NIST Technical Note 1669

An Experimental and Computational

Study of Steel Moment Connections 

under a Column Removal Scenario

Fahim Sadek

Joseph A. Main

H.S. Lew

Stephen D. Robert

Vincent P. Chiarito

Sherif El-Tawil

National Institute of Standards and Technology U.S. Department of Commerce

NIST Technical Note 1669 

An Experimental and Computational 

Study of Steel Moment Connections 

under a Column Removal Scenario 

Fahim Sadek 

Joseph A. Main 

H.S. Lew 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

Stephen D. Robert 

Vincent P. Chiarito 

Engineer Research and Development Center

U.S. Army Corps of Engineers 

Sherif El-Tawil 

Department of Civil and Environmental Engineering 

University of Michigan 

September 2010 

U.S. Department of Commerce 

Gary Locke, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Director 
Disclaimer

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 in-pound units, it is more practical and less confusing to use inch-pound units, in 

some cases, rather than metric units within quoted text. However, in most cases, units are 

presented in metric and the inch-pound system. 

Disclaimer

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

describe a procedure or concept adequately or to trace the history of the procedures and practices used. 

Such identification is not intended to imply recommendation, endorsement, or implication that the 

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

iii

ABSTRACT

This report presents an experimental and computational study of two steel beam-column assemblies, each 

comprising three columns and two beams. The two beam-column assemblies represent portions of the 

structural framing system of two ten-story steel frame buildings, which were designed as part of the 

National Institute of Standards and Technology research program aimed at prevention of disproportionate 

structural collapse. One building was designed for Seismic Design Category C (SDC C) and the other for 

Seismic Design Category D (SDC D). The beam-column assemblies were taken from the exterior 

moment-resisting frames of these buildings. One test specimen, which was part of the SDC C building, 

had welded unreinforced flange-bolted web (WUF-B) connections, and the other, which was part of the 

SDC D building, had reduced beam section (RBS) connections. The specimens were subjected to 

monotonically increasing vertical displacement of the unsupported center stub column to observe their 

behavior under a simulated column removal scenario, including the development of catenary action in the 

beams. The test was terminated when a collapse mechanism of each assembly was developed and the 

vertical load-carrying capacity was depleted. The primary test specimen response characteristics were 

measured. These included vertical and horizontal displacements at specific locations, rotations at beam 

ends, strains at various locations, and the applied load. In addition, a high speed video camera was used to 

record the specimen response, including the failure mode and sequence of the beam-to-column 

connections at the center column. 

For both the WUF-B and RBS test specimens, the beam-column assemblies remained initially in the 

elastic range at small displacements of the center column, where the behavior of the beams was 

dominated by flexure. With increased vertical displacement, the beam connections exhibited yielding and 

large tensile axial forces developed in the beams. The axial tension in the beams increased until the 

connections could no longer sustain the combined bending and axial stresses, and the beam-column 

assemblies failed. 

The failure of the WUF-B test specimen was characterized by the following sequence: (1) local buckling 

of the top flanges of the beams near the center column, (2) successive shear fracture of the lowest and 

middle bolts connecting the beam web to a shear tab at the center column, and (3) fracture of the bottom 

flange near the weld access hole. The failure of the RBS test specimen was characterized by the fracture 

of the bottom flange in the middle of the reduced section near the center column. The fracture propagated 

through the web until the vertical load-carrying capacity of the beam was lost. 

Computational simulations of the beam-column assembly tests were carried out using two levels of 

modeling complexity: (1) detailed models with a large number of elements, primarily solid and shell 

elements, and (2) reduced models with a limited number of elements, primarily beam and spring 

elements. The analyses conducted using these models provided insight into the behavior and failure 

modes of the connections, including their capacity to carry the tensile forces that developed in the beams. 

The analyses showed a good agreement between the experimental results and the computational 

predictions. Both detailed and reduced models were capable of capturing the primary response 

characteristics and failure modes. The validated reduced models developed in this study will be valuable 

in the analysis of complete structural systems for assessing the reserve capacity and robustness of 

building structures. The analyses confirm that the ultimate loads under this column removal scenario are 
primarily resisted through catenary action, wherein axial tension develops in the beams. These tensile 

forces increase until the connection can no longer sustain the combined tensile and flexural stresses and 

failure occurs. 

The test results show that the rotational capacities of both the WUF-B and the RBS connections under 

monotonic column displacement are about twice as large as those based on seismic test data. The 

rotations at peak load were about 0.081 rad and 0.140 rad for the WUF-B and RBS connections, 

respectively, whereas the rotational capacities of these connections based on seismic testing data are 

approximately 0.047 rad and 0.073 rad, respectively. 

Keywords: buildings; computational model; computer simulation; design standards; disproportionate 

collapse; finite element analysis; moment resisting connections; progressive collapse; steel structures; 

structural robustness; testing. 
 

v

PREFACE

This research was carried out by the National Institute of Standards and Technology (NIST) in 

partnership with the Engineer Research and Development Center (ERDC) of the U.S. Army Corps of 

Engineers. NIST designed the test specimens, one with welded unreinforced flange, bolted web (WUFB) connections and the other with reduced beam section (RBS) connections. These connections were 

part of steel frame buildings designed for Seismic Design Categories C and D, 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), Andrew W. Taylor (KPFF 

Consulting Engineers, Seattle, WA). 

ERDC fabricated and erected the test specimens, deployed the instruments, performed the test, and 

collected the test data. NIST developed the finite-element based computational models and performed 

pre-test analyses to guide the development of the instrumentation plan, test setup, and loading procedure 

for each test. NIST validated the computational models against experimental data and used the models to 

study the behavior and failure modes of the connections. 

The study reported herein was supported partially by the following organization and federal agencies: the 

American Institute of Steel Construction, the Air Force Research Laboratory, and the Defense Threat 

Reduction Agency. 

The authors gratefully acknowledge the thorough review of the report by Therese P. McAllister of NIST 

and Ronald O. Hamburger of Simpson, Gupertz & Heger. 
 

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vi
 

TABLE OF CONTENTS

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

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

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

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

List of Tables ..............................................................................................................................................xii

List of Acronyms and Abbreviations.........................................................................................................xiii

Executive Summary..................................................................................................................xv

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

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

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

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

1.4 References........................................................................................................................................ 2

Chapter 2 Description of Prototype Building Designs ...............................................................3

2.1 Prototype Building Designs ............................................................................................................. 3

2.2 Description of Moment Resisting Frames ....................................................................................... 5

2.2.1 Welded Unreinforced Flange-Bolted Web (WUF-B) Connection ....................................... 7

2.2.2 Reduced Beam Section (RBS) Connection .......................................................................... 9

2.3 References...................................................................................................................................... 12

Chapter 3 Test Program ..............................................................................................................13

3.1 Introduction.................................................................................................................................... 13

3.2 Test Specimens .............................................................................................................................. 13

3.3 Test Setup ...................................................................................................................................... 16

3.4 Loading Aparatus and Test Sequence............................................................................................ 19

3.5 Instrumentation .............................................................................................................................. 19

3.5.1 Displacement Transducers.................................................................................................. 19

3.5.2 Inclinometers...................................................................................................................... 19

3.5.3 Strain Gages ....................................................................................................................... 22

3.6 References...................................................................................................................................... 22

vii
Table of Contents 

Chapter 4 Experimental Results.................................................................................................23

4.1 Introduction.................................................................................................................................... 23

4.2 WUF-B Specimen.......................................................................................................................... 23

4.2.1 Observed Behavior and Failure Modes .............................................................................. 23

4.2.2 Displacement Measurements.............................................................................................. 25

4.2.3 Rotation Measurements...................................................................................................... 28

4.2.4 Strain Measurements .......................................................................................................... 29

4.3 RBS Specimen ............................................................................................................................... 35

4.3.1 Observed Behavior and Failure Modes .............................................................................. 36

4.3.2 Displacement Measurements.............................................................................................. 37

4.3.3 Rotation Measurements...................................................................................................... 40

4.3.4 Strain Measurements .......................................................................................................... 42

4.4 Discussion of Test Results............................................................................................................. 51

4.5 References...................................................................................................................................... 52

Chapter 5 Computational Modeling and Analysis of Test Specimens....................................53

5.1 Introduction.................................................................................................................................... 53

5.2 Material Models............................................................................................................................. 53

5.2.1 Steel Sections and Plates .................................................................................................... 53

5.2.2 High Strength Bolts............................................................................................................ 56

5.2.3 Diagonal Braces ................................................................................................................. 59

5.3 WUF-B Finite Element Models..................................................................................................... 59

5.3.1 Detailed (Solid/Shell Element) Model ............................................................................... 60

5.3.2 Reduced (Beam/Spring Element) Model............................................................................ 66

5.4 RBS Finite Element Models .......................................................................................................... 69

5.4.1 Detailed (Shell Element) Model......................................................................................... 69

5.4.2 Reduced (Beam Element) Model ....................................................................................... 74

5.5 Summary and Discussion of Analysis Results............................................................................... 76

5.6 References...................................................................................................................................... 76

Chapter 6 Summary and Conclusions .......................................................................................77

viii
 

ix

LIST OF FIGURES

Figure 2–1 Plan layout for SDC C building............................................................................................4

Figure 2–2 Plan layout for SDC D building ...........................................................................................4

Figure 2–3 East-west elevation of the steel frame buildings ..................................................................5

Figure 2–4 WUF-B connection details – N-S frames, second floor of SDC C building ........................9

Figure 2–5 Detail of weld access holes for the WUF-B connection.......................................................9

Figure 2–6 RBS connection details – N-S frames, second floor of SDC D building ...........................11

Figure 2–7 RBS connection details – plan view of beam’s top and bottom flanges.............................11

Figure 2–8 Detail of weld access holes for the WUF-B connection.....................................................12

Figure 3–1 Details of WUF-B specimen ..............................................................................................14

Figure 3–2 Details of RBS specimen....................................................................................................15

Figure 3–3 Schematic of test setup .......................................................................................................17

Figure 3–4 Photograph of the WUF-B specimen..................................................................................18

Figure 3–5 Photograph of the RBS specimen.......................................................................................18

Figure 3–6 Instrumentation layout of the WUF-B specimen................................................................20

Figure 3–7 Instrumentation layout of the RBS specimen .....................................................................21

Figure 3–8 Inclinometer attachment to RBS specimen ........................................................................21

Figure 4–1 Overall view of the WUF-B specimen subjected to large displacements...........................24

Figure 4–2 Failure mode of the WUF-B specimen...............................................................................24

Figure 4–3 Applied vertical load versus vertical displacements at (a) 1/4 span of beams (D2 and D9), 

(b) 1/2 span of beams (D3 and D8), (c) 3/4 span of beams (D4 and D7), and (d) center 

column (D5 and D6) for the WUF-B specimen .................................................................26

Figure 4–4 Vertical displacement profiles of beams corresponding to indicated vertical loads for the 

WUF-B specimen (displacements magnified)....................................................................27

Figure 4–5 Horizontal displacement of end columns at beam mid-height (D1, D10, and their average) 

versus vertical displacement of center column for the WUF-B specimen .........................27

Figure 4–6 Applied vertical load versus angles of rotation at (a) connections to end columns and (b) 

connections to center column for the WUF-B specimen....................................................28

Figure 4–7 Angle of rotation at (a) connections to end columns and (b) connections to center column 

versus vertical displacement of center column for the WUF-B specimen .........................29

Figure 4–8 Locations of cross sections with strain gages for the WUF-B specimen............................30

Figure 4–9 Mid-span strain gage measurements at (a) Section B2 and (b) Section B5 versus vertical 

displacement of center column for the WUF-B specimen..................................................31

Figure 4–10 Average strains at Sections B2 and B5 versus vertical displacement of center column for 

the WUF-B specimen .........................................................................................................32

Figure 4–11 Axial force in the beams versus vertical displacement of center column for the WUF-B 

specimen.............................................................................................................................32
List of Figures 

Figure 4–12 Strain distributions along the depth of the beam at (a) Section B1 and (b) Section B6 near 

the connections to the end columns for the WUF-B specimen ..........................................33

Figure 4–13 Strain distributions along the depth of the beam at (a) Section B3 and (b) Section B4 

near the connections to the center column for the WUF-B specimen ................................34

Figure 4–14 Strain gage measurements at Sections C1 and C2, along with their average, versus 

vertical displacement at center column for the WUF-B specimen .....................................35

Figure 4–15 Axial forces in the end columns versus vertical displacement of center column for the 

WUF-B specimen ...............................................................................................................35

Figure 4–16 Overall view of the RBS test specimen..............................................................................36

Figure 4–17 Failure mode of the RBS specimen ....................................................................................37

Figure 4–18 Applied vertical load versus vertical displacements at (a) 1/3 span of beams (D3 and D8), 

(b) 2/3 span of beams (D4 and D7), and (c) center column (D5 and D6) for the RBS 

specimen.............................................................................................................................38

Figure 4–19 Vertical displacement profiles of beams corresponding to indicaged vertical loads for the 

RBS specimen (displacements magnified) .........................................................................39

Figure 4–20 Horizontal displacements of end columns at (a) column top and (b) beam mid-height 

versus center column displacement for RBS specimen......................................................40

Figure 4–21 Vertical load versus angle of rotation at connections to end and center columns for RBS 

specimen.............................................................................................................................41

Figure 4–22 Angle of rotation at connections to end column and center column versus center column 

displacement for RBS specimen.........................................................................................41

Figure 4–23 Locations of cross sections with strain gages.....................................................................42

Figure 4–24 Strain versus center column displacement at (a) Section B2 and (b) Section B7 of RBS 

specimen.............................................................................................................................43

Figure 4–25 Average strains at Sections B2 and B7 versus center column displacement of RBS 

specimen.............................................................................................................................44

Figure 4–26 Axial force in beams versus center column displacement of RBS specimen.....................44

Figure 4–27 Strain distributions along the depth of beam at (a) Section B1 and (b) Section B8 near the 

connections to the end columns of RBS specimen.............................................................46

Figure 4–28 Strain distributions along the depth of beam at (a) Section B4 and (b) Section B5 near the 

connections to the center column of RBS specimen ..........................................................47

Figure 4–29 Strain distributions along the depth of beam at (a) Sections B2 and B7, and (b) Sections 

B3 and B6 of RBS specimen ..............................................................................................48

Figure 4–30 Strain measurements at Sections C1 and C2, along with their average, versus center 

column displacement of RBS specimen .............................................................................49

Figure 4–31 Axial force in end columns versus center column displacement of RBS specimen..........49

Figure 4–32 Strain measurements at Sections W1 and W2, along with their average, versus center 

column displacement of RBS specimen .............................................................................50

Figure 4–33 Axial compressive force in each diagonal brace versus center column displacement of 

RBS specimen ....................................................................................................................51

Figure 5–1 Example finite element models of ASTM 370 coupon tensile samples: (a) solid element 

model with 0.18 in (4.6 mm) element size; (b) shell element model with 0.75 in (19 mm) 

element size ........................................................................................................................55

x
List of Figures 

Figure 5–2 True stress-strain curves for the solid, shell, and beam elements used in modeling the 

beam flanges of the WUF-B specimen...............................................................................55

Figure 5–3 Engineering stress-strain curves obtained from coupon tests and from the analysis using 

solid and shell elements for modeling the beam flanges of the WUF-B specimen ............56

Figure 5–4 True stress-strain curve for the solid elements used in modeling the bolts of the WUF-B 

specimen.............................................................................................................................57

Figure 5–5 Finite element model of a bolt double shear test ................................................................57

Figure 5–6 Response of the bolt double shear model ...........................................................................58

Figure 5–7 Measured and calculated shear load-deformation curves for 1 in, A490 bolt ....................58

Figure 5–8 Axial load-displacement curve for diagonal braces for the WUF-B and RBS specimens .60

Figure 5–9 Overview of the detailed model of the WUF-B specimen .................................................61

Figure 5–10 Detailed views of the WUF-B connection in the detailed model of the WUF-B specimen62

Figure 5–11 Deflected shape of WUF-B detailed model at a center column vertical displacement of 19 

in (483 mm). Contours represent vertical displacements in inches. ..................................63

Figure 5–12 Failure mode of the WUF-B detailed model. Contours represent plastic strains ..............63

Figure 5–13 (a) Applied vertical load, (b) beam axial force, (c) horizontal displacement of end column 

at beam mid-height, and (d) end column axial force; all plotted against vertical 

displacement of center column for the WUF-B specimen..................................................64

Figure 5–14 Comparison of the WUF-B connection moment-axial interaction diagram with the limit 

interaction diagram of the gross beam cross section ..........................................................65

Figure 5–15 Overview of reduced model of the WUF-B specimen .......................................................66

Figure 5–16 Detailed view of the WUF-B connection in the reduced model of the WUF-B specimen.66

Figure 5–17 Shear load-deformation curves for bolted lap joint ............................................................68

Figure 5–18 Deflected shape of WUF-B reduced model (fixed columns) at a center column vertical 

displacement of 20.1 in (511 mm)......................................................................................68

Figure 5–19 Failure sequence from the WUF-B reduced model ............................................................69

Figure 5–20 Overview of the detailed model of the RBS specimen.......................................................70

Figure 5–21 Detailed view of the RBS connection in the detailed model of the RBS specimen ...........70

Figure 5–22 Deflected shape of RBS detailed model at a center column vertical displacement of 37 in 

(944 mm). Contours represent (a) vertical and (b) horizontal displacements in inches. ...71

Figure 5–23 Failure mode from the RBS detailed model. Contours represent plastic strains .............72

Figure 5–24 Vertical displacement of center column versus applied vertical load, and individual 

member forces and displacements of RBS specimen.........................................................73

Figure 5–25 Comparison of RBS connection moment-axial interaction diagram with the interaction 

diagram of gross beam cross section ..................................................................................74

Figure 5–26 Overview of the reduced model of the RBS specimen.......................................................75

Figure 5–27 Deflected shape of RBS reduced model (fixed columns) at a center column displacement 

of 34.1 in (866 mm)............................................................................................................75

xi
 

xii

LIST OF TABLES

Table 2–1. Member sizes for moment resisting frames of SDC C building ................................................6

Table 2–2. Member sizes for moment resisting frames for SDC D building...............................................7

Table 3–1 Mechanical properties of the steels used to fabricate the specimens .......................................16

Table 4–1. Comparison of rotation capacities of WUF-B and RBS connections based on seismic data and 

monotonic column displacement.............................................................................................52
 

LIST OF ACRONYMS AND ABBREVIATIONS

Acronyms 

AISC American Institute of Steel Construction 

ASCE American Society of Civil Engineers 

D Dead load 

DoD U.S. Department of Defense 

DTRA Defense Threat Reduction Agency of the U.S. DoD 

FE Finite element 

FEMA Federal Emergency Management Agency of the U.S. Department of Homeland Security 

GSA U.S. General Services Administration 

L Live load 

LRFD Load and resistance factor design 

SDC Seismic Design Category 

UFC Unified Facilities Criteria 

U.S. United States 

Unit Abbreviations 

ft foot 

fy specified yield strength of steel 

h hour 

in inch 

kip 1000 lbf 

kN kilonewton 

kPa kilopascal 

ksi kip per square inch 

lbf pound-force 

m meter 

mm millimeter 

MPa megapascal 

xiii
List of Acronyms and Abbreviations 

psf pound-force per square foot 

psi pound-force per square inch 

s second 

xiv
 

xv

EXECUTIVE SUMMARY

Since the destruction of the Alfred P. Murrah Federal Building in 1995, caused by a truck bomb attack, 

and the collapse of the World Trade Center towers in 2001, caused by the impact of large passenger jets, 

greater attention has been paid to the performance of buildings that may be subjected to local damage 

from abnormal events. In the U.S., the American Society of Civil Engineers Standard 7 (ASCE 7) and 

the guidelines of the U.S. General Services Administration and the Department of Defense provide 

guidance to prevent disproportionate collapse (also known as progressive collapse). Disproportionate 

collapse occurs when an initial local failure spreads progressively, resulting in total collapse or collapse of 

a disproportionately large part of a structure. Resistance to disproportionate collapse is achieved either 

implicitly, by providing minimum levels of strength, continuity, and ductility; or explicitly, by (1) 

providing alternate load paths so that local damage is absorbed and major collapse is averted or (2) 

providing sufficient strength to structural members that are critical to global stability. In the alternate 

path method, the structural integrity is assessed through analysis to ascertain whether the structural 

system can bridge over failed structural members. In order to assure the efficacy of the analytical 

procedure, physical tests must be conducted to validate computational methods. In assessing the potential 

for disproportionate collapse, accurate characterization of the nonlinear, large-deformation behavior 

associated with the transfer of forces through structural connections is essential. 

This report presents an experimental and computational study of two steel beam-column assemblies, each 

comprising three columns and two beams. The two beam-column assemblies represent portions of the 

structural framing system of two ten-story steel frame buildings. One building was designed for Seismic 

Design Category C (SDC C) and the other for Seismic Design Category D (SDC D). The beam-column 

assemblies were taken from the exterior moment resisting frames of these buildings. One test specimen, 

which was part of the SDC C building, had welded unreinforced flange-bolted web (WUF-B) 

connections, and the other, which was part of the SDC D building, had reduced beam section (RBS) 

connections. The specimens were subjected to monotonically increasing vertical displacement of the 

unsupported center stub column to observe their behavior under a simulated column removal scenario, 

including the development of catenary action in the beams. The vertical displacement of the center 

column was increased until the vertical load-carrying capacity was depleted. 

The overall behavior of each beam-column assembly was analyzed using two levels of modeling 

complexity: (1) detailed models with a large number of elements, primarily solid and shell elements, and 

(2) reduced models with a limited number of elements, primarily beam and spring elements. The analyses 

conducted using these models provided insight into the behavior and failure modes of the connections, 

including their capacity to carry tensile forces that developed in the beams. 

The tests and associated computational models help fill the gap in defining the response characteristics of 

the moment-resisting connections under collapse scenarios and contribute to establishing a library of 

validated connection models that can be used to assess the robustness of structural systems. 

Based on the study reported herein, the following conclusions are reached: 
Executive Summary 

1. For both the WUF-B and RBS connection assemblies, the behavior of the beams was dominated 

by flexure in the early stages of the response. With increased vertical displacement of the center 

column, the beam connections exhibited yielding, and tensile axial forces developed in the beams, 

indicating catenary action. 

2. Distinct modes of failure were observed for each of the two test specimens. The failure of the 

WUF-B test specimen was characterized by: (1) local buckling of the top flanges of the beams 

near the center column, (2) successive shear fractures of the lowest and middle bolts connecting 

the beam web to a shear tab at the center column, and (3) fracture of the bottom flange near the 

weld access hole immediately thereafter. The failure of the RBS test specimen was characterized 

by: (1) fracture of the bottom flange in the middle of the reduced section and (2) propagation of 

the fracture through the web until the vertical load-carrying capacity was depleted. 

3. The test results show that the rotational capacities of both the WUF-B and RBS connections 

under monotonic column displacement are about twice as large as those based on seismic test 

data. The beam chord rotations at peak load were about 0.081 rad and 0.140 rad for the WUF-B 

and RBS connections respectively, whereas the rotational capacities of these connections based 

on seismic testing data are approximately 0.047 rad and 0.073 rad, respectively. 

4. This study indicates generally good agreement between the experimental and the computational 

results. Both detailed and reduced models were capable of capturing the primary response 

characteristics and failure modes of the test specimens. 

In summary, this study shows that analysis using reduced models composed of beam and spring elements 

can predict the response characteristics of both the WUF-B and the RBS connections. Furthermore, the 

validated reduced models developed in this study would be valuable in the analysis of complete structural 

systems for assessing reserve capacity and robustness of building structures. 

xvi
 

1

Chapter 1

INTRODUCTION

1.1 BACKGROUND 

Since the destruction of the Alfred P. Murrah Federal Building in 1995, caused by a truck bomb attack, 

(FEMA 1996) and the collapse of the World Trade Center towers in 2001, caused by the impact of large 

passenger jetliners (NIST 2005), the engineering community, including codes and standards development 

organizations and public regulatory agencies, has paid greater attention to the performance of buildings 

when subjected to local damage sustained from abnormal events. In the U.S., the American Society of 

Civil Engineers Standard 7 (ASCE 2010, Section C1.4), and the guidelines of the U.S. General Services 

Administration (GSA 2003) and the Department of Defense (DOD 2009) provide guidance to prevent 

disproportionate collapse (also known as progressive collapse). Disproportionate collapse occurs when 

an initial local failure spreads progressively, resulting in total collapse or collapse of a disproportionately 

large part of a structure. Resistance to disproportionate collapse is achieved either implicitly, by 

providing minimum levels of strength, continuity, and ductility; or explicitly, by (1) providing alternate 

load paths so that local damage is absorbed and major collapse is averted or (2) providing sufficient 

strength to structural members that are critical to global stability. 

In the alternate path method, the structural integrity is assessed through analysis, to ascertain whether the 

structural system can bridge over failed structural members. For example, if a column is damaged, 

continuity of the beams adjacent to the top of the damaged column is required to redistribute the loads 

formerly carried by the damaged column. The analysis must demonstrate the adequacy of the beams and 

their connections to redistribute these loads, potentially through catenary action. An accurate 

characterization of the nonlinear, large-deformation behavior associated with the transfer of forces 

through the connections in such scenarios is critical in assessing the potential for disproportionate 

collapse. Physical tests are indispensible to validate the analytical models used to represent nonlinear 

connection behavior in such scenarios. At present, design and evaluation of structures for 

disproportionate collapse potential are typically based on acceptance criteria obtained from seismic 

research (e.g., FEMA 350, 2000). As will be shown in this study, using this approach to predict the 

response to monotonic loading similar to that expected during column removal scenarios underestimates 

the rotational capacities of the connections. 

The National Institute of Standards and Technology (NIST) is conducting a comprehensive research 

program to study the behavior of structures that, when exposed to abnormal loads, might experience 

disproportionate collapse. To understand the behavior of structural systems near their ultimate-strength 

limit states and to develop reliable tools to quantify the reserve capacity and robustness of structural 

systems, the NIST study proposes to develop three-dimensional models of building structures with 

various materials and structural systems. To validate these models, full-scale tests of beam-column 

assemblies representing portions of a structural system are carried out. The experimental results are used 

to validate reduced connection models that will be incorporated into the three-dimensional models for 

analysis of disproportionate collapse vulnerability. 
Chapter 1 

1.2 SCOPE OF STUDY 

The study reported herein includes both full-scale testing and finite-element based analysis of two steel 

beam-column assemblies, each comprising three columns and two beams and representing part of the 

second floor framing of a ten-story building. While both test specimens have moment resisting beam-tocolumn connections, one specimen has welded unreinforced flange-bolted web (WUF-B) connections, 

which are typically used for intermediate moment frames, and the other has reduced beam section (RBS) 

connections, which are typically used for special moment resisting frames. The specimens are 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 catenary action in the 

beams. The test is terminated upon reaching the collapse mechanism of the assembly. Both detailed and 

reduced finite element models of the test specimens are developed, and the model predictions show good 

agreement with the experimental results. The reduced models can be used for analysis of complete 

structural systems to assess their vulnerability to disproportionate collapse. 

The tests and associated computational models help fill the gap in defining the response characteristics of 

the moment-resisting connections under collapse scenarios and contribute to establishing a library of 

validated connection models that can be used to assess the robustness of structural systems. 

1.3 REPORT OUTLINE 

The report summarizes the experimental and computational approaches used in this study for the two 

moment resisting connections, along with the results of both tests and analyses. Chapter 2 provides a 

description of the prototype steel building designs that have been developed by NIST. Special emphasis 

is placed on describing the details of the moment resisting connections used in this study. Chapter 3

presents the test setup for both specimens, including the test configuration, the loading apparatus and 

sequence, and the instrumentation used. 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 various finite element models used in 

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

models against experimental results. Chapter 6 presents a summary and conclusions of the report. 

1.4 REFERENCES 

ASCE (2010). Minimum Design Loads for Buildings and Other Structures, SEI/ASCE 7-10, American 

Society of Civil Engineers, Reston, VA 

DOD (2009). Design of Buildings to Resist Progressive Collapse, Unified Facilities Criteria (UFC) 4-

023-03, Department of Defense, 25 January 2009. 

FEMA (1996). The Oklahoma City Bombing: Improving building performance through multi-hazard 

mitigation, FEMA Report 277, Federal Emergency Management Agency, Washington, D.C. 

FEMA (2000). Recommended Seismic Design Criteria for New Steel Moment-Frame buildings, FEMA 

350, SAC Joint Venture and Federal Emergency Management Agency, Washington, D.C. 

General Services Administration (GSA ), (2003), “Progressive Collapse Analysis Design Guidelines for 

New Federal Office Buildings and Major Modernization Projects,” GSA, Washington, D.C. 

NIST (2005). The Collapse of the World Trade Center Towers, NIST NCSTAR 1, National Institute of 

Standards and Technology, Gaithersburg, MD.

2
 

3

Chapter 2

DESCRIPTION OF PROTOTYPE BUILDING DESIGNS

2.1 PROTOTYPE BUILDING DESIGNS 

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

engineers across the U.S., developed the overall configuration and dimensions of the prototype buildings 

to be considered in this research program. For simplicity of design and analysis, a 10-story building with 

rectangular plan for office occupancy was chosen as the prototype building. For the study reported herein, 

two steel frame buildings were designed, each having the plan dimensions of 100 ft × 150 ft (30.5 m × 

45.7 m), with five bays in both longitudinal and transverse directions. The detailed design of the building 

was carried out by a consulting engineering firm (Liang et al., 2008). 

To examine the effectiveness of seismic design and detailing, including seismic connections, in resisting 

disproportionate collapse, one building was designed for Seismic Design Category (SDC) C and the other 

for SDC D. The lateral loads are resisted by exterior moment resisting frames. All interior frames were 

designed to support gravity loads only. The types of moment resisting frames for the two Seismic Design 

Categories are: 

• SDC C – (Atlanta, Georgia), which resulted in a design using Intermediate Moment Frames 

(IMF) for the lateral load resisting system as defined in the American Institute of Steel 

Construction (AISC) Seismic Provisions (2002), and 

• SDC D – (Seattle, Washington), which resulted in a design using Special Moment Frames (SMF) 

for the lateral load resisting system. 

Plan views of the buildings in the SDC C and SDC D regions are shown in Figure 2–1 and Figure 2–2, 

respectively, and elevation views are shown in Figure 2–3. 

The buildings were designed according to the American Society of Civil Engineers (ASCE 7-02) 

standard. The material design standards used in the design of the members and their connections were 

those referenced in ASCE 7-02, including: 

• The American Institute of Steel Construction (AISC) Load and Resistance Factor Design (LRFD) 

Specification for Structural Steel Buildings (1999), hereafter referred to as AISC LRFD. 

• The AISC Seismic Provisions for Structural Steel Buildings (2002), hereafter referred to as AISC 

Seismic Provisions. 

• FEMA Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings (2000), 

hereafter referred to as FEMA 350. 
Chapter 2 

A 

1 

G1 G1 G1

G1 G1 G1 

B C D E F 

2 

3 

4 

5 

6 

W16x26

N 30’-0” 30’-0” 30’-0” 30’-0” 30’-0” 20’-0” 20’-0” 20’-0” 20’-0” 20’-0” 

G2 G2 G2 

do do do 

do do do 

do do 

W16x26 

W16x26 

do 

W16x26 

do 

W16x26 

do 

W16x26 

do 

W16x26 

do 

W16x26 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

W14x22 40 W14x22 40

W14x22 40 W14x22 40 

W14x22 40

W14x22 40 

W14x22 40 W14x22 40 W14x22 40 

W14x22 40

44 G2 G2 G2 

44 

do 

do do W16x26 

W16x26 

do 

Figure 2–1 Plan layout for SDC C building 

G1 G1

A 

1 

G1

G1

G2 G2 

B C D E F

2 

3 

4 

5 

6 

N 30’-0” 30’-0” 30’-0” 30’-0” 30’-0” 20’-0” 20’-0” 20’-0” 20’-0” 20’-0” 

G2 G2 

do do do 

do do 

do do 

W16x26 

W16x26 

do 

W16x26 

do 

W16x26 

do 

W16x26 

do 

W16x26 

do 

W16x26 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

W14x22 40

W14x22 40

W14x22 40 

W14x22 40 

W14x22 40 W14x22 40

G1

G2 

44 

G2 

do 

G1

do 

G1

G2 

G2 

G1 

W14x22 40 W14x22 40 W14x22 40

W14x22 40 

W16x26 W16x26 

W16x26 

Figure 2–2 Plan layout for SDC D building 

4
Description of Prototype Building Designs 

A B C D E F 

30’-0” 30’-0” 30’-0” 30’-0” 30’-0”

9 @ 13’-9” 17’-6” 

141’-3” 

Figure 2–3 East-west elevation of the steel frame buildings 

For typical floors, the dead load consisted of the self-weight of the floor of 46 psf (2.2 kN/m2

) and a 

superimposed dead load of 30 psf (1.44 kN/m2

), and a design live load of 100 psf (4.79 kN/m2). For the 

roof, the self-weight of the slab was 46 psf (2.2 kN/m2

), the superimposed dead load was 10 psf 

(0.48 kN/m2

), and the design live load was 20 psf (0.96 kN/m2). The reduction of live loads was based on 

Section 1607.9.1 of IBC (2003). 

Because the lateral load resisting system was located only around the perimeter of both buildings, the 

design of all interior floors and columns was the same for both buildings. The floor system consisted of 

3 1⁄4 in (83 mm) lightweight concrete (110 pcf, 17.3 kN/m3

) topping on a 3 in (76 mm) metal deck. The 

slab acted compositely with the steel beams through shear studs. The steel beams in the gravity frames 

were connected to the columns using single plate (simple shear) connections. 

The lightweight concrete topping slab in the floor system had a nominal compressive strength of 3000 psi 

(20.7 MPa). ASTM A992 structural steel (Fy = 50 ksi, 344.8 MPa) was used in all beams, columns, and 

doubler plates in the panel zones. ASTM A36 steel (Fy = 36 ksi, 248.2 MPa) was used for the shear tabs 

and continuity plates at beam-column connections. For the bolted moment connections, ASTM A490 

high strength bolts were used, and welding requirements followed the recommendations in FEMA 353 

(2000). 

2.2 DESCRIPTION OF MOMENT RESISTING FRAMES 

Design of the moment-resisting frames was based on three-dimensional analyses of the buildings using a 

commercially available computer program for linear elastic analysis. Only members that are part of the 

lateral load resisting system were considered in the model. Fixed-base connections were assumed at the 

structure-foundation interface. Panel zone deformations were directly included in the analysis, using 

5
Chapter 2 

elastic properties of the column and doubler plates, if present. A rigid diaphragm was assigned at every 

floor level. The contribution of the floor slab to the beam moment capacity was neglected in the momentresisting frames. The designs of the steel frames were governed by story drift limitations specified in 

Table 9.5.2.8 of ASCE 7-02 rather than by strength requirements. 

The members of IMFs used in the SDC C building were designed according to Section 10 of the AISC 

Seismic Provisions. For the SDC C building, six IMFs were incorporated in the East-West (E-W) and 

North-South (N-S) directions, see Figure 2–1. The cross sections of the beams and columns are given in 

Table 2–1. 

The members of SMFs used for the SDC D building were designed in accordance with Section 9 of the 

AISC Seismic Provisions. Eight SMFs were incorporated in the exterior frames in the E-W and N-S 

directions (see Figure 2–2). The cross sections of the beams and columns for this building are given in 

Table 2–2. Column sizes were increased in some cases to satisfy the strong column/weak beam 

requirement and to avoid using doubler plates in the one-sided (exterior) moment connections. 

Connections used in the moment resisting frames of both buildings were selected from the prequalified 

steel connections specified in FEMA 350 (2000): 

• Welded Unreinforced Flange-Bolted Web (WUF-B) connections for the IMF in the SDC C 

building, and 

• Reduced Beam Section (RBS) connections for the SMF in the SDC D building. 

Table 2–1. Member sizes for moment resisting frames of SDC C building 

Member Floor Range Section 

1-5 W24x76 

6-7 W24x62 Girders G1 

8-10 W21x50 

1-3 W21x73 

4-6 W21x68 Girders G2 

7-10 W21x44 

1-3 W18x119 

4-7 W18x97 

Columns A1, A6, B1, C1, C6, D1, 

D6, E6, F1, and F6 

8-10 W18x55 

1-4 W18x119 

5-7 W18x97 

Columns A3, A4, A5, F2, F3, and F4 

8-10 W18x55 

6
Description of Prototype Building Designs 

Table 2–2. Member sizes for moment resisting frames for SDC D building 

Member Floor Range Section 

1-4 W27x102 

5-7 W27x94 

8-9 W21x50 

Girders G1 

10 W16x26 

1-5 W24x94 

6-7 W24x68 

8-9 W21x44 

Girders G2 

10 W16x26 

1-4 W24x146 

5-7 W24x131 

8-9 W24x117 

Columns A1, B1, C1, D1, E1, B6, 

C6, D6, E6, and F6 

10 W24x84 

1-5 W24x131 

6-9 W24x117 Columns A2, A3, A4, A5, A6, F1, F2, 

F3, F4, and F5 

10 W24x84 

For the beam-column assembly tests, two-span beams connected to three columns were selected from the 

second floor of the moment resisting frames in the transverse direction (N-S direction) of each of the two 

buildings. The beams had a span length (center to center of columns) of 20 ft (6.10 m). For the SDC C 

building with the WUF-B connections, the two spans were selected from the two bays of the moment 

frame spanning between grid points A3 and A5 in Figure 2–1. For the SDC D building with the RBS 

connections, the two spans were selected from two bays of the moment frame spanning between grid 

points A3 and A5 in Figure 2–2. Based on Figure 2–1 and Table 2–1, the beams selected from the SDC C 

building were W21x73 sections and were connected to W18x119 columns using WUF-B connections. 

Based on Figure 2–2 and Table 2–2, the beams selected from the SDC D building were W24x94 sections 

and were connected to W24x131 columns using RBS connections. 

2.2.1 Welded Unreinforced Flange-Bolted Web (WUF-B) Connection 

The WUF-B connection is similar to the connections commonly used prior to the 1994 Northridge 

earthquake. After significant research (FEMA 355D), it was determined that with several improvements 

and appropriate quality assurance, this connection can perform reliably. Improvements over the typical 

pre-Northridge connections included: using weld metal with appropriate toughness; removing weld 

backing from bottom-beam-flange-to-column-flange welds, back-gouging and addition of a reinforcing 

fillet weld; using improved weld access hole shape and finish (Figure 2–5); and applying better weld 

quality control and quality assurance. FEMA 355D (2000) provides extensive information on the testing 

and performance of the WUF-B connections (pre- and post- Northridge) under seismic loading. 

7
Chapter 2 

The WUF-B connections were pre-qualified by FEMA 350 (2000) for use in Ordinary Moment Frames 

(OMFs). Note that the IMF defined in the AISC Seismic Provisions (2005) is equivalent to the OMF 

defined in FEMA 350. As such, these connections are also pre-qualified by the AISC Seismic Provisions 

(2005) for use in IMF. According to the AISC Seismic Provisions (2005), SMF, IMF, and OMF are 

generally expected to withstand significant (total inter-story drift or rotation in the range of 0.04 radians), 

limited (total rotation in the range of 0.02 radians), and minimal (total rotation in the range of 0.01 

radians) inelastic deformations, respectively, during large seismic events. 

The inter-story drift angle or rotation capacity of the WUF-B connection specified in FEMA 350 were 

based on a statistical analysis of results from cyclic tests of full-scale connection assemblies. The rotation 

capacity, θU, corresponding to collapse prevention, characterized by the inability of the connection to 

maintain its integrity under gravity loading, was estimated for the WUF-B connection as: 

θU = 0.060 − 0.0006db (2.1)

where db is the beam depth in inches. The rotation capacity, θSD, corresponding to initiation of strength 

degradation, characterized by degradation in connection behavior (e.g., fracture of a weld or a bolt) or 

framing behavior (e.g., buckling of a beam), was estimated as: 

θSD = 0.031 − 0.0003db (2.2)

For the W21x73 beam section used with the WUF-B connection in this study, θU = 0.047 rad and θSD = 

0.025 rad. The behavior of the WUF-B connections under the monotonic loading conditions expected in 

disproportionate collapse scenarios, in which connections are subjected to monotonically increasing 

combined bending and tension, has not been previously studied and is the subject of this report. 

In this study, the WUF-B connection was chosen for its popularity, after consulting with several structural 

engineers in the Atlanta area. Design of the connections followed provisions in the AISC Seismic 

Provisions and recommendations of FEMA 350. When there was a conflict between these two 

documents, the requirements of AISC Seismic Provisions were followed. The WUF-B connection used 

in this study is shown in Figure 2–4. The figure represents both an interior and an exterior connection. In 

the test specimen (see Chapter 3), exterior connections were used at the end columns and interior 

connections were used at the center column. 

As shown in Figure 2–4, the beam web is connected to the column flange using a shear plate (shear tab), 

which is fillet welded to the column flange using 5/16 in (7.94 mm) weld (on both sides of the plate) and 

bolted to the beam web using three 1 in (25.4 mm) diameter, high strength bolts. The size of the shear tab 

is 1⁄2 in × 12 in × 6 in (12.7 mm × 304.8 mm × 152.4 mm). The bolt holes are standard holes with an edge 

distance (between the center of the standard hole to the shear plate edge) of 2.75 in (69.85 mm), resulting 

in a clear distance (between the edge of the hole and the edge of the shear plate) of 2.25 in (57.15 mm). 

The beam flanges are joined to the column flange using complete joint penetration (CJP) groove welds. 

Weld access holes are cut from the beam flanges per the recommendations of FEMA 350 (2000) as 

shown in the detail in Figure 2–5. Continuity plates are provided for both interior and exterior columns as 

shown in Figure 2–4. No doubler plates, however, were required for either column since the shear 

capacity of the column in the panel zone satisfied the requirements of the AISC LRFD Specification. 

8
Description of Prototype Building Designs 

or

CJP Typical

PL 1⁄2 x12x6 (A36) 

Continuity plate (A36): 

3/4” thick (Int. panels)

3/8” thick (Ext. panels)

3 A490 H.S.B. of D = 1”. 

(Class A Faying surfaces)

or

Beam W21x73 

Column W18x119 5/16

or

CJP Typical

PL 1⁄2 x12x6 (A36) 

Continuity plate (A36): 

3/4” thick (Int. panels)

3/8” thick (Ext. panels)

3 A490 H.S.B. of D = 1”. 

(Class A Faying surfaces)

or

Beam W21x73 

Column W18x119 5/16

Figure 2–4 WUF-B connection details – N-S frames, second floor of SDC C building 

Beam Web

Beam Top Flange

Beam Bottom Flange

Weld Access Holes

Figure 2–5 Detail of weld access holes for the WUF-B connection 

2.2.2 Reduced Beam Section (RBS) Connection 

The Reduced Beam Section (RBS) connection has been developed as a result of extensive research 

following the 1994 Northridge earthquake (Chen, 1996, Iwankiw and Carter, 1996, Engelhardt el al., 

1996, Engelhardt el al., 1998). The RBS connection is created by cutting away a portion of the top and 

bottom flanges of the beam at a distance from the beam-column interface so that yielding is concentrated 

in this reduced area. The reduced section, thus, acts as a fuse to protect the connection against premature 

9
Chapter 2 

fracture. Various shapes of the reduced section have been suggested and studied, including straight cut 

sections, tapered beam sections, and circular radius cuts. Out of the three, the radius cut section was 

found to yield the most reliable performance. The RBS connection has been commonly used for seismic 

design since the Northridge earthquake. FEMA 355D (2000) provides extensive information on the 

testing and performance of the RBS connections under seismic loading. 

RBS connections were pre-qualified by FEMA 350 (2000) for use in OMF and SMF. These connections 

were also pre-qualified by the AISC Seismic Provisions (2005) for use in IMF and SMF. Note that the 

design of the RBS connections in Liang et al. (2008) specified a bolted single plate shear connection 

between the beam web and the column per the AISC Seismic Provisions (2002). The latest AISC Seismic 

Provisions (2005), however, specify that for RBS connections in SMF, the beam web shall be connected 

to the column flange using a CJP groove weld, extending between the weld access holes. As a result, for 

the testing and modeling conducted in this study, the connection design in Liang et al. (2008) was 

modified to meet the requirements of the 2005 edition of the AISC Seismic Provisions. 

The inter-story drift angle or rotation capacity of the RBS connection specified in FEMA 350 were based 

on a statistical analysis of the results from cyclic tests of full-scale connection assemblies. The rotation 

capacity corresponding to collapse prevention was estimated as: 

θU = 0.080 − 0.0003db (2.3)

The rotation capacity corresponding to initiation of strength degradation was defined as: 

θSD = 0.060 − 0.0003db (2.4)

For the W24x94 beam section used with the RBS connection, θU = 0.073 rad and θSD = 0.053 rad. Similar 

to the WUF-B connection, the behavior of the RBS connection under the monotonic loading conditions 

expected during disproportionate collapse scenarios has not been previously investigated and is the 

subject of this report. 

In this study, the RBS connection was selected for its popularity and excellent seismic performance, after 

consulting with several structural engineers in the West Coast. Design of the connections followed 

provisions in the AISC Seismic Provisions and recommendations of FEMA 350. When there was a 

conflict between these two documents, the requirements of AISC Seismic Provisions were followed. The 

RBS connection used in this study is shown in Figure 2–6, after modifying the beam web to column 

flange connection (see above). The figure represents both an interior and an exterior connection. In the 

test specimen (see Chapter 3), exterior connections were used at the end columns and interior connection 

was used at the center column. 

As shown in Figure 2–6, the beam flanges and web are connected to the column flange using CJP groove 

welds. The connections utilize circular radius cuts in both top and bottom flanges of the beam as shown 

in Figure 2–7. The dimensions of the reduced beam sections are as follows: 

 a ≅ 0.55 bf (limits for a ≅ (0.5 to 0.75) bf) 

 b ≅ 0.7 db (limits for b ≅ (0.65 to 0.85) db)

 c = 0.25 bf (limits for c ≤ 0.25 bf) 

10
Description of Prototype Building Designs 

where bf and db are the width of the beam flange and the depth of the beam, respectively. 

Weld access holes were cut from the beam flanges per the recommendations of FEMA 350 (2000) as 

shown in the detail in Figure 2–8. Continuity plates are provided for both center and end columns as 

shown in Figure 2–6. Doubler plates were required only for the center column, based on the design 

calculations for the shear capacity of the column in the panel zone. 

or

CJP Typical

Doubler plates: 

9/16” thick (Int. panels)

None (Ext. panels)

3/8x6x18-1/4 

(A36) 

Continuity plate (A36): 

7/8” thick (Int. panels)

7/16” thick (Ext. panels)

3 A490 H.S.B.

of D = 1”

Beam W24x94

Column W24x131 

For 

erection 

purposes 

only

Reduced Section

or

CJP Typical

Doubler plates: 

9/16” thick (Int. panels)

None (Ext. panels)

3/8x6x18-1/4 

(A36) 

Continuity plate (A36): 

7/8” thick (Int. panels)

7/16” thick (Ext. panels)

3 A490 H.S.B.

of D = 1”

Beam W24x94

Column W24x131 

For 

erection 

purposes 

only

Reduced Section

Figure 2–6 RBS connection details – N-S frames, second floor of SDC D building 

a b

c

c

b a

c

c

a b

c

c

b a

c

c

Figure 2–7 RBS connection details – plan view of beam’s top and bottom flanges 

11
Chapter 2 

Beam Web

Beam Top Flange

Beam Bottom Flange

Weld Access Holes

Figure 2–8 Detail of weld access holes for the WUF-B connection 

2.3 REFERENCES 

AISC (1999). Load and Resistance Factor Design Specifications for Structural Steel Buildings, 

American Institute of Steel Construction, Chicago, IL. 

AISC (2002). Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, 

Chicago, IL. 

AISC (2005). Seismic Provisions for Structural Steel Buildings, Including Supplement No. 1, American 

Institute of Steel Construction, Chicago, IL. 

ASCE (2002). Minimum design loads for buildings and other structures, SEI/ASCE 7-02, American 

Society of Civil Engineers, Reston, VA. 

Chen, S.J., (1996), “A simple and effective retrofit method for steel beam-to-column connections,” 

Seventh US-Japan Workshop on the Improvement of Structural Design and Construction Practices, 

Applied Technology Council, Redwood City, CA. 

Engelhardt, M.D., Winneberger, T., Zekany, A.J., and Potyraj, T.J., (1996), “The dogbone connection: 

Part II,” Modern Steel Construction, 36(8), American Institute of Steel Construction, Chicago, IL. 

Engelhardt, M.D., Winneberger, T., Zekany, A.J., and Potyraj, T.J., 1998, “Experimental investigation of 

dogbone moment connections,” Engineering Journal, 35(4), 128-139. 

FEMA (2000). Recommended seismic design criteria for new steel moment-frame buildings, FEMA 350, 

SAC Joint Venture and Federal Emergency Management Agency, Washington, D.C. 

FEMA (2000). State of the art report on connection performance, FEMA 355D, SAC Joint Venture and 

Federal Emergency Management Agency, Washington, D.C. 

Iwankiw, N.R., and Carter, C.J., (1996), “The dogbone: A new idea to chew on,” Modern Steel 

Construction, Vol. 36, No. 1, American Institute of Steel Construction, Chicago, IL. 

International Code Council (ICC). (2003), International Building Code, Falls Church, VA. 

Liang, X., Shen, Q., and Gosh, S. K. (2008), “Assessing ability of seismic structural systems to withstand 

progressive collapse: Design of steel frame buildings.” Report submitted to the Building and Fire 

Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. 

12
 

13

13

Chapter 3

TEST PROGRAM

3.1 INTRODUCTION 

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

including instrumentation, and test procedure. The primary objectives of these tests are (1) to define the 

response characteristics of beam-column assemblies under a column removal scenario, including the 

capacity of the beams and their connections to carry loads through catenary action; and (2) to provide 

experimental data for validation of beam-column connection models to be used in assessing the 

robustness of structural systems. The test specimens were beam-column assemblies from the secondfloor framing system of the ten-story buildings described in Chapter 2. Thus, one specimen had WUF-B 

connections (SDC C building) and the other had RBS connections (SDC D building). Throughout this 

chapter, the beam-column assembly with the WUF-B connections will be referred to as the WUF-B 

specimen while the assembly with the RBS connections will be referred to as the RBS specimen. 

Section 3.2 presents in detail the description of the test specimens, while Section 3.3 describes the test 

setup for both specimens including boundary conditions. Section 3.4 describes the loading apparatus and 

loading sequence, and Section 3.5 presents the instrumentation plan for each of the two tests. 

3.2 TEST SPECIMENS 

Figure 3–1 and Figure 3–2 show layout, member sizes, and beam-to-column connection details for the 

WUF-B specimen and the RBS specimen, respectively. All beams, columns, and doubler plates were 

made of ASTM A992 steel. Shear tabs and continuity plates were made of ASTM A36 steel. Note that 

all three columns of the RBS specimen had 9/16 in (14 mm) thick doubler plates welded to the column 

web at the connection, whereas the WUF-B specimen did not have any doubler plates (see Chapter 2). 

The beam webs of the WUF-B specimen were connected to the shear plate by 1 in diameter ASTM A490 

bolts. The beam webs of the RBS specimen and the flanges of the beams of both specimens were welded 

to the column flanges in accordance with the guides and requirements in the AISC Seismic Provisions in 

AISC 358-05 (AISC 2005). Note that in Figure 3–2, the 3/8 in (10 mm) plate and the A490 1 in (25 mm) 

diameter, high strength bolts were used for erection purposes only. The mechanical properties of the 

materials used to fabricate the specimens (including yield stress and strain and ultimate stress and strain) 

were determined by ASTM tensile coupon tests and are given in Table 3–1. Engineering stress and strain 

values are reported, and the ultimate strain is the strain corresponding to the ultimate stress. Except 

where indicated, the values shown in the table are averages from three tests. 
Chapter 3 

20’‐0 20’‐0

12’‐0

7’‐1 1/4

1’‐9 1

/4 3’‐0 3/4

W21x73 W21x73 1’‐9 1/4 2’‐7 7/8 2’‐7 7/8

W18x119

W18x119

BASE PL 3/4 x 48 x 4’‐0

3/4

6 5/8 44

W21x73 W21x73

3

/4 ” STIFF PL’S

3‐1 W18x119 φ A490 BOLTS

TOP FLANGE

&BEAM WEB

TC‐U4a‐GF

Figure 3–1 Details of WUF-B specimen 

14
Test Program 

20’‐0 20’‐0

12’‐0

6’‐5 3

/4

2’‐0 5

/16 3’‐5 3

/16

W24x94 W24x94 2’‐0 5

/16

3’‐0 1/2 3’‐0 1/2

W24x131

W24x131

BASE PL 3/4 x 48 x 4’‐0

3

/4

5 5

/32 77

W24x94 W24x94

9

/16 ” DOUBLER PL

W24x131

3‐1φ A490 BOLTS

TOP FLANGE

&BEAM WEB

TC‐U4a‐GF

7/8 ” STIFF

PL’S

45o

Figure 3–2 Details of RBS specimen 

15
Chapter 3 

Table 3–1 Mechanical properties of the steels used to fabricate the specimens 

Specimen Component Yield Stress 

ksi (MPa) 

Ultimate Stress

ksi (MPa) 

Yield Strain * Ultimate Strain *

Shear tab 44.9 (309) 67.5 (465) 0.0016 0.183 

Continuity plate 41.9 (288) 65.3 (450) 0.0015 0.200 

Beam web 57.3 (395) 72.6 (500) 0.0019 0.189 

Beam flange † 52.1 (359) 72.0 (496) 0.0017 0.174 

WUF-B 

Column † 51.2 (352) 66.2 (456) 0.0018 0.190 

Shear tab 45.6 (317) 65.7 (453) 0.0017 0.188 

Continuity plate 40.3 (277) 63.5 (478) 0.0013 0.233 

Doubler plate 46.2 (318) 66.2 (457) 0.0016 0.180 

Beam web 66.1 (455) 80.4 (554) 0.0024 0.143 

RBS 

Column 54.9 (378) 71.6 (494) 0.0018 0.189 

* Strain values reported correspond to a gage length of 2 in (51 mm). 

† Values for the components indicated are averages from two tests; all other values are averages from three tests. 

3.3 TEST SETUP 

A schematic view of the test setup used for both the WUF-B specimen and the RBS specimen is shown in 

Figure 3–3. For each specimen, the tops of the two end columns were restrained by two diagonal braces 

for each column, one on each side of the beam. These braces were rigidly attached to the top of the 

columns and anchored to the strong floor of the test facility. The diagonal braces simulated the bracing 

effect provided by the upper floors in a multi-story building. A pair of columns straddling each beam at 

mid-span provided lateral bracing for the beams. Photographs of the loading arrangement and the lateral 

bracing for the beams at mid-span are shown in Figure 3–4 and Figure 3–5 for the WUF-B specimen and 

the RBS specimen, respectively. The vertical load was applied to the top of the center stub column by a 

single hydraulic ram acting through a load cell and a steel plate. The horizontal movements of the steel 

plate were restrained by four columns positioned at each corner of the plate. These steel columns were 

welded to base plates and bolted to the test floor. A special roller bearing support arrangement at the four 

corners of the plate allowed free vertical displacement of the plate along the four columns. The steel plate 

also restrained the horizontal movements of the top of the center stub column, thereby keeping the applied 

load in the vertical direction and limiting eccentrically applied loading. A pair of steel plates on each side 

of the center stub column restrained out-of-plane motion at the lower end of the center stub column.

16
Steel loading plate Hydraulic ram and load cell

Pair of columns for

lateral bracing

of beam

Pair of columns 

lateral bracin

of beam

Steel

loading

plate

Pair of columns for

lateral bracing of beam

17

Pair of plates

for lateral

bracing of

column

Pair of plates

for lateralbracing of

column

Columns for lateral bracing

of centerstub column (4)

Pair of column

lateral bracing of 

Columns for lateral bracing

of centerstub column

ELEVATION VIEW

PLAN VIEW

Columns for lateral bracing

of centerstub column

Figure 3–3 Schematic of test setup
Chapter 3 

Figure 3–5 Photograph of the RBS specimen 

Figure 3–4 Photograph of the WUF-B specimen 

18
Test Program 

3.4 LOADING APARATUS AND TEST SEQUENCE 

A hydraulic ram with a capacity of 600 kip (2669 kN) and a 20 in (508 mm) stroke was used to apply a 

vertical downward load to the center column of the test specimens. The load was applied under 

displacement control at a rate of 1 in/min (25 mm/min). 

Pre-test predictions of both the WUF-B and RBS specimens indicated that the stroke capacity of the 

hydraulic ram was not adequate to accommodate the maximum expected vertical displacement of the 

center column at failure. To adjust the stroke of the hydraulic ram, the specimen was unloaded when the 

ram had extended about 18 in (457 mm). Steel blocks were inserted between the hydraulic ram and the 

top of the center column, and the specimen was reloaded. 

3.5 INSTRUMENTATION 

Four different types of measurements were taken for each specimen. Figure 3–6 and Figure 3–7 present 

schematics of the WUF-B and RBS test specimens, respectively, showing the instrumentation layout. 

The uncertainty in the measured data from the load cells, deflection (D) and strain (S) gages, and 

inclinometers (I) was within ± 1 %. In addition to these digital measurements, a high-speed video camera 

was used to capture the failure sequence of components at the beam-to-column connection zone at the 

center column. The WUF-B specimen was tested first, and differences between the instrumentation 

layouts for the RBS specimen (Figure 3–7) and the WUF-B specimen (Figure 3–6) reflect changes made 

as a result of experience gained from testing of the WUF-B specimen. 

3.5.1 Displacement Transducers 

The center stub column was expected to undergo large displacements of up to 34 in (860 mm) prior to 

final failure. To accommodate such large displacements, spring-loaded string-type displacement 

potentiometers having a 72 in (1830 mm) range and a 0.001 in (0.025 mm) accuracy were used. A total 

of ten potentiometers were used in each test, designated as D1 through D10 in Figure 3–6 and Figure 3–7. 

3.5.2 Inclinometers 

To measure the rotation of the beam ends, digital inclinometers were attached to the beam webs near the 

column flanges. Figure 3–6 and Figure 3–7 show the locations of four inclinometers designated as I1 

through I4. Figure 3–8 shows the general appearance of an inclinometer that was attached to the beam 

away from the reduced beam section for the RBS specimen. 

19
Chapter 3 

D9

D10 D1

D8 D7

D6 D5

D4 D3 D2

I4 I3 I2 I1

Hydraulic Ram and Load Cell

DeflectionGages and Inclinometers

StrainGages

S1 S2 S3

S4,S5

S6

S7

S8

S9,S10

S11

S12

S13

S34

S35

S36

S37,S38

S42,S43

S41

S40

S39

S46 S45 S44

S27

S28

S29

S30

S31

S24,S25,S26

S32,S33

S17

S18

S19

S20

S21

S14,S15,S16

S22,S23

Figure 3–6 Instrumentation layout of the WUF-B specimen 

20
Test Program 

D9 D2

D8 D7

D6 D5

D4 D3

I4 I3 I2 I1

Hydraulic Ram and Load Cell

DeflectionGages and Inclinometers

D10 D1

StrainGages

S1 S2 S3

S4

S5

S6

S7

S8

S9

S35

S37

S39

S17

S20

S19

S18

S47 S46 S45 S10 (W)

S12 (E)

S11 (W)

S13 (E)

S14

S15

S16

S26

S30

S29

S28

S27

S32 (E)

S34 (W)

S31 (E)

S33 (W)

S21

S25

S24

S23

S22

S38

S36

S40

S42

S44

S43

S41

Figure 3–7 Instrumentation layout of the RBS specimen 

Figure 3–8 Inclinometer attachment to RBS specimen 

21
Chapter 3 

3.5.3 Strain Gages 

A total of 46 and 47 uniaxial strain gages were attached to beam and column surfaces for the WUF-B 

specimen and the RBS specimen, respectively, to measure strains across the depth of the members. The 

locations of strain gages are shown in Figure 3–6 and Figure 3–7. The primary purposes of strain 

measurements were: (1) to compute axial forces in the beams and columns and (2) to observe 

experimentally the onset of catenary action in the beams. For the RBS test, strain gages were also placed 

on the diagonal bracing members so that the axial forces in the diagonal bracing members could be 

determined. 

3.6 REFERENCES 

AISC (2005). Seismic Provisions for Structural Steel Buildings, Including Supplement No. 1, American 

Institute of Steel Construction, Chicago, IL. 

22
23 

Chapter 4

EXPERIMENTAL RESULTS

4.1 INTRODUCTION 

This chapter presents the test results of both the WUF-B and RBS test specimens, described in Chapter 3. 

The test results include the observed behavior and failure modes of each specimen, along with the 

primary response parameters of the test specimens measured during the experiment. Such measurements 

include vertical and horizontal deflections, rotations of connections at beam ends, and strains and 

associated forces. The response parameters also include the vertical load applied by the hydraulic ram to 

the top of the center column, measured using a load cell. Both the observed behavior and the measured 

response provide insights into the behavior of the specimens prior to and during the failure process. 

Sections 4.2 and 4.3 provide experimental results obtained from the WUF-B and RBS specimens, 

respectively, while Section 4.4 presents a summary and discussion of the test results. 

4.2 WUF-B SPECIMEN 

4.2.1 Observed Behavior and Failure Modes 

Under monotonic vertical displacement of the center column, the WUF-B specimen experienced large 

deflections and rotations prior to failure (Figure 4–1). A WUF-B connection to the center column failed 

at a vertical displacement of the center column of about 19.5 in (495 mm), with a corresponding beam 

chord rotation of about 0.081 rad, obtained by dividing the center column displacement at failure by the 

centerline-to-centerline beam span of 240.0 in (6096 mm). At that displacement, the applied vertical load 

was about 200 kip (890 kN). The failure was characterized by the following sequence (see Figure 4–2): 

(1) local buckling of the top flanges of the beams near the center column, (2) successive shear failure of 

the lowest and middle bolts connecting the beam web to a shear tab at the center column, and (3) fracture 

of the bottom flange near the weld access hole. 
Chapter 4 

Figure 4–1 Overall view of the WUF-B specimen subjected to large displacements 

Figure 4–2 Failure mode of the WUF-B specimen 

24
 Experimental Results 

4.2.2 Displacement Measurements 

The plots in Figure 4–3 show the vertical load versus vertical displacements at (a) 1/4 span of the beams 

(D2 and D9), (b) 1/2 span of the beams (D3 and D8), (c) 3/4 span of the beams (D4 and D7), and (d) the 

center column (D5 and D6). The locations of the displacement transducers were shown in Figure 3–6. 

As the plots indicate, the specimen was unloaded at a vertical displacement of the center column of about 

18 in (457 mm) to adjust the stroke of the hydraulic ram and was then reloaded again to failure (see 

Chapter 3). Figure 4–3(d) indicates that the assembly remained in the elastic range up to a vertical 

displacement of the center column of about 2 in (50 mm). With increased vertical displacement, the 

assembly behaved nonlinearly. The specimen failed at a vertical displacement of the center column of 

about 19.5 in (495 mm). The pairs of load deformation curves were nearly the same in each of the four 

plots in Figure 4–3 which indicate that symmetry was largely maintained during the experiment. In 

subsequent plots, the average of D5 and D6 is used to represent the vertical displacement of the center 

column. 

Figure 4–4 depicts the displacement profile of the beams (D2 through D9) at different load values. The 

figure shows that at each level of loading, the displacement profile of each beam can be approximated by 

a straight line, which indicates the formation of plastic hinges at the WUF-B beam-to-column 

connections. 

Figure 4–5 shows the horizontal displacement of the end columns at beam mid-height (D1 and D10) 

versus the vertical displacement at the center column (average of D5 and D6). In the plot, positive values 

signify an inward displacement. The figure indicates that displacement transducer D10 showed an initial 

outward displacement followed by an inward displacement as the behavior became dominated by tensile 

forces in the beam (catenary behavior). Displacement transducer D1, however, maintained an inward 

displacement throughout the initial (behavior dominated by flexure) and later (behavior dominated by 

tensile forces or catenary behavior) portions of the response. This difference seems to violate the 

symmetric characteristics of the response. The reason for this difference appears to be a slight rigid-body 

rotation of the specimen at the early stages of loading, possibly due to some slip in one of the connections 

of a diagonal brace or column end. To adjust the deformations for this effect, the average of the two 

horizontal displacement measurements (D1 and D10) was calculated and plotted in Figure 4–5 to be 

representative of the inward displacement of the end columns at beam mid-height. This average will be 

used for comparison with the computational modeling results in Chapter 5. 

25
Figure 4–3 Applied vertical load versus vertical displacements at (a) 1/4 span of beams (D2 and D9), (b) 1/2 

and D8), (c) 3/4 span of beams (D4 and D7), and (d) center column (D5 and D6) for the WUF-B s

0 101.6 203.2 304.8 406.4 508 609

Vertical Displacement (mm)

0 4 8 12 16 20 24 

0

50

100150200

Vertical Displacement (in)

Vertical Load (kip)

Displacement gage 5Displacement gage 6

0 101.6 203.2 304.8 406.4 508 609.6 711.2

0222445667890

Vertical Displacement (mm)

Vertical Load (kN)

0 4 8 12 16 20 24 28 0

50

100150200

Vertical Displacement (in)

Vertical Load (kip)

Displacement gage 4Displacement gage 7

0 101.6 203.2 304.8 406.4 508 609

Vertical Displacement (mm)

0 4 8 12 16 20 24 

0

50

100150200

Vertical Displacement (in)

Vertical Load (kip)

DisplacemenDisplacemen

0 101.6 203.2 304.8 406.4 508 609.6 711.2

0222445667890

Vertical Displacement (mm)

Vertical Load (kN)

0 4 8 12 16 20 24 28 0

50

100150200

Vertical Displacement (in)

Vertical Load (kip)

Displacement gage 2Displacement gage 9

(a) (b)(c) (d)

26 
 Experimental Results 

Figure 4–5 Horizontal displacement of end columns at beam mid-height (D1, D10, and their 

average) versus vertical displacement of center column for the WUF-B specimen 

Figure 4–4 Vertical displacement profiles of beams corresponding to indicated vertical loads 

for the WUF-B specimen (displacements magnified) 

27

-6096 -3048 0 3048 6096

-508

-381

-254

-127

Spanwise Distance (mm)

Vertical Dis

placement (mm)

-240 -120 0 120 240

-20

-15

-10

-5

Spanwise Distance (in)

Vertical Displacement (in)

185 kip

171 kip

155 kip

133 kip

196 kip

D9

D7

D3

D4

D6 D5

D8

D2

0 101.6 203.2 304.8 406.4 508 609.6 711.2

-2.54

0

2.54

5.08

7.62

10.16

12.7

Vertical Displacement of Center Column (mm)

Horizontal Displacement (mm)

0 4 8 12 16 20 24 28

-0.1

0

0.1

0.2

0.3

0.4

0.5

Vertical Displacement of Center Column (in)

Horizontal Displacement (in)

Displacement gage 1

Displacement gage 10

Average
Chapter 4 

4.2.3 Rotation Measurements 

Figure 4–6 shows plots of the vertical load versus the four inclinometer measurements (I1 and I4 for 

connections to end columns and I2 and I3 for connections to the center column, as shown in Figure 3–6), 

representing angle of rotation in the vicinity of the WUF-B connections. The plots indicate that the 

specimen remained in the elastic range up to a rotation of about 0.5° (0.01 rad) and that the rotation at 

failure (peak load) was about 4.5° (0.088 rad). Figure 4–7 presents the beam angle of rotation versus the 

vertical displacement of the center column. This figure shows that the rotations were essentially linearly 

proportional to the vertical displacement of the center column up to the failure of the connection at a 

displacement of 19.5 in (495 mm). This is due to the formation of plastic hinges at the beam-to-column 

connections that allowed rotation of the beam at those locations. 

0 0.0175 0.0349 0.0524 0.0698 0.0873 0.1047

0

222

445

667

890

Rotation (rad)

Vertical Load (kN)

0 1 2 3 4 5 6 0

50

100

150

200

Rotation (°)

Vertical Load (kip)

Inclinometer 2

Inclinometer 3

0 0.0175 0.0349 0.0524 0.0698 0.0873 0.1047

0

222

445

667

890

Rotation (rad)

Vertical Load (kN)

0 1 2 3 4 5 6 0

50

100

150

200

Rotation (°)

Vertical Load (kip)

Inclinometer 1

Inclinometer 4

(a)

(b)

Figure 4–6 Applied vertical load versus angles of rotation at (a) connections to end columns 

and (b) connections to center column for the WUF-B specimen 

28
 Experimental Results 

0 101.6 203.2 304.8 406.4 508 609.6 711.2

0

0.0175

0.0349

0.0524

0.0698

0.0873

0.1047

Vertical Displacement of Center Column (mm)

Rotation (rad)

0 4 8 12 16 20 24 28 0

1

2

3

4

5

6

Vertical Displacement of Center Column (in)

Rotation (°)

Inclinometer 2

Inclinometer 3

0 101.6 203.2 304.8 406.4 508 609.6 711.2

0

0.0175

0.0349

0.0524

0.0698

0.0873

0.1047

Vertical Displacement of Center Column (mm)

Rotation (rad)

0 4 8 12 16 20 24 28 0

1

2

3

4

5

6

Vertical Displacement of Center Column (in)

Rotation (°)

Inclinometer 1

Inclinometer 4

(a)

(b)

Figure 4–7 Angle of rotation at (a) connections to end columns and (b) connections to center 

column versus vertical displacement of center column for the WUF-B specimen 

4.2.4 Strain Measurements 

The strain gages were located at eight cross sections, which are labeled in Figure 4–8. Gages at Sections 

B2 and B5 provide information about the strains at mid-span of the beams, which was used to estimate 

the axial force in the beams. Gages at Sections B1, B3, B4, and B5 provide the strain distribution along 

the beam height in the vicinity of the connections. Gages at Sections C1 and C2 provide information 

about the strains in the end columns, which was used to estimate the axial force in the end columns. 

29
Chapter 4 

S1

S2

S3

S4,S5

S6

S7

S8

S9,S10

S11

S12

S13

S14,S15,S16

S22,S23

S24,S25,S26

S32,S33

S34

S35

S36

S37,S38

S42,S43

S41

S40

S39

S46

S45 S44

S27

S29

S31

S17

S19

S21

Strain Gages

C2 C1

B6 B5 B4 B3 B2 B1

Figure 4–8 Locations of cross sections with strain gages for the WUF-B specimen 

Figure 4–9 depicts the strain gage measurements at (a) Section B2 (S11, S12, and S13) and (b) Section 

B5 (S34, S35, and S36) versus the vertical displacement of the center column. Strain gage S11 

malfunctioned during the experiment and did not provide meaningful data. The plots in Figure 4–9 show 

that all strains at Sections B2 and B5 were significantly less than the nominal yield strain of the steel 

(0.2% or 2×10−3

), indicating that at mid-span the beam remained in the elastic range throughout the 

loading scenario. 

From Figure 4–9(b), it can be observed that the beam initially behaved primarily in bending up to a center 

column displacement of slightly less than 2 in (51 mm), with the top flange (S34) in compression, the 

bottom flange in tension (S36), and the neutral axis located approximately at mid-height of the web (S35). 

At a center column displacement of about 3 in (76 mm), the beam section at mid-span experienced very 

small bending moment and axial forces due to the development of negative and positive plastic moments 

with approximately the same magnitude (associated with the formation of plastic hinges) at the WUF-B 

connections to the end column and the center column, respectively. Beyond 3 in (76 mm) of center 

column displacement, the beam section at mid-span was subjected primarily to axial tension, while the 

bending moment effects at this cross section continued to be relatively small. The tensile strains in the 

beam increased with increased center column vertical displacement until the connection at the center 

column failed. Similar behavior can be observed for Section B2, Figure 4–9 (a), albeit without the strain 

data for S11. 

Figure 4–10 presents the average strains in Section B5, computed as the average of the strain 

measurement at the top and bottom flanges (B34 and B36, respectively). The figure also shows the 

average strains in Section B2, estimated as the strain measurement at web mid-height (S12) due to the 

lack of meaningful data from the strain gage at the top flange (S11). Both average strains are plotted 

versus the vertical displacement of the center column. The figure shows good agreement between the 

average strains at the mid-span of each beam. These strains were used to calculate the axial force in the 

beams. The axial force in the beams versus the vertical displacement of the center column is presented in 

Figure 4–11. It can be observed that in the early stages of the response, the behavior was dominated by 

flexure, indicated by the slight compressive axial force in the beams. With increased vertical 

displacement, tensile axial forces developed in the beams and the behavior was dominated by catenary 

action. At the time of failure, the axial tension in the beams was slightly greater than 150 kip (667 kN). 

30
 Experimental Results 

0 101.6 203.2 304.8 406.4 508

Vertical Displacement of Center Column (mm)

0 4 8 12 16 20

-300

-200

-100

0

100

200

300

400

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Strain gage 34

Strain gage 35

Strain gage 36

0 101.6 203.2 304.8 406.4 508

Vertical Displacement of Center Column (mm)

0 4 8 12 16 20

-300

-200

-100

0

100

200

300

400

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Strain gage 12

Strain gage 13

(a)

(b)

Figure 4–9 Mid-span strain gage measurements at (a) Section B2 and (b) Section B5 versus 

vertical displacement of center column for the WUF-B specimen 

31
Chapter 4 

0 101.6 203.2 304.8 406.4 508

Vertical Displacement of Center Column (mm)

0 4 8 12 16 20 -50

0

50

100

150

200

250

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Strain gage 12

Average of 34,36

Figure 4–10 Average strains at Sections B2 and B5 versus vertical displacement of center 

column for the WUF-B specimen 

0 101.6 203.2 304.8 406.4 508

-133

0

133

267

400

534

667

Vertical Displacement of Center Column (mm)

Beam Axial Force (kN)

0 4 8 12 16 20 -30

0

30

60

90

120

150

Vertical Displacement of Center Column (in)

Beam Axial Force (kip)

Abeam = 21.5 in2 (W21x73)

Axial strain estimated as an

average from gages 12, 34, 36 

Figure 4–11 Axial force in the beams versus vertical displacement of center column for the 

WUF-B specimen 

Plots of strain gage measurements along Sections B1 and B6 in the vicinity of the WUF-B connections to 

the end columns are presented in Figure 4–12. Strain distributions correspond to applied vertical loads of 

32 kip, 64 kip, 100 kip, 128 kip, and 156 kip (142 kN, 285 kN, 445 kN, 569 kN, and 694 kN). These 

loads correspond to center column vertical displacements of 0.5 in, 1.0 in, 2.0 in, 3.0 in, and 7.0 in 

(13 mm, 25 mm, 51 mm, 76 mm, and 178 mm). Similar plots are provided in Figure 4–13 for Sections 

B3 and B4 near the connections to the center column. The plots in both figures indicate that in the initial 

stages of loading, the beam and its end connections behaved elastically and the response was primarily 

32
 Experimental Results 

flexural (the neutral axis was slightly shifted to the tensile side, indicating slight compressive forces). 

With increased loading (increased vertical displacement of center column), the neutral axis shifted toward 

the compression side due to the presence of axial tensile loads. At vertical loads above 128 kip (569 kN), 

the strain distributions clearly deviated from linearity, signifying plastic behavior. 

-254

-127

0

127

254

Vertical Distance from Beam Centroid (mm)

-2000 -1000 0 1000 2000

-10

-5

0

5

10

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

32 kip / 0.5 in

64 kip / 1 in

110 kip / 2 in

128 kip / 3 in

156 kip / 7 in

Average of S42, S43

S41

S40

Average of 

S37, S38

S39

-254

-127

0

127

254

Vertical Distance from Beam Centroid (mm)

-2000 -1000 0 1000 2000

-10

-5

0

5

10

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

32 kip, 0.5 in

64 kip, 1 in

110 kip, 2 in

128 kip, 3 in

156 kip, 7 in

Average of S9, S10

S8

S7

Average 

of S4, S5

S6

(a)

(b)

Figure 4–12 Strain distributions along the depth of the beam at (a) Section B1 and (b) Section 

B6 near the connections to the end columns for the WUF-B specimen 

33
Chapter 4 

-254

-127

0

127

254

Vertical Distance from Beam Centroid (mm)

-2000 0 2000 4000 6000

-10

-5

0

5

10

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

32 kip, 0.5 in

64 kip, 1 in

110 kip, 2 in

128 kip, 3 in

156 kip, 7 in

Average of 

S32, S33

S31

S28

Average of 

S24, S25, S26

S30

S29

S27

-254

-127

0

127

254

Vertical Distance from Beam Centroid (mm)

-2000 0 2000 4000 6000

-10

-5

0

5

10

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

32 kip, 0.5 in

64 kip, 1 in

110 kip, 2 in

128 kip, 3 in

156 kip, 7 in

Average of 

S22, S23

S21

S18

Average of 

S14, S15, S16

S20

S19

S17

(a)

(b)

Figure 4–13 Strain distributions along the depth of the beam at (a) Section B3 and (b) 

Section B4 near the connections to the center column for the WUF-B specimen 

Figure 4–14 depicts the strain gage measurements at Sections C1 (S1, S2, and S3) and C2 (S44, S45, and 

S46) on the end columns below the beams versus the vertical displacement of the center column. The 

figure indicates that the end columns at this level were subjected to axial forces in addition to bending. 

The figure shows that all strains at these sections were significantly less than the yield strain of the steel 

(about 2×10−3

), indicating that the columns remained elastic. Plotted in Figure 4–14 is the average strain 

in the end columns. The average strain was used to calculate the axial force in the end columns. The 

axial force in the end columns versus the vertical displacement of the center column is presented in Figure 

4–15, where it can be observed that at the early stages of the response, the end columns were in 

compression. With increased vertical displacement and applied load, large compressive forces developed 

in the diagonal braces, and as a result, axial tension developed in the end columns. 

34
 Experimental Results 

0 101.6 203.2 304.8 406.4 508

Vertical Displacement of Center Column (mm)

0 4 8 12 16 20

-300

-200

-100

0

100

200

300

Vertical Displacement of Center Column (in)

Strain (x 10-6)

S44

S45

S2

S46

S1

S3

Average

Figure 4–14 Strain gage measurements at Sections C1 and C2, along with their average, 

versus vertical displacement at center column for the WUF-B specimen 

0 101.6 203.2 304.8 406.4 508

-89

0

89

178

267

356

Vertical Displacement of Center Column (mm)

End Column Axial Force (kN)

0 4 8 12 16 20 -20

0

20

40

60

80

Vertical Displacement of Center Column (in)

End Column Axial Force (kip)

Acolumn = 35.1 in2 (W18x119)

Axial strain estimated as an average 

from gages 1, 2, 3, 44, 45, 46 

Figure 4–15 Axial forces in the end columns versus vertical displacement of center column for 

the WUF-B specimen 

4.3 RBS SPECIMEN 

35
Chapter 4 

4.3.1 Observed Behavior and Failure Modes 

lumn, the RBS specimen (see Figure 4–16) 

men before failure occurred. In 

m). 

Under monotonic vertical displacement of the center co

experienced even larger deflections and rotations than the WUF-B speci

this test, the RBS specimen failed at a vertical displacement of the center column of about 33.5 in 

(851 mm), with a corresponding to a beam chord rotation of about 0.140 rad, obtained by dividing the 

center column displacement at failure by the centerline-to-centerline beam span of 240.0 in (6096 m

At that displacement, the applied vertical load was about 400 kip (1780 kN). The failure was 

characterized by the fracture of the bottom flange in the middle of the reduced section of one of the 

connections near the center column. As shown in Figure 4–17, the fracture propagated through the web 

until the specimen could no longer carry the applied load. 

Figure 4–16 Overall view of the RBS test specimen 

36
 Experimental Results 

Figure 4–17 Failure mode of the RBS specimen 

4.3.2 Displacement Measurements 

The plots in Figure 4–18 show the vertical load versus vertical displacements at (a) 1/3 span of the beams 

(D3 and D8), (b) 2/3 span of the beams (D4 and D7), and (c) the center column (D5 and D6). The 

locations of the displacement transducers were shown previously in Figure 3–7. As the plots indicate, the 

specimen was unloaded twice at vertical displacements of the center column of about 17 in (432 mm) and 

32 in (813 mm) to adjust the stroke of the hydraulic ram, and then the specimen was loaded again to 

failure. Figure 4–18(c) indicates that the assembly remained in the elastic range up to a vertical 

displacement of the center column of about 2 in (50 mm). With increased vertical displacement, the 

assembly behaved nonlinearly until it failed at a vertical displacement of the center column of about 33.5 

in (838 mm). The corresponding peak vertical load was about 400 kip (1780 kN). The pairs of nearly 

identical load deformation curves in each of the three plots in Figure 4–18 indicate that symmetry was 

largely maintained during the experiment. In subsequent plots, the average of D5 and D6 is used to 

represent the vertical displacement of the center column. 

37
Figure 4–18 Applied vertical load versus vertical displacements at (a) 1/3 span of beams (D3 and D8), (b) 2/3 

and D7), and (c) center column (D5 and D6) for the RBS specimen

0 127 254 381 508 635 762 889

02224456678901112133415571779

Vertical Displacement (mm)

Vertical Load (kN)

0 5 10 15 20 25 30 35 0

50

100150200250300350400

Vertical Displacement (in)

Vertical Load (kip)

Displacement gage 5Displacement gage 6

0 127 254 381 508 635 

Vertical Displacement (mm)

0 5 10 15 20 25 

0

50

100150200250300350400

Vertical Displacement (in)

Vertical Load (kip)

Displacement gage 4Displacement gage 7

0 127 254 381 508 635 762 889

02224456678901112133415571779

Vertical Displacement (mm)

Vertical Load (kN)

0 5 10 15 20 25 30 35 0

50

100150200250300350400

Vertical Displacement (in)

Vertical Load (kip)

Displacement gage 3Displacement gage 8

(a) (b)

(c)

38 
39 

Figure 4–20 shows the horizontal displacement of the end columns at (a) the column tops (D1 and D10) 

and (b) the beam mid-height (D2 and D9) versus the vertical displacement of the center column (average 

of D5 and D6). In the plots, positive values signify an inward displacement. The plots indicate that the 

end columns maintained an inward, and largely symmetric, displacement throughout the response. The 

average of the horizontal displacements at the beam mid-height and at the column tops were calculated 

and plotted in Figure 4–20 as representative of the inward displacement of the end columns. These 

averages will be used for comparison with the computational modeling results in Chapter 5. 

Figure 4–19 shows the displacement profile of the beam (D3 through D8) at different load values. In the 

figure, dotted lines are used to connect the measured deflections since straight lines do not accurately 

represent the deflected shape of the beams due to the presence of kinks at the reduced sections, where 

plastic hinges formed. Notice also that the small differences between the displacement measurements on 

each side of the center column indicate a slight rigid body rotation of the test specimen. 

Figure 4–19 Vertical displacement profiles of beams corresponding to indicaged vertical loads 

for the RBS specimen (displacements magnified) 

-6096 -3048 0 3048 6096

-889

-762

-635

-508

-381

-254

-127

Spanwise Distance (mm)

Vertical Displacement (mm)

-240 -120 0 120 240

-35

-30

-25

-20

-15

-10

-5

Spanwise Distance (in)

Vertical Displacement (in)

336 kip

289 kip

250 kip

223 kip

D8

D7 390 kip

D3

D4

D6 D5
Chapter 4 

0 127 254 381 508 635 762 889

0

12.7

25.4

38.1

50.8

63.5

76.2

88.9

Vertical Displacement of Center Column (mm)

Horizontal Displacement (mm)

0 5 10 15 20 25 30 35

0

0.5

1

1.5

2

2.5

3

3.5

Vertical Displacement of Center Column (in)

Horizontal Displacement (in)

Displacement gage 1

Displacement gage 10

Average

0 127 254 381 508 635 762 889

0

12.7

25.4

38.1

50.8

63.5

76.2

88.9

Vertical Displacement of Center Column (mm)

Horizontal Displacement (mm)

0 5 10 15 20 25 30 35

0

0.5

1

1.5

2

2.5

3

3.5

Vertical Displacement of Center Column (in)

Horizontal Displacement (in)

Displacement gage 2

Displacement gage 9

Average

(a)

(b)

Figure 4–20 Horizontal displacements of end columns at (a) column top and (b) beam midheight versus center column displacement for RBS specimen 

4.3.3 Rotation Measurements 

During the experiment, inclinometers I3 and I4 malfunctioned. Plots of the vertical load versus the 

measurements from inclinometers I1 and I2 (see Figure 3–7), representing angle of rotation at an end 

column connection and a center column connection, respectively, are shown in Figure 4–21. Note that 

these rotations do not represent the overall rotation of the beam due to the fact that plastic hinges formed 

in the middle of the reduced sections, resulting in kinking away from the face of the beam-column 

interface, where the inclinometers were located. Figure 4–22 presents the angle of rotation versus vertical 

displacement at the center column. This figure shows that the rotations were essentially linearly 

proportional to the vertical displacement of the center column up to the failure of the connection at a 

displacement of 33.5 in (851 mm). 

40
 Experimental Results 

0 0.0087 0.0175 0.0262 0.0349 0.0436 0.0524

0

222

445

667

890

1112

1334

1557

1779

Rotation (rad)

Vertical Load (kN)

0 0.5 1 1.5 2 2.5 3 0

50

100

150

200

250

300

350

400

Rotation (°)

Vertical Load (kip)

Inclinometer 1

Inclinometer 2

Figure 4–21 Vertical load versus angle of rotation at connections to end and center columns 

for RBS specimen 

0 127 254 381 508 635 762 889

0

0.0087

0.0175

0.0262

0.0349

0.0436

0.0524

Vertical Displacement of Center Column (mm)

Rotation (rad)

0 5 10 15 20 25 30 35

0

0.5

1

1.5

2

2.5

3

Vertical Displacement of Center Column (in)

Rotation (°)

Inclinometer 1

Inclinometer 2

Figure 4–22 Angle of rotation at connections to end column and center column versus center 

column displacement for RBS specimen 

41
Chapter 4 

4.3.4 Strain Measurements 

The strain gages mounted to the test specimen provided valuable information on the state of strain and 

stress at multiple locations. The strain gages were located at twelve cross sections, which are labeled in 

Figure 4–23. Gages at Sections B2, B3, B6, and B7 provide information about the strains in the beams 

outside of the connection regions and are used to estimate the axial force in the beams. Gages at Sections 

B1, B4, B5, and B8 provide the strain distribution along the beam height in the vicinity of the reduced 

sections. Gages at Sections C1 and C2 provide information about the strains in the end columns that are 

used to estimate their axial forces, while gages at Sections W1 and W2 provide information about the 

strains in the lateral braces that are used to estimate their axial forces. 

S1

S2

S3

S4

S6

S7

S8

S9

S17

S20

S21

S25

S40

S44

S43

S42

S41

S47

S46 S45

S5

S14

S15

S16

S10 (W)

S12 (E)

S11 (W)

S13 (E)

S18

S19

S22

S23

S24

S26

S30

S27

S28

S29

S32 (E)

S34 (W)

S31 (E)

S33 (W)

S35

S37

S39

S36

S38

Strain Gages

C2 C1

B8 B7 B6 B5 B4 B3 B2 B1

Figure 4–23 Locations of cross sections with strain gages 

Figure 4–24 depicts the strain gage measurements at (a) Section B2 (S7, S8, and S9) and (b) Section B7 

(S35, S36, S37, S38, and S39) versus the vertical displacement of the center column. This figure shows 

that all strains at these sections were significantly less than the nominal yield strain of the steel (0.2% or 

2×10−3

), indicating that at these cross sections, outside of the connection regions, the beam remained in 

the elastic range during the entire response. From Figure 4–24 it can be observed that the beam initially 

behaved primarily in bending up to a center column displacement of about 3 in (76 mm) where the top 

flanges in these sections were in tension, the bottom flanges were in compression, and the neutral axis 

was approximately at mid-height of the web. With increased center column displacement, axial tensile 

forces developed in the beams, as demonstrated by the tensile strains at mid-height of the beams. The 

tensile strains in the beams increased with increased center column vertical displacement until failure 

occurred at the reduced beam section. 

42
 Experimental Results 

0 127 254 381 508 635 762 889

Vertical Displacement of Center Column (mm)

0 5 10 15 20 25 30 35

-800

-400

0

400

800

1200

1600

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Strain gage 35

Strain gage 36

Strain gage 37

Strain gage 38

Strain gage 39

0 127 254 381 508 635 762 889

Vertical Displacement of Center Column (mm)

0 5 10 15 20 25 30 35

-800

-400

0

400

800

1200

1600

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Strain gage 7

Strain gage 8

Strain gage 9

(a)

(b)

Figure 4–24 Strain versus center column displacement at (a) Section B2 and (b) Section B7 of 

RBS specimen 

Figure 4–25 presents the average strains in Section B2 and Section B7, plotted against the vertical 

displacement of the center column. The figure indicates good agreement between the average strains 

from both sections. These average strains were used to calculate the axial force in the beams. The axial 

force in the beams versus the vertical displacement of the center column are presented in Figure 4–26, 

where it can be observed that in the early stages of the response, the behavior was dominated by flexure 

with minor axial forces in the beams. With increased vertical displacement, tensile axial forces developed 

in the beams. At the time of failure, the axial tension in the beams was about 550 kip (2447 kN). 

43
Chapter 4 

0 127 254 381 508 635 762 889

Vertical Displacement of Center Column (mm)

0 5 10 15 20 25 30 35

0

100

200

300

400

500

600

700

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Average of S7, S8, S9

Average of S35, S36, S37, S38, S39

Figure 4–25 Average strains at Sections B2 and B7 versus center column displacement of 

RBS specimen 

0 127 254 381 508 635 762 889

0

445

890

1334

1779

2224

2669

Vertical Displacement of Center Column (mm)

Beam Axial Force (kN)

0 5 10 15 20 25 30 35

0

100

200

300

400

500

600

Vertical Displacement of Center Column (in)

Beam Axial Force (kip)

Abeam = 27.7 in2 (W24x94)

Axial strain estimated as 

an average from gages 

7, 8, 9, 35, 36, 37, 38, 39

Figure 4–26 Axial force in beams versus center column displacement of RBS specimen 

44
 Experimental Results 

Plots of strain gage measurements along Sections B1 and B8 in the vicinity of the reduced sections near 

the end columns are presented in Figure 4–27, corresponding to applied vertical loads of 13 kip, 76 kip, 

152 kip, and 192 kip (58 kN, 338 kN, 676 kN, and 854 kN). These loads correspond to center column 

vertical displacements of 0.13 in, 0.75 in, 1.65 in, and 2.6 in (3 mm, 19 mm, 42 mm, and 66 mm). 

Similar plots are provided in Figure 4–28 for Sections B4 and B5 at the reduced sections near the center 

column for applied vertical loads of 22 kip, 76 kip, 131 kip, and 170 kip (98 kN, 338 kN, 583 kN, and 

756 kN), corresponding to center column vertical displacements of 0.22 in, 0.75 in, 1.36 in, and 1.97 in 

(6 mm, 19 mm, 35 mm, and 50 mm). Note that these strains are plotted for selected applied loads and 

displacements up to the onset of yielding for the specified cross sections. Since these strain distributions 

describe the response at the early stages of loading (prior to significant yielding and catenary behavior), 

the plots in both figures indicate that the beams behaved essentially elastically for the selected load range. 

Figure 4–29 shows the strain gage measurements outside of the connection regions, along (a) Sections B2 

and B7 and (b) Sections B3 and B6. Strain distributions are shown corresponding to applied vertical 

loads of 100 kip, 225 kip, 275 kip, and 375 kip (445 kN, 1001 kN, 1223 kN, and 1668 kN), which 

correspond to center column vertical displacements of 1.0 in, 5.0 in, 15.0 in, and 30.0 in (25 mm, 

128 mm, 383 mm, and 765 mm). The plots in this figure indicate that in the initial stages of loading, the 

beam behaved elastically and the response was primarily flexural (the neutral axis was always at midheight of beam web). With increased loading (and vertical displacement of the center column), the 

neutral axis shifted toward the compression side due to the presence of axial tensile loads. At a vertical 

load of about 375 kip (1668 kN), the strain distributions at Sections B3 and B6 deviated from linearity, 

signifying the onset of yielding, while the strain distributions at Sections B2 and B7 remained linear, 

signifying elastic behavior. 

Figure 4–30 depicts the strain gage measurements at Sections C1 (S1, S2, and S3) and C2 (S45, S46, and 

S47) on the end columns, below the beams, versus the vertical displacement of the center column. The 

figure indicates that the end columns at this level were subjected to axial force in addition to bending. 

The figure shows that all strains at these sections were significantly less than the nominal yield strain of 

the steel (0.2% or 2×10−3

), indicating that the columns remained in the elastic range throughout the test. 

Plotted in Figure 4–30 is the average strain in the end columns. The average strain was used to calculate 

the axial force in the end columns. The axial force in the end columns versus the vertical displacement of 

the center column is presented in Figure 4–31, where it can be observed that in the early stages of the 

response, the end columns were in compression. With increased vertical displacement and applied load, 

large compressive forces developed in the diagonal braces (see Figure 4–33), and as a result, axial tension 

developed in the end columns. 

45
Chapter 4 

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-3000 0 3000 6000

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

13 kip, 0.13 in

76 kip, 0.75 in

152 kip, 1.65 in

S6 192 kip, 2.60 in

S5

S4

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-3000 0 3000 6000

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

13 kip, 0.13 in

76 kip, 0.75 in

152 kip, 1.65 in

192 kip, 2.60 in

S41

S40

S44

S42

S43

(a)

(b)

Figure 4–27 Strain distributions along the depth of beam at (a) Section B1 and (b) Section B8 

near the connections to the end columns of RBS specimen 

46
 Experimental Results 

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-3000 0 3000 6000 9000

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

22 kip, 0.22 in

76 kip, 0.75 in

131 kip, 1.36 in

170 kip, 1.97 in

S17

S18

S19

S20

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-3000 0 3000 6000 9000

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

22 kip, 0.22 in

76 kip, 0.75 in

131 kip, 1.36 in

170 kip, 1.97 in

S21

S22

S24

S25

S23

(a)

(b)

Figure 4–28 Strain distributions along the depth of beam at (a) Section B4 and (b) Section B5 

near the connections to the center column of RBS specimen 

47
Chapter 4 

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-500 0 500 1000 1500 2000

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

100 kip, 1 in

225 kip, 5 in

275 kip, 15 in

375 kip, 30 in

S14

S15

S16 -304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-500 0 500 1000 1500 2000

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

100 kip, 1 in

225 kip, 5 in

275 kip, 15 in

375 kip, 30 in

S26

S27

S28

S30

S29

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-600 -300 0 300 600 900 1200 1500

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

100 kip, 1 in

225 kip, 5 in

275 kip, 15 in

S9 375 kip, 30 in

S8

S7

-304.8

-152.4

0

152.4

304.8

Vertical Distance from Beam Centroid (mm)

-600 -300 0 300 600 900 1200 1500

-12

-6

0

6

12

Strain (x 10-6)

Vertical Distance from Beam Centroid (in)

100 kip, 1 in

225 kip, 5 in

275 kip, 15 in

S39 375 kip, 30 in

S37

S35

S38

S36

(a)

(b)

Figure 4–29 Strain distributions along the depth of beam at (a) Sections B2 and B7, and (b) 

Sections B3 and B6 of RBS specimen 

48
 Experimental Results 

0 127 254 381 508 635 762 889

Vertical Displacement of Center Column (mm)

0 5 10 15 20 25 30 35

-400

-300

-200

-100

0

100

200

300

400

Vertical Displacement of Center Column (in)

Strain (x 10-6)

S45

S46

S1

S3

S2 Average

S46

Figure 4–30 Strain measurements at Sections C1 and C2, along with their average, versus 

center column displacement of RBS specimen 

0 127 254 381 508 635 762 889

0

222

445

667

890

Vertical Displacement of Center Column (mm)

End Column Axial Force (kN)

0 5 10 15 20 25 30 35

0

50

100

150

200

Vertical Displacement of Center Column (in)

End Column Axial Force (kip)

Acolumn = 35.5 in2 (W24x131)

Axial strain estimated as 

an average from gages 

1, 2, 3, 45, 46, 47 

Figure 4–31 Axial force in end columns versus center column displacement of RBS specimen 

49
Chapter 4 

Figure 4–32 depicts the strain gage measurements at Section W1 (S10 and S11 for the east brace and S12 

and S13 for the west brace) and Section W2 (S31 and S32 for the east brace and S33 and S34 for the west 

brace) on the diagonal braces versus the vertical displacement at the center column. The figure indicates 

that each brace was subjected to both axial force and bending. The figure shows that all strains at these 

sections were significantly less than the nominal yield strain of the steel (0.2% or 2×10−3

), indicating that 

the braces remained in the elastic range throughout the test. The average strain plotted in Figure 4–32 is 

the average of all the eight strain measurements. This average strain was used to calculate the axial force 

in each diagonal brace. The axial force in the diagonal braces versus the vertical displacement of the 

center column is presented in Figure 4–33, where it can be observed that the diagonal braces were always 

in compression during the response. 

0 127 254 381 508 635 762 889

Vertical Displacement of Center Column (mm)

0 5 10 15 20 25 30 35

-400

-300

-200

-100

0

100

Vertical Displacement of Center Column (in)

Strain (x 10-6)

Average

Figure 4–32 Strain measurements at Sections W1 and W2, along with their average, versus 

center column displacement of RBS specimen 

50
 Experimental Results 

0 127 254 381 508 635 762 889

0

445

890

1334

Vertical Displacement of Center Column (mm)

Axial Compression in Brace (kN)

0 5 10 15 20 25 30 35 0

100

200

300

Vertical Displacement of Center Column (in)

Axial Compression in Brace (kip)

Figure 4–33 Axial compressive force in each diagonal brace versus center column 

displacement of RBS specimen 

4.4 DISCUSSION OF TEST RESULTS 

This chapter presented the experimental performance of beam-column assemblies with two types of 

moment resisting connections under vertical column displacement. The connections considered include 

(1) a welded unreinforced flange-bolted web (WUF-B) connection and (2) a reduced beam section (RBS) 

connection. The experimental results included the observed behavior and failure modes, along with 

response measurements from the displacement transducers, inclinometers, strain gages, and load cell. 

For both the WUF-B and RBS test specimens, the beam-column assembly initially remained in the elastic 

range at small displacements of the center column. In that early stage of the response, the behavior was 

dominated by flexure. With increased vertical displacement, yielding occurred at the beam-to-column 

connections, and axial tension developed in the beams, indicating catenary behavior. The axial tension in 

the beams increased until the connections could no longer sustain the combined bending and axial 

stresses, and the beam-column assemblies failed. 

The failure of the WUF-B test specimen was characterized by the following sequence: (1) local buckling 

of the top flanges of the beams near the center column, (2) successive shear failure of the lowest and 

middle bolts connecting the beam web to a shear tab at the center column, and (3) fracture of the bottom 

flange near the weld access hole immediately thereafter. The failure of the RBS test specimen was 

51
Chapter 4 

characterized by the fracture of the bottom flange in the reduced section of a connection near the center 

column. The fracture propagated through the web until the vertical load-carrying capacity was lost. 

Table 4–1 summarizes the rotation capacities based on the tests conducted in this study and on prior 

seismic test data (see Chapter 2). As the table indicates, the rotations at peak load based on the 

experimental results in this study were about 0.081 rad for the WUF-B connections, obtained by dividing 

the center column displacement at failure of 19.5 in (495 mm) by the centerline-to-centerline beam span 

of 240.0 in (6096 mm), and 0.140 rad for the RBS connection, obtained by dividing the center column 

displacement at failure of 33.5 in (851 mm) by the centerline-to-centerline beam span of 240.0 in 

(6096 mm). The rotational capacities of these connections based on seismic testing data are 

approximately 0.047 rad for the WUF-B connection, based on Equation (2.1), and 0.073 rad for the RBS 

connection, based on Equation (2.3). These results show that the rotational capacities of these 

connections under monotonic column displacement are about twice as large as those based on seismic test 

data. Contributors to this difference may include: (1) cyclic loading leads to significant degradation in the 

strength and stiffness of the connection, while no such degradation is expected under monotonic loading, 

and (2) the applied loads are resisted by different mechanisms in the two cases, with the connection in 

pure flexure for seismic loading but subjected to combined flexure and tension under vertical column 

displacement. 

Table 4–1. Comparison of rotation capacities of WUF-B and RBS connections based on 

seismic data and monotonic column displacement 

Rotational Capacities (rad) 

Connection 

Type Seismic Data 

(FEMA 350) 

Monotonic Loading 

(This Study) 

WUF-B 0.047 0.081

RBS 0.073 0.140

4.5 REFERENCES 

FEMA (2000). Recommended seismic design criteria for new steel moment-frame buildings, FEMA 350, 

SAC Joint Venture and Federal Emergency Management Agency, Washington, D.C. 

52
 Computational Modeling and Analysis of Test Specimens 

53

Chapter 5

COMPUTATIONAL MODELING AND ANALYSIS OF TEST SPECIMENS

5.1 INTRODUCTION 

This chapter presents a computational investigation of the response of steel beam-column assemblies with 

moment resisting connections under the monotonic loading conditions expected in column removal 

scenarios, in which connections are subjected to combined bending and tension. The objectives of the 

analyses are to: (1) develop validated, detailed models of the assemblies, including the moment 

connections that mimic the behavior and failure modes of the test specimens, (2) develop reduced models 

of the connections that can be used in future studies to conduct three-dimensional system-level analyses 

of structures for assessment of their disproportionate collapse vulnerability, and (3) gain insight into the 

behavior and failure modes of the moment resisting connections, including the capacity of the 

connections to carry tensile forces that develop in the beams. 

The finite element analyses presented in this study are conducted using explicit time integration in LSDYNA (Hallquist, 2007), a general-purpose finite element software package. The analyses account for 

both geometrical and material nonlinearities, including element failure and erosion. In all analyses the 

center stub column is pushed down under displacement control until failure occurs. Displacements are 

increased at a slow rate to ensure a static response (no dynamic amplification), similar to the test loading. 

Comparisons between the analysis results of the detailed and reduced models and the experimental results 

are presented to validate the models developed herein. 

Section 5.2 provides an overview of the material models used in the analyses. Sections 5.3 and 5.4

provide details on the model development and the analysis results for the WUF-B specimen and the RBS 

specimen, respectively. Section 5.5 presents a summary and discussion of the analysis results. 

5.2 MATERIAL MODELS 

5.2.1 Steel Sections and Plates 

Various material models are available in LS-DYNA that can capture the nonlinear behavior and failure of 

the steel components. The primary material model used in the analyses presented in this study was a 

piecewise linear plasticity model (material model 24 in LS-DYNA; Hallquist, 2007). In this model, an 

effective stress versus effective plastic strain curve is specified, along with a plastic strain to failure. 

Once the failure strain is reached, the element is eroded, simulating fracture of the steel. 

For the various types of steel used in the test specimens, the material model parameters were developed 

based on engineering stress-strain curves obtained from coupon tensile tests for all steel sections and 

plates (see Chapter 3). The coupon tensile tests applied the ASTM 370 test standard (ASTM Designation 

A 370-03a 2003). For both the WUF-B and RBS specimens, the coupon tests provided data for beam 

webs, beam flanges, column webs, column flanges, shear tabs, continuity plates, and any doubler plates. 
Chapter 5 

For the solid and shell elements used in the detailed models, the approach to developing the material 

model parameters for each steel type was as follows: 

• The engineering stress-strain curve was converted to a true stress vs. plastic strain curve. The 

true stress σT is based on the load divided by the actual cross sectional area of the sample and is 

equal to the engineering stress σeng multiplied by a term to correct for the change in cross section: 

(1 ) T eng σ = σ + e (5.1) 

where e is the engineering strain. Prior to the onset of localization (necking), the natural or true 

strain εT is defined as 

ln(1 ) T ε = + e (5.2) 

The plastic strain is then obtained as εp = εT – σT/E, where E is the elastic modulus and σT/E

represents the elastic strain. 

• Since for each steel type, a number of coupon tests were conducted, the converted true stressstrain curves were averaged. The averaged true stress-strain curve was then extrapolated beyond 

the point of necking onset. 

• Iterative finite element analyses of the tensile test were carried out, and the failure strain εf and 

the extrapolation of the true stress-strain curve were adjusted until quantitative agreement of the 

measured and calculated engineering stress-strain behavior in the softening region beyond the 

maximum stress was reached. Due to the dependence of strain to failure on mesh size, the finite 

element models were developed, using the same mesh type (shell or solid element) and size as 

those used in the various models of the test specimens for each steel type. 

This approach ensured that the measured nonlinear material behavior up to failure was accurately 

captured in the material model. In addition, the simulation of the material testing provided a validation 

that the material model parameters were defined accurately and that the model could reproduce the 

measured response for the test conditions. 

For the beam elements used in the reduced models, Eqs. (5.1) and (5.2) do not apply for large strains, 

because the beam model does not account for changes in cross-sectional area. Rather than using Eq. (5.1), 

the engineering stress values were input directly in the beam material models. The corresponding plastic 

strain values were adjusted so that the engineering stress-strain curves obtained computationally from 

uniaxial tension matched those obtained experimentally. Values of the failure strain εf for a particular 

beam element size were determined such that the extension at fracture was consistent with the results of a 

detailed solid or shell element model with a corresponding gage length. 

Figure 5–1 shows examples of detailed finite element models of a coupon sample obtained from the 

flanges of the W21x73 beam section used in the WUF-B specimen. For modeling the beam flanges in the 

WUF-B specimen, the detailed solid/shell element model (see Section 5.3.1) used two different mesh 

types: (1) a solid element mesh with element size of approximately 0.18 in (4.6 mm), typical of that used 

in the vicinity of the connections, and (2) a shell element mesh with element size of approximately 0.75 in 

(19 mm), typical of that used away from the connections. These mesh types and sizes were used in the 

modeling of the coupons as shown in Figure 5–1. Figure 5–2 shows the true stress-true strain curves used 

as input for the beam flange steel for the solid, shell, and beam element models. As is evident in the 

figure, coarser meshes entail the use of smaller values of the failure strain εf to achieve consistent results. 

54
 Computational Modeling and Analysis of Test Specimens 

Note that the true stress vs. plastic strain curve used for the shell elements is extrapolated horizontally 

beyond the point of necking onset, while the curve used for the solid elements is extrapolated tangentially. 

Figure 5–3 presents the measured engineering stress-strain curve from the coupon test samples along with 

the analysis results of the solid and shell element models of the coupons. Strain values in the figure 

correspond to a gage length of 2 in (51 mm), and results from the beam element model are not included, 

as they correspond to a longer gage length. The comparison between the measured and calculated stressstrain behavior indicates that the material models capture the constitutive relationships for the steel of the 

beam flange with reasonable accuracy. The process shown here was repeated for all coupon tests to 

develop the constitutive material models for beam webs and flanges, column webs and flanges, shear tabs, 

continuity plates, and doubler plates corresponding to the various element types and sizes considered in 

the finite element models. For the reduced models, in which wide flange sections were represented by 

beam elements, material models were based on stress-strain data from the flanges, rather than the webs. 

(a)

(b)

2 in 

(51 mm)

Figure 5–1 Example finite element models of ASTM 370 coupon tensile samples: (a) solid 

element model with 0.18 in (4.6 mm) element size; (b) shell element model with 

0.75 in (19 mm) element size 

0

20

40

60

80

100

120

0 0.1 0.2 0.3 0.4 0.5 0.6

True Stress, 

σT (ksi)

Plastic Strain, ε p

827

689

552

414

276

138

0

True Stress, 

σT (MPa)

Solid Elements

εf = 0.55

Shell Elements

εf = 0.4

Solid and Shell 

Elements

Beam Elements

εf = 0.23

Figure 5–2 True stress-strain curves for the solid, shell, and beam elements used in 

modeling the beam flanges of the WUF-B specimen 

55
Chapter 5 

0

15

30

45

60

75

90

0 0.1 0.2 0.3 0.4 0.5

Engineering Stress, 

σeng (ksi)

Engineering Strain, e

517

414

310

207

103

Engineering Stress, 

σeng (MPa)

0

621

Shell Element Analysis

Solid Element Analysis

Coupon Test Results

Figure 5–3 Engineering stress-strain curves obtained from coupon tests and from the 

analysis using solid and shell elements for modeling the beam flanges of the 

WUF-B specimen 

5.2.2 High Strength Bolts 

The bolts connecting the shear tabs to the beam webs in the WUF-B specimen were 1 in (25.4 mm) 

diameter ASTM A490 high strength bolts. Data in the open literature (Kulak et al., 1987) were used to 

calibrate the stress-strain relationships for the bolt material. The bolt material was represented by a 

piecewise linear plasticity model (material model 24 in LS-DYNA; Hallquist, 2007), which was used for 

the steel sections and plates. The true stress-strain relationship for the bolt material used in this model is 

shown in Figure 5–4. 

The approach taken to develop the stress-strain relationship for the bolt material shown in Figure 5–4 was 

to develop a solid element model of the bolt for a double shear test and calibrate the resulting shear loaddeformation curve against experimental data reported in Kulak et al. (1987). The finite element mesh 

used to model the bolt was identical to that used in the detailed solid/shell element model of the WUF-B 

specimen (see Section 5.3.1). The model of the double shear bolt test is shown in Figure 5–5 and the 

deformed shape and failed bolt are shown in Figure 5–6. Due to symmetry, only one half of test sample 

with appropriate boundary conditions was considered in the analysis. Figure 5–7 shows the calculated 

load-deformation curve along with the experimental data from Kulak et al. (1987). Note that the load 

values reported in Figure 5–7 are for single shear (double shear divided by two). For the calculated shear 

load-deformation curve, the deformations reported are those for the bolt only (between the bolt head and 

shank), whereas the data from Kulak includes the test jig deformations. That may explain the difference 

in elastic stiffness between the measured and calculated responses. Overall, the agreement between the 

measured and calculated responses was good. In the reduced model of the WUF-B specimen (Section 

5.3.2), spring elements were used to model the shear behavior of the bolts. 

56
 Computational Modeling and Analysis of Test Specimens 

0

25

50

75

100

125

150

175

0 0.1 0.2 0.3 0.4 0.5 0.6

True Stress, 

σT (ksi)

Plastic Strain, ε p

εf = 0.55

1207

1034

862

689

517

345

172

0

True Stress, 

σT (MPa)

Figure 5–4 True stress-strain curve for the solid elements used in modeling the bolts of the 

WUF-B specimen 

Plane of symmetry

1 in diameter, A490 

high strength bolt 

Figure 5–5 Finite element model of a bolt double shear test 

57
Chapter 5 

Figure 5–6 Response of the bolt double shear model 

0

15

30

45

60

75

90

0 0.05 0.1 0.15 0.2 0.25

Shear Load (kip)

Shear Deformation (in)

400

334

267

Experimental Result

(Kulak et al., 1987) 

Finite Element

Analysis

200

133

67

Shear Load (kN)

0

0 1.27 2.54 3.81 5.08 6.35

Shear Deformation (mm)

Figure 5–7 Measured and calculated shear load-deformation curves for 1 in, A490 bolt 

58
 Computational Modeling and Analysis of Test Specimens 

5.2.3 Diagonal Braces 

In the experimental setup for both specimens (see Chapter 3), two diagonal braces were rigidly attached 

to the top of each end column to simulate the bracing effect provided by the upper floors in a multi-story 

building. Since the details of the brace and its connections were not of primary importance to the 

computational effort, these diagonal braces were represented as an arrangement of spring elements in all 

models. The spring elements accounted for various sources of nonlinearity that might include the brace 

response and the end connections behavior (plasticity, slip, etc). The load-deformation characteristics of 

these springs, for each specimen, were estimated as follows: 

• The axial force in each brace was estimated based on: 

o RBS specimen: the strain gage measurements on the braces (see Figure 4–33) 

o WUF-B specimen: force equilibrium considering the axial force in the end columns (see 

Figure 4–15) and the applied vertical load (strain measurements on the braces were 

unavailable for this specimen) 

• The axial displacement (or shortening) of each brace, calculated as the component (along the axis 

of the brace) of the lateral displacement of the end column at mid-depth of the brace, was 

estimated based on: 

o RBS specimen: interpolation of the measured horizontal displacements of the end 

columns at (a) column top and (b) beam mid-height (see Figure 4–20) 

o WUF-B specimen: measured horizontal displacements of the end columns at mid-height 

of the beam (see Figure 4–5), from which displacements at mid-depth of the brace were 

estimated based on analyses using the reduced model (see Section 5.3.2) with the loaddisplacement curve for the braces updated iteratively until convergence was achieved 

(displacement measurements at the top of the end columns were unavailable for this test). 

Figure 5–8 shows the load-deformation curves for each diagonal brace for both specimens based on the 

methodology outlined above. Nonlinear behavior of the braces is evident, most likely associated with 

yielding and slippage where the braces were connected to the strong floor of the testing facility. 

5.3 WUF-B FINITE ELEMENT MODELS 

Two finite element models of the WUF-B specimen were developed to study the response characteristics 

of the specimen and to compare the calculated response with that measured during the test. The first was 

a detailed model of the specimen with approximately 300 000 solid and shell elements, while the second 

was a reduced model with about 150 beam and spring elements. The following sections provide 

descriptions of the models and the analysis results. 

59
Chapter 5 

0 0.25 0.5 0.75 1 1.25 1.5 0

50

100

150

200

250

300

Brace Axial Displacement (in)

Brace Axial Force (kip)

RBS

WUF-B

0 6.4 12.7 19 25.4 31.8 38.1

0

222

445

667

890

1112

1334

Brace Axial Displacement (mm)

Brace Axial Force (kN)

0 0.25 0.5 0.75 1 1.25 1.5 0

50

100

150

200

250

300

Brace Axial Displacement (in)

Brace Axial Force (kip)

RBS

WUF-B

0 6.4 12.7 19 25.4 31.8 38.1

0

222

445

667

890

1112

1334

Brace Axial Displacement (mm)

Brace Axial Force (kN)

Figure 5–8 Axial load-displacement curve for diagonal braces for the WUF-B and RBS 

specimens 

5.3.1 Detailed (Solid/Shell Element) Model 

An overview of the detailed model used in the analysis of the WUF-B specimen is shown in Figure 5–9. 

Due to symmetry, only one half of the beam-column assembly with appropriate boundary conditions was 

modeled. The detailed model consisted of finely meshed solid (brick) elements representing the beams, 

columns, continuity plates, shear tabs, bolts, and welds in the vicinity of the connection. The details of 

the connection model are shown in Figure 5–10. Four layers of solid elements were used for all beam and 

shear tab plates and welds, which resulted in an element size in the range of 0.11 in to 0.19 in (2.8 mm to 

4.8 mm). Two to four layers of solid elements were used for all column and continuity plates, which 

resulted in an element size in the range of 0.22 in to 0.53 in (5.6 mm to 13.5 mm). Solid elements with a 

minimum dimension of 0.07 in (1.8 mm) were used for the bolts. Contact with friction was defined 

between the bolts, shear tabs, and beam web to model the transfer of forces through the bolted connection. 

Contact was also defined between the shear tab and beam web to ensure that the beam web did not 

penetrate the shear tab, or vice versa. Hand calculations showed that the stresses in the fillet weld 

connecting the shear tab to the column flange were low compared to their strength. As a result, the shear 

tab was modeled as rigidly connected to the column flange. 

Away from the connection zones, the beam and columns were modeled with shell elements (see Figure 5–

9 and Figure 5–10). Appropriate constraints were imposed at the interface between the shell and solid 

elements to ensure that nodes on the solid elements remained in the same direction as the fiber of the shell 

elements. Spring elements were used to model the diagonal braces at the top of the end columns (see 

Section 5.2.3). All nodes were fixed at the bases of the end columns. Similar to the test configuration, 

out-of-plane lateral displacements of the beam flanges were constrained at mid-span. 

60
 Computational Modeling and Analysis of Test Specimens 

The steel materials for the beams, columns, and connection components, including the bolts, were 

modeled using a piecewise linear plasticity model as described in Section 5.2. Elements were eroded 

when a pre-specified strain-to-failure f ε was reached, signifying fracture of the steel. 

The deflected shape of the WUF-B specimen based on this analysis is shown in Figure 5–11. During the 

response, the beam-column assembly responded initially in a purely flexural mode before catenary 

behavior developed. The beam remained essentially elastic except for sections in the vicinity of the 

connections next to the center and end columns where significant yielding was observed. The failure 

mode of the connection in the analysis, shown in Figure 5–12, was very similar to that observed in the 

experiment, shown previously in Figure 4–2. The lowermost bolt connecting the beam web to the shear 

tab at the center column failed in shear at a vertical displacement of the center column of about 17.5 in 

(445 mm), which was immediately followed by failure of the middle bolt. The bottom flange of the beam 

near the weld access hole began to fracture at a center column vertical displacement of approximately 

19 in (483 mm). The fracture initiated at the root of the access hole (center of flange) and propagated 

outward until the bottom flange completely fractured as can be seen in Figure 5–12. 

Axis of symmetry

Beam Web

Shell Elements

Solid Elements

(WUF-B Connection)

Solid Elements

(WUF-B Connection)

Spring Elements (Brace)

20 ft 0 in.

(6.10 m)

7 ft 2-3/8 in.

(2.19 m)

1 ft 8-1/2 in.

(0.52 m)

3 ft 1-1/8 in.

(0.94 m)

Shell Elements

Shell Elements

Axis of symmetry

Beam Web

Shell Elements

Solid Elements

(WUF-B Connection)

Solid Elements

(WUF-B Connection)

Spring Elements (Brace)

20 ft 0 in.

(6.10 m)

7 ft 2-3/8 in.

(2.19 m)

1 ft 8-1/2 in.

(0.52 m)

3 ft 1-1/8 in.

(0.94 m)

Shell Elements

Shell Elements

Figure 5–9 Overview of the detailed model of the WUF-B specimen 

61
Chapter 5 

Beam Web

Shear Tab

Bolts

Beam Flange

complete joint 

penetration groove weld 

Column Flange

Column Web

Continuity

Plate

Solid/Shell

Element Interface

Beam Web

Shear Tab

Bolts

Beam Flange

complete joint 

penetration groove weld 

Column Flange

Column Web

Continuity

Plate

Solid/Shell

Element Interface

Figure 5–10 Detailed views of the WUF-B connection in the detailed model of the WUF-B 

specimen 

62
 Computational Modeling and Analysis of Test Specimens 

Figure 5–11 Deflected shape of WUF-B detailed model at a center column vertical 

displacement of 19 in (483 mm). Contours represent vertical displacements in 

inches. 

Beam 

Web

Figure 5–12 Failure mode of the WUF-B detailed model. Contours represent plastic strains 

Figure 5–13 shows (a) the applied vertical load, (b) the beam axial force, (c) the horizontal (inward) 

displacement of the end columns at beam mid-height, and (d) the end column axial force, all plotted 

against the vertical displacement of the center column. These plots compare the experimental results with 

the results from the detailed finite element model presented in this section and with the results from the 

reduced model presented in Section 5.3.2. The plots show good agreement between the experimental and 

computational results, providing validation for the finite element models. 

63
Figure 5–13 (a) Applied vertical load, (b) beam axial force, (c) horizontal displacement of end column at beam 

end column axial force; all plotted against vertical displacement of center column for the WUF-B 

0 127 254 381 

Vertical Displacement of Center Column 

0 5 10 15 

-50

0

50

100

Vertical Displacement of Center Colum

End Column Axial Force (kip)

ExperimentalDetailed modelReduced model (fixed)Reduced model (pinned)

0 127 254 381 508

02.55.17.6

Vertical Displacement of Center Column (mm)

Horizontal Displacement of End Column (mm)

0 5 10 15 20 0

0.10.20.3

Vertical Displacement of Center Column (in)

Horizontal Displacement of End Column (in) Experimental Detailed model Reduced model (fixed) Reduced model (pinned)

0 127 254 381 

Vertical Displacement of Center Column 

0 5 10 15 

-50

0

50

100150

Vertical Displacement of Center Colum

Beam Axial Force (kip)

ExperimentalDetailed modelReduced model (fixed)Reduced model (pinned)

0 127 254 381 508

0222445667890

Vertical Displacement of Center Column (mm)

Vertical Load (kN)

0 5 10 15 20 0

50

100150200

Vertical Displacement of Center Column (in)

Vertical Load (kip) Experimental

Detailed modelReduced model (fixed columns)Reduced model (pinned columns)

(a)

(c)

(b)

(d)

64 
 Computational Modeling and Analysis of Test Specimens 

Similar to the experimental results, the results of the detailed model shown in Figure 5–13(a) indicate that 

the assembly remained in the elastic range up to a vertical displacement of the center column of about 2 in 

(50 mm). The analysis indicates that in the early stages of the response the behavior was dominated by 

flexure, as indicated by the axial compression in the beams shown in Figure 5–13(b). With increased 

vertical displacement, axial tension developed in the beams and the behavior was dominated by catenary 

action. As Figure 5–13(b) indicates, the axial tensile force in the beams increased with increased 

downward displacement of the center column until the connection could no longer carry the combined 

axial and flexural stresses, resulting in the failure of the assembly. Similar to the experimental results, the 

results of the detailed model shown in Figure 5–13(d) indicate that in the initial stages of the response, the 

end columns were in compression, but with increased vertical displacement, axial tension developed in 

the end columns, as a result of the large compressive axial loads carried by the diagonal braces. 

Figure 5–14 shows the bending moment-axial force interaction diagram for the WUF-B connection, based 

on the detailed analysis in this section and the reduced model analysis in Section 5.3.2. The bending 

moment and axial force were calculated at the face of the center column, where failure of the connection 

was observed. Superimposed on the connection response are the limiting bending moment-axial tension 

interaction diagrams for the gross beam cross section (W21x73) calculated based on the actual yield and 

ultimate strengths of the beam material. The limiting interaction diagrams for the beam cross section 

were calculated based on Chapter H of the 2005 AISC Specification (AISC 2005) using yield and 

ultimate stress values obtained from tensile tests (see Table 3–1). The figure shows that the capacity of 

the WUF-B connection exceeds the yield capacity of the beam gross cross section under combined axial 

and flexural loads, but is somewhat less than the ultimate strength of the beam. 

Figure 5–14 Comparison of the WUF-B connection moment-axial interaction diagram with the limit 

interaction diagram of the gross beam cross section 

65

0 226 452 678 904 1130 1356

0

2224

4448

6672

Beam Axial Load (kN)

Bending Moment (kN⋅m)

0 2 4 6 8 10 12

0

500

1000

1500

Bending Moment (kip⋅in ×103)

Beam Axial Load (kip)

Detailed model

Reduced model (fixed)

Reduced model (pinned)
Chapter 5 

5.3.2 Reduced (Beam/Spring Element) Model 

The reduced model of the WUF-B specimen, shown in Figure 5–15, used Hughes-Liu beam elements 

(Hallquist 2007) to represent the beams and columns, as well as the shear tabs and beam flanges in the 

connection regions (see Figure 5–16). The Hughes-Liu beam elements used cross section integration with 

the proper cross-sectional geometry defined for each component. A piecewise linear plasticity model was 

used to represent the steel materials, with stress-strain curves based on tensile test data as discussed in 

Section 5.2.1. An arrangement of beam and spring elements connected with rigid links was used to model 

the WUF-B connections, as shown in Figure 5–16. 

Figure 5–15 Overview of reduced model of the WUF-B specimen 

shear

tab

beam

flange

beam

flange

column: W18x119

beam: W21x73

nonlinear panel zone spring

rigid link

rigid link

moment releases

rigid

link

moment releases

rigid

link

rigid

links

nonlinear

bolt springs: 

vertical and 

horizontal shear

shear

tab

beam

flange

beam

flange

column: W18x119

rigid link

rigid link

moment releases

nonlinear panel zone spring

rigid

link

moment releases

beam: W21x73

rigid

link

rigid

links

nonlinear

bolt springs: 

vertical and 

horizontal shear

Figure 5–16 Detailed view of the WUF-B connection in the reduced model of the WUF-B 

specimen 

66
 Computational Modeling and Analysis of Test Specimens 

Zero-length spring elements (shown with finite length in Figure 5–16 for clarity) were used to model the 

shear behavior of the bolts, along with bearing-induced deformations of the shear tab and beam web, in 

the reduced model of the WUF-B specimen. These elements are capable of representing bolt shear in any 

direction in the vertical plane, allowing modeling of combined vertical and horizontal shear. The 

piecewise linear shear load-deformation curve shown in Figure 5–17 was used for the springs 

representing the bolts in the reduced model. This simplified piecewise-linear curve is based on the results 

of a detailed solid-element model of the bolted lap joint illustrated in the inset of Figure 5–17. The 

material properties and thicknesses of the two connected plates in this model correspond to those of the 

shear tab and the beam web used in the detailed model of the WUF-B specimen (see Section 5.3.1). One 

bolt was considered in the model, and the width of each connected plate was 4 in (102 mm), 

corresponding to the vertical spacing between bolts in the WUF-B connection. A shear load-deformation 

curve obtained from this model is also shown in Figure 5–17. Note that the failure displacement obtained 

from this single-shear model is more than twice the failure displacement of the bolt obtained from the 

double-shear model considered previously (see Figure 5–7), while the yield and ultimate loads are 

comparable. Note also that the plates considered in the single-shear configuration were approximately 

half as thick as those used in the double-shear configuration, resulting in much more extensive bearinginduced plastic deformations of the plates around the bolt holes. Deformation of the bolt holes in the 

single-shear configuration also permitted rotation of the bolt shank, evident in the inset of Figure 5–17. 

The larger failure displacement in the single-shear configuration therefore represents the combined effects 

of bolt shear deformation, bearing-induced plate deformation, and bolt shank rotation. 

0

20

40

60

80

0 0.1 0.2 0.3 0.4 0.5 0.6

Shear Load (kip)

Shear Deformation (in)

0 2.54 5.08 7.62 10.16 15.24

Shear Deformation (mm)

12.70

356

267

178

89

Shear Load (kN)

0

Simplified Piecewise-Linear Curve

Detailed Single-Shear

Model Results

Shear Tab

Beam Web

Section view of detailed model at ultimate load:

67
Chapter 5 

Figure 5–17 Shear load-deformation curves for bolted lap joint 

Spring elements were also used to model the diagonal braces (see Section 5.2.3) and the shear behavior of 

the panel zone. For the panel zone, the diagonal springs had an elastic, perfectly plastic load deformation 

curve based on the stiffness and strength of the panel zone (Khandelwal et al. 2008). The stiffness of the 

panel zone spring, kpz, was defined using equilibrium relationships that equate the response of the panel 

zone spring model with the column web in the panel zone region deforming in pure shear as: 

2

( )

( )cos

c cf pz

pz

b bf

Gd t t

k

d t θ

− = − (5.3) 

2

2

2

( )

cos

( )(

c cf

c cf b bf

d t

dt dt

θ − = − +− 2

) (5.4) 

where dc is the column depth, db is the beam depth, tcf is the column flange thickness, tbf is the beam 

flange thickness, tpz is the panel zone thickness, and G is the shear modulus of steel. Using similar 

equilibrium relationships and using the panel zone strength equation in the AISC Seismic Provisions 

(2005), the yield capacity of the panel zone spring is: 

2 0.6 3

1

cos

y c pz cf cf

pz

b c pz

Fdt b t

f θ ddt

⎡ ⎤

= + ⎢ ⎥ ⎢⎣ ⎥⎦

 (5.5) 

Where bcf is the column flange width. Since the panel zone region is very ductile, it is unlikely that it will 

fail prior to other components in the model. Therefore, a failure deformation limit on the panel zone 

spring was not enforced. 

Two analyses were conducted in which the bases of the end columns were modeled as either fixed or 

pinned. In general, the results from the reduced model were consistent with those from the detailed 

model. The deflected shape of the WUF-B specimen based on the reduced model with fixed column 

bases is shown in Figure 5–18. The failure sequence of the center column connection is indicated in 

Figure 5–19 for the reduced models with fixed and pinned column bases. The lowermost bolt connecting 

the beam web to the shear tab failed first, and was followed by the nearly simultaneous failures of the 

middle bolt and the bottom flange of the beam. This failure sequence is very similar to what was observed 

in both the experiment and the detailed model (see Section 5.3.1). 

Contours of Vertical Displacement (in)

Figure 5–18 Deflected shape of WUF-B reduced model (fixed columns) at a center column 

vertical displacement of 20.1 in (511 mm). 

68
 Computational Modeling and Analysis of Test Specimens 

1) Lowest bolt failure:

fixed: 18.1 in (460 mm)

pinned: 18.3 in (465 mm)

2) Bottom flange failure:

fixed: 19.8 in (503 mm)

pinned: 20.0 in (508 mm)

3) Middle bolt failure:

fixed: 20.1 in (511 mm)

pinned: 20.2 in (513 mm)

WUF-B connection failure sequence with 

vertical displacements of center column:

Figure 5–19 Failure sequence from the WUF-B reduced model 

Figure 5–13 shows plots of the primary response parameters based on the reduced models (both fixed and 

pinned end columns), along with the results obtained from the experiment and the detailed model. The 

plots show good agreement between the results produced by the reduced model and those from the 

experiment and the detailed model, providing a validation of the reduced model. This indicates that while 

the reduced model uses fewer elements, it is capable of capturing the primary response characteristics and 

failure modes of the test specimen. 

5.4 RBS FINITE ELEMENT MODELS 

Similar to the WUF-B specimen, two finite element models of the RBS specimen were developed to 

study the response characteristics of the connections and to compare the calculated response with that 

measured during the experiment. The first was a detailed model of the assembly with approximately 

235 000 shell elements, while the second was a reduced model with about 130 beam and spring elements. 

The following sections provide descriptions of the models and the analysis results. 

5.4.1 Detailed (Shell Element) Model 

An overview of the detailed model used in the analysis of the RBS specimen is shown in Figure 5–20. 

The model consisted of shell elements representing the columns, beams, continuity and doubler plates, 

and welds. In the vicinity of the reduced section, the beams and columns were modeled using a fine shell 

element mesh with an element size of about 0.25 in. (6.4 mm), as shown in Figure 5–21. Away from the 

connection zones, the beams and columns were modeled using a coarser mesh with an element size of 

1 in (25 mm). Spring elements were used to model the diagonal braces at the top of the end columns (see 

Section 5.2.3). All nodes were fixed at the bases of the end columns. Similar to the test configuration, 

out-of-plane lateral displacements of the beam flanges were constrained at mid-span. The steel materials 

for the beams, columns, and doubler and continuity plates were modeled using a piecewise linear 

plasticity model as described in Section 5.2. 

69
Chapter 5 

Figure 5–20 Overview of the detailed model of the RBS specimen 

Figure 5–21 Detailed view of the RBS connection in the detailed model of the RBS specimen 

The deflected shape of the RBS specimen based on the detailed analysis is shown in Figure 5–22. The 

beam-column assembly responded initially in a purely flexural mode before catenary action developed. 

The beam remained essentially elastic except for the reduced sections where significant yielding was 

observed. The failure mode of the connection according to the analysis, shown in Figure 5–23, was very 

similar to that observed in the experiment, shown in Figure 4–17. The failure was characterized by the 

fracture of the bottom flange in the reduced section near the center column, which displaced about 33 in 

(838 mm). The fracture immediately propagated through the web until the vertical load-carrying capacity 

of the specimen was lost. 

70
 Computational Modeling and Analysis of Test Specimens 

(a)

(b)

Figure 5–22 Deflected shape of RBS detailed model at a center column vertical displacement 

of 37 in (944 mm). Contours represent (a) vertical and (b) horizontal 

displacements in inches. 

71
Chapter 5 

 

Figure 5–23 Failure mode from the RBS detailed model. Contours represent plastic strains 

Figure 5–24 shows (a) the applied vertical load, (b) the beam axial force, (c) the horizontal (inward) 

displacement of the end columns at beam mid-height, (d) the horizontal (inward) displacement of the top 

of the end columns, (e) the end column axial force, and (f) the axial compression in each diagonal brace, 

all plotted against the vertical displacement of the center column. These plots compare the experimental 

results with the results from the detailed finite element model presented in this section and with the results 

from the reduced model presented in Section 5.4.2. The plots show good agreement between the 

experimental and computational results, providing validation for the finite element models. 

Similar to the experimental results, the results of the detailed model shown in Figure 5–24(a) indicate that 

the assembly remained in the elastic range up to a vertical displacement of the center column of about 2 in 

(50 mm). The analysis indicates that in the early stages of the response, the behavior was dominated by 

flexure, as indicated by the slight compressive axial forces in the beams shown in Figure 5–24(b). With 

increased vertical displacement, tensile axial forces developed in the beams and the behavior was 

dominated by catenary action. As Figure 5–24(b) indicates, the axial tensile force in the beams increased 

with increased downward displacement of the center column until the connection could no longer carry 

the combined axial and flexural stresses (axial tension in excess of 500 kip), resulting in fracture of the 

bottom flange at the center of the reduced section. Similar to the experimental results, the results of the 

detailed model shown in Figure 5–24(e) indicate that in the initial stages of the response (when the 

response was dominated by flexure), the end columns were in compression. With increased vertical 

displacement, axial tension developed in the end columns, as a result of the large compressive axial loads 

carried by the diagonal braces, as shown in Figure 5–24(f). 

72
 Computational Modeling and Analysis of Test Specimens 

0 5 10 15 20 25 30 35 0

50

100

150

200

250

300

350

400

Vertical Displacement of Center Column (in)

Vertical Load (kip)

Experimental

Detailed model

Reduced model (fixed columns)

Reduced model (pinned columns)

0 127 254 381 508 635 762 889

0

222

445

667

890

1112

1334

1557

1779

Vertical Displacement of Center Column (mm)

Vertical Load (kN)

0 127 254 381 508 635 762 889

0

445

890

1334

1779

2224

2669

3114

Vertical Displacement of Center Column (mm)

Beam Axial Force (kN)

0 5 10 15 20 25 30 35 -100

0

100

200

300

400

500

600

700

Vertical Displacement of Center Column (in)

Beam Axial Force (kip)

Experimental

Detailed model

Reduced model (fixed)

Reduced model (pinned)

0 127 254 381 508 635 762 889

0

8

15

23

30

38

46

Vertical Displacement of Center Column (mm)

Horizontal Displacement of End Column

at Beam Mid-Height (mm)

0 5 10 15 20 25 30 35 0

0.3

0.6

0.9

1.2

1.5

1.8

Vertical Displacement of Center Column (in)

Horizontal Displacement of End Column

at Beam Mid-Height (in)

Experimental

Detailed model

Reduced model (fixed)

Reduced model (pinned)

0 127 254 381 508 635 762 889

0

13

25

38

51

64

76

89

Vertical Displacement of Center Column (mm)

Horizontal Displacement of End Column

at Column Top (mm)

0 127 254 381 508 635 762 889

0

13

25

38

51

64

76

89

Vertical Displacement of Center Column (mm)

Horizontal Displacement of End Column

at Column Top (mm)

0 5 10 15 20 25 30 35 0

0.5

1

1.5

2

2.5

3

3.5

Vertical Displacement of Center Column (in)

Horizontal Displacement of End Column

at Column Top (in)

Experimental

Detailed model

Reduced model (fixed)

Reduced model (pinned)

0 127 254 381 508 635 762 889

-222

0

222

445

667

890

1112

1334

Vertical Displacement of Center Column (mm)

End Column Axial Force (kN)

0 5 10 15 20 25 30 35 -50

0

50

100

150

200

250

300

Vertical Displacement of Center Column (in)

End Column Axial Force (kip)

Experimental

Detailed model

Reduced model (fixed)

Reduced model (pinned)

0 127 254 381 508 635 762 889

0

222

445

667

890

1112

1334

Vertical Displacement of Center Column (mm)

Axial Compression in Brace (kN)

0 5 10 15 20 25 30 35 0

50

100

150

200

250

300

Vertical Displacement of Center Column (in)

Axial Compression in Brace (kip)

Experimental

Detailed model

Reduced model (fixed)

Reduced model (pinned)

(a)

(c)

(b)

(d)

(e) (f)

Figure 5–24 Vertical displacement of center column versus applied vertical load, and 

individual member forces and displacements of RBS specimen 

Figure 5–25 shows the bending moment-axial force interaction diagram for the RBS connection, based on 

the detailed analysis in this section and the reduced model analysis in Section 5.4.2. The bending 

moment and axial force were calculated at the center of the reduced section near the center column, where 

failure of the connection was observed. Superimposed on the connection response are the limiting 

bending moment-axial tension interaction diagrams for the gross beam cross section (W24x94) and for 

the reduced beam section calculated based on the actual ultimate strength of the beam material. The 

limiting interaction diagrams were calculated based on Chapter H of the 2005 AISC Specification (AISC 

73
Chapter 5 

2005) using yield and ultimate stress values obtained from tensile tests (see Table 3–1). The figure shows 

that the capacity of the connection slightly exceeds the capacity of the reduced section under combined 

axial and flexural loads, as calculated based on the AISC Specification, but is less than the calculated 

ultimate capacity of the gross beam cross section. 

0 452 904 1356 1808 2260

0

2224

4448

6672

8896

Bending Moment (kN⋅m)

Beam Axial Load (kN)

0 4 8 12 16 20

0

500

1000

1500

2000

Bending Moment (kip⋅in ×103)

Beam Axial Load (kip)

Detailed model

Reduced model (fixed)

Reduced model (pinned)

Figure 5–25 Comparison of RBS connection moment-axial interaction diagram with the 

interaction diagram of gross beam cross section 

5.4.2 Reduced (Beam Element) Model 

The reduced model of the RBS specimen, shown in Figure 5–26, consisted of Hughes-Liu beam elements 

representing the beams and columns in the specimen. In addition, each reduced beam section was 

modeled using five beam elements with varying section properties. The beam elements used cross section 

integration with the proper cross-sectional geometry defined for each type of section. A piecewise linear 

plasticity model was used to represent the steel materials, with stress-strain curves based on tensile test 

data as discussed in Section 5.2.1. Spring elements were also used to model the diagonal braces (see 

Section 5.2.3) and the shear behavior of the panel zone (see Section 5.3.2). Both fixed and pinned bases 

were considered for the end columns. 

74
 Computational Modeling and Analysis of Test Specimens 

Figure 5–26 Overview of the reduced model of the RBS specimen 

In general, the results from the reduced model were consistent with those from the detailed model. The 

deflected shape of the RBS specimen based on the reduced model with fixed column bases is shown in 

Figure 5–27. The failure sequence and mode of the connection based on this analysis (for both fixed and 

pinned end columns) were very similar to those observed in the experiment and detailed model. The 

beam element at the center of the reduced section experienced large strains, associated with combined 

flexural and axial tensile stresses. Once a critical strain was reached, the element was eroded, resulting in 

the failure of the assembly (see Figure 5–27). 

Contours of Vertical Displacement (in)

Figure 5–27 Deflected shape of RBS reduced model (fixed columns) at a center column 

displacement of 34.1 in (866 mm). 

Figure 5–24 shows plots of the primary response parameters based on the reduced models (both fixed and 

pinned end columns), along with the results obtained from the experiment and the detailed model. The 

plots show good agreement between the results produced by the reduced model and those from the 

experiment and the detailed model, providing validation for the reduced models. This indicates that while 

the reduced model uses fewer elements, it is capable of capturing the primary response characteristics and 

failure modes of the test specimen. 

75
Chapter 5 

5.5 SUMMARY AND DISCUSSION OF ANALYSIS RESULTS 

This chapter presented a computational assessment of the performance of beam-column assemblies with 

two types of moment resisting connections under vertical column displacement. The connections 

considered include (1) a welded unreinforced flange – bolted (WUF-B) web connection and (2) a reduced 

beam section (RBS) connection. The study considered two levels of modeling complexity: (1) detailed 

models with a large number of elements, primarily solid and shell elements, and (2) reduced models with 

a limited number of elements, primarily beam and spring elements. The analyses conducted using these 

models provided insight into the behavior and failure modes of the connections, including their capacity 

to carry tensile forces that developed in the beams. 

This study indicates a good agreement between the experimental results and the computational 

predictions. Both detailed and reduced models were capable of capturing the primary response 

characteristics and failure modes. The validated reduced models developed in this study will be valuable 

in the analysis of complete structural systems for assessing the reserve capacity and robustness of 

building structures. The analyses confirm that the loads under a column removal scenario are resisted 

through catenary action, in which tensile axial forces develop in the beams. These tensile forces increase 

until the connections can no longer sustain the combined axial and flexural stresses and failure occurs. 

5.6 REFERENCES 

AISC (2005). Specification for Structural Steel Buildings, ANSI/AISC 360-05, American Institute of 

Steel Construction, Chicago, IL. 

Hallquist, J. (2007), LS-DYNA Keyword User’s Manual, Livermore Software Technology Corporation, 

Livermore, CA, Version 971. 

Khandelwal, K., El-Tawil, S., Kunnath, S.K., Lew, H.S. (2008) “Macromodel-based simulation of 

progressive collapse: steel frame structures.” Journal of Structural Engineering, 134(7), 1070-1078. 

Kulak, G. L., Fisher, J. W., and Struik, J. H. A., (1986), Guide to Design Criteria for Bolts and Riveted 

Joints, 2nd Ed., John Wiley & Sons, New York. 

76
 

Chapter 6

SUMMARY AND CONCLUSIONS

This report presented an experimental and analytical study of two steel beam-column assemblies, each 

comprising three columns and two beams. The two beam-column assemblies represent portions of the 

structural framing system of two ten-story steel frame buildings. One building was designed for Seismic 

Design Category C (SDC C) and the other for Seismic Design Category D (SDC D). The beam-column 

assemblies were taken from the exterior moment resisting frames of these buildings. One test specimen, 

which was part of the SDC C building, had welded unreinforced flange-bolted web (WUF-B) 

connections, and the other, which was part of the SDC D building, had reduced beam section (RBS) 

connections. The specimens were subjected to monotonically increasing vertical displacement of the 

unsupported center stub column to observe their behavior under a simulated column removal scenario, 

including the development of catenary action in the beams. The vertical displacement of the center stub 

column was increased until the vertical load-carrying capacity was depleted. 

The overall behavior of each beam-column assembly was analyzed using two levels of modeling 

complexity: (1) detailed models with a large number of elements, primarily solid and shell elements, and 

(2) reduced models with a limited number of elements, primarily beam and spring elements. The analyses 

conducted using these models provided insight into the behavior and failure modes of the connections, 

including their capacity to carry tensile forces that developed in the beams. 

Based on the study reported herein, the following conclusions are reached: 

1. For both the WUF-B and RBS connection assemblies, the behavior of the assemblies was 

dominated by flexure in the early stages of the response. With increased vertical displacement of 

the center column, the beam connections exhibited yielding and tensile axial forces developed in 

the beams and the behavior was dominated by catenary action. 

2. Distinct modes of failure were observed for the two test specimens. The failure of the WUF-B 

test specimen was characterized by: (1) local buckling of the top flanges of the beams near the 

center column, (2) successive shear fractures of the lowest and middle bolts connecting the beam 

web to a shear tab at the center column, and (3) fracture of the bottom flange near the weld access 

hole immediately thereafter. The failure of the RBS test specimen was characterized by: (1) 

fracture of the bottom flange in the middle of the reduced section and (2) propagation of the 

fracture through the web until the vertical load-carrying capacity was lost. 

3. The test results show that the rotational capacities of both the WUF-B and RBS connections 

under monotonic column displacement are about twice as large as those based on seismic test 

data. The rotations at peak load were about 0.081 rad and 0.140 rad for the WUF-B and RBS 

connections respectively, whereas the rotational capacities of these connections based on seismic 

testing data are approximately 0.047 rad and 0.073 rad, respectively. Contributors to this 

difference include: (1) cyclic loading leads to significant degradation in the strength and stiffness 

of the connection, while no such degradation is expected under monotonic loading, and (2) the 

applied loads are resisted by different mechanisms in the two cases, with the connection in pure 
Chapter 6 

flexure for seismic loading but subjected to both flexure and tension under vertical column 

displacement. 

4. This study indicates generally good agreement between the experimental and the computational 

results. Both the detailed and reduced models were capable of capturing the primary response 

characteristics and failure modes of the test specimens. 

In summary, this study shows that analysis using reduced models consisting of beam and spring elements 

can accurately predict the response characteristics of both the WUF-B and RBS connections. 

Furthermore, the validated reduced models developed in this study would be valuable in the analysis of 

complete structural systems for assessing the reserve capacity and robustness of building structures. 

78