ABSTRACT 
 
 
 
 
Title of Dissertation: AN EXPERIMENTAL INVESTIGATION 
OF THE FLEXURAL RESISTANCE OF 
HORIZONTALLY CURVED STEEL I-
GIRDER SYSTEMS  
  
 Joseph Lawrence Hartmann, Doctor of 
Philosophy, 2005 
Dissertation Directed By: Professor Emeritus Pedro Albrecht and 
Affiliated Associate Professor Chung Fu, 
Department of Civil and Environmental 
Engineering 
 
 
In 1998 the Federal Highway Administration (FHWA) began executing the 
experimental component of a multi-year program investigating horizontally curved 
steel I-girder bridges.  This experimental program consists of full-scale testing to 
determine the effects of horizontal curvature on the structural performance of I-
girders subject to moment and shear, to investigate moment/shear interaction, and to 
assess the behavior and ultimate capacity of a composite bridge. 
The experiments that are the focus of this dissertation are the component tests 
designed to determine the bending strength of horizontally curved steel I-girders.  
These tests were conducted at full-scale using a 3-girder system in order to eliminate 
concerns with modeling and scaling of the results.  Also, the boundary conditions 
supplied to the components by the full-scale 3-girder system are considered to be 
comparable if not equal to those produced on real bridges. 
  
The seven bending component tests were designed to examine the influence of 
compression flange slenderness, web slenderness and transverse stiffener spacing on 
bending capacity.  The components were loaded within a constant moment region of 
the test frame eliminating applied vertical shear loads from affecting their 
performance.  For each test, an attempt was made to capture the strains due to 
installation of the component into the test frame and the strain due to dead-load 
deflection, as well as the strains due to the applied loading. 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
AN EXPERIMENTAL INVESTIGATION OF THE FLEXURAL 
RESISTANCE OF HORIZONTALLY CURVED STEEL I-GIRDER SYSTEMS 
 
 
 
By 
 
 
Joseph Lawrence Hartmann 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2005 
 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor Emeritus Pedro Albrecht, Chair 
Affiliated Associate Professor Chung Fu, Co-Chair 
Professor Amde Amde  
Professor Amr Baz, Dean?s Representative 
Professor Emeritus Bruce Donaldson 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Joseph Lawrence Hartmann 
2005 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
Preface 
This report is one of several that will include data and analyses specific to the Curved 
Steel Bridge Research Project conducted at the Federal Highway Administration?s 
Turner-Fairbank Highway Research Structures Laboratory. This multi-year project 
investigated the effects of horizontal curvature on steel I-girder systems during erection, 
subject to uniform moment, subject to moment-shear interaction, and in composite 
construction. This report is specific to the experimental results of the investigation on 
uniform moment. 
The Curved Steel Bridge Research Project was a pooled-fund effort. In addition to the 
Federal Highway Administration, the following state Departments of Transportation 
contributed funding to this project:  Alabama, Arkansas, California, Florida, Georgia, 
Iowa, Illinois, Kansas, Kentucky, Louisiana, Minnesota, Missouri, Nebraska, Nevada, 
New Hampshire, New Jersey, New York, North Carolina, Oklahoma, Tennessee, Texas, 
Utah, Virginia, Wisconsin, and Wyoming.  
 
 
 
 
 
 
 
ii 
 Dedication 
To my wife, Tracy, and daughters, Sara and Hannah. 
iii 
Acknowledgements 
The author wishes to gratefully acknowledge the contributions made to this report by 
his advisor, Professor Emeritus Pedro Albrecht, and co-advisor, Affiliated Associate 
Professor Chung Fu.  In particular, the author would like to thank Dr. Albrecht for the 
steadfast support and encouragement he has provided during 15 years of graduate school 
advisement. 
The author would also like to recognize the direct and indirect contributions made to 
this report by Dr. William Wright (Federal Highway Administration), Professor Donald 
White (Georgia Institute of Technology), and Mr. Michael Grubb (BSDI Ltd.).  The 
author is pleased to be able to refer to these gentlemen as mentors, colleagues and 
friends. 
Finally, the author wishes to thank his colleagues at the Turner-Fairbank Highway 
Research Center Structures Laboratory who were a part of the Curved Steel Bridge 
Research Project for their contributions to this report; Mr. Zuhan Xi, Dr. Hernando 
Chandra and Dr. Fassil Beshah.  Without their professionalism and participation, these 
experiments and this report would not have been a success. 
iv 
Table of Contents 
 
 
Preface           ii 
Dedication          iii 
Acknowledgements         iv 
Table of Contents         v 
List of Tables          viii 
List of Figures          xi 
List of Abbreviations         xvi 
Chapter 1. Introduction        1 
1.1 Background/Problem       1 
1.2 Objective and Scope       6 
1.3 Previous Experimental Work      6 
1.3.1 CURT Tests       7 
1.3.2 University of Maryland Tests     12 
1.3.3 Japanese Tests       14 
1.3.4 Other Experimental Testing     16 
1.4 Strength Predictor Equations      17 
Chapter 2. Experiment Design       19 
2.1 Test Frame Concept        20 
2.2 Component Test Matrix       27 
2.2.1 Bending Component Series      27 
2.2.2 Moment-Shear Interaction Component Series   30 
2.3 Fabrication of the Test Frame and Bending Components   30 
2.3.1 Materials       30 
2.3.1.1 Girders     31 
2.3.1.2 Cross-Frames and Diaphragms   31 
2.3.1.3 Bending Components     32 
2.3.2 As-Built Geometry       32 
2.4 Material Properties        33 
2.4.1 Plate Coupon Locations      34 
2.4.2 Tensile Strength Testing      34 
2.4.3 Compressive Strength Testing     35 
2.4.4 Elastic Modulus Testing      35 
2.5 Instrumentation Plan       36 
2.5.1 Test Frame Instrumentation     36 
2.5.2 Bending Component Instrumentation    47 
2.6 Laboratory Equipment       48 
2.6.1 Loading Apparatus      48 
2.6.2 Instrumentation       51 
2.6.2.1 Electrical Resistance Strain Gages   51 
2.6.2.2 Vibrating Wire Strain Gages    52 
2.6.2.3 Load Cells     52 
2.6.3 Data Acquisition Systems      53 
2.6.3.1 MicroMeasurements 4000    53 
v 
2.6.3.2 MicroMeasurements 5000    53 
2.6.3.3 Geokon Micro-10     53 
2.6.3.4 Hewlett-Packard VXI     54 
Chapter 3.   Analysis of Experimental Data      55 
3.1 Execution of the Experiments      55 
3.2 Data Analysis        58 
3.3 Installation Strains        66 
3.4 Bending Component B1 Test      77 
3.5 Bending Component B2 Test       91 
3.6 Bending Component B3 Test      103 
3.7 Bending Component B4 Test      120 
3.8 Bending Component B5 Test      132 
3.9 Bending Component B6 Test      143 
3.10 Bending Component B7 Test      156 
3.11 Boundary Conditions       167 
3.12 Effect of Installation Strains on Capacity     168 
3.13 Effect of Compression Flange Slenderness on Capacity   169 
3.14 Effect of Web Slenderness on Capacity     172 
3.15 Effect of Transverse Stiffener Spacing on Capacity   172 
Chapter 4.  Analytical Results       173 
4.1 Finite Element Model       173 
4.1.1 Stress-Strain Relationship      176 
4.1.2 As-Built Geometry      183 
4.1.3 Installation Strains      184 
4.1.4 Modeling of Residual Stress     185 
4.1.5 Modeling of Boundary Conditions    191 
4.1.6 Predictions       191 
4.1.6.1 B1 Finite Element Model Results   193 
4.1.6.2 B2 Finite Element Model Results   195 
4.1.6.3 B3 Finite Element Model Results   198 
4.1.6.4 B4 Finite Element Model Results   200 
4.1.6.5 B5 Finite Element Model Results   202 
4.1.6.6 B6 Finite Element Model Results   205 
4.1.6.7 B7 Finite Element Model Results   208 
4.2 AASHTO Guide Specifications Predictions    211 
4.2.1 Non-Compact Compression Flange Example   212 
4.2.2 Compact Compression Flange Example    216 
4.3 Unified Design Method Predictions     219 
4.3.1 Non-Compact Compression Flange Example   220 
4.3.2 Compact Compression Flange Example    224 
4.4 Summary of Predictions       228 
Chapter 5. Conclusions        230 
5.1 Summary          230 
5.2 Findings          231 
5.3 Research Needs        233 
Appendix A. Steel Properties Data       235 
vi 
A.1 Plate Coupon Locations       235 
A.2 Tension Testing        253 
 A.2.1 Yield Strength Results      292 
A.2.1.1 Offset Yield Strength     292 
A.2.1.2 Upper Yield Strength     295 
A.2.1.3 Lower Yield Strength     297 
A.2.1.4 Static Yield Strength     298 
 A.2.2 Yield Point Elongation Results     298 
 A.2.3 Tensile Strength Results      299 
A.3 Compression Testing       299 
 A.3.1  Yield Strength Results      301 
A.3.1.1 Offset Yield Strength     301 
A.3.1.2 Upper Yield Strength     301 
A.3.1.3 Lower Yield Strength     301 
A.3.1.4 Static Yield Strength     302 
 A.3.2 Yield Point Elongation Results     302 
A.4 Young?s Modulus Testing       302 
 A.4.1 Young?s Modulus Testing Results    304 
  A.4.2 Young?s Modulus From Tension Testing    304 
 A.4.3 Young?s Modulus From Compression Testing   305 
A.5 True Stress-Strain        305 
 A.5.1 True Strain       306 
 A.5.2 True Stress       306 
Appendix B. Design Equations       308 
 B.1 Summary of the Guide Specifications Provisions for the Design of  
 Non-Composite I-Girders in Flexure     308 
 B.1.1 I-Girder Flanges       308 
B.1.1.1 Partially Braced Compression Flanges  309 
B.1.1.2 Partially Braced Tension Flanges   311 
 B.1.2 I-Girder Webs       311 
 B.1.2.1 Unstiffened Webs     311 
 B.1.2.2 Transversely Stiffened Webs    312 
 B.1.2.3 Transversely and Longitudinally Stiffened Webs 313 
B.2 Summary of the Unified Design Method Equations for the Design of  
Non-Composite I-Girders in Flexure     313 
 B.2.1 Discretely Braced Compression Flanges    314 
B.2.1.1 Flange Local Buckling    314 
B.2.1.2 Lateral Torsional Buckling    315 
 B.2.2 Discretely Braced Tension Flanges    316 
Refrences           317 
 
vii 
List of Tables 
 
 
Table 1-1:   Summary of Previous Experimental Work That Produced  
Flexural or Flexural/Shear Failures     8 
Table 2-1:   CSBRP Bending Specimen Target Parameter Test Matrix  29 
Table 2-2:   CSBRP Bending Specimen As-Built Parameter Test Matrix  33 
Table 2-3:   Configuration and Location of Strain Gaged Sections   37 
Table 3-1:   Installation Strain Data Analysis Results for Specimens B4, B5,  
 B6 and B7        68 
Table 3-2:   Installation Strain Data Used in Bending Component Capacity  
 Analysi         74 
Table 3-3:   B1 Applied Load Steps and Resulting Girder Moments  80 
Table 3-4:   B1 Mid-Span Stresses and Moments     81 
Table 3-5:   B2 Applied Load Steps and Resulting Girder Moments  93 
Table 3-6:   B2 Mid-Span Stresses and Moments     94 
Table 3-7:   B3 Applied Load Steps and Resulting Girder Moments (Part I) 104 
Table 3-8:   B3 Applied Load Steps and Resulting Girder Moments (Part II) 105 
Table 3-9:   B3 Mid-Span Stresses and Moments     106 
Table 3-10:  B4 Applied Load Steps and Resulting Girder Moments  121 
Table 3-11:  B4 Mid-Span Stresses and Moments     123 
Table 3-12:  B5 Applied Load Steps and Resulting Girder Moments (Part I) 133 
Table 3-13:  B5 Applied Load Steps and Resulting Girder Moments (Part II) 134 
Table 3-14:  B5 Mid-Span Stresses and Moments     135 
Table 3-15:  B6 Applied Load Steps and Resulting Girder Moments (Part I) 144 
Table 3-16:  B6 Applied Load Steps and Resulting Girder Moments (Part II) 145 
Table 3-17:  B6 Mid-Span Stresses and Moments     147 
Table 3-18:  B7 Applied Load Steps and Resulting Girder Moments  157 
Table 3-19:  B7 Mid-Span Stresses and Moments     160 
Table 3-20:  Summary of Experimental Results     169 
Table 4-1:   Cross-reference of  Steel Plate Number and Bending Component  
 Element         176 
Table 4-2:   Average Steel Plate Properties for Selected Steel Plates  177 
Table 4-1:   Equations Used to Establish Typical Stress-Strain Relationships  
 for the FE Model       178 
Table 4-2:  Bending Specimen As-Built Plate Dimensions    184 
Table 4-3:   Compression Flange Plate Residual Stresses    188 
Table 4-4:   Web Plate Residual Streses      188 
Table 4-5:   Tension Flange Plate Residual Stresses     189 
Table 4-6:   B1 Test and Finite Element Model Results    193 
Table 4-7:  B2 Test and Finite Element Model Results    196 
Table 4-8:   B3 Test and Finite Element Model Results    198 
Table 4-9:   B4 Test and Finite Element Model Results    201 
Table 4-10:  B5 Test and Finite Element Model Results    203 
Table 4-11:  B6 Test and Finite Element Model Results    206 
Table 4-12:  B7 Test and Finite Element Model Results    208 
viii 
Table 4-13:   Summary of Guide Specifications Flexural Capacities and  
Staistcs         212 
Table 4-14:   Summary of Unified Design Method Flexural Capacities and  
Staistcs         220 
Table 4-15:   Summary of Predicted Vertical Bending Moments   229 
Table A-1:   Summary of Plate 1 Tension Test Results    255 
Table A-2:   Summary of Plate 2 Tension Test Results    256 
Table A-3:   Summary of Plate 3 Tension Test Results    257 
Table A-4:   Summary of Plate 4 Tension Test Results    258 
Table A-5:  Summary of Plate 5 Tension Test Results    259 
Table A-6:   Summary of Plate 6 Tension Test Results    260 
Table A-7:   Summary of Plate 7 Tension Test Results    261 
Table A-8:   Summary of Plate 8 Tension Test Results    262 
Table A-9:   Summary of Plate 9 Tension Test Results    263 
Table A-10:  Summary of Plate 10 Tension Test Results    264 
Table A-11:  Summary of Plate 11 Tension Test Results    265 
Table A-12:  Summary of Plate 12 Tension Test Results    266 
Table A-13:  Summary of Plate 13 Tension Test Results    267 
Table A-14:  Summary of Plate 14 Tension Test Results    268 
Table A-15:  Summary of Plate 15 Tension Test Results    269 
Table A-16:  Summary of Plate 16 Tension Test Results    270 
Table A-17:  Summary of Plate 18 Tension Test Results    271 
Table A-18:  Summary of Plate 19 Tension Test Results    272 
Table A-19:  Summary of Plate 20 Tension Test Results    273 
Table A-20:  Summary of Plate 21 Tension and Compression Test Results  274 
Table A-21:  Summary of Plate 22 Tension and Compression Test Results  275 
Table A-22:  Summary of Plate 23 Tension and Compression Test Results  276 
Table A-23:  Summary of Plate 24 Tension and Compression Test Results  277 
Table A-24:  Summary of Plate 25 Tension and Compression Test Results  278 
Table A-25:  Summary of Plate 26 Tension Test Results    279 
Table A-26:  Summary of Plate 27 Tension Test Results    280 
Table A-27:  Summary of Plate 28 Tension Test Results    281 
Table A-28:  Summary of Plate 29 Tension Test Results    282 
Table A-29:  Summary of Plate 30 Tension and Compression Test Results  283 
Table A-30:  Summary of Plate 31 Tension and Compression Test Results  284 
Table A-31:  Summary of Plate 32 Tension Test Results    285 
Table A-32:  Summary of Plate 33 Tension Test Results    286 
Table A-33:  Summary of Plate 34 Tension Test Results    287 
Table A-34:  Summary of Plate 35 Tension Test Results    288 
Table A-35:  Summary of Structural Steel Tube 674 Tension Test Results  289 
Table A-36:  Summary of Structural Steel Tube 811 Tension Test Results  290 
Table A-37:  Summary of Structural Steel Tube 871 Tension Test Results  291 
Table A-38:  A572 Steel Tension Testing Statistics     293 
Table A-39:  A852 Steel Tension Testing Statistics     294 
Table A-40:  A572 Steel Compression Testing Statistics    300 
Table A-41:  Young?s Modulus Testing Statistics     303 
ix 
Table A-42:  Young?s Modulus Statistics from Tension and Compression  
Testing         304 
x 
List of Figures 
 
 
Figure 1-1:   All Previous Experimental Slenderness Combinations   4 
Figure 1-2:   Slenderness Combinations From All Previous Uniform  
 Bending Experiments       5 
Figure 1-3:   All Previous Uniform Bending Experiments with Realistic  
 Boundary Conditions       5 
Figure 2-1:   Plan View of Test Frame      22 
Figure 2-2:   Cross-Section of Test Frame at a Cross Frame Location 6L  23 
Figure 2-3:   The Test Frame in the FHWA Structures Laboratory   24 
Figure 2-4:   Bending Component Test Matrix     26 
Figure 2-5:   Location of Instrumented Cross-Sections    38 
Figure 2-6:   Instrumentation Configuration (1)      39 
Figure 2-7:  Instrumentation Configuration (2)      40 
Figure 2-8:  Instrumentation Configuration (3)      41 
Figure 2-9:  Instrumentation Configuration (V1)      42 
Figure 2-10:  Instrumentation Configuration (V2)      43 
Figure 2-11:  Instrumentation Configuration (V3)      44 
Figure 2-12:  Instrumentation Configuration (V5)      45 
Figure 2-13:  Instrumentation Configuration (V6)      46 
Figure 2-14:  Typical Load Frame        49 
Figure 3-1:   No-Load Condition Support Layout      56 
Figure 3-2:   I-Girder Coordinate System      60 
Figure 3-3:   Identification of Strain Measurement and Resultant Locations  61 
Figure 3-4:  Cross-Sectional Parameters       62 
Figure 3-5:   Components of Longitudinal Strain      65 
Figure 3-6:   B4 Installation Strain Data       70 
Figure 3-7:   B5 Installation Strain Data       71 
Figure 3-8:   B6 Installation Strain Data       72 
Figure 3-9:   B7 Installation Strain Data       73 
Figure 3-10:  B1 Installation Strain Data with Regression Line Estimates   75 
Figure 3-11:  B2 Installation Strain Model From Regression Line Estimates  76 
Figure 3-12:  B3 Installation Strain Data With Regression Line Estimates   77 
Figure 3-13:  B1 Vertical Bending Moment       82 
Figure 3-14:  Test Frame Mid-Span Vertical Bending Moments, B1 Test   82 
Figure 3-15:  B1 Mid-Span Longitudinal Strain State Resulting From  
 Installations and Dead Load (Step 1)      84 
Figure 3-16:  B1 Mid-Span Longitudinal Strain State During Step 8   85 
Figure 3-17:  Longitudinal Strain State in B1 Near Cross-Frame N6L  
 During Step 8 (Excluding Installation Effects)     86 
Figure 3-18:  B1 Mid-Span Longitudinal Strain State During Step 11   87 
Figure 3-19:  B1 Mid-Span Longitudinal Strain State During Step 18   88 
Figure 3-20:  B1 Mid-Span Longitudinal Strain State During Step 28   89 
Figure 3-21:  Most Critical G2 Mid-Span Longitudinal Strain State B1 Test  
 (Step 29)        90 
xi 
Figure 3-22:  B2 Vertical Bending Moment in Elastic Range    95 
Figure 3-23:  Test Frame Mid-Span Vertical Bending Moments, B2 Test   95 
Figure 3-24:  B2 Mid-Span Longitudinal Strain State Resulting From  
 Installation and Dead Load (Step 1)      96  
Figure 3-25:  B2 Mid-Span Longitudinal Strain State During Step 10   97 
Figure 3-26:  Longitudinal Strain State in B2 Near Cross-Frame N6L  
 During Step 10 (Excluding Installation Effects)    98 
Figure 3-27:  B2 Mid-Span Longitudinal Strain State During Step 13   99 
Figure 3-28:  Longitudinal Strain State in B2 Near Cross-Frame N6L  
 During Step 22 (Excluding Installation Effects)    100 
Figure 3-29:  Longitudinal Strain State in B2 Near Cross-Frame N6R  
 During Step 22 (Excluding Installation Effects)    101 
Figure 3-30:  B2 Mid-Span Longitudinal Strain State During Step 33   102 
Figure 3-31:  Most Critical G2 Mid-Span Longitudinal Strain State During  
 B2 Test (Step 36)        103 
Figure 3-32:  B3 Vertical Bending Moment       107 
Figure 3-33:  Test Frame Mid-Span Vertical Bending Moments, B3 Test   108 
Figure 3-34:  B3 Mid-Span Longitudinal Strain State Resulting From  
 Installation and Dead Load (Step 1)      109 
Figure 3-35:  B3 Mid-Span Longitudinal Strain State During Step 10   110 
Figure 3-36:  Longitudinal Strain State in B3 Near Cross-Frame N6L  
 During Step 10 (Excluding Installation Effects)    111 
Figure 3-37:  Longitudinal Strain State in B3 Near Cross-Frame N6R  
 During Step 10 (Excluding Installation Effects)    112 
Figure 3-38:  B3 Mid-Span Longitudinal Strain State During Step 14   113 
Figure 3-39:  Longitudinal Strain State in B3 Near Cross-Frame N6L  
 During Step 21 (Excluding Installation Effects)    114 
Figure 3-40:  Longitudinal Strain State in B3 Near Cross-Frame N6R  
 During Step 21 (Excluding Installation Effects)    115 
Figure 3-41:  Longitudinal Strain State in B3 Near Cross-Frame N6R  
 During Step 22 (Excluding Installation Effects)    116 
Figure 3-42:  Longitudinal Strain State in B3 Near Cross-Frame N6L  
 During Step 23 (Excluding Installation Effects)    117 
Figure 3-43:  B3 Mid-Span Longitudinal Strain State During Step 31   118 
Figure 3-44:  B3 Mid-Span Longitudinal Strain State During Step 44   119 
Figure 3-45:  Most Critical G2 Mid-Span Longitudinal Strain State During  
 B3 Test         120 
Figure 3-46:  B4 Vertical Bending Moment       122 
Figure 3-47:  Test Frame Mid-Span Vertical Bending Moments, B4 Test   124 
Figure 3-48:  B4 Mid-Span Longitudinal Strain State Resulting From  
 Installation and Dead Load (Step 1)      125 
Figure 3-49:  B4 Mid-Span Longitudinal Strain State During Step 8   126 
Figure 3-50:  Longitudinal Strain State in B4 Near Cross-Frame N6L  
 During Step 8 (Excluding Installation Effects)     127 
Figure 3-51:  Longitudinal Strain State in B4 Near Cross-Frame N6R  
 During Step 8 (Excluding Installation Effects)     128 
xii 
Figure 3-52:  Longitudinal Strain State in B4 Near Cross-Frame N6R During  
 Step 18 (Excluding Installation Effects)     129 
Figure 3-53:  Longitudinal Strain State in B4 Near Cross-Frame N6L During  
 Step 19 (Excluding Installation Effects)     130 
Figure 3-54:  B4 Mid-Span Longitudinal Strain State During Step 29   131 
Figure 3-55:  Most Critical G2 Mid-Span Longitudinal Strain State During  
 B4 Test         132 
Figure 3-56:  B5 Vertical Bending Moment       136 
Figure 3-57:  Test Frame Mid-Span Vertical Bending Moments, B5 Test   137 
Figure 3-58:  B5 Mid-Span Longitudinal Strain State Resulting From  
 Installation and Dead Load (Step 1)      138 
Figure 3-59:  B5 Mid-Span Longitudinal Strain State During Step 9   139 
Figure 3-60:  Longitudinal Strain State in B5 Near Cross-Frame N6L  
 During Step 9 (Excluding Installation Effects)     140 
Figure 3-61:  Longitudinal Strain State in B5 Near Cross-Frame N6L  
 During Step 16 (Excluding Installation Effects)    141 
Figure 3-62:  B5 Mid-Span Longitudinal Strain State During Step 38   142 
Figure 3-63:  Most Critical G2 Mid-Span Longitudinal Strain State During  
 B5 Test         143 
Figure 3-64:  B6 Vertical Bending Moment       148 
Figure 3-65:  Test Frame Mid-Span Vertical Bending Moments, B6 Test   149 
Figure 3-66:  B6 Mid-Span Longitudinal Strain State Resulting From  
 Installation and Dead Load (Step 1)      150 
Figure 3-67:  B6 Mid-Span Longitudinal Strain State During Step 13   151 
Figure 3-68:  Longitudinal Strain State in B6 Near Cross-Frame N6L  
 During Step 13 (Excluding Installation Effects)    152 
Figure 3-69:  Longitudinal Strain State in B6 Near Cross-Frame N6R  
 During Step 13 (Excluding Installation Effects)    153 
Figure 3-70:  B6 Mid-Span Longitudinal Strain State During Step 28   154 
Figure 3-71:  B6 Mid-Span Longitudinal Strain State During Step 38   155 
Figure 3-72:  Most Critical G2 Mid-Span Longitudinal Strain State During  
 B6 Test         156 
Figure 3-73:  B7 Vertical Bending Moment       158 
Figure 3-74:  Test Frame Mid-Span Vertical Bending Moments, B7 Test   159 
Figure 3-75:  B7 Mid-Span Longitudinal Strain State Resulting From  
 Installation and Dead Load (Step 1)      161 
Figure 3-76:  B7 Mid-Span Longitudinal Strain State During Step 8   162 
Figure 3-77:  Longitudinal Strain State in B7 Near Cross-Frame N6L  
 During Step 8 (Excluding Installation Effects)     163 
Figure 3-78:  Longitudinal Strain State in B7 Near Cross-Frame N6R  
 During Step 8 (Excluding Installation Effects)     164 
Figure 3-79:  B7 Mid-Span Longitudinal Strain State During Step 10   165 
Figure 3-80:  B7 Mid-Span Longitudinal Strain State During Step 13   166 
Figure 3-81:  Most Critical G2 Mid-Span Longitudinal Strain State During 
 B7 Test         167 
Figure 3-82:  Effect of Compression Flange Slenderness     170  
xiii 
Figure 3-83:  Effect of Compression Flange Slenderness (w/o B7)    171 
Figure 4-1:   Typical Finite Element Model Used in this Study    174 
Figure 4-2:   Typical Bending Component Finite Element Mesh Density   175 
Figure 4-3:   Typical Engineering Stress-Strain Relationship Used by FE  
 Model         178 
Figure 4-4:   Engineering Versus True Stress-Strain      181 
Figure 4-5:   Plate 21 Compression and Tension Test Results Compared  
 with the FE Material Model in Engineering Stress-Strain   182 
Figure 4-6:   Plate 21 Compression and Tension Test Results Compared  
 with the FE Material Model in True Stress-Strain    183 
Figure 4-7:   Example Flange Plate Residual Stress Profile    190 
Figure 4-8:   Example Web Plate Residual Stress Profile     190 
Figure 4-9:   B1 Test Mid-Span Moments and Finite Element Predictions   194 
Figure 4-10:   B1 Mid-Span Moment vs. Deflection     195 
Figure 4-11:   B2 Test Mid-Span Moments and Finite Element Predictions  196 
Figure 4-12:  B2 Mid-Span Moment vs. Deflection      197 
Figure 4-13:  B3 Test Mid-Span Moments and Finite Element Predictions   199 
Figure 4-14:  B3 Mid-Span Moment vs. Deflection      200 
Figure 4-15:  B4 Test Mid-Span Moments and Finite Element Predictions   201 
Figure 4-16:  B4 Mid-Span Moment vs. Deflection      202 
Figure 4-17:  B5 Test Mid-Span Moments and Finite Element Predictions   204 
Figure 4-18:  B5 Mid-Span Moment vs. Deflection      205 
Figure 4-19:  B6 Test Mid-Span Moments and Finite Element Predictions   206 
Figure 4-40:  B6 Mid-Span Moment vs. Deflection      207 
Figure 4-41:  B7 Test Mid-Span Moments and Finite Element Predictions   209 
Figure 4-42:  B7 Mid-Span Moment vs. Deflection      210 
Figure A-1.  Layout of Cutting Plates in Full Scale Test of Curve Girders 
 Bridge (See Table 1 for Cutting Schedule)     237 
Figure A-2.  Location of Tensile Coupons on Plate: 1     238 
Figure A-3.  Location of Tensile Coupons on Plate: 2    238  
Figure A-4.  Location of Tensile Coupons on Plate: 3     239 
Figure A-5.  Location of Tensile Coupons on Plate: 4     239 
Figure A-6.  Location of Tensile Coupons on Plate: 5     240 
Figure A-7.  Location of Tensile Coupons on Plate: 6     240 
Figure A-8.  Location of Tensile Coupons on Plate: 7     241 
Figure A-9.  Location of Tensile Coupons on Plate: 8     241 
Figure A-10. Location of Tensile Coupons on Plate: 9     242 
Figure A-11. Location of Tensile Coupons on Plate: 10     242 
Figure A-12. Location of Tensile Coupons on Plate: 11     243 
Figure A-13. Location of Tensile Coupons on Plate: 12     243 
Figure A-14. Location of Tensile Coupons on Plate: 13     244 
Figure A-15. Location of Tensile Coupons on Plate: 14     244 
Figure A-16. Location of Tensile Coupons on Plate: 15     244 
Figure A-17. Location of Tensile Coupons on Plate: 16     245 
Figure A-18. Location of Tensile Coupons on Plate: 17     245 
Figure A-19. Location of Tensile Coupons on Plate: 18     245 
xiv 
Figure A-20. Location of Tensile Coupons on Plate: 19     246 
Figure A-21. Location of Tensile Coupons on Plate: 20     246 
Figure A-22. Location of Tensile Coupons on Plate: 21     246 
Figure A-23. Location of Tensile Coupons on Plate: 22     247 
Figure A-24. Location of Tensile Coupons on Plate: 23     247 
Figure A-25. Location of Tensile Coupons on Plate: 24     247 
Figure A-26. Location of Tensile Coupons on Plate: 25     248 
Figure A-27. Location of Tensile Coupons on Plate: 26     248 
Figure A-28. Location of Tensile Coupons on Plate: 28     248 
Figure A-29. Location of Tensile Coupons on Plate: 32     249 
Figure A-30. Location of Tensile Coupons on Plate: 34     249 
Figure A-31. Location of Tensile Coupons on Plate: 30     250 
Figure A-32. Location of Tensile Coupons on Plate: 31     250 
Figure A-33. Location of Tensile Coupons on Plate: 33     251 
Figure A-34. Location of Tensile Coupons on Plate: 35     251 
Figure A-35. Location of Tensile Coupons on Plate: 27     252 
Figure A-36. Location of Tensile Coupons on Plate: 29     252 
Figure A-37: Typical Tension Test Records       296 
 
xv 
List of Abbreviations 
A = I-girder cross-sectional area 
AF = 1
st
 order lateral flange bending stress amplification factor 
Bi = bimoment 
C
b
 = moment gradient correction factor 
C
w
 = warping constant 
D = web depth 
D
c
 = depth of web in compression in the elastic range 
E = modulus of elasticity of steel  
E
st
 = strain hardening modulus 
F
bs
 = critical average flange stress 
F
cr
 = critical average flange stress or critical compressive longitudinal 
stress in the web for the Guide Specifications; critical buckling stress 
for the Unified Design Method 
F
cr1
 = critical average flange stress calculated from reduction factors 
F
cr2
 = critical average flange stress determined from partial yielding  
F
n
 = nominal flexural resistance in terms of stress 
F
nc
 = nominal flexural resistance of the compression flange in terms of stress 
F
nc(FLB)
 = nominal flexural resistance of the compression flange based on flange 
  local buckling in terms of stress  
F
nc(LTB)
 = nominal flexural resistance of the compression flange based on lateral 
  torsional buckling in terms of stress 
F
nt
 = nominal flexural resistance of the tension flange in terms of stress 
F
y
 =  specified minimum yield strength of steel 
F
yc
 = specified minimum yield strength of compression flange steel  
F
yt
 = specified minimum yield strength of tension flange steel  
F
yw
 = specified minimum yield strength of web plate steel 
I
x
 = moment of inertia about the x-axis 
I
y
 = moment of inertia about the y-axis 
L
b
 = unbraced length  
L
p
 = lateral bracing limit for flexural capacity governed by plastic bending  
L
r
 = lateral bracing limit for flexural capacity governed by inelastic lateral 
torsional buckling  
M
lat
 = lateral flange bending moment  
M
n
 = nominal vertical bending moment 
M
x
 = moment about x-axis 
M
x
yield
 = moment about x-axis that will cause yield in the compression flange 
M
y
 = moment about y-axis 
P
z
 = axial force in the z-direction 
R = girder radius; minimum girder radius within a panel or over a specified 
length  
R
b
 = flange-stress reduction factor to account for load shedding from web 
buckling 
R
h
 = flange-stress reduction factor to account for load shedding from hybrid 
web yielding 
xvi 
Sxc = section modulus with respect to the compression flange 
W
n
 = normalized unit warping 
b = minimum flange width 
b
f
 = flange width  
b
fc
 = compression flange width  
b
ft
 = tension flange width  
d
o
 = actual distance between transverse stiffeners  
d
s
 = distance between longitudinal stiffener and compression flange  
f
b
 = calculated factored average flange stress at the section under consideration 
f
bu
 = flexural flange stress due to primary bending from factored loads  
f
l1
 = 1
st
 order lateral flange bending stress  
f
l
 = 2
nd
 order lateral flange bending stress or 1
st
 order lateral flange bending 
stress corrected with AF 
k = coefficient of web bend-buckling 
l = unbraced length 
r
t
  = radius of gyration of the compression flange taken about the vertical axis 
t
f
 = flange thickness  
t
fc
 = thickness of the compression flange  
t
s
 = transverse web stiffener thickness  
t
t
 = thickness of the tension flange  
t
w
 = web thickness  
x = normal distance to the x-axis 
y = normal distance to the y-axis 
y
NA
 = distance from web mid-depth to neutral axis 
y
SC
 = distance from neutral axis to shear center 
?  = longitudinal strain 
?
eng
 = engineering strain 
?
st
 = strain at the onset of strain hardening 
?
true
 = true strain 
?
u
 = strain at tensile strength 
?
f
 = compression flange slenderness parameter 
?
pf
 = limiting slenderness parameter for compact flange local buckling behavior 
?
rf
 = limiting slenderness parameter for non-compact flange local buckling 
behavior 
b
?  = curvature factor for non-compact flange strength 
w
?  = curvature factor for non-compact flange strength 
w1
?  = curvature factor for non-compact flange strength 
w2
?  = curvature factor for non-compact flange strength 
b
?  = curvature factor for compact flange strength 
w
?  = curvature factor for compact flange strength 
?
eng
 = engineering stress 
?
sy
 = static yield strength 
?
true
 = true stress 
?
u
 = tensile strength 
xvii 
?
z
 = stress in the z-direction 
?
0.2%
 = offset yield strength 
?
f
 = resistance factor for flexure
xviii 
Chapter 1.  Introduction 
1.1 Background/Problem 
Horizontally curved girder bridges represent approximately 30% of the steel bridge 
market in the United States today. The current market share is a significant increase from 
25 years ago when these types of structures represented only a single digit percentage of 
the market. The increased use of this bridge type reflects the significant attention that is 
now given to land usage, aesthetics, and complex roadway and viaduct alignments that 
are mostly found in and around urban centers.  
The first significant investigations into the design and analysis of horizontally curved 
steel I-girder bridges began in 1969. At that time, the Federal Highway Administration 
(FHWA) formed the Consortium of University Research Teams (CURT). This group 
consisted of researchers from Carnegie-Mellon University, the University of 
Pennsylvania, the University of Rhode Island, and Syracuse University. CURT?s 
analytical and experimental work, combined with research efforts conducted at the 
University of Maryland, formed the basis for the American Association of State Highway 
and Transportation Officials? (AASHTO) Guide Specification for Horizontally Curved 
Highway Bridges (herein referred to as the Guide Specifications). This document was 
first issued in 1980 and was subsequently updated in 1993 and 2003. However, the 
document was never adopted by AASHTO as a full or standard specification because of 
knowledge gaps that existed in the entire design and analysis processes for this type of 
bridge.  
1 
In the early 1990s, the Curved Steel Bridge Research Project (CSBRP) was initiated. 
This project focuses on the area of horizontally curved steel girders. The research project 
participants include the FHWA, the Transportation Research Board (TRB), and the 
participating states of the Highway Planning and Research (HP&R) study. The primary 
objective of this research study is to better define the behavior of such bridges. The study 
involves theoretical work leading to the development of refined predictor equations and 
to the verification of those equations through linear and non-linear analyses and 
experimental testing.  
The CSBRP effort was largely based on recommendations of the Structural Stability 
Research Council?s (SSRC) Task Group 14 [SSRC (1991)]. Several priorities were 
identified for research by the SSRC group: 
? develop an understanding of construction issues including fabrication and 
erection 
? determine nominal bending and shear strengths 
? understand the behavior of diaphragms, cross-frames, and lateral bracings 
? define the effect of lateral loads 
? determine the level of analysis needed for analyzing curved girders 
? determine serviceability issues  
The goals of the CSBRP were to address these knowledge gaps, to generate enough 
information to improve the current Guide Specifications, and to incorporate curved steel 
girder design provisions into the AASHTO LRFD Bridge Design Specifications (herein 
referred to as the LRFD Specifications). 
2 
The Guide Specifications is the only consensus document available to the bridge 
community that supports the design and construction of horizontally curved steel I-girder 
bridges. In its current form, the guide is disjointed and difficult to follow. The 
commentary in the guide is incomplete and lacks the necessary details needed to explain 
the development of many of the provisions. Many of the original key references are not 
available to most designers. And when the references are available, they require a great 
deal of interpretation. The general lack of comprehensible support material available for 
understanding and clarifying the Guide Specifications can lead to misinterpretation of its 
provisions. This misinterpretation may result in overly conservative and uneconomical 
structures or in the development of bridges that do not meet the intended safety levels. 
This economic and safety uncertainty on structures that represent 30% of the steel bridge 
market is significant. 
In 1994, AASHTO published the first edition of the LRFD Specifications. These 
provisions introduced the load and resistance factor design method for the design of 
tangent girder bridges to the bridge engineering community. Since then, AASHTO, 
through the National Cooperative Highway Research Council (NCHRP), has been 
broadening the scope of the LRFD Specifications to make a fully integrated specification 
for the design of all common bridge types. The FHWA mandated that beginning in 2007 
all bridges that are built with Federal Aid money must use the LRFD Specifications as 
the governing design provisions. To incorporate the horizontally curved girder bridge 
design into the LRFD Specifications, statistically significant data are needed to produce 
calibrated and refined predictor equations. Calibrated equations will produce a uniform 
3 
level of safety across bridge types and will improve the community?s ability to design 
and build economic structures.  
A review of the existing experimental data reveals a lack of appropriate results for 
inclusion into the statistical models. Figure 1-1 shows flange and web slenderness 
combinations from all previous experimentation that produced a flexure or flexure-shear 
combination failure. Figure 1-2 restricts the previous experimental data to just those tests 
performed in uniform bending. Figure 1-3 eliminates tests performed with unrealistic 
boundary conditions from the Figure 1-2 data. All of these figures show the design limits 
for both web and flange compact and non-compact behavior. The limited data shown in 
Figure 1-3 represent two points with slenderness combinations far from those that 
represent current best practice. These data cannot realistically be used to anchor the large 
analytical parametric study needed to produce statistically relevant information for use in 
the formulation and calibration of predictor equations for the LRFD Specifications. 
 
0
50
100
150
200
250
300
0 5 10 15 20 25 30 35 40
Compression Flange Slenderness
W
e
b
 S
l
en
der
n
es
s
CURT P2(PB)
CURT P3(PB)
Nakai(PB)
CURT P1
CURT P2
CURT P3
Fukumoto
Shanmugan
23 18 
Compact
Flange 
Limit 
Non- 
Compact
Flange 
Limit 
Non-Compact Web Limit 
Compact Web Limit
 
Figure 1-1:  All Previous Experimental Slenderness Combinations 
 
4 
 
0
50
200
W
b
 S
l
en
e
r
n
100
150
300
0 5 10 15 20 25 30 35 40
ession Flange Slenderness
e
d
ess
250
Compr
CURT P2
CURT P3
Nakai
23 18 
Limit 
Non-Compact Web Limit 
 
Figure 1-2:  Slenderness Combinations From All Previous Uniform Bending Experiments 
 
Compact
Flange 
Limit 
n- 
Compact
Flange 
No
Compact Web Limit
 
0
50
150
200
250
300
W
e
b S
l
e
r
n
e
100
0 5 10 15 20 25 30 35 40
ge Slenderness
nde
s
s
Compression Flan
CURT P3
23 18 
Compact Non- 
Limit 
Non-Compact Web Limit 
Compact Web Limit
 
F tions 
element based study. 
Flange 
Limit 
Compact
Flange 
igure 1-3:  All Previous Uniform Bending Experiments with Realistic Boundary Condi
 
A large suite of experimental tests with the appropriate parameters would obviously 
be cost prohibitive for the community. Therefore, a focused and deliberate experimental 
effort is needed to supply significant and sufficient physical results to anchor a finite 
5 
1.2 Objective and Scope 
The objective of this experimental effort is to determine the flexural resistance of a 
 White et al. (2001), herein referred to as the Unified Design 
Method. 
variety of full scale horizontally curved girder components with realistic boundary 
conditions. The test matrix will examine the influence of (i), compression flange 
slenderness, (ii), web slenderness, and (iii), web stiffening on moment capacity. These 
results will be used to validate a computer model similar to that used to produce the 
hundreds of virtual test results that form the statistical basis of the recently developed 
predictor equations by
1.3 Previous Experimental Work 
With a few exceptions, previous investigations have focused on single, scaled, 
doubly-symmetric horizontally curved I-sections tested with artificial torsional restrai
provided at the ends. In some cases, this restraint was full fixity of the end. In other cases,
a sole restraint against lateral movement provided at the end was used. In either ca
end conditions of the girders in these investigations did not accurately represent the 
conditions produced by a horizontally curved girder bridge.  
Recently, several researchers [Linzell (1999), White et al. (2001), Grubb and Ha
Zureick et al.(1994)] reviewed, critiqued, and synthesized most of the previous work
this area as part of the FHWA CSBRP. The following sections will highlight previous 
experimental work performed on horizontally curved steel I-girders. An emphasis is 
nt 
  
se, the 
ll, 
 in 
placed on those individual experiments from each investigation that produced a bending 
capacity type failure. 
6 
1.3.1 CURT Tests 
d t Carne niversity performed most of the experimental 
testing done for the CURT Pro tests are documented in great detail in Mozer 
ulver (1  Mozer, Oh nd Mozer, C er 
5). A tota 22 failure loa ts on 11 plate I-girder specimens are described in the 
CURT Project. Twelve of thes ced information on moment or 
nt-shear capacity of horizontally curved girders (refer to Table 1-1 for a list of 
s). Data are  erved elastic d 
n calculations b  on analytic
ped as f the C s include d 
uter aide deling analy ecause neither the finite elemen ware 
he microc uter were re  or available tools to the researc me. 
Culver an  Mozer a gie Mellon U
ject. These 
and C 975); l nd Culver (197son a 5); a ook and Culv
(197 l of d tes
e experiments produ
mome
selected parameter  presented comparing obs behavior an
ultimate load capacity with predictio ased al methods 
develo part o URT ect. These inves Proj tigation d very limite
comp d mo ses b t method soft
nor t omp liable hers at that ti
7 
 
 Specimen ID Curvature 
l
R
 
Compression 
Slenderness 
Flange 
fc
fc
t
b
 
Web 
Slenderness 
w
t
D
 
Overall 
mm (in.) 
Depth,  
CURT P1 Tests (1970) 
C8(2) 18.6 20.3 141 474.7 (18.69) 
C9(2) 6.3 20.3 150 476.0 (18.74) 
D13 7.4 23.4 150 474.5 (18.68) 
D14 7.4 23.0 149 476.0 (18.74) 
CURT P2 Tests (1971) 
L1(A) 9.9 15.2 149 473.7 (18.65) 
L2(A) 10.1 15.4 151 475.2 (18.71) 
L2(B) 10.1 15.4 151 475.2 (18.71) 
L2(C) 10.1 15.4 151 475.2 (18.71) 
CURT P3 Tests (1973) 
GI(3) 10.0 7.82 150 482.1 (18.98) 
GI(4) 10.0 7.82 150 482.1 (18.98) 
GI(5) 10.0 7.82 150 482.1 (18.98) 
GO(8) 10.6 15.7 58 476.8 (18.77) 
Fukumoto and Nishida Tests (1980) 
AR1 13.6 12.1 45 268.2 (10.56) 
AR2 29.8 12.2 44 268.5 (10.57)
AR3 99.8 12.1 44 268.5 (10.57) 
BR1 12.1 12.0 45 267.0 (10.51) 
BR2 25.8 12.1 44 268.2 (10.56) 
BR3 172 12.0 45 267.0 (10.51) 
Nakai et al. Tests (1985) 
M1  15.0 178 824.0 (32.44) 
M2 14.7 15.2 177 821.4 (32.34)
M3 12.3 15.0 178 821.7 (32.35) 
M4 5.2 15.0 177 821.7 (32.35) 
M5 5.3 15.1 248 824.0 (32.44) 
M6 5.4 15.3 257 821.4 (32.34) 
M7 5.3 15.1 178 824.0 (32.44) 
M8 4.7 7.6 175 824.0 (32.44) 
M9 4.5 15.0 175 824.2 (32.45) 
Shanmugan et al. Tests (1995) 
CB1 5.3 10.27 35.3 306.6 (12.07) 
CB2 7.9 10.27 35.3 306.6 (12.07) 
CB3 13.2 10.27 35.3 306.6 (12.07) 
CB4 19.7 10.27 35.3 306.6 (12.07) 
CB5 39.5 10.27 35.3 306.6 (12.07) 
CB6 18.9 10.27 35.3 306.6 (12.07)
CB7 2.0 10.27 35.3 306.6 (12.07) 
WB1 5.3 10.33 35.25 306.1 (12.05) 
WB2 13.2 10.33 35.25 306.1 (12.05) 
WB3 39.5 10.33 35.25 306.1 (12.05) 
 
Flexural/Shear Failures 
Table 1-1:  Summary of Previous Experimental Work That Produced Flexural or 
8 
Mozer and Culver (1975) contains the results from static load tests on seven scaled, 
doubly symmetric, welded plate girders (herein referred to as the P1 tests). The primary
focus of this investigation was to determine the influence that a variety of geometric
stress parameters had on flange local buckling for this type of girder. However, onl
 
 and 
y three 
of t
ft) 
meters for 
l 
f local flange buckling compared 
fav
ign 
can be conservatively used for horizontally curved girder design if the flanges are cut 
hese tests produced that failure mode. One experiment displayed a moment/shear 
interaction failure while the remaining investigations produced shear failures.  
The test components had radii that ranged from 115.2 m (378 ft) to 339.2 m (1,113 
and were either heat curved or cut curved to produce their final horizontal geometry. 
Flange and web steels were ASTM A36 and AISI 1008, respectively. Other geometric 
variables included compression flange slenderness, web slenderness, and transverse 
stiffener spacing. Table 1-1 contains a specimen matrix of limit geometric para
the specimens from this set of tests that exhibited flexural or flexure-shear interaction 
failure.  
The P1 test girders had 3.0 m (10 ft) arc length spans that were supported on radia
aligned rollers at both ends. The girder ends were also restrained from lateral translation 
and twisting by radial aligned bracing. Load was applied eccentrically at mid-span to 
produce a desired combination of warping and primary bending stresses in the 
compression flange. All specimens had 1.5 m (5 ft) unbraced lengths. 
The results of the P1 tests that failed as a result o
orably with predictions made using equations based on the Elastic Beam theory 
developed by Culver and McManus (1971). The authors concluded that the 
contemporaneous compression flange slenderness limitations for straight girder des
9 
cur  
 
slen
 
 
 a desired ratio of warping to bending stress. These tests were done with a 3 m 
(10  at one end of the overall 4.6 
m (15 ft i
designed to produce either a shear failure (L1 series) or a flexure-shear interaction failure 
(L2 seri  
The  sistent with those employed 
for the P te perties are 
ved, and first yield is defined at the flange tip where the primary bending and warping
stresses are additive. If the design preference was to neglect consideration of warping
stresses, then the authors recommended limiting curved girder compression flange 
derness to the contemporaneous straight girder compact section requirements. 
Mozer, Ohlson, and Culver (1975) investigated two horizontally curved I-girders, 
each tested with three separate loading arrangements (herein referred to as the P2 tests). 
The primary difference between the two specimens, designated as L1 and L2, was the 
transverse stiffener detail that was used. One focus was to determine the effects of partial
versus full depth stiffeners on flexural resistance. Each specimen was failed using three
loading regimes, A, B, and C. The A regime consisted of 4 point loading applied at the 
third points along the 4.6 m (15 ft) arc length of each simple span girder. The 
arrangement was designed to produce a flexural failure in the compression flange within 
the constant moment region of the girder. The B regime and C regime were nearly 
identical, involving a single point load located eccentrically similar to the P1 tests to 
produce
 ft) arc length simple span leaving a 1.5 m (5 ft) overhang
) g rder. All tests had 1.5 m (5 ft) unbraced lengths. The experiments were 
es) in the girder panel adjacent to the load.  
 P2 tests used bearing, bracing, and load details con
1 sts. The P2 girders had a 15.2 m (50 ft) radius. Relevant girder pro
tabulated in Table 1-1 for the four tests in which flexural was involved in failure.  
10 
The author?s P2 test conclusions for flexural resistance supported those conclusions 
made in the P1 tests. The conclusions also indicated that adequately braced compact 
compression flanges were capable of developing significant post-yield bending capacity. 
he 
5.7 m 
 
ich detail a capacity failure. Tests 5 
and te 
 
e inside 
The P3 test program included the following objectives: 
? determining the bending strength of a curved plate girder in a curved bridge 
system 
? monitoring the inelastic redistribution of load within the bridge system 
ining the capacity of curved web plates 
curved I-girder bridge behavior when the structure is an open grid, the Culver-McManus 
Mozer, Cook, and Culver (1975) investigated a pair of doubly symmetric I-girders 
that were concentrically curved, transversely spaced at 0.9 m (3 ft), and connected by five 
rigid cross frames and two rigid end diaphragms (herein referred to as the P3 tests). T
P3 test frame had a centerline span of 4.7 m (15.5 ft) and a radius of curvature of 1
(51.5 ft). The girder ends were held down to prevent unpredictable uplift during testing.
Eight individual test results are reported, six of wh
 8 used third point loading to produce a constant moment region over an approxima
1.5 m (5 ft) unbraced length and local flange buckling failures in the inside (GI) and 
outside (GO) girders respectively. The remaining tests used a single applied load at mid-
span. Tests 3 and 4 produced flexure-shear interaction failures at different locations of the
inside girder. Test 1 and Test 2 produced shear failures on different panels of th
girder. 
? determ
? monitoring the influence of transverse stiffeners on web behavior  
Among other conclusions, the researchers stated that cross-frames play a major role in 
11 
equations [Culver and McManus (1971)] are conservative when used to calcula
resistance, and that a considerable degree of reserve streng
te flexural 
th above initial yield exists in 
cur
ed 
ers. 
e 
al 
g 
 
con
1.3.2 University of Maryland Tests 
Contemporaneous to the CURT program, several experimental studies were 
conducted at the University of Maryland on the behavior of curved I-girders, box-girders, 
and systems as part of a large experimental and analytical program titled The Design of 
Curved Viaducts. This program was co-sponsored by the Maryland State Highway 
Administration and the FHWA. The program?s objectives were to produce analytical 
tools for the design and evaluation of curved girder bridges. A series of progress and 
ved plate girders with compact compression flanges. 
To prove their analytical methods and the computer analysis program developed as 
part of the CURT program, Brennan and Mandel (1971, 1974) built and elastically test
small-scale similitude structures. These small-scale structures were used to develop 
influence lines for deflection, moment, and shear for each girder of the structures 
modeled. The experimental results were compared with the computer generated results 
with good agreement reported by the research
Shore and Lapore (1975) built several very small curved girder and curved bridg
models that were exercised elastically to produce data that would support their numeric
efforts. Their report details the experimental work and results as well as the work bein
done to develop a finite element approach to curved girder analysis. However, the report
does not draw conclusions. The researchers planned to report comparisons and 
clusions in a follow-up effort. 
12 
interim reports were issued to the sponsoring agencies detailing the individual 
experimental and analytical efforts of the larger program. 
Spates and Heins (1968) used four individual elastic loadings to evaluate the be
of a single curved beam cold rolled to a 15.2 m (50 ft) radius. The arc length of the span 
was 9.1 m (30 ft), and the ends were designed to be fixed with respect to bending and 
torsion. The steel section used, S180x22.8 (S7x15.3), had a nominal yield strength of 2
MPa (30 ksi). Load was applied by radially cantilevering
havior 
07 
 lead weight off the beam at 
mid
 
estigators? 
red
 ft) single composite girders with varying 
end conditions and slab thickness. Torsion was applied at one end of the girder using a 
force couple while the other girder end was either pinned or fixed. All tests utilized a 0.3 
-span. Strain and deflection information was compared with analytical predictions 
from equations developed for single girders. 
The major problem encountered during this investigation was the experimental 
control or establishment of the desired end conditions. Even with extensive effort, the
experimental data showed that truly fixed ends were not achieved. The inv
uction of data and analytical comparisons lead them to conclude that end conditions 
can be very significant on curved girder plane bending behavior of a single girder. 
In the analytical portion of their investigation, Spates and Heins demonstrated how 
predictor equations developed for a line girder design were very conservative when used 
to design the individual girders of a curved bridge system. 
Kuo and Heins (1971) conducted experimental testing to determine the torsional 
rigidity, warping behavior, and failure mode of composite I-girders subject to torsion. 
Four experiments were performed on 5.5 m (18
13 
m (1 ft) deep wide flange section and a 0.9 m (3 ft) wide composite slab with a 51 mm (
in.), 76 mm (3 in.), 102 mm (4 in.), or 152 mm (6 in.) thickness. 
In all four tests, the results indicated that the concrete slab dominates torsional 
behavior and that warping effects were negligible for t
2 
he slab, but were very significant 
for ause 
ory 
 the 
ctors and can be neglected if the source of the effects is from vertical loads 
acti he 
ction. 
sign 
1.3.3 Japanese Tests 
Two major experimental programs were conducted in Japan to support the Hanshin 
Expressway Corporation?s Guidelines for the Design of Horizontally Curved Girder 
the girder. Rupture of the concrete slab due to diagonal tension was the reported c
of failure for each experiment. Analytical comparisons using the Thin-Walled the
yielded excellent correlation with experimental results. 
The main objective of Colville (1972) was to develop appropriate design criteria for 
welded stud shear connectors in curved composite sections. The experimental program 
consisted of four individual tests on 5.4 m (17.75 ft) arc length horizontally curved and 
composite concrete slabs and I-beams. Test parameters included radius of curvature, 
girder size, number of shear connectors per section, and type of loading.  
Colville concluded that the effects of torsion and warping are not significant on
shear conne
ng on curved members. However, the design procedure developed does consider t
transverse shear forces that result from the bending and warping of the composite se
The design procedure does converge to the straight girder procedure when the radius 
becomes large. The reader is also reminded that the data used to develop the de
procedure were generated from composite slabs in compression; therefore, the results 
may not be valid in negative moment regions. 
14 
Bridges. These guidelines and the Guide Specifications are the only two specifications 
for horizontally curved steel bridges in the world. While most of the literature associated 
wit hite et 
Load was supplied with a gravity simulator 
at mid-span; although, the details of the system used were not reported. These specimens 
had a nominal compression flange slenderness of 12 and web slenderness of 45, which is 
very unrepresentative of bridge girders. The girders had an overall depth of less than 279 
mm (11 in.) and had radii of 23.2 m (76 ft) to approximately 483 m (1,584 ft). Table 1-1 
contains parameters for individual specimens. The experimental results showed good 
agreement to both the theoretical solution presented and the approximate solution 
proposed. 
Nakai et al. tested nine scaled doubly symmetric components. Parameters for all 
specimens, M1 through M9, are included in Table 1-1. The girders were tested for 
flexural capacity in near uniform negative bending with the ends completely restrained 
from translation or out-of-plane rotation. All but one of these specimens had a 
compression flange slenderness of 15, and most had a web slenderness of approximately 
175. Specimen M8 had a compression flange slenderness of 7.6. Two specimens, M5 and 
M6, had a web slenderness of approximately 250. One of these pair of specimens 
employed a longitudinal stiffener to stabilize the web while the other did not in an effort 
to quantify the effect of that web attachment on bending capacity. A reduction in capacity 
h these programs is published in Japanese, other researchers [Linzell (1999), W
al. (2001), Grubb and Hall] have reviewed this work. 
Fukomoto and Nishida (1981) tested six simple-span scaled doubly symmetric I-
girders that had laterally restrained ends that were fabricated out of steel with an 
approximate 235 MPa (34 ksi) yield strength. 
15 
com er analytical prediction was reported for these 
test
f 
the difference in behavior between hot-rolled 
beam ntal 
ing. Also, nearly a dozen field test studies 
have reported m
pared with an equivalent straight gird
s. 
While the Nakai tests were conducted with girders of appropriate slenderness 
combinations and section depths for bridges, the specimens had a span to depth ratio o
approximately 2.5. At this ratio, an assumption is made that the highly restrained girder 
ends affected the demonstrated flexural resistance. At the very least, the configuration 
tested relates poorly to bridge girder realties. 
1.3.4 Other Experimental Testing 
Shanmugam et al. (1995) compared experimental results with predictions made with a 
refined finite element model. The experimental program consisted of 10 tests to failure of 
single simple-span curved girders with various unsupported lengths and end conditions 
fabricated out of steel with a nominal strength of approximately 276 MPa (40 ksi). The 
primary focus of the testing was to contrast 
s and welded plate girders. All specimens were cold-bent into their final horizo
curvature and had load applied at a single point. These girders were very small with an 
overall depth of about 305 mm (12 in.). 
Daniels et al. (1979) at Lehigh University primarily investigated fatigue issues on 
horizontally curved steel I-girders. Nakai and Kotoguchi tested a pair of horizontally 
curved I-girders for systematic lateral buckl
ostly limited elastic behavior data acquired primarily during the 
construction of horizontally curved steel I-girder bridges or from structures already in 
service. 
16 
1.4 Strength Predictor Equations 
The current Guide Specifications (2003) uses governing equations for flange stress 
that are slight modifications of the original work by Culver and McManus (1971) that 
was sponsored by the CURT program. Culver and McManus built on the First-Order 
theory for determining the stresses and deformations in horizontally curved beams
normal to their plane of curvature. This theory was first developed by Vlasov (1961) and 
Dabrowski (1968). The derivation of the Culver-McManus equations was based on 
doubly-symmetric and prismatic curved I-girders with compact and non-compact 
compression flanges that were braced at a un
 loaded 
iform spacing and subject to a constant 
ver  
 
cts 
ted for by the ? -factors defined in Appendix B. Culver and McManus 
developed the ? -factors by performing approximate second order elastic analyses on a 
range of I-girder geometric parameters, subtracting first order behavior from the results, 
and fitting a curve through the findings.  
The ? -factors are also the weakness of the Guide Specifications. Their derivation 
includes many assumptions that cannot be uncoupled from the results. A predictor 
equation is also used for tangent girder lateral torsional flange buckling (Equation B-3 in 
Appendix B) that has since been replaced in the AASHTO Standard Specifications for 
tical bending moment. The Guide Specifications? equations have been extended to be
valid for singly symmetric I-girders by Hall and Yoo (1998). The Guide Specifications?
provisions that apply to the design of non-composite I-girders in flexure are summarized 
in Appendix B. 
The strength of the Guide Specifications? provisions is that an engineer is only 
required to produce a first order analysis of the structure for design. Second order effe
are accoun
17 
the Design of Highway Bridges and LRFD Specifications for straight girder design with a 
more accurate formulation. The ? -factor equations fail to recognize the amount of rigor 
emp
 
n 
nd, they can be used to design for lateral loading from all 
sou
lly, 
act 
loyed in the structural analysis process forcing a common design procedure for all 
levels of investigation. Also, a careful review of the ? -factor formulations by Hall et al. 
(1999) has revealed some inaccuracies in how warping stresses are accounted for 
resulting in an unintended doubling of their effect. Finally, the ? -factor equations do not 
converge to any resemblance of the tangent girder design equations when the radius of
curvature becomes very large. They also include a step discontinuity in behavior betwee
compact and non-compact flanged sections. 
The Proposed Unified Design Method provisions are also summarized in Appendix 
B. This design method has several advantages. First, the provisions are independent of 
the analysis method used. Seco
rces, not just vertical loading on horizontally curved girders. Third, the design 
equations reduce to the tangent girder design equations when the radius is large. Fina
this method has eliminated the step discontinuity between non-compact and comp
behavior.
18 
Chapter 2.  Experiment Design 
ogy on the philosophy behind the Curved Steel 
Bridge Research Project (CSBRP) including the development of the experiment design 
was reported by Grubb and Hall. A review of the limited curved girder experimentation 
to date demonstrates the significant challenges inherent with producing relevant capacity 
data for this very complex structure type. As previously mentioned most documented 
experimental investigations have been tests on individual, doubly symmetric I-sections 
with proportions or scale that do not represent the family of girders typically used for 
bridges. Also, these investigations generally assumed some level of restraint for the ends 
of the test girder and at bracing or loading locations that does not replicate the structural 
behavior of a bridge system.  
t of 
d to live-load stresses in the 
gird
A very detailed and complete chronol
Full scale testing eliminates scaling issues. In many of the previous tests described 
above, girders were fabricated from very thin plate and sometimes from sheet steel. 
Steels in this thickness range retain very high levels of residual stress and distort 
significantly out-of-plane as a result of the high heat that they are subjected to as par
any welding process. These stresses and distortions can cause premature yielding or 
buckling that can decrease the ultimate capacity of a section. Also, many structural 
relationships are not linearly dependent. For instance, in dynamic tests, dead load?often 
called compensatory loading?needs to be added to a scaled bridge system without 
adding stiffness to produce a representative ratio of dead-loa
ers or for added inertia. In static structural experimentation, the desired moment/shear 
19 
capacity ratios are difficult to maintain using scaled geometric properties. The full-scale 
structure used for this experimental program mitigates all of these concerns. 
2.1 Test Frame Concept 
le 
demonstrated the highly non-linear behavior of the post-peak single girder. In the final 
analysis of the project team, testing of a three-girder system was necessary to avoid the 
limitations and weaknesses of previous work and to safely produce the quantity and type 
of physical data needed within the financial means provided. 
The CSBRP team employed the following philosophy to develop the test frame: The 
test frame needed to be flexible enough to accommodate testing components that would 
be subjected to a constant moment (pure bending) and moment-shear interaction, and the 
test frame had to be adaptable for a composite bridge test. The method for both sets of 
component tests was to insert a test specimen into the exterior test frame girder and 
connect it to the test frame with bolted splices and cross-frames. The test frame girders 
and the cross-frames were proportioned using a variety of materials and sections to 
remain elastic while providing realistic interaction to the test component as it experienced 
significant inelastic deformation. Once a test was finished, the component was replaced 
and the process was repeated until the series was complete. 
The CSBRP team developed the three-girder bridge system shown in Figures 2-1 and 
2-2. The span of the test frame was limited to 27.4 m (90 ft) because the FHWA 
The feasibility of single girder testing was considered for the CSBRP. Considerab
analytical effort was focused on designing a set of bracing, loading and bearing details 
that could mimic the boundary conditions and internal load sharing of a bridge system, 
particularly the distribution of lateral flange bending moment. These analyses 
20 
21 
conducted additional unrelated experimental research in the Structures Laboratory during 
the tenure of the CSBRP. A radius and unbraced length of 61.0 m (200 ft) and 4.57 m (15 
ft) respectively, measured along the centerline of the middle girder were selected to test 
the upper range of the practical limits of 
R
l
 for a structure of this span. Once a span, 
radius and unbraced length were determined, the project team solved for an overall girder 
depth for the test frame using best practice design tools. Figure 2-3 shows the test frame 
in the FHWA Structures Laboratory configured for one of the bending component tests. 
25'-4 3/4"
R
=
1
9
1
'
-
3
"
R
=
200'
-
0
"
R
=
2
0
8
'
-
9
"
12 SP
ACES
@ 7'-6" = 90'-0" ? G
IRD
ER 
G2
MEASURED A
LONG
76L
5L
4L
3L
2L
1L
6R
5R
4R
3R
2R
1R
CROS
S FRAMING SPACIN
G
1
'-
0
"
 T
Y
P
.
C
 R
E
A
C
T
IO
N
L
C
 R
E
A
C
TI
O
N
1
'-
0
"
 T
Y
P
.
L
GIRD
ER G
290'-0
" MEASU
RED ALONG ?
LA
TE
R
LA
L
B
R
A
C
IN
G
 (T
YP
.)
30
'-3
 3
/1
6"
4'-0 1
/16"
C OF BOLTED
FIELD SPLICE
L
4'-0 1
/16"
30
'-3
 3
/1
6"
28
'-6
 1
/4"
28
'-6
 1/
4"
32'-11 1/2"
26
'-9
 3
/8
" 26'
-9
 3
/8"
32'-6"
C O
F L
OA
D
PO
INT
L
C O
F L
OA
D
PO
INT
EXAMPLE CROSS-FRAM
E
DESIGNATION: S - 2L
CROSS FRAME LINE
SOUTH BAY
EXAMPLE LATERAL BRACING
DESIGNATION:   LAT - SE
SOUTH BAY EAST END
LATERAL BRACE
L
C
R
O
S
S
 F
R
A
M
E
L
IN
E
S
L
C
 G
IR
D
E
R
 G
3
C
 G
IR
D
E
R
 G
2
L
C
 G
IR
D
E
R
 G
1
L
8
'
-
9
"
8
'
-
9
"
S
OU
T
H
 
B
A
Y
N
OR
T
H
 
B
A
Y
CR
OS
S
FR
AM
E 
(T
YP
.)
 
Figure 2-1:  Plan View of Test Frame
 
L
C G2
L
C G1
4
'
-
0
"
8'-9" 8'-9"
NORTH BAY SOUTH BAY
C G3
L
 
Figure 2-2:  Cross-Section of Test Frame at a Cross Frame Location 6L 
 
 
F  T es m th W tr yt Fra e in e FH A S uctures Laboratorigure 2-3:  he T
 
The exterior girder on the inside radius of the test frame is herein referred to as G1. 
G1 is doubly symmetric and prismatic with flange plates measuring approximately 27 
mm x 406 mm (1 1/16 in. x 16 in.) and a web plate measuring approximately 11 mm x 
1,219 mm (7/16 in. x 48 in.).  
The interior girder of this three-girder system, referred to as G2, is also doubly 
symmetric and prismatic. The flange plates are approximately 30 mm x 508 mm (1 3/16 
in. x 20 in.), and the web plate is approximately 13 mm x 1219 mm (? in. x 48 in.). 
The exterior girder on the outside radius of the test frame, G3, is made up of three 
doubly symmetric and prismatic sections connected by two bolted splices. The flange 
plates of G3 measure approximately 57 mm x 610 mm (2 1/4 in. x 24 in.), and the web 
plate is approximately 13 mm x 1219 mm (? in. x 48 in.). This girder was fabricated in 
three sections so that the center section could be replaced with each of the bending or 
moment-shear interactio o develop the full 
plastic moment of the strongest bending component (component B6) without slip. 
ombinations slightly exceed the limits in 
the ile 
n components. The splices were designed t
With the overall depth of the girders established, the matrix of test specimens was 
easily developed for both the bending component and moment-shear interaction 
component series. The tested parameter combinations were selected to best fulfill the 
objective and to provide a broad enough set of information on which the analytical work 
could be based. Figure 2-4 shows how the slenderness combinations for the bending 
component series of tests compare with the current Guide Specifications compact and 
non-compact limits. The selected slenderness c
figure because the Guide Specifications slenderness limits were altered in 2003 wh
the test matrix was originally designed using the 1993 version of this document. 
 25
Compression Flange Slenderness
0 10203040
W
eb S
l
er
ness
end
0
50
150
250
100
200
300
Compact 
Flange 
Limit
Non-Compact Web Limit 
Non-Compact 
 
. 
he 
 
 
ter of 127 mm (5 in.) and a wall thickness of 6 mm (? 
in.). Th n its flexural capacity approximated that of the 
mem
determined by two independent methods throughout the elastic range of behavior. These 
Flange 
Limit
Compact Web Limit 
 
Figure 2-4:  Bending Component Test Matrix 
 
The test frame utilized the ?K-type? cross-frame and diaphragm shown in Figure 2-2
However, to reduce the instrumentation demand and to ease interpretation of results, t
single-leg angles that typically are used to make up horizontal and inclined legs of the
cross-frames and diaphragms were replaced with round structural steel tubing. The tubing
used had a nominal outside diame
is tubi g size was selected because 
bers used in a more conventional design. 
Use of the test frame also provides for redundancy in the analysis of the inelastic 
behavior of the test components. Flexural resistance of the test components can be 
 26
analysis methods, called the Direct Method and the Indirect Method, rely on different 
instrument subsets from the extensive instrumentation plan (800+ channels of data 
acquisition) for their calculation. The instruments are primarily made up of strain, load 
and t 
 
2.2 Component Test Matrix
 displacement indication devices and are applied to strategic locations within the tes
frame and the bending components. Besides insuring an appropriate interpretation of
results, the experiment data were used to validate a fully material and geometric non-
linear finite element model. This model incorporates the as-built steel plate widths and 
thicknesses, and steel plate specific material properties based on the large suite of 
materials tests performed as a part of this project.  
 
The test frame was designed to be versatile. By reconfiguring the load and reaction 
locations, the test component location in G3 could be subjected to either constant moment 
(referred to herein as the bending component series of tests) or to a combination of high 
moment and high shear (referred to herein as the moment-shear interaction component 
series of tests). The bending component series included seven individual component 
specimen tests and are the primary subject of this dissertation. The moment-shear 
component series included individual tests conducted on four component specimens that 
are the subject of another report. 
erlapping set of parameters by incorporating characteristics shared by 
other members of the test matrix. These shared characteristics were intended to produce 
2.2.1 Bending Component Series 
Each of the bending components, identified as B1 through B7, was designed to 
investigate an ov
 27
suff
The B1 web design was also used for components B5, B6 
and
oubly mpon 2 and esi ith a thic  
plate than B1 lowering their web slenderness to 128.0. The differing characteristic 
between B2 and B3 is how their web plate was stiffened. While the web plate of 
component B2 had transverse stiffeners spaced again at approximately 0.98D, the web 
plate of component B3 was left unstiffened between cross-frame locat
in a  3.92D for onent B3
C onent B4 designed ession f slend  of 23.
section was made s ymmetri a larg ang rea  
compression of approximately 0.62D, which re  web slenderne
The doubly symmetric component B5 was d ith a flange slende  17.5, 
which is close to the compact flange 
Specifications.  
icient information to quantify the effects of compression flange slenderness, web 
slenderness and transverse web stiffening on the flexural capacity of horizontally curved 
steel I-girders. 
Component B1 was designed doubly symmetric with a flange slenderness, b
f
/t
f
, of 
23.3, a web slenderness, 2D
c
/t
w
 or for doubly symmetric sections D/t
w
, of 153.6 and 
transverse stiffener spacing, d
o
, of 0.98D. These slenderness values slightly exceed the 
limits, 23 and 150 respectively, included in the AASHTO Guide Specifications for a 
stiffened non-compact girder. The B1 compression flange design was also used for 
components B2, B3 and B4. 
 B7. 
The d  symmetric co ents B B3 were d gned w ker web
ions. This resulted 
d
o
 of  comp . 
omp had a  compr lange erness 3, but the 
ingly s c with e tension fl e to c te a depth of web in
sulted in a ss of 189.2.  
esigned w rness of
limit of 17.0 specified in the AASHTO Guide 
 28
Com c with compact flanges. B6 
was f 
n flange 
of e n 
 
 
s of the bending component test series are compiled in Table 2-1. 
Test 
Co
Compression 
Slenderness 
ponent B6 was also designed to be doubly symmetri
 detailed with a flange slenderness of 13.6, which is well within the compact range o
the AASHTO Guide Specifications. 
The singly symmetric component B7 was designed with a slender compressio
qual area to the tension flange. This flange combination generates a depth of web i
compression that is very close to the mid-height of the girder maintaining the desired web
slenderness of 153.6. This test component was designed to investigate the effects of a 
compression flange slenderness of 33.6, which is well in excess of the AASHTO Guide
Specifications? limit of 23.  
The target parameter
Web 
 
mponent Flange 
fc
fc
t
b
 
Slenderness 
w
c
D2
 
mm 
 
t
Overall 
 
(in.) 
 
Panel 
t 
Ratio 
Notes 
Depth Aspec
B1 23.3 153.6 1257 0.98 Top flange and 
limits 
(49.5) 
web 
near non-compact 
B2 23.3 128.0 1257 0.98 B1 with a stockier 
(49.5) web 
B3 23.3 128.0 1257 3.90 B2 with an 
(49.5) unstiffened web 
B4 23.3 189.2 1270 (50) 0.98 Singly symmetric 
B5 17.5 153.6 1267 0.98 Top flange near 
(49.875) compact limit 
B6 13.6 153.6 1280 
(50.375) 
0.98 Very compact top 
flange 
B7 33.6 153.6 1254 
(49.375) 
0.98 Slender top flange 
Table 2-1:  CSBRP Bending Specimen Target Parameter Test Matrix 
 29
2.2. action Component Series 
ess combinations that duplicated 
tho
o 
= 
s placed at a 
spa
2.3 Fabrication of Test Frame and Bending Components
2 Moment-Shear Inter
Although the results of the moment-shear interaction component series tests are not 
included in this report, a brief description of these components is included in this section 
because the test frame was also designed to appropriately test these specimens.  
The moment-shear interaction components were labeled MV1, MV1-S, MV2 and 
MV2-S. MV1 and MV1-S had flange and web slendern
se used for B1. MV2 and MV2-S had flange and web slenderness combinations that 
duplicated those used for B5. MV1 and MV2 had a transversely unstiffened web, d
3.92D, while the webs of MV1-S and MV2-S had transverse stiffener
cing of d
o
 = 0.98D.  
 
All test series components and test frame components were fabricated with material 
and workmanship in accordance with the provisions and tolerances of the AASHTO 
Standard Specifications (15
th
 Edition including the 1993 and 1994 Interims) and the 
American National Standards Institute (ANSI)/AASHTO/American Welding Society 
(AWS) D1.5 Bridge Welding Code (1988 Edition including 1989-1994 Interims). In 
addition, the design drawings specified that all girder and component specimen flanges 
should be cut curved and that heat adjustments could be made to obtain the desired final 
geometry with approval of the design engineer. 
me girders, the cross-
frames and diaphragms, and the different component test series.  
2.3.1 Materials 
A variety of steels were used in the fabrication of the test fra
 30
2.3.1.1 Girders 
Two steels were used to fabricate the horizontally curved girders of the test frame. G
and G3 were fabricated from AASHTO M270M Grade 345 (M270 Grade 50) or A
A572M Grade 345 (A572 Grade 50) steel herein referred to as A572 steel. G2 was 
fabricated from plates of AASHTO M270M Grade 480W (M270 Grade 70W) or AST
A852M (A852) steel herein referred to as A852 stee
1 
STM 
M 
l. 
 
 at approximately 6.1 m (20 
ft) measured along the girder centerline from either end of each flange. 
2.3.1.2 Cross-Frames and Diaphragms 
ural 
f 
ss-
e 
ding experienced by cross-frames N6L and N6R during testing, their 
connections were made using ASTM A490 high strength bolts. 
 
Both the flange and web plates were cut curved to produce the necessary horizontal 
and vertical curvature for each girder. Flange and web plates were attached using 
overmatched fillet welds produced with the submerged arc process.  
Because of the quenching and tempering process required to produce the A852 steel
limits plate lengths to approximately 15.4 m (50 ft), two butt welds were needed in each 
flange of G2. These full penetration groove welds were made
The K-type cross-frames and diaphragms used an ASTM A513 Grade 1026 struct
steel tube for all horizontal and inclined legs. The tubes were attached to double gusset 
plates of A572 steel at each bolted connection location with a full penetration groove 
weld. To ease erection, the lower legs could be removed from the upper delta portion o
the cross-frames and diaphragms (see Figure 2-2). All connections, except those on cro
frames N6L and N6R, were made with ASTM A325 high strength bolts. Because of th
level of loa
 31
2.3.1.3 
All bending component and moment-shear interaction component flanges and webs 
were fabricated from A572 steel. The bending components, with the exception of 
spe n B7, were fabricated in the same manner as the girders of the test frame. The 
splice plates used to secure the inserted bending co t into the te e were 
dril n place and w so made of A572 steel.  
ding compon  was an addition to the original test matrix. This component 
test was add t six 
bending component tests and the beginning of the moment-shear interaction series of 
tests. B7 was fabricated by using heat to restore, within tolerance, the tension (bottom) 
flan
s 
lated in 
Tab
Bending Components 
cime
mponen st fram
led i ere al
Ben ent B7
ed to most effectively use the downtime between the end of the firs
ge and web of bending component B1 and by replacing the compression (top) flange 
with a plate of almost equal area and increased slenderness.  
2.3.2 As-Built Geometry 
While the component fabrication was completed within the AWS and AASHTO 
tolerances, the as-built geometry slightly altered the target design slenderness of both the 
flanges and the web at the critical section (mid-length) of each member. In most cases, 
these minor changes in the slenderness ratio were the result of plate material that wa
slightly thicker than the nominally specified thickness due to permitted manufacturing 
tolerances. The bending component series as-built slenderness ratios are tabu
le 2-2.
 32
Component Compression Flange 
Slenderness 
fc
b
Web 
fc
t
 
Slenderness 
w
c
t
D2
Tension Flan
 
 
ge 
Slenderness 
ft
ft
t
b
 
 
B1 22.8 147.0 22.9 
B2 22.8 119.6 22.8 
B3 22.7 119.5 22.9 
B4 22.8 188.0 16.5 
B5 17.0 143.6 17.1
B6 13.4 141.5 13.3 
B7 32.5 144.2 23.2
 
Table 2-2:  CSBRP Bending Specimen As-Built Parameter Test Matrix 
 
2.4 Material Properties 
Tension test specimens were cut from coupons taken from each steel plate used in th
fabrication of the test frame and components. Coupons were a
e 
lso taken from the rolled 
sections that m  and the tangential support frame, and from the 
stru
 
as 
lication of flange and web thicknesses used throughout the test matrix, 
sev flanges of 
ade up the lateral bracing
ctural steel tube sections from which the cross-frames were comprised. Three 
coupons were taken from each steel plate used for flange material and six coupons were 
taken from each steel plate used for web material. Static yield testing in accordance with
the Structural Stability Research Council (SSRC) (see Galambos, 1988) provisions w
conducted on most of the tension test specimens cut from each coupon. In general, 
tension tests were performed until two qualified results were obtained for each coupon 
location. A detailed set of results for these tests is available in Appendix A. 
Due to the dup
eral elements often could be cut from the same steel plate. The compression 
components B1, B2, B3 and B4 were all cut from Plate 21. The tension flanges of 
components B1, B2 and B3 were all cut from Plate 22. Both the compression and tension 
 33
flanges of components B5 and B6 were cut from Plates 23 and 24, respectively. The 
tension flange of component B4 was cut from Plate 25.  
2.4.1 Plate Coupon Locations 
Figures A-2 through A-14 show the location and orientation of the six coupons take
from the steel plates used for web material in both the test frame and bending 
components. The location and orientation for the three coupons taken from the steel 
plates used for flange material can be seen in Figures A-15 through A-27. The co
taken from either end of the steel plate, designated as A and C on these figures, are 
located at mid-depth and oriented to be parallel to a tangent to the end of the horizontally 
curved flanges. The coupon at mid-length, designated B, is locate
n 
upons 
d near one side of the 
plate and is oriented to be parallel to the direction of rolling.  
 
ses, 
ngation and tensile strength. In this 
doc d in 
static yield strength and the ultimate yield strength results from 
individual plates were used to build true stress-true strain relationships suitable for use by 
2.4.2 Tensile Strength Testing 
The tensile tests were performed in accordance with the ASTM E8, Standard Test
Methods for Tension Testing of Metallic Materials standard test method. In most ca
the E8 procedures were supplemented with the Structural Stability Research Council?s 
(SSRC) Technical Memorandum No. 7: Tension Testing to generate consistent and 
uniform static yield strength levels. The E8 methods and procedures are designed to 
specifically determine yield strength, yield point elo
ument, the definitions of these terms are consistent with those definitions provide
the E8 Standard.  
The static yield strength of individual plates was used in the analysis of the 
experimental data. The 
 34
the pendix A contains a complete discussion of the tensile 
test
 the 
brication of the CSBRP bending component 
compression flanges. The purpose for this series of tests was to confirm that the behavior 
of t  of 
, 
used without m
analytical modeling effort. Ap
 results and their conversion to true stress-true strain. 
2.4.3 Compressive Strength Testing 
The compressive strength tests were performed in accordance with the ASTM E9, 
Standard Test Methods of Compression Testing of Metallic Materials at Room 
Temperature standard test method. These tests were limited to specimens taken from
steel plates that were used in the fa
he steels used was complementary in both tension and compression. A complete set
results for the compression tests is also included in Appendix A. 
2.4.4 Elastic Modulus Testing 
The elastic modulus testing was performed in accordance with the ASTM E111, 
Standard Test Method for Young?s Modulus, Tangent Modulus and Chord Modulus
standard test method. Ten Young?s modulus tests were conducted as a part of this 
program. Parameters included steel grade and plate thickness. The E111 Standard was 
odification to conduct the testing. Standard plate-type tension specimens, 
as described in Appendix A.1.2, were selected as the test specimens because the testing 
was performed in the tension stress-strain domain. 
As a result of this testing, a Young?s modulus of 204,000 MPa (29,600 ksi) was 
selected for use in both the experimental data analysis and in the finite element analysis 
of this project. Appendix A contains a discussion that details how this value of Young?s 
modulus was selected. 
 35
2.5 Instrumentation Plan 
A detailed and sc  of h  inst  as developed 
for these experim  how these instruments were deployed is included in Linzell 
This plan ts of ove 800 hard- ired instru
ated by four separate data acquisition systems. Only the instruments that 
data tha were used in  analysis and that a ssential to this report are 
n this s n. 
2.
Each of the girders, cross-frames and lateral braces were instrumented at multiple 
sections during each of the bending component tests. Load cells monitored reactions at 
the girder ends as well as applied load at the hydraulic jack locations. Both of the 
independent channels of each load cell were recorded by separate data acquisition 
systems during testing to ensure redundancy of information. The load cells used to 
measure girder reactions had a 1,335,000 N (300 kip) capacity, while those used to 
monitor applied load had a 445,000 N (100 kip) capacity. 
Strain gages were used to characterize sectional behavior at 10 locations throughout 
the test frame. On G1 and G2, strain gaged sections near each load point and at mid-span 
were monitored during each test. G3 sections near each load point and near cross-frames 
N4L and N4R were monitored during each bending component test. The location of each 
instrumented cross-section within the test frame is shown in Figure 2-5. This figure also 
indicates the instrument configuration at each location. A summary of instrument 
configurations and locations is contained in Table 2-3. The instrument configurations 
used are illustrated in Figures 2-5 through 2-12. 
 complete de
ents and
ription ow the rumentation plan w
(1999).  consis r w ments, subsets of which are 
interrog
produced t this re e
described i ectio
5.1 Test Frame Instrumentation 
 36
 
Configuration 
(Figure) 
 
1 (2-5) 
2 (2-6) 
3 (2-7) 
V1 
V2 
V3 
V5 
V6 
 
37
G3 and  
Bending 
Component 
Location 
Label 
G2 
Location 
Label 
G1 
Location 
Label 
# 
Electrical 
Resistance 
Strain 
Gages 
# 
Vibrating 
Wire 
Strain 
Gages 
     
D, E   22  
A, J A A 15  
C, H   4  
(2-8) F   7 15 
(2-9)  B B 7 8 
(2-10) G   4 18 
(2-11) B, I   11 11 
(2-12)  C C 11 4 
 
Table 2-3:  Configuration and Location of Strain Gaged Sections 
38
B
R
B
B
R
B
R
B
R
 
(
T
Y
P
.
)
R
B
R
B
R
N
26
'-2
" 
(B
)
A
(2)
B
(V2)
C
(V6
)
A
(2)
B
(V5
)
C 5L
L
8"
B
R
 
(
T
Y
P
.
)
8"
C 
4L
L
41'-0 3/8" (C)
A
(2)
8"
C 6L
L
C
(3)
B
(V2)
C
(V6
)
8"
C 5
R
L
I
(V5)
J
(2)
8"
C 
4R
L
F
(V1)
8"
L
C 7
E
(1)
D
(1)
H
(3)
8"
C 6R
L
8"3'-3
"
G
(V3)
3'-3"
88'-0 15/16" (A)
25
'-6
" 
(D
)
35
'-3
 3
/8
" 
(F
)
25'-4 3/4" (G)
35
'-3
 3
/8
" 
(E
)
SECTION LOCATIO
N
(TYP.)
INSTRUMENTATIO
N
CONFIGURATION
 (TYP.)
 
Figure 2-5:  Location of Instrumented Cross-Sections 
 
B5 B6 B7
B1 B2 B3
B8
B4
W3 W6
W2 W5
W1 W4
Center of
Curvature
T5
T1
T7T6
T2 T3
T8
T4
D
D
/
4
D
/
4
D
/
4
D
/
4
Electrical Resistance
Strain Gage (Typ.)
Location (Typ.)
Strain Gage
SYM.
b  /2
ft
b  /4
ftft
b  /8
ft
b  /8
fc fc
b   /2
fc
b   /4
fc
b   /8
S M.Y
b   /8
 
Figure 2-6:  Instrumentation Configuration (1) 
 39
D
/
4
B5 B6
B1
SYM.
B7 B8
B4
W6
Location (Typ.)
Strain Gage
Strain Gage (Typ.)
Center of
Curvature
Electrical Resistance
W4
D
/
4
D
/
4
D W5
D
/
4
T8T5
T2T1 T3 T4
b  /2
b  /4b  /8
ft
ft
ft
b  /8
ft
b   /8
SYM.
b   /8
fc
b   /4
fc
b   /2
fc
fc
 
Figure 2-7:  Instrumentation Configuration (2) 
 40
B5
SYM.
D
/
4
B8
SYM.
D
/
4
D
D
/
4
D
/
4
T1
Center of
Electrical R
Strain Gag
esistance
e (Typ.)
Curvature
Location (Typ.)
Strain Gage
T4
b  /2
ft
ft
b  /8
fc
b   /8
b   /2
fc
 
Figure 2-8:  Instrumentation Configuration (3) 
 41
D
/
4
B5 B6
B1 B2
SYM.
B7 B8
B3 B4
W3 W6
Location (Typ.)
Strain Gage
Strain Gage (Typ.)
Center of
Curvature
Electrical Resistance
W1 W4
D
/
4
D
/
4
D W2 W5
D
/
4
T8T7T6T5
T2T1 T3 T4
Vibrating Wire
Strain Gage (Typ.)
b  /4
b  /2
ft
ft
ft
b  /8
ft
b  /8
SYM.
fc
b   /8
fc
b   /8
fc
b   /2
fc
b   /4
 
Figure 2-9:  Instrumentation Configuration (V1) 
 
 42
B7
B1
B5 B6
SYM.
D
/
4
W6
B8
B4
W4
D
/
4
D W5
D
/
4
T5
D
/
4
T1 T3T2
Center of
Electrical Resistance
Strain Gage (Typ.)
Curvature
Location (Typ.)
Strain Gage
T8
T4
Vibrating Wire
Strain Gage (Typ.)
ftftft
b  /2
ft
b  /4b  /8 b  /8
SYM.
b   /8
fc
b   /2
fc fc fc
b   /8 b   /4
 
Figure 2-10:  Instrumentation Configuration (V2) 
 43
D
/
4
B5 B6
B1 B2
SYM.
B7 B8
B3 B4
W3 W6
Location (Typ.)
Strain Gage
Strain Gage (Typ.)
Center of
Curvature
Electrical Resistance
W1 W4
D
/
4
D
/
4
D W2 W5
D
/
4
T8T7T6T5
T2T1 T3 T4
Strain Gage (Typ.)
Vibrating Wire
b   /8
SYM.
b   /8
fc
b   /4
fc
b   /2
fc
fc
b  /2
b  /4b  /8
ft
ft
ft
b  /8
ft
 
Figure 2-11:  Instrumentation Configuration (V3) 
 44
D
/
4
Electrical Resistance
Strain Gage (Typ.)
B5 B6 B7
SYM.
B8
D
/
4
B2B1 B4B3
W3 W6
Curvature
Center of
Strain Gage
Location (Typ.)
D
/
4
D W2 W5
W1 W4
D
/
4
T4T3T1 T2
T6T5 T7 T8
Strain Gage (Typ.)
Vibrating Wire
ftftft
b  /2
ft
b  /4b  /8 b  /8
SYM.
fc
b   /2
b   /8
fc
b   /8
fc
b   /4
fc
 
Figure 2-12:  Instrumentation Configuration (V5) 
 45
B7
B1
B5 B6
SYM.
D
/
4
W6
B8
B4
W4
D
D
/
4
W5
/
4
D
T5
D
/
4
T1 T3T2
Center of
Electrical Resistance
Strain Gage (Typ.)
Curvature
Location (Typ.)
T4
Strain Gage
T8
Strain Gage (Typ.)
Vibrating Wire
b  /2
b  /4b  /8
ft
ft
ft
b  /8
ft
SYM.
b   /8 b   /8b   /4
b   /2
fc
fc fc
 
fc
Figure 2-13:  Instrumentation Configuration (V6) 
 46
 
2.5.2 Bending Component Instrumentation 
instrumented at the six sections indicated in Figure 2-5. 
The sections labeled E and F are located 200 mm (8 in.) either side of mid-length of the 
component. These sections were used to determine the critical mid-span strains during 
each bending component test.  
Section F used Instrumentation Configuration (V1) shown in Figure 2-9. The data 
produced by this instrumentation configuration captured the installation and dead-load 
effects experienced by each component prior to the applied load test. However, the 
instrumentation used at this section is primarily comprised of vibrating wire strain gages 
which have a limited reliable strain capacity, (<1800 ?e) and are very sensitive to 
distortion. Therefore, as the steel flanges of the components approaches yield these 
instruments generally become inoperative. 
Section E employed Instrument Configuration (1) shown in Figure 2-6. This 
configuration used only electrical resistance strain gages which have relatively large 
reliable strain capacities (>10,000 ?e). However, this gage type tends to drift over 
extended periods of time. For this reason, the data needed to determine mid-span effects 
during the applied load portion of the component tests was acquired using the 
instrumentation at this section. 
The Sections labeled C and H in Figure 2-5 employed Instrument Configuration (3) 
shown in Figure 2-8. These sections are located 200 mm (8 in.) towards mid-length of the 
component from the cross-frames N6L and N6R. The data acquired from these sections 
Each bending component was 
 47
during the applied load portion of the bending component tests was used to interpret the 
affect of the lateral bracing on the component. 
2.6 Laboratory Equipment 
2.6.1 Loading Apparatus 
For the bending component testing, the curved steel girder test frame was loaded from 
above with six load frames at the locations indicated on Figure 2-1. These frames reacted 
off the floor of the structural laboratory and consisted of five major components, which 
are identified in Figure 2-14 and described below: 
? The Cross Beam was comprised of two 2438 mm (8 ft) long MC310 x 67 
(MC12 x 45) ASTM A572M Grade 345 (A572 Grade 50) channels bolted together 
around a series of spacers with 22 mm (7/8 in.) diameter ASTM A325 high strength 
bolts. The spacers were 7  40 pipe. The channels were 
set back-to-back with the spacers between them. The bolts passed through the web of 
one anne el.  
near each end that allowed the attachment of the Brace Beams.  
5 mm (3 in.) lengths of schedule
 ch l, then through the spacer and finally through the web of the other chann
? The End Beams were duplicates of the Cross Beam with additional bolt 
holes in the webs 
 48
 
End Beam 
Brace Beam
Cross Beam
Hydraulic Jack 
Dywidag 
Bar 
 
r 
strength thread-bars were used to attach each load assembly to the reaction floor. 
? 
e by reacting off the loading 
fixture. These jacks had an 890 kN (100 ton) capacity and a 457+ mm (18+ in.) 
 
Figure 2-14:  Typical Load Frame 
 
? Approximately 1,372 mm (4 ft 6 in.) C250 x 22.8 (C10 x 15.3) ASTM 
A572M Grade 345 (A572 Grade 50) channels were used as braces and separators fo
the End Beams.  
? Four 25 mm (1 in.) diameter Dywidag Grade 1030 (Grade 150) high 
An Enerpac Model RR-10018 Heavy Duty Solid Plunger Double Acting 
Hydraulic Cylinder (jack) was used to load the test fram
stroke. 
 49
The load frames were secured to the reaction floor at tie down locations that wer
placed in a grid pattern at 914 mm (3 ft) centers. The four Dywidag bars of each load 
frame were connected to the floor tie downs at the corners of the 1829 mm (6 ft) north-
south east-west square that was most centered on the load point. The bars extended from 
the floor to approximately 2438 mm (8 ft) above the top of the curved girder test frame.
One End Beam was connected to each of the northern and southern pair of Dywidag 
bars at approximately 610 mm
e 
 
 (2 ft) above the top of the curved girder test frame. The 
bar
el, 
The eastern and western ends of the End Beams were connected to a Brace Beam 
with 178 mm (7 in.) long L152 x 89 x 9.5 (L6 x 3? x 3/8) angles. Two 22 mm (7/8 in.) 
diameter A325 bolts connected one leg of the angle to the web of the End Beam through 
standard holes. Two additional 22 mm (7/8 in.) diameter A325 bolts connected the other 
leg of the angle to the web of the Brace Beam through slotted holes.  
The Cross Beam, with its weak axis in a vertical position, was then placed to span 
perpendicularly from one End Beam to the other over the load point on the curved girder 
test frame. The Cross Beam was connected to each of the End Beams with ?1219 mm 
(?4 ft) lengths of Dywidag thread-bars. At each of these connections, the Dywidag bar 
passed between the spaced webs of both the Cross Beam and the End Beam and was 
tensioned to securely hold the assembly together. 
Before incorporation into the load frame assembly, the base of the hydraulic jack was 
attached to the center of a 305 mm x 610 mm x 51 mm (1 ft x 2 ft x 2 in.) thick steel 
s passed through the spaced webs of the End Beams, which were held in place with 
anchor plates and nuts both above and below the beams. The End Beams were parall
ran east-west and were 1829 mm (6 ft) apart. 
 50
plate. The Jack was then attached to the Cross Beam at the load point location with 
?1219 mm (?4 ft) lengths of Dywidag thread-bars. These bars passed between the spaced 
web e 
e load point on the curved 
girder test 
2.6.2 Instrumentation 
The instrumentation plan was devised to provide redundancy in both the acquisition 
of data and analysis techniques. The plan was comprised of nearly 800 individual 
instruments, the vast majority of which were uni-axial electrical resistance strain gages. 
2.6.2.1 Electrical Resistance Strain Gages 
All electrical resistance strain gages used in this experimental program were 
manufactured by Measurements Group Incorporated and had an internal resistance of 120 
ohms. Two types of electrical resistance strain gages were used: uni-axial or single-arm 
gages with a 6 mm (1/4 in.) gage length and rosettes with a 3 mm (1/8 in.) gage length. 
Uni-axial gages or single-arm gages measure strain in one direction along the 
longitudinal axis of the gage. Rosette gages incorporate three uni-axial gages whose 
longitudinal axes coincide at a single point but are each separated by an angle of 50 
s of the Cross Beam and through pre-drilled holes in the 51 mm (2 in.) plate and wer
tensioned to securely hold the assembly together. The Jack loaded the curved girder test 
frame through a machined ball and socket joint. The ball was attached to the hydraulic 
jack cylinder while the socket was attached to a load cell at th
frame. 
All six hydraulic jacks were extended with a common pressure line. This line was fed 
by an Enerpac PEM-8418 Hi-Flow Hydraulic Pump capable of delivering up to 7.8 
liters/minute (2 gallons/minute) at 68.9 MPa (10 ksi). 
 51
gradients (45 degrees). This configuration allowed the three individual strain reading
be appropriately combin
s to 
ed to determine the shear strain at that location.  
 
f 
sting of each bending component. 
2.6.2.2 Vibrating Wire Strain Gages 
Vibrating wire strain gages use changes in the natural frequency of vibration of a wire 
stretched between two points to measure strain. As the wire?s length changes, the tension 
in the wire changes, which proportionally affects the wires natural frequency. The change 
in frequency can be mathematically equated to the change in length between the two 
points over which the wire is stretched. The gages used on this project were the Geokon 
models VK4100 that have a 51 mm (2 in.) gage length.  
2.6.2.3 Load Cells 
Load cells are essentially scales capable of measuring load along one axis. They use a 
circuit of multiple uni-axis strain gages, called a bridge, to determine load. All load cells 
used have an internal resistance of 350 ohms and have two electrical bridges that were 
independently monitored during testing by the MicroMeasurement 5000 (MM5000) and 
the Hewlett-Packard VXI (HP) data acquisition systems that are described in Sections 
2.6.3.2 and 2.6.3.4, respectively. 
StrainSert Model FL100U(C)-2DGKT Universal Flat Load Cells were used at each 
load point to determine the load applied to the test frame from the hydraulic rams. These 
Electrical resistance strain gages are very sensitive, have a large strain capacity and 
can be interrogated very quickly by a data acquisition system. However, they tend to drift
over extended periods of time (days). Therefore, these gages were the primary source o
data during the capacity te
 52
load cells have a capacity of 445 kN (100 kip) and are capable of measuring load to 
within 56 N (12.5 lbs). 
StrainSert Model FL300U(C)-2DGKT Universal Flat Load Cells were used at each 
poi
2.6.3 Data Acquisition Systems 
Four data acquisition devices were required to support the instrumentation plan. As 
previously stated, this plan included more than 800 instruments and required redundancy 
in many of the measurements. Of particular importance was the requirement to be able to 
interpret the data in near-real-time to direct the course of each experiment.  
2.6.3.1 MicroMeasurements 4000 
The MicroMeasurements 4000 (MM4000) has a 200-channel capacity and was used 
to monitor the 176 resistance strain gages on the cross-frames and lateral bracing in the 
south bay of the test frame between G1 and G2. 
2.6.3.2 MicroMeasurements 5000 
The MicroMeasurements 5000 (MM5000) data acquisition system has an 80-channel 
capacity. This system was used to monitor the rosette resistance gages on G3 as well as 
the load cells at the abutment and at the hydraulic actuator locations. 
2.6.3.3 Geokon Micro-10 
The Geokon Micro-10 system has an 80-channel capacity and was used in 
combination with five Model 8032 Multiplexers to monitor all 79 vibrating strain gages 
nt of support to determine the vertical reaction of the test frame from all loads. These 
load cells have a capacity of 1,335 kN (300 kip) and are capable of measuring load to 
within 167 N (37.5 lbs).  
 53
used during each component test. This system was also used to monitor strains on the 
bending components as they were being installed. 
XI 
le 
disp
se 
2.6.3.4 Hewlett-Packard V
The Hewlett-Packard VXI (HP) data acquisition system has a 640-channel capacity. It 
was the workhorse of these experiments?monitoring a minimum of 576 instruments 
during each test. This system was used to monitor a majority of the electrical resistance 
strain gages and the entire set of load cells, potentiometers, tiltmeters, linearly variab
lacement transducers (LVDTs) and instrumented studs used during the bending 
component experiments. The HP system is capable of manipulating and displaying the 
acquired data in near-real-time (about 90 seconds from recording initiation for the
experiments).
 54
 
Chapter
55
 3.  Analysis of Experimental Data 
3.1 Execution of the Experiments 
The test frame consisted of a three-girder bridge that was horizontally curved. Before 
any of the component testing began, the frame was erected with a prismatic outside girder 
(girder G3). This system was instrumented and elastically exercised over a period of 
months to prove the variety of instrumentation and data acquisition systems used.  
The test fram e nine locations, shown in Figure 3-1, to begin the 
component testing. Load cells were utilized to monitor and to record the shoring reaction 
loads. Screw jacks were used to adjust the elevation of the shores?increasing or 
decreasing the shoring load?to obtain a desired reaction.  
The shoring was used to eliminate as much of the dead load deflection from the 
structure as possible. The desired reactions were determined by constructing a finite 
element model shored at complimentary locations and by applying traction to simulate 
gravity. The results of the finite element analysis for the six girder abutment reactions 
and for the nine shoring reactions were used to establish a structural state that minimized 
the dead load effects within the test frame. This state will be referred to herein as the ?no-
load? condition. 
e was shored at th
56
 
 
AL
RAM
EASU
O
F IN
M R
O
NG ?
G
ED AL NG
R=
2
0
8
'
-
9
"
R
=
2
0
0
'
-
0
"
R
=
1
9
1
'
-
3
"
1
'-
0
"
 T
Y
P
.
1L
C
TI
 R
E
A
C
O
N
L
12 S
P C
ES
3L
4L
A
2L
5L
ME
E
C
@ = 
9
6L 7
ASUR D
ROSS
 7'-6" 90'-0"
0'-0"
4R
6
5R
RDE
R 2
?
IRD
E
G2
R
GI
 G
 G
R 
SP I
NGAC
3
R
R
2
C
 G
D
E
R
 
G
IR
D
 G
3
1
'
"
 T
Y
P
.
S
O
U
T
L
 G
IR
D
R
 G
1
RO
S
S
RA
M
E
NE
S
1R
IR
G
2
C
 
E
R
-0
H
 
B
A
Y
C
E
C
 F
L
I
N
O
R
T
H
 
B
A
Y
C
E
A
C
T
I
N
8
'
-
9
"
8
'
-
9
"
 R
O
L
L
L
STR CTURA
100 LOAD 
U L  W
K CE P.)
SHORE ITH
LL (TY
 
ition S pport LayoutFigure 3-1:  No Load-  Cond u
 
Once the no-load condition was established, a bending component could be inserted 
into the outside girder (G3) of the test frame between the bolted field splices. After a 
bending component was bolted into G3, any outstanding instrumentation was applied, 
and all instruments were wired to one of the data acquisition systems. The shoring 
beneath the entire test frame and the component was then removed, and the dead load 
effects were captured using the data acquisition systems. This step, referred to as 
Shakedown-1 for each bending component test, was the first time the instrumentation 
supplied to the bending component was exercised over a significant range of strain. A 
complete set of data was acquired during Shakedown-1 in most of the bending 
component tests. However, individual pieces of instrumentation or the data acquisition 
systems occasionally did not perform as intended, and some data were corrupted or lost. 
These losses proved insignificant to the analysis of the results.  
After the shoring was removed, frames were erected that supplied the load to two 
locations on the top flange of each of the three girders. These frames were tied to the 
reaction floor of the laboratory using four high-strength steel rods. Double action 
hydraulic actuators that were connected to the frames supplied the load to the top flanges 
through a ball and socket joint. The joint acted on a load cell attached to the top flange at 
each load point. The load frames are described in detail in Section 2.6.1. 
If issues with the instrumentation or data acquisition systems arose during 
Shakedown-1, a series of loadings were applied to the entire test frame using the load 
frames. These proof tests were conducted repeatedly to exercise and prove the 
instrumentation and electronic equipment. These series of proof tests, referred to as 
 57
Shakedown-2, Shakedown-3 etc., were continued until all devices were working properly 
and as expected.  
3.2 Data Analysis 
nalysis in this report focuses primarily on the strain data acquired from two 
instrum ions, labeled E and F in Figure 2-5, were 
located 203 mm (8 in.) from id-span of each bending component. The 
off he  these instrumented cross-sections 
was necessary due to the local influences of the mid-span transverse stiffener present on 
six t even the vertical bending, horizontal bending 
and n dia his 
unif tion of the results. 
ith vibrating wire strain gages that had 
a long-term sta  the data collected 
at t n, ulti-day process for the bending component 
installation, were used to determine the installation effects at mid-span. Cross-section E 
was instrumented com cal resistance strain gages. Because these gages 
are highly accurate over large ranges of strain, their data are used to determine the 
onditions at mid-span thr ch experiment. 
e 
propriately 
The a
ented cross-sections. These cross-sect
 either side of the m
set from t  actual mid-span location for each of
 of he s  bending components. However, 
 torsio grams were all relatively constant throughout this range of the girder. T
ormity allowed a collective interpreta
Cross-section F was primarily instrumented w
bility but a relatively small strain range. For this reason,
his sectio  during the usually m
pletely with electri
c oughout the applied-load portion of ea
Analysis results included in this report for cross-sections other than E and F on the 
bending component are appropriately labeled. 
Four force actions cause normal strain, ? , in an I-girder cross-section: bending about 
the strong axis, bending about the weak axis, warping torsion and axial load. Using th
Beam theory, the normal strains that result from these force actions are ap
 58
combined at any point on the I-girder cross-section (shown in Figure 3-2) using Equation 
3-1.  
EA
P
EC
BiW
EI
xM
EI
yM
z
w
n
y
y
x
x
+++?=?       Equation 3-1 
Where: 
P
z
 = Axial force in the z-direction 
E = Modulus of elasticity of steel 
A = Cross-sectional area of the I-girder 
M
x
 = Moment about the x-axis 
y =  Normal distance from the y-axis 
I
x
 = Moment of inertia of the cross-section about the x-axis 
M
y
 = Moment about the y-axis 
x = Normal distance from the x-axis 
I
y
 = Moment of inertia of the cross-section about the y-axis 
C
w
 = Warping constant 
Bi = 
W
n
 = Normalized unit warping
Bimoment  
  
 59
Y
C.G.
Z
X
 
Figure 3-2:  I-Girder Coordinate System 
 
respective force action. The following equations utilize the magnitude of norma
determine the complementary strains in the tension (bottom) flange tips. 
The aggregate normal strain distributions in the flanges can be separated using the 
thin-walled, open-section, Beam theory into each component of strain associated with a 
l strain in 
the compression (top) flange tips as a unit quantity that can be scaled as indicated to 
 60
?
?
?
B
Out
?
Out
B,M
B5 B6 B7
B1 B2 B3
B8
?
B
In
B4 ?
B,M
In
W3 W6
W2 W5
W1 W4
Center of
Curvature
T5Out
T,M
T1
T7T6
T2 T3
T
Out
?
T8
T4
In
T,M
?
?
In
T3
T
(Typ.)
 
Figure 3-3:  Identification of Strain Measurement and Resultant Locations 
 
    Equation 3-2 
    Equation 3-3 
    Equation 3-4 
    Equation 3-5 
Where: 
zzyx
PzMzMzMz
out
MT ,,,,
.
,
????? ?++?=
zzyx
PzMzMzMz
in
MT ,,,,
.
,
????? ????=
zzyx
PzMzMzMz
out
MB ,,,,
.
,
???????? ??+=
zzyx
PzMzMzMz
in
MB ,,,,
.
,
???????? ?+?=
 61
 62
?
?
?
?
?
?
?
?
++
+?
=
fcNA
ftNA
tyD
tyD
2
2
?       Equation 3-6 
?
?
?
?
?
?
?
?
=
fc
ft
b
b
?         Equation 3-7 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+++
+??
=
fc
ft
fcSCNA
ftSCNA
b
b
tyyD
tyyD
22
22
?     Equation 3-8 
The location of these strain quantities on the cross-section of the girder is shown in 
Figure 3-3. The geometric characteristics are defined on Figure 3-4.  
Out
?
B,M
In
?
B,M
?
Out
T,M
Web mid-depth
?
In
T,M
Neutral Axis
Shear Center
b
ft
t
f
t
S
C
y
y
N
A
C.G.
S.C.
'
d
D
b
fc
f
c
t
 
Figure 3-4:  Cross-Sectional Parameters 
In the tests of the cross-sections that are doubly symmetric, the scalars defined in 
Equations 3-6 through 3-8 are approximately equal to 1.0, which reduces Equations 3-4 
and 3-5 to the following: 
.
????? ??+=      Equation 3-9 
of the 
ain 
ending neutral axis 
sho in F
n flange using the first term in Equation 3-1, then this magnitude can be 
scaled by ?
oduce gradients of strain along the width 
of t lang
fined in Figure 3-3, 
bec e thi s 
rmine the extreme fiber tension flange tip 
strains. 
 ma
 
 is used to determine the normal strain due to 
warping. This term is presented using the Bimoment, Bi, so that it takes a familiar form. 
zzyx
PzMzMzMzMB ,,,,,
zzyx
PzMzMzMz
in
MB ,,,,
.
,
????? ?+?=     Equation 3-10 
The resulting strain distribution from each described force action can be seen in 
Figure 3-5. Strong-axis bending produces a gradient of strain through the thickness 
flanges. At any location on the cross-section, the magnitude of strong axis bending str
is proportional to the normal distance from that location to the b
out
wn igure 3-4. If this strain is determined for the extreme fiber tip of the 
compressio
 (Equation 3-6) to determine the extreme fiber tip strain in the tension flange.  
Weak-axis bending and torsional warping pr
he f es. For all I-girders, the magnitude of weak-axis bending strain is proportional 
to the normal distance from the location of interest to the y-axis de
aus s is an axis of symmetry for these section types. Weak-axis bending strain i
determined by the second term in Equation 3-1. The extreme fiber compression flange tip 
strains are modified by ?  (Equation 3-7) to dete
The gnitude of flange tip torsional warping strain is proportional to the aggregate 
normal distances from the location of interest to both the y-axis and to the shear center of
the section. The third term of Equation 3-1
 63
The Bimom arping torsion 
ltiplied by the distance between flange centroids. The torsional warping 
stra
in in the tension flange. 
h the fourth term in Equation 3-1.
ent represents the magnitude of lateral flange bending due to w
in each flange mu
in at the extreme fiber tip in the compression flange is scaled by ?  (Equation 3-8) to 
obtain the extreme fiber tip stra
The axial load produces a uniform strain throughout the cross-section. The magnitude 
of this strain is determined wit
 64
 
Z
?
?
Z
,
Z
?
Z
,
Z
,
P
Z
?
?
PZ
Z
P
,
P
Z
?
PZ
?
?
M
Z
Z
,
M
Z
+
?
?
Z
,
M
?
?
?
Z
Z
,
M
?
Z
M
Z
+
?
Z
Y
-M
Z
?
,
Z
Y
Y
Y
+
?
?
Z
,
Z
,
M
Y
+
Y
,
M
?
?
M
Y
M
?
+
?
?
Z
,
M
Z
?
?
?
,
M
X
Z
?
X
?
,
?
?
Z
+
?
?
Z
X
X
,
M
Z
X
,
M
-M
XX
B
O
Out
T
B
?
In
?
ut
?
T
?
In
IA E N OR
COMPRESSION
TORSIONAL
R G
K AX
DIN
BE
S
RAIN
IDENT O
IS
G
NDI
STRONG AXI
NG
AX L T NSIO
WA PIN
WEA
BEN
ST
IFICATI N
 
Fi ure 3 :  Cog -5 mponents of Longitudinal Strain
 
3.3 Installation Strains 
The installation of each of the bending components into the test frame locked forces 
into the system through the completion of each bolted field splice and the insertion of the 
cross-frames at locations N6L and N6R. The strain effects from this erection were 
monitored at two sections on the bending component with vibrating wire strain gages. 
The following process, used to acquire these strains, was designed to minimize the 
amount of longitudinal warping strain and primary-axis bending strain present in the 
bending component prior to being installed into the test frame.  
1. Block bending component at approximately 1/3
rd
 points while standing 
vertically. 
2. Measure and record straight-line distance from inside of the flange tips at one 
end to inside of the flange tips at the other end. 
3. Lay specimen on its side with blocking now provided at the ends and the 1/3
rd
 
points. Adjust blocking to recreate flange distance measurements. 
4. Apply vibrating wire gages at all accessible locations. Read and record all 
applied gages three times. Individual gage readings should not be consecutive, but should 
be the result of a circuitous reading procedure. 
5. Return component to vertical position blocked again at 1/3
rd
 points. 
6. Apply remaining vibrating wire gages. Read and record all gages, both those 
applied in this step and those applied previously, three times as stated above. Also, read 
and record all test frame instrumentation. 
 66
7. Bolt component into test frame. Read and record all operating 
instrumentation. 
8. Bolt cross-frame N6L to the test frame and to the component. Read and record 
all operating instrumentation. 
9. Bolt cross-frame N6R to the test frame and to the component. Read and record 
all operating instrumentation. 
The acquisition of the vibrating wire strain gage data during the installation of 
bending component B1 was accomplished using a vibrating wire gage readout box and a 
single gage reader. The reader was manually placed over one gage at a time, and the 
readout box indication was recorded by hand. After reviewing the data, it became 
apparent that the strain readings were very sensitive to operator technique. This 
sensitivity was confirmed by having three individuals independently produce the 
vibrating wire gage data with the bending component and test frame in a steady-state 
condition. While some of the cross-referenced strain indications were consistent, large 
groups of the data included at least one divergent reading. 
 acquired with this acquisition 
sys
Therefore, to increase the consistency and value of the installation strain data, the 
process of manual readings was replaced with automatic strain data collection using an 
acquisition system. Each vibrating wire gage was hardwired to a data acquisition system 
as the gage was installed on the bending component. The installation strain data for 
bending components B2, B3, B4, B5, B6 and B7 were
tem. Unfortunately, in spite of the best efforts of the laboratory staff, most of the 
recorded data from the installation of components B2 and B3 was corrupted. 
 67
An analysis of the insta onents B4 through B7 
instills high confidence in the data. Using the Beam theory analysis, detailed earlier in 
this Section, on independent subsets of the data produces the same group of equilibrated 
internal forces at the instrumented section. The results of the analysis on the installation 
strain data are summarized in Table 3-1 for these specimens. 
Normal strain (?e) from  
llation strains collected for the comp
Specimen 
M
x
 M
y
 M
z
 P
z
 
B4 257 22 82 -31
B5 172 4 236 1
B6 157 -24 12 3
B7 74 199 122 -29
 
Table 3-1:  Installation Strain Data Analysis Results for Specimens B4, B5, B6 and B7 
 
The installation strain analysis for component B4 shows that the vast majority of 
strain is the result of strong-axis bending. The analysis also indicates that a small axial 
force, 6 MPa (0.9 ksi), is also present in the component. However, the presence of this 
force is not supported by other test frame data. This apparent axial force is most likely the 
result of distortion in the web plate, which has a slenderness of 188.0 due to the section 
geometry that is singly symmetric. A review of the web data collected during installation 
supports this interpretation. However, the review was not definitive because information 
for only one face of the web was available. 
Figure 3-6 plots the B4 installation strain magnitudes onto their respective I-girder 
plate component. This figure is the first in a series used throughout this report to show the 
distribution of longitudinal strain along an I-girder cross-section. On these figures 
ind
 
ividual longitudinal strains are plotted at the location where they were recorded using 
the scales attached to each plate of the cross-section. Then, a line representing the linear
 68
regression result of the family of data from any one surface is also plotted using the s
scales. These linear regression lines essentially indicate the distribution of longitudinal 
strain along each plate and project a plate tip strain. 
ame 
 from the 
e 
f the 
 web are indicated 
with a shaded square. 
Returning to Figure 3-6, the regression line for the web data shown crosses the web at 
the
) 
Flange strains are indicated with triangles. Triangles that point up show data
top of the plate. Triangles that point down show data from the bottom of the plate. Th
shaded triangles indicate that the data is from the outside of the plate at the location o
extreme fiber for strong-axis bending. The open triangles indicate that the data is from 
the inside surface of the plate i.e. top of the bottom flange or bottom of the top flange. 
Web strains on the inside of the web, the face closest to the center of curvature, are 
indicated with an open diamond. Web strains on the outside face of the
 approximate location of the bending neutral axis. However, its fit to the individual 
strain data is poor, which supports the hypothesis of web flexing as the cause of the 
apparent axial force. Also, while the data for the top and bottom of the compression (top
flange indicate similar trends, the tension (bottom) flange data reveal a slight localized 
bending on the outside of the plate by the intersection of the regression lines. 
 69
Center of 
Curvature
B4 Section F
Strains
-
4
0
0
-200
0
2
0
0
400
-600
-400
-200
20
400
0
0
Installation 
-400
00-2
0
200
400
600
 
Figure 3-6:  B4 Installation Strain Data 
ajority 
 the cross-frames between B5 and G2. The remainder of the installation 
stra
of the component suspended between supports.  
 
The installation strain analysis for doubly symmetric B5 reveals that a slight m
of the installation strain resulted from torsion in the component. This torsion was caused 
by the insertion of
ins were caused by strong-axis bending due to the bolted field splices and to the dead 
load 
Figure 3-7 shows the linear behavior of the B5 installation strains. The flange strain 
gradients, which trend oppositely in the constructed figure, indicate a large torsional 
warping component in the strain data. 
 70
Center of 
Curvature
-400 -200
0
200 400
-600
-400
-200
0
200
400
B5 Section F
Installation
Strains
-400
-200
0
200
400
600
 
Figure 3-7:  B5 Installation Strain Data 
 
The in tion of 
the cross-frames was insignificant on this component. The strain from installation can be 
attributed almost entirely to the effect of the bolted field splices and to the vertical 
bending due to dead load. Figure 3-8 shows the near uniform strain across both flanges 
that supports the analysis. 
stallation strain analysis for doubly symmetric B6 shows that the inser
 71
Center of 
Curvature
-4
00
-2
00
0
20
0
40
0
-600
-400
-200
0
200
400
B6 Section F
Installation 
Strains 
-400
-200
0
200
400
600
 
Figure 3-8:  B6 Installation Strain Data 
 
l 7 is also singly symmetric. While the strain data 
that s did 
com
cross-frames between B7 and G2. The figure indicates that the weak-axis bending and 
Simi ar to B4, bending component B
 were acquired during installation are held in high confidence, the data analysi
not produce an ideal strain distribution and resulted in an apparent small axial stress 
acting on the cross-section, 6 MPa (0.9 ksi). However, this result is most likely due to the 
fabrication process used to create B7 that is described in Section 2.3.1.3. 
Figure 3-9 shows the installation strains and associated regression lines for 
ponent B7. While the overall installation had little effect on the web and bottom 
(tension) flange, the top (compression) flange was influenced by the insertion of the 
 72
warping components of normal strain are of similar magnitude because they nega
other in the tension flange and combined to produce a significant strain gradient in the 
ted each 
compression flange. This graphic evidence supports the data analysis. 
B7 Section F
Strains
Center of 
Curvature
-
400
-
200
20
0
40
0
0
-600
-400
-200
0
400
200
Installation
-400
-200
0
200
400
600
 
Figure 3-9:  B7 Installation Strain Data 
 
Because the installation strain data for B1 are considered suspect and the data f
and B3 were largely corrupted, an estimate of the installation strain levels for these 
components was made using the data from B5 and B6. The data from B4 were slightly 
affected by the single axis symmetric of the section; therefore, they were excluded from 
this estimate. The data from B7 were influenced by the fabrication process employed 
or B2 
with this component and were also excluded from this estimate.  
 73
To create the model of the estimated installation strain levels for B1, B2 and B3, the 
strain data analyses for B5 and B6 were used to determine the moments about each a
that resulted from the installation process. These moments were averaged, and the
averages we
xis 
 
re analyzed for their effects on sections B1, B2 and B3. The results of this 
ope e 
 
ration are the sets of strain listed in Table 3-2 for components B1, B2 and B3. Thes
strains are contrasted with the actual installation strain data for components B4 through
B7 also in Table 3-2. These estimated installation strain levels were used to analyze the 
experimental data of B1, B2 and B3. 
Bending Specimen 
B1* B2* B3* B4 B5 B6 B7 
Strain 
Location 
Installation Strain (?e) 
Gage 
T1 -118 -110 -110 -136 -4 -168 183
T2 -182 -175 -174 -197 -106 -167 38
T3 -247 -240 -238 -247 -264 -166 -128
T4 -311 -304 -302 -280 -350 -150 -273
T5 -112 -104 -104 -153 25 -162 213
T8 -304 -298 -296 -322 -349 -144 -297
W4 -105 -102 -102 -143 -50 -97 -5
W5 -2 -2 -2 -186 -21 34 -11
W6 100 97 97 57 106 79 16
B1 85 78 78 191 11 132 141
B4 321 314 313 144 351 166 82
B5 92 85 84 170 -21 114 88
B6 170 163 162 176 137 138 71
B7 249 242 241 202 208 180 65
B8 327 321 319 239 332 185 102
*Strain levels estimated using B5 and B6 data. 
 
Table 3-2:  Installation Strain Data Used in Bending Component Capacity Analysis 
 
Figure 3-10 shows the regression lines that are the result of the estimated installation 
strain levels and the suspect installation strain data from B1. The estimated levels 
primarily indicate vertical bending and warping in the girder flanges and bound most of 
the suspect data. 
 74
Figure 3-11 shows the effect s ponent 
B2
Figure 3-12 shows the effects of the estimated installation strain levels on component 
B nd the that we rmin liabl m the actual f B3. The 
ac l data ce ag uat und e e e, n fidence in the 
estimation procedure. 
s of the e timated installation strain levels on com
. 
3 a  data re dete ed re e fro  installation o
tua  are on ain adeq ely bo  by th stimat instilli g con
Center of 
Curvature
-400 -
2
0
0 0
200 400
-600
0
0
0
0
0
-40
-20
20
40
B1 Section F
In n
St
stallatio
rains
-400
0
200
400
600
-200
 
Figure 3-10:  B1 Installation Strain Data with Regression Line Estimates 
 75
 76
Center of 
Curvature
-
4
0
0
-
2
0
0 0
200 400
-60
-40
0
0
-200
0
20
40
0
0
B2 Section F
Installation
Strains 
Estimates
-400
-200
0
0
200
40
600
 
Figure 1: m ssion Line Estim 3-1   B2 Installation Strain Model Fro  Regre ates 
Center of 
Curvature
-400 -200
0
200 400
-600
-400
-200
0
200
400
B3 Section F
Installation 
Strains
-400
-200
0
200
400
600
 
 
3.4 Bending Component B1 Test
Figure 3-12:  B3 Installation Strain Data With Regression Line Estimates 
 
The test frame containing bending component B1 was loaded in 28 steps to a 
maximum applied load of 1,354 kN (304.3 kip). As indicated in Table 3-3, the majority 
of these steps represent approximately 27 kN (6 kip) increments in applied load. Once the 
system became non-linear, both load increment and displacement increment were 
monitored in an effort to capture the peak resistance of each bending component. 
The component behavior analyses in this report utilize the steel plate specific yield 
criteria established from material testing and reported in Appendix A. That is, each plate 
 77
of a
nt to 
l 
 
1 and G2, and then subtracting them from the total. 
Wh
n the 
p 
ben
his table shows that the ratio of 
ver
moment to calculated vertical yield moment, M
x
yield
,of 0.69, and during the maximum 
n I-girder cross-section has an associated yield strength determined through 
experimentation, which is used to interpret the behavior and performance of that plate. 
Vertical bending moments at mid-span of the component are calculated by two 
methods in the elastic range; the direct method and the indirect method. The direct 
method converts the individual strain readings recorded at mid-span of the compone
a moment using the Beam theory describe earlier in this Chapter.  
The indirect method considers a free body of half the test frame between mid-span 
and one of the abutments. Using the applied loads and end reactions a mid-span vertica
bending moment can be determined for the entire test frame. This moment can then be 
reduced to a component mid-span moment by employing the Beam theory to solve for the
vertical bending moments in both G
ile the indirect method is proven by and is redundant to the direct method in the 
elastic range, it is the sole method of determining the component mid-span moment i
inelastic range. 
First yield in B1 occurred at the inside tip of the compression flange during load ste
8 at a total applied load of 826 kN (185.6 kip). At the step 8 load level, the vertical 
ding moment resisted by B1 was determined to be 3,513 kN-m (2,591.0 k-ft) using 
the direct method of calculation and 3,516 kN-m (2,593.0 k-ft) using the indirect method 
of calculation. Table 3-4 contains a summary of the B1 mid-span stresses and the 
moments that are a result of the strain data analysis. T
tical flange bending stress to lateral flange bending stress was between 0.46 and 0.47 
throughout the elastic load range. Also, first yield occurred at a ratio of vertical bending 
 78
sustained applied load this ratio rose to 0.90. M
x
yield
 is calculated using the yield strength 
of the compression flange and is the strong-axis bending moment required to cause 
yielding at the extreme fiber of the compression flange without consideration for 
Figure 3-13 shows a comparison of the resisted vertical bending moment for each 
method of calculation, direct and indirect, throughout the elastic range of loading. The 
purpose of this figure is to establish the accuracy of the indirect method of calculation in 
determining the vertical bending moment being resisted by the component. The direct 
method relies on the principles of the Beam theory. Therefore, at load levels that cause 
the component to exceed its yield strength or distort significantly out of plane this method 
of determining the resisted vertical bending moment no longer applies. Accordingly the 
indirect method is relied upon in the non-linear region of component behavior.
instability. 
 79
Load  Total Applied Mx (Total) Mx (G1) Mx (G2) Mx (B1)   
Step Load      Indirect Direct   
        (a) (b) (a)/(b) 
  KN kN-m kN-m kN-m kN-m kN-m   
B1 Elastic 
1 0.0 -1.0 0.4 -0.2 -1.1 -2.6 0.44 
2 63.8 242.9 24.8 88.2 129.9 116.5 1.11 
3 187.8 759.1 52.4 293.1 413.6 397.6 1.04 
4 329.7 1379.3 84.2 53 .3 756.8 735.8 1.03 8
5 459.8 1953.0 115.0 773.6 1064.4 1050.8 1.01 
6 650.0 2798.1 158.1 1103.8 1536.3 1506.9 1.02 
7 802.7 3481.2 1 4.2 1888.9 1.01 87.7 1379.4 191
8 825.6 3582.1 190.8 1434.2 1957.1 1954.4 1.00 
B1 Plastic 
9 844.5 3666.6 193.9 1468.9 2003.7 2004.9 1.00 
10 878.1 3816.3 198.6 1537.0 2080.7 2116.2 0.98 
11 900.0 3913.7 200.3 1582.9 2130.4 2201.0 0.97 
12 923.8 4023.4 198.9 1633.8 2190.8   
13 957.0 4168.9 200.3 1703.2 2265.4   
14 982.6 4283.9 195.1 1764.2 2324.6   
15 1012.3 4415.9 193.7 1834.0 2388.2   
16 1035.5 4518.0 188.6 1894.7 2434.6   
17 1068.9 4668.2 192.1 1961.3 2514.8   
18 1094.2 4780.0 187.3 2018.8 2573.9   
19 1119.0 4893.7 185.4 2086.6 2621.6   
20 1139.7 4988.2 183.4 2145.2 2659.6   
21 1166.0 5106.3 177.1 2216.1 2713.1   
22 1197.5 5245.8 168.1 2308.7 2768.9   
23 1216.4 5314.1 155.2 2369.0 2789.9   
24 1248.3 5452.1 150.0 2457.9 2844.2   
25 1265.8 5528.1 140.1 2517.3 2870.6   
26 1296.8 5661.1 123.3 2631.9 2905.9   
27 1329.4 5803.4 96.9 2759.7 2946.9   
28 1353.5 5910.4 79.3 2850.9 2980.3   
29 1344.6 5860.0 8.2 3026.0 2825.8     
 
Table 3-3:  B1 Applied Load Steps and Resulting Girder Moments 
 80
Load otal Co pressi  T m on Flange, Inside Tip, Extreme Fiber Stress Moments at Section 
Case A plied ? ?
z
 p
z
 ?
z
?
z
 ?
z
 ?
z
(lat.)   M
x
 M
x
 M
y
 Bi M
lat.
    
  oad To l from FrL ta om from from     Direct Indirect     Comp.   
   M
x
   M
y
 M
z
 P
z
            Flange   
          (b) (b)/(a)   (c)       (c)/M
x
yield
  (a) 
  N M  MPa Mk Pa Pa MPa MPa MPa   kN-m kN-m kN-m kN-m
2
 kN-m  
Elastic 
Instal    -69. 7 43.24 2l. 9 - . 9.06 -0.52 -26.20 0.61 536.8   -3.7 45.8 16.8  86 -2
DL . - .06 9.63 4.11 -31.68 0.38 1022.1   2.6 46.6 20.3   -109 90 82.33 -2  -2
In +D . -1 .80 8.69 3.59 -57.88 0.46 1559.0   -1.0 92.4 37.0  stall. L  -179 87 25.57 0  -5
(1 .0 -179 66 25.36 0) 0 . -1 .86 8.73 3.58 -57.87 0.46 1556.4 1557.8 -1.1 92.5 37.0 0.31  -5
(2 3.8 -193 78 34.96 -0) 6 . -1 .10 2.26 3.54 -62.36 0.46 1675.5 1688.9 0.1 98.0 39.9 0.33  -6
(3 7.8 -226 50 57.60 -1) 18  . -1 .82 0.68 3.59 -72.49 0.46 1956.5 1972.6 2.3 111.3 46.3 0.39  -7
(4 9.7 -265 90 84.84 -3) 32  . -1 .84 0.91 3.69 -84.75 0.46 2294.7 2315.8 4.9 127.4 54.2 0.46  -8
(5 9.8 -302 76 10.21 -5) 45  . -2 .71 0.64 3.79 -96.34 0.46 2609.8 2623.4 7.3 142.7 61.6 0.52  -9
(6) 0. -356 4 46.9  -865 0 .7  -2 5 .9 04.75 3.96 -113.74 0.46 3065.9 3095.3 11.5 164.9 72.7 0.61 9 -1
(7) 2. -403 5 77.7  -180 7 .3  -2 2 2.54 17.10 4.00 -129.64 0.47 3447.8 3473.2 16.0 184.3 82.9 0.68  -1
(8) 5. -411 2 83.0  -182 6 .8  -2 0 3.47 19.61 4.27 -133.09 0.47 3513.4 3516.1 17.2 188.3 85.1 0.69  -1
Plastic 
(9) 4. -419 9 87.0  -184 5 .2  -2 6 4.58 21.79 4.15 -136.37 0.48 3563.9 3562.7 18.7 191.7 87.2 0.70  -1
(10) 8. -441 0 96.0  -187 1 .2 -2 3 9.25 28.76 2.84 -148.01 0.50 3675.2 3639.7 24.6 202.7 94.6 0.72  -1
. .       .    . 
. .   .    . 
. .       .    . 
(28) 1353.5                  4539.2       0.90 
 
le 3-4:  B1 Mid-Span Stresses and Moments Tab
 
B1 Vertical Bending Moment (Mx)
0.0
500.0
1000.0
1500.0
Total Applied Load (kN)
o
me
2000.0
25
3000.0
4000.0
0.0 200.0 400.0 600.0 800.0 1000.0
M
n
t
 (
k
N
-
m)
3500.0
00.0
Direct Indirect
 
ending Moment Figure 3-13:  B1 Vertical B
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
0
1000
2000
3000
4000
5000
6000
G1 Test
G2 Test
B1 Test
 
 
Figure 3-14:  Test Frame Mid-Span Vertical Bending Moments, B1 Test 
)
 82
Figure 3-14 compares the mid-span vertical bending moments carried by B1, G2 and 
G1 due to the applied loading. The maximum sustained vertical bending moment in B1 
was 4,539 kN-m (3,347.5 k-ft) and occurred at load step 28. Failure of B1 occurred 
during the displacement increase associated with load step 29. Failure is defined as the 
point at which a decrease in the component mid-span vertical bending resistance is 
associated with an increase in either the total load sustained by the test frame or the 
vertical displacement of the test frame. As the result of yielding and/or local compression 
flange buckling, the point of failure is generally coupled with dramatic load shedding 
from the component to G2. This is the condition illustrated by the last points (load step 
29) of the B1 and G2 plots in Figure 3-14. At this load step, G2 is resisting more applied 
vertical bending moment than B1. 
The effects of installation and dead load on the mid-span of B1 can be seen in Figure 
3-15. The seemingly complementary strain gradients in the flanges indicate that the 
primary cause of longitudinal strain is strong-axis bending and warping. If a significant 
weak-axis bending moment was present its effect would increase the gradient of strain 
across the co nge. 
The mid-span longitudinal strain state at first yield in B1, load step 8, is shown in 
Figure 3-16. In addition to the longitudinal strains plotted on each plate as in previous 
figures, this figure and those in the subsequent sections also show the individual steel 
plate yield strain limits with dashed lines labeled ?
y
.  
Returning to Figure 3-16, despite the slight separation of the regression lines at the 
inside tip of the compression flange and at the top of the web, the section is essentially 
mpression flange and decrease this gradient across the tension fla
 83
behaving linearly elastically. This deduction is proven by the ratio of the direct to indirect 
calculation of resisted vertical moment, see Figure 3-13 and Table 3-4. 
Center of 
B1 Section E
Step 1
Curvature
-2000 -1000
0
00 00
10 20
-5000
-4000
-3000
-2000
-1000
0
-?
y
 
?
y
 
0
2000
4000
1000
3000
5000
-?
y
 ?
y
 
B1 Mid-Span Longitudinal Strain State Resulting From Installations and Dead Load 
(Step 1) 
 
Figure 3-15:  
 84
Center of 
Curvature
-2000 -1000
0
10
00
20
00
-5000
-4000
-3000
-2000
-1000
0
B1 Section E
Step 8
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-16:  B1 Mid-Span Longitudinal Strain State During Step 8 
 
The longitudinal strain state at the more critical cross-frame section for the B1 test at 
first yield (step 8) is shown in Figure 3-17. While this plot does not include the effects of 
installing the bending component on the cross-section, the most critical flange tip is more 
than 500 ?e away from its yield limit supporting the assertion that first yield in this 
component occurred at mid-span. At this cross-section, the flange strain gradients trend 
opposite to those for the mid-span cross-section because the lateral bending effect in the 
flange due to warping has gone through the expected inflection near the brace point. 
 85
Center of 
Curvature
-5000
0
0
-2000
000
0
-400
-300
-1
B1 Section C
Step 8
?
y
 
-?
y
 
0
000
000
000
000
000
1
2
3
4
5
 
Figure 3-17:  dinal tate  Nea Fram  During tep 8 (Excluding 
Installation Effects) 
d step the m n of  shown in Figure 3-18. At this load level, the 
inside compre lange expe ng t  thic ieldin . Al , first yield 
in the tension flange has been reached at the inside tip. The separation of the regression 
lines at the in  of th ression flange  the th  web ind ates the 
presence of local plate bending or, perhaps, the onset of buckling.  
Longitu  Strain S  in B1 r Cross- e N6L  S
 
Loa  11 for id-spa  B1 is
ssion f  tip is rienci hrough kness y g so
side tip e comp  and at  top of e ic
 86
 87
Cent
Curvature
er of 
-
2
0
0
0 0 0 0 0
-
1
0
0
10
0
20
0
-5000
-3
-2000
-4000
000
-1000
0
B1 Section E
1Step 1
?
y
 
-?
y
 
0
3000
10
20
00
00
40
50
00
00
 
Figure 3-18:  B1 Mid-Span Longitudinal Strain State During Step 11 
Mid-span of B1 at load 9. is sustained load, 
ro r tension flange have 
excee their y th e tip of the 
compress  nge that w owever, the 
While the strain gradient across the tension flange has increased slightly through the 
sion of loading th oint, the gradient of strain across the compprog
web strains are now indicating 
app
 
res
ded 
xim
ion
-?
y
 ?
y
 
step 1
preately half of the com
fla
ield stren
 to 
gt
a
hs.
s fi
is p
 Th
rst
the distortions consistent with racking of the flanges. 
e 
 ob
8 i
ssi
loc
se
s s
on
al 
rve
ho
 fl
wn
ang
pla
d a
te 
t load step 8 has increased. H
 in
e 
 Fi
and
bend
gu
 a
ing
re 
 qu
3-1
arte
 at e in
 A
of 
t th
the 
sid
ression flange 
is nearly four times what it was across the tension flange at this load step. This 
amplification is the result of the increase lateral bending of the compression flange due to 
the P-delta effects of the horizontally curved flange.  
Center of 
Curvature
-2000 -1000
0
20
000
0
10
-5000
-4000
-3000
-2000
-1000
0
B1 Section E
Step 18
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-19:  B1 Mid-Span Longitudinal Strain State During Step 18 
 
The effects of the maximum sustained load during the B1 test are shown in Figure 3-
20. The regression lines for the top flange data have been replaced with simple linear 
links. When the strain data across any surface of a plate becomes non-linear due to 
excessive yielding or buckling the regression line for that particular data set is replaced 
 88
with simple linear links. Shaded symbols are connected with a solid gray line while open 
symbols are connected with a dashed black line. 
Returning to Figure 3-20, the maximum sustained load during the B1 test has caused 
through thickness yielding over approximately 5/8 of the compression flange and over 
half of the tension flange. The compression flange and web have buckled significantly as 
evidenced by the grossly disparate regression lines. 
Center of 
Curvature
-2000 -1000
0
10
00
20
00
-5000
-4000
-3000
-2000
-1000
0
B1 Section E
Step 28
(Max. Load)
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-20:  B1 Mid-Span Longitudinal Strain State During Step 28 
 
 89
Figure 3- an 
longitudinal strains of G2. At this load step, G2 is resisting a majority of the applied 
moment, and B1 has failed. While the figure does not include any effects for installation 
of the B1 into the test frame, the applied load effects are far enough from the indicated 
yield limits to ensure elastic behavior. G2 and G1 as well as all cross-frame members 
were continuously monitored during each test to ensure they remained elastic as the 
bending component exceeded this limit. 
21 shows the effects of the applied loads at step 29 on the mid-sp
Center of 
Curvature
-2
000
-1
000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B1-G2
Step 29
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-21:  Most Critical G2 Mid-Span Longitudinal Strain State B1 Test (Step 29) 
 
 90
3.5 Bending Component B2 Test 
The test frame that contains bending component B2 was loaded to a maximum of 
1,434 kN (322.4 kip) in 33 steps. The applied load levels for each step and the associa
vertical bending resistance for each girder element are listed in Table 3-5.  
Table 3-6 contains the mid-spa
ted 
n stresses and moments experienced by B2 throughout 
the elastic range of loading. When yield was first reached in the bending component at 
load step 10, the normalized vertical bending strength ratio was 0.67. Also, for the 
com
 comparison of the direct versus indirect methods of determining the vertical 
bending moment at mid-span of B2 is shown in Figure 3-22. The plot indicates good 
agreement between the two methods for determining the vertical bending resistance of 
B2. At first yield in B2, load step 10, the ratio of indirect to direct resistance is 0.98 (see 
Table 3-5). 
Figure 3-23 shows the vertical bending moments at mid-span of each of the three 
girders of the test frame throughout the B2 test. The test progressed until G2 carried a 
greater percentage of the applied load than B2.  
The installation and dead load effects on the longitudinal strain state at mid-span of 
B2 are shown on Figure 3-24. Recall that the installation strain data used in this analysis 
were derived from the B5 and B6 tests. The complementary gradients of strain in the 
flanges indicate that these effects are dominated by strong-axis bending and warping. The 
pression flange, the ratio of lateral bending stress to vertical bending stress ranged 
from 0.50 to 0.52 in this regime. A maximum vertical bending moment of 4,730 kN-m 
(3,487.9 k-ft) corresponding to a normalized ratio of 0.90 was sustained by B2 during 
step 33. 
A
 91
web data are consistent and linear indicating a lack of plate flexing at this initial load 
level.  
 92
 
Load  Total Applied Mx (Total) Mx (G1) Mx (G2) Mx (B2)   
Step Load      Indirect Direct   
        (a) (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
B2 Elastic 
1 0.0 -0.4 0.0 -0.4 0.0 0.6 -0.05
2 26.1 111.4 8.1 37.9 65.4 57.3 1.14
3 137.5 602.7 35.3 206.2 361.2 314.9 1.15
4 274.8 1204.6 70.6 451.6 682.4 643.2 1.06
5 404.7 1779.1 97.2 656.0 1025.9 957.4 1.07
6 535.5 2363.2 122.8 873.7 1366.7 1279.2 1.07
7 664.1 2937.2 150.4 1149.0 1637.7 1626.4 1.01
8 794.5 3510.4 160.8 1406.0 1943.6 2008.4 0.97
9 826.7 3651.9 165.4 1472.0 2014.6 1979.6 1.02
10 852.8 3767.4 169.6 1526.4 2071.3 2103.1 0.98
B2 Plastic 
11 874.0 3858.2 170.3 1572.9 2115.0 2179.5 0.97
12 907.8 4009.8 176.0 1630.2 2203.6 2251.5 0.98
13 938.5 4145.0 178.9 1690.5 2275.6 2353.1 0.97
14 963.7 4254.1 179.5 1740.9 2333.7  
15 983.0 4341.0 178.0 1789.5 2373.5  
16 1015.6 4485.6 180.7 1849.7 2455.2   
17 1040.9 4599.1 184.3 1905.5 2509.3   
18 1071.1 4732.4 186.2 1967.0 2579.2   
19 1090.9 4817.4 184.6 2015.1 2617.7   
20 1112.8 4909.6 177.1 2065.4 2667.1   
21 1143.3 5049.6 178.9 2129.7 2741.1   
22 1167.4 5153.9 178.3 2190.2 2785.4   
23 1199.9 5301.9 177.5 2255.0 2869.4   
24 1223.2 5405.1 173.6 2321.7 2909.8   
25 1251.6 5531.8 172.1 2388.2 2971.5   
26 1280.0 5660.0 168.5 2463.6 3028.0   
27 1306.5 5777.6 163.9 2528.3 3085.4   
28 1331.3 5884.8 154.4 2603.1 3127.3   
29 1358.1 6001.4 143.1 2683.5 3174.7   
30 1382.5 6110.3 131.5 2763.5 3215.3   
31 1410.8 6223.7 113.7 2855.9 3254.1   
32 1417.9 6256.3 94.8 2911.2 3250.3   
33 1434.1 6327.1 80.9 2981.5 3264.7   
34 1423.8 6277.7 50.9 3050.9 3176.0   
35 1392.4 6130.9 23.5 3042.5 3064.9   
36 1384.7 6095.6 -6.8 3115.1 2987.2   
37 1349.3 5935.6 -43.7 3099.7 2879.7     
 
Table 3-5:  B2 Applied Load Steps and Resulting Girder Moments 
 93
Load  Total Compression Flange, Inside Tip, Extreme Fiber Stress o s ctiM ment at Se on 
Case Applied ?  ?  ?  ?  ?  ? (lat.) 
x
 
x
 M
lat.
 
z z z z z z
 M M
y
 Bi M  
  Load Total fr ct direct   mom from from from     Dire In   Co p.   
     M
x
 M
y
 M
z
 P
z
        Flange       
     (a)       (b) (b)/(a) )   (c
yiel
  (c     )/M
x
d
 
  kN MPa M a m N k
2
-  Pa MPa MPa MPa MP   kN-m kN-  k -m N-m  kN m 
Elastic 
Install.   -68.64 -41.81 2.88 -29.23 -0.48 -26.35 0.63 536.8 -3 .7  .7 45.8 16    
DL  -72. -31.53 0.44 .1 4. .0  -100.96 29 -3.55 -27.98 2.86 928   5 43.8 20    
Install.+DL   -169.60 -11 88 .9 0. .84.10 -0.67 -57.21 2.38 -57. 0.51 1464   8 89.6 36    
(1) 0.0 -169.60 -11 90 0.51 .5 4. 0. .7 .84.14 -0.59 -57.31 2.44 -57.  1465 146 9 7 89 36  0.28 
(2) 26.1 -176.09 -118.56 -1.09 -58.96 2.53 -60.05 0.51 1522.2 0. 1. .3 .2153 3 4 92 38  0.29 
(3) 137.5 -205.88 -138.63 -2.83 -66.84 2.42 -69.67 0.50 .8 1826. 3. 6 .31779 1 6 104. 44  0.35 
(4) 274.8 -243.54 -16 76 .50 .2 2147. 6. 5 .04.20 -4.79 -76.97 2.42 -81.  0 2108 3 1 120. 52  0.41 
(5) 404.7 -279.74 -188.67 -6.67 -86.84 2.43 -93.50 0.50 .3 2490. 8. 9 .4  2422 9 5 135. 59  0.47
(6) 535.5 -317.23 .74 -8.85 -97.18 2.54 -106  0.50 4.1 2831. 1 1 .4  -213 .03 274 6 1.2 152. 67  0.54
(7) 664.1 -359.61 .78 -11.29 -110.14 2.61 -121  0.50 1.3 3102. 14   -240 .43 309 6 .4 172.4 77.2 0.59
(8) 794.5 -407.85 -270.53 -15.61 -124.98 3.27 -140.59 0.52 .3 3408. 19  3473 5 .8 195.6 89.3 0.65
(9) 826.7 -404.06 -26 . 0.52 .5 3479. 19  8.29 -15.22 -124.09 3.53 -139 31 3444 5 .3 194.2 88.5 0.66
(10) 852.8 -419.90 -277.91 -16.95 -128.54 3.51 -145.49 0.52 .0 3536. 21  3568 2 .6 201.2 92.5 0.67
Plastic 
(11) 874.0 -430.12 -28 149.75 .53 3644.4 3579. 23  3.86 -18.13 -131.62 3.49 -  0  9 .0 206.0 95.2 0.68
(12) 907.8 -441.56 -28 . 3716.5 3668. 25  9.47 -20.05 -135.23 3.19 -155 27 0.54 6 .5 211.7 98.7 0.70
. .       .    .
. .   .   .
. .    .        .
  4729.    6     0.90(33) 1434.1               
 
Table 3-6:  B2 Mid-Span Stresses and Moments
 
B2 Vertical B ng M nt (M
0.0
500.0
1000.0
1500.0
2000.0
2500.0
3000.0
3500
000.0
0.0 200.0 400.0 600.0 800.0 1000.0
Total Applied Load (kN)
M
o
me
n
t
 (
k
N
-
m)
endi ome x)
4
.0
Direct Indirect
 
Figure 3-22:  B2 Vertical Bending Moment in Elastic Range 
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
)
0
1000
2000
3000
4000
5000
6000
G1 Test 
G2 Test
B2 Test
 
 
Figure 3-23:  Test Frame Mid-Span Vertical Bending Moments, B2 Test 
 95
Center o
urvatur
f 
C e
-2 -
1
0000
0
0 0
1
000
0
0
2
0
-5000
-4000
00
00
-1000
0
-30
-20
B2 Section E
Step 1
?
y
 
-?
y
 
0
00
00
3000
00
00
10
20
40
50
-?
y
 ?
y
 
 
Figure 3-24:  B2 Mid-Span Longitudina in Sta lting F nstallatio  and Dead oad 
Step 1
ield B2 te urred e inside compression flange tip at mid-span of 
the component during load step 10. The longitu rain  the m -span cro -
section at in the 
tension (bottom) flange compared with the compression (top) flange indicates that there 
is a significant weak-axis bending effect at mid-span of B2 at this load level. The 
regression lines fit the data well, which is representative of linear-elastic behavior. 
l Stra te Resu rom I n  L
( ) 
 
First y  in the st occ  at th
dinal st state of id ss
step 10 can be seen in Figure 3-25. The slightly flatter strain gradient 
 96
 97
C
C
enter
urva
 of
tu
 
re
-2
0
0 0 0 0
0
-1
0
0 0 0
1
0
2
0
0
-5000
-2000
-4
-3
000
000
-1000
0
B2 Section E
Step 10
?
y
 
-?
y
 
0
1000
4000
2
3
000
000
5000
-?
y
 ?
y
 
 
Figure 3- St ing Step 10 
 
Th ost critical b n nted section adjacent to 
e outside tension flange tip is still more than 500 ?e from its 
yiel id-span of B2 
s test. 
25:  B2 Mid-Span Longitudinal Strain ate Dur
e m raced section of B2 at step 10, the i strume
cross-fram
included in this figure, th
e N6L, is shown in Figure 3-26. Although the effects of installation are not 
d limit. This result supports the conclusion that first yield occurred at m
during thi
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B2 Section C
Step 10
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-26:  Longitudinal Strain State in B2 Near Cross-Frame N6L During Step 10 (Excluding 
Installation Effects) 
 
Figure 3-27 depicts the longitudinal strain state at mid-span of B2 when the tension 
flange also reaches its yield limit. At this point, the inside tip of the compression flange is 
experiencing through-thickness yielding and the regression lines of the compression 
flange are starting to slightly separate. This separation indicates that the local plate 
bending or buckling has initiated. 
 98
Center of 
Curvature
-2000 -1000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B2 Section E
Step 13
-?
y
 
?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-27:  B2 Mid-Span Longitudinal Strain State During Step 13 
 
At step 22 of the B2 test, the outside tip of the tension flange at cross-frame N6L and 
the outside tips of both flanges of the cross-section at cross-frame N6R have reached their 
yield limits as can be seen in Figures 3-28 and 3-29 respectively. At load step 27, the 
cross-sections adjacent to N6L and N6R were experiencing yielding in all outside flange 
tips. 
 99
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B2 Section C
Step 22
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-28:  Longitudinal Strain State in B2 Near Cross-Frame N6L During Step 22 (Excluding 
Installation Effects) 
 
 100
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B2 Section C
Step 22
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-29:  Longitudinal Strain State in B2 Near Cross-Frame N6R During Step 22 (Excluding 
Installation Effects) 
 
The longitudinal strain state of mid-span B2 during the maximum sustained moment 
of the test, step 33, is illustrated in F ure shows that approximately 5/8 
of the compression flange and ? of the tension flange had yielded at this load level. The 
separations of the compression flange and web data regression lines indicate local 
bending and buckling of these plates.  
igure 3-30. The fig
 101
Center of 
Curvature
-2
000
-1
000
0
1
000
2
000
-5000
-4000
-3000
-2000
-1000
0
B2 Section E
Step 33
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-30:  B2 Mid-Span Longitudinal Strain State During Step 33 
 
Figure 3-31 illustrates the strain state of the mid-span of G2 at the maximum load that 
this girder sustained during the B2 test. The data reveal linear elastic behavior well below
the yield limit in all three plates of the cross-section.  
 
 102
Center of 
Curvature
-200
0
-100
0 0
100
0
200
0
-5000
-4000
-3000
-2000
-1000
0
B2-G2
Step 36
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-31:  Most Critical G2 Mid-Span Longitudinal Strain State During B2 Test (Step 36) 
 
3.6 Bending Component B3 Test 
The test frame containing component B3 was loaded in 45 steps to a maximum 
represent approximately 27 kN (6 kip) increases in applied load. From step 31 to the end 
of the test, the experiment was conducted in displacement control. The maximum applied 
vertical bending moment sustained by B3, 3,375 kN-m (2,489.2 k-ft), occurred during 
applied load of 1,504 kN (338.1 kip). From step 8 to step 31, these load step increments 
 103
load step 44. Table 3-7 and Table 3-8 contain these results along with other selected 
information regarding the B3 test. 
Load  
Total 
Applied Mx (Total) Mx (G1) Mx (G2) Mx (B3)   
Step Load     Indirect Direct   
        (a) (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
B3 Elastic 
1 0 -0.7 -0.1 0.4 -1 0.2 -5.4 
2 56.4 240.9 14.2 81.7 144.9 126.9 1.14 
3 148.9 651.2 40.4 231.4 379.4 338.4 1.12 
4 276.5 1219.2 70.3 451.8 697.1 644.6 1.08 
5 406.5 1793.6 96.9 674.8 1021.9 962.6 1.06 
6 536 2362.5 119.6 901 1341.8 1283.3 1.05 
7 664.9 2931.3 141.9 1135.5 1654 1604.4 1.03 
8 802.3 3545.4 172.2 1373.7 1999.5 1936.9 1.03 
9 826 3650.1 178.8 1419.1 2052.2 1998.5 1.03 
10 852.7 3766.8 178 1469.1 2119.8 2075.8 1.02 
B3 Plastic 
11 872.2 3850 180.7 1511.3 2158.1 2137.9 1.01 
12 906.6 4005.6 189.6 1569.7 2246.3 2229.9 1.01 
13 934.8 4129.4 193.6 1625.9 2309.9    
14 960.4 4239.7 193.1 1686.1 2360.5    
15 984.3 4347.6 190 1737.8 2419.8    
16 1012.9 4474 194.3 1792.5 2487.2    
1033.9 4566 2535.8    17 189.2 1841 
18 1060.8 4684.5 193 1900.7 2590.8    
19 1092.1 4823.4 193 1966.1 2664.2    
20 1116.5 4930.9 189.2 2017.1 2724.6    
21 1141.4 5039.1 188.8 2080 2770.4    
22 1169.6 5167.8 193.7 2138.3 2835.8     
 
Table 3-7:  B3 Applied Load Steps and Resulting Girder Moments (Part I) 
 104
 
Total 
Load  Applied Mx (Total) Mx (G1) Mx (G2) Mx (B3)   
Step Load     Indirect Direct   
        (a) (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
23 1195.5 5281.5 185.2 2205.5 2890.8    
24 1223.4 5407.3 185.1 2279.2 2943    
25 1249.4 5524.3 181 2340.4 3002.9    
26 1273.7 5633.7 176 2403.7 3054    
27 1299.6 5748.6 171.8 2471.3 3105.6    
28 1326.3 5868.3 160.5 2549.1 3158.6    
29 1347.9 5962.8 146.5 2629 3187.2    
30 1371.9 6068.6 153.1 2678.9 3236.6    
31 1401.8 6201.2 140.9 2777.5 3282.9    
32 1417.9 6271.6 128.9 2830.3 3312.4    
33 1434.6 6345.2 111.6 2896.9 3336.7    
34 1445.2 6395.5 103.8 2940.9 3350.8    
35 1452.6 6426.7 94.6 2966.8 3365.2    
36 1454.9 6436.9 85.4 2996.4 3355.2    
37 1457.8 6450.3 79 3009.6 3361.7    
38 1406.5 6203.7 44.1 2950.2 3209.4    
39 1452.6 6426.4 71.2 3023.6 3331.5    
40 1455.5 6440.7 68.7 3034.7 3337.3    
41 1459.9 6459.8 65.2 3046.5 3348    
42 1458.6 6457.1 62.8 3055.7 3338.6    
43 1460.4 6463.9 59.4 3062.5 3342    
44 1499.7 6620 68.7 3175.9 3375.4    
45 1503.8 6634.5 21.9 3329.1 3283.5    
46 1479.9 6533.4 -154.5 3671.2 3016.7   
 
Table 3-8:  B3 Applied Load Steps and Resulting Girder Moments (Part II)
 105
Load  Total Compression Flange, Inside Tip, Extr e Fiber Stress Moments a tiem t Sec on 
Case Applied ?
z
 ?
z
 ?
z
 ?
z
 t.)
x
 M
y
 
lat.
?
z
 ?
z
(la   M
x
 M Bi M   
  Load Total from from from fr ct irect     mom     Dire Ind Co p.   
     M
x
 M
y
 M
z
        Flange P
z
       
     (a)   b) (c)       (c
el
    (b) ( /(a)   )/M
x
yi d
 
 kN MPa MPa MPa M  M a m -m  k
2
-m  Pa Pa MP   kN-  kN kN-m N-m  kN  
Elastic 
Install.  86 -2 -0 8 4 0.  8   45.8  -68.26 -41.64 2. 9.00 .4 -26.1  63 536.  -3.7  16.7 
DL   -102.30 -71.53 -4.12 -27  1. 8 0. 2   43.9 .4 .85 21 -31.9  45 922. 5.3 20   
Install.+DL   -170.56 -113.17 -1.2 -5 0. 2 0. .1   89.7 .0 6 6.85 73 -58.1  51 1459 1.6 37   
(1) 0.0 1.2  0. 0 0. 2 58.1  89.7 .0 28 -170.52 -113.18 - 5 -56.84 76 -58.1  51 1459.  14 6.9 37  0.
(2) 56.4 -2.4 -6  0. 9 0. 9 04.0  95.9 .3 30 -185.29 -123.01 2 0.76 91 -63.1  51 1585.  16 8.5 40  0.
(3) 148.9 -209.34 -139.41 -4.03 -67  1. 4 0. 4 38.5  105.7 .3 35 .00 11 -71.0  51 1797.  18 15.4  45  0.
(4) 276.5 -244.41 -163.17 -6.4 -7  1. 2 0. 7 56.2  120.2 .6 41 2 6.20 38 -82.6  51 2103.  21 23.9  52  0.
(5) 406.5 -280.65 -187.83 -8.71 -8  1. 3 0. 7 2481.0  135.4 .2 47 5.81 71 -94.5  50 2421. 39.3  60  0.
(6) 536. -317.54 -212.71 - 8 -9  2. 0.  4 2800.9  151.00 11.2 5.70 15 -106.99 50 2742. 63.3  68.2 0.53 
(7) 664. -354.77 -237.61 - 9 -10  2 81 0. 4 3113.0 166.8 .3 59 9 14.0 5.71 .65 -119.  50 3063. 102.6  76  0.
(8) 802.3 -394.28 -263.40 -17.49 -11  2 83 0. 0 3458.6 9 183.6 .3 66 6.34 .95 -133.  51 3396. 165.  85  0.
(9) 826.0 8. -11  3 82 0. 6 3511.2 5 187.2 .2 67 -401.90 -268.18 -1 16 8.65 .10 -136.  51 3457. 268.  87  0.
(10) 852.7 -411.88 -274.18 -19.21 -12 65 3. 85 0. 9 3578.9 3 191.9 .7 68 1. 15 -140.  51 3534. 434.  89  0.
Plastic 
(11) 872.2 0. .98 3. 67 0. 9 3617.1 8 204.5 .8 69 -421.46 -278.99 -2 69 -124 19 -145.  52 3596. 702.  92  0.
(12) 906.6 3.  3.02 73 0. 0 3705.3 1 89.7 .3 70 -435.84 -286.13 -2 11 -129.62 -152.  53 3689. 1137. 97  0.
.      . .   
.     .    .  
.   . .   
(44)      4834.4      0.92        1499.7       
 
pan resses and MomentsT  3-9:  B3 Mid-S Stable
 
Tabl 9 con he  mi  str nd ts  First yield occurred at 
the insid  of po mp  fl rin 0  At this ad level, B3 
was resisting a vertical bending mom 3,535 kN-m (2,606.8 k-ft), which represents 
approxim ly 6 he  yie me is t. This rmalized 
ratio wa sed at wh wa ng m m of 4,834 kN-m 
(3,565.2 ). Th  of flan ndi s to lange b ding stress 
ranged b een d 0 ug e e egi  test. 
A co e f d i  the ver al moment 
resistance of the B3 component is presented in Figure 3-32. The individual results are 
included in Table 3-7. At first yield, step 10, these results differ by 2%. 
e 3- tains t B3 test d-span esses a momen .
e tip the com nent co ression ange du g step 1 . lo
ent of 
ate 8% of t vertical ld mo nt for th componen no
s rai to 0.92 step 44 en B3 s resisti  a maxi u
 k-ft e ratio  lateral ge be ng stres  vertical f en
etw 0.50 an .51 thro hout th lastic r me of this
mparison of the indirect and direct m thods o etermin ng tic
B3 Vertical Bending Moment (Mx)
0.0
500.0
1000.0
1500.0
2000.0
2500.0
3000.0
3500.0
4000.0
0.0 200.0 400.0 600.0 800.0 1000.0
Total Applied Load (kN)
M
o
me
n
t
 (
k
N
-
m)
Direct Indirect
 
Figure 3-32:  B3 Vertical Bending Moment 
 
Figure 3-33 illustrates the mid-span vertical bending moments of G1, G2 and B3 as a 
function of the total applied load for this component test. The test progressed until G2 
 107
resisted a majority of the applied mid-span moment. However, this condition was not 
assu nts red until load step 46, because at load step 45 the applied vertical bending mome
carried by G2 and B3 were very similar 3,329 kN-m vs. 3,284 kN-m (2,455.1 k-ft vs. 
2,421.5 k-ft).  
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
0
1000
2000
3000
4000
5000
6000
G1 Test
)
G2 Test
B3 Test
 
 
Figure 3-33:  Test Frame Mid-Span Vertical Bending Moments, B3 Test 
 
The effects of dead load and installation on the longitudinal strain state at mid-span of 
B3 are shown in Figure 3-34. The overlapping regression lines indicate linear-elastic 
behavior and the absence of local plate distortion at this cross-section under these small 
loads. Figure 3-35 shows the state of B3 mid-span longitudinal strain at the load level 
required to produce first yield in the cross-section. At this load level, step 10, the 
separating regression lines of the web in compression as well as the crossing and 
 108
 
separating regression lines across the com
bending in the cross-section. 
109
pression flange are evidence of local plate 
Center of 
Curvature
-
2
0
0
0
-
1
0
0
0 0
1000 2000
-50
-40
00
00
-3000
0
-20
-1000
00
B
St
3 Section E
ep 1
?
y
 
-?
y
 
0
00
1000
20
3000
4000
5000
-?
y
 ?
y
 
 
ure 3-34:  B3 Mid-S su rom Installation and Dead Load Fig pan Longitudinal Strain
(Step 1) 
 S
 
tate Re lting F
Center of 
Curvature
-2000 -1000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B3 Section E
Step 10
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-35:  B3 Mid-Span Longitudinal Strain State During Step 10 
 
Figures 3-36 and 3-37 show the very similar longitudinal strain states at cross-frames 
N6L and N6R, respectively, produced during step 10. In fact, both braced sections 
behaved almost identically throughout both the elastic and inelastic portions of the B3 
test.  
 110
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B3 Section C
Step 10
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-36:  Longitudinal Strain State in B3 Near Cross-Frame N6L During Step 10 (Excluding 
Installation Effects) 
 
 111
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B3 Section H
Step 10
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-37:  Longitudinal Strain State in B3 Near Cross-Frame N6R During Step 10 (Excluding 
Installation Effects) 
 
The yield limit of the steel in the tension flange of B3 at mid-span was first reached 
during step 14. As seen in Figure 3- l there is evidence of through 
thickness yielding at the inside tip of the com
l
38, at this load leve 
pression flange and of an increase in the 
ocal plate bending in this flange and along the depth of the web in compression. 
 112
Center of 
Curvature
-2000 -1000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B3 Section E
Step 14
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-38:  B3 Mid-Span Longitudinal Strain State During Step 14 
 
Figures 3-39 and 3-40 show the longitudinal strain state at cross-sections N6L and 
N6R, respectively, during step 21. At this load level, the outside tip of tension flange at 
N6R reaches yield during step 22, and the outside tip of the compression flange at N6L 
r
load
both locations has just reached its yield limit. The outside tip of the compression flange at 
eaches yield at step 23. The longitudinal strain states at these locations at the respective 
 steps can be seen in Figures 3-41 and 3-42.  
 113
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B3 Section C
Step 21
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-39:  Longitudinal Strain State in B3 Near Cross-Frame N6L During Step 21 (Excluding 
Installation Effects) 
 
 114
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B3 Section H
Step 21
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-40:  Longitudinal Strain State in B3 Near Cross-Frame N6R During Step 21 (Excluding 
Installation Effects) 
 
 115
Center of 
Curvature
-5000
-4000
00
-1000
0
-30
-2000
B3 Section H
Step 22
-?
y
 
?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-41:  L inal tate ear rame uring S p 22 (Exc ding 
Installation Effects) 
 
ongitud  Strain S  in B3 N Cross-F  N6R D te lu
 116
B3 S
Step
ec
 23
tion C
Center of
rvatu
 
Cu re
-5000
-4000
-3000
-2000
000
0
-1
?
y
 
-?
y
 
0
000
2000
000
000
5000
1
3
4
 
Figure 3-42:  inal tate ear rame uring S p 23 (Exc ding 
The test fram e weak
state at th ate 
significant buckling across the plate and through-thickness yielding on the inside half of 
the plate. The web data also indicate significant plate bending at the cross-section. While 
the tension flange data at this location show yielding across half of the plate, little 
evidence of significant local plate bending is displayed. 
Longitud  Strain S  in B3 N Cross-F  N6L D te lu
Installation Effects) 
 
e?s response briefly becam er after step 31. The longitudinal strain 
at load step is shown in Figure 3-43. The compression flange data indic
 117
 118
Center of 
Curvature
-
2
0
0
0 0 0 0 0
-
1
0
0
1
0
0
2
0
0
-5000
-3
-2000
-4000
000
-1000
0
B ction E
St p 31
3 Se
e
?
y
 
-?
y
 
0
3000
10
20
00
00
40
50
00
00
-?
y
 ?
y
 
 
Figure 3-43:  B3 Mid-Span Longitudinal Strain State During Step 31 
In a post-buckled state, the stiffness of B3 remained stable until an applied load of 
s)
h  level corresponds to the 
maximum resisted ver ,8 -m (3,565.2 k-ft). The 
ained stable enough to sustain an addi
applied load of 1,504 kN (338.1 kip), despite the failure of B3. 
 
1,50
mid-span section at this step is shown in 
0 kN (337.2 kip  was reached during step 44. The longitudinal strain state of the B3 
Fig
en
ur
t b
e 3
y B
-4
3 
4. T
of 4
is l
34
oad
 kNtical bending mom
frame rem tional load increment, step 45, at a total 
Center of 
Curvature
-2
00
-1
00
10
00
20
00
0 0 0
-5000
-4000
-3000
-2000
-1000
0
B3 Section E
Step 44
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-44:  B3 Mid-Span Longitudinal Strain State During Step 44 
 
Figure 3-45 depicts the longitudinal strain state of the mid-span of G2 while it 
experienced the greatest demand of the B3 test, step 46. While the data plotted do not 
include the effects of installation of the B3 component, all measurements are far enough 
away from their respective yield limits to ensure that this girder remained elastic 
throughout the test. 
 119
Center of 
Curvature
-200 -100
100 200
0 0 0 0 0
-5000
-3000
-1000
-4000
-2000
0
B3-G2
Step 46
-?
y
 
?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-45:  Most Critical G2 Mid-Span Longitudinal Strain State During B3 Test 
 
3.7 Bending Component B4 Test 
The test frame, including the singly symmetric B4 component, was loaded to a 
maximum applied load level of 1,354 kN (304.5 kip) during step 29 of this test. This load 
level corresponded to an applied vertical bending moment of 3,223 kN-m (2,376.9 k-ft) at 
mid-span of the component. The individual applied load levels and the effects of each 
step on the test frame girders are summarized in Table 3-10.  
 120
Load  
Total 
Applied Mx (Total) Mx (G1) Mx (G2) Mx (B4)   
Step Load      Indirect Direct   
        (a) (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
B4 Elastic 
1 0.0 -2.2 0.1 0.5 -2.8 -0.2 16.78 
2 45.8 196.4 16.9 61.3 118.2 106.5 1.11 
3 143.9 623.6 42.8 195.4 385.4 344.1 1.12 
4 268.5 1174.1 76.5 363.4 734.3 653.4 1.12 
5 405.7 1774.9 121.7 606.5 1046.7 997.4 1.05 
6 535.1 2345.6 157.4 801.6 1386.6 1327.2 1.04 
7 672.5 2954.5 201.4 1037.3 1715.8 1676.1 1.02 
8 802.7 3530.6 228.3 1262.4 2039.9 2060.3 0.99 
B4 Plastic 
9 826.5 3635.2 232.9 1303.8 2098.5 2136.2 0.98 
10 855.8 3765.3 241.9 1357.2 2166.3 2222.6 0.97 
11 879.5 3871.0 242.3 1398.8 2229.9 2302.1 0.97 
12 908.3 3998.4 251.2 1452.8 2294.3   
13 934.6 4116.5 254.8 1501.2 2360.5   
14 959.9 4227.8 259.7 1551.1 2417.0   
15 985.9 4342.1 261.5 1598.7 2481.9   
16 1012.6 4462.3 270.8 1650.6 2541.0   
17 1040.6 4587.1 271.6 1702.8 2612.7   
18 1065.7 4698.4 274.9 1753.1 2670.3   
19 1093.5 4820.2 277.7 1811.4 2731.0   
20 1117.6 4931.3 278.9 1860.8 2791.7   
21 1142.1 5041.6 276.1 1916.3 2849.2   
22 1169.2 5166.3 277.0 1976.7 2912.7   
23 1193.6 5271.9 272.3 2037.2 2962.5   
24 1219.9 5390.8 268.5 2106.1 3016.2   
25 1246.3 5511.7 264.0 2176.6 3071.1   
26 1269.4 5616.4 252. 6.0 3118.2   1 224
27 1295.1 5732.6 245.7 2323.0 3163.9   
28 1319.8 5841.8 239.6 2402.1 3200.1   
29 1354.5 5995.8 224.1 2548.6 3223.0   
30 1295.0 5719.8 122.6 2707.6 2889.6   
31 1267.4 5596.4 -65.7 3049.3 2612.8     
 
Table 3-10:  B4 Applied Load Steps and Resulting Girder Moments 
 
The ratio of indirect to direct method for determining the mid-span moment of B4 
was 0.99 for load step 8, which is the load level that produced first yield in B4. This ratio 
is illustrated t re 3-46.  hroughout the entire range of elastic behavior of this test in Figu
 121
B4 Vertical Bending Moment (Mx)
0.0
500.0
1000.0
1500.0
2000.0
2500.0
3000.0
0.0 50.0 100.0 150.0 200.0
Total Applied Load (kN)
M
o
me
n
t
 (
k
N
-
m)
Direct Indirect
 
Figure 3-46:  B4 Vertical Bending Moment 
 
Table 3-11 contains the B4 mid-span stresses and moments for the entire elastic 
regime of loading. The table also includes selected information at the maximum resisted 
vertical bending moment in the component. The ratio of lateral flange bending stress to 
vertical flange bending stress in the compression flange of this component ranged from 
0.43 to 0.49 in the elastic load range. At first yield in B4, the ratio of mid-span vertical 
bending moment to yield moment was 0.69. This ratio increased to 0.90 at the maximum 
sustained load level.
 122
Load  Total Compression Flange, Inside Tip, Extreme Fiber Stress oM ments at Section 
Case Applied ?
z
 ?
z
 ?
z
 ?
z
 ?
z
 ?
z
(lat.)   M  M
lat.x
 M
x y
 Bi M    
  Load Total from from from from     Dir pect Indirect     Com .   
     M
x
 M
y
 M
z
 P
z
            Flange   
     (a)       (b) (b)/(a)  (c
eld
   (c)       )/M
x
yi
 kN MPa MPa MPa MPa MPa MPa  kN  m N k  -m-m kN-  k -m N-m
2
kN   
Elastic 
Install.   -67.45 -52.46 -4.55 -16.82 6.38 -21.37 0.41 69 0 1  .8  6.  1 .3 51 13.6 
DL   -104.75 -72.41 -3.00 -29.58 0.24 -32.57 0.45 96 7. .7 0.7   5 91.1 20   
Install.+DL   -172.20 -124.88 -7.55 -46.39 6.62 -53.94 0.43 165 18 1 .3 6.7   .8 42.9 34   
(1) 0.0 -172.34 -124.86 -7.58 -46.48 6.58 -54.06 0.43 165 .9 18  1 3  6.5 1653  .8 43.1 34.  0.31
(2) 0.0 -184.23 -132.90 -8.17 -49.72 6.57 -57.90 0.44 176 .9 20  1 8  3.2 1774  .3 53.1 36.  0.33
(3) 0.4 -210.62 -150.81 -9.44 -56.90 6.52 -66.33 0.44 200 .1 23  1 1  0.7 2042  .5 75.2 42.  0.38
(4) 0.4 -245.02 -174.13 -10.82 -66.58 6.51 -77.40 0.44 231 .9 26  2 2  0.1 2390  .9 05.0 49.  0.44
(5) 0.4 -283.33 -200.06 -12.20 -77.56 6.49 -89.76 0.45 265 .3 30  2 0  4.1 2703  .3 38.8 57.  0.50
(6) 0.4 -320.36 -224.92 -13.68 -88.28 6.52 -101.96 0.45 298 .3 34  2 8  3.9 3043  .0 71.8 64.  0.56
(7) 0.4 -360.63 -251.22 -15.53 -100.20 6.31 -115.73 0.46 333 .5 38 3 5 5  2.8 3372  .6 08. 73.  0.62
(8) 0.4 -411.08 -280.18 -18.53 -117.66 5.28 -136.18 0.49 371 .6 46 3 3 5  7.0 3696  .1 62. 86.  0.68
Plastic 
(9) 0.4 -421.11 -285.90 -19.20 -121.14 5.12 -140.34 0.49 379 .2 47 3 0 2  2.9 3755  .7 73. 89.  0.69
(10) 0.5 -433.11 -292.41 -20.02 -125.48 4.80 -145.50 0.50 387 .0 49 3 4 5  9.3 3823  .8 86. 92.  0.71
. .          .  .
. .  .  .
. .          .  .
(29) 0.0                 7948 .7      0.90 
 
Table 3-11:  B4 Mid-Span Stresses and Moments
 
The mid-span vertical bending moments for each of the girders of the test frame 
during the B4 test are shown in Figure 3-47. The plots in this figure illustrate the data 
included for G1, G2 and B4 (indirect method) in Table 3-10. While the maximum 
sustained load occurred at step 29, the test was continued until step 31. At this point, G2 
was resisting a majority of the applied vertical bending moment. The last point in each 
plot of the figure describes this condition. 
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
)
0
1000
2000
3000
4000
5000
6000
G1 Test
G2 Test
B4 Test
 
 
 
Figure 3-48 shows the longitudinal strain state of the B4 mid-span resulting from the 
installa eral, 
the data indicate linear-elastic behavior of the section. The magnitude and gradient of 
Figure 3-47:  Test Frame Mid-Span Vertical Bending Moments, B4 Test 
tion of the component and from the dead load effects of the test frame. In gen
 124
stra ection are consistent with the expected singly 
sym
in in each of the plates of this cross-s
metric behavior. 
Cent
Cu
er of 
rvature
-20
0
-10
0
0 0 0
10
00
20
00
-5000
-4000
-3000
-2000
-1000
0
B4 Section E
Step 1
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-48:  B4 Mid-Span Longit  Strain State Resulting From
ep 1)
Figure 3-49 illustrates the first yield s  at mid-span of B4 that occurred at 
step 8 of the te his lo l, the  data ig t loc l
bending that is the result o evat  slen s, 18 e cross ections a
N6L and N6R during step 8 are shown in Figures 3-50 and 3-51 respectively. These plots 
do not include the effects that the inst  had e cros ns. Ho ever, the
udinal  Installation and Dead Load 
(St  
 
train state
st. At t ad leve  web  indicate s nifican al elastic p ate 
f the el ed web dernes 8.0. Th -s t 
allation  on th s-sectio w  
 125
data  far en om t ated limi port clusion hat first ld 
occurred at mi . 
 are ough fr he indic  yield t to sup the con  t yie
d-span
Center of 
Curvature
-2
000
-1
000
0
1
000
2
000
-5000
-4000
-3000
-2000
-1000
0
B4 Section E
Step 8
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-49:  B4 Mid-Span Longitudinal Strain State During Step 8 
 
 126
Center of
vature
 
Cur
-5000
-4000
-3000
-2000
000
0
-1
B4 S
Step
ect
 8
ion C
?
y
 
-?
y
 
0
0
0
0
0
0
100
200
300
400
500
 
Figure 3-50:  dina State  Near ram uring S ng 
 
Longitu l Strain  in B4  Cross-F e N6L D tep 8 (Excludi
Installation Effects) 
 127
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B4 Section H
Step 8
-?
y
 
?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-51:  Longitudinal Strain State in B4 Near Cross-Frame N6R During Step 8 (Excluding 
Installation Effects) 
 
The outside tip of the top flange at N6L (Figure 3-52) and at N6R (Figure 3-53) 
reached their yield limit at steps 18 and 19 respectively. However, the tension (bottom) 
flange of B4 never came close to the yield limit at anytime during the test. 
 128
 129
Cent
Cur
er
vat
 of 
ure
-5000
-2000
-1000
-400
-300
0
0
0
B4 Section H
Step 18
?
y
 
-?
y
 
0
1000
2
3
000
000
4
5000
000
 
:  Longitudinal s-F ur ep 18 (Excluding Figure 3-52  Strain State in B4 Near Cros rame 
Installation
 
 Effects) 
N6R D ing St
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B4 Section C
Step 19
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Installation Effects) 
Figure 3-53:  Longitudinal Strain State in B4 Near Cross-Frame N6L During Step 19 (Excluding 
  
The maximum sustained applied load during the B4 test produced the longitudinal 
strain state shown in Figure 3-54 at mid-span ponent. The associated vertical 
bending moment being resisted by the section at this load step was 4,880 kN-m (3,598.6 
k-ft
tion 
l. 
 of the com
). The figure indicates significant buckling and yielding in the compression flange. 
The data also project yielding within the compression depth of the web in conjunc
with significant web distortion. The state of longitudinal strain in the tension flange is 
linear and consistent at this load leve
 130
Center of 
Curvature
-2000 -1000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B4 Section E
Step 29
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-54:  B4 Mid-Span Longitudinal Strain State During Step 29 
 
Figure 3-55 demonstrates that G2 remained elastic throughout the loading regime. 
The strain data plotted are significantly below the respective yield limits shown. Also, the 
regression lines do not indicate any degree of local plate bending. 
 131
Center of 
Curvature
-200
0
-100
0 0
100
0
200
0
-5000
-4000
-3000
-2000
0
-1000
B4-G2
Step 31
-?
y
 
?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-55:  Most Critical G2 Mid-Span Longitudinal Strain State During B4 Test 
 
3.8 Bending Component B5 Test 
1,833 kN (412.2 kip). However, the  resisted by B5 occurred at step 38 
at an applied load level of 1,732 kN (389.5 kips). A summary of applied loading 
inform
 The test frame containing component B5 was loaded in 46 steps to a maximum of 
 maximum moment
ation for this component test is presented in Table 3-12 and Table 3-13. 
 132
 
Total 
Load  Applied Mx (Total) Mx (G1) Mx (G2) Mx (B5)   
Step Load     Indirect Direct   
      (a)   (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
B5 Elastic 
1 0 0.9 -0.1 0.4 0.6 0.7 0.92 
2 57.7 271.9 20 85 166.9 135.3 1.23 
3 151.9 668.4 49.8 215.5 403.1 351.1 1.15 
4 274.2 1203.1 75.5 419.3 708.4 658 1.08 
5 406.2 1786.2 107.7 641 1037.5 990.7 1.05 
6 534.9 2358.8 137.6 862.5 1358.6 1328.1 1.02 
7 670.1 2957.5 162.7 1105.1 1689.6 1697 1 
8 798.8 3525.8 185.6 1338.7 2001.5 2052.7 0.98 
9 917.2 4037.7 198.8 1568.9 2269.9 2393.8 0.95 
B5 Plastic 
10 1066.4 4703 226.4 1833.9 2642.7 2792.8 0.95 
11 1101.5 4857.8 232.6 1888.6 2736.6 2884.5 0.95 
12 1130.6 4982 237.7 1949.7 2794.5     
13 1159.3 5110.7 245.4 2008.9 2856.5     
14 1184.5 5222.5 245.8 2055.6 2921.2    
15 1208.1 5327.7 248.1 2113.1 2966.5    
16 1243.2 5481.9 251.5 2185.2 3045.2    
17 1268.9 5596.4 251.5 2225.7 3119.2    
18 1290 5690.5 248.4 2280.1 3162    
19 1314.3 5797.9 251.2 2338.6 3208.1    
20 1346.2 5936.4 249.7 2406.1 3280.6    
21 1365.6 6019.3 240.3 2469.7 3309.3    
22 1396.7 6157.6 240.8 2532.7 3384.1    
23 1425.4 6285.1 237.1 2602.1 3445.9    
24   1449.7 6393.4 231.8 2680.7 3480.9   
 
Table 3-12:  B5 Applied Load Steps and Resulting Girder Moments (Part I) 
 133
Load  Applied Mx (Total) Mx (G1) Mx (G2) Mx (B5)   
Total 
Step Load     Indirect Direct   
        (a) (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
25 1483.2 6540.3 225.4 2768.1 3546.8    
26   1493.5 6587 200.1 2841.3 3545.6  
27 1529.6 6745.4 203.2 2908.2 3634    
28 1554.6 6854.8 189.6 3008.5 3656.7    
29 1587.6 6999.9 173.4 3091.3 3735.2    
30 1616.8 7128.8 169.2 3193.7 3765.8    
31 1642.8 7246.3 135.6 3276.6 3834.1    
32 1662.9 7336.1 127.4 3392.6 3816    
33 1696.1 7479.2 103.8 3526.9 3848.5    
34 1703.8 7517.8 68.1 3585.2 3864.5    
35 1654.5 7298 8.9 3549.7 3739.4    
36 1680.5 7416.8 20.8 3605.9 3790.1    
37 1708 7537.5 35.5 3662.7 3839.3    
38 1732.7 7646 31.7 3745 3869.3    
39 1733.2 7647.3 -0.6 3794.6 3853.2    
40 1749.9 7719.9 -19.3 3877 3862.2    
41 1768.5 7803.9 -35.1 3987.7 3851.3    
42 1782.1 7861 -71 4110.1 3821.9    
43 1799.1 7937.9 -108.2 4210.7 3835.4    
44 1814.2 8006 -166.2 4391.5 3780.7    
45 1826.8 8061.5 -214.9 4531.1 3745.3    
46 1833.3 8092.1 -265.9 4664.7 3693.3    
47 1819.8 8030.6 -347.6 4809.1 3569.1    
48 1809.1 7983.8 -428 4990.4 3421.3    
49 1804.1 7961.9 -506.2 5122.2 3345.9   
 
Table 3-13:  B5 Applied Load Steps and Resulting Girder Moments (Part II)
 134
Load  Total Compression Flange, Inside Tip, Extreme Fiber Stress oM ments at Section 
Case Applied ?
z
 ?
z
 ?
z
 ?
z
 ?
z
 ?
z
(lat.)   M
x
 
x
 M
lat.
 M
y
 Bi M  
  Load Total from from from from     Direct Indire   mct   Co p.   
     M
x
 M
y
 M P
z
   Flange 
z
           
     (a)       (b) (b)/(a)   (c)   (c
yiel
    )/M
x
d
 
 kN MPa MPa MPa MPa MPa MPa  kN-m kN-m N k
2
-   k -m N-m  kN m 
Elastic 
Install.  -84.28 -35.14 -0.91 -48.08 -0.15 -49.00 1.39 51  1. .2  1.9 3 86 35.4 
DL   -89.63 -61.57 -5.19 -22.35 -0.52 -27.54 0.45 896.9   7. .95 40.1 19    
Install.+DL   -173.91 -96.71 -6.10 -70.44 0.79 1408.8   8.  .3-0.66 -76.54 8 126.3 55    
(1) 0.0 -173.96 -96.75 -6.18 -70.44 -0.59 -76.62 0.79 1409.5 409. 8 1 4 .9 126.3 55.3 0.24 
(2) 57.7 -187.78 -106.00 -7.17 -73.86 -0.75 -81.04 0.76 1544.1 575. 1 4 .5   1 7 0.4 132. 58  0.27
(3) 151.9 -209.70 -120.81 -8.78 -79.33 -0.78 -88.11 0.73 1759.8 811. 1 2 .6   1 9 2.7 142. 63  0.31
(4) 274.2 -240.77 -141.88 -10.89 -87.16 -0.84 -98.05 0.69 66.8 117. 1 3 .8   20  2 1 5.8 156. 70  0.37
(5) 406.2 -274.40 -164.72 -13.13 -95.77 99.5 446. 1 7 .6  -0.77 -108.91 0.66 23  2 2 9.0 171. 78  0.43
(6) 534.9 -307.69 -187.88 -14.89 -105.03 0.10 -119.92 0. 2736.9 2767. 21 3 .6  64  4 .5 188. 86  0.48
(7) 670.1 -343.90 -213.20 -16.55 -115.84 1.69 -132.39 0.6 3105.8 098. 23 7 .6  2  3 4 .9 207. 95  0.54
(8) 798.8 -378.93 -237.62 -18.09 -126.47 61.4 410. 26 8 4.   3.25 -144.56 0.61 34  3 3 .2 226. 10 4 0.59
(9) 917.2 -411.94 -261.03 -19.25 -136.61 02.6 678. 27 0 2.   4.94 -155.85 0.60 38  3 7 .8 245. 11 5 0.64
Plastic 
(10) 5 1.37 0.59 420  4051. 32 1 3.   1066.4 -453.46 -288.43 -22.42 -148.9 6.34 -17 1.6 5 .4 267. 12 7 0.70
(11) 7  4145. 33 0 6.   1101.5 -462.69 -294.72 -23.13 -151.6  6.84 -174.80 0.59 4293.3 4 .5 272. 12 2 0.72
. .       .  .
. .  .      .
. .    .    .
5278.        0.921 (38) 1732.7                 
 
Table 3-14:  B5 Mid-Span Stresses and Moments
 
Table 3-14 p  sh e e ang id-span stresses and mom nts. First 
yield in the component was projected to have occurred during load step 9 at a load level 
of 917.2  (206 . A ep, al  mi vertic l bendin moment 
in B5 wa ,679 2,7 -ft) mo hen lized by the vertical 
bending yield mo res  pe nc of 0  the m ximum vertical 
bending mom s 
normalized ratio increased to 0.92. 
A comparison of the direct and indirect methods to determine the resisted vertical 
moment in B5 is shown in Figure 3-56. While this comparison shows good agreement 
throughout most of the elastic regime of loading, the methods have diverged 
approximately 5% at the point that inelasticity is introduced into the system.  
rimarily ows th lastic r e B5 m e
 kN .2 kip) t this st  the tot resisted d-span a g 
s 3  kN-m ( 12.9 k . This a unt, w  norma
ment, ults in a rforma e ratio .64. At a
ent resisted by B5 during step 38, 5,278 kN-m (3,892.4 k-ft) thi
B5 Vertical Bending Moment (Mx)
0.0
500.0
1000.0
2000.0
2500.0
0.0 200.0 400.0 600.0 800.0 1000.0
Total Applied Load (kN)
M
o
n
t
 (
N
-
m)
1500.0
3000.0
3500.0
4000.0
me
k
Direct Indirect
 
Figure 3-56:  B5 Vertical Bending Moment 
 
 136
The mid-span vertical bending moments of the test frame that result from the applied 
loading are shown in Figure 3-57 for the B5 test. The B5 test record shows a small 
plateau of post-peak stability prior to ultimate failure of the section and a dramatic 
shedding of load to the test frame, in particular for G2.  
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
)
0
1000
2000
3000
4000
5000
6000
G1 Test
G2 Test
B5 Test
 
Figure 3-57:  Test Frame Mid-Span Vertical Bending Moments, B5 Test 
ges 
indicate the presence of a significant torsional warping strain. The separation of the 
regression lines across the tension flange is evidence of some local vertical plate bending. 
 
 
The effects of installation and dead load on the mid-span longitudinal strain state of 
B5 are shown in Figure 3-58. The complementary strain gradients across the flan
 137
 138
C
C e
ent
urv
er of
atur
 
-
2
0
0
0
0
0
0
0
0
0
-
1
0 0 0
1 2
0
-5000
-4000
-300
-2000
-1000
0
0
B5 Section E
Step 1
?
y
 
-?
y
 
-100
1000
2000
3000
4000
0
0
-?
y
 ?
y
 
 
udinal
 
t p  in re 3-59, the compression 
ge  a  has al n ver, the web plate data 
cate a uniform flexing that caus si e in pression on the 
out o e lted from the 
i d effects h  a oad l. 
Figure 3-58:  
flan
indi
B5 Mid-Span Longit  Strain State Resulting From
tep
 Installation and Dead Load 
(S  1) 
At the firs rojected yield in the B5 test, shown  Figu
 of the mid-sp n section mi
es
nim
 ten
 di
on
sto
 on
rtio
 th
. H
si
owe
de face and com
side face f the w b. Also, the distortion in the tension flange that resu
nstallation and dead loa as not progressed t this l leve
Center of 
Curvature
-2000 -1000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B5 Section E
Step 9
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-59:  B5 Mid-Span Longitudinal Strain State During Step 9 
 
The cross-section at N6L, shown in Figure 3-60, was the braced-section during step 9 
that was the most critical. While the strain data plotted do not include the effects of 
installation on the cross-section, the magnitudes fall significantly short of the yield limits 
indicated. The tension flange at this section does reach its indicated yield limit at step 16 
(see Figure 3-61). 
 139
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B5 Section C
Step 9
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-60:  Longitu ng 
 
dinal Strain State in B5 Near Cross-Frame N6L During Step 9 (Excludi
Installation Effects) 
 140
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B5 Section C
Step 16
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
Figure 3-61
ace 
of the web plate in this region has been prevented from yielding by the tensile strains 
caused by the its yield 
:  Longitudinal Strain State in B5 Near Cross-Frame N6L During Step 16 (Excluding 
Installation Effects) 
 
The effects on the longitudinal strain state at mid-span of B5 during the maximum 
sustained moment of the test, step 38, are shown in Figure 3-62. At this load step, most of 
the compression flange has yielded and distorted significantly. Also, a large portion of 
the depth of web in compression has yielded the outside face of the plate. The inside f
 local buckling of the plate. The tension flange has also reached 
 141
limit over approximately the inside half of the plate. However, the regression lines for 
each surface of data do not indicate an increase in the local level of lateral distortion. 
Center of 
Curvature
-2
00
0
-1
00
0 0
10
00
20
00
-5000
-4000
-3000
-2000
-1000
0
B5 Section E
Step 38
?
y
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
?
y
 
Figure 3-62:  B5 Mid-Span Longitudinal Strain State During Step 38 
 
Figure 3-63 shows the longitudinal strain state at mid-span of G2 during the 
maximum vertical bending moment that it experienced during the B5 test, step 49. This 
figure confirms that G2 remained well within the elastic region throughout this 
component test. 
 142
Center of 
Curvature
-200
0
-100
0 0
100
0
200
0
-5000
-3000
-1000
0
-4000
-2000
B5-G2
Step 49
-?
y
 
?
y
 
0
1000
2000
3000
5000
4000
 
Figure 3-63:  Most Critical G2 Mid-Span Longitudinal Strain State During B5 Test 
 
3.9 Bending Component B6 Test 
Table 3-15 and Table 3-16 contain the applied load levels associated with eac
the B6 component test. The mid-span girder vertical bending moments that resulted from
the applied loading for G1, G2 and B6 are also in Table 3
h step of 
 
-15 and Table 3-16. First yield 
in B6 was projected to occur during step 13 with a sustained load level of 1,354 kN 
(304.5 kip). At this step, the resisted vertical bending moment due to the applied loading 
 143
in B moment resisted by 
B6 
6 was 3,442 kN-m (2,538.3 k-ft). The maximum vertical bending 
was 4,886 kN-m (3,603.4 k-ft) and occurred during step 38. 
Load Total Applied Mx (Total) Mx (G1) Mx (G2) Mx (B6)   
Step Load      Indirect Direct   
        (a) (b) (a)/(b) 
  kN kN-m kN-m kN-m kN-m kN-m   
B6 Elastic 
1 0.1 -0.5 0.1 0.6 -1.2 0.2 -6.83 
2 51.9 216.6 17.1 69.3 130.3 122.3 1.06 
3 136.1 594.3 46.4 180.8 367.1 326.3 1.12 
4 271.8 1188.5 88.4 384.8 715.3 671 1.07 
5 404 1771.4 130 583.3 1058.1 1004.6 1.05 
6 535.3 2355.6 169.5 793.1 1393 1355.7 1.03 
7 670.7 2953.2 208.4 1003.7 1741.1 1724 1.01 
8 804.9 3541 244.3 1223.7 2073 2095.1 0.99 
9 937.6 4133.2 278.8 1436.1 2418.4 2462.6 0.98 
10 1068.8 4707.4 306.1 1659.5 2741.8 2839.7 0.97 
11 1197.9 5278 334.4 1878.6 3065 3210.8 0.95 
12 1331.1 5858.3 359.7 2097.5 3401.1 3592.7 0.95 
13 1354.2 5960.4 365.4 2153.1 3441.9 3665.2 0.94 
B6 Plastic 
14 1378.4 6065.3 371 2192.8 3501.4 3732.6 0.94 
15 1405.5 6187.1 369.8 2236.8 3580.5 3814.7 0.94 
16 1432.1 6306.1 389.1 2279.2 3637.7    
17 1486.3 6544.5 403.1 2365.7 3775.7 
18 1517.2 6681.2 405.3 2429.8 3846.1    
19 1541.8 6788.5 405.8 2464 3918.6 
20 1566.3 6898.1 412.6 2522.7 3962.9    
21 1594.4 7024.3 414.5 2567.4 4042.4     
 
Table 3-15:  B6 Applied Load Steps and Resulting Girder Moments (Part I) 
 144
Load Applied M    
Total 
x (Total) Mx (G1) Mx (G2) Mx (B6) 
Step Loa ct t   d    Indire Direc
  (b) (a)/(b) (a)
  kN kN   kN-m   -m kN-m kN-m kN-m
22 16 7 1 4    25 157.1 418.7 2627. 4111.
23 164 7   6.8 251.5 414 2674.8 4162.7
24 16 7      73 367.8 415 2731.9 4220.8
25 170 7 4 8 7.7 520.7 419.5 2794. 4306.
26 172 7 3 5    6.3 603.1 416.3 2853. 4333.
27 176 7 3 1 5.4 771.8 421.4 2937. 4413.
28 177 78 .7    2.9 07.3 403.4 2982.2 4421
29 18 8 1 12 7981 409.1 3048. 4523.
30 1839.6 7 2    8102 405.1 3119. 4577.
31 18 8 1 6 71 243.4 397.7 3217. 4628.
32 190 8 7 4    3.2 385.5 394.4 3306. 4684.
33 192 8 5  2.7 472.3 372.8 3378. 4721
34 1949.1 8590.6 365.4 55.7 4769.5    34
35 1981.1 8736.4 343 3588.3 4805.1 
36 2007.6 8856.8 319.6 3693 4844.2    
37 2033.9 8973.3 295.5 3807.8 4870  
38 2071.6 9140.3 248.2 4006 4886.2    
39 2095.4 9252.8 183.9 4195.9 4873  
40 2113.2 9332.8 138.9 4335.8 4858.1  
41 2138.3 9446.9 46.6 4626.2 4774.1   
42 2165.1 9572.4 -85.9 4981.9 4676.4   
43 2171.4 9598.2 -208.7 5282 4525     
 
Table 3-16:  B6 Applied Load Steps and Resulting Girder Moments (Part II) 
 
Selected stresses and moments, primarily from the elastic regime of loading, are listed 
in Table 3-17 for the mid-span cross-section of B6. These data indicate that at first yield 
in the component, the ratio of compression flange lateral bending stress to vertical 
bending stress was 0.37. Also, the largest sustained vertical bending moment in the 
elastic range was 4,955 kn-m (3,654.3 k-ft). This amount, when normalized by the 
theoretical vertical bending yield moment, yields a performance ratio of 0.73. This ratio 
 145
increases to 0.94 at the maximum moment resisted by B6, 6,400 kN-m (4,719.4 k-ft), 
which occurred during step 38 of this test. 
The direct and indirect methods of determining the resisted vertical bending moment 
at mid-span of B6 during the elastic loading regime of this component test are contrasted 
in Figure 3-64. The methods again begin to diverge at about the 890 kN (200 kip) total 
applied load level. This separation represents approximately 6% at the load step during 
which first yield is projected to have occurred.
 146
Load Total C  F , e Tip, Extreme Fib es me t onompression lange  Insid er Str s Mo nts a Secti  
Case Applied ?
z
 ?  ? ?  
yz
 ?
z z
 ?
z
 
z
(lat.)  M
x
M
x
 M Bi M
lat.
  
 Load Total fro  m fro  f   D  In .  m fro  m rom  irect direct   Comp  
    M     e  M
x
 M
y z
 P
z
   Flang  
   (a)   )/(a)   (c)/M
d
  (b) (b (c)   
x
yiel
 kN MP M a a M   k  k -m N  kNa P MP  Pa MPa MPa  N-m N-m kN k -m
2
-m  
Elastic 
Install.  -30.18 31. 4 -2.  -  46 .0  56   5. - 98 4.8  38 0.66 2. -0 8 1.9 -8.6 3 2.2  
DL  -74.77 54.  -2 4 18.  -  -2  8 39 - 15 .1  - 12 0.36 0.25 0.37 951.5  3.  .9 -17.9  
Install.+DL  -104.95 86.  20.  -  -  .8 45 7  - 13 2.70 - 50 1.02 17.79 0.21 1513.3  -4  .2 -15.  
(1) 0.1 -104.82 86.  20.  -  -  15 8 45 7 0.   - 14 2.73 - 49 0.93 17.75 0.21 1513.5 12.2 -4.  .2 -15. 22
(2) 51.9 -114.86 93.  22.  -  -  16 5 50 4 0.   - 09 1.99 - 83 0.93 20.84 0.22 1635.7 43.6 -3.  .3 -18. 24
(3) 136.1 -131.63 0 26.  -  -  1880.4 6 58 8 0.   -1 4.70 0.92 - 74 1.11 25.82 0.25 1839.6  -1.  .9 -22. 28
(4) 271.8 -159. 2  3.  -  -3 2 21  2228.6 8 73 8 0.04 -1 4.31 -0.44 -3 22 1.07 3.66 0. 7 84.3  0.  .2 -29. 33 
(5) 404.0 -185. 4  9.  -  -4 2 25  2571.4 9 87 5 0.53 -1 3.30 -1.63 -3 65 0.95 1.28 0. 9 17.9  2.  .4 -36. 38 
(6) 535.3 -212. 6  6.  -  -4 3 28  2906.3 3 0 5 0.55 -1 3.29 -2.41 -4 77 0.08 9.18 0. 0 69.1  4.  1 3.1 -43. 43 
(7) 670.7 -240. 8  4.   -5 3 32  3254.4 5 2 0 0.61 -1 4.24 -3.09 -5 54 1.27 7.63 0. 1 37.3  5.  1 0.2 -51. 48 
(8) 804.9 -269. 0  2.  -6 3 36  3586.4 3 3 8 0.15 -2 5.36 -4.12 -6 32 2.66 6.44 0. 2 08.4  7.  1 7.4 -58. 53 
(9) 937.6 -297. 2  9.  4.12 -7 3 3975.9 3931.7 6 5 6 0.49 -2 6.28 -5.43 -6 90 5.33 0. 3  9.  1 4.1 -66. 58 
(10) 1068.8 -326. 4  7.  5.73 -8 3 4353.0 4255.2 .4 7 1 0.92 -2 7.74 -7.56 -7 35 4.91 0. 4  13  1 0.5 -75. 62 
(11) 1197.9 -356.30 6 86 14 84.  7.33 -9 4724.1 4578.4 8 0.   -2 8. -10.  - 62 4.76 0.35  18.0 1 6.5 -83.8 67
(12) 1331.1 -387.18 9 60 58 92.  9.02 -1 5106.1 4914.4 0 0.   -2 0. -13.  - 02 05.60 0.36  24.0 2 2.8 -93.4 72
(13) 1354.2 -393.05 9 72 48 93.  9.49 -1 5178.5 4955.3 0 0.   -2 4. -14.  - 35 07.83 0.37  25.6 2 5.8 -95.4 73
Plastic 
(14) 1378.4 -398.68 -29 56 30 94.  9.83 -1 5246.0 5014.7 0 0.  8. -15.  - 65 09.95 0.37  27.1 2 8.6 -97.3 74
(15) 1405.5 -405.70 -30 23 44 96.  10.32 -1 5328.0 5093.8 1 0.  3. -16.  - 35 12.79 0.37  29.1 2 2.4 -99.8 75
. .       .   .
. .     . .
. .       .   .
(38) 2071.6     6399.5 0          .94
 
B6 Mid-Span StresseTable 3-17:  s and Moments
 
B6 Vertical Bending Moment (Mx)
50
6000.0
N
0.0
1000.0
2000.0
3000.0
4000.0
0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0
Total Applied Load (kN)
M
o
me
n
t
 (
k
-
m)
00.0
Direct Indirect
 
 
Figure 3-64:  B6 Vertical Bending Moment 
 
The mid-span vertical bending moments in G1, G2 and B6, which are due to the 
applied loading throughout the entire regime of the B6 test, are plotted in Figure 3-65. 
The peak resisted vertical bending moment in B6 occurred during load step 38. The 
section initially remained viable post-peak as the test frame continued to take load up 
until load step 43 when the test was halted. At this load level, 2,172 kN (488.2 kip), B6
was carrying significantly less of the applied moment than girder G2. 
 148
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
)
0
1000
2000
3000
4000
5000
6000
 
G1 Test
G2 Test
B6 Test
 
ents, B6 Test 
itudinal s  state are 
shown in Figure 3-66. This plot primarily indicates that vertical bending was the 
dominate force effect that resulted from these loadings. The data describ
behavior in all plates of the section. 
 
Figure 3-65:  Test Frame Mid-Span Vertical Bending Mom
 
The dead load and installation effects on the mid-span long
149
train
e linear elastic 
Center of 
Curvature
-2000 -1000
0
1000 2000
-5000
-4000
-3000
-2000
-1000
0
B6 Section E
Step 1
?
y
 
-?
y
 
0
1000
2000
4000
3000
5000
-?
y
 ?
y
 
 
Figur ngitudinal Strain State Resulting From Installation and Dead 
 
Figure 3-67 presents the m ongitudinal s  of B6 at loa  This 
load step is projected to have caused first yield in the cr section on the inside tip of the 
compression flange. However, first yield in the component most likely occurred at the 
brace point cross-sections. The data from the cross-sections near the cross-fra  N6L 
and N6R, shown in Figures 3-68 and 3-69 respectively, also projected strain levels in the 
utside tips of the tension flange. These levels also exceed the yield strain limits at this 
e 3-66:  B6 Mid-Span Lo
Load (Step 1) 
id-span l train state d step 13.
oss-
mes
o
 150
same load step. These data do not include any effects for installation of the component; 
therefore, they m kely re  their yi limits ea n the loa g regimost li ached eld rlier i din e. 
Center of 
Curvature
B6 Se
Step 13
-2000 -1000
10
00
20
00
0
-5000
-4000
-3000
-2000
-1000
0
ction E
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
ure 3-67:  B6 Mid-Span Longitudinal Strain State During Step 13 
 
Fig
 151
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B6 Section C
Step 13
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
ure 3-68:  Longitudinal Strain State in B6 Near Cross-Frame N6L During Step 13 (Excluding 
Installation Effects) 
 
Fig
 152
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B6 Section H
Step 13
?
y
 
-?
y
 
0
1000
2000
4000
3000
5000
 
Figure 3-69:  Longitudinal Strain State in B6 Near Cross-Frame N6R During Step 13 (Excluding 
Installation Effects) 
 
Approximately half of each flange of B6 has exceeded its yield limit by load step 28, 
shown in Figure 3-70. At this load level, the plotted data indicate that the compression 
flan , 
 the web data on the figure. 
ge has buckled while the tension flange displays no evidence of local bending. Also
very little out of plane effect exists in
 153
Center of 
Curvature
-2
000
-1
000
0
1
000
2
000
-5000
-4000
-3000
-2000
-1000
0
B6 Section E
Step 28
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-70:  B6 Mid-Span Longitudinal Strain State During Step 28 
 
Figure 3-71 shows the mid-span longitudinal strain state during the maximum 
sustained vertical bending moment in the component during the B6 test. The compression 
flange data indicate gross yielding and buckling across most of the plate. The top of the 
we
yielded along its outside face. The tension flange data again indicate yielding across most 
of t
b has also picked up much of the buckling evident in the compression flange and has 
he plate, but there is no evidence of local bending. 
 154
Center of 
Curvature
-2
000
-1
000
0
000
2
000
1
-5000
-4000
-3000
-2000
-1000
0
B6 Section E
Step 38
?
y
 
-?
y
 
0
2000
4000
1000
3000
5000
-?
y
 ?
y
 
 
Figure 3-71:  B6 Mid-Span Longitudinal Strain State During Step 38 
 
Figure 3-72 illustrates the linear elastic state of the mid-span of G2 at its critical load 
of the B6 component test. 
 155
Center of 
Curvature
-200
0
-100
0 0
100
0
200
0
-5000
-4000
-3000
-2000
-1000
0
B6-G2
Step 43
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
3.10 Bending Component B7 Test
Figure 3-72:  Most Critical G2 Mid-Span Longitudinal Strain State During B6 Test 
 
 
The maximum sustained vertical bending moment due to the applied loading at mid-
span of B7 was 2,501 kN-m (1,844.5 k-ft). This moment occurred very early in this 
component test during step 13. First yield in the component was projected at load step 8. 
The test frame continued to take load until the test was halted at step 38 with a total 
applied load of 1,317 kN (296.1 kip). The resulting vertical bending moment in G2 was 
 156
 4,635 kN-m (3,418.5 k-ft). Table 3-18 contains a selected set of data from this test.  
Total 
Load Applied Mx (Total) Mx (G1) Mx (G2) Mx (B7)  
Step Load    Indirect Direct 
    (a) (b) (a)/(b) 
 kN kN-m kN-m kN-m kN-m kN-m  
B7 Elastic 
1 0.0 -0.7 0.2 0.0 -0.8 -0.1 7.34 
2 55.1 254.6 13.9 78.3 162.4 126.3 1.29 
3 139.2 609.0 33.6 209.6 365.7 316.0 1.16 
4 275.2 1210.8 59.7 432.3 718.7 650.7 1.10 
5 403.7 1779.3 81.8 678.5 1019.0 973.2 1.05 
6 532.4 2359.3 98.0 930.8 1330.5 1280.2 1.04 
7 672.1 2966.5 104.3 1240.2 1622.1 1596.4 1.02 
8 808.5 3565.9 105.8 1540.4 1919.7 1908.7 1.01 
B7 Plastic 
9 939.3 4143.0 109.0 1837.0 2197.0 2193.2 1.00 
10 991.1 4370.7 107.1 1954.8 2308.8 2537.6 0.91 
11 1041.8 4595.7 97.8 2078.2 2419.7   
12 1071.1 4724.6 95.3 2167.5 2461.8   
13 1095.5 4830.5 81.0 2248.4 2501.1   
14 1123.6 4956.3 42.1 2415.0 2499.2   
15 1109.2 4892.7 12.0 2416.8 2463.9   
16 1114.4 4912.2 -8.4 2510.0 2410.6   
17 1122.8 4950.9 -41.2 2588.3 2403.8   
18 1123.6 4956.4 -65.7 2617.5 2404.6   
19 1138.3 5020.3 -92.2 2734.0 2378.5   
20 1149.3 5070.9 -123.9 2829.5 2365.2   
21 1157.5 5105.9 -158.6 2930.5 2334.0   
22 1171.4 5169.8 -188.8 3031.4 2327.2   
23 1179.5 5206.6 -213.0 3067.5 2352.0   
24 1195.7 5277.5 -232.5 3194.9 2315.1   
25 1200.3 5298.8 -280.3 3293.3 2285.9   
26 1216.2 5371.3 -311.3 3408.8 2273.8   
27 1224.1 5406.5 -346.9 3522.2 2231.2   
28 1232.7 5446.2 -385.4 3606.4 2225.1   
29 1243.0 5492.4 -418.9 3733.4 2177.9   
30 1255.0 5548.1 -452.7 3812.2 2188.6   
31 1262.3 5581.6 -487.1 3926.2 2142.5   
32 1270.2 5614.6 -520.9 4010.3 2125.2   
33 1273.7 5630.5 -567.2 4134.6 2063.0   
34 1285.7 5685.9 -605.2 4228.2 2062.9   
35 1292.2 5713.9 -638.2 4325.7 2026.3   
36 1301.4 5755.8 -669.4 4444.7 1980.5   
37 1306.3 5777.4 -704.1 4540.9 1940.5   
38 1317.2 5828.0 -741.2 4635.5 1933.7   
 
pplied Load Steps and Resulting Girder Moments Table 3-18:  B7 A
 
 157
Figure 3-73 contrasts the direct and indirect methods of determining the resisted 
vertical bending moment at mid-span of B6 during the elastic loading regime of this 
component test. The methods again show good agreement throughout the elastic range. 
At a total applied load of 808.5 kN (182.8 k), the point at which first yield is projected to 
have been reached in B7, the results of these analysis methods are less than one percent 
different. 
B7 Vertical Bending Moment (Mx)
0.0
500.0
1000.0
2000.0
2500.0
3000.0
1 500.0 600.0 700.0 800.0 900.0
Total Applied Load (kN)
M
o
me
n
t
 (
k
N
-
m)
1500.0
3500.0
0.0 00.0 200.0 300.0 400.0
Direct Indirect
 
Figure 3-73:  B7 Vertical Bending Moment 
 
The mid-span vertical bending moments in G1, G2 and B7, which are due to the 
applied loading throughout the entire load regime of the B7 test, are plotted in Figure 3-
74. The peak resisted vertical bending moment in B7 occurred very early in the tes
during load step 13. The section remained viable post-peak as the test frame continued to 
take load up until load step 38 when the test was halted. At this load level, 1,317 kN 
t 
(296.1 kip), B7 was carrying significantly less of the applied moment than girder G2. 
 158
0 500 1000 1500 2000 2500
M
d-S
i
pan M
o
ment (kN-m
)
0
2000
1000
3000
40
5000
00
6000
G1 Test
Total Applied Load (kN)
G2 Test
B7 Test
 
 
Figure 3-74:  Test Frame Mid-Span Vertical Bending Moments, B7 Test 
 
d-span B7 stresses and m
the component, the ratio of lateral flange bending stress to vertical bending stress was 
7 was 2,922 kN-
m (2,154.8 k-ft). A ratio of 0.61 resulted when the maximum elastic vertical bending 
moment was normalized by the vertical yield moment. At the maximum vertical bending 
moment sustained by B7, 3,503 kN-m (2,583.6 k-ft), this ratio increased to 0.73.
The mi oments are presented in Table 3-19. At first yield in 
0.68. The maximum elastic regime vertical bending moment carried by B
 159
Loa l Compression Flange, Inside Tip, Extreme Fiber Stress Mome t ond Tota nts a Secti  
Ca ed ?
z
 ?
z
 ?
z
 ?
z
 ?
z
 ?
z
(lat.)  M
x
 M
x
 
y
 se Appli  M Bi M
lat.
 
 Loa  d Total from from from from   Direct Indirect .    Comp  
   M
x
 M
y
 M
z
 P
z
     e    Flang  
   (a)    (b) (b)/(a)  (c)  (c)/M
d
   
x
yiel
 kN MPa MPa MPa MPa MPa MPa  kN-m kN-m kN-m N  kNk -m
2
-m  
Elastic 
Install.  -74.84 -15.07 -40.71 -24.99 5.93 -65.71 4.36 190.  53.1 40 4  .2 -51.2  
DL  -90.04 -64.26 -4.34 -21.58 0.14 -25.92 0.40 811.  5.7 34.7  8  -20.2 
Install 164. -79.33 - 6 -46.57 6.07 -91.63 1.16 1002.  58.8 74.+DL  - 88 45.0 2 .9 -71.4  
(1) 0. 164. -79.32 - 8 -46.62 6.04 -91.70 1.16 1002.  1001.4 58.8 75.0 0.21 0 - 98 45.0 1 -71.5 
(2) 55 179. -89.33 - 6 -49.73 5.93 -95.99 1.07 1128. 1164.6 60.4 80 0.24 .1 - 39 46.2 5 .0 -74.8 
(3 201. -104.34 - 3 -54.59 5.99 -102.83 0.99 1318. 1367.9 63.0 87 0.29 ) 139.2 - 17 48.2 2 .9 -80.1 
(4 240. -130.83 - 1 -63.12 4.94 -114.72 0.88 1652. 1720.9 67.4 10 6 0.36 ) 275.2 - 62 51.6 9 1. -89.4 
(5 277. -156.36 - 9 -71.29 4.12 -125.58 0.80 1975. 2021.2 70.9 11 7 0.42 ) 403.7 - 82 54.2 4 4. -97.9 
(6 312. -180.66 - 4 -78.75 3.32 -134.79 0.75 2282. 2332.7 73.1 12 7 - 1 0.49 ) 532.4 - 13 56.0 4 6. 105.  
(7 35  -87.81 2.61 -147.86 0.72 25  78.4 14 3 - 2 0.55 ) 672.1 - 0.94 -205.69 -60.05 98.6 2624.3 1. 115.  
(8 385. -230.41 - 9 -95.26 2.18 -157.75 0.68 2910. 2921.9 81.6 15 3 - 9 0.61 ) 808.5 - 98 62.4 9 3. 122.  
Plastic 
(9 413. -252.92 - 9 -100.42 2.91 -163.30 0.65 3195. 3199.2 82.1 16 6 - 3 0.67 ) 939.3 - 32 62.8 4 1. 127.  
(1 1 531. 80.19 -1 04 -130.65 -15.15 -235.69 0.84 3539. 3311.0 137.1 21 - 7 0.0) 991.  - 03 -2 05. 9 0.3 183.  69 
.       .  . .   
. . .  .   
(13) .5        3503.3  0.1095  73 
 
Table 3-19:  B7 Mid-Span Stresses and Moments
 
The longitudinal strain state at the mid-span of B7 resulting from the installation and
dead load effects is sh
 
own in Figure 3-75. All data indicate a linear elastic response from 
the steel plates of the cross-section. The warping strain has pushed the outside tip of the 
compression flange into tension at this low load level. 
Center of 
Curvature
-2
000
-1
000
0
1
000
2
000
-5000
-4000
-3000
-2000
-1000
0
B7 Section E
Step 1
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Load 
ring step 8, shown in 
Figure 3-76. At this load level, the compression depth of the web is already showing 
significant out-of-plane bending effects. The strain data for the inside tip of the 
Figure 3-75:  B7 Mid-Span Longitudinal Strain State Resulting From Installation and Dead 
(Step 1) 
 
The projected first yield in the component occurs at mid-span du
 161
com e pression flange also contains evidence of local bending, which is illustrated by th
separating regression lines. 
Center of 
Curvature
-2
000
-1
000
0
1
000
2
000
-5000
-4000
-3000
-2000
-1000
0
B7 Section E
Step 8
-?
y
 
?
y
 
0
2000
1000
3000
4000
5000
-?
y
 ?
y
 
 
 
Figures 3-77 and 3-78 support the assertion that first yield occurred at mid-span in the 
B7 component during step 8. The data in these figures do not include any effect for 
installation of B into the test frame. However, the strain levels plotted fall significantly 
from the indicated yield limits.  
Figure 3-76:  B7 Mid-Span Longitudinal Strain State During Step 8 
 162
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B7 Section C
Step 8
?
y
 
-?
y
 
 
Installation Effects) 
0
1000
2000
3000
4000
5000
Figure 3-77:  Longitudinal Strain State in B7 Near Cross-Frame N6L During Step 8 (Excluding 
 
 163
Center of 
Curvature
-5000
-4000
-3000
-2000
-1000
0
B7 ction H Se
Step 8
?
y
 
-?
y
 
0
2000
1000
3000
4000
5000
 
Figure 3-78:  Longitudinal Strain State in B7 Near Cross-Frame N6R During Step 8 (Excluding 
Installation Effects) 
 
The B7 mid-span longitudinal strain state at step 10 is shown in Figure 3-79. At this 
load step, the first evidence of local buckling pears in the compression flange data. The 
com
 ap
pression depth of the web data shows increased levels of local bending as the web 
tries to restrain the now buckled compression flange. 
 164
Center of 
Curvature
-2000 -1000
0
10
00
20
00
-5000
-4000
-3000
-2000
-1000
0
B7 Section E
Step 10
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3 Step 10 
 
The ma id-span B7 occurred during 
load
g 
 
-79:  B7 Mid-Span Longit dinal Strain State During u
ximum sustained vertical bending moment by m
 step 13. The longitudinal strain state at that cross-section during step 13 is shown in 
Figure 3-80. The strain data indicate that the inside half of the compression flange has 
surpassed its yield limit and is buckled. The web data contain evidence of local bendin
that could also be the result of buckling. Finally, the tension flange is still linearly elastic
at this load step. 
 165
Center of 
Curvature
-2
00
0
-1
00
0 0
10
00
20
00
-5000
-4000
-3000
-2000
-1000
0
B7 Section E
Step 13
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
-?
y
 ?
y
 
 
Figure 3-80:  B7 Mid-Span Longitudinal Strain State During Step 13 
 
While the maximum vertical bending moment sustained by B7 occurred at step 13, 
the test progressed through step 38 when the test frame was resisting a maximum applied 
load of 1,31
through step 38. 
7 kN (296.1 kip). Figure 3-81 ind cates that G2 remained linearly-elastic i
 166
Center of 
Curvature
-200
0
-100
0 0
100
0
200
0
-5000
-4000
-2000
-3000
-1000
0
B7-G2
Step 38
?
y
 
-?
y
 
0
1000
2000
3000
4000
5000
 
:  Most Critical G2 Mid-Span Longitudinal Strain State During B7 Test 
 
3.11 Boundary Conditions
Figure 3-81
 
The test frame was loaded from above. The hydraulic actuators reacted off floating 
frames that were anchored to the laboratory floor using high-strength steel rods. This 
loading system is described in detail in Section 2.6.1. Radially aligned abutm
end supported the test frame. Each end of the three girders that made up the test frame sat 
on a compound polytetrafluoroethylene
ents at each 
 (PTFE) sliding surface bearing. 
 167
The bearings that supported either end of G1 and G3 were free to rotate and slide in 
any direction. The bearings that supported both ends of G2 were free to rotate in any 
direction and were guided to slide in a direction along the tangent to the radius of 
curvature at the point of support. While approximately 6 mm (1/4 in.) of play existed in 
the guided direction, these bearing were essentially fixed radially.  
An attempt to monitor horizontal loads transmitted through the bearings was made 
using two 
supported the coefficient of friction, determined for the bearings with a proof load test, 
the data from the instrumented studs were inconclusive.  
sets of instrumented studs. However, beyond providing evidence that 
3.12 Effect of Installation Strains on Capacity 
The effect of including the strains captured as a result of the installation process o
the moment at first yield and the maximum resisted moment for each component can
seen in the data contained in Table 3-20. Recall that while the installation strains applied 
to B1, B2 and B3 were derived from the data acquired during the installation of B5 and 
B6, the regression line models used reasonably captured any uncorrupted data from those
n 
 be 
 
components. Also recall that the installation of B7 was accomplished relatively free of 
installation effects because the splice plates for the compression flange were drilled in 
place for this component.
 168
Component Total w/Installation Effects w/o Installation Effects 
 Applied Moment Normalized Moment Normalized 
 Load Resisted Moment Resisted Moment 
  M M/M
x
yield
 M M/M
x
yield
 
 kN kN-m  kN-m  
At First Yield 
B1 825.5 3516.1 0.69 2979.3 0.58 
B2 852.7 3536.2 0.67 2999.3 0.57 
B3 852.7 3578.9 0.68 3042.1 0.58 
B4 802.9 3696.6 0.68 3000.6 0.55 
B5 917.2 3678.7 0.64 3166.8 0.55 
B6 1354.4 4955.2 0.73 4393.4 0.65 
B7 808.6 2921.9 0.61 2731.5 0.57 
At Maximum Moment 
B1 1353.5 4539.2 0.90 4002.4 0.79 
B2 1434.0 4729.6 0.90 4192.8 0.80 
B3 1499.9 4834.4 0.92 4297.6 0.82 
B4 1354.4 4879.7 0.90 4183.7 0.77 
B5 1732.5 5278.1 0.92 4766.2 0.83 
B6 2071.4 6399.5 0.94 5837.7 0.86 
B7 1095.5 3503.4 0.73 3313.0 0.69 
 
Table 3-20:  Summary of Experimental Results 
 
With the exception of B7, the data indicate that the effect of including installation 
strains on the capacit  for approximately 
10% of the te strength. The reduced effect 
of i
y calculations were in effect uniform accounting
 moment capacity at either first yield or ultima
nstallation on B7 was expected due to the manner in which this component was 
installed as noted above. 
3.13 Effect of Compression Flange Slenderness 
The effect of compression flange slenderness on the moment at first yield and t
maximum moment resisted are illustrated in Figure 3-82 (also see Table 3-20). Both sets 
of data trend as expected with compress
he 
ion flange slenderness having a smaller effect on 
the moment at first yield than on maximum moment.  
 169
Compression Flange Slenderness
10 15 20 25 30 35
M
te
st
/M
x
yi
el
d
0.0
0.2
0.4
0.6
0.8
1.0
Maximum Moment
Moment at First Yield
 
 
Figure 3-82:  Effect of Compression Flange Slenderness 
 
However, with the exception of B7, which has a very slender compression flange, the 
normalized maximum moments seemed relatively unaffected by compression flange 
slendernes  to 0.94). 
Also, with B7 removed from the data set, the trends shown in Figure 3-83 for both 
moment at first yield and ultimate moment are very similar. These similarities are most 
likely due to the fact that the failure mode in all cases was a lateral mechanism at mid-
span of the component. This mechanism was initially made by a local flange buckle on 
the inside half of the compression flange and yielding on the outside half.   
s. Results for all specimens excluding B7 fell within a 4% range (0.90
 170
Compression Flange Slenderness
10 15 20 25 30 35
M
te
st
/M
yi
el
d
x
0.0
0.2
1.0
0.4
0.6
0.8
Maximum Moment
Moment at First Yield
 
 
Figure 3-83:  Effect of Compression Flange Slenderness (w/o B7) 
 
While compression flange slenderness had little effect on either the moment at first 
yield or the maxim st-peak capacity 
of these sections. Components B5 and B6 ha compact flanges and exhibited a post-peak 
cap
0%. 
um moment sustained, it did have an effect on the po
d 
acity reduction of less than 0.5%. The remaining components, all with non-compact 
or slender compression flanges, exhibited post-peak capacity reductions of 3% to 1
Also unlike the remaining components, B5 and B6 never exhibited a dramatic unloading 
prior to the ending of these tests. 
 171
3.14 Effect of Web Slenderness on Capacity 
Web slenderness did not effect moment at first yield or ultimate moment for these 
sections. However, the slender web of B4 had significantly more buckling as eviden
by the strain measurements than did the non-compact webs of the remaining componen
ced 
ts. 
3.15 Effect of Transverse Stiffener Spacing 
The presence of transverse stiffeners had no effect on vertical bending capacity. The 
performance ratios of B2 and B3, components with a stiffened and unstiffened web of 
identical slenderness, were essentially the same for all conditions. However, the absence 
of stiffeners on B3 elevated the level of cross-sectional distortion in both the flange and 
web when compared to the behavior of B2 at similar load levels. 
 172
Chapter 4.  Analytical Results 
4.1 Finite Element Model  
The finite element software ? ABAQUS, Version 6.4 (ABAQUS, 2003) ? was used 
to conduct the linear-elastic and fully non-linear (geometric and material) analytical 
studies that were conducted during this research. Girder flanges and webs were modeled 
using the general-purpose conve e members and 
the lateral bracing were modeled with B32 beam elements. Figure 4-1 shows a typical 
undeformed finite element model used in this investigation. 
Mesh density was chosen based on the recommendation reported in White et al. 
(2001). Figure 4-2 shows the typical mesh densities used to model the individual 
members of these investigations. Bending component flanges were modeled with 10 
elements across their width. Bending component webs were modeled with 20 elements 
along their depth. An element aspect ratio of approximately one was maintained along the 
length of the girder. In general, G1, G2 and G3 had coarser mesh densities. G1 and G2 
utilized four elements across a flange and five elements along the depth of a web. G3 
used six elements across a flange and 10 elements along the depth of the web. However, 
mesh densities were increased on all three girder models on elements local to the cross-
frame connections.
ntional shell element S4R. The cross fram
 173
X
Y
Z
 
Figure 4-1:  T ca ite Element Model Used in this S  tudyypi l Fin
 
X
Y
Z
 
r : c ndin mponent Finite Element Mesh Densityg CoFigu e 4-2  Typi al Be
 
4.1.1 Stress-Strain Relationship 
Engineering stress-strain relationships were constructed for each of the steel plates 
used in the fabrication of the bending components. After considering the property test 
data produced as a part of the CSBRP, a generic stress-strain relationship was developed 
that was easily tailored to represent the behavior of individual steel plates. An example of 
the generic seven part linear construction is shown in Figure 4-3. The following process 
is used to modify this construction to represent individual steel plate properties: 
1. Average the static yield strength (?
sy
), the offset yield strength (?
0.2%
), the 
strain at the onset of strain hardening (?
st
), the strain hardening modulus (E
st
), the 
tensile strength (?
u
) and the strain at the tensile strength (?
u
) for all tension test 
results produced by specimens from a particular steel plate. Table 4-1 cross-
references each bending component element to the steel plate from which it was 
cut. Table 4-2 contains a summary of the average material properties used to 
construct the stress-strain relationships used by the finite element models for the 
bending components. 
 Bending 
Component 
Compression 
Flange Plate 
Number 
Web 
Plate 
Number 
Tension 
Flange Plate 
Number 
B1 21 8 22 
B2 21 9 22 
B3 21 10 22 
B4 21 11 25 
B5 23 12 23 
B6 24 13 24 
B7 30 8 22 
 
Table 4-1:  Cross-reference of  Steel Plate Number and Bending Component Element 
 
 176
 
%2.0
?  
sy
?  
st
?  
st u
E  ?  
u
?  
Steel Plate 
Number 
MPa MPa % GPa % MPa 
8 460.1 445.4 1.978 3.110 16.38 592.2 
9 405.5 393.6 1.941 3.195 16.11 530.3 
10 407.8 396.3 2.171 3.149 16.87 540.6 
11 457.8 445.2 2.182 2.901 16.51 584.6 
12 455.6 439.6 2.089 3.050 15.17 585.6 
13 454.8 439.7 2.044 2.995 16.72 584.6 
21 425.1 408.5 1.472 4.170 15.88 582.6 
22 417.4 406.9 1.711 3.775 16.18 575.2 
23 405.2 395.0 1.632 4.111 16.11 570.4 
24 401.1 388.1 1.704 3.695 16.68 558.5 
25 404.4 390.5 1.753 3.984 16.60 564.7 
30 390.2 378.3 1.291 3.422 12.36 530.5 
 
Table 4-2:  Average Steel Plate Properties for Selected Steel Plates 
 
2. Use the averaged results, a Young?s modulus (E) of 204 GPa (29,600 ksi)
and the functional relationships in Table 4-3 to construct a specific engineering 
stress-strain curve for each steel plate. 
 
 177
Strain 
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
St
r
ess
 (M
Pa)
0
200
0
400
500
600
3 
4 
5 
 
neering Stress-Strain Relationship Used by FE Model 
Stress (MPa) 
6 7
1 2 
3 0
100
Figure 4-3:  Typical Engi
 
Point Strain
1 
E
sy
?
 
sy
?  
2 
st
?  
sy
?  
3 ( ) ()
sy
stust
E
?
??
+
10
 
?
st
stu
?
??
+
?
 
10
4 
( ) ()
3
36
3
36
7
?
2 ??
+
?
 
7
4
?
??
+
?
 
5 ( )
4
36
7
2
?
??
+
?
 
()
4
36
7
2
?
??
+
?
 
6 ( )
()
10
stu
u
??
?
?
?  
st
E?
?? %2.0
stu
u
sy
??
?
?
?
?
?
?
?
?
?
? 100
 
7 
u
?  
u
sy
?
?
?
?
?
?
?
?
?
?
?
%2.0
 
 
Table 4-1:  Equations Used to Establish Typical Stress-Strain Relationships for the FE Model 
 178
The Young?s modulus that was used to determine the yield strain for Point 1 of the 
curve, ?
eng ,1
, of the finite-element model?s stress-strain relationship was 204 GPa (29,600 
ksi). As reported in hat were preformed 
determined an average modulus of 204.7 GPa (29,700 ksi) for the steels used in these 
exp m andard deviation of 0.6 GPa (87 ksi) which is 
ver  
,700 
rmined from tension and 
com s a much larger standard deviation than the 
modulus determined using the more accurate Young?s modulus test. After all of these 
results were reviewed, a Young?s modulus of 204 GPa (29,600 ksi) was chosen for use in 
all analytical efforts throughout this report.  
The tension testing that was conducted as a part of this study was done in accordance 
wit ctural Stability 
Research Council?s (SSRC) Technical Memorandum No. 7 to produce static yield 
strengths. The SSRC procedure eliminates any effect that strain-rate may have on the 
demonstrated yield strength of the material. In general, strain-rate affected the yield 
strengths of the plate steels used in this tudy by elevating their values by approximately 
2%. This result was determined by comparing the static yield strength values to the offset 
yield strength values for individual tests. 
Analyses of the tension test data did not support the determination of any functional 
relationship between strain-rate and its effect on yield strength. Therefore, demonstrated 
tensile strengths, ?
u
, were also scaled by the ratio of associated static to offset yield 
 Appendix A, the Young?s modulus tests t
eri ents. This result has an associated st
y small. The Young?s modulus for these steels was also determined during the tension
and compression testing. These results are 201.5 GPa (29,200 ksi) and 204.5 GPa (29
ksi) respectively. The Young?s modulus that was dete
pression testing is slightly lower and ha
h the ASTM E8 standard except that it was modified by the Stru
s
 179
strength in an attempt to eliminate the strain-rate effect from the stress-strain model. This 
adjustment is detailed in the calculation for the engineering strain at Point 7, ?
eng ,7
, in 
Table 4-1. 
The relationships for Points 1, 2 and 7 on the engineering stress-strain model are 
taken directly from the summary record of the tension tests. Points 3 and 6 also utilize 
information from the summary record; however, the strain step that was indicated was 
selected to best capture the general shape of the family of A572 tension test records. The 
stress and strain relationships for Points 4 and 5 were also selected to best capture the 
general shape of the tension test records and to rely on coordinate calculations from 
else odel.   
The engineering stress-strain curves were converted to true stress-stain curves for use 
by the finite element program using the following relationships that are derived in 
Appendix A: 
where in the m
)1ln(
engtrue
?? +=        Equation 4-1 
)1(
engengtrue
??? +=        Equation 4-2 
A comparison between an engineering stress-strain model and its true stress-strain 
conversion is shown in Figure 4-4.  
 180
Strain (?e)
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
S
t
ress (M
P
a
)
100
200
300
500
600
700
400
0
Engineering Stress-Strain
True Stress-Strain
 
 
e Stress-Strain 
 
Figure 4-5 shows the family of tension and compression test results for material 
testing that were performed on samples taken from Plate 21 (see Appendix A for a 
description of this plate) in terial model. These results are 
shown on a field of engineering stress and strain. The test results differ slightly, with 
lower strengths displayed by 
compression test results, due to the specimen necking or barreling that is inherent to each 
respective test method. 
Figure 4-4:  Engineering Versus Tru
addition to the constructed ma
the tension test results and higher strengths by the 
 181
Engineering Strain
-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30
E
ngine
 S
t
ress (MPa
)
0
200
800
Compression Tests 
Tension Tests
600
400
erin
g
Engineering Stress-Strain Model
 
Figure 4-5:  Plate 21 Compression and Tension Test Results Compared with the FE Material 
 
engineering stress-strain to ferences in behavior become 
insignificant. Figure 4-6 shows the same family of Plate 21 results after conversion to 
true stress-strain. Once converted, the tension and compression test results essentially 
overlay each other, as shown in Figure 4-6. This figure supports the widely accepted 
material behavior model for steel with respect to tensile and compressive stress. 
The  tension and compression test results established, a 
separate material model is not needed to account for the stress-strain behavior of these 
 
Model in Engineering Stress-Strain 
However, when the tension and compression test results are converted from 
true stress-strain the dif
refore, with the agreement between
 182
steels in the compression domain. All material properties used in any associated 
analytical efforts will be drawn from the tension test results. 
Strain
-0.05 0.00 0.05 0.10 0.15 0.20 0.25
T
r
ue
 St
re
ss (MP
a
)
0
200
400
600
800
Compression Tests
Tension Tests
True Stress-Strain Model
 
 
Figure 4-6:  Plate 21 Compression and Tension Test Results Compared with the FE Material 
Model in True Stress-Strain 
 
4.1.2 As-Built Geometry 
Prior to testing, the flanges and web of each bending component were measured at 
regular intervals for width or depth, and thickness. Six sets of measurements were taken 
alon e lo ations 6L and 6R. The numbers reported 
in Table 4-2 are the averages for the center four sets of those measurements. A decision 
was made to use these measurements for the analytical model because this middle section 
was the location of failure in all of the experiments. 
g each component between cross-fram c
 183
b
f
t
f
Dt
w
b
f
t
f
(mm) (mm) (mm) (mm) (mm) (mm)
B1 443.7 19.5 1210.7 8.2 444.5 19.4
B2 442.9 19.4 1211.9 10.1 442.9 19.4
B3 442.9 19.5 1213.4 10.2 444.5 19.4
B4 442.9 19.4 1212.4 8.1 533.4 32.4
B5 419.1 24.7 1215.2 8.5 419.9 24.6
B6 414.4 30.9 1213.6 8.6 413.9 31.0
B7 533.4 16.4 1215.2 8.4 444.5 19.2
Bending 
Component
Compression Flange Web Tension Flange
 
 
Table 4-2:  Bending Specimen As-Built Plate Dimensions 
 
The thickness measurements were made with an ultrasonic device. The device 
employed had a 12.7mm (? in.) diameter transducer. Three individual thickness 
measurements were taken at each measurement location. During each successive 
me  previous measurement. 
The echeck the calibration. 
The width and depth measurements were made using a steel tape that was scaled in 
U.S. Customary units.  
All pieces of the test frame had their dimensions measured and recorded in the same 
manner that was used for the bending components. These measurements have been 
summarized by Linzell (1999). 
4.1.3 Installation Strains 
The installation strains that were recorded during the erection of each bending 
component and that were used in the analysis of the experimental data (discussed in 
Chapter 3) were not utilized to refine the predictions of the analytical model. Although 
these strains do exist and were captured for the mid-span section of each component, not 
asurement, the transducer partially covered the area used in the
 device had an integrated platen that was regularly used to r
 184
enough information was obtained to determine their distribution along the length of each 
component to appropriately model their effects. 
4.1.4 Modeling of Residual Stresses 
The fabrication process to construct I-girders from steel plates requires both flame 
cutting and welding. In the areas adjacent to the application of these processes, sufficient 
thermal stresses are created to plastically deform the steel plate. The steel is affected by 
the heat, and as it cools its elastic recovery is constrained by cooler portions of the plate. 
The elastic recovery and constraint compete until an equilibrium of internal stress is 
achieved. This remaining internal stress profile is referred to as residual stress because it 
is a consequence of either the cutting or welding process. 
Several researchers have attempted to measure residual stresses. The sectioning 
method, which is employed most often, requires careful monitoring of changes in the 
strain profile throughout a cross-section of a plate as a portion or section of that plate is 
rem
tes. For 
he 
ebs that were 
subjected to both flame cutting and welding. Each plate modeled is divided into zones of 
tension and compression. The heat affected zones from flame cutting or welding are 
modeled as small regions of uniform high tensile stress. The remainder of the plate is 
considered to be at a constant compressive stress level of necessary scale to equilibrate 
the aggregate tensile stresses. 
oved. These studies along with many analytical efforts have resulted in the 
publication of several residual stress models for I-girders fabricated from steel pla
this investigation, residual stress predictions are made using the recommendations of t
European Convention for Constructional Steelwork (ECCS, 1976).  
The ECCS method includes residual stress models for flanges and w
 185
The ECCS procedure specifies the equivalent rectangular tension block width, c
f
, 
adjacent to a flame cut plate edge as: 
y
F
where: 
f
c = 4-3 
t = plate thickness (mm) 
F
y
 = plate yield strength (MPa) 
For single pass welds, the ECCS procedure specifies an equivalent rectangular 
tension block width, c
w
, for each plate joined at that weld of: 
t1100
        Equation 
?
=
)(
)(12000
tF
Ap
c
y
w
w
       Equation 4-4 
where: 
p = efficiency factor (0.9 for the submerged arc welding process) 
w
 = etal (mm
2
) 
simultaneously at the top and bottom of 
one side of the web during the fabrication of the bending components. This method of 
fabrication resulted in the web-to-flange fillet welds being placed on opposite faces of the 
web at different times. In the flange plate, both of the consecutive welds both slightly 
lowered the residual tensile stresses caused at each flange tip by the flame cutting 
process. Also, this two?step welding procedure lowered the level of residual stress at the 
weld location because the heat input from the second weld relieved the tensile stresses 
A cross-sectional area of weld m
F
y
 = plate yield strength (MPa) 
? t = sum of plate thicknesses meeting at the weld (mm) 
The web-to-flange fillet welds were placed 
 186
cre  method, the resulting equivalent stress 
block for the two welds placed consecutively and spaced d mm apart is given by: 
        Equation 4-5 
where: 
c = equivalent tension block width of a single pass or weld (mm) 
d ? 2c 
In the web plate, the residual stresses of the flame cut edge are partially relieved by 
both the first and second welds. In addition, the residual stresses from the first weld are 
partially relieved by the heat input of the second weld. To account for this combination of 
effects, the ECCS method suggests that the combined tension block width created by 
welding and flame cutting, c
fw
, is approximated by the following relationship: 
        Equation 4-6 
where: 
 c
f
 = equivalent tension block width created by flame cutting (mm) 
 c
w
 = equivalent tension block idth due to welding (mm) 
The ECCS method also includes a predictor for the final tension block width 
produced by multi-pass welds or superimposed welds of equal size.  
         Equation 4-7 
where: 
 c = equivalent tension block width of a single pass or weld (mm) 
 n =  number of weld passes or superimposed welds of equal size 
The residual stress profiles that resulted from flame cutting and welding were 
determined for each flange and web of the bending components using equations 4-3 
ated by the first weld. According to the ECCS
 dcc 5.0
2
+=
444
wffw
ccc +=
w
4/1
cnc
n
=
 187
through 4-6. The equivalent widths of the rectangular tension block do not match the 
element size of the finite element model. Therefore, net element stresses were also 
det of a flange and to each of 
the 20 elements along the depth of a web. The results of these calculations for each 
com ending components are compiled in 
Tables 4-3 through 4-5. 
 
MPa)
B1 374.2 11.9 56.7 408.5 34.4 121.7 -59.5
B2 363.9 11.9 56.7 408.5 33.4 119.3 -57.8
11.9
-60.1
B6 346.1 15.8 96.1 388.1 26.7 85.8 -59.6
B7 338.5 11.8 37.2 378.3 40.7 114.4 -49.8
Component Tension at Each Flange Tip Tension at Welds Compression
ermined to apply to each of the 10 elements across the width 
pression flange, web and tension flange of the b
Resultant Width Net per 
Element
Resultant Width Net per 
Element
(MPa) (mm) (MPa) (MPa) (mm) (MPa) (
B3 364 11.9 56.8 408.5 33.4 119 -57.7
B4 362.7 55.5 408.5 34.5 124.3 -59
B5 350.6 13.8 76.9 395 30.9 106.4
 
 
ble 4-3:  Compression Flange Plate Residual Stresses 
 
et per 
Element
(MPa (mm) (MPa) (MPa) (mm) (MPa) (MPa)
B1 445.4 31.9 221.3 445.4 31.9 221.3 -24.8
B2 393.6 34.5 212.4 393.6 34.5 212.4 -23.8
B3 396.3 34.2 211.9 396.3 34.3 212.6 -23.7
B4 445.2 32 223.6 445.2 23 154.8 -21.2
B5
439.6 27.7 188.2 439.6 27.8 189 -21.1
B6 439.7 24 162.1 439.7 23.9 161.4 -18.1
B7
445.4 35.2 246.2 445.4 32.1 222.2 -26.1
Component Tension at Top of Web Tension at Bottom of Web Compression
Ta
Resultant Width Net per Resultant Width N
Element
)
 
 
Table 4-4:  Web Plate Residual Stresses 
 
 188
 
104.4 -61
B6 361.5 15.8 100.1 388.1 26.6 83 -61.1
397.3 11.1 55.1 431.9 33 123 -59.4
Component Tension at Each Flange Tip Tension at Welds Compression
Resultant Width Net per 
Element
Resultant Width Net per 
Element
(MPa) (mm) (MPa) (MPa) (mm) (MPa) (MPa)
B1 397.5 11.2 56 431.9 32.8 121.9 -59.3
B2 398.4 11.2 57.3 431.9 31.9 118 -58.5
B3 398.5 11.2 57.2 431.9 31.9 117.5 -58.2
B4 370.7 16 79.2 390.5 25.7 59.1 -46.1
B5 364.1 13.8 78.8 395 30.5
B7
 
 
Typical residual stress profiles for a flange and web are shown in Figures 4-5 and 4-6. 
These figures illustrate profiles that represent both the resultant residual stresses 
determined using the ECCS method for flame cutting and welding and the net residual 
stre
analytical model. 
Table 4-5:  Tension Flange Plate Residual Stresses 
 
sses determined to apply to individual elements that make up each flange or web of 
the 
 189
Flange Width (mm)
0 100 200 300 400
Re
sid
u
a
l
 S
t
re
ss (MPa
)
-100
0
100
200
300
400
500
Net Per Element
Resultant
 
Figure 4-7:  Example Flange Plate Residual Stress Profile 
 
Residual Stress (MPa)
100 0 100 200 300 400 50
W
eb Depth (
mm)
0
200
400
600
800
1200
1000
Net Per Element
Resultant
 
 
ofile Figure 4-8:  Example Web Plate Residual Stress Pr
 190
4.1.5 Modeling of Boundary Conditions 
Reactions were modeled using a gap element that prevented vertical deflection but 
allowed lift-off. These elements incorporate a frictional resistance to horizontal 
translation that was set at the experimentally determined frictional coefficient for the 
actual bearings. Reactions under G1 and G3 were free to translate in any horizontal 
direction while the G2 reactions allowed only tangential translation as they were fixed 
radially. All reactions allowed rotation about the point of support.  
The loads were applied to the top flange of all three girders as a point load at the 
appropriate node. Early results were scrutinized to insure that this method of applying 
load did not cause any local instability. 
A tangential support frame was attached to the west end of the experimental test 
frame as a safety precaution. This fram  was mounted to the floor of the structural 
laboratory and was attached to the test frame with a large cotter pin. The pin passed 
through one side of a double gusset plate that was attached to the tangential support 
fram  and finally through the other side of 
the tangential support frame?s double gusset. This structure was intended to prevent the 
test frame from a global translation off of the bearings. This structure was not modeled in 
the finite element analyses since the strain readings recorded during each test indicated 
that it was never engaged. 
4.1.6 Predictions 
kness and width of the 
steel plates used in the fabrication of the test frame and bending components. However, 
with the exception of B7, the finite element models predicted less component mid-span 
e
e, then through an oversized slot in the G2 web
A diligent effort was made to account for the variation in thic
 191
moment due to self-weight than what was measured during the tests. These results are not 
uncommon, especially on a large structure in which the weight of weld metal, bolts, nuts, 
washers, instrumentation etc. cannot be dismissed as insignificant. Also, the gusset plates, 
con quately incorporated in 
the finite element models for the software to predict a representative weight. Regardless, 
the self-weight moment predictions were within 5% of the measured values for all 
components except for B1 and B2.  
The prediction for B1 dramatically departed from the measured value by a reduction 
of 17%. A review of the experimental test log and other test documentation, as well as a 
careful review of the finite element model provide no explanations as to why this 
difference is so great. However, this difference did not adversely affect the flexural 
capacity analysis for B1 that is presented in Section 4.1.6.1. 
The predicted self-weight moment for B2 was 7% less than that deduced from the 
measured strains. This difference is acceptable and had no effect on the flexural capacity 
ana
ted self-weight moment for B7 was greater than that generated from the 
strain measurements by 5%. This difference is not alarming, and is only of interest 
because it is an over prediction that is contrary to the displayed and expected trend. It is 
however an indication that all force-actions were not properly accounted for prior to the 
applied loading portion of this test. 
 Also, with B6 as the only exception, the finite element models predicted a greater 
maximum applied load than what was measured during the experiments. This additional 
applied load accounted for the differences in self-weight and installation effects between 
nections and stiffening on each of the cross-frames are not ade
lysis of this component (similar to B1). 
The predic
 192
the 
predicted vertical moment capacities considered the influences of residual 
stress but were primarily the result of self-weight and applied load.  The experimental 
data contains measurements of strain associated with self-weight, installation and applied 
load. Regardless of what combination of loads caused the maximum mid-span moment, 
the measured and predicted flexural resistance of the bending components were virtually 
the same for all bending components with the exception of B7. 
4.1.6.1 B1 Finite Element Model Results 
The finite element model of the B1 component test predicted a maximum sustainable 
applied load of 1532.3 kN. This load equated to a mid-span moment of 3726.3 kN-m. 
When combined with the self-weight effects the predicted maximum mid-span moment 
resisted by B1 was 4573.9 kN-m which is comparable to the measured maximum mid-
span resisted moment of 4539.2 kN-m. These results are summarized in Table 4-6. 
predictions and the experimental data in most of the analyses. That is, the finite 
element model 
Test FE Ratio
(a) (b) (b)/(a)
Max. Applied Load (kN) 1353.5 1532.3 1.13
Mid-Span Moment 
Self-Weight (kN-m) 1022.2 847.6 0.83
Installation (kN-m) 536.8
Max. Applied Load (kN-m) 2980.2 3726.3 1.25
Flexural Resistance (kN-m) 4539.2 4573.9 1.01
B1
 
 
Table 4-6:  B1 Test and Finite Element Model Results 
 
Figure 4-9 shows the effect of the applied loads on the G1, G2 and B1 mid-span 
moments from both the experimental test and the finite element model. The predictions 
match the physical results very well indicating that the load is being distributed as 
expected within the load frame.  
 193
0 500 1000 1500 2000 2500
M
d-
 M
ment (
k
N-
m)
i
Span
o
0
2000
4000
6000
1000
3000
5000
G1 Test
G1 FE
G2 Test
G2 FE
B1 Test
B1 FE
Total Applied Load (kN)
 
 
Figure 4-10 shows the B1 mid-span moment from the applied loads normalized with 
yield
finite element model and the experimental data. The test results fall short of the predicted 
capacity and contain some pre-peak non-linearity. However, the shapes of the curves are 
very similar. The exhibited and predicted flexural resistance capacities are within 1% 
once the differences in self-weight and the effects of the recorded installation strains are 
added to the test results. 
 
Figure 4-9:  B1 Test Mid-Span Moments and Finite Element Predictions 
respect to the strong-axis yield moment, M
x
, as a function of deflection for both the 
 194
0 100 200 300 400
M/
x
yi
e
l
d
M
0.0
0.2
0.4
0.8
Deflection (mm)
0.6
1.0
B1 Test
B1 FE 
 
e 4-7. 
. 
t 
by B2 was 4774.5 kN-m. This amount is comparable to the measured maximum 
mid
 
Figure 4-10:  B1 Mid-Span Moment vs. Deflection 
 
4.1.6.2 B2 Finite Element Model Results 
A summary of the B2 experimental and finite element results is included in Tabl
The finite element model of the B2 component test predicted a maximum sustainable 
applied load of 1596.8 kN. This load equated to a mid-span moment of 3910.8 kN-m
When combined with the self-weight effects the predicted maximum mid-span momen
resisted 
-span resisted moment of 4729.6 kN-m. 
 195
Test FE Ratio
Max. Applied Load (kN) 1432.3 1596.8 1.11
(a) (b) (b)/(a)
Mid-Span Moment 
Self-Weight (kN-m) 928.0 863.6 0.93
Installation (kN-m) 536.8
Max. Applied Load (kN-m) 3264.7 3910.8 1.20
Flexural Resistance (kN-m) 4729.6 4774.5 1.01
B2
 
Table 4-7:  B2 Test and Finite Element Model Results 
 
 
Figure 4-11 shows the effect that the applied loads had on the mid-span moments of 
G1, G2 and B2 from both the experimental test and the finite element model. The 
predictions match the physical results very well indicating that the load is being 
distributed as expected within the load frame. 
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-
Span
 M
o
ment (
k
N-
m)
0
1000
2000
3000
4000
6000
G1 Test 
G1 FE
G2 Test
5000
G2 FE 
B2 Test
B2 FE 
 
Figure 4-11:  B2 Test Mid-Span Moments and Finite Element Predictions 
 
 196
 
Figure 4-12 shows the normalized B2 mid-span moment from the applied loads as
function 
 a 
of deflection for both the finite element model and the experimental data. The 
test
ever, the shapes of the curves are very similar. The exhibited and 
 results fall short of the predicted capacity and contain a greater degree of pre-peak 
non-linearity. How
predicted flexural resistance capacities are within 1% once the difference in self-weight 
and the recorded installation strains are added to the test results. 
  
Deflection (mm)
0 100 200 300 400
M/
e
l
d
0.0
1.0
B2 Test
B2 FE 
 
 
 
0.6
0.8
M
x
yi
0.2
0.4
Figure 4-12:  B2 Mid-Span Moment vs. Deflection 
 
 
 197
 
inite Element Model Results 
mum mid-span moment resisted by B3 was 4778.0 kN-
nt of 
483 ent 
res
4.1.6.3 B3 F
The B3 finite element model predicted a maximum sustainable applied load of 1598.2 
kN which resulted in a mid-span moment of 3904.6 kN-m. When combined with the self-
weight effects the predicted maxi
m. This moment is comparable to the measured maximum mid-span resisted mome
4.4 kN-m. Table 4-8 contains a summary of the B3 experimental and finite elem
ults.  
Test FE Ratio
Max. Applied Load (kN) 1499.9 1593.2 1.06
Mid-Span Moment 
Self-Weight (kN-m) 922.2 873.4 0.95
(a) (b) (b)/(a)
Installation (kN-m) 536.8 0.0
Max. Applied Load (kN-m) 3375.4 3903.3 1.16
Flexural Resistance (kN-m) 4834.4 4776.7 0.99
B3
 
Table 4-8:  B3 Test and Finite Element Model Results 
 
Figure 4-13 shows the effect that the applied loads had on the m
 
id-span moments of 
odel. 
The figure indicates that the finite elem
of load within the te
the experiment. 
the test frame girders from both the B3 experimental test and the finite element m
ent model is accurately predicting the distribution 
st frame and that the pre-peak behavior prediction agrees well with 
 198
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-S
pan M
o
ment (kN-m
)
0
1000
2000
3000
4000
5000
6000
G1 Test
G1 FE
G2 Test
G2 FE
B3 Test
B3 FE
 
 
Figure 4-13:  B3 Test Mid-Span Moments and Finite Element Predictions 
 
Figure 4-14 shows the normalized B3 mid-span moment from the applied loads as a 
function of deflection for both the finite element model and the experimental data. The 
experimental results indicate that the component was initially stiffer than the predicted 
behavior. The test results cross the prediction curve prior to the predicted maximum 
capacity and return to the prediction curve again in the post-peak field of behavior. 
However, the analytical results predict a severe post-peak capacity drop that was not 
captured during the physical test. After adjusting for the difference in self-weight and the 
recorded installation effects, the results are within 1% of the predicted flexural capacity. 
 199
Deflection (mm)
0 100 200 300 400
M/
M
x
e
l
d
yi
0.0
0.4
0.6
0.8
0.2
1.0
B3 Test
B3 FE
 
9. 
t test. This load equated to a mid-span moment of 3790.7 kN-
m. eight effects the predicted maximum mid-span 
mom
 
Figure 4-14:  B3 Mid-Span Moment vs. Deflection 
 
4.1.6.4 B4 Finite Element Model Results 
A summary of the B4 experimental and finite element results is included in Table 4-
A maximum sustainable applied load of 1475.4 kN was predicted by the finite element 
model for the B4 componen
When combined with the self-w
ent resisted by B4 was 4718.3 kN-m is comparable to the measured maximum mid-
span resisted moment of 4879.7 kN-m. 
 200
Test FE Ratio
(a) (b) (b)/(a)
Max. Applied Load (kN) 1354.4 1475.4 1.09
Mid-Span Moment 
Self-Weight (kN-m) 960.7 927.6 0.97
Installation (kN-m) 696.0 0.0
Max. Applied Load (kN-m) 3223.1 3790.7 1.18
Flexural Resistance (kN-m) 4879.7 4718.3 0.97
B4
 
 
Table 4-9:  B4 Test and Finite Element Model Results 
 
Figure 4-15 shows the effect that the applied loads had on the mid-span moments of 
G1, G2 and B2 from both the experimental test and the finite element model. The 
predictions match the physical results very well prior to the failure of B4, indicating that 
the model is accurately accounting for the actual physical behavior. 
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-
Span
 M
o
ment (
k
N-
m)
0
1000
2000
3000
4000
5000
6000
G1 Test
G1 FE
G2 Test
G2 FE
B4 Test
B4 FE
 
 
Figure 4-15:  B4 Test Mid-Span Moments and Finite Element Predictions 
 201
 202
Figure 4-16 shows the normalized B4 mid-span moment from the applied loads as a 
function of deflection for both the finite element model and the experimental data. The 
test results fall short of the predicted capacity and contain some pre-peak non-linearity. 
However, the shape of the curves is very similar, and when the test resu
difference in self-weight and the recorded installation effects the exhibited and predicted 
flexural resistance capacities are within 3%. 
Deflection (mm)
0 100 200 300 400
 
 
Figure 4-16:  B4 Mid-Span Moment vs. Deflection 
 
B5 Finite Element Model Results 
odel of the B5 test predicted a maximum sustainable applied 
oment of 4361.3 kN-m at mid-span of the 
4.1.6.5 
The finite element m
load of 1742.7 kN, which produced a m
M/
M
x
yi
e
l
d
0.0
0.2
0.4
0.6
0.8
1.0
B4 Test
B4 FE
lts include the 
component. When combined with the self-weight effects the predicted maximum mid-
span moment resisted by B5 was 5255.2 kN- e as the 
easured maximum mid-span resisted moment of 5278.1 kN-m. A summary of the B4 
experimental and finite element results is included in Table 4-10.  
 
m. This result is essentially the sam
m
Test FE Ratio
(a) (b) (b)/(a)
Max. Applied Load (kN) 1732.5 1742.7 1.01
Mid-Span Moment 
Self-Weight (kN-m) 896.9 893.9 1.00
Installation (kN-m) 511.9 0.0
Max. Applied Load (kN-m) 3869.3 4361.3 1.13
Flexural Resistance (kN-m) 5278.1 5255.2 1.00
B5
 
 
T  
 
Figure 4-17 shows the effect that the app ents of 
1, G2 and B2 from both the experimental test and the finite element model. The 
predictions match the physical results very well early in the loading regime and maintain 
the same characteristic shape throughout the figure. 
able 4-10:  B5 Test and Finite Element Model Results
lied loads had on the mid-span mom
G
 203
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-
Span
 M
o
ment (
k
N-
m)
0
1000
2000
3000
4000
5000
6000
G1 Test
G1 FE
G2 Test
G2 FE
B5 Test
B5 FE
 
Figure 4-17:  B5 Test Mid-Span Moments and Finite Element Predictions 
 
Figure 4-18 shows the normalized B1 mid-span moment from the applied loads as a 
function of deflection for both the finite element model and the experimental data. The 
test results fall short of the predicted capacity and contain additional pre-peak non-
linearity. However, the shapes of the curves are very similar. When the test results are 
include the difference in self-weight and the recorded installation effects, the exhibited 
and predicted flexural resistance capacities are nearly identical. 
 
 204
Deflection (mm)
0 100 200 300 400
M/
M
x
yi
e
l
d
0.0
0.2
0.4
0.6
0.8
1.0
B5 Test
B5 FE
 
 
Figure 4-18:  B5 Mid-Span Moment vs. Deflection 
 
4.1.6.6 B6 Finite Element Model Results 
A summary of the B6 experimental and finite element results is included in Table 4-
11. The finite element model of the B6 component test predicted a maximum sustainable 
applied load of 2038.5 kN. This load equated to a mid-span moment of 5319.3 kN-m. 
When combined wi id-span moment 
sisted by B6 was 6257.8 kN-m. This result is comparable to the measured maximum 
mid-span resisted m
 
th the self-weight effects the predicted maximum m
re
oment of 6399.5 kN-m. 
 205
Test FE Ratio
(a) (b) (b)/(a)
Max. Applied Load (kN) 2071.4 2038.5 0.98
Mid-Span Moment 
Self-Weight (kN-m) 951.5 938.5 0.99
Installation (kN-m) 561.8 0.0
Max. Applied Load (kN-m) 4886.2 5319.3 1.09
Flexural Resistance (kN-m) 6399.5 6257.8 0.98
B6
 
 
Table 4-11:  B6 Test and Finite Element Model Results 
 
The effect that t e test frame 
girders during the B6 test from both the experimental data and the finite element model 
results are shown in ity for B6 is 
ightly more dramatic than the measured behavior. However, the predictions match the 
physical results very well for the mid-span test frame cross-section.  
he applied loads had on the mid-span moments of th
 Figure 4-19. The predicted post-peak drop in capac
sl
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-
Sp
an
 
M
o
m
e
nt (
k
N
-
m)
0
1000
2000
3000
4000
5000
6000
G1 Test
G1 FE
G2 Test
G2 FE
B6 Test
B6 FE
 
 
Figure 4-19:  B6 Test Mid-Span Moments and Finite Element Predictions 
 206
 
Figure 4-40 shows the normalized B6 mid-span moment from the applied loads as a 
function of deflection for both the finite element model and the experimental data. The 
test results again fall short of the predicted capacity. However, the prediction curve 
matches the measured behavior through the elastic range and maintains a very similar 
shape pre- and post-peak. When the B6 test results are amended for the difference in self-
weight and the recorded installation effects, the exhibited and predicted flexural 
resistance capacities are within 2%. 
Deflection (mm)
0 100 200 300 400
M/
M
x
yi
e
l
d
0.0
0.2
0.4
0.6
0.8
1.0
B6 Test
B6 FE 
 
 
Figure 4-40:  B6 Mid-Span Moment vs. Deflection 
 
 207
4.1.6.7 B7 Finite Element Model Results 
Table 4-12 contains a summary of the B7 experimental and finite element results. The 
B7 finite element model predicted a maximum sustainable applied load of 1269.9 kN. 
This load equated to a mid-span moment of 3138.1 kN-m. When combined with the self-
weight effects the predicted maximum mid-span moment resisted by B7 was 3993.3 kN-
m. This result is a significant over-strength, compared with the measured maximum mid-
span resisted mome
/(a)
Max. Applied Load (kN) 1095.5 1269.9 1.16
Mid-Span Moment 
Self-Weight (kN-m) 811.8 855.2 1.05
Installation (kN-m) 190.4 0.0
Max. Applied Loa
nt of 3503.4 kN-m. 
 
Test FE Ratio
(a) (b) (b)
B7
d (kN-m) 2501.1 3138.1 1.25
Flexural Resistance (kN-m) 3503.4 3993.3 1.14
 
 
Table 4-12:  B7 Test and Finite Element Model Results 
 
The effect that the applied loads had on the mid-span moments of G1, G2 and B7 
from both the experim
he predictions match the physical results very well early in the loading regime 
indicating that the finite element model adequately forecasts the elastic behavior of the 
test frame. 
ental test and the finite element model are shown in Figure 4-41. 
T
 208
Total Applied Load (kN)
0 500 1000 1500 2000 2500
M
i
d-
Span
 M
o
ment (
k
N-
m)
0
1000
2000
3000
4000
5000
6000
G1 Test
G1 FE
G2 Test
G2 FE
B7 Test
B7 FE
 
 
Figure 4-41:  B7 Test Mid-Span Moments and Finite Element Predictions 
 
Figure 4-42 shows the normalized B7 mid-span moment from the applied loads as a 
function of deflection for both the finite element model and the experimental data. 
Although the overall shape of the prediction and experimental curves remains similar 
throughout the figure, the experimental data indicate a significant early stiffness 
difference and, later, a failure of the section well short of the predicted peak. These 
ifferences are most likely due to the nature in which B7 was fabricated and the inability 
to quantify these differences and incorporate them into the model. This resulted in fully 
analyzed test result  self-weight and 
recorded installation effects that are nearly 14% less than  predicted. 
d
s for flexural resistance that include the difference in
 209
In addition to the fabrication issues that affected the performance of B7, it is difficult 
for any general purpose finite element program to predict the onset of local buckling for 
slender plates such as the top flange of this specimen. These slender sections are sensitive 
to geometric imperfections that were not a part of this analytical study. White et al. 
(2001) modeled B7 with and without estimates for geometric imperfections. Their results 
without the geometric imperfection estimates were very similar to those in this study. 
Their results including the geometric imperfection estimates matched the physical test 
results much more  employs 
odeling very similar to that used by White et al. (2001), a similar correction in behavior 
is expected with the 7 model. 
closely; the results are within 4%. Because this study
m
 incorporation of geometric imperfections into the B
Deflection (mm)
0 100 200 300 400
M/
M
x
yi
e
l
d
0.0
0.2
0.4
0.6
0.8
1.0
B7 Test
B7 FE 
 
Figure 4-42:  B7 Mid-Span Moment vs. Deflection 
 210
 
m
linear-elastic behavior. 
211
4.2 AASHTO Guide Specification Predictions 
Bending capacities for each of the bending components can be determined using the 
provisions of the Guide Specifications. These provisions, which are summarized in 
Appendix B.1, utilized the vertical bending stress, f
b
, and the lateral flange bending stress, 
f
l
, results of a 1
st
 order analysis to determine a maximum strong-axis flexural resistance. 
The 1
st
 order analysis used in this report was generated with the same finite element 
odel that was used for the fully non-linear analysis. However, the model was limited to 
Table 4-13 includes the vertical bending capacities, M
n
, as determined by the Guide 
Specifications (example calculations to demonstrate how these numbers were generated 
are included in Sections 4.1.1 and 4.1.2), and a summary of the experimental results for 
these sections, M
x
test
, as reported in Chapter 3. A performance ratio that is produced by 
normalizing the capacity of the Guide Specificatio ental results is listed 
in the far right column of Table 4-13. A statistical summary of the normalized 
performance ratios is shown in the n.  
The average performance ratio was 0.71, or owever, this 
average was associated with a rather large standard deviation of 0.15 or 21% of the mean, 
indicating a very poor consistency of prediction. The range of results extended from 9% 
conservative to 43% conservative.  
ns by the experim
roughly 29% conservative. H
box just under the far right colum
 212
Component M
n 
From f
l
/f
b 
From M
x
test
M
n/
M
x
test
Guide 1st Order
Specifications Analysis
(kN-m) (kN-m)
B1 2702 0.32 4339 0.62
B2 2778 0.33 4730 0.59
B3 2748 0.36 4834 0.57
B4 2900 0.31 4880 0.59
B5 4790 0.32 5278 0.91
B6 5649 0.31 6400 0.88
B7 2775 0.29 3503 0.79
Average 0.71
Std. Dev. 0.15
Maximum 0.91
Minimum 0.57
 
 
Guide Specifications Flexural Capacities and Statistics 
 
lations illustrate the use of the Guide 
Specifications for determining the flexural resistance of a non-compact compression 
flange section and of a compact compression flange section. These calculations are 
usually an iterative process. The las ration of this process is presented in Section 4.1.1 
for brevity. 
4.2.1 Non-Compact Compr on Flange Example 
Bending component B1 was chosen for these example calculations. 
? B1 properties 
F
yc
 = yield stress of the compression flange = 408.5 MPa 
F
yw
 = yield stress of the web = 445.4 MPa 
L
b
 = unbraced arc length of the flange = 4772 mm 
R = minimum girder radius within the panel = 63,630 mm 
b
fc
 = compression flange width = 443.7 mm 
D = web depth = 1211 mm 
Table 4-13:  Summary of 
The following two sets of example calcu
t ite
essi
D
c
 = depth of web in compression = 604.9 mm 
6 3 
st
st
flan
t
fc
 = compression flange thickness = 19.48 mm 
t
w
 = web thickness = 8.230 mm 
S
xc
 = section modulus referred to the compression flange = 12.41x10  mm
f
l1
 = 1  order analysis lateral flange bending stress = 69.64 MPa 
f
bu
 = 1  order analysis flange stress from vertical bending = 217.6 MPa 
? Check flange compactness 
B1 was designed to be non-compact. To be defined as non-compact, the compression 
ge must meet the following criterion: 
()
2302.1
1
??
lbufc
fc
E
b
 
+ fft
()
2.27
64.696.217
204000
02.18.22
48.19
7.443
=
+
?==
fc
t
b
 
fc
238.22 ?=
fc
t
 Therefore, the flange is non-compact. 
fc
b
? Solve for the critical flange stress,
The critical flange stress is the lesser of a flange stress that, when amplified with the 
? -factors, will cause lateral torsional buckling in unbraced length, or the flange yield 
strength reduced by the lateral flange bending stress. 
The lateral torsional buckling stress is: 
cr
F  
?
?
?
?
?
?
?
?
?
?
?=
F
L
FF
yc
b
ycbs
2
31  
??
??
??
Eb
fc
2
9.0 ?
 213
()()
MPaF 0.373315.408 =???=  
bs
204000
5.408
7.4439.0
4772
2
2
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
The non-compact flange ? -factors are: 
fc
bb
b
L
R
L
+
=
1
1
?
b
 
554.0
7.443
4772
630,63
4772
1
=
?
?
?
?
?
?
1
?
?
?
?
?
?
+
=
b
?  
?
?
?
?
?
?
??
=
fc
b
bu
l
w
bf 75
11
1
1
1
?  
??
Lf
()
378.1
7.44375
4772
1
64.69
1
1
?
?
?
?
?
?
??
w
6.217
=
??
=?  
1
?
?
?
?
?
?
?
?
+
??
=
bu
w
f
R
2
6.01
?  
?
?
? ?
l
b
fc
f
L
1
2
1.0000,830
?
+
+
b
b
L
95.0
055.1
6.217
64.69
6.01
630,63
4772
1.0000,830
7.443
4772
95.0
2
2
=
?
?
?
?
?
?
+
?
?
?
?
?
?
?+
+
=
w
?  
0
1
?
bu
l
f
f
, ( ) 055.1,min
21
==
www
??? . Because 
 214
 215
Having determined the ? -factors, solve for the critical flange stress. 
wbbscr
FF ??=
1
 
()()() MPaF
cr
0.218055.1554.00.373
1
==  
lycr
fFF ?=
2
 
MPaF
cr
9.33864.695.408
2
=?=  
() MPafiFFF
bcrcrcr
6.2170.218,min
21
=?==    
? Check the web stress criterion 
k = bend-buckling coefficient = 
2
0.9
?
?
?
?
?
?
?
?
c
D
D
 
07.36
9.604
1211
0.9
2
=
?
?
?
?
?
?
=k  
()
yw
w
cr
F
t
D
Ek
webF ?
?
?
?
?
?
?
?
?
=
2
9.0
 
(())
MPaweb 9.305
230.8
1211
07.362040009.0
)
2
=
?
?
?
?
?
?
=  
Because the critical web stress, 305.9 MPa (44.367 ksi) is greater than the vertical 
bending stress in the section 217.6 MPa (31.560 
? Determine the equivalent vertical bending moment
n
M =  
F
cr
(
xcbu
Sf
( ) mkNmmNxxM
n
?=?== 27001027001041.12
66
 6.217
ksi) the web condition is acceptable. 
 
 216
Please refer to Table 4-17 to see how this capacity compares to the experimental 
measurement. 
4.2.2 Compact Compression Flange Example 
Bending component B5 was chosen for these example calculations. 
? B5 properties 
F
yc
 = compression flange yield strength = 395.0 MPa 
F
yw
 = web plate yield strength = 445.2 MPa 
L
R inimum girder radius within the panel = 63,630 mm 
b pression flange width = 419.1 mm 
D
 
t
fc
pression flange thickness = 24.66 mm 
t
w
 
S odulus referred to the compression flange = 14.56x10
6
 mm
3
 
f
l1
st
 order analysis lateral flange bending stress = 105.3 MPa 
f
bu
 = 1
st
 order analysis flange stress from vertical bending = 329.0 MPa 
? Check the flange compactness 
B5 was designed to have a compact compression flange. To be defined as compact, 
the compression flange must meet the following criterion: 
b
 = unbraced arc length of the flange = 4772 mm 
 = m
fc
 = com
 = web depth = 1215 mm 
c
 = depth of web in compression = 607.3 mm
 = com
 = web thickness = 8.458 mm
xc
 = section m
 = 1
D
18?
fc
fc
t
b
 
 
?
strength reduced by the lateral flange bending stress. 
217
180.17
66.24
1.419
?==
fc
fc
t
b
 Therefore, the flange is compact. 
? Solve for the critical flange stress,
cr
F  
The critical flange stress is the lesser of a flange stress that, when amplified with the 
-factors, will cause lateral torsional buckling in unbraced length, or the flange yield 
The lateral torsional buckling stress is: 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?=
E
F
b
L
FF
yc
fc
b
ycbs
2
2
9.0
31
?
 
()()
MPaF
bs
8.357
204000
0.395
1.4199.0
4772
310.395
2
2
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?=
?
 
The compact flange ? -factors are: 
2
01.0
6
11
1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
++
=
R
L
b
L
b
L
b
fc
b
fc
b
b
?  
()
878
0
630,63
4772
1.4196
4772
1
1.419
4772
1
1
?
?
?
?
?
?
?
?
?
?
?
?
++
=
b
?  .0
01.
2
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
yc
bs
fc
bb
F
F
b
L
R
L
1.
?
?
?
?
?
+?
?
?
?
?
?
?+=
b
bu
lb
w
f
f
R
L
?
?
03.0
1.01895.0
1
2
 
048.1
0.395
8.357
878.0
630,63
4772
1.03.0
0.329
3.105
630,63
4772
1.01895.0
2
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?
?
?
?
?
?
?+=
w
?  
1.419
4772
?
?
?
?
?
?
?
?
?
 218
() 0.1920.0048.1878.0 <==
wb
??   
Having determined the ? -factors, solve for the critical flange stress. 
wbbscr
FF ??=
1
 
() MPaF
cr
2.329920.08.357
1
==  
3
1
2
l
ycr
f
FF ?=  
MPaF
cr
9.359
3
3.105
0.395
2
=?=  
() MPafMPaFFF
bucrcr
0.3292.329,min
21cr
=>=  
? eb stress criterion 
k
=
Check the w
 = bend-buckling coefficient = 
2
0.9
?
?
?
?
?
?
?
?
c
D
D
 
02.36
3.607
1215
0.
2
=
?
?
?
?
?
?
k  9=
()
yw
w
F
t
D
Ek
F ?
?
?
?
?
?
?
?
?
=
2
9.0
 
()
cr
web
()
MPafMPawebF
bucr
0.3295.320
458.8
1215
02.362040009.
(
2
=<=
?
?
?
?
?
?
 
pressive stress is less than th
the f etermine the vertical bending stress based on the critical web stress. 
0
) =
Because the critical web com e vertical bending stress in 
lange, d
bu
fcc
c
cr
f
tD
D
?
?
?
?
?
?
?
?
+
?)( webF
 219
() MPaMPawebF
cr
5.3201.3160.329
66.243.607
3.607
)( <=
?
?
?
?
?
?
+
?  okay 
Therefore this design meets the critical web stress criterion.  
? Determine the equivalent vertical bending moment 
xcbun
SfM =  
( ) mkNmmNxxM
n
?=?== 47901047901056.140.329
66
 
Please refer to Table 4-17 to see how this capacity compares to the experimental 
measurement. 
4.3 Unified Design Method Predictions 
The estimated capacities derived by using the Unified Design Method for the entire 
suite of bending components can be seen in the top section of Table 4-14. These 
capacities, M
n
ined by using a 1
st
 order analysis with the suggested 
lateral flange stre ication factor, and by using a 2
nd
lysis. Similar to with 
the Guide Specification results, each calculated capacity has been normalized by the 
appropriate experimental result, M
x
test
, from Chapter 3 to pro mance ratios 
in the far right column of each section of Table 4-14. The lo le 
contains a statistical summary of the performance ratios for each analysis method.  
For the 1
st
 order analysis results, the average performance ratio was 0.85, or roughly 
15% conservative. This average was associated with a standard deviation of 0.03 or 
approximately 4% of the mean. The range of results extended from 10% conservative to 
19% conservative.  
nd
 order analysis results are very similar to the statistical results 
for the 1
st
 order analysis results. The average performance ratio was 0.84 or 16% 
The statistics for the 2
, have been determ
ss amplif  order ana
duce the perfor
wer section of this tab
 
conservative with an ass
tightened slightly extending from
220
ociated standard deviation of 0.03 or 4%. The range of results 
 12% conservative to 18% conservative. 
Component 
M
x
test
M
n 
AF(f
l
/f
b
)M
n/
M
x
test
M
n 
f
l
/f
b 
M
n/
M
x
test
(kN-m) (kN-m) (kN-m)
B1 4339 3908 0.37 0.90 3835 0.33 0.88
B2 4730 4022 0.38 0.85 3944 0.34 0.83
B3 4834 4006 0.42 0.83 3942 0.43 0.82
B4 4880 3967 0.36 0.81 4007 0.28 0.82
B5 5278 4618 0.38 0.87 4590 0.34 0.87
B6 6400 5512 0.37 0.86 5316 0.43 0.83
0.83 2928 0.28 0.84
0.85 Average 0.84
0.03 Std. Dev. 0.03
0.90 Maximum 0.88
0.81 Minimum 0.82
1st Order Analysis 2nd Order Analysis
B7 3503 2919 0.29
Average
Std. Dev.
Maximum
Minimum
 
thod Flexural Capacities and Statistics 
tions illustrate the use of the Unified 
 resistance of a discretely braced non-
com a discretely braced compact compression 
flange section using the results of a 1
st
 order analysis. Appendix B.2 contains a summary 
of the Unified Design Method provisions for non-composite I-girders. 
4.3.1 Non-Compact Compression Flange Example 
As before, bending component B1 was chosen for these example calculations. The B1 
section properties listed in Section 4.1.1 still apply. However, the unique set of 
coincidental loads from the 1
st
 order analysis that are needed for these calculations are 
listed here:
 
f
l1
 = 1
st
 order analysis lateral flange bending stress = 100.8 MPa 
 
Table 4-14:  Summary of Unified Design Me
 
The following two sets of example calcula
Design Method for determining the flexural
pact compression flange section and of 
 
flange slend
221
f
bu
 = 1
st
 order analysis flange stress from vertical bending = 314.9 MPa 
? Check the flange compactness 
B1 was designed to be non-compact. To be defined as compact, the compression 
erness must meet the following criterion:
 
yc
pf
F
E
38.0=?  
49.8
5.408
204000
38.0 ==
pf
?  
fc
fc
f
t
b
2
=?  
()
49.839.11
48.192
7.443
=>==
pff
??  
Because 
pff
?? > , the flange is non-compact. 
? Determine critical flange local buckling stre
Because the flange is non-compact, first determine the critical flange stress that will 
cause local buckling of the flange. 
yr
F
rf
E
56.0=?  
96.1456.0 ==
rf
?  
Because F
yc yw
R
h
, is taken as 1.0. 
Determine the web load shedding factor, R
b
. 
0.286
204000
 < F
[ ]
ycywycyr
FFFF 5.0,7.0min >=  
()[] MPaFF
ycyr
3.2045.02864.4455.4087.0min
ss 
MPa0.,0.286 =>===  
 the hybrid web reduction factor, 
 222
If 
yrw
c
F
E
t
D
76.5
2
? , then R
b
 = 1.0 
()
8.153
0.286
204000
76.50.147
230.8
9.6042
=?=  Therefore R
b
 = 1.0 
ychb
pfrf
pff
ych
yr
FLBnc
FRR
FR
F
F
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??=
??
??
11
)(
 
MPaF
FLBnc
6.3535.408
49.896.14
49.839.11
5.408
0.286
11
)(
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??=  
? l torsional buckling stress 
The critical lateral torsional buckling stress is based on the unbraced length of the 
comp
Determine the critical latera
ression flange. 
?
?
?
?
?
?
?
?
+
fcfc
wc
fc
tb
tD
b
r
3
1
112
 =
t
()
()
mmr 3.117
48.197.443
230.89.604
3
1
112
7.443
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+
 
yc
tp
F
E
rL 0.1=  
() mmL
p
2621
5.408
204000
3.1170.1 ==  
yr
tr
F
E
rL ?=  
() mmL
r
9842
0.286
204000
3.117 ==?  
t
=
 223
Because
rbp
LLL ?< , the unbraced length is non-compact. 
[ ] MPaFFFF
ycywycyr
0.2865.0,7.0min =?=  
C
b
 = 1.0 for constant vertical bending moment 
ychbychb
pr
pb
ych
yr
bLTBnc
FRRFRR
LL
LL
FR
F
CF ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??= 11
)(
 
MPaF
LTBnc
0.3725.408
26219842
26214772
5.408
0.286
110.1
)(
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??=  
? Determine the vertical bending moment capacity using the 1/3 rule  
[ ] MPaFFF
LTBncFLBncnc
6.353,min
)()(
==  
Because f
l1
 is from a 1
st
 order analysis, apply the recomm plification factor, 
AF, to account for the 2 etric effects on lateral flange bending, f
l
.  
ended am
nd
 order geom
?
?
?
?
?
?
?
cr
bu
F
f
1
85.0
 
F
cr
 is the fl
?
?
?
?
?
?
=AF
where ange elastic lateral-torsional buckling s . 
2
2
?
?
?
?
?
?
?
?
=
t
b
bb
cr
r
L
ERC
F
?
 
()()( )
F
cr
1217
3.117
4772
2040000.10.1
2
2
=
?
?
?
?
?
?
=
?
147.1
1217
9.314
1
85.0
=
?
?
?
?
?
?
?
?
?
?
?
?
?
=AF  
MPa  
tress
 224
()
1ll
fAFf =  
() MPaf
l
6.1158.100147.1 ==  
Apply the 1/3
rd
 rule to determine the vertical bending capacity. 
?
f
 = 1.00 
lbunf
ffF
3
1
+??   
MPaF
nf
6.353=?  
() MPaMPa 4.3536.115
3
1
9.314353 =+?
 
Therefore f
bu
 = 314.9MPa is acceptable and the equivalent vertical bending moment 
is: 
xcbu
SfM  
6.
n
=
( ) mkNmmNxxM ?=?= 39081039081041.129.314
66
 
Please refer to Table 4-18 to see how this capacity compares to the experimental 
measurement. 
 Compact Comp ple 
The properties for bending com nt B5 are listed in Section 4.1.2. The 1
st
 order 
or appropriate for this set of calculations are: 
f
l1
 = 1
st
ge bending stress = 101.5 MPa 
f
bu
 = 1
st
 order analysis flange stress from vertical bending = 317.2 MPa 
? actness 
pact compression flange. Therefore it must meet the 
following slenderness limit. 
loads f
 order analysis lateral flan
Check the flange comp
B5 was designed to have a com
n
=
4.3.2 ression Flange Exam
pone
 225
yc
pf
F
E
38.0=?  
64.8
0.395
204000
38.0 ==
pf
?  
fc
fc
f
t
b
2
=?  
()
64.850.8
66.242
1.419
=<==
pff
??  
Because 
pff
?? ? , the flange is compact. 
? Determine the critical flange local buckling stress 
Because the compression flange is compact, 
ychbFLBnc
FRRF =
)(
. 
Determine the hybrid girder reduction factor, . 
F
yc
<F
yw 
Therefore R
h 
= 1.0 
Determine the web load shedding factor, R
R
h
b
. 
[ ]
ycywycyr
MPaFFF 5.05.276,7.0min ?==
If 
F  
yrw
c
F
E
t
D
76.5
2
? , then R
b
 = 1.0 
()
4.156
5.276
204000
76.56.143 =?=  Therefore R
b
 = 1.0 
() MPaFRR
ychb
0.3950.10.1
)(
458.8
3.6072
F
FLBnc
0.395 ===  
? Determine the critical lateral torsional buckling stress 
?
?
?
?
?
?
?
+
=
fcfc
wc
t
tb
t
r
3
112
 
?
fc
D
b
1
 226
()
()
mmr
t
1.112
66.241.419
458.83.607
3
1
112
1.419
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+
=  
yc
tp
F
E
rL 0.1=  
() mmL
p
2548
0.395
204000
1.1120.1 ==  
yr
tr
F
E
rL ?=  
() mmL 9566
5.276
204000
1.112 =?  
Because
rbp
LLL ?< , the unbraced length is non-compact. 
C oment 
r
=
b
 = 1.0 for constant vertical bending m
ychbychb
pr
pb
ych
yr
b
FRRFRR
LL
LL
FR
F
CF ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??= 11
)
 
LTBnc(
MPaMPa 0.3954.3570.395
25489566
25484772
0.395
5.276
110.1
)
?=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??=  
? nt capacity using the 1/3 rule  
F
LTBnc(
Determine the vertical bending mome
[ ] MPaF
ncFLB
,
()(
FF
LTBncnc
4.357min
)
==  
Determ lange stress amplification actor, AF.  
?
?
?
?
?
?
cr
bu
AF  
where F
cr
 is the flange elastic lateral-torsinal buckling stress. 
?
?
?
?
?
?
?
=
F
f
1
85.0
ine the lateral f  f
 227
2
2
?
?
?
?
?
?
?
?
=
t
b
bb
cr
r
L
ERC
F
?
 
()()( )
MPaF
cr
1111
1.112
4772
2040000.10.1
2
2
=
?
?
?
?
?
?
=
?
 
186.1
1111
9.314
1
85.0
=
?
?
?
?
?
?
?
?
?
?
?
?
?
=AF  
()
1ll
fAFf =  
() MPaf
l
4.1205.101186.1 ==  
Apply the 1/3
rd
 rule to determine the vertical ben ity. 
?
f
 = 1.00 
ding capac
lbunf
ffF
3
1
+??   
MPaF
nf
4.357=?  
() MPa3.3574.120
3
1
2.357 =+
 
Therefore, the design is acceptable and the equivalent vertical bending m
xcbun
SfM =  
MPa 3174. ?
oment is: 
( ) mkNmmN
n
??== 46181056.142.317
6
 
Please refer to Table 4-18 to see how this capacity compares to the experimental 
measurement. 
xM = 4618
 228
4.4 Summary of Predictions 
Table 4-15 includes a summary of the predicted vertical bending capacities for each 
of the bending components as determined with the finite element model in Section 4.1, 
the Guide Specifications in Section 4.2, and the Unified Design Method in Section 4.3. 
The performance of each family of results is interpreted by the statistics in the middle and 
lower sections of this table. The middle section contains a statistical summary of the 
performance ratios for all bending components by prediction type. Because the B7 finite 
elem itive to geometric imperfections (White et 
al., 2001) that are not a part of this study, and the parameters of B7 fall outside the scope 
of either set of design provisions, the statistics in the lower section of Table 4-15 exclude 
the B7 performance data.  
The statistics in either the middle or lower section show that the finite element model 
very accurately and consistently predicted the behavior of the physical experiments. The 
statistics also show that using either a 1
st
 order analysis or a 2
nd
 order analysis, the 
Unified Design Method predictions of the physical behavior are approximately 15% 
conservative but nearly as consistent as the finite element predictions.  Finally, the 
statistics for the Guide Specification predictions indicate the poorest performance of the 
methods used. The Guide Specifications predicted the physical behavior approximately 
30% conservative.  However this family of data had a standard deviation of nearly 24% 
of the mean that indicates a poor consistency of calculation. 
ent prediction was shown to be very sens
 229
Component Experiment
kN-m kN-m kN-m kN-m kN-m
[a] [b] [b]/[a] [c] [c]/[a] [d] [d]/[a] [e] [e]/[a]
B1 4539 4574 1.01 2702 0.60 3910 0.86 3835 0.84
B2 4730 4775 1.01 2778 0.59 4022 0.85 3944 0.83
B3 4834 4778 0.99 2748 0.57 4006 0.83 3942 0.82
B4 4880 4718 0.97 2900 0.59 3967 0.81 4007 0.82
B5 5278 5255 1.00 4860 0.92 4621 0.88 4590 0.87
B6 6400 6258 0.98 5813 0.91 5512 0.86 5316 0.83
B7 3503 3993 1.14 2775 0.79 2919 0.83 2928 0.84
Including B7
Average 1.01 0.71 0.85 0.84
Standard Deviation 0.06 0.16 0.02 0.02
Maximum 1.14 0.92 0.88 0.87
Minimum 0.97 0.57 0.81 0.82
Excluding B7
Average 0.99 0.70 0.85 0.84
0.17 0.02 0.02
0.92 0.88 0.87
0.57 0.81 0.82
Finite Element Model Guide Specifications Unified Design Method
1st Order Analysis 2nd Order Analysis
Standard Deviation 0.02
Maximum 1.01
Minimum 0.97
 
Predicted Vertical Bending Moments 
 
 
Table 4-15:  Summary of 
 
Chapter
230
 5.  Conclusions 
5.1 Summary 
Tests were conducted on seven steel I-girders that were horizontally curved. The 
objective of the tests was to determine the ultimate vertical bending capacity of these I-
girders within the frame of a full-scale, single span, three-girder bridge. Each of these test 
girders or components had an approximate length of 7.62 m (25 ft) long, a radius along 
its web centerline of 63.63 m (208.75 ft), and a unique combination of flange slenderness, 
web slenderness and web stiffening. Ultimate capacity was defined as the point at which 
the com oment to the remainder of the test frame. 
This condition was always associated with a lateral mechanism within the compression 
flange of the component. This lateral mechanism consisted of through thickness yielding 
and of a flange local buckle on the inside half of the compression flange. Both strong-axis 
(vertica nding and torsion were additive at this location within the cross-section. 
The experimental data from each component test were reduced using both the direct 
and indirect methods within the elastic range to prove the indirect technique. In the 
inelastic range, the indirect method of analysis was solely used. The physical test ultimate 
vertical bending capacities were determined using three sets of data; the installation 
strains, the self-weight strains and the applied-load effects generated with the indirect 
method. 
In all cases, except for B6, first yield in the component was reached at mid-span on 
the inside tip of the compression flange. Although direct evidence does not exist, there is 
strong support that yield was first reached within the compression flange of B6 at the 
ponent began to shed vertical bending m
l) be
 
cross-fram
231
e locations. However, this was shortly followed by yielding, and eventually the 
same half-flange local buckle at mid-span that was apparent in the remaining 
experiments. 
The analytical predictions were produced using a finite element model that was fully 
nonlinear. This model was virtually constructed with ABAQUS general purpose software 
using the recommendations of White et al. (2001). The model was created using as-built 
plate dimensions and individual plate material behavior curves that were generated with 
the results of a large suite of material tests. Ad ents were also made to the model so 
that the effects of residual stress from fabricatio ould impact the results.  
The predictor equations of both the AASHTO Guide Specifications and the Unified 
Design Method were also used to evaluate the vertical bending capacity of each of the 
bending components. The Guide Specifications requires the use of a 1
st
 order analysis to 
determine capacity. The Unified Design Method ake use of results from either a 1
st
 
order or 2
nd
 order analysis to determine capacity.
5.2 Findings
justm
n w
can m
 
 
In general, all of the test results support the use of the Unified Design Method for the 
design of horizontally curved steel I-girder bridges. The Unified Design Method retains 
the strength of the Guide Specifications, which is the use of a first order analysis to 
determine vertical bending capacity of horizontally curved steel I-girders. This method 
also eliminates the step discontinuity that existed in the Guide Specifications between the 
behavior of compact and non-compact flanges. Finally, the Unified Design Method 
provisions reduce the design equations for straight girders as the radius of curvature 
becomes larger. This reduction brings cohesiveness to the entirety of the I-girder design 
 
for steel bridges. For all of 
constructive and positive change for the de
owners. 
specific find
? 
capacity of these com
experim
232
these reasons, the use of the Unified Design Method will be a 
sign consultant community and for bridge 
In addition, the experimental testing and analytical modeling yielded the following 
ings: 
Installation strains had a small but significant effect on the ultimate vertical bending 
ponents.  However, the installation process used in these 
nts was difficult and not typical to bridge construction.  
? W spacing had a negligible effect on the 
ultim tical bending capacity of these sections. 
? C ression flange slenderness did affect ultimate vertical bending capacity with 
norm ance decreasing as slenderness rose. Also, post-peak behavior of the 
comp s was stable while the non-compact flanged sections experienced 
a dram rop in capacity. 
? Predictions of a fully nonlinear finite element model that incorporated actual plate 
geom aterial properties agreed exceptionally well with the physical behavior 
for all specimens, with the exception of B7. The very slender flange of B7 was shown by 
others (White et al., 2001) to be sensitive to geometric imperfections that were not a part 
of this study. 
? Regardless of whether a first or second order analysis was used to determine the 
vertical and lateral flange bending stress, the Unified Design Method provided a more 
accurate, consistent and robust determination of vertical bending capacity compared with 
the Guide Specifications. 
e
eb slenderness and transverse stiffener 
ate ver
omp
alized perform
act flanged section
atic d
etry and m
 233
 
5.3 Research Needs 
Extensive experimental and analytical work have recently been conducted in the area 
of horizontally curved steel I-girders through the FHWA CSBRP. However, some topics 
still need further investigation. 
? Hybrid girders. The use of horizontally curved hybrid sections is currently not 
permitted by either AASHTO Specification. These sections have become more 
widely used in straight girder design since the introduction of high performance 
steels. DOTs in several states have reported cost savings when using hybrid sections 
in negative moment regions. However, an e ental investigation of the effect of 
hybrid girder web yielding at the strength limit state has never been conducted. 
? Cross-frame forces. Additional work perf ed on the experimental data generated 
during the CSBRP should result in guidance for the design of cross-frames for 
horizontally curved bridges. Design forces ese primary members are difficult to 
determine with the currently available tools. 
? Fatigue issues. Moving to the Unified De  Method removes much of the 
conservatism from the stress ranges that are predicted using the Guide Specifications. 
The effects of a realized increase in stress range and any accompanying sectional 
distortion on fatigue need to be investigated. 
? Systematic collapse. The test frame of the CSBRP was designed to withstand the load 
shedding of a bending component as it failed. However, the current practice will not 
necessarily result in such a design. An analytical investigation could determine 
xperim
orm
for th
sign
 234
whether additional precautions are needed to prevent a systematic collapse due to 
progressive load shedding that begins with a failing exterior girder.  
 
   
Appendix 
insures proper interp
perform
exclus
Steel Bridge Research Proj
conducted on sam
235
A.  Steel Properties Data 
Determining the mechanical properties of the materials used in structural experiments 
retation of the results and supports any analytical evaluation 
ed using the finite element method. The body of this dissertation deals 
ively with the bending component tests that were a part of the much larger Curved 
ect (CSBRP). However, material property testing was 
ples taken from all steel plates used in the fabrication of e 
and the additional component test series; high-shear low-moment components and high-
shear high-moment components. Also, tension testing was conducted on samples taken 
from the structural steel tubes that make up the individual members of the cross-frames 
and diaphragms. The results of the tension, compression and Young?s modulus tests for 
the entire program are reported in this appendix. When appropriate, the f  data is 
reduced to those specific tests that affect the analysis of the bending component tests.  
While a limited number of compression and Young?s modulus tests were conducted, 
most material property tests performed were tension tests. Web plates were sampled at 
six locations, flange plates at three locations. Each coupon, or sample, produced as many 
as three individual results.  
A.1 Plate Coupon Locations
 the test-fram
amily of
 
Figure A-1 shows a plan view of the test-frame and the individual components. This 
figure also indicates the limits of the section marks used to identify where individual steel 
plates where used in fabricating each item. Figures A-2 through A-36 show the location 
   
and orien
web.
236
tation of each coupon with respect to either a corresponding girder flange or 
35
'-3
 3
/8
" (
E)
25'-5 1/8" (G)
35
'-3
 3
/8
" 
(F
)
88'-0 15/16" (A)
26
'-2
" 
(B
)
41'-0 3/8" (C)
25
'-6
" 
(D
)
25'-5 1/8" (B1 to B7)
B1
B2
B3
B4
B5
B6
B7
 
 
Figure A-1. Layout of Cutting Plates in Full Scale Test of Curve Girders Bridge (See Table 1 for Cutting Schedule)
   
   238
A1
B1
C1 D1
E1
F1
WEB PLATE: 1
TESILE TEST
COUPON (TYP)
? 87'-3 5/8"
 
Figure A-2. Location of Te
 
 
nsile Coupons on Plate: 1 
? 25'-2"
B2
A2
COUPON (TYP)
TESILE TEST
WEB PLATE: 2
C2 D2
F2
E2
 
 
Figure A-3. Location of Tensile Coupons on Plate: 2 
   239
? 40'-0 3/8"
WEB PLATE: 3
B3
A3
C3 D3
E3
F3
TESILE TEST
COUPON (TYP)
 
cation of Te
 
 
Figure A-4. Lo nsile Coupons on Plate: 3 
? 24'-6"
WEB PLATE: 4
B4
A4
TESILE TEST
COUPON (TYP)
C4 D4
E4
F4
 
Figure A-5. Location of Te
 
 
nsile Coupons on Plate: 4 
WEB PLATE: 5
   240
? 35'-3 1/4"
B5
TESILE TEST
A5
COUPON (TYP)
C5 D5
E5
F5
 
Figure A-6. Location of Te
 
 
nsile Coupons on Plate: 5 
E6A6
WEB PLATE: 6
B6
C6 D6
F6
? 25'-4 7/8"
TESILE TEST
COUPON (TYP)
 
Figure A-7. Location of Te
 
 
nsile Coupons on Plate: 6 
   241
? 35'-3 1/4"
WEB PLATE: 7
B7
A7
TESILE TEST
COUPON (TYP)
C7 D7
E7
F7
 
ocation of Te
 
 
Figure A-8. L nsile Coupons on Plate: 7 
? 25'-4 7/8"
WEB PLATE: 8
COUPON (TYP)
TESILE TEST
B8
A8
C8 D8
F8
E8
 
Figure A-9. Location of Te
 
 
nsile Coupons on Plate: 8 
E9A9
   242
WEB PLATE: 9
B9
C9 D9
F9
? 25'-4 7/8"
COUPON (TYP)
TESILE TEST
 
Location of T
 
 
Figure A-10. ensile Coupons on Plate: 9 
? 25'-4 7/8"
WEB PLATE: 10
COUPON (TYP)
TESILE TEST
B10
A10
C10 D10
F10
E10
 
Figure A-11. Location of T
 
ensile Coupons on Plate: 10 
   243
A11
? 25'-4 7/8"
B11
WEB PLATE: 11
TESILE TEST
COUPON (TYP)
C11 D11
F11
E11
 
Location of T
 
 
Figure A-12. ensile Coupons on Plate: 11 
A12 E12
WEB PLATE: 12
B12
C12 D12
F12
? 25'-4 7/8"
TESILE TEST
COUPON (TYP)
 
Figure A-13. Location of Tensile Coupons on Plate: 12 
 
 
   244
A13
? 25'-4 7/8"
WEB PLATE: 13
B13
TESILE TEST
COUPON (TYP)
C13 D13
E13
F13
 
Figure A-14. Location of T
 
ensile Coupons on Plate: 13 
TOP FLANGE PLATE: 14
? 87'-8"
TESILE TEST
A14
COUPON (TYP)
B14
C14
BOT. FLANGE PLATE: 14 1
6
"
1
6
"
 
Figure A-15. Location of T
 
ensile Coupons on Plate: 14 
? 41-1 1/2"
BOT. FLANGE PLATE: 15
TOP FLANGE PLATE: 15
COUPON (TYP)
A15
TESILE TEST
1
6
"
1
6
"
B15
C15
 
Figure A-16. Location of T
 
 
ensile Coupons on Plate: 15 
   
 
 
245
? 25-7 1/2"
BOT. FLANGE PLATE: 16
TOP FLANGE PLATE: 16
COUPON (TYP)
A16
TESILE TEST
2
0
"
B16
2
0
"
C16
 
Figure A-17. Location of Tensile Coupons on Plate: 16 
? 26'-3"
BOT. FLANGE PLATE: 17
TOP FLANGE PLATE: 17
COUPON (TYP)
A17
TESILE TEST
2
0
"
B17
2
0
"
C17
 
Figure A-18. Location of Tensile Coupons on Plate: 17 
 
 
? 35'-5"
BOT. FLANGE PLATE: 18
TOP FLANGE PLATE: 18
COUPON (TYP)
A18
TESILE TEST
2
4
"
2
4
"
B18
C18
 
Figure A-19. Location of Tensile Coupons on Plate: 18 
 
 
   
 
 
246
? 35-5"
BOT. FLANGE PLATE: 19
TOP FLANGE PLATE: 19
COUPON (TYP)
A19
TESILE TEST
2
4
"
B19
2
4
"
C19
 
Figure A-20. Location of Tensile Coupons on Plate: 19 
? 25-6 1/2"
BOT. FLANGE PLATE: 20
TOP FLANGE PLATE: 20
COUPON (TYP)
A20
TESILE TEST
2
4
"
B20
2
4
"
C20
 
Figure A-21. 0 
 
 
Location of Tensile Coupons on Plate: 2
? 25'-6 1/2"
TOP FLANGE COMP. B1
TESILE TEST PL: 21
COUPON (TYP)
A21
B21
?
 
2
0
"
C21TOP FLANGE COMP. B2
TOP FLANGE COMP. B3
TOP FLANGE COMP. B4
?
 
2
0
"
?
 
2
0
"
?
 
2
0
"
 
Figure A-22. 1 
 
Location of Tensile Coupons on Plate: 2
 
   247
A22
?
 
2
0
"
?
 
2
0
"
?
 
2
0
"
BOT. FLANGE COMP. B1
B22
C22
? 25'-6"
TESILE TEST PL: 22
COUPON (TYP)
BOT. FLANGE COMP. B2
BOT. FLANGE COMP. B3
 
Figure A-23. Location of Tensile Coupons on Plate: 22 
 
 
? 25-6 1/2"
TESILE TEST PL: 23
COUPON (TYP)
A23
B23
C23
BOT. FLANGE COMP. B5
TOP FLANGE COMP. B5
?
 
1
8
"
?
 
1
8
"
 
Figure A-24. Location of T ns on Plate: 23 
 
 
A24
?
 
1
8
"
?
 
1
8
"
? 25-6 1/2"
BOT. FLANGE COMP. B6
TESILE TEST PL: 24
TOP FLANGE COMP. B6
COUPON (TYP)
B24
C24
 
Figure A-25. Location of Tensile Coupons on Plate: 24 
 
 
ensile Coupo
   
 
 
248
? 25-6 1/2"
?
 
2
4
 
1
/
2
"
BOT. FLANGE COMP. B4
A25
B25
TESILE TEST PL: 25
COUPON (TYP)
C25
 
Figure A-26. Location of Tensile Coupons on Plate: 25 
? 38'-4"
? 38-4"
TOP FLANGE
BOT. FLANGE
F1
TESILE TEST
COUPON (TYP)
F2
F3
TOP FLANGE
BOT. FLANGE
PLATE: 26
 
Figure A-27. 
 
Location of Tensile Coupons on Plate: 26 
? 38-4"
? 38'-4"
BOT. FLANGE
F1
BOT. FLANGE
TOP FLANGE
TOP FLANGE
F2
TESILE TEST
COUPON (TYP)
F3
PLATE: 28
 
Figure A-28. Location of Tensile Coupons on Plate: 28 
   
 
 
F1-32
TESILE TEST PL: 32
COUPON (TYP)
TOP FLANGE MV1
BOT. FLANGE MV1
BOT. FLANGE MV2
TOP FLANGE MV2
F3-32
F2-32
? 25'-5"
 
Figure A-29. Location of Te 2 
 
 
249
nsile Coupons on Plate: 3
TOP FLANGE MV3
BOT. FLANGE MV3
BOT. FLANGE MV4
TOP FLANGE MV4
F6-34
F5-34
F4-34
TESILE TEST PL: 34
COUPON (TYP)
? 25'-5"
 
Figure A-30. Location of Tensile Coupo 4 
 
 
ns on Plate: 3
   250
? 20'-0"
TESILE TEST
COUPON (TYP)
F1
TOP FLANGE
TOP FLANGE TOP FLANGE
LONG. STIFFENER
LONG. STIFFENER
F2
F3
? 19'-2"
PLATE: 30
 
Location of T
 
 
Figure A-31. ensile Coupons on Plate: 30 
? 19'-2"
TOP FLANGE
F4
TOP FLANGE
F5
F6
? 20'-0"
COUPON (T
TESIL
YP)
E TEST
TOP FLANGE
: 31PLATE
 
Figure A-32. Location of Tensile Coupons on Plate: 31 
 
 
W3-33
W
2
-
3
3
COUPON (TYP)
TESILE TEST PL: 33
W7-33
W
6
-
3
3
W5-33W
4
-
3
3
WEB PLATE MV1 WEB PLATE MV1
? 25-5" ? 25-5"
 
Figure A-33. Location of Tensile Coupons on Plate: 33 
 
 
   
WEB PLATE MV3 WEB PLATE MV4
TESILE TEST PL: 35
COUPON (TYP)
W9-35
W
8
-
3
5
W13-35
W
1
2
-
3
5
W11-35
W
1
0
-
3
5
? 25-5"? 25-5"
 
Figure A-34. Location of Tensile Coupons on Plate: 35 
 
 
? 38-0"
   
 
? 38'-0"
C UPON YP)
T ILE T T PL: 2
W B PLA E
O (T
ES ES 7
E T
W4
W
3
W6
W
5
W AEB PL TE
W8
W
7
? 0-6" 8
PL E: 27AT
 
 
 
Figure A-35. Location of Tensile Coupons on Plate: 27
 
? -6"80
? 38-0"? 3 '-0"8
W4
TE
W
3
WEB PLA
T LE TE  PL: 2
C PON P)
ESI ST 9
OU  (TY
W6
W
5
WEB PL EAT
W
W
7
8
PL TE: 29A
Figure A-36. Location of Tensile Coupons on Plate: 29
A.2 Tension Testing 
The tensile tests were performed in accordance with the St
Methods for Tension Testing of Metallic Materials  most cases, the E8 procedures 
pplem  the Struct tability rch Coun (SSRC) Technical 
Memorandum No. 7:  Tension Testing in order to generate consistent and uniform static 
yield strength levels. The E8 methods and procedures are designed to specifically 
point elongation, and tensile str  In this d
definition of these terms is consistent with those definitions provided in the E8 Standard.  
With few exceptions, standard plate-type rect ular test spe ens of full plate 
s were ensio g. These specimens are 450mm (18 in.) long, 
 reduced  225mm (9 in.) by 38mm (1? in.), and have a 200mm (8 in.) 
gage length. A aper of 0.15% was used to reduce the ss-sectiona a of 
 t at the  of th ength. This taper is per by 
E8 to insure th ccurs within the gage length. The E8 Standard contains a 
complete set o s for the ngular te n test spec
The remainder of the tension testing was co d on sta ound sp s. 
These specimens (referred to as Specimen 1 in the E8 Standard) are 125mm (5 in.) long, 
have a reduce pproxim  75mm (3 in.), a radius of 12.7mm (? in.), and a 
50mm (2 in.) g ngth. Only three (3) ten  tests in this program utilized standard 
round specimens. These test specimens were achined from Plate 34 and are identified 
as 34-F6-1-1R, 34-F6-1-2R and 34-F6-1-3R. 
The SSRC procedure requires that once a specimen reaches yield as defined by a 
0.2% elastic modulus offset, the testing should be interrupted and a constant strain 
 ASTM E8, andard Test 
. In
were su ented with ural S  Resea cil?s 
determine yield strength, yield ength. ocument the 
ang cim
thicknes
have a
 used for 
 section of
the t n n testi
 maximum t  cro l are
the specimen o a minimum  middle e gage l mitted 
at rupture o
f dimension  recta nsio imens.  
nducte ndard r ecimen
d section of a
age le
ately
sion
m
   253
maintained until the load stabilizes but for no longer than 5 minutes. This interruption 
process should occur at least two es a rain prior to the 
onset of strain hardening. Once strain hardening of the material begins, the interruption 
rocessed sho ted. C ion of this process w uce the ry 
 determ eld stren r the m  tested by f two me  
outlined in the orandum
The steels used for this program minal yield strengths 
M ). The AS 572 Gr. 345 steel generally exhibited a well 
defined yield strength and extended yield plateau prior to the onset of strain hardening 
during tension testing. The ASTM A852 steel generally produced a round-house curve 
 well eld point.
Tension tests were conducted on 292 specimens taken from 34 steel plates and 17 
specimens taken from 3 structural steel tubes. This appendix focuses on the plate steel 
tension tests. Tables A ults for all steel 
plates used in this program. 
A summary of the structural steel tube tension test results is contained in Tables A-35 
through A-37. These results have been previously discussed by Linzell (1999). 
more tim t 0.005 increments of st
p uld be termina omplet ill prod necessa
data to ine static yi gth fo aterial  one o thods
 SSRC mem . 
 had no between 345 MPa (50 
ksi) and 485 Pa (70 ksi TM A
without a  defined yi   
-1 through A-34 summarize the tension test res
   254
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)
0
(MPa)(m)(MPa)
1 A (G1) A572 345 11.113 390 54
Young's Mod. e h
E (GPa)
? (%) ? (MPa)
LengtGag
?
st
?  (%
 
(G
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
 (%)
apparent
) E
st
Pa)
? (%) ? (MP
388 6.0 .811 2.041 2 01 2.25 515.1
388 5.6 .754 2.118 2 02 2.13 513.4
.378 0.1 .086 1.466 3 02 5.58 531.4
7.0 .120 1.405 3 21 5.47 530.5
1.3 .213 1.412 3 65 5.87 524.3
0.1 .087 1.336 3 85 7.31 522.2
8.0 .180 1.788 2 49 6.11 526.2
6.2 .960 1.474 2 16 6.26 526.1
4.0 .987 1.483 2 51 5.75 525.8
6.8 .907 1.398 3 93 6.44 525.2
3.2 .975 1.427 2 44 7.28 524.9
6.2 .189 1.577 2 57 5.50 524.1
.1 .308 0.275 0 73 1.74 5.5
9.2 .904 0.782 0 82 5.18 18.0
6.8 .907 1.336 2 02 2.13 513.4
6.0 .811 2.118 3 85 7.31 531.4
11 11 11 1 11 11
is norm l to the irecti  rollin
gitudin  axis in e dire ion of r lling)
S ain Ha ening ensile trengtStatic Y eld
24
ificate ropert s
longation
(%)
a)
(m
A1-2 205.4 0.191 405.8 0.832 387.4 0.392 394.2 0. 38 1 .7 1 20
A1-3 205.5 0.191 405.2 0.184 386.1 0.391 391.8 0. 38 1 .6 1 20
D1-1 213.7 0.195 401.0 0.333 389.0 0.384 392.1 0 38 1 .1 1 50
D1-2 218.7 0.188 403.9 0.261 384.8 0.379 388.5 0.374 37 1 .1 1 50
F1-1 204.3 0.165 390.4 0.270 381.1 0.399 385.4 0.392 37 1 .2 1 50
F1-2 203.8 0.165 387.9 0.347 376.2 0.386 379.6 0.381 37 1 .3 1 50
B1-2 204.6 0.158 397.1 0.221 387.7 0.389 391.7 0.383 37 1 .7 1 50
C1-1 199.3 0.175 395.2 0.253 384.2 0.394 388.6 0.388 37 0 .6 1 50
C1-2 187.0 0.170 393.1 0.253 379.6 0.398 381.5 0.394 37 0 .9 1 50
E1-1 204.8 0.174 394.4 0.210 379.5 0.395 382.1 0.388 36 0 .1 1 50
E1-2 185.5 0.175 391.3 0.251 381.3 0.395 380.2 0.391 37 0 .8 1 50
Mean 203.0 0.177 396.8 0.310 383.4 0.391 386.9 0.386 37 1 .9 1
Standard Deviation 9.8 0.012 6.3 0.179 4.1 0.006 5.3 0.006 6 0 .2
Range 33.2 0.037 17.9 0.647 12.7 0.020 14.6 0.020 1 0 .7
Minimum 185.5 0.158 387.9 0.184 376.2 0.379 379.6 0.374 36 0 .6 1
Maximum 218.7 0.195 405.8 0.832 389.0 0.399 394.2 0.394 38 1 .3 1
Count 11 11 11 11 11 11 11 11 1
Tension Tests (LT direction:  longitudinal ax a  d on of g)
Tension Tests (L direction:  lon al  th ct o
Statistics
tr rd T  S hi
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Web
Location Mill Cert  P ie
E
m)
3.2
3.2
.8
.8
.8
.8
.8
.8
.8
.8
.8
 
 
Table A-1:  Summary of Plate 1 T o t lt
 
ensi n Tes Resu s 
Plate Section Steel Nominal Nominal Mill Certificate Properties
Number Mark Type Strength Thickness F
y
F
u
Elongation
(MPa) (mm) (MPa) (MPa) (%)
2 B (G2) A852 485 12.700 614 722 26
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
A2-1 196.5 0.519 669.1 0.515 661.9 0.519 0.519 4.859 6.556 765.4 203.2
A2-2 202.1 0.532 675.4 0.529 668.3 0.532 0.532 3.971 6.541 765.3 203.2
F2-1 205.2 0.540 700.4 0.533 686.1 0.540 0.540 1.653 6.065 774.2 50.8
F2-2 208.8 0.518 662.7 0.509 644.4 0.518 0.518 3.235 6.815 755.1 50.8
B2-1 202.4 0.536 684.8 0.529 670.3 0.521 0.690 1.579 8.234 768.3 50.8
B2-2 205.3 0.520 699.4 0.513 685.5 0.424 0.597 1.275 7.929 778.0 50.8
E2-1 193.4 0.559 697.2 0.551 681.7 0.769 0.781 1.232 8.033 772.7 50.8
E2-2 207.3 0.537 705.6 0.527 683.9 0.552 0.688 1.314 7.487 780.6 50.8
Mean 202.6 0.533 686.8 0.526 672.8 0.547 0.608 2.390 7.21 770.0
Standard Deviation 5.3 0.014 16.2 0.013 14.6 0.098 0.100 1.427 0.82 8.2
Range 15.4 0.041 42.9 0.042 41.7 0.345 0.263 3.627 2.17 25.5
Minimum 193.4 0.518 662.7 0.509 644.4 0.424 0.518 1.232 6.06 755.1
Maximum 208.8 0.559 705.6 0.551 686.1 0.769 0.781 4.859 8.23 780.6
Count 888888888
Tension Tests (LT direction:  longitudinal axis normal to the direction of rolling)
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Web
Locatio
Specimen ID
0.2% Offset Yield
n
 
 
Table A-2:  Summary of Plate 2 Tension Test Results 
 
   
   
Plate Section
er Ma
C (G
Young' Mod.
E (G a)
? (
Stee No omin Mill
Type Stre th T ickne s
y
(M ) (mm) Pa)
A852 48 12.700 535
l minal N al  Certific ro e
Numb rk ng h s F F E at
Pa (M MP
3 2) 5 67
s G  Le
P
%
ate P perti s
u
long ion
( a) (%)
2 36
age ngth
) ? (MPa) ? (%) ? (M a)P
?
st
 (%) ?
ap rent
 (%
pa
) (GE
st 
Pa)
? (%) ? ( Pa)
4.28
3.82
10 54 3.61
4.92
10 96 3.36
4.72
10 91 2.81
3.26
4.58
4.06
4.31
3.08
3.90
0.68 2 .7
2.11 6 .7
2.81
10 54 4.92
12
 the ti  rol
direct n of r ling)
ng Tensi Stre gth
M
mm)
A3- .6 6 7 4 3. 0 7.938 5 855.6 203.2
A3- .6 8 7 7 2. 0 8.058 3 883.5 203.2
D3-1 .6 7 7 8 3. 0 .7 8 849.3 203.2
D3-2 .3 9 7 8 4. 0 7.279 5 891.0 203.2
F3-1 .9 7 7 4 3. 0 .2 0 849.1 203.2
F3-2 .4 4 7 4 0. 0 7.300 4 845.3 203.2
B3-1 .2 6 7 1 9. 0 .4 2 847.3 203.2
B3-2 .6 5 7 6 7. 0 9.602 7 857.5 203.2
C3-1 .5 7 7 1 9. 0 8.225 8 877.0 203.2
C3-2 .9 93 7 6 7. 0 7.507 0 870.8 203.2
E3-1 .8 60 7 3 0. 0 7.915 3 821.3 203.2
E3-2 .9 66 7 8 7. 0 9.497 5 831.4 3
Mean .0 71 7 2. 0 8.739 5 856.6
Standard Deviatio 4 16 2 6 .7 0 1.302 6 0
Range 0 53 8 5 .2 0 3.475 3 9
Minimum .6 42 7 0. 0 7.279 2 821.3
Maximum .6 95 7 4. 0 .7 5 891.0
Count 2 2 12 12
si s  d on gi al nor to direc on of ling)
T s ( c  lo di is e io ol
sti
S  H ni le nStatic Y ld
Web
Location
Specim
 t 
(
20 .2
1 206 0.5
2 202 0.5
198 0.5
201 0.5
199 0.5
202 0.5
204 0.5
202 0.5
204 0.5
202 0.5
198 0.5
199 0.5
202 0.5
n 2. 0.0
8. 0.0
198 0.5
206 0.5
12 1
en ID
0.2%
6
9
3
5
1
2
8
4
9
Ten
Offse
58.8 0.55 73 4 0.566 .566
96.0 0.57 77 1 0.589 .589
43.8 0.56 73 9 0.573 .573
98.3 0.58 78 6 0.595 .595
47.8 0.56 73 3 0.571 .571
36.9 0.53 72 6 0.542 .542
54.1 0.56 73 7 0.568 .568
64.3 0.54 74 4 0.554 .554
76.0 0.57 75 9 0.579 .579
80.7 0.58 76 6 0.593 .593
15.2 0.55 70 3 0.560 .560
33.5 0.55 71 4 0.566 .566
58.8 0.563 74 5 0.571 .571
5.5 0.01 24 0.016 .016
3.2 0.05 84 0.053 .053
15.2 0.534 70 3 0.542 .542
98.3 0.588 78 6 0.595 .595
12 12 1 12 12
on Te ts (LT irecti :  lon tudin axis mal 
ension Test L dire tion: ngitu nal ax  in th
Stati cs
train ardeieYield
 
 
l  T o t ltResu s Table A-3:  Summary of P ate 3 ensi n Tes
   
Plate Section Steel Nom
Stre
(M )
48
inal N al  C ic ropertie
Number Mark Type ngth Th s F E at
Pa (M MP
4 D (G2) 5 72
Young's Mod. G  Le
E (GPa)
?
ngth
omin Mill ertif ate P
ickne s F
y u
(mm) Pa) ( a)
12.700 614 2
s
long ion
(%)
26
age
A852
(%) ? (MPa) ? (%) ? (M a)P
?
st
 (%) ?
ap rent
 (% E
st 
Pa)
pa
) (G
? (%) ? ( Pa)
(m
5.72 20
5.87 20
6.41 20
6.94 20
5.84 20
6.87 20
6.65 20
6.92 20
5.44 20
7.29 20
7.08 20
7.02 20
6.50
0.62 1 .6
1.84 7 .7
5.44
7.29
12
f rol
ling)
Tensi Stre gth
M
m
A4-1 205.5 0. 6 4 6. 0.521 0 4.946 1 770.3 3
A4-2 198.2 0. 6 6 5. 0.543 0 3.915 2 768.7 3
D4-1 197.4 0. 6 7 1. 0.554 0 3.589 3 771.1 3
D4-2 193.0 0. 6 3 3. 0.570 0 2.719 0 765.4 3
F4-1 200.7 0. 6 9 3. 0.535 0 3.737 7 762.0 3
F4-2 201.4 0. 6 9 4. 0.542 0 3.955 3 778.3 3
B4-1 198.7 0. 6 8 3. 0.535 0 2.624 9 781.0 3
B4-2 200.8 0. 7 7 5. 0.543 0 2.033 4 786.5 3
C4-1 202.3 0. 6 2 3. 0.511 0 4.878 9 724.4 3
C4-2 194.3 0.535 6 0 2. 0.535 0 4.075 0 751.1 3
E4-1 200.9 0.549 6 2 6. 0.549 0 2.660 7 781.7 3.2
E4-2 202.0 0.556 7 0 4. 0.556 0 2.434 4 796.1 3.2
Mean 199.6 0.541 6 0. 0.541 0 3.464 8 769.7
Standard Deviation 3.5 0.016 2 6 .4 0.016 0 0.959 7 8
Range 12.5 0.058 8 0 .0 0.058 0 2.914 1 1
Minimum 193.0 0.511 6 3. 0.511 0 2.033 9 724.4
Maximum 205.5 0.570 7 4. 0.570 0 4.946 0 796.1
Count 12 12 2 12 12 12
eb
Location
Specimen ID
0.2 fset 
ensi s  d on gitudinal nor to direc  o ling)
T s ( c  longitudi is  the di io ol
Statisti
S  H ni le nati ld
)
.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
.521
.543
.554
.570
.535
.542
.535
.543
.511
.535
.549
.556
.541
.016
.058
.511
.570
12
axis mal  the tion
nal ax  in rect n of r
cs
train arde ng
521
543
554
570
535
542
535
543
511
W
% Of
T
81.7 0.51
79.7 0.53
84.0 0.54
77.5 0.56
75.3 0.52
92.3 0.53
98.9 0.52
07.6 0.53
32.4 0.50
51.9 0.53
99.5 0.54
15.9 0.55
83.1 0.535
3.2 0.01
3.6 0.06
32.4 0.502
15.9 0.563
12 12
Yield
on Te ts (LT
ension Test
St
66 9
66 3
67 0
66 9
66 5
68 6
68 7
69 4
61 8
64 9
68 4
70 8
67 2
24
91
61 8
70 8
1
irecti :  lon
L dire tion: 
c Yie
 
 
late 4 T o t lt
 
ensi n Tes Resu s  of PTable A-4:  Summary
   
Plate ection
ber Mark
E (G3) A
Yo ng's M d.
 (GPa
? ) ? ( Pa)
S Ste m No
Num Ty Strengt F
u
()() Pa Pa
5 5 34 1
u o  L
E )
 (% M
el No inal minal
pe h Thickness F
y
MPa m (M)(M
72 5 2.700 409 541
)
Gage ength
? (%) ? ( Pa)M ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 ?
ap
%) G(%)
parent
 ( E
st 
( Pa)
? (%) ? (MPa
m)
2.26 537.2 2 .2
2.06 536.0 2 .2
5.97 528.1 .8
6.27 529.3 .8
5.69 529.6 .8
5.19 530.3 .8
5.44 527.8 .8
5.34 533.8 .8
5.64 532.2 .8
5.42 529.6 .8
5.64 527.9 .8
4.99 531.1
.43 3.3
.20 9.5
527.8
537.2
11
nsile S rength
)
(m
A5 20 408.0 .8 95 0 8 1 26 1 03
A5 20 417.3 .6 96 0 5 1 16 1 03
D5- 18 403.7 .2 84 0 4 1 04 1 50
D5-2 17 402.2 .3 85 0 1 1 27 1 50
F5-2 17 399.4 .2 84 0 4 0 33 1 50
B5-1 17 395.2 .2 86 0 7 0 29 1 50
B5-2 17 395.7 .2 81 0 0 372.3 1 50 1 50
C5-1 18 409.8 .2 91 0 4 379.3 1 09 1 50
C5-2 18 411.5 .0 91 0 7 381.0 1 93 1 50
E5-1 16 399.9 .2 89 0 0 374.9 1 15 1 50
E5-2 17 401.0 .2 86 0 5 377.6 1 59 1 50
Mean 18 404.0 .4 88 0 3 379.5 1.067 33 1
Standard Deviatio 01 6.9 .2 4.7 0 8 7.9 0.082 29 1
Range 04 2. .8 14 0 4 22.8 0.295 10 4
Minimum 16 395.2 .2 81 0 4 372.3 0.953 93 12.06
Maximum 20 417.3 .0 96 0 8 395.1 1.248 04 16.27
Count 11 11 11 11 11 11 11 11
nsio ts rec lo nal ormal di  o g)
T n T L d n: udi is in th cti oll
istics
ra de Te ttic
Spec
Up el L er Yield 0.
42
ill Certificate Properties
Elongatio
(%)
-1 199.9 0. 0 0
-2 202.4 0. 7 0
1 215.0 0. 5 0
205.6 0. 2 0
203.3 0. 4 0
199.9 0. 0 0
208.0 0. 4 0
204.5 0. 2 0
213.9 0. 7 1
208.1 0. 7 0
203.5 0. 6 0
205.8 0. 1 0
n 5.0 0. 3 0
15.1 0. 0 2 1 0
199.9 0. 7 0
215.0 0. 7 1
11
imen ID
per Yi d
Web
Location
47 3 .6 .400 398.8 0.39
53 3 .2 .397 398.5 0.39
47 3 .5 .379 385.1 0.37
40 3 .0 .387 388.5 0.38
99 3 .6 .391 389.6 0.38
99 3 .8 .393 389.2 0.38
66 3 .7 .386 383.3 0.38
66 3 .2 .390 393.1 0.38
37 3 .8 .383 394.6 0.37
80 3 .7 .387 390.8 0.38
31 3 .8 .381 389.9 0.37
33 3 .5 .389 391.0 0.38
80 .007 4.9 0.00
06 .5 .021 15.5 0.02
31 3 .7 .379 383.3 0.37
37 3 .2 .400 398.8 0.39
11 11 11
Te n Tes  (LT di tion:  ngitudi
ensio ests ( irectio  longit
Stat
Staow 2% Offset Yield
M
395.1
394.2
373.9
375.0
375.0
376.7
 axis n
nal ax
 Yield
.092 1.343 3. 1
.081 1.363 3. 8
.248 1.446 4. 0
.050 1.372 3. 6
.953 1.299 3. 0
.971 1.289 3. 5
.034 1.273 3. 3
.131 1.470 3. 5
.038 1.427 2. 8
.017 1.458 3. 0
.123 1.343 3. 4
1.371 3. 2
0.070 0. 7
0.197 1. 2
1.273 2. 8
1.470 4. 0
11
 to the rection f rollin
e dire on of r ing)
St in Har ning
n
 
 
atTable A-5:  Summary of Pl e 5 Tension Test lt
 
Resu s 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)
7
(MPa)(m)(MPa)
G (G3) A572 345 12.700 432 55
Young's Mod. e h
E (GPa)
? (%) ? (MPa)
6
Gag Lengt
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
?  (%
 
(G (%)
apparent
) E
st
Pa)
? (%) ? (MP
m)
6.78 539.9 .8
6.29 535.8 .8
6.06 543.1 .8
5.53 545.1 .8
6.02 532.7 .8
5.87 533.9 .8
5.51 540.5 .8
6.17 536.8 .8
5.34 541.6 .8
6.03 530.3 .8
7.07 531.0 .8
6.45 529.2 .8
6.09 536.7
0.51 5.3
1.73 15.9
5.34 529.2
7.07 545.1
12 12
ensile trengt
a)
(m
193.0 0.188 0.453 1.6 39 0. 38 1 .6 1 50
194.5 0.183 0.304 9.2 39 0. 37 1 .0 1 50
195.4 0.169 0.300 4.8 38 0. 37 0 .4 1 50
213.5 0.182 0.268 6.1 3 0. 37 0 .6 1 50
219.0 0.173 0.283 1.0 401.4 0. 39 1 .6 1 50
204.2 0.203 0.278 397.5 402.5 0. 38 1 .8 1 50
2 39 0. 38 1 .5 1 50
1 38 0. 37 1 .9 1 50
2 38 0. 37 0 .4 1 50
2 37 0. 36 0 .5 1 50
2 398.5 0. 38 1 .8 1 50
1 395.6 0. 38 1 .0 1 50
2 0.1 89. 392.6 0. 38 1 .3 1
a iation 0. 6.9 7.4 0. 8 0 .3
R 26.1 0.034 0.23 24.0 22.7 0. 2 0 .2
Mi 193.0 0.169 0.21 77.0 379.8 0. 36 0 .6 1
Ma m 219.0 0.203 0.45 01.0 402.5 0. 39 1 .9 1
C 12 12 12 12 12 1 1
Web
Location Mill Cert  P ie
E
e  ID
Upper Yield Lower Yield 0.2% Offset Yield
ction git  ax a  d on of g)
Tension  (L dire on al  th ct o
cs
tr rd T  S hi
A6-1
A6-2
D6-1
D6-2
F6-1
F6-2
B6-1
B6-2
C6-1
C6-2
E6-1
E6-2
Mean
Stand rd Dev
ange
nimum
ximu
ount
Sp cimen
404.8
401.1
393.2
398.6
407.6
414.4
39
38
38
38
40
0.404
0.404
0.383
0.364
0.374
0.399
 Tests
7.0
1.3
6.9
86.3
ction:  l
397 3.6 .452 1.768 3 37
398 9.6 .185 1.728 3 09
376 2.5 .908 1.304 3 68
357 2.8 .897 1.173 3 47
369 1.4 .417 2.058 2 59
393 9.8 .621 2.018 2 81
388 7.6 .254 1.262 3 94
384 1.6 .386 1.538 3 07
371 8.1 .936 1.299 3 79
372 3.9 .997 1.313 3 05
391 6.4 .545 1.960 2 81
389 3.4 .581 2.062 3 98
382 0.1 .265 1.624 3 14
013 .5 .274 0.347 0 90
040 7.5 .724 0.888 1 48
357 3.9 .897 1.173 2 59
398 1.4 .621 2.062 3 07
2 12 12 12 2
25
ificate ropert s
longation
(%)
udinal is norm l to the irecti  rollin
gitudin  axis in e dire ion of r lling)
Statisti
S ain Ha eningStatic Y eld
05.7
95.6
08.4
05.8
00.1
97.1
02.7
8.2
0.17
0.17
0.18
0.17
0.19
0.17
8
6
9
6
3
6
82
010
408.
393.
401.
387.
414.
410.
402.9
8.8
27.6
387.3
414.9
12
3 0
0 0
2 0
3 0
9 0
2 0
.219
.303
.285
.252
.344
.251
0.295
0.05
3
3
3
3
3
3
3
9
4
9 3
3 4
Ten
93.1
79.4
87.9
77.0
93.6
91.1
sion 
0.39
0.39
0.37
0.38
0.39
0.39
0.388
0.013
0.041
0.364
0.404
12
s (LT
3
0
7
0
7
5
 dire
8.8
4.1
8.9
9.8
:  lon
4
Test
 
 
Table A-6:  Summary of Pl  T o t lt
 
ate 6 ensi n Tes Resu s 
   
Plate
Numbe
7
Section
3)
 Mod.
a)
? (%)
Steel omin Nom
Type Strengt Thick
(MP)(m)(
A572 345 12.7 0
N al inal
r Mark h ness F
y
F
a MPa)(
F (G 0 409 54
's e h
GP
? )
u
MPa)
1
Young
E (
Gag Lengt
 (MPa ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 ?
ap
%) G(%)
parent
 ( E
st 
( Pa) ? (%) ? (MP m)
530.8 .8
.8
.8
.8
.8
.8
.8
.8
8
rengt
a)
(m
200.1 86 89 .3 37 0 76 1 50
193.3 395.2 97 86 .39 37 1 89 1 530.0 50
4. 76 91 .371 38 1 67 1 528.7 50
1. 32 87 .426 37 1 17 1 525.0 50
1. 09 86 .404 37 1 76 1 527.2 50
6. 93 81 .386 36 1 54 1 525.6 50
7. 0.324 89 93 .383 37 1 51 1 529.7 50
9. 0.243 14 89 .409 37 0 96 1 529.8 50
0. 0.495 00 88 .394 37 1 53 15.91 528.3
andar vi 7.6 0.356 18 3.6 .018 4 0 31 0.51 2.2
3.4 0.849 56 12 .055 12 0.2 93 1.81 5.9
M m 191.0 0.219 76 .371 36 0 96 14.87 525.0
M m 214.4 402.1 1.068 32 93.5 0.426 38 1 89 16.68 530.8
t 8 88 8
Web
Location Mill Cert Pr es
E
Sp
er er  O Yi
T T T on tudinal axi al di  o g)
sio sts ct n al  th cti oll
Statistics
ra de T  St hie
A7-1
A7-2
F7-1
F7-2
B7-1
B7-2
E7-1
E7-2
Mean
St d De ation
Range
inimu
aximu
Coun
ecimen ID
0.200
0.173
4 0.161
0 0.184
6 0.173
7 0.174
3 0.168
1 0.177
4 0.176
0.012
0.039
0.161
0.200
88
Upp
396.7
402.1
399.0
394.8
390.1
399.9
397.6
396.9
3.7
12.0
390.1
Yield
1.057 376.7 0.3 3
1.068 384.5 0.3 3
0.219 387.1 0.3 3
0.278 382.7 0.4 3
0.350 383.4 0.4 3
0.420 381.4 0.3 3
388.5 0.3 3
387.6 0.4 3
384.0 0.4 3
3.9 0.0
11.7 0.0
376.7 0.3 3
388.5 0.4 3
888
Low  Yield 0.2% ffset 
ension ests (L directi
Ten n Te  (L dire
.3 0
.4 0
.1 0
.4 0
.9 0
.5 0
.5 0
.0 0
.1 0
0
.0 0
81.5 0
eld
:  longi
ion:  lo
78 2.7 .969 1.057 3. 7
2 7.7 .001 1.155 3. 5
0.0 .185 1.307 3. 3
4.8 .014 1.413 3. 4
6.1 .003 1.219 3. 3
8.0 .119 1.266 3. 2
9.3 .184 1.407 3. 4
9.3 .917 1.444 2. 5
6.0 .049 1.284 3. 6
.1 .101 0.136 0. 8
.0 68 0.387 0. 0
8.0 .917 1.057 2. 5
0.0 .185 1.444 3. 5
888
42
ificate operti
longation
(%)
s norm  to the rection f rollin
gitudin axis in e dire on of r ing)
St in Har ningStatic Y ld
5.79
6.68
6.09
5.98
4.87
6.04
6.09
5.75
ensile
21
19
20
19
20
19
20
2
 
 
 of Plate 7 T n  lt
 
ensio  Test Resu s Table A-7:  Summary
   
P te ection
Nu ber Mark
B1, B7
Yo ng's M d.
 (GPa
? ) ? (
la S Steel Nominal Nominal
m Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
8 A572 345 7.938 434 554
u o e h
E )
 (% MPa)
Gag Lengt
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
ap
%) G
parent
 ( E
st 
( Pa)
? (%) ? (MP
600.6
592.4
591.9
595.5
588.7
591.0
587.7
594.1
588.2
592.2
4.1
12.9
rength
a)
(m
A8 35 65.9 0.496 445.2 0.472 454.2 0.461 436.1 3 73 1 50
A8 22 73.2 0.320 459.6 0.463 461.8 0.459 452.7 6 94 1 50
D8- 48 70.9 1.687 454.0 0.486 470.9 0.471 446.3 8 15 1 20
D8- 29 69.8 1.406 455.7 0.446 459.3 0.439 445.5 6 10 1 50
D8- 25 64.2 1.403 453.1 0.424 459.2 0.418 448.1 3 64 1 50
B8- 22 74.7 0.271 454.6 0.441 459.7 0.435 448.2 0 29 1 50
B8- 21 81.2 0.265 463.5 0.425 466.9 0.418 453.8 3 74 1 50
C8- 24 59.2 0.333 443.0 0.420 449.2 0.412 433.4 4 49 1 50
C8- 21 78.1 0.296 458.1 0.437 459.5 0.430 444.3 2.522 86 1 50
e .3 70.8 0.7 454.1 0.446 460.1 0.438 445.4 1.978 2.362 11 1
St d io .1 6.9 0.6 6.5 0.023 6.3 0.021 6.8 0.188 0.329 32 0
a .3 22.0 1.4 20.5 0.066 21.7 0.058 20.3 0.547 1.029 91 2
ni .2 59.2 0.3 443.0 0.420 449.2 0.412 433.4 1.683 1.678 73 1 587.7
xi .5 81.2 1.7 463.5 0.486 470.9 0.471 453.8 2.230 2.707 64 1 600.6
o 99999999 99
Up eld Lower Yield 0.2% Offset Yield
Tension Tests (LT direction:  longitudinal axis nor  the di n of g)
Tension Tests (L direction:  longitudinal axis i irecti oll
Statistics
Stra de Te tStatic Yield
Location Mill Certificate Properties
Elongation
(%)
27
m)
.8
.8
3.2
.8
.8
.8
.8
.8
.8
-1 169.2 0. 8 4
-2 187.6 0. 4 4
1 164.0 0. 6 4
2 187.0 0. 9 4
3 203.5 0. 5 4
1 189.6 0. 1 4
2 206.7 0. 5 4
1 204.0 0. 7 4
2 210.3 0. 5 4
M an 191.3 0 4
andar Deviat n 16.5 0
R nge 46.3 0
Mi mum 164.0 0 4
Ma mum 210.3 0 4
C unt 99
Specimen ID
per Yi
Web
1.68
2.14
2.03
1.88
1.98
2.23
2.12
1.71
2.001
mal to
n the d
1.678 2. 1 7.04
2.624 2. 2 7.85
2.330 3. 5 5.91
2.398 3. 5 5.69
2.164 3. 9 5.53
2.681 3. 6 6.99
2.707 2. 9 6.03
2.152 3. 9 6.46
2. 4 5.95
3. 0 6.38
0. 5 .77
0. 8 .32
2. 1 5.53
3. 9 7.85
9
rectio  rollin
on of r ing)
in Har ning nsile S
 
 
Table A-8:  Summary of Plate 8 Tension Test Result
 
s 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
a) (mm) (MPa)
9 B2 A572 345 9.525 414
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa)
F
u
(MPa)
535
(MP
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%)
t
 (%) Pa)?
apparen
E
st 
(G ? (%) ? (MPa)
552.4
545.5
427.2
2.4
(mm)
A9-1 203.5 0.203 430.4 0.412 414.6 0.405 14.6 405. .282 02 4 50.8
A9-2 201.4 0.220 423.9 1.159 410.2 0.424 12.1 400. .094 13 1 50.8
D9-1 198.0 0.180 406.5 0.766 0.400 97.8 384.  . . . 56 . 50.8
D9-2 200.7 0.180 413.1 0.270 0.407 03.0 393. .060 61 3 53 50.8
F9-1 190.0 0.192 405.3 0.350 0.406 397.8 0.401 389.5 .140 2.439 18.02 532.2 50.8
F9-2 200.2 0.201 412.7 0.593 0.419 400.0 0.412 387.6 2.158 2.184 3.420 17.20 529.7 50.8
B9-1 192.3 0.267 438.0 1.208 .171 564.7 50.8
B9-2 200.3 0.190 444.0 0.251 .177 566.4 50.8
C9-1 190.6 0.172 394.2 2.044 .023 516.4 50.8
C9-2 202.1 0.182 410.2 0.219 0. 97 .018 78 3 527.5 50.8
E9-1 199.9 0.187 415.6 0.457 0 03 .263 39 8 535.1 50.8
E9-2 204.5 0.191 405.8 1.978 0.392 397.0 385.4 .966 534.1 50.8
Mean 198.6 0.197 416.6 0.809 0. 405 .9 15 5 53
Standard Deviation 4.9 0.026 14.7 0.651 0. 13.9 .5 83 3 35
Range 14.5 0.095 49.8 1.824 0 48.1 .111 13
Minimum 190.0 0.172 394.2 0.219 0.392 382.9 0.386 370.5 0.171 1.978 2.673 3.13 427.2
Maximum 204.5 0.267 444.0 2.044 0.424 431.0 0.418 419.3 2.282 2.615 4.182 18.67 566.4
Count 12 12 12 12 12 12 12 12 11 12 11 12 12
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Te  T l to the
Tension Tests tion:  l dinal ax he dire of rollin
isti
Strain Hardening Tensile StrengthStatic Yield
Web 27
Location Mill C ate Properties
Elongation
(%)
4
4
3
4
 (L direc
0.400
0.418
0.393
0.402
ongitu
2 2
3 2
5
0 2
2
is in t
2.6
2.4
2.5
2.4
ction 
3.07
3.09
. . 
3.02
3.181
g)
16.31
16.20
3.13
17.84
0.423
0.412
0.400
394
.399
ests (LT di
4
4
3
3
4
recti
31.0 0
29.1 0
82.9 0
.5 0
.6 0
on:  long
.411
.407
.394
.389
.393
0.386
itudi
408.1
419.3
370.5
388.3
391.9
nal axis n
0
2
2
2
2
1
orma
2.3
2.3
2.6
2.4
2.5
1.978
 direc
26
92
15
tion of ro
4.1
3.5
2.9
2.67
3.03
2.925
lling
82 1
56 1
85 1
1
)
6.61
6.93
7.18
7.29
18.67
17.97
407
011
.032
.5 0
0
0
.401
.010
.032
Stat
393.6
12.8
48.7
cs
1
0
2
41
96
2.4
0.1
0.637
3.19
0.40
1.508
1
1
6.11
4.15
5.54
0.3
.8
9.1
ertific
392.2
400.6
394.7
396.2
417.0
424.6
377.7
396.1
403.8
382.1
400.8
14.0
46.9
377.7
424.6
12
nsion
 
 
Table A-9:  Summary  9 sion su
 
 of Plate  Ten Test Re lts 
   
Pl
Num
ate Section St
Mark Ty
(M
B3 A5 2 3
g's M .
? ( ) ? (M a)
eel Nominal Nominal
ber pe Strength Thickness F
y
F
Pa) (mm) (MPa)
10 7 45 9.525 414
un od Gage Length
E (GPa)
% P
u
(MPa)
535
Yo
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
0- 201.2 9 9. .320 2. 0.400 41 0.395 2.0 2 3. 16.16 55 50.8
0- 201.2 9 9. .320 2. 0.409 41 0.403 2.0 2 3. 17.07 56 50.8
0- 175.7 4 5. .331 3. 0.422 39 0.414 1.9 2 2. 17.38 53 50.8
0- 198.2 7 4. .230 7. 0.401 40 0.397 2.4 2 2. 17.90 53 50.8
0- 194.1 2 4. .728 4. 0.414 42 0.410 412.5 2 92 4.8 550.9 50.8
0- 201.7 8 1. .272 9. 0.420 40 0.414 398.1 2.164 2.695 2.937 15.83 53 50.8
0- 201.8 7 1. .295 6. 0.385 39 0.381 390 2.076 2.547 3.137 17.06 53 50.8
0- 204.3 8 2. .392 2. 0.393 39 0.386 2 18.69 52 50.8
ean 197.3 9 9. .736 1. 0.406 40 0.400 16.87 54
Sta  D n 9.2 2 .5 .837 1. 0.013 8 0.013 10.5 0.191 0.269 0.441 1.22 14
ng 28.7 7 .0 .162 2. 0.037 23 0.033 29.4 0.595 0.952 1.447 3.85 38.3
m 175.7 7 5. .230 2. 0.385 0.381 383.1 1.904 2.024 2.499 14.84 522.3
aximum 204.3 4 4. .392 4. 0.422 42 0.4 8.6
un 8 8
ecimen ID
Upp eld o eld .2% O  Yi
io ts (LT io itudina ormal of rollin
Te  Tests rec ongitudi is in tio lling)
Statis
Strain Hardening Tensile StrengS ield
L n Mill Cert erties
Elongat
A1 1
A1 2
F1 1
F1 2
B1 1
B1 2
E1 1
E1 2
M
ndard eviatio
Ra e
Mini um
M
Co t
Sp
0.1 5 42 8 0 41
0.1 5 42 8 0 41
0.2 8 40 5 0 39
0.1 7 41 9 0 39
0.2 9 43 5 1 41
0.1 9 42 0 0 39
0.1 6 41 1 0 39
0.1 4 41 2 2 38
0.1 9 41 8 0 40
0.0 6 10 0 1
0.0 2 29 2 3
0.1 6 40 5 0 38
0.2 8 43 5 2 41
88
er Yi L wer Yi
Tens
Web
ocatio
8
8
8
8
6
2
8
5
3
3
1
5
6
8
0
n Tes
nsion
5.7
5.0
8.3
4.6
1.3
9.6
9.5
8.3
7.8
.9
.1
.3
1.3
8
eld
n:  long
tion:  l
404.8
403.1
383.3
395.4
l axis n
nal ax
57
46
04
99
.312
to the
 the direc
.461
.480
.024
.976
ction 
n of ro
400
359
499
756
3.164
g)
8.6
0.6
0.6
3.2
2.4
 dire
1 4
7.8
0.8
2.3
0.6
.3
.3
1
.3
383.
396
tics
2.30
2.17
6
1
.392
2.509
3.9
3.1
46
49
398
14
8
412.5
8
2.499
8
2.976
8
3.946
8
1 9 560.6
8
ffset
 direct
 (L di
thtatic Y
ificate Prop
27
ion
(%)
 
 
Table A-10:  Summary
 
 of Plate 10 Tension Test Results 
   
Plate
ber
Y
Section Steel Nominal Nominal
Num Mark Type Strength Thickness F
y
F
u
(MPa) (mm) (MPa)
11 B4, B8 A572 345 7.938 434
oung's Mod. Gage 
E (GPa)
? (%) ? (MPa)
(MPa)
554
Length
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 
a
(% (G(%) ?
pparent
 ) E
st 
Pa) ? (%) ? (MP
3 31 3.54 579.5
2 08 5.61 585.9
2 09 7.09 592.9
2 23 7.26 593.2
2 66 7.73 585.5
2 89 6.06 587.5
2 21 6.79 588.8
2 28 8.13 564.5
2 32 6.35 583.6
2 01 6.51 584.6
0 69 1.37 8.7
0 42 4.59 28.8
2 89 3.54 564.5
3 31 8.13 593.2
9 9
of rolli )
ling)
ening ensile Strength
a)
(m
D1 176.1 0.439 462.2 1.458 445.1 0.461 454.3 439.0 1. .5 1 20
D1 172.5 0.348 464.5 1.126 448.9 0.467 461.1 441.0 2. .9 1 50
D1 181.2 0.352 469.7 0.450 454.3 0.506 460.0 447.9 2. .8 1 50
F1 176.7 0.370 474.9 0.524 457.7 0.462 463.3 447.8 1. .9 1 50
F1 182.1 0.343 468.3 0.446 454.0 0.451 455.2 449.8 2. .8 1 50
C1 200.8 0.201 475.2 0.287 455.6 0.429 459.1 0.423 447.3 2. .5 1 50
C1 197.1 0.206 477.6 0.275 463.2 0.434 467.9 0.426 453.0 2. .9 1 50
E1 187.0 0.219 461.2 0.348 442.8 0.425 442.7 0.420 434.0 2. .6 1 50
E1 193.0 0.208 475.1 0.249 455.0 0.434 456.9 0.429 446.8 2. .9 1 50
Me 185.2 0.299 469.9 0.574 452.9 0.452 457.8 0.445 445.2 2. .9 1
Standard tio 9.9 0.090 6.2 0.426 6.4 0.026 7.0 0.025 6.0 0. .2
Ra 28.3 0.238 16.4 1.209 20.4 0.081 25.2 0.079 19.0 0. .9
Mini 172.5 0.201 461.2 0.249 442.8 0.425 442.7 0.420 434.0 1. .5 1
Maxi 200.8 0.439 477.6 1.458 463.2 0.506 467.9 0.499 453.0 2. .5 1
Cou 9 9999 9 999 9
Sp
Upper Yield Lower Yield 0.2% Offset Yield
Tension Tests (LT direction:  l  axis norma n ng
Tension Tests (L direction:  l dinal ti ol
Statistics
d Tic Yie
Web
Location Mill Certificate Pr es
El ion
m)
3.2
.8
.8
.8
.8
.8
.8
.8
.8
1-1
1-2
1-3
1-1
1-2
1-1
1-2
1-1
1-2
an
Devia n
nge
mum
mum
nt
ecimen ID
0.453
0.455
0.499
0.454
0.448
ongitudinal
ongitu
Stat
945
124
111
990
069
083
334
525
459
182
206
580
945
525
9
l to the d
axis in the direc
Stld
27
operti
ongat
(%)
2.091
2.636
2.680
2.439
2.619
2.903
2.738
2.936
2.784
2.647
0.258
0.845
2.091
2.936
irectio
on of r
rain Har
 
 
Table A-11:  Summary of Plate 11 Tensio st u
 
lts  Resn Te
   
Plate
umb
12
Young
E (
Section Steel Nominal Nominal
N er Mark Type Strength Thickness
(MPa) (mm) ( (
B5 A572 345 7.938
's .  L
G
? (%) ? (MPa)
F
y
F
u
MPa) MPa)
434 554
 Mod
Pa)
Gage ength
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
?
appar
E
st 
(GPa) (%)
ent
 (%) ? (%) ? (MPa
6.12 579.4
592.6 2
583.4
589.9
582.2
582.2
589.3
585.6
4.9
13.2
579.4
592.6
ensile S ength
)
(m
5 461.4 0.342 444.2 0.449 2. 2. 3.135 1 50
8 466.6 0.788 452.2 0.462 2. 2. 3.045 14.48 0
6 458.5 0.699 443.0 0.440 2. 2. 3.533 14.34 50
84 464.5 0.564 454.2 2. 2. 3.142 14.79 50
0. 464.9 0.430 451.3 2. 2. 2. 15.96 50.8
1.7 469.3 0.747 447.8 1. 2. 2. 14.36 50.8
3.8 474.7 0.261 458.1 2. 2. 2. 16.12 50.8
7.4 465.7 0.547 450.1 2. 2. 3. 15.17
St i 7.6 5.3 0.208 5.4 0. 0. 0. 0.86
e 2.1 16.3 0.527 15.1 0. 0. 0. 1.78
M m 8.8 458.5 0.261 443.0 1. 2. 2. 14.34
M um 0.9 474.7 0.788 458.1 466.6 2. 2. 3. 16.12
t 7 7777 7 777 7 7
Sp
Upper Yield Lower Yield 0.2% Offset 
Tension Test  direct  orma irec f rollin
Tension Tests (L dir   l  in tion ng)
isti
Strain ening T trc 
Web 27
Location Ce te Properties
Elongation
(%)
m)
.8
3.2
.8
.8
A12-2 18
D12-1 17
D12-2 18
D12-3 1
B12-2 20
C12-1 18
C12-2 19
Mean 18
andard Dev ation
Rang 2
inimu 17
axim 20
Coun
ecimen ID
.6
.8
.6
.3
9
0.287
0.469
0.318
0.283
0.207
0.333
0.215
0.302
0.088
0.262
0.207
0.469
445.2 0.445 436.4
466.6 0.447 440.6
449.5 0.431 432.9
454.1 0.466 437.8
452.1 0.420 443.5
460.5 0.440 437.6
461.3 0.428 448.2
455.6 0.439 439.6
7.5 0.015 5.1
21.4 0.046 15.3
445.2 0.420 432.9
0.466 448.2
Yield
ion:  longitudinal axis n
ection: ongitudinal axis
Stat cs
Stati Yield
Mill rtifica
029
183
239
067
077
974
056
089
091
266
974
239
7
l to the d
 the direc
452
308
339
431
525
569
701
475
136
393
308
701
tion o
 of rolli
Hard
0.475
0.425
0.452
0.434
0.448
0.017
0.050
0.425
0.475
s (LT
873
834
787
050
257
745
787
533
7
g)
 
 
Table A-12:  Summary of Plate 12 Tension Test Results 
 
   
Plate Section
ark
B6
? (% (MPa)
Steel Nominal N l
Number M Type Strength Th ss F
y
F
u
(MPa) a) (MPa)
13 A572 345 4 554
Young's Mod. Gage Le
E (GPa)
) ? 
ngth
omina
ickne
(mm) (MP
7.938 43
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 ( ?
appar t
 (%)
st 
(GP%)
en
E a)
? (%) ? (MP
588.5
591.5
586.5
580.2
580.0
590.8
588.9
570.2
584.6
7.3
21.2
570.2
591.5
trength
a)
(mm
D13-1 171.8 9 4 1.055 .3 0.453 436.8 5 2.250 76 203.2
D13-2 185.9 9 4 0.901 .8 0.437 440.6 5 2.320 61 50.8
D13-3 172.6 1 4 0.305 .1 0.452 434.8 7 2.138 39 50.8
F13-1 179.7 7 4 0.446 .5 0.430 432.1 1 2.541 99 50.8
F13-2 190.7 9 4 0.423 .9 0 438.6 9 2.628 89 50.8
C13-1 200.7 7 4 0.295 .1 5 450.8 0 2.590 75 50.8
C13-2 190.0 5 4 0.428 .7 5 449.2 8 2.553 60 50.8
E13-2 193.7 7 4 0.295 .1 4 434.5 0 2.590 75 50.8
Mean 185.6 3 4 0.519 8 5 439.7 4 2.451 72
Standard Deviation 10.2 8 0.294 2 6.9 3 0.187 0
Range 28.8 4 0.761 9 3 18.7 2 0.490 3
Minimum 171.8 5 0.295 .5 0 432.1 7 2.138 76
Maximum 200.7 9 480.5 1.055 .3 3 450.8 9 2.628 89
Count 8 8 88 8 888 8 8
Specimen ID
per Y Lower Yield 0 ffs ld
T  Test  direc   l  axis no ct o
nsion (L ion:  longitudinal axis  the direc  o g)
atistics
rain Har in sile SStatic Yield
Web 2
ocation Mill Cert e
ng
(%
)
2.10 3.381 15.
1.82 3.182 16.
1.81 3.214 16.
1.94 2.858 16.
2.23 2.980 17.
2.17 2.806 16.
2.08 2.833 16.
2.17 2.708 16.
2.04 2.995 16.
0.16 0.238 0.6
0.42 0.673 2.1
1.81 2.708 15.
2.23 3.381 17.
8 8
rmal to the dire ion of r lling)
 in tion f rollin
St den g Ten
7
ificate Prop rties
Elo ation
)
0.48 62.8
0.43 62.7
0.44 61.6
0.30 58.6
0.29 60.9
0.23 80.5
0.21 79.8
0.23 63.8
0.33 66.3
0.10 8.7
0.27 21.9
0.21 458.6
0.48
8
Up ield
L
447.9
452.9
442.0
441.3
449.8
460.3
459.7
444.2
449.8
7.4
19.0
441.3
460.3
ension
Te
0.468 462
0.448 460
0.468 461
0.436 442
0.426 448
0.429 459
0.441 460
0.429 443
0.443 454.
0.017 8.5
0.042 19.
0.426 442
0.468 462
.2% O et Yie
s (LT tion:
Tests  direct
0.42
0.42
0.43
0.42
0.43
0.01
0.03
0.42
0.45
ongitudinal
St
 
Tab -13:  of e 13 Ten  T Re  
 
sion est sults
 
Plat  Summaryle A
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
14 1) A572 345 26.988 430 583
Yo Mod. g th
a)
? (%  (MPa)
Ga e Leng
A (G
ung's 
E (GP
) ? ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (% ?
appar
)
en
E
st 
(GPa)
t
 (%) ? (%) ? (M
9.7 63
10.0 63
12.4 61
12.0 62
13.0 58
12.9 58
11.7 61
1.4 24
3.2 56
9.7 58
13.0 63
6
Tens  Stren
Pa
(
A 2 . . . . . . . . . . . . 0.405 440.1 . . . 4 10.030 7 9.7
A 5 . . . . . . . . . . . . 0.405 434.4 . . . 0.405 4 10.395 8 4.6
8 0.252 436.6 0.349 432.9 0.414 435.6 . . . 0.435 5 4.981 3 4.2
B14-2 4 0.322 431.4 0.393 428.1 0.384 429.9 . . . 0.384 3 7.456 6 2.6
C14-1 1 0.197 423.5 0.601 412.2 0.405 419.0 0.397 5 0.553 6 4.751 5 3.7
C14-2 6 0.199 424.8 0.663 412.7 0.397 418.8 . . . 0.558 6 4.567 0 3.5
Mean 8 0.242 429.1 0.501 421.4 0.402 429.6 0.397 5 0.456 5 7.030 1 3.1
rd Deviat 0.059 6.1 0.154 10.6 0.010 8.9 . . . 0.078 119 2.682 4 .5
Range 0.124 13.0 0.314 20.7 0.031 21 . . . 0.174 279 5.827 9 .2
inimum 4 0.197 423.5 0.349 412.2 0.384 41 0.397 5 0.384 384 4.567 7 3.5
aximum 2 0.322 436.6 0.663 432.9 0.414 44 0.397 5 0.558 663 10.395 5 9.7
Count 6444466 1 6
Both Flanges 1
Location Mill Certificate Prope
Elong
(%
ec
Upper Yield Low 0.2% Offset Yield
Tension Tests (L direction:  longitud is i dir  of g)
Statis
ile gtStatic Yield
)
mm)
50.8
50.8
50.8
50.8
50.8
50.8
h
0.405 0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
6
6
rties
ation
)
n the ection
Strain
05
05
51
84
01
63
01
 rollin
 Hardening
. . .
. . .
. . .
. . .
403.
. . .
403.
. . .
. . .
403.
403.
1
inal ax
tics
.3
8.8
0.1
er Yield
214.
210.
203.
202.
205.
210.
207.
4.7
11.9
202.
214.
14-1
14-2
B14-1
ion
imen ID
Standa
M
M
Sp
 
 
Table A-14:  Summary of Plate 14 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal Mill Certificate Properties
Number Mark Type Strength Thickness F
y
F
u
Elongation
(M
4
Pa) (mm) (MPa) (MPa) )
15 C (G2) A852 85 30.163 598 713
Young's Mod. G  Le
E (GPa)
? (%)
ngth
(%
48
age
? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) (GE
st 
Pa)
? (%) ? (
7
7
7
7
7
7
7
1
3
7
7
6
Stre
M
m
A15-1 210.9 0.512 35.5 04 9.0 0.573 0.929 .9 5 3
A15-2 213.0 0.498 34.2 90 9.0 0.713 0.761 .4 5 3
B15-1 209.7 0.502 33.6 93 3.8 0.517 0.748 .0 5 3
B15-2 209.8 0.496 21.7 88 4.7 0.326 0.359 .3 4 3
C15-1 209.3 0.514 57.1 04 7.3 0.524 0.601 5.3 8 3
C15-2 202.2 0.507 27.2 01 3.1 0.507 0.507 8.6 6 3
Mean 209.1 0.505 34.9 97 7.8 0.527 0.651 5.1 59
Standard Deviation 3.7 0.007 12.1 07 0.9 0.124 0.204 1.8 3
Range 10.9 0.017 35.5 16 2.6 0.387 0.570 4.7 8
Minimum 202.2 0.496 21.7 88 4.7 0.326 0.359 3.9 45
Maximum 213.0 0.514 57.1 04 637.3 0.713 0.929 8.6 84
Count 66 666 6
Tensi sts ection:  longitudinal axis in the ion of roll
Statistics
Strain Harden le nSta eld
Both Flanges
Location
Specimen ID
0.2% Offset Yield
)
.2
.2
.2
.2
.2
.2
(m
20
20
20
20
20
20
Pa)
4.7
4.4
4.0
5.8
4.6
4.3
.6
.6
.8
.8
.6
gth
7.56
7.09
7.73
6.65
7.05
5.51
6.93
0.80
2.22
5.51
7.73
ing)
Tensi
6
6
6
6
6
6
6
6
6
0.5
0.4
0.4
0.4
0.5
0.5
0.4
0.0
0.0
0.4
0.5
on Te
61
61
61
60
63
61
61
1
3
60
6
 (L dir
tic Yi
3
4
4
4
direct
ing
58
46
56
58
67
81
44
03
23
58
81
 
 
le A  Su ary of Plate 15 Tension Test Resu
 
lts mm-15: Tab
   
Plate Section Steel Nominal Nominal Mill Certificate Properties
Number Mark Type Strength Thickness F
y
F
u
Elongation
(MPa) (mm)
63
(MPa) (MPa) (%)
16 D (G2) A85 485 30.1 9 755 18
Young's Mod. Gage Length
E (GPa)
)
2 62
? (% ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
A16-1 215.4 0 68.4 .50 650.4 0.51 10 6.005 6.839 800.1 203.2
A16-2 210.7 7 68.7 .48 651.9 0.43 94 5.082 6.834 800.0 203.2
B16-1 205.3 0 38.9 .52 620.5 0.74 53 3.947 7.652 754.7 203.2
B16-2 210.8 9 51.1 .50 635.3 0.37 01 4.345 6.410 772.6 203.2
C16-1 210.3 7 46.1 .49 628.9 0.56 74 5.584 6.340 775.5 203.2
C16-2 210.0 2 54.5 .49 637.5 0.59 4.585 5.649 779.2 203.2
Mean 210.4 9 54.6 .50 637.4 0.53 0.653 4.924 6.621 780.4
Standard Deviation 3.2 1 12.0 .01 12.2 0.12 0.120 0.779 0.667 17.4
Range 10.1 3 29.8 .03 31.3 0.36 0.342 2.058 2.003 45.4
Minimum 205.3 7 38.9 .48 620.5 0.37 0.510 3.947 5.649 754.7
Maximum 215.4 0 68.7 .521 651.9 0.74 0.853 6.005 7.652 800.1
Count 6 6 6666
es direction:  l  a  th ction of rolling)
Stat
ai rdening Tensile Strengthield
th Flanges
Location
Specimen ID
 Offset Yield
e dire
0
1
3
7
2
0
6
9
6
7
3
6
ongitudinal
istics
Str
0.5
0.6
0.8
0.6
0.5
0.686
xis in
n Ha
0.51
0.49
0.53
0.50
0.50
0.50
0.50
0.01
0.03
0.49
0.53
Bo
0.2%
6
6
6
6
6
6
6
6
6
6
T
0
0
0
0
0
0
0
0
0
0
0
ension T
2
9
1
1
9
4
1
1
2
9
ts (L 
Static Y
6
 
 
le :  mary ate ension Test Results 
 
16 Tof PlSumA-16Tab
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(M
345
Pa)(m) (MPa)
1 E (G3) A572 57.150 3 590
o M Gage Length
a)
? (%) ? (MPa)
(MPa)
968
Y ung's 
E (GP
od.
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
A 0.201 372.4 00 2 0.362 3 0 352.1 .503 0.623 4.750 12.73 546.5 50.8
A18-2 237.5 0.182 369.0 87 0 0.353 3 0.349 353.3 .671 0.680 4.938 13.85 545.3 50.8
B18-1 . . . . . . . . 0.419 3 0. 369.2 .680 0.718 4.830 12.14 565.9 50.8
B18-2 . . . . . . . . 0.559 3 0. 353.9 .508 0.548 5.415 11.68 557.8 50.8
C18-1 0.303 370.7 01 6 0.381 3 0. 358.4 0.635 0.684 5.070 14.37 556.7 50.8
C18-2 0.204 386.0 97 3 0.389 3 0. 342.6 0.670 0.833 4.712 12.67 562.2 8
Mean 0.222 374.5 71 8 3 0. 354.9 0.611 0.681 4.952 12.91 555.7
Standard Deviati 0.055 7.8 38 0. 8.7 0.083 0.095 0.261 1.02 8.3
Range 0.121 17.0 11 1 0. 26.7 0.177 0.285 0.702 2.69 20.6
Minimum 0.182 369.0 87 0 3 0. 342.6 0.503 0.548 4.712 11.68 545.3
Maximum 0.303 386.0 97 3 3 0. 369.2 0.680 0.833 5.415 14.37 565.9
Count 64 466666 666
nsion Tests (L dire lo nal axis in the direction of rolling)
tics
Strain Hardening Tensile Strength Yield
Specimen ID
Upper Yield Low 0.2% Offset Y
Both Flanges
Location Mill Certificate Properties
Elongation
50.
6
18-1 214.8
174.3
105.4
201.1
203.5
189.4
46.0
132.1
105.4
237.5
0.2
0.1
. 
. 
0.4
0.6
0.3
0.2
0.5
0.1
0.6
4
359.
358.
. . .
. . .
368.
377.
365.
9.0
19.3
358.
377.
4
Te
er Yield
62.3
63.1
74.8
71.2
68.8
80.2
70.1
6.9
7.8
62.3
80.2
ction:  
ield
.357
416
543
376
370
402
073
194
349
543
ngitudi
Statis
Static
0
0
0
0
23
(%)
0.411
0.076
0.206
0.353
0.559
on
 
Tab -17:  mar Pl 8 T n Test Res
 
ults ensio
 
ate 1y of Sumle A
   
Pl
Nu
ate Section Steel Nominal No
h Thic
a) m)
57 50
minal
mber Mark Type Strengt kness F
y
F
u
(MP ( (MPa) )
19 F (G A572 345 .1 400
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ?
(MPa
5963)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) (MPa)
(mm)
A19-1 139.1 . . . . . . . . . 0.46 3 0 367.5 53 0.660 4.391 10.27 66.7 50.8
A19-2 171.3 0.495 383.0 0.352 378.6 0.40 381.9 0 342.9 670 0.678 5.225 11.47 67.0 50.8
B19-2 226.2 . . . . . . 0.300 382.5 0.36 3 0 375.1 97 0.530 4.977 12.55 79.4 50.8
C19-1 214.8 . . . . . . . . . . . . 0.37 3 0 368.0 40 0.573 5.048 12.89 70.8 50.8
C19-2 216.3 . . . . . . . . . . . . 0.37 3 0 367.6 09 0.567 4.528 13.68 70.6 50.8
Mean 193.6 0.495 383.0 0.326 380.5 0.39 3 0 364.2 514 0.601 4.834 12.17 70.9
Standard De n 37.1 . . . . . . 0.037 2.8 0.04 0 12.3 100 0.064 0.357 1.33 5.1
Rang 87.1 . . . . . . 0.052 3.9 0.10 0 32.2 261 0.148 0.834 3.41 12.7
Minim 139.1 0.495 383.0 0.300 378.6 0.36 3 0 342.9 0.409 0.530 4.391 10.27 66.7
Maxim 226.2 0.495 383.0 0.352 382.5 0.46 3 0 375.1 0.670 0.678 5.225 13.68 79.4
Count 51122 55555 5
Tens est re   lo nal ax e direction of rolling)
tics
Strain Hardening Tensi ngth Yield
Specime
Upper Yield Lo ield % t Y
Both Fla
Location Mill Certificate Properties
Elongation
5
5
5
5
5
5
5
5
5
le Stre
0.4
0.
0.4
0.5
0.4
0.
0.
0.
is in th
25
(%)
.456
.382
.356
.370
.368
.386
.040
.100
.356
.456
ngitudi
Statis
Static
. . .
nges
7
3
0
5
4
6
3
7
0
7
5
ion T s (L di
0.2  Offse
84.6
85.0
78.2
79.5
81.8
3.0
6.8
78.2
85.0
ction:
ield
viatio
e
um
um
n ID
wer Y
 
 
Table A-18:  Su ar Plate 19 Tension Test Results 
 
y of mm
   
Plate
mber
0
Y
S Steel Nominal Nominal
Nu Type Strength Thickness F
y
F
u
a m)(MPa)(
2 G 72 50 385 60
ou o e 
E
%) Pa
Length
ection
Mark
 (G3)
ng's M d.
 (GPa)
? (
(MP
345
)(
57.1
MPa)
2A5
? (M )
Gag
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
appar
Pa)
ent
 (%) E
st 
(G
? (%) ? (MPa
574.2
572.9
561.3
563.0
561.0
566.5
6.5
13.2
561.0
574.2
rength
)
(m
A20-1  . .  . . . 0.389 375.5 0.385 368.4 0.211 0. 1 13.95 50.8
A20-2  . .  . . . 0.484 373.3 0.478 365.6 0.484 0. 3 17.46 50.8
B20-1 278 .0 04 0.387 369.9 0.382 359.1 0.424 0. 5 12.49 50
B20-2  . .  . . . 0.399 0.394 365.2 09 0. 8 12.80 50
C20-2  . .  . . . 0.348 0.344 365.9 04 0. 0 14.05 50
Mean 278 .0 04 0.401 373.8 0.397 364.9 0.426 0. 6 14.15
S rd Deviati  . . . . 0.050 2.4 0.049 3.4 0.125 0. 9 1.97
Range  . . . . . . . 0.136 6.1 0.134 9.3 0.299 0. 5 4.97
nimum 278 374.0 04 0.348 369.9 0.344 359.1 0.211 0. 3 12.49
aximum 278 374.0 04 0.484 0.478 368.4 09 0. 8 17.46
Count 51 1155555555
ion Tests (L direction:  longitudinal axis in the direction in
Statistics
Strain Tensile StStatic Yield
c
pp ld ower 0.2% Offset Yield
oth es 33
Mill Certificate Properties
Elongation
(%)
m)
.8
.8
.8
321 4.92
484 4.55
433 5.21
449 5.23
498 4.80
437 4.94
070 0.28
178 0.68
321 4.55
498 5.23
 of roll g)
 Hardening
199.6 .
136.6 .
190.4 0.
188.8 .
245.3 .
192.2 0.
38.7 .
108.7 .
136.6 0.
245.3 0.
U
B
. . . 
. . . 
374 0.3
. . . 
. . . 
374 0.3
. . . . 
. 
0.3
0.3
1
er Yie L
 Flang
Location
. . .
. . .
369.7
. . .
. . .
369.7
. . .
. . .
369.7
369.7
Tens
Yield
374.2
376.0
376.0
0.5
0.5
0.5
tanda
Mi
M
Spe
on
imen ID
 
 
Table A-19:  Summary of Plate 20 Tension Test Results
 
 
   
ength
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MP
A57 34
)
a) (mm) (M (MPa)
21 B1, B2, B3, B4 2 5 19.050 4 592
You Mod.  L
)
%) MPa
Pa)
34
ng's 
E (GPa
? (
Gage
? ( ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (% ?
appa
)
rent
 (%) E
st 
(GPa)
? (%) ? (MPa)
m
A21-1 83 1.2 59 .8 0.407 415.5 0.401 403.3 1 716 4.594 5.45 577.8 50.
A 71 5.4 34 .4 0.426 430.2 0.418 4.8 8 434 4.996 5.88 592.4 50.
B 42 9.3 92 .7 0.428 429.3 0.416 7.0 3 654 3.894 5.43 581.1 03
B 85 3.0 93 .4 0.422 432.3 0.410 8.9 5 588 2.927 8.78 584.2 50.
B 13 3.6 82 .5 0.425 425.0 0.417 0.8 545 4.609 5.75 585.4 50.
C 46 4.6 37 .2 0.415 422.3 0.408 9.9 1.567 735 3.885 4.47 579.8 50.
C 50 7.7 32 .2 0.408 421.1 0.400 5.1 1.547 701 4.288 5.38 577.5 50.
M 13 0.7 33 .6 0.419 425.1 0.410 8.5 1.472 625 4.170 5.88 582.6
ar iation 74 .8 0.009 5.9 0.008 3.8 0.151 109 0.680 1.36 5.3
R 96 .8 0.902 0.021 16.8 0.018 1.5 0.446 300 2.070 4.31 14.9
Mi 46 4.6 0.532 .8 0.407 415.5 0.400 3.3 1.165 434 2.927 14.47 577.5
a 42 5.4 1.434 .4 0.428 432.3 0.418 4.8 1.611 735 4.996 18.78 592.4
7 77 7 7 7 7 7 7
B21-1 54 8.4 1.132 .9 0.435 454.8 . . .  . . 1.498 355 6.873 50.
B21-2 47 459.8 1.173 .4 0.425 449.9 . . .  . . 1.507 493 6.116 50.
B21-3 40 458.0 0.498 .2 0.428 451.0 0.414 2.7 1.485 493 5.881 50.
Mean 47 458.7 0.934 0.430 451.9 0.414 2.7 1.497 447 6.290
Standard Deviation 07 0.9 0.379 1.6 0.005 2.6 . . .  . . 0.011 080 0.518
Range 14 1.8 0.675 0.010 4.9 . . .  . . 0.022 138 0.991
Minimum 40 458.0 0.498 .2 0.425 449.9 0.414 2.7 1.485 355 5.881
Maximum 54 459.8 1.173 .4 0.435 454.8 0.414 2.7 1.507 493 6.873
Count 3 333 3 3 3 3
Statis
Statis
Compres ests
ion Tests (L direction:  longitudinal axis di n of rolling)
 Hardening imate StrengthStatic Yield
Speci ID
eld ow d 0.2% Offset Yield
mp. Flange 2
Location Mill Certificate Proper
Elong
(%
m)
8
8
.2
8
8
8
8
8
8
8
(
2
1
1
1
1
1
1
1
1
Ult
1.61 1.
1.42 1.
1.54 1.
1.16 1.
1.440 1.
1.
1.
1.
0.
0.
1.
1.
1.
1.
1.
1.
0.
0.
1.
1.
in the rectio
Strain
6
ties
ation
)
41
40
40
41
40
40
40
1
40
41
777
.
.
42
42
.
.
42
42
311
tics
tics
sion T
0.5 413
1.4 423
0.8 417
0.9 415
0.8 419
1.2 418
0.5 415
0.9 417
0.330 3.2
9.6
413
423
440
442
439
440.9
3.3
439
442
Tens
L er Yiel
188.7 0.2
192.1 0.2
194.5 0.4
190.5 0.3
184.3 0.3
194.8 0.2
201.5 0.2
192.3 0.3
5.4 0.0
17.1 0.1
184.3 0.2
201.5 0.4
195.5 0.3
199.4 0.3
195.9 0.3
196.9 0.3
2.1 0.0
3.9 0.0
195.5 0.3
199.4 0.3
U
Co
43
43
42
43
43
42
42
43
3
10
42
43
7
45
pper Yi
21-2
21-1
21-2
21-3
21-1
21-2
ean
d Dev
ange
nimum
ximum
Count
men 
Stand
M
 
 
Table A-20:  Summary of Plate 21 Tension and Compression Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
22 B1, B2, B3 A572 345 19.050 443 597
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) m)
2-1 189.9 0.189 432.2 0.703 417.1 0.413 417.5 .407 406.7 1.790 2.080 4.2 16.16 576.2 50.8
2-2 187.2 0.190 428.4 0.8 410.3 0.4 412.1 0.417 406.4 1.444 1.953 3.1 16.75 572.8 50.8
2-1 190.1 0.196 439.1 0.8 423.4 0.4 430.7 0.425 417.5 1.884 2.108 3.6 15.35 582.9 203.2
2-2 205.2 424.8 0.6 415.9 0.4 417.1 0.399 408.5 1.658 1.966 3.6 16.02 577.9 50.8
2-1 187.7 0.190 417.4 0.7 406.7 0.4 411.3 0.410 396.8 1.671 1.980 3.8 16.68 569.7 50.8
2-2 193.7 0.210 437.1 0.5 414.4 0.4 415.9 0.408 405.4 1.819 2.096 4.0 16.12 571.3 50.8
ean 192.3 0.195 429.8 0.7 414.6 0.4 417.4 0.411 1.711 2.030 3.7 16.18 575.2
Sta  Deviation 6.8 0.008 8.1 0.1 5.8 0.0 7.0 0.009 6.6 0.157 0.071 0.4 0.51 4.9
nge 18.1 0.021 21.7 0.3 16.7 0.0 19.4 0.027 20.8 0.440 0.155 1.1 1.40 13.2
mum 187.2 0.189 417.4 0.5 406.7 0.4 411.3 0.399 396.8 1.444 1.953 3.1 15.35 569.7
mum 205.2 0.210 439.1 0.8 423.4 0.4 430.7 0.425 417.5 1.884 2.108 4.2 16.75 582.9
unt 666 66666 66
2-1 206.4 0.235 478.5 0.4 447.2 0.417 450.0 0.409 431.9 2.077 2.0 7.2 50.8
2-2 205.5 0.240 472.4 0.9 451.4 0.423 459.2 0.415 442.5 1.947 1. 6.511 50.8
2-3 207.2 0.233 479.8 0.5 450.3 0.418 452.5 0.410 436.9 1.823 1. 5.566 50.8
ean 147.9 1.018 330.7 1.3 314.6 1.160 318.4 1.155 307.5 2.231 2. 4.845
Standard Deviation 93.2 2.198 217.7 2.0 207.8 2.139 209.5 2.141 201.5 1.752 1. 2.127
Range 201.2 5.979 473.8 5.6 445.4 5.970 453.2 5.973 436.5 5.560 5. 6.069
Minimum 6.0 0.021 6.0 0.3 6.0 0.030 6.0 0.027 6.0 0.440 0. 1.184
Maximum 207.2 6.000 479.8 6.0 451.4 6.000 459.2 6.000 442.5 6.000 6. 7.253
Count 777 777777
Compression Tests
Statistics
Tensi sts ection:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2 et Yield
Ten. Flange 27
Location Mill Certificate Properties
Elongation
(%)
(m
92
08
78
92
06
72
75
04
84
08
92
6
5312
990
784
286
774
845
155
000
7
406.9
0
20
32
03
18
13
16
10
30
03
32
6
 (L dir
% Offs
A2
A2
B2
B2
C2
C2
M
ndard
Ra
Mini
Maxi
Co
B2
B2
B2
M
80
09
71
49
32
24
20
48
32
80
6
50
14
83
87
45
52
48
00
7
6
on Te
0.196
 
 
 of Plate 22 Tension and Compression Test Results 
 
Table A-21:  Summary
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(
3
MPa)(MPa)
23 B5 A572 345 23.81 419 571
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) GPa)? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
( ? (%) ? (MPa) (mm)
A23-1 190.1 0.273 432.1 1.011 409.2 .410 40 0.404 398.0 1.787 1.915 4. 15.49 575.8 50.8
A23-2 214.2 0.194 413.9 0.214 399.6 .389 39 0.384 387.5 1.721 1.986 3. 17.31 565.5 50.8
B23-1 165.4 0.221 433.1 1.421 413.5 .441 42 0.434 409.6 1.492 2.085 3. 15.62 579.0 203.2
B23-2 196.0 0.190 411.2 1.865 395.1 .405 40 0.401 393.8 1.789 1.831 4. 16.84 566.2 50.8
B23-3 207.0 0.206 425.4 1.527 393.4 .401 40 0.396 392.0 1.453 1.534 4. 16.63 569.8 50.8
C23-1 211.4 0.182 414.8 1.347 401.2 .392 40 0.387 393.9 1.505 1.796 3. 15.79 569.3 50.8
C23-2 202.9 0.193 415.4 0.372 399.5 .395 39 0.390 389.9 1.675 1.991 4. 15.12 567.4 50.8
Mean 198.1 0.209 420.8 1.108 401.6 .405 40 0.399 395.0 1.632 1.877 4. 16.11 570.4
Standard Deviation 16.7 0.031 9.2 0.613 7.3 .018 8 0.017 7.3 0.145 0.181 0. 0.81 5.1
Range 48.8 0.091 22.0 1.651 20.1 .052 23 0.050 22.1 0.336 0.552 1. 2.19 13.6
Minimum 165.4 0.182 411.2 0.214 393.4 .389 39 0.384 387.5 1.453 1.534 3. 15.12 565.5
Maximum 214.2 0.273 433.1 1.865 413.5 .441 42 0.434 409.6 1.789 2.085 4. 17.31 579.0
Count 7777 7777777
B23-1 206.7 0.226 455.3 0.776 428.1 .412 439.8 0.401 416.8 1.626 1.766 5.745 50.8
B23-2 205.7 0.230 445.1 0.368 432.9 .410 432.5 0.402 416.6 1.727 1.673 6.273 50.8
B23-3 207.8 0.252 455.4 1.765 429.6 .412 438.9 0.404 422.6 1.634 1.775 6.172 50.8
Mean 206.7 0.236 451.9 0.970 430.2 .411 437.1 0.403 418.7 1.662 1.738 6.063
Standard Deviation 1.0 0.014 5.9 0.718 2.5 .001 4.0 0.001 3.4 0.056 0.057 0.280
Range 2.1 0.026 10.2 1.397 4.8 .002 7.3 0.003 6.0 0.101 0.102 0.528
Minimum 205.7 0.226 445.1 0.368 428.1 .410 432.5 0.401 416.6 1.626 1.673 5.745
Maximum 207.8 0.252 455.4 1.765 432.9 .412 439.8 0.404 422.6 1.727 1.775 6.273
Count 3333 3333333
Compression Tests
Statistics
Tensio s (L ti ngitudinal axis in the direction of rolling
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2% O Yi
Both Flanges 27
Location Mill Certificate Properties
Elongation
(%)
713
921
675
564
046
782
077
111
389
038
675
713
)
9.7
8.6
2.0
2.0
1.5
3.5
9.1
5.2
.3
.4
8.6
2.0
7
on:  lo
eld
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
3
n Test
7
 direc
ffset 
 
 
Table A-22:  Summary of Plate 23 Tension and Compression Test Results 
 
   
Plate
Number
24
S
You
E
ection
ark
6
's Mod.
GPa)
? (%) ?
St m
M T k
y
( M )
B A .1 7
ng ge
 (
 (
eel Nominal No
ype Strength Thic
(MPa)
572 345 30
inal
ness F
m)(
63 44
F
u
Pa)(MPa
575
Ga  Length
MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa)
8.2
2.3
6.4
9.6
6.2
8.5
8.5
8.5
.5
7.9
8.5
6.4
7
Strength
(mm)
20 41 1. .3 .1 1.951 3.552 55 50.8
201.0 41 0. .3 .6 1.950 4.298 56 50.8
198.9 42 0. .4 .1 2.027 3.691 56 203.2
214.8 42 1. .3 .7 2.192 3.195 55 50.8
236.5 41 1 .3 .6 1.989 3.962 55 50.8
209.9 41 0.855 .3 .8 2.022 3.062 54 50.8
204.0 40 0.443 .3 .4 1.940 4.103 55 50.8
210.3 41 0.878 .3 .1 388.1 2.010 3.695 55
Stan at 12.8 6 0.399 .0 9 7.4 0.088 0.461 5
37.6 1 1.023 .0 .0 23.6 0.253 1.236 1
198.9 40 0.352 .3 .1 375.7 1.940 3.062 54
236.5 42 1.375 .4 .1 399.3 2.192 4.298 56
7 7 7
209.7 45 1.489 .4 .9 412.4 1.600 6.573 50.8
210.5 45 0.893 .4 .4 414.5 1.360 4.531 50.8
207.9 45 1.504 .4 .9 411.4 1.516 5.824 50.8
209.4 45 1.295 .4 .4 0 412.7 1.492 5.643
Stan ation 1.4 0 0.349 .0 3 0 1.6 0.122 1.033
2.6 1 0.611 .0 5 0 3.1 0.240 2.042
207.9 45 0.893 .402 .4 0 411.4 1.360 4.531
210.5 45 1.504 .406 .9 0 414.5 1.600 6.573
33 3
C ion Te
tics
S D
Yi % el
s n in tion of rolling)
tics
in Hardening e c Y
an
tio il e 
A24-1
A24-2
B24-1
B24-2
B24-3
C24-1
C24-2
Mean
dard Devi
Range
Minimum
Maximum
Count
B24-1
B24-2
B24-3
Mean
dard Devi
Range
Minimum
Maximum
Count
pecimen I
6.9 0.193
0.215
0.192
0.202
0.207
0.208
0.174
0.199
0.014
0.041
0.174
0.215
77
0.228
0.217
0.224
0.223
0.005
0.011
0.217
0.228
33
Upper 
Both Fl
Loca
5.9
6.9
7.6
5.0
6.5
4.0
8.6
7.8
.5
9.0
8.6
7.6
2.0
2.8
1.2
2.0
.8
.5
1.2
2.8
3
eld
ges
n
243 393.8 0
352 398.5 0
713 405.9 0
167 400.1 0
.375 396.1 0
396.5 0
399.0 0
398.6 0
3.9 0
12.1 0
393.8 0
405.9 0
77
423.7 0
424.8 0
415.6 0
421.4 0
5.0 0
9.2 0
415.6 0
424.8 0
33
Lower Yield 0.2
Tension Test
88 395
95 398
08 413
89 403
72 399
90 397
96 399
91 401
11 5.
36 18
72 395
08 413
7
06 433
02 427
06 429
05 430
02 3.
04 6.
427
433
3
 Offset Yi
(L directio
M
0.379
0.392
0.401
0.383
0.367
0.384
0.390
0.385
0.011
0.035
0.367
0.401
7
0.396
0.396
0.397
.396
.001
.002
.396
.397
ompress
Statis
d
:  longitud
Statis
Stati
l Certificat
375.7 1.529
391.5 1.787
399.3 1.729
391.4 1.876
387.2 1.630
383.2 1.607
388.7 1.772
1.704
0.120
0.347
1.529
1.876
77
1.768
1.516
1.535
1.606
0.140
0.252
1.516
1.768
33
sts
al axis in the direc
Straield
26
Properties
Elongation
(%)
17.17
15.73
15.98
17.82
17.23
16.57
16.25
16.68
0.75
2.08
15.73
17.82
7
3
Tensil
ion
 
 
ensioTable A-23:  Summary of P 24 T n an sion Test Res
 
ults d Compreslate 
   
Plate
Number
25
Sectio
Mark
B4
Young's 
E (GPa
n Steel Nominal
Strength T
(MPa)
345
N
Type hi F
(
A572 3 4
Mo ngth
)
MPa)
Gage Le
ominal
ckness
(m)
1.750
y
F
u
MPa)(MPa)
60 606
d.
? (%) ? ( ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
 
(G
apparent
 (%) E
st
Pa) ? (%) ? (M )
24.0 1.351 0.394 40 39 .9 1 65
13.0 1.927 0.397 39 38 .3 1 58
20.5 0.488 0.390 41 39 .0 68 2
17.6 1.533 0.428 40 39 .1 16.72 64
21.6 0.907 0.387 40 38 .4 17.09 66
14.7 0.450 0.393 40 38 .8 15.36 64
25.6 0.465 0.390 40 39 .9 16.08 66
19.6 1.017 0.397 40 39 .9 16.60 64
Stand tio 4.7 0.595 0.014 4 3 .2 0.96 3.
12.6 1.477 0.041 14 1 .9 2.45 10.4
13.0 0.450 0.387 39 38 .4 15.36 58.0
M 25.6 1.927 0.428 41 39 .3 17.81 68.4
7 7
44.8 1.232 0.410 43 40 .0
45.4 1.542 0.413 43 40 .4
28.2 0.309 0.391 4 40 .7
39.5 1.028 0.405 428.7 40 .0
Stand tion 9.8 0.642 0.012 13.3 3 .3
17.3 1.233 0.022 25.1 5 .7
28.2 0.309 0.391 413.7 40 .7
M 45.4 1.542 0.413 438.8 40 .447
3 3 3 3
n 
cs
ests ( ti a re g)
cs
tr T nYiield Lowe 0.2% Yi
nge
on  P
E
Pa)
(mm
.0 50.8
.0 50.8
.4 203.
.7 50.8
.2 50.8
.0 50.8
.7 50.8
.7
3
7
50.8
50.8
50.8
gth
A25-1
A25-2
B25-1
B25-2
B25-3
C25-1
C25-2
Mean
ard Devia
Range
Minimum
aximum
Count
B25-1
B25-2
B25-3
Mean
ard Devia
Range
Minimum
aximum
Count
Specimen ID
209.0
198.9
214.8
179.0
221.1
219.9
222.0
209.2
n 15.6
43.0
179.0
222.0
206.3
205.8
205.6
205.9
0.3
0.7
205.6
206.3
0.224 4
0.213 4
0.277 4
0.231 4
0.291 4
0.203 4
0.209 4
0.236 4
0.035
0.088
0.203 4
0.291 4
77
0.252 4
0.287 4
0.216 4
0.252 4
0.036
0.072
0.216 4
0.287 4
3
Upper Y
Ten. Fla
Locati
401.9
390.1
404.7
401.8
398.6
401.9
406.0
400.7
5.2
15.9
390.1
406.0
77
414.1
414.9
414.8
414.6
0.4
0.7
414.1
414.9
33
Tension T
r Yield
5.2 0.387
5.6 0.392
0.0 0.383
3.2 0.421
6.8 0.378
2.6 0.386
7.5 0.384
4.4 0.390
.6 0.014
.4 0.043
5.6 0.378
0.0 0.421
77
3.7 0.398
8.8 0.397
13.7 0.386
0.393
0.007
0.012
0.386
0.398
33
Compressio
Statisti
on:  longitudin
Statisti
Static eld
Mill Certificate
1.0 1.780
4.2 1.702
4.5 1.871
0.4 1.720
8.2 1.597
9.7 1.770
5.7 1.831
0.5 1.753
.9 0.090
1.5 0.273
4.2 1.597
5.7 1.871
7
9.0 1.680
5.0 1.607
3.3 1.642
5.8 1.643
.0 0.037
.8 0.073
3.3 1.607
9.0 1.680
3
Tests
l axis in the di
Seld
27
roperties
longation
(%)
1.995 3
1.932 4
2.017 4
2.020 4
1.928 3
1.972 3
2.022 3
1.984 3
0.041 0
0.093 0
1.928 3
2.022 4
7
1.630 6
1.544 6
1.710 5
1.628 6
0.083 0
0.166 0
1.544 5
1.710 6
3
ction of rollin
ain Hardening
83
96
92
94
53
60
13
84
97
43
53
96
7
95
47
12
85
68
35
12
7.59 5
7.81 5
15.57 5
5
5
5
5
5
5
5
7
ensile Stre
7
3
L direc
Offset 
 
able A-24: ry o e 25 n and
 
ression Test Results  Comp
 
 Tensiof Plat SummaT
   
Plate Se
M
S1,
Youn
E (
ction
rk
1-S
s Mod.
Pa)
? (%) ? (MPa
Steel Nomin
Type Streng
(M
A572 345
al in
Number a th n F
u
Pa m Pa)(MPa)
26  S 22 560
g' ng
G
)
Nom
Thick
)(
22.
al
ess F
y
)(M
5 412
Gage Le th
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st parent
 (% a) (%) ?
ap
) E
st 
(GP ? (%) ? (M )
26-F1-1 94 03 3 0.395 380.0 1 1.954 1 39 2
26-F1-2 89 10 1 0.401 381.1 1 1.932 1 40 2
26-F1-3 93 06 9 0.397 381.1 1 2.007 1 39 2
26-F2-1 78 03 7 0.395 372.3 1 1.012 1 39 2
26-F2-2 73 18 9 0.410 371.3 1 1.234 1 36 2
26-F2-3 72 21 9 0.414 372.2 1 1.204 1 35 2
26-F3-1 82 06 6 0.397 372.6 1 1.239 1 42 2
26-F3-3 94 00 8 0.393 375.3 1 1.640 1 39 2
Mean 84 08 6 0.400 375.7 1 1.528 1 39
Standard Deviatio 9.4 08 0.008 4.3 0 0.402 2.
Range 2. 21 0.021 9.8 0 0.995 6.
Minimum 72 00 9 0.393 371.3 1 1.012 1 35
Maximum 94 21 9 0.414 381.1 1 2.007 1 42
Count 888 8
ns sts n:  longitudinal axis in th n of ro
Statistics
 H nStatic Yield
Specimen
% d
2
ill Certificate Prop
Elon
(
Pa)
(mm
.1 203.
.7 203.
.7 203.
.0 203.
.7 203.
.4 203.
.0 203.
.9 203.
.1
1
6
.4
.0
8
gth
1
1
1
1
1
1
1
1
1
n
2
1
1
 ID
.9 0.349 399.4
.2 0.369 401.0
.5 0.343 402.3
.0 0.431 388.7
.6 0.427 386.7
.1 0.443 384.1
.7 0.373 390.6
.0 0.327 390.1
.8 0.383 392.9
0.044 7.0
8 0.115 18.3
.1 0.327 384.1
.9 0.443 402.3
88
Upper Yield
Both Flanges
Location
0.462 386.4
0.479 385.7
0.478 384.8
0.545 385.3
0.503 382.8
0.553 382.1
1.187 383.7
1.027 380.5
0.654 383.9
0.285 2.0
0.725 5.9
0.462 380.5
1.187 386.4
88
Te
Lower Yield
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.0
0.0
0.4
0.4
ion Te
0.2
394.
397.
397.
387.
385.
383.
389.
388.
390.
5.2
14.0
383.
397.
8
 (L directio
Offset Yiel
M
.890
.934
.920
.003
.232
.200
.288
.561
.504
.373
.931
.003
.934
8
e directio
Strain
8
erties
gation
%)
3.570
3.570
3.480
2.999
3.454
3.394
3.912
3.717
3.512
0.265
0.913
2.999
3.912
8
lling)
ardening
2.31 5
2.37 5
2.40 5
2.46 5
2.34 5
2.40 5
2.47 5
2.26 5
2.38 5
0.07
0.20
2.26 5
2.47 5
8
Tensile Stre
 
 
2 u of Plate 26 Tensi Resu
 
lts on Test mmary 5:  STable A-
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
27 S1, S1-S A572 345 7.938 430 565
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
27-W4-1 207.5 0.229 442.9 1.551 418.1 0.407 425.3 0.397 405.2 2.015 2.349 3.297 12.17 565.5 203.2
27-W4-2 210.5 0.240 446.8 0.562 427.0 0.409 432.9 0.398 410.2 2.141 2.400 3.308 12.39 567.0 203.2
27-W6-1 207.4 0.238 448.3 0.516 426.6 0.411 432.8 0.403 415.9 1.969 2.354 3.273 12.28 573.0 203.2
27-W6-2 210.4 0.243 449.4 0.933 429.5 0.408 434.3 0.401 417.7 1.996 2.356 3.379 12.23 573.2 203.2
27-W8-1 203.0 0.224 413.1 0.278 393.5 0.396 399.4 0.392 389.8 1.968 2.168 3.475 11.29 556.2 203.2
27-W8-2 228.0 0.226 409.7 0.366 386.9 0.377 388.1 0.374 381.9 2.090 2.224 3.403 11.04 548.4 203.2
27-W3-1 207.9 0.229 453.2 0.819 423.7 0.407 428.5 0.399 412.3 2.104 2.415 3.267 12.22 567.5 203.2
27-W3-2 210.1 0.233 446.6 1.352 424.2 0.407 432.8 0.400 418.5 2.107 2.408 3.272 12.40 566.6 203.2
27-W5-1 208.7 0.235 447.2 1.038 424.5 0.417 428.3 0.409 412.6 2.015 2.366 3.352 12.16 566.3 203.2
27-W5-2 210.8 0.235 452.3 1.166 428.2 0.406 430.8 0.400 418.8 2.013 2.425 3.250 12.20 571.1 203.2
27-W7-2 206.8 0.221 432.2 0.784 407.2 0.402 417.0 0.392 394.8 1.967 2.075 3.622 . . . 564.1 203.2
27-W7-3 216.2 0.233 422.4 0.783 401.7 0.395 407.8 0.389 395.3 1.591 1.859 3.851 12.49 561.1 203.2
Mean 210.6 0.232 438.7 0.846 415.9 0.404 421.5 0.396 406.1 1.998 2.283 3.396 12.08 565.0
Standard Deviation 6.3 0.007 15.4 0.387 14.8 0.010 15.2 0.009 12.6 0.142 0.173 0.179 0.47 7.1
Range 25.0 0.022 43.5 1.273 42.6 0.040 46.3 0.035 36.8 0.550 0.565 0.600 1.46 24.8
Minimum 203.0 0.221 409.7 0.278 386.9 0.377 388.1 0.374 381.9 1.591 1.859 3.250 11.04 548.4
Maximum 228.0 0.243 453.2 1.551 429.5 0.417 434.3 0.409 418.8 2.141 2.425 3.851 12.49 573.2
Count 12 12 12 12 12 12 12 12 12 12 12 12 11 12
Tension Tests (LT direction:  longitudinal axis normal to the direction of rolling)
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Web 23
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-26:  Summary of Plate 27 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
28 S2, S2-S A572 345 22.225 412 560
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
28-F1-1 197.3 0.330 426.9 0.457 407.8 0.411 417.7 . . . . . . 1.990 2.198 3.686 12.30 559.5 203.2
28-F1-2 200.2 0.337 427.1 1.109 406.9 0.414 423.8 . . . . . . 1.845 2.111 3.706 12.40 560.9 203.2
28-F1-3 201.5 0.294 426.3 0.453 406.3 0.408 413.4 0.401 398.8 1.999 2.122 3.695 12.31 559.5 203.2
28-F2-1 203.6 0.346 423.0 0.440 404.3 0.405 415.6 . . . . . . 1.901 2.059 3.624 12.19 558.7 203.2
28-F2-2 201.5 0.364 423.9 1.803 400.6 0.410 422.6 . . . . . . 1.682 1.814 3.945 12.36 561.0 203.2
28-F2-3 199.3 0.338 422.4 0.484 401.6 0.412 418.6 0.398 391.2 1.945 2.019 3.667 12.39 559.5 203.2
28-F3-1 204.2 0.282 420.7 0.389 402.2 0.398 402.8 . . . . . . 1.915 2.130 3.635 12.39 555.9 203.2
28-F3-2 203.9 0.295 420.9 0.379 401.9 0.400 406.3 . . . . . . 1.918 2.056 3.743 12.42 558.1 203.2
28-F3-3 208.9 0.267 420.1 0.318 403.3 0.396 407.1 0.390 394.4 1.951 2.109 3.666 12.49 556.2 203.2
Mean 202.3 0.317 423.5 0.648 403.9 0.406 414.2 0.396 394.8 1.905 2.069 3.708 12.36 558.8
Standard Deviation 3.4 0.033 2.7 0.492 2.6 0.007 7.4 0.006 3.8 0.096 0.109 0.096 0.09 1.8
Range 11.6 0.098 7.0 1.485 7.1 0.018 21.1 0.011 7.6 0.317 0.385 0.321 0.30 5.1
Minimum 197.3 0.267 420.1 0.318 400.6 0.396 402.8 0.390 391.2 1.682 1.814 3.624 12.19 555.9
Maximum 208.9 0.364 427.1 1.803 407.8 0.414 423.8 0.401 398.8 1.999 2.198 3.945 12.49 561.0
Count 99999993399999
Both Flanges 28
Location Mill Certificate Properties
Elongation
(%)
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
 
 
Table A-27:  Summary of Plate 28 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
29 S2, S2-S A572 345 7.938 430 565
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
29-W4-1 195.3 0.295 428.2 0.667 411.4 0.415 418.0 . . . . . . 2.216 2.497 3.235 12.18 555.9 203.2
29-W4-2 194.9 0.277 433.4 0.414 409.4 0.412 413.5 . . . . . . 2.355 2.624 2.915 12.25 554.8 203.2
29-W4-3 208.3 0.314 428.7 0.406 410.2 0.401 414.7 0.396 404.2 2.135 2.204 3.453 12.34 557.2 203.2
29-W6-1 185.0 0.348 418.6 0.553 406.1 0.424 411.6 . . . . . . 1.614 1.665 3.880 12.32 559.8 203.2
29-W6-2 198.8 0.363 430.5 0.500 412.4 0.416 428.6 . . . . . . 1.827 1.950 3.511 12.22 562.0 203.2
29-W6-3 200.2 0.334 429.8 1.547 407.3 0.411 419.7 0.400 397.2 1.452 1.852 3.522 12.04 562.4 203.2
29-W8-1 174.9 0.393 425.4 0.961 411.5 0.442 423.6 . . . . . . 1.663 1.926 3.420 12.26 565.6 203.2
29-W8-2 195.1 0.376 438.1 0.469 421.8 0.421 433.7 . . . . . . 1.834 2.152 3.241 12.28 565.5 203.2
29-W8-3 202.7 0.342 435.1 0.445 416.4 0.413 427.8 0.405 412.0 1.916 2.104 3.183 12.31 564.1 203.2
29-W3-1 195.3 0.286 441.2 0.386 412.9 0.418 422.0 . . . . . . 1.923 2.509 3.133 12.24 556.1 203.2
29-W3-2 204.1 0.248 446.8 1.498 418.0 0.412 429.1 . . . . . . 2.251 2.544 3.175 . . . 560.8 203.2
29-W3-3 210.5 0.230 445.7 0.708 424.7 0.407 432.2 0.399 414.5 2.373 2.455 3.219 12.15 562.8 203.2
29-W5-1 200.9 0.279 442.1 0.368 408.1 0.412 419.3 . . . . . . 1.682 1.976 3.302 12.21 557.7 203.2
29-W5-2 190.3 0.261 432.9 0.353 408.1 0.418 415.5 . . . . . . 1.657 1.970 3.157 11.90 551.0 203.2
29-W5-3 206.9 0.266 442.7 0.336 416.6 0.406 424.4 0.400 410.8 1.634 1.847 3.598 12.16 566.8 203.2
29-W7-1 204.8 0.275 457.9 0.385 428.6 0.413 435.2 . . . . . . 2.096 2.392 2.986 12.25 564.3 203.2
29-W7-2 200.2 0.263 449.8 1.334 417.3 0.416 431.2 . . . . . . 2.075 2.385 2.826 12.26 556.8 203.2
29-W7-3 215.5 0.252 445.0 0.910 426.5 0.403 434.1 0.393 412.3 2.096 2.352 2.989 12.30 564.0 203.2
Mean 199.1 0.300 437.3 0.680 414.8 0.415 424.1 0.399 408.5 1.933 2.189 3.264 12.22 560.4
Standard Deviation 9.5 0.048 9.9 0.404 6.9 0.009 7.7 0.004 6.5 0.279 0.289 0.265 0.11 4.5
Range 40.7 0.163 39.4 1.211 22.5 0.041 23.6 0.012 17.2 0.921 0.959 1.054 0.45 15.8
Minimum 174.9 0.230 418.6 0.336 406.1 0.401 411.6 0.393 397.2 1.452 1.665 2.826 11.90 551.0
Maximum 215.5 0.393 457.9 1.547 428.6 0.442 435.2 0.405 414.5 2.373 2.624 3.880 12.34 566.8
Count 18 18 18 18 18 18 18 6 6 18 18 18 17 18
Tension Tests (LT direction:  longitudinal axis normal to the direction of rolling)
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Web 23
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-28:  Summary of Plate 29 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
30 B7 A572 345 15.875 389 531
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
30-F1-1 209.1 0.217 402.8 1.595 375.8 0.387 389.5 . . . . . . 1.365 1.595 3.621 12.27 527.2 203.2
30-F1-2 210.2 0.197 408.0 0.210 382.3 0.384 390.3 . . . . . . 1.265 1.634 3.230 . . . 531.4 203.2
30-F1-3 217.3 0.205 407.6 0.266 379.8 0.379 389.7 0.373 376.9 1.394 1.486 3.509 12.44 530.3 203.2
30-F2-1 213.7 0.210 411.9 0.284 375.5 0.381 387.1 . . . . . . 1.144 1.533 3.299 12.33 530.9 203.2
30-F2-2 210.2 0.211 412.2 0.252 385.0 0.386 389.4 . . . . . . 1.351 1.579 3.616 12.44 531.5 203.2
30-F3-1 216.9 0.220 410.9 0.299 385.1 0.381 388.1 . . . . . . 1.211 1.590 3.363 12.30 529.1 203.2
30-F3-2 211.7 0.214 410.0 0.318 380.5 0.384 387.9 . . . . . . 1.263 1.556 3.378 12.39 529.1 203.2
30-F3-3 208.0 0.208 417.7 1.594 386.8 0.393 399.4 0.383 379.6 1.335 1.594 3.359 . . . 534.3 203.2
Mean 212.1 0.210 410.1 0.602 381.4 0.384 390.2 0.378 378.3 1.291 1.571 3.422 12.36 530.5
Standard Deviation 3.5 0.007 4.3 0.613 4.2 0.004 3.9 0.007 1.9 0.085 0.045 0.144 0.07 2.1
Range 9.3 0.023 14.9 1.385 11.3 0.013 12.3 0.010 2.7 0.250 0.148 0.391 0.17 7.0
Minimum 208.0 0.197 402.8 0.210 375.5 0.379 387.1 0.373 376.9 1.144 1.486 3.230 12.27 527.2
Maximum 217.3 0.220 417.7 1.595 386.8 0.393 399.4 0.383 379.6 1.394 1.634 3.621 12.44 534.3
Count 88888882288868
30-F2-3-1 202.0 0.206 414.8 1.067 395.6 0.397 399.9 0.391 386.2 0.996 1.067 4.692 50.8
30-F2-3-2 201.7 0.202 415.9 0.766 392.4 0.384 397.0 0.377 383.2 1.392 1.504 5.667 50.8
30-F2-3-3 204.2 0.202 423.8 0.577 389.6 0.382 398.4 0.375 382.4 1.136 1.263 5.080 50.8
Mean 202.6 0.203 418.2 0.803 392.5 0.388 398.4 0.381 383.9 1.174 1.278 5.146
Standard Deviation 1.4 0.002 4.9 0.247 3.0 0.008 1.4 0.009 2.0 0.201 0.219 0.491
Range 2.5 0.004 9.0 0.490 6.0 0.015 2.9 0.016 3.9 0.397 0.437 0.975
Minimum 201.7 0.202 414.8 0.577 389.6 0.382 397.0 0.375 382.4 0.996 1.067 4.692
Maximum 204.2 0.206 423.8 1.067 395.6 0.397 399.9 0.391 386.2 1.392 1.504 5.667
Count 333333 33333
Compression Tests
Statistics
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Comp. Flange 24
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-29:  Summary of Plate 30 Tension and Compression Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
31 B8 A572 345 19.050 378 526
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
31-F4-1 212.5 0.206 395.3 0.307 363.5 0.379 380.0 . . . . . . 1.335 1.574 3.376 12.30 515.1 203.2
31-F4-2 207.0 0.200 396.5 0.228 367.2 0.383 377.4 . . . . . . 1.368 1.526 3.623 12.32 514.6 203.2
31-F5-1 206.1 0.209 392.2 0.527 365.6 0.385 376.3 . . . . . . 1.440 1.650 3.667 12.23 513.4 203.2
31-F5-2 211.4 0.205 400.2 0.228 370.0 0.381 378.0 . . . . . . 1.285 1.617 3.295 12.40 516.7 203.2
31-F5-3 207.2 0.200 393.6 0.238 364.3 0.381 374.4 . . . . . . 1.347 1.578 3.410 12.35 516.6 203.2
31-F6-1 208.3 0.195 400.8 1.477 365.7 0.381 378.3 . . . . . . 1.187 1.477 3.395 12.05 516.3 203.2
31-F6-2 205.6 0.200 389.1 1.560 366.6 0.384 377.9 . . . . . . 1.302 1.560 3.326 12.02 513.7 203.2
31-F6-3 208.0 0.201 401.2 0.883 370.2 0.381 376.1 0.374 361.6 1.456 1.639 3.612 12.38 514.1 203.2
Mean 208.3 0.202 396.1 0.681 366.6 0.382 377.3 0.374 361.6 1.340 1.578 3.463 12.26 515.1
Standard Deviation 2.5 0.004 4.4 0.563 2.4 0.002 1.7 . . . . . . 0.086 0.058 0.147 0.15 1.3
Range 6.9 0.014 12.0 1.332 6.7 0.006 5.6 . . . . . . 0.269 0.173 0.372 0.38 3.3
Minimum 205.6 0.195 389.1 0.228 363.5 0.379 374.4 0.374 361.6 1.187 1.477 3.295 12.02 513.4
Maximum 212.5 0.209 401.2 1.560 370.2 0.385 380.0 0.374 361.6 1.456 1.650 3.667 12.40 516.7
Count 88888881188888
31-F4-3-1 204.9 0.207 399.0 1.239 372.5 0.374 378.3 0.366 362.6 1.116 1.239 4.990 50.8
31-F4-3-2 205.2 0.211 395.3 1.216 370.6 0.363 378.3 0.358 367.2 1.119 1.228 5.033 50.8
31-F4-3-3 201.4 0.211 390.4 1.266 367.5 0.384 375.8 0.378 362.6 1.185 1.266 5.358 50.8
Mean 203.8 0.210 394.9 1.241 370.2 0.374 377.4 0.367 364.1 1.140 1.244 5.127
Standard Deviation 2.1 0.002 4.3 0.025 2.5 0.010 1.4 0.010 2.6 0.039 0.020 0.201
Range 3.8 0.004 8.6 0.050 5.0 0.021 2.5 0.020 4.6 0.070 0.038 0.367
Minimum 201.4 0.207 390.4 1.216 367.5 0.363 375.8 0.358 362.6 1.116 1.228 4.990
Maximum 205.2 0.211 399.0 1.266 372.5 0.384 378.3 0.378 367.2 1.185 1.266 5.358
Count 333333 33333
Compression Tests
Statistics
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Comp. Flange 26
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-30:  Summary of Plate 31 Tension and Compression Test Results 
 
   
Table 7.1-32:  Summary of Plate 32 Tension Test Results
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
32 MV1, MV2 A572 345 19.050 458 620
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
32-F1-3 213.5 0.240 484.4 0.305 447.2 0.411 452.1 0.406 442.5 1.110 1.351 4.511 11.72 622.2 203.2
32-F1-4 218.3 0.260 477.3 0.315 449.6 0.405 451.0 0.401 443.0 1.033 0.993 4.971 8.19 615.6 203.2
32-F2-1 209.6 0.273 452.5 0.317 434.5 0.416 433.4 0.413 428.0 0.897 0.953 5.238 11.76 612.6 203.2
32-F2-2 205.4 0.293 448.8 0.342 429.4 0.407 432.5 0.402 423.1 0.849 0.896 5.307 11.75 611.2 203.2
32-F3-1 222.5 0.228 466.5 0.279 438.0 0.397 441.2 0.393 432.0 0.851 1.032 4.976 11.75 619.6 203.2
32-F3-2 228.8 0.226 468.3 0.283 438.6 0.392 440.4 0.389 432.5 0.908 1.012 5.242 11.73 620.3 203.2
Mean 216.3 0.3 466.3 0.3 439.5 0.4 441.8 0.4 433.5 0.9 1.0 5.0 11.2 616.9
Standard Deviation 8.6 0.0 13.8 0.0 7.6 0.0 8.4 0.0 7.9 0.1 0.2 0.3 1.4 4.5
Range 23.4 0.1 35.6 0.1 20.2 0.0 19.6 0.0 19.9 0.3 0.5 0.8 3.6 11.1
Minimum 205.4 0.2 448.8 0.3 429.4 0.4 432.5 0.4 423.1 0.8 0.9 4.5 8.2 611.2
Maximum 228.8 0.3 484.4 0.3 449.6 0.4 452.1 0.4 443.0 1.1 1.4 5.3 11.8 622.2
Count 6666666666666
Both Flanges 21
Location Mill Certificate Properties
Elongation
(%)
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
 
 
Table A-31:  Summary of Plate 32 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
33 MV1, MV2 A572 345 7.938 425 506
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
33-W3-1 213.5 0.200 422.6 1.196 393.1 0.388 401.0 0.384 392.9 2.402 2.963 1.789 12.42 472.8 203.2
33-W3-2 214.1 0.205 430.4 2.262 396.8 0.377 401.0 0.374 394.1 2.684 2.960 2.170 12.34 476.7 203.2
33-W5-1 214.0 0.210 446.1 1.572 407.5 0.392 412.5 0.388 403.3 2.305 2.446 2.484 12.49 491.4 203.2
33-W5-2 214.5 0.206 439.6 1.573 408.9 0.392 410.9 0.388 402.4 2.422 2.646 2.233 . . . 493.9 203.2
33-W7-1 215.1 0.202 434.4 1.614 408.1 0.392 412.4 0.388 404.3 2.527 3.168 1.745 12.32 481.5 203.2
33-W7-2 214.6 0.205 438.4 2.644 404.8 0.392 411.7 0.388 403.9 2.569 2.913 2.132 . . . 485.3 203.2
33-W2-1 216.0 0.197 419.7 0.579 394.6 0.386 400.9 0.382 393.2 2.829 3.301 1.562 12.22 474.1 203.2
33-W2-2 214.6 0.193 419.5 0.263 396.2 0.385 397.5 0.382 389.9 2.956 3.269 1.875 11.06 473.4 203.2
33-W4-1 215.3 0.207 444.9 0.524 408.7 0.390 409.5 0.387 401.6 2.150 2.725 1.919 . . . 492.8 203.2
33-W4-2 214.1 0.211 449.1 0.791 409.8 0.393 414.2 0.390 406.5 2.290 2.680 2.050 12.19 492.0 203.2
33-W6-1 218.8 0.205 447.6 2.623 411.2 0.381 418.2 0.377 410.1 2.061 2.623 1.951 12.26 492.8 203.2
33-W6-2 216.2 0.207 448.7 2.593 401.7 0.412 415.7 0.409 407.6 2.241 2.589 2.178 12.14 492.5 203.2
Mean 215.1 0.204 436.7 1.519 403.4 0.390 408.8 0.386 400.8 2.453 2.857 2.007 12.16 485.0
Standard Deviation 1.4 0.005 11.3 0.868 6.6 0.009 6.9 0.009 6.6 0.271 0.282 0.251 0.43 8.7
Range 5.3 0.018 29.6 2.381 18.1 0.035 20.7 0.035 20.2 0.894 0.855 0.922 1.43 21.1
Minimum 213.5 0.193 419.5 0.263 393.1 0.377 397.5 0.374 389.9 2.061 2.446 1.562 11.06 472.8
Maximum 218.8 0.211 449.1 2.644 411.2 0.412 418.2 0.409 410.1 2.956 3.301 2.484 12.49 493.9
Count 12 12 12 12 12 12 12 12 12 12 12 12 9 12
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Tension Tests (LT direction:  longitudinal axis normal to the direction of rolling)
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Web 36
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-32:  Summary of Plate 33 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
34 MV3, MV4 A572 345 23.813 396 545
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
34-F6-2a 206.1 0.355 394.7 0.510 388.6 0.390 389.7 0.384 377.2 0.712 0.830 4.026 12.488 546.7 203.2
34-F6-1-1R 219.0 0.183 380.1 0.241 361.5 0.368 368.6 0.363 356.3 0.584 0.741 4.221 13.065 535.9 50.8
34-F6-1-2R 214.9 0.191 380.7 0.241 363.3 0.382 369.5 0.377 358.6 0.614 0.675 4.322 13.561 536.8 50.8
34-F6-1-3R 207.8 0.197 375.2 0.245 360.9 0.363 366.7 0.358 356.7 0.533 0.662 4.521 12.423 537.9 50.8
Mean 212.0 0.2 382.7 0.3 368.6 0.4 373.6 0.4 362.2 0.6 0.7 4.3 12.9 539.4
Standard Deviation 6.1 0.1 8.4 0.1 13.4 0.0 10.8 0.0 10.1 0.1 0.1 0.2 0.5 5.0
Range 12.9 0.2 19.5 0.3 27.7 0.0 23.0 0.0 20.9 0.2 0.2 0.5 1.1 10.8
Minimum 206.1 0.2 375.2 0.2 360.9 0.4 366.7 0.4 356.3 0.5 0.7 4.0 12.4 535.9
Maximum 219.0 0.4 394.7 0.5 388.6 0.4 389.7 0.4 377.2 0.7 0.8 4.5 13.6 546.7
Count 44444 44444 44
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Both Flanges 23
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-33:  Summary of Plate 34 Tension Test Results 
 
   
Plate Section Steel Nominal Nominal
Number Mark Type Strength Thickness F
y
F
u
(MPa)(m)(MPa)(MPa)
35 MV3, MV4 A572 345 7.938 425 506
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa) ? (%) ? (MPa) (mm)
35-W9-1 218.2 0.192 419.0 1.258 397.7 0.384 402.3 0.381 395.1 2.249 3.152 1.557 12.18 473.7 203.2
35-W9-2 213.8 0.194 415.6 0.202 388.6 0.383 391.5 0.381 386.5 2.680 3.127 2.047 12.47 466.7 203.2
35-W11-1 218.1 0.211 451.5 0.273 411.4 0.379 413.6 0.375 404.8 1.773 2.560 1.883 12.21 499.2 203.2
35-W11-2 214.6 0.208 444.0 0.734 407.0 0.392 411.1 0.388 402.4 2.041 2.485 1.943 12.27 492.4 203.2
35-W13-1 213.5 0.215 452.7 1.078 415.4 0.396 419.2 0.393 411.5 2.528 2.816 1.758 12.28 493.2 203.2
35-W13-3 213.2 0.211 450.2 1.492 413.2 0.395 416.9 0.390 406.0 2.003 3.124 1.427 . . . 490.8 203.2
35-W8-1 215.6 0.207 447.2 1.569 412.6 0.393 416.0 0.390 409.2 2.128 2.741 2.060 12.27 493.5 203.2
35-W8-2 215.8 0.206 449.3 0.910 410.6 0.391 413.7 0.387 405.4 2.293 2.536 2.337 12.25 494.5 203.2
35-W10-1 213.3 0.211 448.7 0.268 409.4 0.392 410.1 0.389 403.1 2.052 2.478 1.934 11.72 493.1 203.2
35-W10-2 213.2 0.210 441.3 0.372 407.4 0.391 408.1 0.386 397.9 2.014 2.491 1.933 11.71 492.7 203.2
35-W12-1 216.3 0.213 459.9 0.238 423.9 0.399 430.8 0.396 422.8 1.445 2.826 1.363 12.13 502.2 203.2
35-W12-2 215.0 0.217 466.3 0.291 431.7 0.403 436.6 0.398 425.9 2.257 2.680 2.135 . . . 509.5 203.2
Mean 215.1 0.208 445.5 0.724 410.7 0.392 414.2 0.388 405.9 2.122 2.751 1.865 12.15 491.8
Standard Deviation 1.8 0.008 14.7 0.521 11.0 0.007 11.8 0.006 10.9 0.324 0.262 0.291 0.24 11.5
Range 5.1 0.025 50.7 1.367 43.1 0.024 45.1 0.023 39.3 1.235 0.674 0.974 0.76 42.8
Minimum 213.2 0.192 415.6 0.202 388.6 0.379 391.5 0.375 386.5 1.445 2.478 1.363 11.71 466.7
Maximum 218.2 0.217 466.3 1.569 431.7 0.403 436.6 0.398 425.9 2.680 3.152 2.337 12.47 509.5
Count 12 12 12 12 12 12 12 12 12 12 12 12 10 12
Tension Tests (LT direction:  longitudinal axis normal to the direction of rolling)
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Specimen ID
Upper Yield Lower Yield 0.2% Offset Yield
Web 36
Location Mill Certificate Properties
Elongation
(%)
 
 
Table A-34:  Summary of Plate 35 Tension Test Results 
 
   
Sturctual Steel Tube Location Nominal Nominal Mill Certificate Properties
ID Strength Thickness F
y
F
u
Elongation
(MPa) (mm) (MPa) (MPa) (%)
674 Cross-Frames 448 6.350 555 666 18.0
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
674-J1-1 205.4 0.425 492.8 0.419 478.7 0.425 0.425 15.975 6.33 645.6 50.8
674-J1-2 231.5 0.421 570.6 0.417 561.0 0.421 0.421 6.969 5.88 666.9 50.8
674-J2-1 235.7 0.428 561.5 0.424 551.3 0.428 0.428 4.993 5.96 657.3 50.8
674-J2-2 217.6 0.387 477.9 0.379 456.2 0.387 0.387 18.093 5.93 647.1 50.8
674-J3-1 170.1 0.500 528.8 0.476 486.3 0.500 0.500 11.984 5.60 655.7 50.8
674-J3-2 215.4 0.409 484.9 0.403 471.0 0.409 0.409 17.128 6.19 649.5 50.8
Mean 212.6 0.428 519.4 0.420 500.7 0.428 0.428 12.524 5.98 653.7
Standard Deviation 23.6 0.038 40.3 0.032 44.2 0.038 0.038 5.513 0.25 8.0
Range 65.6 0.113 92.7 0.097 104.8 0.113 0.113 13.100 0.73 21.2
Minimum 170.1 0.387 477.9 0.379 456.2 0.387 0.387 4.993 5.60 645.6
Maximum 235.7 0.500 570.6 0.476 561.0 0.500 0.500 18.093 6.33 666.9
Count 6666666666
Outside 
Diameter
(mm)
Specimen ID
0.2% Offset Yield
127.0
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening Tensile StrengthStatic Yield
Steel
Type
A513 Grade 1026
 
 
Table A-35:  Summary of Structural Steel Tube 674 Tension Test Results 
 
   
Sturctual Steel Tube Location Nominal Nominal Mill Certificate Properties
ID Strength Thickness F
y
F
u
Elongation
(MPa) (mm) (MPa) (MPa) (%)
811 Cross-Frames 448 6.350 584 679 19.0
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
811-J1-1 234.1 0.399 529.1 0.394 513.9 0.399 0.399 6.465 6.85 634.8 50.8
811-J1-2 237.7 0.392 513.6 0.385 494.3 0.392 0.392 12.646 6.69 656.2 50.8
811-J2-2 268.6 0.359 504.5 0.353 483.5 0.359 0.359 10.503 6.85 628.8 50.8
811-J3-1 193.9 0.427 474.4 0.415 448.9 0.427 0.427 16.727 6.46 634.6 50.8
811-J3-2 205.8 0.439 531.5 0.430 512.8 0.439 0.439 8.327 6.52 647.0 50.8
Mean 228.0 0.403 510.6 0.395 490.7 0.403 0.403 10.934 6.67 640.3
Standard Deviation 29.3 0.031 23.1 0.030 26.6 0.031 0.031 3.983 0.18 11.1
Range 74.7 0.079 57.0 0.078 65.0 0.079 0.079 10.262 0.39 27.4
Minimum 193.9 0.359 474.4 0.353 448.9 0.359 0.359 6.465 6.46 628.8
Maximum 268.6 0.439 531.5 0.430 513.9 0.439 0.439 16.727 6.85 656.2
Count 5555555555
Specimen ID
0.2% Offset Yield
Outside 
Diameter
(mm)
127.000
Static Yield Tensile Strength
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Statistics
Strain Hardening
Steel
Type
A513 Grade 1026
 
 
Table A-36:  Summary of Structural Steel Tube 811 Tension Test Results 
 
   
Sturctual Steel Tube Location Nominal Nominal Mill Certificate Properties
ID Strength Thickness F
y
F
u
Elongation
(MPa) (mm) (MPa) (MPa) (%)
871 Cross-Frames 448 6.350
Young's Mod. Gage Length
E (GPa)
? (%) ? (MPa) ? (%) ? (MPa)
?
st
 (%) ?
apparent
 (%) E
st 
(GPa)
? (%) ? (MPa)
(mm)
871-J1-1 202.3 0.462 555.6 0.457 546.0 0.462 0.462 9.400 5.27 669.1 50.8
871-J1-2 216.5 0.404 486.3 0.395 466.5 0.404 0.404 17.916 5.86 643.9 50.8
871-j2-1 228.8 0.447 546.9 0.436 522.0 0.447 0.447 15.255 6.07 684.8 50.8
871-J2-2 202.3 0.431 553.4 0.423 533.0 0.431 0.431 12.813 5.85 673.9 50.8
871-J3-1 282.6 0.359 510.1 0.349 478.6 0.359 0.359 18.814 6.07 674.0 50.8
871-J3-2 195.7 0.484 546.8 0.471 520.9 0.484 0.484 12.510 6.00 671.3 50.8
Mean 221.4 0.431 533.2 0.422 511.2 0.431 0.431 14.451 5.85 669.5
Standard Deviation 32.3 0.045 28.4 0.044 31.5 0.045 0.045 3.568 0.30 13.6
Range 86.9 0.125 69.4 0.122 79.5 0.125 0.125 9.414 0.80 40.8
Minimum 195.7 0.359 486.3 0.349 466.5 0.359 0.359 9.400 5.27 643.9
Maximum 282.6 0.484 555.6 0.471 546.0 0.484 0.484 18.814 6.07 684.8
Count 6666666666
Outside 
Diameter
Specimen ID
0.2% Offset Yield
(mm)
127.0
Statistics
Static Yield Strain Hardening Tensile Strength
Tension Tests (L direction:  longitudinal axis in the direction of rolling)
Steel
Type
A513 Grade 1026
 
 
Table A-37:  Summary of Structural Steel Tube 871 Tension Test Results
   292
The matrix of tension test results was intended to include the following variables:  
steel grade, plate thickness and specimen orientation. However, due to the volume of 
tension testing additional variables were introduced into the results. These parameters 
include steel manufacturer, testing laboratory/load frame and data acquisition instrument 
gage length. These additional parameters are discussed when their effect is manifested in 
the test results.  
A.2.1 Yield Strength Results 
Modifying the E8 Standard by SSRC Technical Memorandum No. 7 permits the 
determination of up to four individual yield strengths from each test record. The offset 
yield strength is determined by the intersection of the stress-strain record with a line 
parallel to the exhibited initial modulus but offset 0.2% in strain. The upper yield strength 
is the first maximum stress associated with discontinuous yielding. The lower yield 
strength is the minimum stress recorded during discontinuous yielding neglecting any 
transient effects. Finally, the static yield strength is determined by essentially eliminating 
the loading rate effect on specimen behavior. 
A.2.1.1 Offset Yield Strength 
The offset yield strength mean and standard deviation for all A572 and A852 tension 
tests were 410.6 ? 25.7 MPa (59.55 ? 3.73 ksi) and 693.9 ? 47.9 MPa (100.64 ? 6.95 
ksi), respectively. As expected for both steel grades, the thicker flange plates displayed 
lower yield strengths than the thinner web plates. Test specimen orientation, either in the 
direction of plate rolling (longitudinal) or normal to the direction of plate rolling 
(transverse) did not influence test results. A summary of these results is contained in 
Tables A-38 and A-39 
   293
Sample 
Description 
All 
Plates 
Web Plates 
(thickness ? 12.7 mm) 
Flange Plates
Specimen 
Orientation 
 Longitudinal Transverse Longitudinal 
Strength 
Statistic     
Mean (MPa) 410.6 416.5 417.8 400.7 
Standard 
Deviation 
(MPa) 
25.7 25.9 26.3 21.7 
 
Offset 
Yield 
Number of 
Tests 
248 72 77 99 
Mean (MPa) 425.7 430.8 433.1 415.0 
Standard 
Deviation 
(MPa) 
26.8 25.4 28.8 22.8 
 
Upper 
Yield 
Number of 
Tests 
236 77 72 87 
Mean (MPa) 406.3 412.4 411.7 396.6 
Standard 
Deviation 
(MPa) 
25.0 24.9 25.7 21.5 
 
Lower 
Yield 
Number of 
Tests 
237 77 72 88 
Mean (MPa) 398.3 404.9 403.6 387.4 
Standard 
Deviation 
(MPa) 
25.9 25.0 26.5 22.6 
 
Static Yield 
Number of 
Tests 
212 71 66 75 
Mean (MPa) 551.2 545.3 542.3 562.1 
Standard 
Deviation 
(MPa) 
32.5 35.2 31.5 27.8 
 
Tensile 
Number of 
Tests 
247 76 72 99 
 
Table A-38:  A572 Steel Tension Testing Statistics 
 
   294
 
Sample 
Description 
All 
Plates 
Web Plates 
(thickness ? 12.7 mm) 
Flange Plates
Specimen 
Orientation 
 Longitudinal Transverse Longitudinal 
Strength 
Statistic     
Mean (MPa) 693.9 711.2 713.6 644.7 
Standard 
Deviation 
(MPa) 
47.9 45.7 41.0 15.4 
 
Offset 
Yield 
Number of 
Tests 
44 16 16 12 
Mean (MPa) 678.8 697.1 698.8 627.6 
Standard 
Deviation 
(MPa) 
47.9 43.0 40.9 15.0 
 
Static Yield 
Number of 
Tests 
44 16 16 12 
Mean (MPa) 793.5 803.1 801.6 770.0 
Standard 
Deviation 
(MPa) 
42.7 49.0 44.4 18.4 
 
Tensile 
Number of 
Tests 
44 16 16 12 
 
Table A-39:  A852 Steel Tension Testing Statistics 
 
The average yield strength for all A572 tension tests, 410.6 MPa, was very near the 
average yield strength of 420 MPa reported on the mill certificates that accompanied the 
steel plate from the producer and represents a consistent 19% over-strength when 
normalized by the nominal specified yield strength for this material. However, the 
average yield strength for all A852 tension tests, 693.9 MPa, was well in excess of an 
average mill certification reported value of 598 MPa. The A852 over-strength apparent in 
all tension tests averages 43%. This strength level is significantly greater than the over-
strength expected based on the mill certification data. The mill certification data suggests 
an average over-strength of approximately 23% which is much more consistent with the 
   295
A572 over-strength results. No explanation as to the considerable difference between the 
physical test data and the mill certification test data which were both produced in 
accordance with the same testing standard is available.  
A.2.1.2 Upper Yield Strength 
Upper yield strength is defined by the E8 Standard as the first stress maximum 
associated with discontinuous yielding prior to the onset of strain hardening. Figure A-37 
shows a typical tension test records for the A572 and A852 steel specimens tested as a 
part of this program as well as typical tension test records for HPS 485W and HPS 690W 
steels. The A572 and HPS steels exhibit well defined yield plateaus which are clearly 
evident in the figure. For steels that inelastically deform in this manner it is possible to 
determine upper and lower yield strengths that will permit engineers to better understand 
the materials behavior. 
   
Strain (%)
0 5 10 15 20 25 30
Stress (MPa)
0
200
400
600
800
1000
HPS 485W
HPS 690W
A852
A572
 
 
Figure A-37:  Typical Tension Test Records
   297
For the A572 specimens tested in this program the average upper yield strength was 
425.7 MPa (61.74 ksi) which is approximately a 4% increase compared to the offset yield 
strength. All of the conclusions and trends reported for the offset yield strength results 
also apply to the A572 upper yield strength values. 
The A852 specimens exhibited the round-house type curve shown in Figure A-37. 
With sufficient scrutiny of the results, upper yield strength can sometimes be identified in 
the A852 test records. However, these initial instances of discontinuous yielding are 
associated with very slight load reductions and are immediately followed by strain 
hardening of the material and therefore it is inappropriate to report these values.  
The HPS steel test records are included on Figure A-37 as an aside. The American 
Association of State Highway and Transportation Officials (AASHTO), which maintains 
the codes and specifications that govern bridge design in the United States, recently 
replaced A852 and A514 steels, which have nominal yield strengths of 485MPa and 
690MPa respectively, with HPS 485W and HPS 690W as the approved steels for bridge 
construction at those strength levels. The change was made in part to bring more 
uniformity to the post yield behavior of steels used to construct bridges.  
A.2.1.3 Lower Yield Strength 
Lower yield strength is defined by the E8 Standard as the minimum stress recorded 
during discontinuous yielding, ignoring transient effects. The average lower yield 
strength for the A572 specimens was 406.3 MPa (58.93 ksi). This strength is generally 
used to establish the stress level of the yield plateau for stress-strain relationship models 
for materials of this type. 
   298
No lower yield strength results are reported for the A852 test results for the reasons 
discussed in Section A.1.2.1.2 above. 
A.2.1.4 Static Yield Strength 
Static Yield Strength is defined by SSRC Technical Memorandum No. 7 as the yield 
strength of a material absent of any strain-rate effects. Procedures for determining the 
static yield strength for mild steels that exhibit either a yield plateau or a round-house 
tensile stress-strain behavior are discussed in the Technical Memorandum.  
The A572 specimens had an average static yield strength of 398.3 MPa (57.77 ksi). 
This strength level is approximately 2% less than the lower yield strengths and 
approximately 3% less than the offset yield strengths determined for this steel. These 
reductions account for the strain rate effect that is inherent to the lower and offset yield 
strength results. 
The A852 specimens displayed an average static yield strength of 678.8 MPa (98.45 
ksi) which was only 2% less than the average offset yield strength for this material. 
No functional relationship between individual test strain-rate and the static 
yield/offset yield or static yield/lower yield ratio was evident from the test data.  
A.2.2 Yield Point Elongation Results 
Yield Point Elongation is defined by the E8 Standard as the strain, expressed in 
percent, separating the stress-strain curve?s first point of zero slope from the point of 
transition from discontinuous yielding to uniform strain hardening. Simply, this is the 
strain capacity of the yield plateau. The A572 specimens had an average yield point 
elongation of 1.42%. As discussed previously, the A852 specimens did not exhibit a yield 
plateau. 
   299
A.2.3 Tensile Strength Results 
Tensile Strength is defined by the E8 Standard as the maximum stress recorded 
during a tension test. The average tensile strength for A572 specimens was 551.2 MPa 
(79.94 ksi) which was produced at a strain of approximately 14.38%. The average offset 
yield-to-tensile strength ratio for this material was 0.75. This ratio was very consistent 
and had an associated standard deviation of 0.04. 
The average tensile strength for the A852 specimens was 793.5 MPa (115.09 ksi) 
which occurred at approximately 6.00% strain. The average offset yield-to-tensile 
strength ratio for the A852 specimens was more consistent but a significantly higher 
value of 0.87 (standard deviation of 0.02).  
A.3 Compression Testing 
Compression testing was conducted in accordance with ASTM E9, Standard Test 
Methods of Compression Testing of Metallic Materials at Room Temperature. These tests 
were limited to specimens taken from the steel plates that where used in the fabrication of 
the CSBRP bending test component compression flanges. Three specimens from each of 
seven plates of A572 steel were tested for a total of twenty-one compression tests.  
The test data obtained using the E9 Standard may be used to determine yield strength, 
yield point elongation and compressive strength. However, since the steels used in this 
program do not fail in compression by shattering, the compressive strength is a value that 
is dependent on concurrent strain and specimen geometry. Selection of this point from the 
stress-strain record is arbitrary and therefore results for compressive strength are not 
presented in this report. 
   300
As defined by the E9 Standard, medium-length cylindrical specimens were used for 
the compression testing. Medium-length specimens have an approximate length-to-
diameter ratio of 3.0 and are generally used to determine the compressive strength 
properties of steels. The diameter of each specimen was kept as near as possible, with 
allowances for machining, to the full thickness of the plate from which it was cut. 
Compression test specimens in this program had nominal thicknesses of 19mm (3/4 in.). 
Although SSRC Technical Memorandum No. 7 was developed to modify the E8 
Standard in order to eliminate the strain rate effects from tension test yield strength 
results, it was also successfully employed during the compression testing for the same 
purpose. Plate specific static yield strength results, and all other individual compression 
test results can be see on Tables A-21 through A-25 and Tables A-30 and A-31. A 
summary of the compression test data appears on Table A-40. 
Strength Statistic  
Mean (MPa) 425.4 
Standard Deviation (MPa) 27.0 
 
Offset Yield 
Number of Tests 21 
Mean (MPa) 441.7 
Standard Deviation (MPa) 26.3 
 
Upper Yield 
Number of Tests 21 
Mean (MPa) 417.1 
Standard Deviation (MPa) 26.4 
 
Lower Yield 
Number of Tests 21 
Mean (MPa) 404.7 
Standard Deviation (MPa) 24.3 
 
Static Yield 
Number of Tests 19 
 
Table A-40:  A572 Steel Compression Testing Statistics. 
 
A significant assumption of the structural engineering community is that the steels 
commonly used for the design and construction of buildings and bridges behave 
   301
similarly, if not identically, within the tension and compression stress-strain domains. 
The purpose of these compression tests within this program was to either validate this 
assumption, or to provide sufficient data to adequately construct the compressive stress-
strain relationship for A572 steel plate for use in the analysis of the data and finite 
element modeling. 
A.3.1 Yield Strength Results 
Since these results, like the tension test results, are engineering stress-strain 
quantities, small increases in all strength categories are expected. These increases account 
for the difference in cross-sectional area of a necking tension test specimen and a 
barreling compression test specimen. However, once these properties are converted to a 
true stress-strain relationship the differences become slight as is demonstrated in Section 
4 of this dissertation. 
A.3.1.1 Offset Yield Strength 
The offset yield strength for compression tests were determined using a 0.2% initial 
modulus strain offset. The average offset yield strength for the compression tests was 
425.4 MPa (61.70 ksi) which represents approximately a 3.6% increase compared to the 
appropriate tension test result.  
A.3.1.2 Upper Yield Strength 
The average upper yield strength of the compression tests was 441.7 MPa (64.06 ksi). 
This strength level is 3.8% greater than the tension test result for upper yield strength. 
A.3.1.3 Lower Yield Strength 
The average compression test lower yield strength is 417.1 MPa (60.49 ksi). This 
strength represents a small, 2.6%, increase over the average tension test lower yield 
strength reported as 406.3 MPa (58.93 ksi). 
   302
A.3.1.4 Static Yield Strength 
Static yield strengths produced during the compression tests averaged 404.7 MPa 
(58.70 ksi). This represents only a slight 1.6% increase strength increase when compared 
to the tension test results.  
A.3.2 Yield Point Elongation Results 
Yield point elongation averaged 1.28% for the compression tests. This property was 
the most effected by the difference in test method between tension and compression 
testing. The tension test result of 1.42% represents an increase of almost 11% in strain 
capacity prior to strain hardening. 
A.4 Young?s Modulus Testing 
The Young?s Modulus testing was conducted in accordance with ASTM E111, 
Standard Test Method for Young?s Modulus, Tangent Modulus, and Chord Modulus. Ten 
(10) Young?s modulus tests were conducted as a part of this program. Parameters include 
steel grade and plate thickness. The E111 Standard was used without modification to 
conduct the testing. Standard plate-type tension specimens as described in Section A.1.2 
were selected as the test specimens since the testing was performed in the tension stress-
strain domain. 
Two independent methods of acquiring uniaxial test specimen deformation were 
used. On one side of each plate-type specimen was place a 6.35mm (1/4 inch) long 
electrical resistance strain gage. The strain gage data averages or smears the behavior of 
the steel under the length of the gage. On the opposite side of the test specimen a clip 
gage with a 50.8mm (2 inch) gage length was used. This device also reports the average 
behavior of the specimen but now over a length 8 times as long as the strain gage. 
   303
Three (3) sets of loadings and unloadings were recorded during each test. The results 
are shown in Table A-41. 
 
Young?s Modulus 
Mean Standard 
Deviation 
Number of 
Results 
Sample 
Description 
Data 
Acquisition 
Device 
Data Source 
(GPa) (GPa)  
Initial Slope 200.9 5.5 10 Clip Gage 
Unloading 
Slope 
209.4 4.4 10 
Initial Slope 204.7 0.6 10 
All 
Strain Gage 
Unloading 
Slope 
205.0 0.6 10 
Initial Slope 200.2 6.2 6 Clip Gage 
Unloading 
Slope 
210.1 4.3 6 
Initial Slope 204.9 0.7 6 
A572 Steel  
Strain Gage 
Unloading 
Slope 
205.3 0.7 6 
Initial Slope 202.1 4.8 4 Clip Gage 
Unloading 
Slope 
208.4 5.2 4 
Initial Slope 204.4 0.5 4 
A852 Steel 
Strain Gage 
Unloading 
Slope 
204.7 0.2 4 
 
Table A-41:  Young?s Modulus Testing Statistics 
 
   304
Qualified Young?s modulus results can also be obtained from both tension testing and 
compression testing. These results are summarized in Table A-42 
.  
Sample 
Description 
Specimen 
Orientation 
Girder 
Component
Modulus 
 
(GPa) 
Standard 
Deviation 
(GPa) 
Number of Tests 
Tension 
Tests 
All 201.5 14.4 292 
All 201.2 15.5 248 
All 200.2 17.5 176 
Webs 198.7 14.4 77 
Longitudinal 
Flanges 201.4 19.5 99 
 
A572 
Tension 
Tests 
Transverse All 203.5 8.8 72 
All 203.6 5.3 44 
All 204.9 5.7 28 
Webs 201.3 4.0 16 
Longitudinal 
Flanges 209.8 3.4 12 
 
A852 
Tension 
Tests 
Transverse All 201.3 3.7 16 
Compression 
Tests 
All 204.5 4.0 21 
Note:  Web plate thicknesses are less than or equal to 12.7mm (1/2 inch). 
 
Table A-42:  Young?s Modulus Statistics from Tension and Compression Testing 
 
A.4.1 Young?s Modulus Testing Results 
If the initial slope and unloading slope from each set of test data is averaged then the 
mean Young?s modulus for all tests performed is 205.2 GPa (29,762 ksi) from the clip 
gage data and 204.9 GPa (29,718 ksi) from the strain gage data. Table A-41 shows that 
the average results for steel type differ insignificantly from the average for the entire 
body of data. 
A.4.2 Young?s Modulus from Tension Testing 
Determining Young?s modulus from a tension test is permitted by the E111 Standard 
as long as the result is reported as being produced during such a test. The reason that the 
   305
result must be qualified is that specimen deformation during the single loading cycle of a 
tension test is often affected by the flatness of the specimen, the alignment of the data 
acquisition device, the alignment of the grips, and the seating of the specimen within the 
test frame.  
The average Young?s modulus determined from tension testing is 201.5 GPa (29,225 
ksi) and the associated standard deviation is 14.4 GPa (2089 ksi). Table A-42 illustrates 
that neither steel type, plate thickness [web plate thicknesses are less than or equal to 12.7 
mm (1/2 in.)] nor specimen orientation significantly effected the test results. 
A.4.3 Young?s Modulus from Compression Testing 
The average Young?s modulus determined during the compression testing was 204.5 
GPa (29,660 ksi).  
A.5 True Stress-Strain 
In order to elevate the accuracy of their predictions, finite element programs require 
true stress-strain relationships be constructed for the materials they are modeling. True 
stress-strain relationships are produced by modifying engineering stress-strain 
relationships that result from tension or compression testing for the necking or barreling 
of the specimen, respectively, as they undergo plastic deformation. It is particularly 
important to incorporate true stress-strain relationships into analytical models when 
materials will be loaded significantly beyond their proportional limit since a material?s 
cross-sectional dimensions can experience substantial changes from its original state.  
By their nature, the tension and compression tests described in Sections A.1.2 and 
A.1.3 and conducted as a part of this program produce engineering stress-strain 
   306
relationships. Conversion of those characteristics to true stress-strain was accomplished 
using the relationships derived in the following sections. 
A.5.1 True Strain 
Engineering strain, ?
e
, is classically defined as a non-dimensionalized change in 
length that relates the new length, L
i
, of a material to the original length, L
o
, with the 
following equation: 
1?=
?
=
o
i
o
oi
e
L
L
L
LL
?       Equation A-1 
True strain, ?
t
, is defined by the following differential:   
L
dL
d
t
=?         Equation A-2 
where the material?s length, L, is measured in the direction of the strain. The true 
strain in any direction results from integrating Equation A-2 over the change in length 
experienced by a material in that direction.  
?
?
?
?
?
?
?
?
==
?
o
i
L
L
t
L
L
L
dLi
o
ln?       Equation A-3 
Solving Equation A-1 for 
o
i
L
L
 and substituting the result into Equation A-3 produces 
the following relationship for converting engineering strain, ?
e
, to true strain, ?
t
. 
()1ln +=
et
??        Equation A-4 
A.5.2 True Stress 
Engineering stress, ?
e
, in a material is classically defined as the total load at any 
point, P, acting over the undeformed cross-sectional area, A
o
, of material normal to that 
force at that point. This relationship is represented by the following equation: 
   307
o
e
A
P
=?         Equation A-5 
True stress, ?
t
, is determined by distributing the same load, P, over the deformed area, 
A
i
. 
i
t
A
P
=?         Equation A-6 
As metallic materials exceed their yield strengths they plastically deform with 
negligible change in overall volume, V. During a tension test increases in length are offset 
by decreases in cross-sectional area. Likewise, during a compression test decreases in 
length are offset by increases in cross-sectional area. If an material?s volume remains 
constant and can be expressed as its cross-sectional area, A, times its concurrent length, L, 
then 
iiooio
LALAVV =?=       Equation A-7 
Solving Equation A-5 for the load P and Equation A-7 for the area A
i
, and then 
substituting for those expressions in Equation A-6 results in the following equation: 
?
?
?
?
?
?
?
?
=
o
i
et
L
L
??        Equation A-8 
Again solving Equation A-1 for the ratio 
o
i
L
L
 and substituting the result into Equation 
A-8 produces the following relationship for converting engineering stress, ?
e
, to true 
stress, ?
t
. 
()1+=
eet
???        Equation A-9 
  
   308
Appendix B.  Design Equations 
B.1 A Summary of the Guide Specification Provisions for the Design of Non-
Composite I-Girders in Flexure 
The following section summarizes the Guide Specification provisions for determining 
critical flange and web longitudinal stresses, 
cr
F , in singly symmetric horizontally curved 
I-girders. 
B.1.1 I-Girder Flanges 
The Guide Specification provisions are valid for I-girder flanges that meet the 
following criteria:  
ycl
Ff 5.0
1
?           
if ,33.0min(
ycbu
Ff ?  )117MPa  then 5.0
1
?
bu
l
f
f
 
fcb
bL 25?  
10
R
L
b
?  
Db
fc
15.0?  
wfc
tt 5.1?  
where: 
f
l1
 = total factored lateral flange bending stress at the section under consideration 
f
bu
 = largest computed factored average flange stress at the section under 
consideration 
F
yc
 = yield strength of the compression flange 
   309
L
b
 = unbraced arc length of the flange  
b
f
 = minimum flange width in the panel  
R = minimum girder radius within the panel  
b
fc
 = compression flange width at section under consideration  
D = web depth at section under consideration 
t
fc
 = compression flange thickness at section under consideration 
t
w
 = web thickness at section under consideration 
B.1.1.1 Partially Braced Compression Flanges 
? Compact Flanges 
For flanges that meet the following criteria: 
18?
fc
fc
t
b
 
MpaF
yc
345?  
the critical compressive longitudinal stress, 
cr
F , is the smaller of 
1cr
F
 
or 
2cr
F : 
wbbscr
FF ??=
1
       Equation B-1 
3
1
2
l
yccr
f
FF ?=        Equation B-2 
where:  
   310
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?=
E
F
b
L
FF
yc
fc
b
ycbs
2
2
9.0
31
?
     Equation B-3 
 
2
01.0
6
11
1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
++
=
R
L
b
L
b
L
b
fc
b
fc
b
b
?     Equation B-4 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?
?
?
?
?
?
?+=
yc
bs
b
fc
bb
bu
lb
w
F
F
b
L
R
L
f
f
R
L
?
?
1.03.0
1.01895.0
1
2
  Equation B-5 
and 0.1?
wb
?? . 
? Non-Compact Flanges 
For flanges that meet the following slenderness criteria: 
()
2302.1
1
?
+
?
lbufc
fc
ff
E
t
b
     Equation B-6 
the critical compressive longitudinal stress, 
cr
F  is the smaller of 
1cr
F
 
or 
2cr
F : 
wbbscr
FF ??=
1
       Equation B-7 
12 lyccr
fFF ?=        Equation B-8 
where 
bs
F  is given in Equation B-3 above and: 
   311
fc
bb
b
b
L
R
L
+
=
1
1
?        Equation B-9 
?
?
?
?
?
?
?
?
??
=
fc
b
bu
l
w
b
L
f
f
75
11
1
1
1
?       Equation B-10 
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?+
+
=
bu
l
b
fc
b
w
f
f
R
L
b
L
1
2
2
6.01
1.0000,830
95.0
?     Equation B-11 
and, if 0
1
?
bu
l
f
f
, then ( )
21
,min
www
??? = . Otherwise 
1ww
?? = . 
B.1.1.2 Partially Braced Tension Flanges 
For flanges that meet the following slenderness criteria: 
()
2302.1
1
?
+
?
lbufc
fc
ff
E
t
b
     Equation B-12 
the critical compressive longitudinal stress, 
cr
F  is the smaller of 
1cr
F
 
or 
2cr
F where: 
wbycr
FF ??=
1
       Equation B-13 
and where 
b
? , 
w
?  and 
2cr
F  are given by Equations B-4, B-5 and B-2, respectively.  
B.1.2 I-Girder Webs 
B.1.2.1 Unstiffened Webs  
For unstiffened webs that meet the following slenderness criteria: 
for mR 213?  
   312
100?
w
t
D
 
for mR 213>  
150)213(125.0100 ??+? R
t
D
w
 
the critical compressive longitudinal stress, 
cr
F,is: 
yc
w
cr
F
t
D
Ek
F ?
?
?
?
?
?
?
?
?
=
2
9.0
      Equation B-14 
where: 
k = bend-buckling coefficient = 
2
2.7
?
?
?
?
?
?
?
?
c
D
D
 
D
c
 = depth of web in compression  
B.1.2.2 Transversely Stiffened Webs 
For transversely stiffened webs that meet the following slenderness and stiffener 
spacing criteria: 
150?
w
t
D
 
for mR 213?  
Dd
o
?  
for mR 213>  
()DDRd
o
3)213(00506.00.1 ??+?  
the critical compressive longitudinal stress, 
cr
F , is given by Equation B-14 above but 
where: 
   313
k = bend-buckling coefficient = 
2
0.9
?
?
?
?
?
?
?
?
c
D
D
 
B.1.2.3 Transversely and Longitudinally Stiffened Webs 
For transversely and longitudinally stiffened webs that meet the transverse stiffener 
spacing requirements of Section B.1.2.2 and the following slenderness criteria: 
300?
w
t
D
 
the critical compressive longitudinal stress is given by Equation B-14 above but 
where the bend-buckling coefficient is: 
2
17.5
?
?
?
?
?
?
?
?
=
s
t
D
k
 for 4.0?
c
s
D
d
 
or 
2
64.11
?
?
?
?
?
?
?
?
?
=
sc
dD
D
k  for 4.0<
c
s
D
d
 
where: 
d
s
 = distance along web between longitudinal stiffener and compression flange 
B.2 A Summary of the Unified Design Method Equations for the Design of Non-
Composite I-Girders in Flexure 
The Unified Design Method provisions to determine the flange longitudinal stress 
limit, 
nf
F? , are valid for I-Girders that meet the following criteria: 
Compression flanges width, b
f
, shall be at least 30% of the depth of the web in 
compression, D
c
. 
Tension flanges shall meet the following slenderness requirement: 
   314
0.12
2
?
ft
ft
t
b
 
Webs shall meet the following slenderness requirements: 
For unstiffened or transversely stiffened webs 
150?
w
t
D
 
For longitudinally stiffened webs 
300?
w
t
D
 
For all strength limit state load combinations the governing design equation for 
longitudinal flange stress is: 
lbunf
ffF
3
1
+??        Equation B-15 
where 
yl
Ff 6.0?  
?
f
 = 1.00 
and 
n
F  is determined for either the compression flange, 
nc
F , or the tension flange, 
nt
F , by the provisions outlined below. 
B.2.1 Discretely Braced Compression Flanges 
The longitudinal compressive stress limit, 
ncf
F? , is the smaller of 
)(FLBncf
F?  or 
)(LTBncf
F?  determined from the Flange Local Buckling and Lateral Torsional Buckling 
limits. 
B.2.1.1 Flange Local Buckling 
If 
pff
?? ? , then the flange is compact and 
   315
ychbFLBnc
FRRF =
)(
       Equation B-16 
where 
fc
fc
f
t
b
2
=?  
yc
pf
F
E
38.0=?  
If 
pff
?? > , then the flange is non-compact and  
ychb
pfrf
pff
ych
yr
FLBnc
FRR
FR
F
F
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??=
??
??
11
)(
   Equation B-17 
where 
[ ]
ycywycyr
FFFF 5.0,7.0min >=  
yr
rf
F
E
56.0=?  
B.2.1.2 Lateral Torsional Buckling 
If 
pb
LL ? , then compact unbraced length and  
ychbLTBnc
FRRF =
)(
       Equation B-18 
where 
?
?
?
?
?
?
?
?
+
=
fcfc
wc
fc
t
tb
tD
b
r
3
1
112
 
yc
tp
F
E
rL 0.1=  
If 
rbp
LLL ?< , then non-compact unbraced length and 
   316
ychbychb
pr
pb
ych
yr
bLTBnc
FRRFRR
LL
LL
FR
F
CF ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??= 11
)(
 Equation B-19 
where 
[ ]
ycywycyr
FFFF 5.0,7.0min ?=  
yr
tr
F
E
rL ?=  
If 
rb
LL > , then slender unbraced length and  
ychbcrLTBnc
FRRFF ?=
)(
      Equation B-20 
where 
2
2
?
?
?
?
?
?
?
?
=
t
b
bb
cr
r
L
ERC
F
?
 
B.2.2 Discretely Braced Tension Flanges 
The longitudinal tensile stress limit, 
ntf
F? , is 
ythntf
FRF =?        Equation B-21 
 
 
 
   317
References 
 
AASHTO, 2004. LRFD Bridge Design Specifications, American Association of State 
Highway and Transportation Officials, 3
rd
 Edition with 2005 Interim Provisions, 
Washington, DC. 
 
AASHTO, 2003. Guide Specifications for Horizontally Curved Steel Girder Highway 
Bridges.  American Association of State Highway and Transportation Officials, 
Washington, DC. 
 
Adams, P.F., Lay, M.G. and Galambos, T.V., 1964. ?Experiments on High Strength Steel 
Members?, Fritz Engineering Laboratory Report No. 297.8, Lehigh University. 
 
Brennan, P.J. and Mandel, J.A., 1971. ?Analysis of Seekonk River Bridge Small Scale 
Structure Through Three Dimensional Mathematical Method and Structural Testing,? 
Syracuse University Report, Research Project HPR-2(111), Syracuse, NY. 
 
Brennan, P.J. and Mandel, J.A., 1974. ?Analysis of Small Scale Structure of Ramp P 
Over Interstate I291 in Springfield, Massachusetts, Through Three Dimensional 
Mathematical Method and Structural Testing,? Syracuse University Report, Research 
Project HPR-2(111), Syracuse, NY. 
 
Colville, J., 1972. ?Shear Connector Studies on Curved Girders?, University of Maryland 
Civil Engineering Research Report #45, College Park, MD. 
 
Culver, C.G. and Nasir, G., 1970. ?Instability of Horizontally Curved Members,? 
Pennsylvania Department of Highways Research Project No. 68-32. 
 
Daniels, J.H., Zettlemoyer, N., Abraham, D., and Batcheler, R.P., 1979. ?Fatigue of 
Curved Steel Bridge Elements ? Ultimate Strength Tests of Horizontally Curved Plate 
and Box Girders,? Lehigh University.  Pennsylvania Department of Transportation 
Report No. DOT-FH-11.8198.7. 
 
Donaldson, B.K., 1993. Analysis of Aircraft Structures:  An Introduction, McGraw-Hill. 
 
Duwadi, S.R., Grubb, M.A., Yoo, C.H., and Hartmann, J.L., 2000. ?Federal Highway 
Administration?s Horizontally Curved Steel Bridge Research Project,? Proceedings of the 
5
th
 International Bridge Engineering Conference, Transportation Research Board, Paper 
No. 5B0011, Tampa, FL. 
 
European Convention for Constructional Steelwork (ECCS), 1976. Manual on Stability 
of Steel Structures, 2
nd
 Edition, Publication No. 22. 
 
Farrar, C.R., and Duffey, T.A., 1998. ?Bridge Modal Properties Using Simplified Finite 
Element Analysis,? Journal of Bridge Engineering, American Society of Civil Engineers, 
Reston, VA. 
   318
 
Frank, K.H., George, D.A., Schluter, C.A., Gealy, S., and Horos, D.R., 1993. ?Notch 
Toughness Variability in Bridge Steel Plates?, National Cooperative Highway Research 
Council Report 355, Washington, DC. 
 
Fukomoto, Y., Itoh, Y., and Kubo, M., 1980.  ?Strength Variation of Laterally 
Unsupported Beams,? Journal of the Structural Division, American Society of Civil 
Engineers, Vol. 106, No. ST1, Reston, VA. 
 
Galambos, T.V., 1988. Guide to Stability Design Criteria for Metal Structures, 4
th
 
Edition, Wiley-Interscience. 
 
Galambos, T.V., 1968. Structural Members and Frames, Prentice-Hall. 
 
Grubb, M.A., and Hall, D.H., CSBRP work product report to be published. ?Curved Steel 
Bridge Research Project ? Volume II:  I-Girder Bending Component Tests,? Federal 
Highway Administration, Report No. FHWA-RD-XX-XXX, Washington, DC. 
 
Grubb, M.A., Yadlosky, J.M., Zureick, A.H., Hall, D.H., Yoo, C.H., and Duwadi, S.R., 
1995. ?FHWA Curved Steel Bridge Research Project,? Proceedings 13
th
 ASCE 
Structures Congress, American Society of Civil Engineers, Boston, MA. 
 
Hall, D.H., Grubb, M.A., and Yoo, C.H., 1999. ?Improved Design Specifications for 
Horizontally Curved Steel Girder Highway Bridges,? NCHRP Report 424, National 
Cooperative Highway Research Program, Washington, DC. 
 
Heins, C.P., 1975. Bending and Torsional Design in Structural Members, D.C. Heath and 
Company. 
 
Kuo, J.T.C., and Heins, Jr., C.P., 1971. ?Behavior of Composite Beams Subjected to 
Torsion?, University of Maryland Civil Engineering Research Report #39, College Park, 
MD. 
 
Kollbrunner, C.F., and Basler, K., 1969. Torsion in Structures, Springer-Verlag. 
 
Linzell, D.G., 1999. ?Studies of a Full-Scale Horizontally Curved Steel I-Girder Bridge 
System Under Self-Weight,? Ph.D. Thesis, School of Civil and Environmental 
Engineering, Georgia Institute of Technology, Atlanta, GA. 
 
Mozer, J., Cook, J., and Culver, C.G., 1975. ?Horizontally Curved Highway Bridges, 
Stability of Curved Plate Girders ? Report P3,? Federal Highway Administration, Report 
No. FHWA-RD-75-XXX, Washington, DC. 
 
Mozer, J., and Culver, C.G., 1975. ?Horizontally Curved Highway Bridges, Stability of 
Curved Plate Girders ? Report P1,? Federal Highway Administration, Report No. 
FHWA-RD-75-XXX, Washington, DC. 
   319
 
Mozer, J., Ohlson, R., and Culver, C.G., 1975. ?Horizontally Curved Highway Bridges, 
Stability of Curved Plate Girders ? Report P2,? Federal Highway Administration, Report 
No. FHWA-RD-75-XXX, Washington, DC. 
 
Nakai, H., Kitada, T., and Ohminami R., 1985. ?Experimental Study on Buckling and 
Ultimate Strength of Curved Girders Subject to Combined Loads of Bending and Shear,? 
Proceedings of Japan Society of Civil Engineers, No. 356/I-3. 
 
Nakai, H., and Kotoguchi, H., 1983. ?A Study on Lateral Buckling Strength and Design 
Aid for Horizontally Curved I-Girder Bridges,? Proceedings of Japan Society of Civil 
Engineers, No. 339. 
 
Shanmugam, N.E., Thevendran, V., Liew, J.Y.R., and Tan, L.O.,1995. ?Experimental 
Study on  Steel Beams Curved in Plan,? ASCE Journal of Structural Engineering, V121, 
N2, pp. 249-259. 
 
Shore, S. and Lapore, J.A., 1975. ?Horizontally Curved Highway Bridges ? Small Scale 
Model Tests,? Federal Highway Administration, Report No. FHWA-RD-93-133, 
Washington, DC. 
 
Spates, K.R. and Heins, Jr., C.P., 1968. ?The Analysis of Single Curved Girders with 
Various Loadings and Boundary Conditions,? University of Maryland Civil Engineering 
Research Report #20, College Park, MD. 
 
SSRC, 1991. ?Horizontally Curved Girders ? A Look to the Future,? Report of the 
Annual Task Group 14 Meeting, Structural Stability Research Council. 
 
Timoshenko, S.P., 1953. Collected Papers, McGraw-Hill. 
 
White, D.W. and Grubb, M.A., 2005. ?Unified Resistance Equations for Design of 
Curved and Tangent Steel Bridge I-Girders,? Transportation Research Board, 
Proceedings of the 84
th
 Annual Meeting, Washington, DC. 
 
White, D.W., Zureick, A.H., Phoawanich, N., and Jung, S.-K., 2001. ?Development of 
Unified Equations for Design of Curved and Straight Steel Bridge I Girders,? Final 
Report to American Iron and Steel Institute Transportation and Infrastructure Committee, 
Professional Service Industries, Inc. and the Federal Highway Administration, School of 
Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA. 
 
Zureick, A., Naqib, R., and Yadlosky, J. M., 1994. ?Curved Steel Bridge Research 
Project Report I, Synthesis,? Federal Highway Administration, Report No. FHWA-RD-
93-129, Washington, DC.