

0 5 10 15 20

Bending Moment (kN·m)

Vertical Displacement of Center Column (mm)

Bending Moment (kip∙in)

Vertical Displacement of Center Column (in)

Section LE

Section RE

(a) (b)

Upper anchorage bars

at end columns

Lower anchorage bars

Yield point at center column

Yield point

0.00

111.21

222.41

333.62

444.82

-0.23 0.00 0.23 0.45 0.68 0.90

0

25

50

75

100

-2 0 2 4 6 8 Axial Force (kN)

Bending Moment (kN·m) Axial Force (kip)

Bending Moment (kip·in)

Section LC

Section RC

0.00

111.21

222.41

333.62

444.82

-0.23 0.00 0.23 0.45 0.68 0.90

0

25

50

75

100

-2 0 2 4 6 8 Axial Force (kN)

Bending Moment (kN·m) Axial Force (kip)

Bending Moment (kip·in)

Section LE

Section RE

(a) (b)

Upper anchorage bars

at end columns

Lower anchorage bars

at center column

Yield point

Yield point
Experimental Results

31

Figure 4–19. Axial strain in link plates at end columns (OMF specimen).

Figure 4–20. Axial strain in link plates at center column (OMF specimen).

0 127 254 381 508

0

5000

10000

15000

20000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S107

0 127 254 381 508

0

5000

10000

15000

20000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S104

0 127 254 381 508

-30000

-20000

-10000

0

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S79

0 127 254 381 508

-30000

-20000

-10000

0

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S65 S66 S67

(a)

(c)

(b)

(d)

Top link plate on left end column Top link plate on right end column

Bottom link plate on left end column Bottom link plate on right end column

0 127 254 381 508

-20000

-15000

-10000

-5000

0

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S117

S120

0 127 254 381 508

0

5000

10000

15000

20000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S111 S113 S115

0 127 254 381 508

-20000

-15000

-10000

-5000

0

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S76

0 127 254 381 508

0

5000

10000

15000

20000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S73

S74

(a)

(c)

(b)

(d)

Top left link plate on center column Top right link plate on center column

Bottom left link plate

on center column

Bottom right link plate

on center column
Chapter 4

32

The axial strain measurements on the link plates consistently have a sign that is opposite to what would 

be expected based on their location. For example, compressive strains are observed in the top link plates 

at the end columns [Figure 4–19(a) and (b)] and in the bottom link plates at the center column [Figure 4–

20(c) and (d)], while Figure 4–13 and Figure 4–14 show tensile strains in the anchorage bars at these

locations. Similarly, tensile strains are observed in the bottom link plates at the end columns [Figure 4–

19(c) and (d)] and in the top link plates at the center column [Figure 4–20(a) and (b)], where compressive 

strains would be expected. These seemingly inconsistent measurements can be understood with reference 

to Figure 4–15 by noting that strains were measured on the front surface of the link plates, and that out-ofplane flexure of a link plate can result in surface strains with a sign opposite to that of the average axial 

strain. Tensile forces in the anchorage bars can thus result in concave bending of the link plate with 

compressive strains on the surface [compare Figure 4–8(a) and Figure 4–15(a)], while compressive forces 

in the anchorage bars can results in convex bending of the link plates with tensile strains on the surface 

[compare Figure 4–8(b) and Figure 4–15(b)].

The measured strains in the link plates provide further corroboration of the failure modes observed 

previously. Increases in strain at  = 3.7 in (94 mm) in Figure 4–19(a) correspond to detachment of the 

upper column plate from the left end column [Figure 4–2(d)], and increases in strain at  = 12 in 

(305 mm) in Figure 4–19(b) correspond to detachment of the upper column plate from the right end 

column [Figure 4–2(h)]. Sharp peaks in strain in Figure 4–19(c) and Figure 4–19(d) likely correspond to 

concrete cracking at the lower column plates on the end columns [Figure 4–2(b) and (c)]. Peaks in strain 

at  = 5.7 in (145 mm) in Figure 4–20(c) and (d) correspond to fracture of the anchorage bars at the 

ultimate load of the assembly [Figure 4–2(e)].

Figure 4–21 shows the measured strains in the flexural reinforcing bars at midspan of the beams (see 

Figure 3–10 for gauge locations). Figure 4–22 shows average axial strains in the flexural bars, obtained 

from the two strain measurements on opposite sides of each bar, along with the overall average strain in 

the flexural bars at each cross section, obtained by averaging the measured strains in the top and bottom 

bars. The measured strains at midspan remain very small, with all strains remaining less than 0.02 %, well 

below the yield point of the bars. Small strains would be expected at midspan, because this is the 

inflection point in the initial flexural response, with positive bending moment at the center column, 

approximately equal negative bending moment at the end columns, and zero bending moment near 

midspan of the beams. Detachment of the upper column plate from the left end column at  = 3.7 in 

(94 mm) [see Figure 4–2(d)] is evident through increased tensile strains in the bottom bars of the left 

beam and increased compressive strains in the top bars [Figure 4–22(a)]. This corresponds to an increase 

in positive bending moment, indicating that the inflection point shifted from midspan towards the left end 

column after detachment of the column plate, which reduced the flexural resistance of the left end 

connection. Fracture of the lower anchorage bars on the left side of the center column at  = 5.7 in 

(145 mm) is evident through a sharp reduction in bending moment at midspan of the left beam (strains in 

the top and bottom bars becoming approximately equal) and a sharp increase in negative bending moment 

at midspan of the right beam (tension in top bars, compression in bottom bars), indicating that the 

inflection point in the right beam shifted toward the center column after fracture of the anchorage bars. 

The overall average strain values in Figure 4–22 show tensile strains in the initial flexural response, as the 

beams pull the end columns inward (see Figure 4–12), with reductions in tensile strain and development 

of compressive strains as arching action develops and the beams push the end columns outward. Figure 

4–22 shows increasing tensile strains in the final phase of the response, as the vertical load continued to 
Experimental Results

33

decrease (beyond point f in Figure 4–1). These tensile strains are counterintuitive, since compressive 

arching action was observed. However, note that the average strains in these flexural bars, located near 

the back face of the spandrel beams, do not represent the average strain over the entire cross section. Most 

of the axial force developed in the concrete, where strains are unknown. The measured tensile strains in 

these bars likely resulted from out-of-plane bending of the spandrel beams, caused by eccentricities in the 

transfer of forces through the beam-to-column connections.

Figure 4–21. Strain in flexural reinforcing bars at midspan of beams (OMF specimen).

Figure 4–22. Average strain in flexural reinforcing bars at midspan of beams (OMF specimen).

0 127 254 381 508

-100

-50

0

50

100

150

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S63 (back) S64 (front)

0 127 254 381 508

-100

-50

0

50

100

150

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S55 (back) S56 (front)

0 127 254 381 508

-100

-50

0

50

100

150

200

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S57 (back)

S58 (front)

0 127 254 381 508

-100

-50

0

50

100

150

200

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S49 (back)

S50 (front)

(a)

(c)

(b)

(d)

Top flexural bar: Section LM

(midspan of left beam)

Top flexural bar: Section RM

(midspan of right beam)

Bottom flexural bar: Section LM

(midspan of left beam)

Bottom flexural bar: Section RM

(midspan of right beam)

0 127 254 381 508

-100

-50

0

50

100

150

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

Bottom average

Top average Overall average

0 127 254 381 508

-100

-50

0

50

100

150

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

Bottom average

Top average Overall average

(a) (b)

Flexural bars: Section LM (left beam, midspan) Flexural bars: Section RM (right beam, midspan)
Chapter 4

34

Figure 4–23 shows the measured strains in the front brace beam spanning between the tops of the end 

columns (see Figure 3–11 for gauge locations). Figure 4–24 shows the corresponding axial force in the 

W16x67 brace beam, obtained by multiplying the average axial strain in the beam by the elastic modulus 

of 29 000 ksi (200 GPa) and the cross-sectional area of 19.7 in2(12710 mm2). Compressive forces 

developed in the brace beam initially, as the end columns moved inward at beam mid-height (Figure 4–

12) and as negative moments in the beams tended to rotate the tops of the end columns inward. A drop in 

the compressive force at  = 3.7 in (94 mm) corresponded to detachment of the upper column plate from 

the left end column [Figure 4–2(d)], and a second drop at  = 5.7 in (145 mm) corresponded to anchorage 

bar fracture. Tensile forces subsequently developed in the brace as the tops of the end columns were 

pushed outward by arching action.

Figure 4–23. Axial strain at midspan of front brace beam (OMF specimen).

Figure 4–24. Axial force in front brace beam (OMF specimen).

0 127 254 381 508

-80

-60

-40

-20

0

20

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S97 (top flange)

S98 (web)

S99 (bottom flange)

Front brace beam at midspan

-177.93

-133.45

-88.96

-44.48

0.00

44.48

0 127 254 381 508

-40

-30

-20

-10

0

10

0 5 10 15 20 Axial Force (kN)

Vertical Displacement of Center Column (mm) Axial Force (kip)

Vertical Displacement of Center Column (in)

Front brace beam
Experimental Results

35

4.2 SMF SPECIMEN

4.2.1 Observed Behavior and Failure Modes

Figure 4–25 shows a plot of the applied vertical load versus the vertical displacement of the center 

column for the SMF specimen. The vertical displacement of the center column, , was obtained as an 

average of the displacements measured on each side of the center column (D85 and D86 in Figure 3–12). 

Displacement measurements are further discussed subsequently in Section 4.2.2. The labeled points in 

Figure 4–25 correspond to images in Figure 4–26 that show the progression of damage with increasing . 

The images in Figure 4–26 were obtained from the three video cameras that recorded the test. The value 

of  corresponding to each row of images was estimated by tracking and scaling of vertical displacements 

in the images, and the uncertainty in these displacement estimates is approximately 0.2 in (5.1 mm). 

Figure 4–25. Applied vertical load vs. vertical displacement of center column for SMF specimen (labeled

points correspond to images in Figure 4–26).

The specimen was initially loaded to 89 kip (391 kN) and then unloaded, to confirm that the 

instrumentation, data acquisition, and loading systems were working properly. During the initial phase of 

loading, some limited damage occurred, which included concrete cracking on the right beam near the link 

plates (see Figure 4–26(a)). After unloading, the center column had a residual vertical displacement of 

= 0.65 in (17 mm), corresponding to point a in Figure 4–25. From this point, the specimen was loaded 

under monotonically increasing displacement for the remainder of the test. 

After reaching an initial peak load at point b in Figure 4–25, at a vertical displacement of  = 2.49 in 

(63.3 mm), a significant drop in the vertical load occurred, from 151 kip to 98 kip (672 kN to 435 kN). 

This drop in load was associated with fracture of a No. 11 anchorage bar welded to the bottom connecting 

angle on the left side of the center column (see connection detail in Figure 2–4). Fracture of the anchorage 

bar was evidenced by a widened gap between the left beam and the center column, as indicated in Figure 

4–26(b). Strain data from the link plates, discussed later in Section 4.2.3, indicate that the bottom 

anchorage bar fractured first and that the upper two anchorage bars fractured subsequently. The 

anchorage bars fractured at the end of the flare-bevel-groove weld on the connecting angle, as is evident 

0 127 254 381 508

0

222

445

667

890

0

50

100

150

200

0 5 10 15 20

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

a

b

c

d

e

f g

h
Chapter 4

36

in Figure 4–27, which shows the connecting angle and welded anchorage bars recovered from the 

specimen after the test.

After the drop in load at point b in Figure 4–25, the load increased beyond the initial peak load, reaching a 

peak of 165 kip (735 kN) at point d before dropping sharply again at a displacement of  = 4.88 in 

(124 mm). Between points c and d, the specimen developed additional capacity through arching action, 

with the bottom corner of each beam bearing against the end columns and the top corner of each beam 

bearing against the center column. Such bearing was evidenced by a reduced gap between the beams and 

columns, as indicated for the end columns in Figure 4–26(c) and for the center column in in Figure 4–

26(c). The drop in load at point d was associated with fracture of the two remaining No. 11 anchorage 

bars welded to the bottom connecting angle on the left side of the center column. Fracture of these 

anchorage bars was evidenced by further increases in the gap between the left beam and the center 

column, as well as extensive spalling of concrete near the anchorage bars, as indicated in Figure 4–26(d).

After the drop in load at point d in Figure 4–25, the load increased again up to point f, reaching an 

ultimate peak of 188 kip (836 kN) at a displacement of  = 6.69 in (170 mm). Between points e and f, the 

specimen continued to develop additional capacity through arching action, with the bottom corners of the 

beams pressing outward against the end columns. The sharp drop in load at point f was associated with

bond failure of the upper anchorage bars at the right end column, resulting from the formation of splitting 

cracks and spalling of the concrete covering the upper anchorage bars near the right end column. Initial 

surface cracking at this location is indicated in Figure 4–26(d), and the progression of splitting failure and 

spalling is more evident in Figure 4–26(e). Finally, at point f, extensive spalling had occurred, and a

substantial gap that had opened between the right beam and the right end column provided evidence of 

bond failure, as indicated in Figure 4–26(f). Close-up photographs in Figure 4–28 illustrate the 

progression of spitting failure and concrete spalling that resulted in bond failure at this location.

It is noted that the bond failure of the anchorage bars (Figure 4–28) may have been influenced by the 

inverted installation of the SMF spandrel beams (see Section 3.1). If the longer anchorage bars had been 

at the top of the beams, as designed, bond failure may have been somewhat delayed, or anchorage bar 

fracture may have occurred instead. However, such differences would not be expected to significantly 

change the overall response of the specimen. Computational modeling (discussed in Section 5.1) showed 

that the inverted beams had only a small influence on the computed response of the SMF specimen.

As indicated in Figure 4–26(f), shear deformation of the right end column also commenced with the drop 

in load at point f, accompanied by diagonal cracking and spalling of concrete below the beam level. Shear 

deformation of the right end column continued throughout the remainder of the test, and Figure 4–29

shows the final damage to the right end column viewed from several angles. 

After the drop in load at point f, the load continued to increase, but with a reduced stiffness, reaching 

95 % of the ultimate load at point g. A slight drop in load at point g was associated with diagonal 

cracking of the left end column below the beam level. Shear deformation of the left end column 

commenced at point g, as indicated in Figure 4–26(g), and continued throughout the remainder of the test. 

Figure 4–30 shows the final state of damage of the left end column viewed from several angles. By the 

end of the test, both end columns had displaced noticeably outward below the beam level, as a result of 

arching action, while the tops of both end columns, which were linked by brace beams (see Figure 3–4), 

had displaced noticeably to the right. The left end column thus displaced leftward near its base but 

rightward at its top, as can be seen in Figure 4–26(h), resulting in extensive tensile cracking on its left 
Experimental Results

37

side, which is evident in Figure 4–30. From point g in Figure 4–25, the load gradually decreased, falling 

to 78 % of the ultimate load at point h. Finally, as the load continued to decrease and large chunks of 

concrete spalled from the specimen, the test was terminated at a center column displacement of  = 

17.8 in (452 mm).

Figure 4–26. Progression of damage for SMF specimen (images correspond to labeled points in Figure 

4–25).

Left End Column

(a)

(d)

 ≈ 2.5 in (64 mm)

 ≈ 4.9 in (124 mm)

(b)

(c)

Center Column Right End Column

 ≈ 0.6 in (15 mm)

 ≈ 3.1 in (79 mm)

concrete 

cracking concrete 

cracking

initial anchorage bar fracture 

(indicated by increased gap)

concrete cracking concrete 

cracking

concrete 

spalling

concrete 

spalling

concrete 

cracking

concrete 

cracking

bearing of beam against column

(indicated by reduced gap)

bearing of beam against column

(indicated by reduced gap)

bearing of beams against 

center column (indicated 

by reduced gaps)

fracture of remaining 

anchorage bars
Chapter 4

38

Figure 4–26 (continued). Progression of damage for SMF specimen (images correspond to labeled 

points in Figure 4–25).

Left End Column

(e)

(h)

 ≈ 6.5 in (165 mm)

 ≈ 9.9 in (251 mm)

(f)

(g)

 ≈ 5.7 in (145 mm)

Center Column Right End Column

 ≈ 17.5 in (445 mm)

concrete 

cracking

and spalling

concrete

spalling

concrete spalling and 

shear deformation of 

right column

concrete 

cracking

concrete 

cracking

diagonal

cracking of 

left column

shear deformation 

of left column

concrete 

spalling

increased gap 

resulting from 

anchorage bar 

bond failure
Experimental Results

39

Figure 4–27. Fractured anchorage bars from lower left connection to center column (SMF specimen).

Figure 4–28. Progression of splitting failure and concrete spalling at upper anchorage bars at right end 

column (SMF specimen).

Figure 4–29. Final damage to right end column viewed from several angles (SMF specimen).
Chapter 4

40

Figure 4–30. Final damage to left end column viewed from several angles (SMF specimen).

4.2.2 Displacement and Rotation Measurements

Figure 4–31 shows the vertical load plotted against the vertical displacements at (a) the center column, 

(b) 3⁄4 span of the beams, (c) midspan of the beams, and (d) 1⁄4 span of the beams. Figure 4–32 shows the 

corresponding displacement profile of the beams at selected values of the center column displacement , 

where  is the average of the two displacement measurements on each side of the center column (D85 and 

D86). Figure 4–32 was obtained by plotting displacements from Figure 4–31 at the transducer locations 

shown in Figure 3–12. Figure 4–31 and Figure 4–32 show good agreement between the measurements of 

symmetrically placed displacement transducers up to the initial peak load at  = 2.49 in (63.3 mm), 

indicating that symmetry was largely maintained to this point. Some asymmetry of the displacement 

profile is evident after the initial peak load, with larger displacements on the left side of the center column 

than on the right side. This asymmetry is a result of the anchorage bar fractures on the lower left side of 

the center column, which permitted in-plane rotations of the center column, as is evident in Figure 4–26. 

Figure 4–32 shows that at each level of loading, the deflected profile of each beam was approximately 

linear, indicating that most of the deformations were localized at the beam-to-column connections, with 

the beams primarily rotating as rigid bodies.

Figure 4–33 shows the measured rotation at both ends of the right beam (R93 and R94, see Figure 3–12) 

plotted against the vertical displacement of the center column. Rotation measurements from the left beam 

(R91 and R92) are not presented because these inclinometers appeared to have malfunctioned. Plotted 

with the measured rotations is the beam chord rotation, calculated as  = tan−1(/L), where L = 300 in 

(7620 mm) is the centerline-to-centerline beam span. The measured rotation of the right beam near the 

center column (R93) remained quite close to the calculated chord rotation, being less than the chord 

rotation by about 0.35° (0.0061 rad) for most of the test. A sudden increase in rotation measurement R94 

occurred at  = 6.8 in (172 mm), which was likely associated with spalling of concrete at the upper 

anchorage bars near the right end column, where the inclinometer was mounted [see Figure 4–26(f)]. 

Later in the test, rotation measurement R94 decreased and converged fairly closely to the calculated beam 

chord rotation.
Experimental Results

41

Figure 4–31. Applied vertical load vs. vertical displacements at (a) center column, (b) 3/4 span of beams, 

(c) midspan of beams, and (b) 1/4 span of beams (SMF specimen).

Figure 4–32. Vertical displacement profile of beams corresponding to indicated vertical loads (SMF 

specimen; displacements magnified).

0 127 254 381 508

0

222

445

667

890

0

50

100

150

200

0 5 10 15 20

Vertical Displacement (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement (in)

D83 D88

0 127 254 381 508

0

222

445

667

890

0

50

100

150

200

0 5 10 15 20

Vertical Displacement (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement (in)

D82 D89

0 127 254 381 508

0

222

445

667

890

0

50

100

150

200

0 5 10 15 20

Vertical Displacement (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement (in)

D84 D87

0 127 254 381 508

0

222

445

667

890

0

50

100

150

200

0 5 10 15 20

Vertical Displacement (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement (in)

D85 D86

(a)

(c)

(b)

(d)

Center column

Midspan of beams

3⁄4 span of beams

1⁄4 span of beams

-7620 -3810 0 3810 7620

-508

-381

-254

-127

0

-20

-15

-10

-5

0

-300 -150 0 150 300

Spanwise Distance (mm) Vertical Displacement (mm) Vertical Displacement (in)

Spanwise Distance (in)

16.7 in

 = 8.9 in

4.7 in

2.5 in

 =

 =

 =
Chapter 4

42

Figure 4–33. Beam end rotations (SMF specimen).

Figure 4–34. Horizontal displacement of end columns (SMF specimen).

Figure 4–34 shows the horizontal displacement of the end columns at (a) the column bases and (b) beam 

mid-height, with positive values signifying outward displacement, plotted against the vertical 

displacement of the center column. The footings at the bases of the end columns were clamped to the 

strong floor using post-tensioning bars to prevent horizontal displacement (see Figure 3–4). Figure 4–

34(a) shows that displacements at the column bases remained quite small, with an average outward 

displacement of 0.15 in (3.8 mm) at the end of the test. Plotted along with the measured displacements at 

beam mid-height in Figure 4–34(b) is the average of the two measurements, which cancels out rigid body 

motions. Initially, both end columns displaced slightly inward at beam mid-height, reaching an average 

inward displacement of 0.042 in (1.1 mm) prior to the onset of arching action. After fracture of the 

anchorage bars (point b in Figure 4–25), at a center column displacement of  = 2.6 in (66 mm), both end 

columns began to move outward as a result of arching action in the beams. At  = 6.7 in (170 mm), after 

bond failure of the upper anchorage bars at the right end column, and after shear deformation of the right 

end column commenced (point f in Figure 4–25), the motion of the left column changed direction, and 

both columns moved to the right at beam mid-height. The left column reached a peak inward (rightward) 

0 127 254 381 508

-0.0349

0

0.0349

0.0698

0.1047

-2

0

2

4

6

0 5 10 15 20

Vertical Displacement of Center Column (mm) Rotation (rad) Rotation ( )

Vertical Displacement of Center Column (in)

R93 (at center column)

R94 (at right end column)

beam chord rotation

Right beam

concrete

spalling

0 127 254 381 508

-12.7

0

12.7

25.4

38.1

50.8

63.5

-0.5

0

0.5

1

1.5

2

2.5

0 5 10 15 20

Vertical Displacement of Center Column (mm) Horizontal Displacement (mm) Horizontal Displacement (in)

Vertical Displacement of Center Column (in)

D81 (left end column) D90 (right end column) Average

0 127 254 381 508

-12.7

0

12.7

25.4

38.1

50.8

63.5

-0.5

0

0.5

1

1.5

2

2.5

0 5 10 15 20

Vertical Displacement of Center Column (mm) Horizontal Displacement (mm) Horizontal Displacement (in)

Vertical Displacement of Center Column (in)

D109 (left end column) D110 (right end column)

(a) (b)

Base of columns Mid-height of beams
Experimental Results

43

displacement of 0.23 in (5.8 mm) at  ≈ 11.7 in (297 mm) before changing direction again and beginning 

to move outward as a result of cracking and shear deformation of the left column. Although the 

displacement of the left column changed directions due to rigid-body motions, the average displacement 

at beam mid-height shows a monotonically increasing outward displacement after the onset of arching 

action, with an average outward displacement of 1.05 in (26.7 mm) at the end of the test.

4.2.3 Strain Measurements

Figure 4–35 and Figure 4–36 present measured axial strains in the link plates of the SMF specimen (see 

Figure 3–15 for gauge locations). For the OMF specimen, strain measurements on the link plates, 

presented previously, had the opposite sign that would be expected based on their location, as a result of

out-of-plane bending of the link plates (see Figure 4–15). However, out-of-plane bending of the link 

plates was less extensive for the SMF specimen than for the OMF specimen (compare Figure 4–28 and 

Figure 4–8, for example). Consequently, the strain measurements on the link plates of the SMF specimen 

generally had the expected sign, with tensile strains in the top link plates at the end columns [Figure 4–

35(a) and (b)] and in the bottom link plates at the center column [Figure 4–36(c) and (d)], and 

compressive strains in the bottom link plates at the end columns [Figure 4–35(a) and (b)] and in the top 

link plates at the center column [Figure 4–36(a) and (b)]. 

Figure 4–37 shows typical deformation and strain profiles for the anchorage bars and link plates of the 

SMF specimen, which exhibit strains of the same sign in the anchorage bar and on the front surface of the 

link plate (contrast with Figure 4–15 for the OMF specimen). The exception to this pattern is for the 

lowest strain gauges on the bottom link plates on the center column [S72 in Figure 4–36(c) and S77 in 

Figure 4–36(c)], where compressive strains developed on the surface of the link plates, as illustrated in 

Figure 4–15(a), indicating more extensive out-of-plane bending near the bottom edge of the bottom link 

plates. Interestingly, this is the location where the initial anchorage bar fracture occurred. In the top link 

plates, out-of-plane bending was greater near the top edge than the bottom edge, as evidenced by the 

lower magnitudes of strain for the upper gauges in Figure 4–35(a) and (b) and in Figure 4–36(a) and (b). 

A fairly consistent pattern is thus observed, in which the extreme edges of the link plates (top edges of top 

link plates and bottom edges of bottom link plates) exhibit more extensive out-of-plane bending, perhaps 

induced by larger tensile forces in the uppermost and lowermost anchorage bars.

The measured strains in the link plates provide further corroboration of the failure modes discussed

previously. Figure 4–36(c) shows a sudden change in sign for strain gauge S72 at  = 2.6 in (66 mm), 

which corresponds to fracture of the lowest anchorage bar on the left side of the center column [Figure 4–

26(b)]. Simultaneous increases in tensile strain for the upper two strain gauges on the same link plate [S70 

and S71 in Figure 4–36(c)] indicate that the two remaining anchorage bars at that location remained intact 

and developed additional load after fracture of the lowest bar. Subsequent reductions in strain for strain 

gauges S70 and S71 at  = 4.9 in (124 mm) correspond to fracture of the two remaining anchorage bars

[Figure 4–26(d)]. Figure 4–35(b) shows sharp increases in strain for gauges S78–S80 on the upper link 

plate on the right end column at  = 6.7 in (170 mm), followed by gradual reductions in strain, 

corresponding to bond failure of the upper anchorage bars at this location [Figure 4–26(f)].
Chapter 4

44

Figure 4–35. Axial strain in link plates at end columns (SMF specimen).

Figure 4–36. Axial strain in link plates at center column (SMF specimen).

0 127 254 381 508

-20000

-15000

-10000

-5000

0

5000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S106 S107 S108

0 127 254 381 508

-20000

-15000

-10000

-5000

0

5000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S103 S104 S105

0 127 254 381 508

-5000

0

5000

10000

15000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S78

S79

S80

0 127 254 381 508

-5000

0

5000

10000

15000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S65

S66

S67

(a)

(c)

(b)

(d)

Top link plate on left end column Top link plate on right end column

Bottom link plate on left end column Bottom link plate on right end column

0 127 254 381 508

-20000

-10000

0

10000

20000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S75 S76 S77

0 127 254 381 508

-20000

-10000

0

10000

20000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S70 S71 S72

0 127 254 381 508

-50000

-40000

-30000

-20000

-10000

0

10000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S73

S74

0 127 254 381 508

-50000

-40000

-30000

-20000

-10000

0

10000

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S68

S69

(a)

(c)

(b)

(d)

Top left link plate on center column Top right link plate on center column

Bottom left link plate

on center column

Bottom right link plate

on center column
Experimental Results

45

Figure 4–37. Deformation and strain profiles in anchorage bar and link plate of SMF specimen: (a) 

tension in anchorage bar; (b) compression in anchorage bar.

Figure 4–38. Strain in shear studs on upper column plate on left end column (SMF specimen).

Figure 4–38 shows measured strains in shear studs on the upper column plate on the left end column (see 

Figure 3–14 for gauge locations). Bending of the shear studs is indicated by nearly equal and opposite 

strains measured on opposite sides of each shear stud. As would be expected, larger strains were observed 

in the studs on the right side of the plate [Figure 4–38(b) and (d)], where loads were transferred to the 

column plate

link plate

2

2

column plate

link plate

Strain profile: section 1 Strain profile: section 2:

+

-

+

Strain profile: section 1 Strain profile: section 2

-

(a)

(b)

+

-

0 127 254 381 508

-2000

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S39 (right side)

S40 (left side)

0 127 254 381 508

-2000

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S37 (right side)

S38 (left side)

0 127 254 381 508

-2000

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S35 (left side) S36 (right side)

0 127 254 381 508

-2000

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S33 (left side) S34 (right side)

(a)

(c)

(b)

(d)

Top left shear stud Top right shear stud

Bottom left shear stud Bottom right shear stud
Chapter 4

46

column plate by the link plate, than in the studs on the left side [Figure 4–38(a) and (c)], which are near 

the free edge of the plate. The measured strains in Figure 4–38 remain less than 0.2 %, which is the 

approximate yield point of the shear studs. Although detachment of column plates was observed for the 

OMF specimen (Figure 4–3 and Figure 4–7), no shear stud failures were observed for the SMF specimen. 

Figure 4–39 shows the measured strains in the flexural reinforcing bars at midspan of the beams (see 

Figure 3–13 for gauge locations). Figure 4–40 shows average axial strains in the flexural bars, obtained 

from the two strain measurements on opposite sides of each bar, along with the overall average strain in 

the flexural bars at each cross section, obtained by averaging the measured strains in the top and bottom 

bars. The measured strains at midspan are very small, with all strains remaining less than 0.06 %, well 

below the yield point of the bars. Small strains would be expected at midspan, because this is the 

inflection point in the initial flexural response, with positive bending moment at the center column, 

approximately equal negative bending moment at the end columns, and zero bending moment near 

midspan of the beams. Fracture of the bottom anchorage bar on the left side of the center column at  = 

2.5 in (64 mm) [Figure 4–26(b)] is evident through increased tensile strains in the top bars of the both

beams and increased compressive strains in the bottom bars (Figure 4–40). This corresponds to an 

increase in negative bending moment, indicating that the inflection points in both beams shifted from 

midspan towards the center column after fracture of the anchorage bar, which reduced the flexural 

resistance at the center column. Fracture of the two remaining anchorage bars on the left side of the center 

column at  = 4.9 in (124 mm) [Figure 4–26(d)] is evident through further increases in negative bending 

moment at midspan of both beams, with these increases being more pronounced in the right beam, where 

the connection to the center column remained intact. Bond failure of the upper anchorage bars at the right 

end column at  = 6.7 in (170 mm) [Figure 4–26(f)] was evident through sharp reductions in the 

measured strains, with these reductions being more pronounced in the right beam, where the bond failure 

occurred.

The plot of overall average strain at midspan of the right beam [Figure 4–40(b)] shows tensile strains in 

the initial flexural response, as the beams pull the end columns inward (see Figure 4–34), with reductions 

in tensile strain and development of compressive strains as arching action develops and the beams push 

the end columns outward. Compressive strains associated with arching action are not evident in Figure 4–

40(a), and both Figure 4–40(a) and (b) show tensile strains developing in the final phase of the response. 

These tensile strains are counterintuitive, since compressive arching action was observed. However, note 

that the average strains in these flexural bars, located near the back face of the spandrel beams, do not 

represent the average strain over the entire cross section. Most of the axial force developed in the 

concrete, where strains are unknown. The measured tensile strains in these bars likely resulted from outof-plane bending of the spandrel beams, caused by eccentricities in the transfer of forces through the 

beam-to-column connections.
Experimental Results

47

Figure 4–39. Strain in flexural reinforcing bars at midspan of beams (SMF specimen).

Figure 4–40. Average strain in flexural reinforcing bars at midspan of beams (SMF specimen).

Figure 4–41 shows the measured strains in the W16x67 brace beams spanning between the tops of the end 

columns (see Figure 3–15 for gauge locations). Figure 4–42 shows the corresponding axial forces in the 

brace beams, obtained by multiplying the average axial strain in each beam by the elastic modulus of 

29 000 ksi (200 GPa) and the cross-sectional area of 19.7 in2(12710 mm2). The total brace force, obtained 

by summing the axial forces in the two brace beams, is also plotted in Figure 4–42. Compressive forces 

developed in the brace beams initially, as the end columns moved slightly inward at beam mid-height 

0 127 254 381 508

0

100

200

300

400

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S31 (back)

S32 (front)

0 127 254 381 508

-600

-400

-200

0

200

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S25 (back)

S26 (front)

0 127 254 381 508

0

100

200

300

400

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S21 (back) S22 (front) S23 (back) S24 (front)

0 127 254 381 508

-600

-400

-200

0

200

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S17 (back) S18 (front) S19 (back) S20 (front)

(a)

(c)

(b)

(d)

Top flexural bars: Section LM

(midspan of left beam)

Top flexural bar: Section RM

(midspan of right beam)

Bottom flexural bars: Section LM

(midspan of left beam)

Bottom flexural bar: Section RM

(midspan of right beam)

0 127 254 381 508

-600

-400

-200

0

200

400

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

Top average Bottom average Overall average

0 127 254 381 508

-600

-400

-200

0

200

400

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

Top average Bottom average Overall average

(a) (b)

Flexural bars: Section LM 

(midspan of 

left beam)

Flexural bars: Section RM 

(midspan of 

right beam)
Chapter 4

48

(Figure 4–34) and as negative moments in the beams tended to rotate the tops of the end columns inward. 

Sudden reductions in the compressive force at  = 2.5 in (64 mm) and at  = 4.9 in (124 mm) 

corresponded to fracture of the lower anchorage bars on the left side of the center column [Figure 4–26(b) 

and (d)]. A steep reversal in the sign of the brace beam forces, from compressive to tensile, occurred at 

= 6.7 in (171 mm), which corresponded to bond failure of the upper anchorage bars at the right end 

column and the onset of shear deformations of the right end column [Figure 4–26(f)]. The top of the right 

end column was subsequently forced outward (rightward) by arching action, pulling the top of the left end 

column rightward as well, and thus developing tensile forces in the brace beams. Differences in strain 

through the depth of the brace beams were indicative of flexure, which was induced by in-plane rotations 

at the tops of the end columns.

Figure 4–41. Strain in brace beams at midspan (SMF specimen).

Figure 4–42. Axial force in brace beams (SMF specimen).

Differences between the axial forces in the two brace beams resulted from torsion in the end columns. 

Because the precast spandrel beams were aligned with the front faces of the columns, rather than their 

centerlines (see top view in Figure 3–4), forces in the link plates produced torsion in the end columns. 

This torsion was resisted by contact with the cross beams used to brace the end column tops at their inside 

0 127 254 381 508

-100

-50

0

50

100

150

200

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S100 (top flange) S101 (web) S102 (bottom flange)

0 127 254 381 508

-100

-50

0

50

100

150

200

0 5 10 15 20

Vertical Displacement of Center Column (mm) Strain (10−6

)

Vertical Displacement of Center Column (in)

S97 (top flange) S98 (web) S99 (bottom flange)

(a) (b)

Front brace beam Back brace beam

0 127 254 381 508

-266.89

-133.45

0.00

133.45

266.89

400.34

-60

-30

0

30

60

90

0 5 10 15 20

Vertical Displacement of Center Column (mm) Axial Force (kip) Axial Force (kN)

Vertical Displacement of Center Column (in)

Front brace beam

Back brace beam

Total
Experimental Results

49

and outside faces, resulting in differential forces in the front and back brace beams. Initially, tensile forces 

in the upper link plates on the end columns tended to pull the front faces of the end columns inward, and 

this torsional rotation was resisted by greater compression in the front brace beam. Subsequently, 

compressive forces associated with arching action tended to push the front faces of the end columns 

outward, and this torsional rotation was resisted by greater tension in the front brace beam.

4.3 SUMMARY AND DISCUSSION

This chapter presented experimental results for the OMF and SMF specimens, which were subjected to 

vertical loading of the unsupported center column to simulate a column removal scenario. Experimental 

measurements were presented, which included the applied vertical load, vertical displacements of the 

center column and beams, horizontal displacements of the end columns, rotations at the beam ends, and

strains in reinforcing bars, anchorage bars, link plates, and other steel components. Photographs and video 

images were also presented to illustrate the behavior, damage progression, and failure modes of the 

specimens. 

The responses of the two specimens consisted of three primary stages, which are illustrated in Figure 4–

43. In the first stage, loads were resisted through flexural action. As illustrated in Figure 4–43(a), tensile 

forces in the bottom link plates at the center column were balanced by compressive forces in the top link 

plates, and tensile forces in the top link plates at the end columns were balanced by compressive forces in 

the bottom link plates. Eccentricities in the transfer of forces through the link plate connections, as 

illustrated in Figure 4–44(a), resulted in out-of-plane bending of the link plates and anchorage bars, as

illustrated in Figure 4–44(a). This out-of-plane bending was evident from strain gauge measurements and 

from photographs of the deformed plates.

In the second stage, loads were resisted through a combination of flexural action and arching action. This 

stage began when deflections and rotations of the beams caused the initial gaps between the beams and 

columns to close, as illustrated in Figure 4–43(b). The top ends of each beam began to bear against the 

center column, while the bottom ends of each beam began to bear against the end columns, enabling the 

development of arching action. Arching action became evident at a center column displacement of about 

3.9 in (99 mm) for the OMF specimen and about 3.1 in (79 mm) for the SMF specimen. Increased vertical 

loads were developed in this stage, along with increased compressive forces in the beams, as the beams 

began to push the end columns outward. 

In the third stage, the specimens continued to carry loads through arching action, but at a reduced capacity 

because of multiple failures that reduced the flexural resistance of the beam-to-column connections. 

Specifically, these failures degraded the capacity for transfer of tensile forces through the link plate 

connections, both at the upper link plates on the end columns and at the lower link plates on the center 

column, as illustrated in Figure 4–43(c). After the flexural resistance was compromised by these failures 

in the transfer of tensile forces, diagonal cracks and shear deformations developed in the lower portions of 

the end columns, as continued arching action forced the end columns outward. 

For the OMF specimen, the first failure in tensile force transfer was at the upper link plate assembly on 

the left end column (see Figure 4–3), where the column plate detached from the column at a center 

column displacement of about 3.7 in (94 mm) (see Figure 4–2(d)). The specimen developed additional 

load through arching action until a second failure in tensile force continuity occurred, which was 
Chapter 4

50

anchorage bar fracture at the lower link plate assembly on the left side of the center column (see Figure 

4–4). This failure occurred at  = 5.7 in (144 mm) (see Figure 4–2(e)) and was associated with the peak 

vertical load. 

Figure 4–43. Three stages in the response of the precast concrete specimens.

Figure 4–44. Top view of link plate connection showing (a) eccentricity in force transfer and (b) resulting 

out-of-plane bending.

failure in transfer

of tensile force

diagonal cracking

failure in transfer

of tensile force

failure in transfer of tensile force diagonal cracking

compression zone compression zone

bearing bearing

bearing bearing

compression zone compression zone

bearing bearing

bearing bearing

tension

compression

tension

compression

compression compression

tension tension

Stage 1: Flexural Action

Stage 2: Flexural Action + Arching Action

Stage 3: Arching Action (Post-Ultimate)

(a)

(b)

(c)

column plate

link plate

anchorage bar

angle

column plate

link plate

(b)

(a)

eccentricity
Experimental Results

51

For the SMF specimen, the first failure in tensile force transfer was at the lower link plate assembly on the 

left side of the center column, where the anchorage bars fractured (see Figure 4–27), first the lowest bar at 

 = 2.6 in (66 mm) (see Figure 4–26(b)) and then the upper two bars at  = 4.9 in (124 mm) (see Figure 

4–26(d)). The SMF specimen also developed additional load through arching action until a second failure 

in tensile force transfer occurred, which was bond failure of the anchorage bars at the upper link plate 

assembly on the right end column, as a result of splitting cracks and spalling of the beam concrete at that 

location (see Figure 4–28). This failure occurred at  = 6.7 in (170 mm) (see Figure 4–26(f)) and was 

associated with the peak vertical load.

The peak vertical load for the OMF specimen was 166 kip (738 kN), while the peak load for the SMF 

specimen was 188 kip (836 kN). Corresponding beam chord rotations at the ultimate load were calculated 

as u = tan−1(u/L), where u is the center column displacement at the ultimate load and L = 25 ft (7.6 m) 

is the centerline-to-centerline span length. Values of u = 0.019 rad and u = 0.022 rad were obtained for 

the OMF and SMF specimens, respectively. Thus, the more stringent seismic design for the SMF 

specimen resulted in an increase of only 13 % in the ultimate capacity under the column removal 

scenario, with an increase of 18 % in the corresponding beam chord rotation. While the initial anchorage 

bar fracture for the OMF specimen occurred at u = 0.019 rad, the initial anchorage bar fracture for the 

SMF specimen occurred at a much smaller beam chord rotation of only 0.0087 rad. Computational results 

presented subsequently in Section 5.6 show that for the prototype span length of L = 30 ft (9.1 m), the 

ultimate capacity of the SMF specimen was actually slightly less than that of the OMF specimen. The

robustness of the OMF and SMF specimens is further discussed and compared in Chapter 6.

In full-scale testing and computational modeling of reinforced concrete moment frames under a column 

removal scenario, Lew et al. (2011) observed that an arching action stage was followed by a catenary 

action stage, in which tensile forces developed in the beams, providing additional load-carrying capacity. 

Tensile forces developed in the beams when the deflection of the center column was approximately equal 

to the depth of the beams. However, the precast concrete spandrel beams considered in this study were 

much deeper than the reinforced concrete beams considered by Lew et al. (2011), and failures of the 

precast concrete specimens occurred when the deflections of the center column remained much less than 

the beam depth. Consequently, catenary action did not develop for the precast concrete specimens

considered in this study.

The diagonal cracking, spalling, and shear deformation of the end columns observed in these tests 

indicate that lateral forces due to arching action could potentially result in shear failure of columns. If 

arching action is to be exploited in resisting vertical loads under column removal scenarios, care must be 

taken to ensure that the columns adjacent to the missing column can resist the lateral loads induced by 

arching action. In evaluating the potential for column shear failure, gravity loads from the upper stories 

should be considered in combination with shear forces due to arching action. The potential for shear 

failure is of particular concern for columns that have spandrel beams framing into the connections from 

only one side, like the end columns considered in these tests. For an intermediate column in a moment 

frame, the spandrel beam framing into the connection from the adjacent bay would provide resistance to

rotation and horizontal displacement of the column, thus reducing the flexural and shear demands on the 

column. Corner columns, therefore, need particular attention in evaluating the potential for shear failure 

due to arching action.
52

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53

Chapter 5

COMPUTATIONAL MODELING AND ANALYSIS

This chapter presents a computational study of the response of the OMF and SMF specimens under the

column removal scenario considered experimentally. The main objectives of the computational study

were to (1) develop finite element models that could adequately capture the experimentally observed 

behaviors and failure modes of the specimens, (2) provide additional insights into behaviors and failure 

modes that could not be directly observed from the experimental data, and (3) evaluate the response of 

specimens having the full prototype span length, which could not be accommodated within the testing 

facility (see Section 3.1). Another important aspect of the computational study is that multiple analyses 

were run for each specimen, with variations in geometric and material parameters. These analyses enabled 

identification of key factors that influenced the responses of the specimens and provided insights into the 

sensitivity of the responses to uncertainties in these factors.

To provide context for the subsequent discussion of computational modeling, Section 5.1 discusses pretest modeling of the test specimens and illustrates the influence of key factors on the computed responses. 

Section 5.2 provides an overview of the finite element models that were developed for the two specimens, 

and Section 5.3 describes the material models used to represent the various components of the specimens. 

Modeling of the welded anchorage bar connections, discussed in Section 5.4, required particular care in 

order to capture the interaction of axial forces with bending moments resulting from connection 

eccentricities, as well as reductions in ductility near the welds. Section 5.5 presents analysis results from 

the computational models of both specimens, including comparisons with the experimental results to 

demonstrate that the models were able to capture the primary response characteristics and failure modes.

As noted previously in Section 3.1, the span length of the test specimens was reduced in order to fit 

within the test facility, and Section 5.6 presents a computational investigation of the influence of span 

length on the responses of the specimens. Finally, Section 5.7 summarizes and discusses the results of the 

computational study.

5.1 PRE-TEST MODELING AND MODEL SENSITIVITIES

Initial pre-test models of each specimen were developed to aid in planning of the tests and layout of the 

instrumentation. These initial models overestimated the resistance of the test specimens relative to the 

experimental data and did not capture some of the failure modes that were observed experimentally. The 

main discrepancies between the pre-test models and the experimental results, along with the key factors 

that were identified as responsible for these differences, can be summarized as follows:

1. Fracture of the welded anchorage bars (see Figure 4–4 and Figure 4–27) occurred significantly 

earlier in the tests than predicted by the pre-test models. This earlier fracture was due to

(a) localized bending moments near the welds and (b) reductions in the ductility of the anchorage 

bars in the heat-affected zones near the welds. As discussed in Section 5.4, the first factor 

affected both test specimens, while the second factor was significant only for the SMF specimen. 

Neither of these factors was adequately captured in the pre-test modeling. After the test, 

component testing of a welded anchorage bar was performed, and a more refined post-test 
Chapter 5

54

modeling approach for the welded anchorage bars was developed to capture these effects (see

Section 5.4).

2. Detachment of the column plates and embedded shear studs from the end columns in the OMF 

specimen was not captured by the pre-test model. This detachment resulted from a complex state 

of loading of the shear studs, in which shear forces were coupled with tensile forces due to out-ofplane bending of the link plates. The effects of this out-of-plane bending were accounted for in 

the post-test models by reducing the effective shear capacity of the shear studs as described in 

Section 5.3.5. Such reductions were significant for the OMF specimen but not for the SMF 

specimen because of the lesser out-of-plane bending of the link plates (see Section 5.3.5). While 

other aspects of the modeling were based on constitutive relationships for the materials, this shear 

stud failure criterion was calibrated to capture the experimentally observed failures.

3. Development of vertical loads through arching action was less than predicted by the pre-test 

model for the OMF specimen. The smaller loads observed experimentally were due to larger 

initial gaps between the beams and columns than were assumed in the pre-test model: the larger 

gaps delayed the development of arching action and reduced its extent. The gap width was not 

specified in the design of the prototype buildings (Kim et al. 2009a,b), and a gap width of 0.50 in 

(13 mm) was assumed in the pre-test modeling. The post-test models used initial gap widths from

the actual test specimens, which were 0.75 in (0.19 mm) for the OMF specimen and 0.35 in 

(9 mm) for the SMF specimen. Use of the actual gap widths allowed the post-test models to better 

capture the experimentally observed arching action.

Results are compared from three models of each specimen, as listed in Table 5–1, in order to illustrate the 

sensitivity of the computed responses to variations in the key factors listed above. These results highlight 

some of the challenges and complexities in modeling of precast concrete moment frames and provide 

helpful perspective on the final post-test modeling approach, which is described in the following sections.

Computed results from the models in Table 5–1 are presented in Figure 5–1 and Figure 5–2 for the OMF 

and SMF specimens, respectively. Models OMF-A and SMF-A were the final post-test models of the two 

specimens, which are compared with experimental measurements in Section 5.5, while the other models 

in Table 5–1 considered variations in the key factors listed above. The three models of each specimen 

were identical apart from variations in the factors listed in Table 5–1.

Table 5–1. Finite element models used to illustrate the influence of key factors on the computed 

responses.

Model Initial Gap Shear Stud Strength Anchorage Bar Model

OMF-A* 0.75 in (19 mm) reduced ductile

OMF-B 0.50 in (13 mm) reduced ductile

OMF-C 0.75 in (19 mm) nominal ductile

SMF-A* 0.35 in (9 mm) nominal reduced ductility

SMF-B 0.35 in (9 mm) nominal ductile

SMF-C 0.50 in (13 mm) nominal reduced ductility

* OMF-A and SMF-A were the final post-test models used throughout the remainder of this report.
Computational Modeling and Analysis

55

Figure 5–1(a) illustrates the influence of the initial gap between the beams and columns (item 3 above) on 

the vertical load-displacement response of the OMF specimen. The initial gap width determines the 

amount of rotation that the connections can accommodate before the gaps close. Once the gaps close, 

arching action develops in the beams, as discussed previously in Chapter 4, resulting in significant 

increases in vertical load accompanied by outward forces on the end columns. The results in Figure 5–

1(a) show that increasing the initial gap from 0.50 in (13 mm) in model OMF-B (as assumed in the pretest modeling) to 0.75 in (19 mm) in model OMF-A (as estimated directly from the test specimen) 

reduced the computed ultimate capacity of the specimen by 35 %. 

Figure 5–1(b) shows the influence of reduced shear stud capacity (item 2 above) on the computed 

response of the OMF specimen. Model OMF-C included no reduction in the shear stud capacity (as in the 

pre-test modeling), while model OMF-A used a reduced shear capacity as discussed in Section 5.3.5. The 

drop in load at  = 3.5 in (90 mm) for model OMF-A was associated with shear stud failure, and the 

ultimate capacity of model OMF-A is 24 % less than that of model OMF-C. Both factors illustrated in 

Figure 5–1 contributed to overestimation of the resistance of the OMF specimen by the pre-test model.

 

Figure 5–1. Influence of key factors on computed response of OMF specimen.

 

Figure 5–2. Influence of key factors on computed response of SMF specimen.

The response of the SMF specimen was strongly influenced by the assumed ductility of the anchorage 

bars near the weld (item 1b above), as illustrated in Figure 5–2(a). Model SMF-B considered no reduction 

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

1334.4

0

50

100

150

200

250

300

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

OMF-C: nominal OMF-A: reduced

Shear stud strength:

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

1334.4

0

50

100

150

200

250

300

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

OMF-B: 0.5 in (13 mm) OMF-A: 0.75 in (19 mm)

Initial gap between beams and columns:

(a) (b)

shear stud 

failure

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

1334.4

0

50

100

150

200

250

300

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

SMF-B: ductile SMF-A: reduced ductility

Anchorage bar model:

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

1334.4

0

50

100

150

200

250

300

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

SMF-A: 0.35 in (8.9 mm) SMF-C: 0.5 in (12.7 mm)

Initial gap between beams and columns:

(a) (b)

anchorage bar 

fracture
Chapter 5

56

in the ductility of the anchorage bars (as in the pre-test modeling), while Model SMF-A accounted for 

reductions in ductility using the approach described in Section 5.4.2. While fracture of the first anchorage 

bar occurred at  = 6.0 in (152 mm) in model SMF-B, Figure 5–2(a) shows that anchorage bar fracture 

occurred at half of this displacement in Model SMF-A, with a corresponding reduction of the ultimate 

capacity by 37 %.

Figure 5–2(b) shows the influence of the initial gap width on the computed response of the SMF 

specimen. Model SMF-C assumed a gap of 0.5 in (13 mm) (as in the pre-test modeling), while model 

SMF-A used the average actual gap width of 0.35 in (8.9 mm) from the test specimen. Figure 5–2(b) 

shows that the smaller initial gap width in model SMF-A resulted in slightly earlier fracture of the 

anchorage bars relative to model SMF-C. Model SMF-A also sustained larger vertical loads after 

anchorage bar fracture than model SMF-C through more extensive arching action resulting from the 

smaller initial gap. However, the influence of the initial gap width was not as great for the SMF specimen 

as for the OMF specimen, and the reduced ductility of the anchorage bars, as illustrated in Figure 5–2(a), 

was the primary reason that the pre-test model overestimated the resistance of the SMF specimen. 

In addition to the three models of the SMF specimen listed in Table 5–1, a fourth model SMF-D was 

developed to investigate the sensitivity of the specimen to installation errors. As noted previously in 

Section 3.1, the beams of the SMF specimen were inadvertently installed in an inverted orientation, so 

that the longer anchorage bars were at the bottoms of the beams rather than at the tops, and a slight 

misalignment of the torsion rod sleeves also prevented installation of the torsion rods. For consistency 

with the test, models SMF-A, SMF-B, and SMF-C considered inverted beams with no torsion bars. Model 

SMF-D included torsion bars and non-inverted beams and was otherwise equivalent to model SMF-A. 

Comparison of the computed results showed small differences, with a slight delay in the fracture of the 

lower anchorage bars at the center column for model SMF-D relative to model SMF-A and an increase of 

the peak vertical load by 3.5 %. These results indicate that the installation errors did not significantly 

influence the response of the SMF specimen.

5.2 FINITE ELEMENT MODELS

Detailed finite element models, as illustrated in Figure 5–3, were developed to study the behavior and 

failure modes of the two test specimens. The finite element analyses were conducted using explicit time 

integration in LS-DYNA (Hallquist 2007), a general-purpose finite element software package. The 

analyses accounted for both geometric and material nonlinearities, including modeling the fracture of 

steel components using element erosion. In the analyses, the center column was pushed downward under 

displacement control until failure occurred. Displacements were increased at a sufficiently slow rate to 

ensure a quasi-static response, simulating the test conditions. 

The models used 8-node solid elements to represent the concrete and the steel plates and angles (shown 

on the left-hand side in Figure 5–3), and 2-node beam elements to represent the reinforcing bars, torsion 

bars, and shear studs (shown on the right-hand side in Figure 5–3). The model of the OMF specimen 

consisted of approximately 346 000 elements, while the model of the SMF specimen consisted of about 

171 000 elements. The characteristic length of the solid elements ranged from 0.25 in to 2.15 in (6.4 mm 

to 54.6 mm), and the level of refinement of the solid-element mesh is illustrated in Figure 5–4, which 

shows the mesh used to represent the moment connections at the center column for the SMF specimen. 

Typical beam elements ranged in length from 2.0 in to 5.3 in (51 mm to 135 mm), with smaller elements 
Computational Modeling and Analysis

57

in locally refined regions near the anchorage bar welds, as illustrated in Figure 5–5 and discussed 

subsequently in Section 5.4.1. An automatic contact interface was activated to prevent interpenetration 

and enable force transfer between the concrete beams and columns and the steel plates and angles.

Figure 5–3. Finite element models: (a) OMF specimen; (b) SMF specimen.

Figure 5–4. Solid-element mesh in connection region (SMF specimen).

Solid elements shown:

concrete, steel plates and angles

Beam elements shown:

reinforcing bars, shear studs

Solid elements shown:

concrete, steel plates and angles

Beam elements shown:

reinforcing bars, torsion bars, shear studs

(a)

(b)

column plate

angle link plate

loading plate

left beam center column

welds

(tied nodes)
Chapter 5

58

Figure 5–5. Modeling details at moment connection (top view).

Shear studs connecting the column plates to the column concrete were modeled using beam elements that 

shared nodes with the surrounding concrete elements. The nonlinear load-slip behavior of the shear studs 

was represented through discrete shear springs that connected the beam elements to the column plates, as 

illustrated in Figure 5–5 and further discussed in Section 5.3.5. Welds on the link plates were modeled 

using constraints that tied the nodes around the edges of the link plates to corresponding nodes on the

angles and column plates, as indicated in Figure 5–4. Welds between the anchorage bars and the 

connecting angles were modeled using rigid links (CONSTRAINED_NODAL_RIGID_BODY in LSDYNA), to capture the offset between the anchorage bar centerline and the surface of the connecting 

angle, as illustrated in Figure 5–5. These offsets contributed to the eccentricity in the transfer of forces 

between the anchorage bars and the link plates, producing significant out-of-plane bending moments in 

the link plates and in the anchorage bars near the welds, as discussed subsequently in Section 5.4.1. Nodal 

constraints (CONSTRAINED_LAGRANGE_IN_SOLID in LS-DYNA) were used to tie the anchorage 

bars, as well as the longitudinal and transverse reinforcing bars, to the surrounding concrete elements, and 

bond-slip effects were neglected. Welding of the column longitudinal bars to steel plates at the column 

bases was modeled by tying the longitudinal bars to nodes of the solid elements representing the steel 

base plates. 

To represent the fixed base conditions for the end columns in the experimental configuration (see Figure 

3–4), all translations were restrained for nodes on the bottom surfaces of the steel base plates. Restraint of 

the end column tops by bracing beams (see Figure 3–4) was represented through contact with rigid 

elements at the inside and outside faces of the end columns. Lateral bracing of the center column and at 

midspan of the beams was modeled using nodal constraints to prevent out-of-plane displacements.

5.3 MATERIAL MODELING

5.3.1 Concrete

A continuous surface cap plasticity model (material 159 in LS-DYNA) was used as the material model for 

concrete, with reduced integration solid elements. This material model was originally developed for 

roadside safety simulations for the Federal Highway Administration (FHWA 2007). Key features of the 

model include isotropic constitutive equations, a yield surface formulated in terms of three stress

invariants with translation for pre-peak hardening, a hardening cap that expands and contracts, and 

damage-based softening with modulus reduction in both compression and tension. The model captures 

confinement effects, which are an important feature of concrete behavior, and uses a constant fracture 

energy approach to regulate mesh size sensitivity in the modeling of softening behavior. The material

anchorage bar

(beam elements)

weld 

(rigid links)

column plate link plate angle

shear studs (beam elements

with shear springs at bases)

refined elements

near weld

shear

springs
Computational Modeling and Analysis

59

model provides initialization routines whereby model parameters are fit to data for normal strength 

concrete with compressive strengths between 2900 psi and 8400 psi (20 MPa and 58 MPa) and aggregate 

sizes between 0.3 in and 1.3 in (8 mm and 32 mm). Required input parameters are the unconfined 

compressive strength and the maximum aggregate size. Because reduced-integration solid elements were 

used to model the concrete, hourglass control was required to suppress spurious zero-energy modes of 

deformation. An assumed strain co-rotational stiffness form of hourglass control was selected with an 

hourglass control coefficient of 0.03.

Figure 5–6 demonstrates the capabilities of the concrete material model to capture confinement effects in 

compression and brittle fracture in tension, based on single-element simulations using a cubic 8-node 

solid element. Figure 5–6(a) illustrates confinement effects by comparing the compressive behavior under 

uniaxial loading with that under triaxial loading with a constant confinement pressure of 600 psi (4 MPa). 

While the stress approaches zero in the softening phase for uniaxial compression, Figure 5–6(a) shows 

that moderate confinement pressure causes the material to maintain a residual compressive strength after 

softening. Figure 5–6(b) illustrates the brittle softening behavior of the material model in uniaxial tension. 

According to the default assumption in the material model, the fracture energy in uniaxial compression is 

taken as 100 times that in uniaxial tension.

Figure 5–6. Stress-strain response of concrete material model: (a) compression; (b) tension.

5.3.2 Steel Plates and Angles

A piecewise linear plasticity model (material 24 in LS-DYNA) was used as the material model for the 

ASTM A36 steel plates and angles, which were modeled using fully integrated solid elements. In this 

model, the plastic material response is defined through a true stress vs. plastic strain curve, which can be 

obtained from an engineering stress-strain curve using the following relationships (e.g., Dieter 1976):

   s e( 1)

(5.1)

   ln( 1) e

(5.2)

where  is the true stress, s is the engineering stress, ɛ is the true strain, and e is the engineering strain.

Letting E denote the elastic modulus, the plastic strain is then obtained as: 

p

E



   

(5.3)

0

6.9

13.8

20.7

27.6

34.5

41.4

48.3

55.2

0

1000

2000

3000

4000

5000

6000

7000

8000

0.000 0.005 0.010 0.015 0.020 0.025

Engineering Stress (MPa)

Engineering Stress (psi)

Engineering Strain

Uniaxial compression

Triaxial compression:

confinement pressure

= 600 psi (4 MPa)

(a)

0

0.69

1.38

2.07

2.76

3.45

0

100

200

300

400

500

0.000 0.001 0.002 0.003 0.004 0.005 0.006

Engineering Stress (psi)

Engineering Stress (MPa)

Engineering Strain

Uniaxial tension

(b)
Chapter 5

60

A representative stress-strain curve was used for the steel plates and angles, based on tensile testing of 

ASTM A36 steel coupons reported by Sadek et al. (2010). This curve, shown up to the ultimate tensile 

strength in Figure 5–7(a), assumed a yield strength of Fy = 42 ksi (290 MPa), an ultimate tensile strength 

of Fu = 65 ksi (448 MPa), and an engineering strain of eu = 0.22 at the ultimate tensile strength. 

Eqs. (5.1) – (5.3) apply only up to the onset of necking at the ultimate tensile strength. To model the 

softening and fracture that could occur beyond this point, the true stress vs. plastic strain curve was 

extended linearly, and a critical plastic strain was defined at which element erosion would be activated, 

removing elements from the analysis to simulate fracture. Because modeling of softening and fracture is 

mesh-size dependent, this approach required calibration of the erosion strain and the post-ultimate tangent 

modulus for the specific element size used at critical regions in the models, in order to achieve values of 

engineering strain that were consistent with coupon tensile testing. However, this post-ultimate modeling 

approach had a negligible influence on the computed results for the test specimens, since fracture did not 

occur in the plates or angles.

Figure 5–7. Stress-strain curves used to model steel components.

5.3.3 Reinforcing Bars

A piecewise-linear plasticity model (material 124 in LS-DYNA) was used as the material model for the 

reinforcing bars, which were modeled using Hughes-Liu beam elements with cross-section integration. 

This material model defines the material response through true stress vs. plastic strain curves, similar to 

the model used for the steel plates and angles. A distinct material model was defined for each size of 

reinforcing bar used in the test specimens, with stress-strain curves for each bar size based on data from 

tensile testing reported in Table 3–1. As noted in Table 3–1, two types of tensile tests were performed for 

the No. 10 and No. 11 bars: (a) direct tensile testing of reinforcing bars and (b) tensile testing of smallerdiameter coupons machined from the reinforcing bars. For the smaller bar sizes, only coupon testing was 

performed, which is known to give consistently higher tensile strength values than bar testing, as 

illustrated in Figure 5–7(b) for a No. 10 reinforcing bar. The lower tensile strength from bar testing is the 

appropriate value to use in modeling of reinforcing bars, and so the stress-strain curves used to model the 

No. 10 and No. 11 bars were based on tensile test results from bar testing, as illustrated in Figure 5–7(b). 

Because only coupon test data were available for the smaller bar sizes, these bars were modeled using 

approximate stress-strain curves that accounted for the reduced tensile strength that would be expected 

from bar testing, based on the reduction factor obtained for the No. 10 and No. 11 bars. This approximate 

reduction in the tensile strength did not significantly affect the overall behavior, because the strains in the 

reinforcing bars remained fairly small except at critical locations in the No. 10 and No. 11 anchorage bars 

near the welds. Modeling of these critical regions is discussed in Section 5.4.

0

138

276

414

552

690

827

965

0

20

40

60

80

100

120

140

0 0.02 0.04 0.06 0.08 0.1

Engineering Stress (MPa)

Engineering Stress (ksi)

Engineering Strain

Torsion bar

Fy = 100 ksi (689 MPa) Fu = 125 ksi (862 MPa) eu = 0.08

0

138

276

414

552

0

20

40

60

80

0 0.1 0.2 0.3

Engineering Stress (MPa)

Engineering Stress (ksi)

Engineering Strain

A36 steel

Fy = 42 ksi (290 MPa) Fu = 65 ksi (448 MPa) eu = 0.22

0

138

276

414

552

690

827

0

20

40

60

80

100

120

0 0.1 0.2

Engineering Stress (MPa)

Engineering Stress (ksi)

Engineering Strain

Coupon test Bar test Model

#10 reinforcing bar

(a) (b) (c)
Computational Modeling and Analysis

61

5.3.4 Torsion Bars

The torsion bars, which were ASTM A193 Grade B7 bolts, were modeled using the same piecewise linear 

plasticity material model and beam element formulation that were used for the reinforcing bars. The 

torsion bars were modeled using the minimum specified tensile strength of Fu= 125 ksi (862 MPa), with 

a yield strength of 100 ksi (689 MPa), and an assumed engineering strain of eu = 0.08 at the ultimate 

tensile strength. A simple bilinear form of stress-strain curve was assumed, as shown in Figure 5–7(c). To 

model the pre-tension introduced in the torsion bars during the assembly process, a coefficient of thermal 

expansion was defined in the material model, and the torsion bar elements were artificially cooled to 

develop tensile stresses through restraint of thermal contraction. Several trial analyses were performed to 

determine the reduction in temperature required to achieve the desired service tension of 18 kip (81 kN), 

as listed in the PCI Design Guide (PCI 2014, page 6–105).

5.3.5 Shear Studs

Discrete shear springs, as illustrated previously in Figure 5–5 (implemented in LS-DYNA using material 

119), were used to represent the nonlinear shear behavior of the shear studs that connected the column 

plates to the column concrete. Figure 5–8 shows the normalized shear force vs. slip model used for the 

shear springs. The initial portion of the model curve is based on the empirical load-slip relationship 

proposed by Ollgaard et al. (1971), and this empirical curve is also plotted in Figure 5–8. While the 

empirical curve is plotted up to a slip of 0.5 in (13 mm), it is noted that this curve is only intended to 

represent the initial load-slip behavior up to the peak load at a slip of 0.2 in (5 mm). After reaching the 

peak load, the shear force is gradually reduced to 80 % of its peak value at a displacement of 0.40 in 

(10 mm) and is then steeply reduced to a constant residual strength equal to 20 % of its peak value. This 

residual strength represents the frictional resistance of crushed concrete that remains even after failure of 

a shear stud.

Figure 5–8. Normalized shear force vs. slip relationship used for shear studs.

For the 1.0 in (25 mm) diameter shear studs used in the OMF and SMF connections (see Figure 2–3 and 

Figure 2–4), a nominal shear strength of Qn = 38 kip (170 kN) was calculated based on the AISC 

Specification (AISC 2010, Section I8.2a), assuming a tensile strength of Fu = 65 ksi (450 MPa) for the 

shear studs, which is the minimum specified tensile strength for AWS D1.1 Type B studs (AWS 2010). 

0 2.54 5.08 7.62 10.16 12.7

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5

Slip (mm) Normalized Shear Force, Q/Qn

Slip (in)

Ollgaard et al. (1971)

Model
Chapter 5

62

This nominal shear strength was used in the model of the SMF specimen, and no shear stud failure 

occurred, consistent with the experimental results. However, using this nominal shear strength for the 

OMF specimen failed to capture the experimentally observed detachment of the upper column plates from 

the end columns and significantly overestimated the vertical load sustained by the OMF specimen (see

results for model OMF-C in Figure 5–1).

As shown in Figure 4–3 and Figure 4–7, detachment of the column plates in the OMF specimen involved 

not only shear slip, but also significant out-of-plane displacement, which resulted from out-of-plane 

bending of the link plates. The shear studs were thus subjected a complex state of loading that involved 

not only shear forces, but also axial tension, and this tension reduced the effective shear capacity of the 

shear studs. This effect was more significant for the OMF specimen than for the SMF specimen because 

of the more extensive out-of-plane bending of the link plates that occurred, as noted previously in Section 

4.2.3. Developing a failure model for the shear studs that explicitly accounts for the complex interaction 

of stresses observed here would require further research and is beyond the scope of this study. The key 

observation is that these effects reduced the effective shear capacity of the shear studs, and accounting for 

this reduction was necessary to capture the experimentally observed failures. In model OMF-A (the final 

post-test model), an effective shear strength of 12 kip (53 kN) was used for the shear studs, which 

represents only 31 % of the nominal shear strength. This value was calibrated to the experimental data in 

order to capture the column plate detachment observed at a center column displacement of  = 3.7 in 

(89 mm). 

An alternative estimate for the effective strength of the shear studs in the OMF specimen can be obtained 

by noting that the upper anchorage bar at the left end column developed a peak axial force of 86.6 kip 

(385 kN) just prior to detachment of the column plate (see Figure 4–16). Assuming that both anchorage 

bars at that location carried approximately the same axial force, the total peak shear force transferred to 

the column by the shear studs was about 173 kip (770 kN). Dividing this force among the nine shear studs 

gives an average shear strength of 19 kip (86 kN) per stud. While this experimentally based estimate is 

somewhat higher than that obtained by calibration of the computational model, it is still only 50 % of the 

nominal shear strength, thus confirming that out-of-plane bending significantly reduced the effective 

strength of the shear studs in the OMF specimen.

5.4 WELDED ANCHORAGE BAR MODELING

Item 1 in Section 5.1 introduced two key factors that influenced the fractures of the welded anchorage 

bars observed in the experiments: (a) localized bending moments near the welds and (b) reductions in the 

ductility of the anchorage bars in the heat-affected zone near the welds. The first of these factors resulted 

in interaction of bending moment and axial tension that played a key role in the fracture of the anchorage 

bars for both the OMF and SMF specimens, and Section 5.4.1 describes the procedure that was used to 

properly capture these effects. The second factor was significant only for the SMF specimen, and Section 

5.4.2 describes the procedure that was used to account for the weld-induced reductions in ductility 

through calibration against component testing of a welded anchorage bar from the SMF specimen.

Weld-induced reductions in ductility of the anchorage bars may have been more significant for the SMF 

specimen than for the OMF specimen because of the greater heat input associated with the larger weld 

size (compare Figure 2–4 and Figure 2–3). Variability in the welding process may also have contributed 

to the differences, because even for the SMF specimen, reductions in ductility seem to have been more 

significant for some bars than for others. In the SMF specimen test (see Section 4.2), the lowest 

anchorage bar at the center column connection fractured first at  = 2.5 in (64 mm), while the upper two 
Computational Modeling and Analysis

63

anchorage bars fractured later at  = 4.9 in (124 mm). This contrasts with the computational results (see 

Figure 5–2(a)), in which all three anchorage bars, which were assumed to have the same ductility, 

fractured nearly simultaneously. These fractures occurred earlier in model SMF-A (with reduced 

ductility) than in model SMF-B (with no reduction in ductility) but were nearly simultaneous in both 

models. The earlier fracture of the lowest anchorage bar in the SMF specimen suggests that reductions in 

ductility caused by welding may have been more significant for this bar than for the upper two bars. This 

indicates the potential for significant variability in the extent to which ductility is reduced by the process 

of hand-welding a deformed bar to a plate or angle. Section 6.7.3 of the PCI Design Handbook (PCI 

2014) discusses preheat and other requirements for welding of reinforcing bars to avoid potential 

crystallization and the associated brittle behavior.

5.4.1 Interaction of Bending Moment and Axial Force

The welded anchorage bars were subjected to a combination of bending and axial loading due to 

eccentricities in the transfer of forces between the link plates and the anchorage bars (see Figure 4–44).

The resulting interaction of bending moment and axial tension (see Figure 4–18) caused the anchorage 

bars to fracture at a lower axial force than if the bars had been subjected to pure tension. Because detailed 

modeling of the welded anchorage bars using solid elements would be too computationally demanding for 

analysis of an entire test specimen, a reduced-order modeling approach was used, illustrated previously in 

Figure 5–5, in which the welded anchorage bars were modeled using beam elements. However, detailed 

solid-element models of welded anchorage bars under eccentric loading were also developed, as 

illustrated in Figure 5–9, to verify the adequacy of the reduced-order modeling approach and to enable

calibration of the failure criterion used to model bar fracture. Figure 5–9 shows detailed and reducedorder models of a welded #10 anchorage bar, as used in the OMF moment connections. Corresponding 

detailed and reduced-order models were also developed of a welded #11 anchorage bar, as used in the 

SMF moment connections. 

Figure 5–9. Finite element models of a welded anchorage bar under eccentric loading: (a) detailed model;

(b) reduced model.

The welded anchorage bar models used for calibration included a single anchorage bar along with strips 

of angle and link plate having widths obtained by dividing the actual widths (see Figure 3–1 and Figure 

3–2) by the number of anchorage bars in the connection. Concrete was excluded from the models, 

because the focus of these analyses was on the transfer of forces through the steel components at the 

welded connections. In the detailed models, the anchorage bars, welds, angles, and link plates were 

modeled using solid elements. The reduced-order models were consistent with the modeling approach 

#10 anchorage bar

(beam elements)

strip of 

link plate

strip of angle

Detailed Model

Reduced-Order Model

#10 anchorage bar

(solid elements)

weld (nodal 

constraints)

weld (solid 

elements)

prescribed 

displacement

fixed end
Chapter 5

64

used for the moment connections in the OMF and SMF specimens (see Figure 5–5), in which the 

anchorage bars were modeled using beam elements, the welds were modeled using nodal constraints, and 

the angles and link plates were modeled using a coarser mesh of solid elements than was used in the 

detailed models. In both the detailed and reduced-order models, the welds between the angle and the link 

plate were modeled by having elements of the two components share common nodes at their interface. 

Only the leg of the angle that was parallel to the link plate was included in the models, because the 

perpendicular leg was not loaded in the configuration being analyzed. The portion of the link plate that 

was welded to the column plate was not included in the model. Instead, the link plate was truncated at the 

edge of the column plate, and this truncated end was modeled as fixed (see Figure 5–9). A segment of 

anchorage bar extending 30 in (762 mm) beyond the end of the angle was modeled, and displacementcontrolled axial loading was applied to the end of this bar segment. Eccentricity in the loading resulted

from the offset (in the direction normal to the link plate) between the load applied to the anchorage bar 

and the reaction at the fixed end of the link plate.

As subsequent computational results show (see Figure 5–12), the bending moment was largest at the end 

of the weld and decayed steeply with distance along the bar. To capture this localized bending of the 

anchorage bars in the reduced-order models, a refined mesh was required near the weld (see Figure 5–5). 

After considering various mesh sizes in this refined zone, a beam element length of 0.2 in (5 mm) was 

selected, which was found to be sufficient to capture the maximum bending moment at the end of the 

weld, as well as the decay in bending moment along the length of the bar. The nonlinear distribution of 

axial stress over the cross-sectional area of the bar was captured using 64 integration points per element. 

Fracture was modeled using element erosion at a specified value of plastic strain. However, plastic strains 

were found to localize in the single element closest to the weld, where the bending moment and 

corresponding stresses were largest. Because of this localization, modeling of fracture in the reducedorder models was found to be mesh-size dependent, and calibration of the erosion strain for the selected 

element size was necessary. As described in the following, the failure criterion used in the detailed 

models was first calibrated against tensile test data, and then the failure criterion used in the reducedorder models was calibrated against the detailed models.

The detailed models used a piecewise linear plasticity model for the anchorage bars (material 24 in LSDYNA), with fully integrated solid elements. True stress vs. plastic strain curves for use in the material 

model were calculated from tensile test data for #10 and #11 bars using Eqs. (5.1) – (5.3), and these true 

stress vs. plastic strain curves were extended linearly beyond the onset of necking to model softening 

prior to fracture. The detailed models used the same material model for the welds as for the anchorage 

bars. Fracture of the anchorage bars in the detailed models was modeled using element erosion, and the 

erosion strain in the detailed models was calibrated against experimental data from tensile tests. This 

calibration was performed by modeling tensile tests of #10 and #11 bars (illustrated in Figure 5–10 for a 

#10 bar) and adjusting the erosion strain so that the engineering strain at fracture (point d in Figure 5–10) 

matched the value obtained experimentally. For consistency with the experimental results (see Table 3–

1), a gauge length of 8 in (203 mm) was used in calculating engineering strain values from the 

computational models. Because modeling of erosion and fracture is mesh-size dependent, the bars in the 

tensile test models used the same solid-element mesh as in the welded bar models (Figure 5–9). 
Computational Modeling and Analysis

65

Figure 5–10. Calibrated detailed model analysis of reinforcing bar tensile test.

After calibrating the modeling of bar fracture under uniaxial tensile loading, the detailed models were 

used to analyze the response of the welded anchorage bars under eccentric tensile loading. Figure 5–11

shows computed results from the detailed model of the welded #10 bar shown in Figure 5–9. The 

interaction diagram of axial tension vs. bending moment is plotted, and for the points labeled on the 

interaction diagram, the corresponding deformed geometry of the finite element mesh is shown with 

contours of effective plastic strain. The computed deformations are comparable to the schematic 

illustration presented previously in Figure 4–15(a). Plastic strains were concentrated in the link plate near 

the fixed end and in the anchorage bar near the end of the weld. The final point on the interaction diagram 

(point d) corresponds to the initiation of fracture at the peak axial load. The deformed shape after 

complete fracture is also shown in Figure 5–11(e).

Figure 5–11. Detailed model analysis of welded anchorage bar under eccentric loading.

The values of bending moment plotted in Figure 5–11 were calculated for the cross section at the end of 

the weld, where the bending moment was largest. Figure 5–12 shows the variation of bending moment 

with distance along the bar for two different levels of axial tension, corresponding to points b and c in 

Figure 5–11. At the lower level of axial tension (point b), the bending moment decays to 50 % of its peak 

value at a distance of 3.3 in (84 mm) from the end of the weld. At the higher level of axial tension (point 

c), the bending moment decays even more steeply, dropping to 50 % of its peak value at a distance of 

only 0.8 in (20 mm) from the end of the weld. This steep decay in bending moment with distance explains 

why the reduced modeling approach required such short beam elements for the anchorage bar near the 

0

89

178

267

356

445

534

0

20

40

60

80

100

0 0.05 0.1 0.15 0.2

Engineering Stress (MPa)

Engineering Stress (ksi)

Engineering Strain

Bar test

Solid-element model

#10 reinforcing bar

a

b c

d

0.35

0.35

0.27

0.23

0.20

0.16

0.12

0.08

0.04

0.00

Contours of effective plastic strain

(a)

(b)

(c)

(d) 0

89

178

267

356

445

534

0.00 0.57 1.13 1.70 2.26 2.83

0

20

40

60

80

100

120

0 5 10 15 20 25 Axial Force (kN)

Bending Moment (kN·m) Axial Tension, T (kip)

Bending Moment (kip·in)

0.35

0.31

0.27

0.23

0.20

0.16

0.12

0.08

0.04

0.00

Contours of effective plastic strain

d

c

b

a

(a)

(b)

(c)

(d)

(e) #10 welded anchorage bar (OMF) initiation of fracture

complete fracture
Chapter 5

66

weld (see Figure 5–5). The pre-test model used much larger beam elements in this region and thus failed 

to adequately capture the local bending effects. 

Figure 5–12. Bending moment in welded anchorage bar vs. distance along bar.

Figure 5–13 shows a comparison of moment-axial interaction diagrams obtained using the detailed and 

reduced models of the welded anchorage bars under eccentric loading. Figure 5–13(a) presents results for 

the #10 anchorage bar models shown in Figure 5–9, while Figure 5–13(b) presents corresponding results 

for the #11 anchorage bar models. For each bar size, the erosion strain used in the reduced model was 

calibrated so that the detailed and reduced models had approximately the same ratio of bending moment 

to axial force at the fracture point. Graphically, this required the fracture points for the detailed and 

reduced models to lie approximately along the same ray directed from the origin of the moment-axial 

interaction diagram, as indicated with the dashed arrow annotation in Figure 5–13. This calibration 

approach was adopted in an effort to best match the degree of moment-axial interaction at the point of 

fracture, rather than seeking to match either the bending moment or the axial force at the expense of the 

other. The results show fairly good agreement between the interaction diagrams obtained using the 

detailed and reduced modeling approaches. The peak bending moment and the peak axial force both agree 

within 6 % for the #10 bar and within 9 % for the #11 bar. This good agreement confirms that the reduced 

modeling approach is able to capture the interaction of bending moment and axial tension leading to 

fracture of the anchorage bars.

0.00

0.57

1.13

1.70

2.26

2.83

0 127 254 381 508

0

5

10

15

20

25

0 5 10 15 20

Bending Moment (kN·m)

Distance along Anchorage Bar (mm)

Bending Moment (kip∙in)

Distance along Anchorage Bar (in)

Point b: T = 57.1 kip (254 kN)

Point c: T = 91.4 kip (407 kN)

#10 welded anchorage bar (OMF)
Computational Modeling and Analysis

67

Figure 5–13. Interaction of axial force and bending moment for welded anchorage bars under eccentric 

loading: (a) #10 bar, (b) #11 bar.

5.4.2 Reduction of Ductility in Heat-Affected Zone

When the calibrated, reduced model of the welded #10 anchorage bar [Figure 5–13(a)] was implemented 

in analysis of the OMF specimen, the model closely captured the center column displacement at which 

anchorage bar fracture occurred. In contrast, when the calibrated, reduced model of the welded #11 

anchorage bar [Figure 5–13(b)] was implemented in analysis of the SMF specimen (model SMF-B in 

Section 5.1), anchorage bar fracture in the model occurred significantly later than observed 

experimentally. To investigate the cause of the earlier anchorage bar fracture observed experimentally, 

component testing of a welded anchorage bar from the SMF specimen was performed, as illustrated in

Figure 5–14. 

The welded anchorage bar connection used in the component test was recovered from a location in the 

tested SMF specimen that was subjected to predominantly compressive loads during the test. The threebar connection (see Figure 2–4) was sawed through the angle and link plate to isolate a single anchorage 

bar for testing, along with a strip of angle with a width of 4.5 in (114 mm) welded to the #11 bar. The 

angle and link plate were welded together along the sawed edge, and the link plate was also sawed flush 

with the heel of the angle. A nut was welded to the perpendicular leg of the angle to receive a 2 in 

(51 mm) diameter threaded rod, through which tensile loading was applied in the testing machine [Figure 

5–14(b)]. The nut was aligned along the axis of the anchorage bar to provide concentric axial loading. 

Steel bars with dimensions of 8 in × 1 in × 0.5 in (203 mm × 25 in × 13 mm) were welded diagonally 

between the two legs of the angle to stiffen the angle and prevent out-of-plane deformations. Elongations 

of the anchorage bar were measured using a displacement transducer spanning a gauge length of 30 in 

(762 mm) and attached to the toe of the angle, at the end of the weld. The estimated uncertainty in the 

measured load and displacement data was ±1 %. The welded anchorage bar was tested under 

displacement-controlled tensile loading until fracture occurred.

The results of the welded bar component test are shown in Figure 5–15. Figure 5–15(a) shows the stressstrain curve obtained from the welded bar component test, along with that obtained from tensile testing of 

a #11 bar for comparison. The yield stress is almost equivalent in both cases, and the welded bar showed

only slightly lower stress in the post-yield work-hardening phase. However, the welded bar had 

significantly reduced ductility, with the ultimate stress being reached at an engineering strain of 9.3 % and 

0

89

178

267

356

445

534

623

712

0.00 0.57 1.13 1.70 2.26 2.83 3.39

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 Axial Force (kN)

Bending Moment (kN·m) Axial Force (kip)

Bending Moment (kip·in)

Detailed model Reduced model

0

89

178

267

356

445

534

623

712

0.00 0.57 1.13 1.70 2.26 2.83 3.39

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 Axial Force (kN)

Bending Moment (kN·m) Axial Force (kip)

Bending Moment (kip·in)

Detailed model Reduced model

(a) (b)

#10 welded anchorage bar (OMF) #11 welded anchorage bar (SMF)
Chapter 5

68

fracture occurring immediately thereafter, without appreciable necking. In contrast, the ultimate stress 

was reached at an engineering strain of 11.1 % in the bar tensile test and was followed by significant 

necking and softening prior to fracture. Figure 5–15(b) shows the fractured anchorage bar after the 

component test, in which it is evident that the fracture occurred at the end of the weld. The reduced

ductility of the welded anchorage bar is believed to have been caused by changes in material properties in 

the heat-affected zone near the weld (e.g., microstructural changes such as the formation of brittle 

martensite). 

Figure 5–14. Component test setup for welded anchorage bar.

Figure 5–15. Results of welded anchorage bar component test: (a) stress-strain curve; (b) fractured 

anchorage bar.

Based on the results of the welded bar component test, the reduced model of the welded #11 anchorage 

bar [Figure 5–13(b)] was recalibrated to account for the reduced ductility that was observed. This 

recalibration followed the same procedure outlined in Section 5.4.1, but with one modification: rather 

than calibrating the anchorage bar material model against a bar tensile test, as illustrated previously in 

Displacement transducer Gauge length = 30 in(762 mm)

nut welded 

to angle

weld

#11 bar

angle

diagonal 

stiffener

link 

plate

(a) (b)

FRONT VIEW SIDE VIEW

0

138

276

414

552

690

0

20

40

60

80

100

0 0.05 0.1 0.15 0.2

Engineering Stress (MPa)

Engineering Stress (ksi)

Engineering Strain

#11 bar test

#11 welded bar component test

(a) (b)
Computational Modeling and Analysis

69

Figure 5–10, the material model was instead calibrated against the welded bar component test, as 

illustrated in Figure 5–16.

Figure 5–16(a) shows the detailed model used to calibrate the anchorage bar material model against the

welded bar component test. The concentric loading conditions in the welded bar component test were 

simulated by constraining axial displacements for all nodes on a plane located 0.45 in (12 mm) from the 

end of the angle, which corresponds to the end of the welds that affixed the diagonal stiffeners the angle. 

This approach was found suitable to achieve concentric loading of the welded anchorage bar without the 

need to model the full details of the diagonal stiffeners and the concentrically located loading nut used in 

the component test (Figure 5–14). The true stress vs. plastic strain curve used in the anchorage bar 

material model was obtained from the welded bar component test data using Eqs. (5.1) – (5.3), with a 

linear extension beyond the ultimate tensile strength. To represent the reduced ductility in the heataffected zone near the weld, as indicated in Figure 5–16(a), element erosion was activated only for 

anchorage bar elements adjacent to the weld and within one row of elements beyond the end of the angle. 

The erosion strain was adjusted to match the experimental engineering strain at fracture, as shown in 

Figure 5–16(b).

Figure 5–16. Calibrated detailed model of welded anchorage bar component test.

After calibrating the anchorage bar material model against the welded bar component test, the welded bar 

was analyzed again under the eccentric loading and support conditions illustrated in Figure 5–9. The 

resulting moment-axial interaction diagram is shown in Figure 5–17, along with corresponding results 

from the reduced model. As was done previously in Figure 5–13, the erosion strain used in the reduced 

model was calibrated so that the detailed and reduced models had approximately the same ratio of 

bending moment to axial force at the fracture point. Comparing Figure 5–17 with Figure 5–13(b) reveals 

that the reduction in ductility due to welding led to a 35 % reduction in the peak tensile force that could 

be sustained under eccentric loading. Because the tensile capacity from the welded bar component test 

(under concentric loading) was only 4 % less than that of the bar without welding [see Figure 5–15(a)], 

this shows that moment-axial interaction under eccentric loading can amplify the effects of reduced 

ductility. This helps to explain why the ultimate capacity of model SMF-A, which had anchorage bars 

with reduced ductility, was so much less than that of model SMF-B, which had ductile anchorage bars 

[see Figure 5–2(a)].

0

138

276

414

552

690

0

20

40

60

80

100

0 0.02 0.04 0.06 0.08 0.1

Engineering Stress (MPa)

Engineering Stress (ksi)

Engineering Strain

Welded bar component test Model

reduced ductility near weld

axial displacements 

constrained

weld

#11 bar

angle

link plate

(a) (b)
Chapter 5

70

Figure 5–17. Interaction of axial force and bending moment for welded #11 anchorage bar with reduced 

ductility under eccentric loading.

5.5 ANALYSIS OF TEST SPECIMENS

This section presents analysis results from the final post-test models of the OMF and SMF test specimens

(models OMF-A and SMF-A in Table 5–1), including comparisons of the computed results with the 

experimental measurements. As discussed in Section 5.1, and further elaborated in Sections 5.3.5 and 5.4, 

the final post-test models incorporated refinements in modeling of the shear studs and the welded 

anchorage bars, in order to better capture the experimentally observed behaviors and failure modes.

In the analysis of each test specimen, self-weight loading was first applied gradually and then held 

constant for the rest of the analysis by imposing a body-force acceleration vs. time curve. After the 

specimen reached an equilibrium configuration under its own self-weight, the unsupported center column 

was pushed downward by prescribing a gradually increasing velocity vs. time curve to the steel loading 

plate at the top of the center column. Loads were transmitted to the center column through contact with 

the steel loading plate, consistent with the experimental configuration. The analysis results for each of the 

specimens are presented in the following subsections.

5.5.1 OMF Specimen

Figure 5–18(a) shows a comparison between the measured and computed curves of the applied vertical 

load vs. the vertical displacement of the center column. A slight drop in the both the measured and 

computed vertical load is evident in Figure 5–18(a) at a center column displacement of  = 3.7 in 

(89 mm), corresponding to shear stud failure at the top column plates on the end columns. As a result of 

this failure, a more severe drop occurred in both the measured and computed horizontal reaction from the 

front brace beam at the tops of the end columns, as shown in Figure 5–18(b).

Inward horizontal forces on the column tops are considered positive in Figure 5–18(b), corresponding to 

tension in the brace beam spanning between the tops of the end columns. The experimental curve in 

Figure 5–18(b) corresponds to the measured axial force in the front brace beam (Figure 4–24). While the 

brace beams themselves were not included in the computational model, their influence was represented 

through contact with rigid elements at the inside and outside faces of the end column tops. For 

0

89

178

267

356

445

534

623

712

0.00 0.57 1.13 1.70 2.26 2.83 3.39

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 Axial Force (kN)

Bending Moment (kN·m) Axial Tension, T (kip)

Bending Moment (kip·in)

Detailed model Reduced model

#11 welded anchorage bar (SMF)

with reduced ductility 
Computational Modeling and Analysis

71

consistency with the experimental measurements, the curve from the computational model in Figure 5–

18(b) represents the portion of the horizontal reaction that would have been transferred to the front 

W16x67 brace beam by the W14x82 cross beams (see Figure 3–4). The computed horizontal reactions at 

the tops of the two end columns were averaged, with inward forces positive. (The horizontal reactions at 

the two end column tops were essentially equivalent initially, but differences became evident after shear 

stud failure occurred and the response was no longer symmetric.) An outward horizontal reaction 

developed in the initial application of self-weight in the computational model, and for consistency with 

the experimental measurements, this initial reaction was deducted from the horizontal force values 

presented in Figure 5–18(b). The peak computed horizontal reaction from the front brace beam, prior to 

shear stud failure, was 29 % less than the peak force from the experimental data. 

 

Figure 5–18. Comparison of experimental and computed results for (a) vertical load and (b) horizontal 

reaction from front brace beam at end column tops (OMF specimen).

Shear stud failure was evident in the computational model by increased displacements of the top column 

plates relative to the end columns, as indicated in Figure 5–19(a). Figure 5–19(a) shows a section view of 

the OMF model at the level of the top anchorage bars on the top link plates, at a center column 

displacement of  = 6.0 in (151 mm), near the peak vertical load. Figure 5–19(b) shows a similar section 

view at the level of the bottom anchorage bars on the bottom link plates, in which shear stud failure is 

also evident through relative displacements of the column plates. As discussed in Section 5.3.5, shear stud 

failure in the OMF specimen was influenced by out-of-plane bending of the link plates, and significant 

out-of-plane bending of the link plates is evident in Figure 5–19, particularly at the center column, where 

balanced forces from the beams on each side prevented shear stud failures. The computed out-of-plane 

deformations of the link plates and anchorage bars shown in Figure 5–19 are consistent with the strain 

gauge measurements presented in Section 4.1.3 and illustrated schematically in Figure 4–15.

0 50.8 101.6 152.4 203.2

-222.4

-177.9

-133.5

-89.0

-44.5

0.0

44.5

-50

-40

-30

-20

-10

0

10

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Axial Force in Brace Beams (kip) Axial Force in Brace Beams (kN)

Vertical Displacement of Center Column,  (in)

Experiment Model

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

0

50

100

150

200

250

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

Experiment Model

OMF Specimen OMF Specimen Horizontal Force at Column Tops (kip)

Horizontal Force at Column Tops (kN)

(a) (b)

Front brace beam

(inward forces on tops of 

columns are positive)
Chapter 5

72

Figure 5–19. Section views of OMF model near the peak vertical load.

After shear stud failure, the OMF specimen developed additional capacity through arching action, with 

the top ends of the beams bearing against the center column, as indicated in Figure 5–19(a), and the 

bottom ends of the beams bearing against the end columns, as indicated in Figure 5–19(b). The deflected 

shape of the OMF specimen near the peak vertical load is shown in Figure 5–20, indicating a 

predominantly linear deflected profile of the beams between the connections, consistent with the 

experimental measurements (Figure 4–10). Contours of the concrete damage index near the peak vertical 

load are presented in Figure 5–21, which shows that concrete damage was concentrated in the regions

surrounding the beam-to-column connections and in the lower portions of the end columns. Shortly after 

the onset of arching action, which was evidenced by bearing of the beams against the columns, inclined 

damage contours developed in the lower portions of the end columns. These inclined damage contours 

indicate the formation of diagonal shear cracks, consistent with the experimental observations (see Figure 

4–5 and Figure 4–6). 

Figure 5–20. Deflected shape of OMF specimen prior to anchorage bar fracture.

Figure 5–21. Concrete damage for OMF specimen prior to anchorage bar fracture.

center column

center column

right end column

right end column

left end column

left end column

displacement of column plate

bearing

bearing

displacement of column plate

displacement of column plate displacement of column plate

(b) Section through bottom anchorage bars on bottom link plates at  = 6.0 in (151 mm):

(a) Section through top anchorage bars on top link plates at  = 6.0 in (151 mm):

bearing

0.0

-1.0

-2.0

-3.0

-4.0

-5.0

-6.0

Vertical displacement (in)

(1 in = 25.4 mm)  = 5.6 in

1.00 

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00 

Damage index

Damage index = 1: completely damaged

Damage index = 0: no damage

 = 5.6 in (142 mm)
Computational Modeling and Analysis

73

Figure 5–22 shows the concrete damage near the top of the center column, a location where extensive 

spalling occurred, comparing (a) a photograph taken after the peak vertical load with (b) damage contours 

from the computational model at  = 6.1 in (156 mm), also after the peak vertical load. While the 

concrete damage model is unable to capture discrete cracking and spalling, which are evident in Figure 5–

22(a), the concentration of damage around the link-plate connections in the computational model is 

generally consistent with the damage in the OMF specimen. Out-of-plane bending of the link plates is 

also evident in Figure 5–22, and the deformed shape of the link plates in the computational model agrees 

quite well with the deformed shape shown in the photograph. 

The computed vertical load reached a peak value of 163 kip (725 kN), within 2 % of the experimental 

peak load, at a center column displacement of  = 5.8 in (147 mm). After reaching this peak value, the 

vertical load dropped sharply as a result of anchorage bar fracture, illustrated in Figure 5–23. Fracture of 

the anchorage bars resulted from a combination of bending moment and axial tension, and significant outof-plane bending of the link plates and anchorage bars is evident in Figure 5–23, as was previously noted 

in Figure 5–19.

Figure 5–22. Concrete damage near top of center column for OMF specimen after anchorage bar fracture: 

(a) photograph; (b) contours of computed damage index.

Figure 5–23. Anchorage bar fracture in OMF model: (a) perspective view; (b) section through bottom 

anchorage bars on bottom link plates.

1.00 

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00 

Damage index = 1: completely damaged Damage index

Damage index = 0: no damage

(a) (b)

 = 6.1 in 

(156 mm)

link

plates

link 

plates

center column anchorage 

bar fracture

(b)

(a) bottom column plate

on center column

 = 6.1 in (156 mm)
Chapter 5

74

Figure 5–24 shows the interaction of the computed bending moment and axial force in the lowest 

anchorage bar on the left side of the center column, in the critical element adjacent to the weld, where the 

initial fracture occurred. Limiting interaction boundaries corresponding to the yield strength and the 

ultimate strength of a #10 bar are also shown in Figure 5–24 for reference, calculated based on Chapter H 

of the 2010 AISC Specification (AISC 2010), where My = S∙fyis the yield moment, Ty = A∙fyis the yield 

capacity in tension, Mu = Z∙fu is the ultimate moment, Tu = A∙fu is the ultimate capacity in tension, S is the 

elastic section modulus, Z is the plastic section modulus, and fy and fu are the yield and ultimate strength 

values of the #10 bar obtained from tensile tests (see Table 3–1). Unloading and reloading of the 

anchorage bar, which occurred before fracture and is evident in Figure 5–24, was caused by the failure of 

shear studs. The final fracture point was slightly beyond the limiting interaction boundary corresponding 

to the ultimate strength. The tensile force at fracture was 84% of the ultimate tensile capacity, indicating a 

moderate reduction in tensile strength as a result of moment-axial interaction. The tensile force in the 

anchorage bar at fracture was within 1 % of the peak axial force calculated from strain gauge 

measurements (Figure 4–18, Section RC), showing excellent agreement between the experimental and

computed fracture points. The computed values of bending moment in Figure 5–24 were larger than the 

experimental values in Figure 4–18 because of the steep decay in bending moment with distance along the 

anchorage bar (see Figure 5–12), since the bending moment was computed for a cross section located at

the end of the weld, whereas the strain gauges were located 3.5 in (89 mm) from the end of the weld (see 

Figure 3–9).

 

Figure 5–24. Bending moment and axial force interaction for anchorage bar of OMF model.

5.5.2 SMF Specimen

Figure 5–25 shows a comparison between the measured and computed curves of (a) the applied vertical 

load and (b) the horizontal reaction force at the end column tops for the SMF specimen, both plotted 

against the vertical displacement of the center column. Inward horizontal reaction forces are considered 

positive in Figure 5–25(b), corresponding to tension in the brace beams spanning between the tops of the 

end columns. The experimental curve in Figure 5–25(b) was obtained as the sum of the axial forces 

measured in the front and back brace beams (see Figure 4–42). The curve computed from the model in 

Figure 5–25(b) was obtained as the average of the horizontal reaction forces at the tops of the two end 

columns, with inward forces positive. An outward horizontal reaction developed in the initial application 

of self-weight in the computational model, and for consistency with the experimental measurements, this 

initial reaction was deducted from the horizontal force values presented in Figure 5–25(b).

0 1.13 2.26 3.39 4.52

0

111

222

334

445

556

0

25

50

75

100

125

0 10 20 30 40

Bending Moment (kN∙m) Axial Tension, T (kN) Axial Tension, T (kip)

Bending Moment (kip∙in)

Mu

Tu

Ty

My

fracture
Computational Modeling and Analysis

75

Figure 5–25. Comparison of experimental and computed results for (a) vertical load and (b) horizontal 

reaction from brace beams at end column tops (SMF specimen).

Figure 5–25(a) shows that the vertical load from the computational model reached an initial peak value of 

163 kip (725 kN) at a vertical displacement of 2.8 in (70 mm), before dropping sharply as a result of 

anchorage bar fracture, shown in Figure 5–26. A corresponding drop in load is also evident in the 

computed horizontal reaction at the column tops in Figure 5–25(b). The measured and computed 

horizontal forces in Figure 5–25(b) agree fairly well initially, both showing outward horizontal reactions 

corresponding to compressive brace forces. However, when the specimen was unloaded and reloaded 

after the initial phase of loading (see Section 4.2.1), the measured horizontal force never again reached 

the peak horizontal force of 43 kip (191 kN) attained in the initial loading. The unloading and reloading 

cycle appears to have introduced some change in the horizontal restraint that was not captured by the 

computational model (which was not unloaded and reloaded), and consequently, the peak computed 

horizontal force exceeded the measured value by 42 %.

The three anchorage bars fractured nearly simultaneously in the model. This contrasts with the 

experiment, in which the lowest anchorage bar fractured first at  = 2.5 in (64 mm) and the upper two 

anchorage bars fractured later at  = 4.9 in (124 mm). As discussed previously in Section 5.4, these 

differences in the experimentally observed fracture points may be due to variations in the ductility of the 

anchorage bars in the heat-affected zones near the welds, whereas the model assumed the same ductility 

for all anchorage bars. Fracture of the anchorage bars resulted from a combination of bending moment 

and axial tension, and out-of-plane bending of the link plates and anchorage bars is evident in Figure 5–

26, although not as pronounced as it was for the OMF specimen in Figure 5–23.

Figure 5–27 shows the interaction of the computed bending moment and axial force in the lowest 

anchorage bar on the left side of the center column, in the critical element adjacent to the weld, where 

fracture occurred. Limiting interaction boundaries corresponding to the yield strength and the ultimate 

strength of a #11 bar are also shown in Figure 5–27 for reference, as were shown previously in Figure 5–

24 for a #10 bar. As a result of the larger bar size, computed values of bending moment in the anchorage 

bars are larger for the SMF specimen in Figure 5–27 than for the OMF specimen in Figure 5–24. The 

final fracture point was slightly beyond the limiting interaction boundary corresponding to the ultimate 

strength. The tensile force at fracture was 66 % of the ultimate tensile capacity, indicating a significant 

reduction in capacity that resulted from the combined effects of (a) moment-axial interaction and 

(b) reductions in ductility of the bar in the heat-affected zone near the weld. 

0 50.8 101.6 152.4 203.2

-333.6

-222.4

-111.2

0

111.2

222.4

-75

-50

-25

0

25

50

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Axial Force in Brace Beams (kip) Axial Force in Brace Beams (kN)

Vertical Displacement of Center Column,  (in)

Experiment Model

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

0

50

100

150

200

250

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

Experiment Model

SMF Specimen SMF Specimen Horizontal Force at Column Tops (kip)

Horizontal Force at Column Tops (kN)

(a) (b)

(inward forces on tops of 

columns are positive)
Chapter 5

76

Figure 5–26. Anchorage bar fracture in SMF model: (a) perspective view; (b) section through bottom 

anchorage bars on bottom link plates.

Figure 5–27. Bending moment and axial force interaction for anchorage bars of SMF specimen.

Figure 5–28 shows the deflected shape of the SMF specimen just prior to anchorage bar fracture, which 

indicates a predominantly linear deflected profile of the beams between the connections, consistent with 

the experimental measurements (Figure 4–32). Contours of the concrete damage index prior to anchorage 

bar fracture are shown in Figure 5–29. Extensive concrete damage is evident at the tops of the beams near

the end columns and at the bottom of the beams near the center column, consistent with the locations 

where cracking and spalling were observed in the test (see Figure 4–26). 

After fracture of the anchorage bars, the SMF specimen developed additional load carrying capacity 

through arching action, with the top ends of the beams bearing against the center column, as indicated in 

Figure 5–30(a), and the bottom ends of the beams bearing against the end columns, as indicated in Figure 

5–30(b). Outward forces, from bearing of the beams against the end columns, resulted in inclined damage 

contours in the lower portions of the end columns, as shown in Figure 5–31(a), indicating the formation 

of diagonal shear cracks consistent with the experimental observations in Figure 5–31(a).

center column

anchorage 

bar fracture

link plate link plate

(b)

(a) bottom column plate

on center column

 = 3.0 in (76 mm)

0 1.13 2.26 3.39 4.52 5.65

0

111

222

334

445

556

667

0

25

50

75

100

125

150

0 10 20 30 40 50

Bending Moment (kN∙m) Axial Tension, T (kN) Axial Tension, T (kip)

Bending Moment (kip∙in)

Mu=ZpFu

Tu=AFu

Ty=AFy

My=SFy

fracture
Computational Modeling and Analysis

77

Figure 5–28. Deflected shape of SMF specimen prior to anchorage bar fracture.

Figure 5–29. Concrete damage for SMF specimen prior to anchorage bar fracture.

Figure 5–30. Section views of SMF model at the peak vertical load.

Figure 5–31. Concrete damage on right end column of SMF specimen: (a) photograph; (b) contours of 

computed damage index.

 = 2.9 in (1 in = 25.4 mm)

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0

Vertical displacement (in)

1.00 

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00 

Damage index

Damage index = 1: completely damaged

Damage index = 0: no damage

 = 2.9 in (74 mm)

center column

center column

right end column

right end column

left end column

left end column

bearing

bearing

(b) Section through bottom anchorage bars on bottom link plates at  = 5.2 in (132 mm):

(a) Section through top anchorage bars on top link plates at  = 5.2 in (132 mm):

anchorage bar fracture 

occurred here at 

ultimate load

bearing

initial anchorage bar 

fracture occurred here

1.00 

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00 

Damage index = 1: completely damaged Damage index

Damage index = 0: no damage

(a) (b)

 = 5.4 in 

(137 mm)
Chapter 5

78

Figure 5–25(a) shows that the computed vertical load eventually reached an ultimate peak value of 

172 kip (765 kN), about 8 % less than the experimental peak, at a center column displacement of u = 

5.1 in (130 mm). The vertical load dropped sharply after reaching the peak value, and a corresponding 

drop in the horizontal reaction force at the column tops is also evident in Figure 5–25(b). Consistent with

the experimental measurements, the horizontal reaction force changed direction from outward to inward 

after the peak vertical load [see Figure 5–25(b)], as arching action began to force the tops of the end 

columns outward.

In the computational model, the failure mode associated with the peak vertical load was fracture of the 

upper anchorage bars at the left end column, as indicated in Figure 5–30(a). In the experiment, the failure 

mode associated with the peak vertical load was bond failure of the upper anchorage bars at the right end 

column, which resulted from the formation of splitting cracks and spalling of the concrete cover [see 

Figure 4–26(f)]. The modeling approach used in this study is unable to capture this failure mode. While 

bond slip and bond failure could be modeled using a 1-dimensional contact interface between the 

reinforcing bar and the surrounding concrete (e.g., Lew et al. 2011), such an approach does not capture 

the influence of discrete crack formation on bond strength, which played an important role in this case. 

However, while the computational model indicated bar fracture rather than bond failure at the peak 

vertical load, the model correctly indicated that the failure mode involved the upper anchorage bars at an 

end column. The computed center column displacement at the peak load was about 22 % less than the 

experimental value. The earlier failure of the upper anchorage bars in the model suggests that these bars 

may have been more ductile than was assumed. While all anchorage bars in the model were assumed to 

have the same ductility, the potential for significant variability in weld-induced reductions in ductility was 

noted in Section 5.4.

5.6 INFLUENCE OF SPAN LENGTH

As noted in Section 3.1, the span length of the test specimens was reduced to 25 ft (7.6 m) from the 

prototype span length of 30 ft (9.1 m), in order to fit within the test facility. Somewhat smaller capacities 

would be expected if the full span length had been used in the test specimens. To investigate the influence 

of span length, finite element models of each specimen were developed in which the span length was 

increased to 30 ft (9.1 m), consistent with the prototype building design (see Section 2.1). Apart from the 

difference in span length, the models were identical to the final post-test models of each specimen 

(models OMF-A and SMF-A in Table 5–1). 

Figure 5–32 shows a comparison of the vertical load-displacement curves computed from the two finite 

element models of each specimen. Because the self-weight differed for the different span lengths, the 

vertical load values in Figure 5–32 include the self-weight sustained by the specimens in addition to the 

load applied to the center column. Only self-weight that was tributary to the center column was added, 

which included the center column and half of each spandrel beam. For the 25 ft (7.6 m) span length, this 

self-weight amounted to 29.3 kip (130 kN) for the OMF specimen and 24.9 kip (111 kN) for the SMF 

specimen, and the vertical load values in Figure 5–32 are thus greater than the corresponding values in 

Figure 5–18 and Figure 5–25 by these respective amounts. For the 30 ft (9.1 m) span length, the selfweight amounted to 33.8 kip (150 kN) for the OMF specimen and 28.8 kip (128 kN) for the SMF 

specimen. The displacement values in Figure 5–32 include displacements due to self-weight in addition to 

the computed displacements due to loading of the center column.
Computational Modeling and Analysis

79

Figure 5–32. Influence of span length on computed vertical load-displacement response:

(a) OMF specimen and (b) SMF specimen.

The behaviors and failure modes observed in the computational models with the 30 ft (9.1 m) span length

were essentially the same as those described in Section 5.5 for the 25 ft (7.6 m) span length. However, 

Figure 5–32 shows that the longer-span specimens had lower ultimate capacities that were achieved at 

larger vertical displacements of the center column. The ratio between the ultimate capacities for the 

longer and shorter spans was 0.857 for the OMF specimen and 0.786 for the SMF specimen. For the SMF 

specimen, the influence of arching action was less significant for the longer span length, so that the 

ultimate peak load at u = 6.3 in (160 mm) was essentially equivalent to the initial peak load at  = 3.8 in 

(96 mm). The center column displacement at the ultimate load, u, was larger for the longer span length

than for the shorter span length, with a ratio of 1.17 for the OMF specimen and 1.22 for the SMF 

specimen. However, the beam chord rotation at the ultimate load, u (calculated as described in Section 

4.3), was nearly equivalent for both span lengths. The ratio between the values of u obtained for the 

longer and shorter span lengths was 0.98 for the OMF specimen and 1.01 for the SMF specimen. 

5.7 SUMMARY AND DISCUSSION

This chapter presented computational modeling and analysis of the precast OMF and SMF specimens

subjected to monotonic loads at the top of the unsupported center column to simulate a column removal 

scenario. Pre-test models significantly overestimated the capacities of the test specimens, largely because 

of the sensitivity of the responses to factors that were not well known prior to the tests. Key factors that 

were found to influence the computed responses included (a) the initial gap width between the spandrel 

beams and columns, (b) the reduction in ductility of the welded anchorage bars in the heat-affected zone 

near the welds, and (c) the reduction in effective shear strength of the shear studs due to out-of-plane 

bending of the link plates. To illustrate the influence of these key factors, computed responses were 

compared from three models of each specimen, in which individual factors were varied to isolate their 

effects. By more carefully accounting for each of these factors in the final post-test models, reasonably 

good agreement with the experimental measurements was achieved. The computed ultimate capacities of 

the test specimens were 163 kip (725 kN) for the OMF specimen and 172 kip (765 kN) for the SMF 

specimen, which were less than the experimental values by 2 % and 8 %, respectively. The computational 

results also provided additional insights into the load-carrying mechanisms and failure modes of the 

precast concrete moment frames. 

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

1334.4

0

50

100

150

200

250

300

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

25 ft (7.62 m)

30 ft (9.14 m)

Span length:

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

1334.4

0

50

100

150

200

250

300

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

25 ft (7.62 m)

30 ft (9.14 m)

Span length:

OMF Specimen SMF Specimen

(a) (b)
Chapter 5

80

For both the OMF and SMF specimens, the failure modes included fracture of anchorage bars at the lower 

link plate connections to the center column. Detailed finite-element modeling of the welded anchorage 

bar connections revealed that these failures were influenced by local bending moments near the welds that 

resulted from eccentricities in the transfer of forces between the link plates and the anchorage bars. For 

the SMF specimen, component testing of a welded anchorage bar showed that these failures were also 

influenced by reductions in ductility in the heat-affected zone near the weld. A reduced-order modeling 

approach for the welded anchorage bar connections that captured these effects was developed, and the 

failure criterion for bar fracture was calibrated against detailed models. As a consequence of these effects, 

the computational models of the moment-frame assemblies showed that anchorage bar fracture occurred 

at 84 % of the ultimate tensile capacity of the anchorage bar for the OMF specimen and at 66 % of the 

ultimate tensile capacity for the SMF specimen.

Another failure mode observed for the OMF specimen was shear stud failure at the upper link plate 

connections to the end columns. These failures were influenced by out-of-plane bending of the link plates, 

which significantly reduced the effective shear capacity of the shear studs relative to their nominal 

capacity, as confirmed by forces calculated from anchorage bar strain measurements. Developing a failure 

model for the shear studs that explicitly accounted for the complex interaction of stresses observed in the 

OMF specimen would have required further research and was not attempted in this study. Rather, the 

effects of out-of-plane bending were accounted for reducing the effective shear strength of each shear 

stud to about 30 % of its nominal value. In contrast with other aspects of the modeling, which were based 

on fundamental constitutive relationships for the various materials, the failure criterion for the shear studs 

was calibrated to capture the experimentally observed shear stud failures in the OMF specimen.

The computational models were able to capture the arching action that was observed for both specimens, 

in which increased vertical loads were developed through bearing forces between the beams and columns. 

Arching action developed when the connection rotations became large enough to close the initial gaps 

between the spandrel beams and the columns. As a result of arching action, the vertical loads sustained by 

the moment-frame assemblies were found to be strongly influenced by the initial gap width, particularly 

for the OMF specimen, which had much deeper spandrel beams. After the development of arching action, 

significant compressive forces were developed through bearing of the spandrel beams against the end 

columns, which resulted in damage to the end columns. Inclined damage contours in the lower portions of 

the end columns became evident in the computational models after the development of arching action, 

indicating the formation of diagonal shear cracks consistent with the experimental observations. Catenary 

action did not develop, because failures depleted the capacity of the specimens when the displacement of 

the center column remained much less than the depth of the spandrel beams.

The test specimens considered in this study had a reduced span length of 25 ft (7.6 m), in order to fit 

within the testing facility. Using models of the two specimens with the full prototype span length of 30 ft 

(9.1 m), ultimate capacities of 165 kip (733 kN) and 155 kip (688 kN) were computed for the OMF and 

SMF specimens, respectively. These capacities include self-weight and represent a reduction relative to 

the shorter-span capacities by 14 % for the OMF specimen and by 21 % for the SMF specimen. 

Thereforce, although the SMF specimen was designed under more stringent seismic requirements, the 

computational models predicted that for the full prototype span length, the ultimate capacity of the SMF 

specimen would actually be somewhat less than that of the OMF specimen. The reduced capacity of the 

SMF specimen relative to the OMF specimen resulted from earlier fracture of the anchorage bars and 

from less extensive arching action because of the reduced beam depth.
81

Chapter 6

EVALUATION OF STRUCTURAL ROBUSTNESS

This chapter presents an evaluation of the structural robustness of the precast moment-frame assemblies 

through a comparison of their ultimate capacities with the applicable gravity loads from the prototype 

buildings. An energy-based procedure was used to account for the dynamic effects of sudden column loss.

Because the test specimens used a reduced span length, computational results from Section 5.6 for 

specimens with the full prototype span length of 30 ft (9.1 m) were used in the evaluation of structural

robustness. This accounted for the reduction in capacities associated with the longer span length and 

enabled a direct comparison with the gravity loads from the prototype buildings.

6.1 GRAVITY LOADS

The following load combination is considered in evaluating applicable gravity loads:

1.2D + 0.5L (6.1)

where D is dead load and L is live load. Eq. (6.1) corresponds to the load combination specified in ASCE 

7-10 (ASCE 2010, Section 2.5.2.2) for evaluating the residual capacity of structural systems following the 

notional removal of load-bearing elements. Although the span length of the test specimens was reduced to 

25 ft (7.6 m) to fit within the test facility, the full span length of 30 ft (9.1 m) is considered in evaluating 

applicable gravity loads on the moment frame assemblies.

A live load of 50 psf (2.40 kN/m2) is considered, corresponding to office occupancy, with a live load 

reduction factor of 0.75 based on Eq. (4.7-1) in ASCE 7-10, resulting in a reduced live load 37.5 psf 

(1.80 kN/m2). Multiplying by the tributary area of (30 ft)(15 ft) = 450 ft2[(9.1 m)(4.6 m) = 42 m

2

)] for an 

edge column (see Figure 2–1) yields an unfactored live load of 16.9 kip (75.1 kN) acting on the column to 

be removed.

The dead load acting on the column to be removed includes self-weight plus a superimposed dead load of 

10 psf (0.48 kN/m2). The unfactored dead load corresponding to the tributary area of the column to be 

removed was estimated from the design documents (Kim, Dasgupta, and Ghosh 2009a,b) as 83 kip 

(369 kN) for the OMF building and 81 kip (360 kN) for the SMF building. Evaluating the load 

combination in Eq. (6.1) with the dead and live loads defined above yields total gravity loads of 108 kip 

(481 kN) and 106 kip (470 kN) acting on the column to be removed for the OMF assembly and the SMF 

assembly, respectively.

6.2 ENERGY-BASED ANALYSIS

Given a load-displacement relationship obtained from static loading of a structure with an unsupported 

column, energy-based analysis can be used to account for the dynamic effects associated with sudden 

column loss, thereby calculating the peak dynamic displacement after sudden column loss under any 

given level of loading (Powell 2003, Izzuddin et al. 2008, Main 2014). The analysis is based on the fact 

that the kinetic energy is zero at the peak displacement, assuming a single predominant mode of 

deformation, so that conservation of energy requires the internal energy in the structure to equal the 

external work done by gravity loads. 
Chapter 6

82

Let Ps() denote a load-displacement relationship obtained from nonlinear static pushdown analysis of a 

structure with an unsupported column, where  is the vertical displacement of the unsupported column. 

The solid curve in Figure 6–1 illustrates such a static load-displacement relationship. Let Pd() denote the 

corresponding relationship between the load and the peak dynamic displacement under sudden column 

loss, illustrated by the dashed curve in Figure 6–1. At a peak dynamic displacement of , the balance 

between the work done by the external load, corresponding to the hatched area in Figure 6–1, and the 

internal energy in the structure, corresponding to the shaded area in Figure 6–1, can be expressed as 

follows:

0

( ) ( ) P P d d s



     

(6.2)

where 



is a dummy variable in the integral representing the vertical column displacement. Rearranging 

Eq. (6.2) yields the following relationship:

0

1

( ) ( ) P P d d s



   





(6.3)

Eq. (6.3) allows the dynamic effects associated with sudden column loss to be evaluated directly from the 

results of a nonlinear static pushdown analysis. 

Figure 6–1. Energy-based analysis of sudden column loss.

6.3 RESULTS

Figure 6–2 shows load-displacement curves for the two moment-frame assemblies for both static loading 

and sudden column loss. The static load-displacement curves in Figure 6–2 were obtained from the 

computational models and are equivalent to the curves presented previously in Figure 5–32 for the 30 ft 

(9.14 m) span length. The curves for sudden column loss were evaluated from Eq. (6.3) by numerical 

integration of the static load-displacement curves. 

Plotted with the load-displacement curves in Figure 6–2 are dashed horizontal lines corresponding to the 

applicable gravity loads from Eq. (6.1). The intersection of the curve for Pd() with this horizontal line in 

each plot gives the peak dynamic displacement under sudden column loss, and peak dynamic 

displacements of 3.3 in (83 mm) and 3.9 in (100 mm) were obtained for the OMF specimen and the SMF 

specimen, respectively. The analyses thus predicted that both precast specimens could sustain the 

applicable gravity loads under sudden column loss without collapse. For both specimens, however, the 

curves for Pd() exceeded the applicable gravity loading only slightly, and the predicted displacements

under sudden column loss were highly sensitive to further increases in the gravity loading.



Vertical Load

Vertical Displacement of Unsupported Column 0 0

( ) Ps 

( ) Pd 

( ) Pd   

0

( ) P d s



  

external work:

sudden column loss,

internal energy:

static loading, ( ) Pd 

( ) Ps 
Evaluation of Structural Robustness

83

Figure 6–2. Load-displacement relationships for static loading and sudden column loss compared with 

applicable gravity loading: (a) OMF specimen; (b) SMF specimen.

The ultimate capacities under static loading in Figure 6–2 were 165 kip (733 kN) and 155 kip (688 kN) 

for the OMF and SMF specimens, respectively, occurring at displacements of u = 6.9 in (174 mm) and 

u = 6.3 in (160 mm). A normalized measure of the ultimate capacity under static loading, denoted s,u, 

can be obtained by dividing the ultimate static capacity by the gravity loading from Eq. (6.1). Values of 

s,u = 1.53 and s,u = 1.46 were obtained for the OMF and SMF specimens, respectively, indicating that 

the specimens could sustain static loads exceeding the applicable gravity loading by about 50 %.

Ultimate capacities under sudden column loss were calculated at the displacement corresponding to the 

ultimate static load, as proposed by Main (2014), and ultimate capacities of Pd (u) = 120 kip (535 kN) 

and Pd (u) = 108 kip (479 kN) were obtained for the OMF and SMF specimens, respectively. Dividing 

these values by the applicable gravity loading yields normalized values of the ultimate capacity under 

sudden column loss, denoted d,u. The quantity d,u was proposed by Bao et al. (2014) as a robustness 

index for structural systems, where values greater than unity indicate that a structure will not collapse 

under sudden column loss. Using this approach, robustness indices of d,u = 1.11 and d,u = 1.02 were 

obtained for the OMF and SMF specimens, respectively. This indicates that the precast specimens could

sustain loads 2 % - 11 % greater than the applicable gravity loads under sudden column loss. 

Table 6–1 summarizes the normalized ultimate capacities obtained from the computational results in 

Figure 6–2 for the full prototype span length. Also presented in Table 6–1 are values of the dynamic 

increase factor (DIF) at the ultimate static load, defined as follows:

, ,

( ) /    u s u d u  

(6.3)

The results indicate that in a nonlinear static analysis, the loads on the precast concrete frames would need 

to be increased by about 40 % to account for the dynamic effects associated with sudden column loss. 

Table 6–1. Normalized ultimate capacities and dynamic increase factors for OMF and SMF specimens 

with prototype span lengths.

Specimen Span Length

ft (m)

Normalized Ultimate Capacity Dynamic Increase 

Static Loading,  Factor, (u)

s,u Sudden Column Loss1

, d,u

OMF 30 (9.14) 1.53 1.11

1.11

1.37

SMF 30 (9.14) 1.46 1.37

1.46

1.02 1.43

1.43 1 Robustness index, obtained using the approximate energy-based analysis of Eq. (6.3)

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

0

50

100

150

200

250

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

Static loading: Sudden column loss:

1.2D+0.5L

SMF Specimen Span = 30 ft (9.14 m)

0 50.8 101.6 152.4 203.2

0.0

222.4

444.8

667.2

889.6

1112.0

0

50

100

150

200

250

0 2 4 6 8

Vertical Displacement of Center Column,  (mm) Vertical Load (kip) Vertical Load (kN)

Vertical Displacement of Center Column,  (in)

Static loading: Sudden column loss:

1.2D+0.5L

OMF Specimen Span = 30 ft (9.14 m)

(a) (b)

Ps()

Pd()

Ps()

Pd()
Chapter 6

84

6.4 DISCUSSION AND LIMITATIONS

The computed results in Table 6–1 indicate that the capacities of the precast moment frames would be 

adequate to withstand sudden column loss, with reserve capacities of 2 % - 11 % against collapse. These

reserve capacities, however, are comparable to the uncertainty in the model predictions. Differences of 

2 % - 8 % were observed between the computed and experimental ultimate capacities for the reduced 

span length of 25 ft (7.6 m), and somewhat larger discrepancies would be expected when extending the 

models to the full prototype span length of 30 ft (9.1 m). In addition, the computed responses were found 

to be highly sensitive to factors such as the initial gap width between the beams and columns (which was 

not specified in the design) and the ductility of the welded anchorage bars. Variations in these factors 

were found to reduce the computed ultimate capacities by 35 % (see Section 5.1). Differences in these 

factors were observed between the two specimens that were tested, with larger gap widths for the OMF 

specimen and greater reductions in anchorage bar ductility for the SMF specimen. Additional variability 

in the test specimens was introduced by installation errors for the SMF specimen (see Section 3.1), 

although computational modeling showed that these errors reduced the ultimate capacity by only about 

4 %. Because of the strong sensitivities observed, significant variability might be expected if multiple 

tests of nominally identical specimens were tested, and some combinations of factors could result in 

specimens that would not sustain the applicable gravity loads under sudden column loss.

The computed results for the full prototype span length (Table 6–1) indicate that the normalized ultimate 

capacities of the OMF and SMF specimens were approximately equivalent. For the reduced span length 

of 25 ft (7.6 m), both the experimental and computational results showed slightly higher capacities for the 

SMF specimen. With increased span length, however, the computational results showed greater 

reductions in capacity for the SMF specimen than for the OMF specimen. As a result, for the full 

prototype span length of 30 ft (9.1 m), the normalized ultimate capacity of the SMF specimen was 

actually slightly less than that of the OMF specimen under both static loading and sudden column loss.

The comparable performance of the OMF and SMF specimens contrasts with previous full-scale testing 

of steel moment frames (Sadek et al. 2010) and cast-in-place concrete moment frames (Lew et al. 2011), 

in which the ultimate capacity of SMF specimens under a column removal scenario was approximately 

twice the ultimate capacity of corresponding intermediate moment frame (IMF) specimens. Because the 

design and detailing requirements for an OMF are less stringent than for a seismically designed IMF, 

even more significant improvements in performance might be expected for an SMF specimen relative to 

an OMF specimen.

For a column removal scenario in an actual building, the response of a precast concrete moment frame 

would depend on the resistance provided by the surrounding structural system, which would vary 

depending on the location within the building. This study considered end columns with spandrel beams 

framing into the connections from only one side. Spandrel beams framing into the columns from both 

sides would provide additional resistance to rotation and horizontal displacement of the columns, thus 

reducing the flexural and shear demands on the columns and providing increased support for the 

development of compressive arching action. Axial forces in the columns due to gravity loads from the 

upper stories, while increasing the stress levels in the columns, would also provide increased resistance to 

shear forces resulting from arching action. In a corner column removal scenario, however, negligible 

arching action would be expected, because of the limited horizontal restraint of the corner column. These 

issues, and other influences of the surrounding structural system on the robustness of precast concrete 

moment frames, can be investigated in future studies using computational modeling.
85

Chapter 7

SUMMARY AND CONCLUSIONS

This report presented an experimental and computational study of two precast concrete moment-frame 

assemblies, each comprising three columns and two beams. The two moment-frame assemblies 

represented portions of the structural framing system of two ten-story precast concrete frame buildings.

One building was designed for Seismic Design Category B (SDC B) and the other for SDC D. The 

moment-frame assemblies were taken from the exterior moment-resisting frames of these buildings. The 

test specimen extracted from the SDC B building was part of an ordinary moment frame (OMF) and the 

test specimen extracted from the SDC D building was part of a special moment frame (SMF). The 

specimens were subjected to monotonically increasing vertical displacement of the unsupported center 

column to observe their behavior under a simulated column removal scenario, including the development 

of arching action in the beams. The vertical displacement of the center column was increased beyond the 

ultimate capacity of the assemblies to characterize the failure modes and collapse mechanisms that 

developed.

The behavior of the moment-frame assemblies was analyzed using detailed finite element models, in 

which solid elements were used to represent the concrete, steel plates, and steel angles, while beam 

elements were used to represent the longitudinal and transverse reinforcement in the beams and columns. 

The analyses conducted using these models were able to capture the primary response characteristics of 

the test specimens, and the analyses provided insight into the overall behavior and failure modes.

Based on the study reported herein, the following conclusions were reached.

1. For both the OMF and the SMF specimens, the behavior was dominated by flexure in the early stages 

of the response. With increased vertical displacement of the center column, the initial gaps between 

the beams and columns closed, and additional resistance was provided through arching action, with 

the top corners of the beams bearing against the center column and the bottom corners of the beams

bearing against the end columns. Computational modeling showed that the vertical resistance 

developed through arching action was sensitive to the initial gap width between the beams and 

columns, with smaller gaps resulting in larger forces from arching action.

2. Catenary action did not develop in either the OMF or the SMF specimen, in contrast with previous 

testing of reinforced concrete moment frames, for which tensile forces developed in the beams when

the deflection of the center column was approximately equal to the beam depth. The precast concrete 

spandrel beams tested in this study had greater depths than the reinforced concrete beams tested 

previously, and failures of the beam-to-column connections depleted the capacities of the specimens 

when the deflections of the center column remained much less than the beam depths.

3. Both the OMF and SMF specimens exhibited the following failure modes: (a) cracking and spalling 

of concrete near the welded link plate connections between the precast concrete beams and columns, 

(b) fracture of the bottom anchorage bars at the welded connection to the center column, and (c) 

diagonal cracking, spalling, and outward shear deformation of the end columns below beam level as a 

result of arching action in the beams.
Chapter 7

86

4. Fracture of the welded anchorage bars occurred at relatively small beam chord rotations of 0.019 rad 

for the OMF specimen and 0.0087 rad for the SMF specimen. The anchorage bars fractured earlier 

than would be expected under tensile loading as a result of the following two factors: (a) local

bending moments in the anchorage bars resulting from eccentricities in the connections, which 

interacted with the tensile forces to produce larger tensile stresses, and (b) reductions in the ductility 

of the anchorage bars as a result of welding the bars to the connecting angles.

5. The diagonal cracking, spalling, and shear deformation of the end columns observed in these tests 

indicate that lateral forces due to arching action could potentially result in shear failure of columns. If 

arching action is to be exploited in resisting vertical loads under column removal scenarios, care must 

then be taken to ensure that the columns adjacent to the missing column can resist the lateral loads 

induced by arching action.

6. Additional failure modes that were observed included (a) detachment of embedded steel column 

plates with welded shear studs from the end columns of the OMF specimen under a combination of 

unbalanced shear forces and out-of-plane bending induced by the link plates and (b) bond failure of 

the upper anchorage bars at the right end column at the ultimate load of the SMF specimen, resulting 

from the formation of splitting cracks and spalling of concrete. 

7. The ultimate capacity of the OMF specimen was 166 kip (738 kN), while the ultimate capacity of the 

SMF specimen was 188 kip (836 kN). Corresponding beam chord rotations at the ultimate load were 

0.019 rad for the OMF specimen and 0.022 rad for the SMF specimen. Thus, the more stringent 

seismic design requirements for the SMF specimen resulted in an increase of only 13 % in the 

ultimate capacity under the column removal scenario, with an increase of 18 % in the corresponding 

beam chord rotation.

8. The test specimens had a reduced span length of 25 ft (7.6 m), and computational modeling showed 

that considering the full prototype span length of 30 ft (9.1 m) reduced the ultimate capacity by 14 % 

for the OMF specimen and by 21 % for the SMF specimen. The ultimate capacities of the prototypespan specimens under static loading exceeded the applicable gravity loading of 1.2D+0.5L by factors

of 1.53 and 1.46 for the OMF and SMF specimens, respectively. Ultimate capacities of the prototypespan specimens under sudden column loss were evaluated using an approximate energy-based 

procedure, and the resulting values slightly exceeded the applicable gravity loading, by factors of 1.11

and 1.02 for the OMF and SMF specimens, respectively. However, given the observed sensitivity of 

the results to factors such as the initial gap width between the beams and columns and the weldinduced reductions in ductility of the anchorage bars, variations in these factors could result in 

specimens that would not sustain the applicable gravity loads under sudden column loss. The 

computational results indicated that for the full prototype span length, the ultimate capacity of the 

SMF specimen was approximately equivalent to that of the OMF specimen, in spite of the more 

stringent design requirements.

Future research on precast concrete structures will involve development and evaluation of modified 

connection details to enhance performance (e.g., by eliminating eccentricities and weld-induced 

embrittlement in the anchorage bar connections). Connections with less sensitivity to factors such as gap 

width and anchorage bar ductility are desirable, so that more consistent and predictable performance 

could be achieved. The influence of the surrounding structural system on the response of precast concrete 

moment frames will also be investigated using computational modeling, including the effects of threedimensional framing under various column removal scenarios.
87

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