Concrete filled rectangular tubular flange girders with corrugated and flat webs

Lehigh UniversityLehigh Preserve

Theses and Dissertations

2004

Concrete filled rectangular tubular flange girderswith corrugated and flat websMark R. WimerLehigh University

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Wimer, Mark R.

Concrete FilledRectangularTubular FlangeGirders withCorrugated andFlat Webs

September 2004

Concrete Filled Rectangular Tubular Flange Girders

with Corrugated and Flat Webs

by

Mark R. Wimer

A Thesis

Presented to the Graduate and Research Committee

of Lehigh University

in Candidacy for the Degree of

Master of Science

In

Department of Civil Engineering

Lehigh University

August 2004

Acknowledgements

First of all, I wish to express my sincere thanks to Dr. Richard Sause for the

guidance he has given me throughout this project. I would also like to thank High

Steel Structures, Inc. for donating the test girders. In addition, Bong-Gyun Kim has

provided me with a great deal of assistance, and his help is greatly appreciated.

I would also like to thank all of the ATLSS laboratory technicians for their

help in preparing and testing my specimen. Most importantly, I want to express my

gratitude to my wife, Brandi, for her daily support and encouragement.

III

Table of Contents

List of Tables

List of Figures

Abstract

1. Introduction1.1 Background1.2 Objectives1.3 Approach1.4 Thesis Outline

2. Background2.1 Previous Research2.2 Tubular Flange Girders vs. Conventional I-Shaped Girders2.3 Additional Consideration for Tubular Flanges2.4 Corrugated Web Girders vs. Conventional Flat Web Girders2.5 Additional Considerations for Corrugated Web Girders2.6 AASHTO LRFD Bridge Design Specifications

3. Prototype Bridge Design Study3.1 Introduction3.2 Prototype Bridge3.3 Limit State Ratios3.4 Design Process3.5 Types of Designs3.6 Selection of Corrugated Web Geometric Parameters3.7 Discussion of Designs3.8 Efficiency of Corrugated Web

4. Test Specimen and Test Procedure4.1 Introduction4.2 Choice of Test Girders4.3 Scaling Process4.4 New Corrugated Web for Test Specimen4.5 Design Details

4.5.1 Stiffener Designs4.5.2 Fillet Weld Designs4.5.3 Selection of Deck4.5.4 Deck Construction

IV

VI

Vll

1

3445

71215152024

3131323336394151

626364666969727677

4.5.5 Shear Stud Design 784.6 Test Procedures 804.7 Test Instrumentation and Data Acquisition System 844.8 Stress-Strain Properties of Test Specimen Materials 864.9 Measured Girder Dimensions and Initial Tube Imperfection 90

5. Discussion of Experimental Results and Comparison with Analytical Results5.1 Introduction 1225.2 Test Stages 1225.3 Coordinate Axes and Instrumentation Identification 1255.4 Strain Gage Data 1265.5 Vertical Deflection Results 1345.6 Lateral Displacement Results 1385.7 Web Distortion 1455.8 Tube and Tension Flange Lateral Curvature of Scaled Design 19 1475.9 Plate Bending in Tension Flange of Scaled Design 19 148

6. Summary, Conclusions, and Recommendations6.1 Summary 2176.2 Conclusions 2186.3 Recommendations for Future Work 222

References 224

V~a 225

List of Tables

Table

3.1 Prototype Corrugated Web Girder Designs (Neglecting FlangeTransverse Bending Moments) 56

3.2 Prototype Conventional Flat Web Girder Designs 573.3 Prototype Corrugated Web Girder Designs (Incorporating Flange

Transverse Bending Moments) 58

4.1 Scaled Girder Designs 13 and 7 924.2 Scaled Girder Designs 19 and 7 (6 in. (152.4 mm) thick deck) 934.3 CW-T (48 ft.) Stress-Strain Properties 944.4 CW-T (12 ft.) Stress-Strain Properties 944.5 CW-W Stress-Strain Properties 944.6 CW-F Stress-Strain Properties 954.7 FW-T Stress-Strain Properties 954.8 FW-W Stress-Strain Properties 954.9 FW-F Stress-Strain Properties 964.10 Average Measured Girder Dimensions 964.11 Initial Imperfection (Sweep) of Tubes 96

5.1 Stage Identification Subscripts 1515.2 Analytical Values for Stiffness and Neutral Axis Location 1515.3 Comparison of Experimental Results and Analytical Results for

Stiffness and Neutral Axis Location 1515.4 Comparison of Experimental Results and Analytical Results for

Stiffness, Including Only Bending Deformation in AnalyticalCalculation 152

5.5 Comparison of Experimental Results and Analytical Results forStiffness, Including Bending and Shear Deformations inAnalytical Calculation 152

5.6 Description of FEM Models 1535.7 Curvatures Observed to Study Plate Bending in Tension Flange

of Scaled Design 19 153

List of Figures

Figure

3.1 Prototype Bridge 593.2 Shear Strength of 50 ksi (345 MPa) and 70 ksi (485 MPa) Flat

Webs 593.3 Prototype Bridge Corrugated Webs 603.4 Comparison of Corrugated Web Shear Strength to Unstiffened Flat

Web Shear Strength for 50 ksi (345 MPa) and 70 ksi (485 MPa)Webs 60

3.5 Comparison of Corrugated Web Shear Strength to Stiffened FlatWeb Shear Strength for 50 ksi (345 MPa) and 70 ksi (485 MPa)Webs 61

4.1 Prototype and Scaled Versions of Designs 13 and 7 974.2 Scaled Corrugated Webs 984.3 Trapezoidal Corrugated Web 984.4 Fatigue Crack 994.5 Web cuts and Splicing Arrangement 1004.6 Stiffener Geometry for Scaled Design 19 1014.7 Stiffener Geometry for Scaled Design 7 1024.8 Scaled Designs 19 and 7 1034.9 Illustrations for Tube Flange-to-Web Fillet Welds 1044.10 Example off(ax) versus ax (Used for Tube-to-Web Fillet Weld

Design) 1054.11 Illustrations for Tube Flange-to-Stiffener Fillet Welds 1064.12 Core Hole in Pre-Cast Deck 1074.13 Shear Studs Mounted in Core Hole 1074.14 Shear Stud Arrangement 1084.15 Core Hole Pattern 1084.16 Loading Arrangements 1094.17 Wood Cribbing 1104.18 Wood Shim 1104.19 Rollers III4.20 Haunch III4.21 Profile View of Scaled Design 7 Instrumentation 1124.22 Details of Scaled Design 7 Instrumentation 1134.23 Profile View of Scaled Design 19 Instrumentation 1144.24 Details of Scaled Design 19 Instrumentation 1154.25 Details of Lateral Displacement Instrumentation 1164.26 I\faterial Test Identifiers 117

VIl

4.27 CW-T (48 ft.) Coupon 1 1184.28 CW-T (12 ft.) Coupon 5 1184.29 CW-W Coupon 1 1194.30 CW-F Coupon 4 1194.31 FW-T Coupon 1 1204.32 FW-W Coupon 2 1204.33 FW-F Coupon 4 1214.34 CW-C and FW-C 121

5.1 Coordinate Axes for Test Girders 1545.2 Scaled Design 19 Instrumentation Identifiers 1555.3 Scaled Design 7 Instrumentation Identifiers 1565.4 Lateral Displacement Instrumentation Identifiers 1575.5 Moment at East Elastic Section versus Strain for Stage 1

(Scaled Design 7) 1585.6 Moment at West Elastic Section versus Strain for Stage 1

(Scaled Design 7) 1585.7 Moment at East Elastic Section versus Strain for Stage 1










(Scaled Design 19) 1635.17 Moment at Midspan Section versus Strain for Stage 1



(Scaled Design 7) 165

VIII

5.20 Moment at Midspan Section versus Strain for Stage 2(Scaled Design 19) 165



5.23 Neutral Axis During Unloading of Scaled Design 7 in Stage 1 1675.24 Neutral Axis During Unloading of Scaled Design 19 in Stage 1 1675.25 Neutral Axis During Unloading of Scaled Design 7 in Stage 2 1685.26 Neutral Axis During Unloading of Scaled Design 19 in Stage 2 1685.27 Neutral Axis During Unloading of Scaled Design 7 in Stage 2-2 1695.28 Neutral Axis During Unloading of Scaled Design 19 in Stage 2-2 1695.29 Neutral Axis During Unloading of Scaled Design 7 in Stage 3 1705.30 Neutral Axis During Unloading of Scaled Design 19 in Stage 3 1705.31 Midspan Moment versus Vertical Deflection at Sections A and E

for Stage 1 (Scaled Design 7) 1715.32 Comparisqn of Experimental and Analytical Results at Section E

for Stage 1 (Scaled Design 7) 1715.33 Midspan Moment versus Vertical Deflection at Sections B and D

for Stage 1 (Scaled Design 7) 1725.34 Comparison of Experimental and Analytical Results at Section D

for Stage 1 (Scaled Design 7) 1725.35 Midspan Moment versus Vertical Deflection at Section C

for Stage 1 (Scaled Design 7) 1735.36 Comparison of Experimental and Analytical Results at Section C

for Stage 1 (Scaled Design 7) 1735.37 Midspan Moment versus Vertical Deflection at Sections A and E

for Stage 1 (Scaled Design 19) 1745.38 Comparison of Experimental and Analytical Results at Section E

for Stage 1 (Scaled Design 19) 1745.39 Midspan Moment versus Vertical Deflection at Sections B and D

for Stage 1 (Scaled Design 19) 1755.40 Comparison of Experimental and Analytical Results at Section D

for Stage 1 (Scaled Design 19) 1755.41 Midspan Moment versus Vertical Deflection at Section C

for Stage 1 (Scaled Design 19) 1765.42 Comparison of Experimental and Analytical Results at Section C

for Stage 1 (Scalcd Design 19) 1765.43 Midspan Moment versus Vertical Deflection at Sections A and E

for Stage 2 (Scaled Design 7) 1775.44 Comparison of Experimental and Analytical Results at Section E

for Stage 2 (Scaled Design 7) 1775.45 Midspan Moment versus Vertical Deflection at Sections Band D

for Stage 2 (Scalcd Design 7) 178

IX

5.46 Comparison of Experimental and Analytical Results at Section Dfor Stage 2 (Scaled Design 7) 178

5.47 Midspan Moment versus Vertical Deflection at Section Cfor Stage 2 (Scaled Design 7) 179

5.48 Comparison of Experimental and Analytical Results at Section Cfor Stage 2 (Scaled Design 7) 179

5.49 Midspan Moment versus Vertical Deflection at Sections A and Efor Stage 2 (Scaled Design 19) 180

5.50 Comparison of Experimental and Analytical Results at Section Efor Stage 2 (Scaled Design 19) 180

5.51 Midspan Moment versus Vertical Deflection at Sections B and Dfor Stage 2 (Scaled Design 19) 181
















5.67 Midspan Moment versus Vertical Deflection at Sections A and E(Scaled Design 7) 189

x

5.68 Midspan Moment versus Vertical Deflection at Sections B and D(Scaled Design 7) 189

5.69 Midspan Moment versus Vertical Deflection at Section C(Scaled Design 7) 190

5.70 Midspan Moment versus Vertical Deflection at Sections A and E(Scaled Design 19) 190

5.71 Midspan Moment versus Vertical Deflection at Sections B and D(Scaled Design 19) 191

5.72 Midspan Moment versus Vertical Deflection at Section C(Scaled Design 19) 191

5.73 Initial Imperfections at Midspan 1925.74 FEM Simulation Results for Model SD7-1 1935.75 FEM Simulation Results for Model SD7-2 1935.76 FEM Simulation Results for Model SD7-3 1945.77 FEM Simulation Results for Model SD7-4 1945.78 FEM Simulation Results for Model SD7-5 1955.79 FEM Simulation Results for Model SD7-6 1955.80 FEM Simulation Results for Model SD7-7 1965.81 FEM Simulation Results for Model SD7-8 1965.82 FEM Simulation Results for Model SD7-9 1975.83 FEM Simulation Results for Model SD7-10 1975.84 FEM Simulation Results for Model SD7-ll 1985.85 FEM Simulation Results for Model SD7-12 1985.86 FEM Simulation Results for Model SD19-1 1995.87 FEM Simulation Results for Model SD19-2 1995.88 FEM Simulation Results for Model SD19-3 2005.89 FEM Simulation Results for Model SD19-4 2005.90 FEM Simulation Results for Model SD19-5 2015.91 FEM Simulation Results for Model SD19-6 2015.92 FEM Simulation Results for Model SD 19-7 2025.93 FEM Simulation Results for Model SD19-8 2025.94 FEM Simulation Results for Model SD19-9 2035.95 FEM Simulation Results for Model SD19-7 (Including Post-Peak) 2035.96 FEM Simulation Results for Model SD 19-8 (Including Post-Peak) 2045.97 FEM Simulation Results for Model SD 19-9 (Including Post-Peak) 2045.98 FEM Simulation Results for Model SD19-8

(Including Initial Imperfections) 2055.99 FEM Simulation Results for Model SD 19-9

(Including Initial Imperfections) 2055.100 Schematic of FEM Simulation Results for Model SD19-8 2065.101 Schematic ofFEM Simulation Results for Model SD19-9 2065.102 Comparison of Experimental and Analytical Midspan Moment

versus Lateral Displacements (Scaled Design 7. Tube) 207

XI

5.103 Comparison of Experimental and Analytical Midspan Momentversus Lateral Displacements (Scaled Design 7, Tension Flange) 207

5.104 Comparison of Experimental and Analytical Midspan Momentversus Lateral Displacements (Scaled Design 19, Tube) 208

5.105 Comparison of Experimental and Analytical Midspan Momentversus Lateral Displacements (Scaled Design 19, Tension Flange) 208

5.106 Lateral Displacements of Scaled Design 7 (Tube, Stage 2) 2095.107 Lateral Displacements of Scaled Design 7

(Tension Flange, Stage 2) 2095.108 Lateral Displacements of Scaled Design 19 (Tube, Stage 2) 2105.109 Lateral Displacements of Scaled Design 19

(Tension Flange, Stage 2) 2105.110 Lateral Displacements of Scaled Design 7 (Tube, Stage 2-2) 2115.111 Lateral Displacements of Scaled Design 7

(Tension Flange, Stage 2-2) 2115.112 Lateral Displacements of Scaled Design 19 (Tube, Stage 2-2) 2125.113 Lateral Displacements of Scaled Design 19

(Tension Flange, Stage 2-2) 2125.114 Curvature throughout Web Depth for Stage 2 2135.115 Curvature throughout Web Depth for Stage 2-2 2135.116 Web Distortion 2145.117 Transverse Curvature Comparison (Tension Flange, Stage 2) 2145.118 Transverse Curvature Comparison (Tension Flange, Stage 2-2) 2155.119 Strain Gages Used to Study Plate Bending in Tension Flange of

Scaled Design 19 216

Xll

Abstract

Two different innovations to steel I-shaped highway bridge girders were

investigated in this thesis: (1) concrete filled tubular flanges and (2) corrugated webs.

Concrete filled tubular flanges make the section stiffer and stronger in bending

than a plate flange with the same amount of steel. The concrete filled tubular flange

increases the lateral torsional buckling capacity of the girder, and allows for a reduced

number of interior diaphragms over the length of the bridge.

Corrugated webs can be thinner than unstiffened flat webs, and therefore

lighter in weight. If a flat web were to be designed with the same thickness as a

corrugated web, then transverse stiffeners would be required. By eliminating the

transverse stiffeners, stiffener fabrication effort and Category C' fatigue details are

eliminated.

A design study was performed for tubular flange girders with corrugated webs

and with flat webs for a four girder, 131.23 ft. (40000 mm) prototype bridge. Two

girders were scaled down by a 0.45 factor, fabricated, and tested to investigate their

ability to carry their design loads. Also, experimental results were compared to

analytical results to verify the adequacy of the analytical models and tools.

TIle design study showed that tubular flanges allow for the use of large girder

unbraced lengths by increasing the torsional stiffness of the girder. The corrugated

web designs were only slightly lighter than their flat web counterparts for the 131.23

ft. (40000 mm) prototype bridge, with a girder length-to-depth ratio of approximately

22. Corrugated webs would be more efficient for deeper girders.

Experimental results showed that the test girders could effectively carry their

design loads, even for conditions with no interior diaphragms within the span.

Experimental results showed nonlinearity in the moment versus strain and moment

versus vertical deflection curves due to the presence of residual stresses in the steel.

After adjustments were made for the presence of the residual stresses, experimental

results compared quite well with analytical results.

Experimental lateral displacement results were generally smaller than those

predicted by Finite Element Method (FEM) simulations. Friction during testing and

uncertainty in actual test girder initial imperfections are possible reasons for this

result.

1. Introduction

1.1 Background

Two different innovations to steel I-shaped highway bridge girders are

investigated in this thesis: (I) concrete filled tubular flanges and (2) corrugated webs.

The behavior of I-shaped girders with tubular flanges and corrugated webs is

investigated with emphasis on the flexural behavior under highway bridge

construction and service conditions. A design study was conducted, and 0.45 scale

girders were fabricated and tested. The motivation for the study is as follows.

Concrete Filled Tubular Flanges

Concrete filled tubular flanges provide several advantages over traditional

plate flanges. Owing to the concrete within the tube, concrete filled tubular flanges

make the section stiffer and stronger in bending than a plate flange with the same

amount of steel. Also, the web depth is reduced when compared to an I-shaped girder

of the same total depth, which reduces web slenderness effects. Finally, the concrete

filled tubular flange increases the torsional stiffness, and therefore the lateral torsional

buckling capacity of the girder. Lateral torsional buckling is a flexural limit state for

non-composite bridges, as well as composite bridges during construction. before the

deck is composite with the girders. The increased lateral torsional buckling capacity

of tubular flange girders allows for an increased spacing of diaphragms. and therefore

a reduced number of diaphragms between girders.

Corrugated Webs

Corrugated webs have several advantages over traditional flat webs.

Corrugated webs can be designed to be thinner than unstiffened flat webs, and

therefore lighter in weight. If a flat web were to be designed with the same thickness

as a corrugated web, then transverse stiffeners would be required. In this case,

corrugated webs reduce the fabrication cost and effort involved with cutting and

welding numerous transverse stiffeners. Also, by eliminating the transverse stiffeners,

Category C' fatigue details are eliminated.

1.2 Objectives

The objectives of this research are: (1) to conduct a design study of tubular

flange girders with corrugated webs and with flat webs for a four girder, 131.23 ft.

(40000 mm) prototype bridge, (2) to design 0.45 scale test girders based on the results

of this design study, (3) to test the scaled girders to investigate their ability to carry

their design loads, and (4) to compare experimental and analytical results to verify the

adequacy of the analytical models and tools.

1.3 Approach

Rectangular tubular flange girder designs were studied because it is much

easier to attach a corrugated web to a rectangular tube than a round tube. A design

study of various combinations of rectangular tubular flange girders with corrugated

4

webs and flat webs was performed. This included composite and non-composite

designs, hybrid and homogeneous designs, as well as braced and unbraced designs.

The designs were generated based on modified AASHTO LRFD Bridge Design

Specifications (1999). Elastic section calculations were performed using equivalent

transformed sections to include the concrete in the tube and deck with the steel in the

girder cross-section properties.

One corrugated web girder design and one flat web girder design were scaled

down by a 0.45 factor and fabricated for use in a two-girder test specimen. The test

specimen was loaded to simulate various design loading conditions, and data was

recorded. Experimental results were compared with analytical results, and it was

determined that the use of modified AASHTO LRFD specifications and the use of

equivalent transformed sections to include the concrete in the cross-section properties

were adequate for design and analysis of tubular flange girders.

1.4 Thesis Outline

Chapter 2 discusses the design methodology used to design the tubular flange

girders in this research. Chapter 3 presents and discusses the results of the design

study. Chapter 4 discusses the selection of the girders to be scaled into test girders.

the scaling process, and design details for the test girders. It also describes the test

procedure and instrumentation used for the test specimen. Chapter 5 presents the

experimental results from the testing and compares these results with analytical

5

results. Chapter 6 summarizes the work and presents conclusions and

recommendations for future work.

6

2. Background

2.1 Previous Research

Previous research performed on tubular flange girders and corrugated web

girders is discussed here. Previous work by Smith (2001) and Kim (2004a) on tubular

flange girders, and by Easley (1975), Elgaaly et al. (1996), and Abbas (2003) on

corrugated web girders is reviewed. Although this section is not comprehensive in

discussing previous research on corrugated web girders, the summary provides

sufficient background for this thesis.

Smith (2001)

Smith (2001) performed design studies of four prototype bridges: (1) a four

girder prototype bridge with conventional composite I-girders, (2) a four-girder

prototype bridge with composite tubular flange girders, (3) a four-girder prototype

bridge with non-composite tubular flange girders, and (4) a through-girder prototype

bridge with two tubular flange girders. All prototype bridges were simple span

bridges with a span of 131.23 ft. (40000 mm). The designs were generated using High

Performance Steel (HPS) girders, including HPS-70W and HPS-I OOW steel. All

tubular flanges were round.

The design studies were perfonned according to AASHTO LRFD Bridge

Design Specifications (1998). Modifications. which \\ill be discussed later. were

made to the AASHTO LRFD specifications in order to account for the use of tubular

7

flanges. Constructability, Service II, Strength I, and Fatigue load combinations and

corresponding limit states were considered when generating the designs.

The results of the design studies showed that tubular flange girders are lighter

and need fewer diaphragms than conventional composite I-girders with flat plate

flanges. Also, as the number of diaphragms and/or transverse stiffeners is increased,

the girder weight will decrease. However, increasing the number ofdiaphragms

and/or transverse stiffeners increases the cost and effort involved in fabrication.

Kim (2004a)

Kim (2004a) is currently finishing a Ph.D. dissertation on tubular flange

girders for bridges. Preliminary design criteria were developed for tubular flange

girders. These criteria are compatible with AASHTO LRFD specifications. These

design criteria were used in the design study by Smith (2001), as well as the design

study presented in this thesis. Kim (2004a) performed design studies of three

prototype bridges: (I) a four-girder prototype bridge with conventional composite 1

girders, (2) a four-girder prototype bridge with composite tubular flange girders, and

(3) a four-girder prototype bridge with non-composite tubular flange girders. All

prototype bridges were simple span bridges with a span of 131.23 ft. (40000 mm).

Constructability, Service II, Strength L and Fatigue load combinations and

corresponding limit states were considered when generating the designs. The designs

used High Performance Steel (HPS) girders. including HPS-70W and HPS-l OOW

s

steel. Designs were optimized to minimize weight. All tubes used in this study were

round.

The Finite Element Method (FEM) package ABAQUS was used to perform a

parameter study of tubular flange girders. This parameter study varied the diameter

to-thickness ratio of the tube and the depth-to-thickness ratio of the web in order to

observe how the cross-section geometry affects the behavior of tubular flange girders.

This study was primarily used to investigate lateral torsional buckling capacity and

ultimate flexural strength of the tubular flange girders.

Tests were performed to verify the results of the FEM analyses. A prototype

bridge girder design was scaled by 0.45 for testing. Upon completion of this research,

tubular flange girder design criteria will be recommended that are compatible with the

AASHTO LRFD specifications.

Easley (1975)

Easley (1975) investigated the elastic shear buckling of light-gage corrugated

metal shear diaphragms. This work has application to corrugated webs for bridge

girders, as discussed later. Three different equations for elastic shear buckling

strength are discussed: (1) the Easley-McFarland equation, (2) the Bergmann-Reissner

equation. and (3) the Hlavacek equation. These equations provide global shear

buckling strength for buckling modes that occur over several folds of the corrugation

shape. Easley studied the theoretical derivation of each equation. and found that the

Easley-McFarland and Bergmann-Reissner equations are essentially the same for most

9

practical applications of light-gage corrugated metal shear diaphragms. The Hlavacek

equation provides results that differ by about 20%. Experimental results support the

theoretical results obtained by the Easley-McFarland and Bergmann-Reissner

equations.

Elgaaly et al. (1996)

Elgaaly et al. (1996) reported the results of shear tests on corrugated web

girders. It was observed that girders with corse corrugations would fail locally in a

single fold, whereas girders with dense corrugations would fail globally over several

corrugation folds. Finite Element Method (FEM) analyses were performed, which

support the results of the experiments. Some of the FEM analytical results provided

shear strengths higher than observed in the experiments, but this difference was due to

initial imperfections in the web. When these web imperfections were included in the

FEM analyses, the analytical and experimental results were very close.

Elgaaly et al. (1996) provided equations for calculating the elastic global and

local shear buckling strengths. When the elastic shear buckling stress is above 80% of

the shear yield stress, additional equations are provided for calculating inelastic global

and local shear buckling strengths. Abbas (2003) has ShO\\'l1 these equations are

unconservative for stocky webs, as discussed below.

IO

Abbas (2003)

Abbas perfonned a rigorous equilibrium analysis of corrugated web girders

under bending and shear forces. It was detennined that in-plane loading will cause

corrugated web girders to twist out of plane. This occurs because the corrugated web

is non-prismatic, and the shear is not always acting through the shear center. This

twisting is resisted by flange transverse bending. Finite Element Method (FEM)

analyses and large scale testing were perfonned to verify the results of the equilibrium

analysis.

Large scale fatigue tests were also perfonned. It was detennined that the

fatigue strength of the corrugated web girders that were studied is greater than that of a

Category C' fatigue detail, but less than that of a Category B fatigue detail. In other

words, the fatigue strength is greater than that of a conventional flat web girder with

transverse stiffeners, but less than that of a flat web girder with no transverse

stiffeners.

Theoretical shear strength equations for corrugated webs were developed by

Elgaaly et al. (1996), based on work by Easley (1975) and on experiments and FEM

analyses. However, using existing test data, Abbas showed that these equations were

unconservative for stocky web sections. This result was supported by additional large

scale shear tests and FEM analyses.

Based on this research. recommendations were made regarding the design of

corrugated webs for flexure, fatigue. and shear. These design criteria were used in this

thesis. and will be discussed later.

11

2.2 Tubular Flange Girders vs. Conventional I-Shaped Girders

Advantages of Tubular Flange Girders

As mentioned in Section 1.1, girders with concrete filled tubular flanges have

several advantages over conventional I-girders with flat plate flanges. The concrete

filled tubular flanges make the section stiffer and stronger in bending than a plate

flange with the same amount of steel. Also, the web depth is reduced when compared

to an I-shaped girder of the same total depth, which helps to reduce the web

slenderness. Finally, the concrete filled tubular flange increases the torsional stiffness,

and therefore increases the lateral torsional buckling capacity of the girder. This

increase in lateral torsional buckling capacity is the topic of the next section.

Lateral Torsional Buckling Strength on-Shaped Girders and Tubular Flange Girders

AASHTO LRFD Bridge Design Specifications (1999) currently provide

equations for the lateral torsional buckling strength of I-shaped girders. Lateral

torsional buckling strength depends on the unbraced length. For girders with slender

webs, the lateral torsional buckling strength is described by the AASHTO LRFD

specifications for three different ranges of unbraced length: (I) an elastic lateral

torsional buckling range. (2) an inelastic lateral torsional buckling range, and (3) a

yield range.

To be controlled by elastic lateral torsional buckling. the unbraced length of a

slender web girder. Lt>. must be greater than Lr :

12

Iycd EL, = 4.44 ----

S xc Fyc(Eq.2.1)

where, lye is the moment of inertia of the compression flange of the steel section about

a vertical axis in the plane of the web, d is the depth of the steel section, Sxe is the

section modulus about the horizontal axis of the section to the compression flange, E

is the modulus of elasticity of steel, and Fye is the yield stress of the compression

flange.

The elastic lateral torsional buckling strength of a girder with a stocky web is:

(Eq.2.2)

where, eb is a correction factor that accounts for moment gradient over the unbraced

length, Rh is a hybrid factor that accounts for a nonlinear variation of stresses when the

web has a lower yield stress than the flanges, Kr is the St. Venant torsional stiffness of

the girder, and My is the yield moment for the compression flange.

For slender web I-shaped girders, the S1. Venant torsional stiffness is taken as

zero. A slender web will distort, and therefore a slender web girder cross-section is

assumed to have little torsional stiffness. The elastic lateral torsional buckling

strength of a girder with a slender web is:

(Eq.2.3)

where. Rh is a factor that accounts for nonlinear variation of stresses caused by local

buckling of slender webs in flexure.

13

For a slender web girder controlled by inelastic lateral torsional buckling (Lp :S

Lb:S Lr), the AASHTO LRFD specifications define the strength by a linear transition

(Eq.2.4)

where, Lp is the unbraced length limit, below which the girder can yield in bending

(i.e., reach My) without lateral torsional buckling:

(Eq.2.5)

where, rt is the radius of gyration of the compression flange taken about the vertical

axIS.

To take advantage of the St. Venant torsional stiffness of the tubular flanges,

tubular flange girders should be designed with stocky webs. The web slenderness

limit for stocky webs is:

(Eq.2.6)

where, Dc is the depth of the web in compression in the elastic range and tw is the

thickness of the web. Ab is equal to 5.76 when Dc is less than half the web depth or

4.64 when Dc is greater than half the web depth.

The AASHTO LRFD specifications consider only elastic latcral torsional

buckling or yielding for stocky web girders. By neglccting inelastic buckling. thc

lateral torsional buckling strcngth. howcvcr. can bc seriously overestimated when Lb is

between Ll1 and Lr. Therefore. Kim (2004a) proposed that the inelastic straight line14

transition of Equation 2.4 be used for stocky web girders as well as slender web

girders. In this equation, Rb is set equal to 1.0 for stocky webs. Lr, for stocky web

girders is redefined as:

(Eq.2.7)

In summary, tubular flange girders are designed for lateral torsional buckling

using Equation 2.2, Equation 2.4 (with Rb=l.O), Equation 2.5, Equation 2.6, and

Equation 2.7.

2.3 Additional Consideration for Tubular Flanges

A tubular flange should not buckle locally before yielding in compression. The

following tube slenderness limit, provided by the AASHTO LRFD specifications for

rectangular tube compression members, was used:

(Eq.2.8)

where, b is the width of a tube wall, t is the wall thickness, E is the modulus of

elasticity. and Fy is the yield stress of the tube steel.

2.4 Corrugated Web Girders vs. Conventional Flat Web Girders

Advantages of Corrugated Web Girders

Corrugated webs have several advantages over traditional flat webs. They can

be designed to be thinner than unstitTened flat webs. and therefore lighter in weight. If

15

a flat web were to be designed with the same thickness as a corrugated web, then

transverse stiffeners would be required. In this case, corrugated webs reduce the

fabrication cost and effort involved with cutting and welding numerous transverse

stiffeners. Also, by eliminating the transverse stiffeners, Category C' fatigue details

are eliminated.

Shear Strength of Girders with Unstiffened Flat Webs

The shear design criteria for girders with unstiffened flat webs are outlined in

the AASHTO LRFD specifications. The unstiffened flat web shear strength equations

summarized here were used in this research. The nominal shear resistance, Vn, of an

unstiffened flat web is:

(Eq.2.9)

where, C is the ratio of the shear buckling stress to the shear yield stress, and V p is the

shear yield force, given by:

v = F'.I..... DtI' .fj " (Eq. 2.10)

where, Fyw is the yield stress of the web steel, D is the web depth, and tw is the web

thickness. The web depth-to-thickness ratio is used to determine the value of C. This

determines whether the web will yield in shear, buckle in the inelastic range. or buckle

in the elastic range.

If then

C =1.016

(Eq.l.ll)

and the shear strength is controlled by yielding.

If then

(Eq.2.12)

and the shear strength is controlled by inelastic buckling.

If then

(Eq.2.13)

and the shear strength is controlled by elastic buckling. In these equations, E is the

modulus of elasticity of steel and k is a shear buckling constant controlled by the web

boundary conditions.

The stiffened flat web shear equations include the effects of tension field

action, provided by the stiffeners. These equations are not presented here because

stiffened flat web designs were not generated for the design study presented in this

thesis.

Shear Strength Equations for Girders with Corrugated Webs

Shear design criteria for corrugated web girders have been developed by Sause

et al. (2003). The shear strength of a corrugated web may be controlled by yielding.

local buckling. or global buckling. Local and global buckling can be elastic or17

inelastic buckling. Local buckling is concentrated in a single corrugation fold with

deformation in the adjacent folds, whereas global buckling spans many corrugation

folds.

The elastic local buckling stress can be determined using classical plate

buckling theory. The elastic global buckling stress can be determined by treating the

corrugated web as an orthotropic plate, based on the work of Easley (1975). An

empirical equation was presented by Elgaaly et al. (1996) to calculate the inelastic

buckling stress for both local and global buckling. This equation is to be used if the

elastic buckling stress is greater than 80% of the shear yield stress. However, Abbas

(2003) showed that these equations do not provide an adequate lower bound to

existing test results. It appears that when the failure is governed by inelastic local

buckling or yield, the test results are lower than calculated by the empirical equation

presented by Elgaaly et al. (1996). Therefore, an interaction equation has been

proposed to better model the test results (Abbas 2003).

In the design criteria developed by Sause et al. (2003), a web slenderness

criterion is imposed to make the calculated global elastic shear buckling stress equal to

1.25 times the shear yield stress. Therefore, corrugated webs of bridge girders are not

permitted to buckle globally. The web slenderness criterion developed by Sause et al.

(2003) was derived for a trapezoidal corrugation. whereas most of the designs

generated in this research used a triangular corrugation. Therefore. the following.

more general equation. was derived for any corrugation shape:

18

(Eq.2.14)

where, Dx and Dy are the flexural rigidities of an orthotropic plate model of the

corrugated web about the weak and strong axes, respectively. Dx and Dy can be

calculated using the method presented by Easley (1975).

If Equation 2.14 is satisfied, then the shear strength is governed by elastic

local buckling, inelastic local buckling, or yield. The dimensionless parameter shown

below determines which of these shear failure modes is used to calculate the shear

strength:

(Eq.2.15)

where, w is the corrugation fold width for a triangular corrugation or the maximum

fold width for a trapezoidal corrugation. If AL ~ 2.586, then the corrugated web will

yield in shear. The shear strength is:

(F,.... )

V" =0.707 jj DI.. (Eq.2.16)

If 2.586 ~ AL ~ 3.233, then inelastic local shear buckling controls, and the shear

strength is:

V = I (F\"')D" 2 I"I + 0.1 50}./. .J3

(Eq.2.17)

If I'L::: 3.233. then elastic local shear buckling controls. and the shear strength is:

I (F,... )V = 4 (;; DI"" I+ 0.01 43)./. v3

19

(Eq.2.18)

As shown in these shear strength equations, the corrugated web shear strength

does not decrease as the web depth-to-thickness ratio increases. Thus, corrugated web

designs can be thinner than flat web designs. There are issues, however, that must be

considered for a corrugated web girder to be more efficient than a flat web girder.

These issues are discussed in Section 3.6.

2.5 Additional Considerations for Corrugated Web Girders

There are additional design considerations for corrugated web girders. These

considerations are flexural strength of corrugated web girders under overall bending,

the fatigue strength of corrugated web girders, and flange transverse bending moments

created by corrugated webs.

Overall Bending of Corrugated Web Girders

It is often assumed that corrugated webs do not carry flexural stresses due to

overall bending. The corrugated web behavior under axial stresses is similar to an

accordion. Therefore, flexural stresses do not develop in the corrugated web. This

assumption was verified by Abbas (2003).

Fatigue Strength of Corrugated Web Girders

Abbas (2003) determined that the fatigue strength of corrugated web girders is

greater than that of a Category C' fatigue detail. but less than that of a Category B

fatigue detail. In other words. the fatigue strength is greater than that of a flat web

20

with stiffeners, but less than that of an unstiffened flat web. The AASHTO LRFD

specifications provide the following equation for fatigue resistance:

(Eq.2.19)

For corrugated web girders, Abbas (2003) recommended using A equal to 6lx108 ksi3

(20xI0 11 MPa\ based on Category B' of the AASHTO LRFD specifications. N is the

number of fatigue cycles to be applied in the design life of the bridge. (i1F)TH is the

constant amplitude fatigue threshold value, which is recommended as 14 ksi (96.5

MPa) by Abbas (2003).

Flange Transverse Bending Moments Created by Corrugated Webs

Abbas (2003) showed that in-plane loading acting on a corrugated web will

cause a corrugated web girder to twist out of plane. This is because the corrugated

web girder is non-prismatic, and the shear does not always act through the shear

center. This resulting twisting moment is carried by flange transverse bending (Abbas

2003).

The corrugated web design criteria developed by Sause et al. (2003) provide an

equation for calculating flange transverse bending moments for a trapezoidal

corrugated web. Most of the designs generated in this thesis have triangular

corrugated webs. so the equation is presented here in its general form (Abbas 2003):

21v IIJI,I = ~d Ao

21

(Eq.2.20)

where, M, is the flange transverse bending moment, Vref is a reference vertical shear

associated with overall bending in the span, 0 is the web depth, and Ao is the

accumulated area under a half wave of the corrugation shape. The flange transverse

bending moment actually varies as the accumulated area varies along the corrugation,

but Ao provides the maximum effect. Sause et al. (2003) recommended using either

25% of the maximum shear in the span or the shear design envelope value at a given

cross-section for Vref. Abbas (2003) proposed that the maximum shear in the span be

used as Vref because of the numerous factors that can influence the value of M,. These

factors include things such as web misalignment and non-uniform web geometry. The

maximum shear in the span was used for this research. Equation 2.20 assumes the

following: (1) shear is constant over the length of a corrugation; (2) there are a large

number ofcorrugations in the span; (3) the girder is braced with diaphragms at the

ends of the span; and (4) the girder bearings are located at the center of inclined folds.

Equation 2.20 is applicable for the following: (1) the girder span contains an even

number of half corrugation wavelengths, regardless of the existence of interior

diaphragms; or (2) the girder span contains an odd number of half corrugation

wavelengths, but is braced by at least one interior diaphragm (if only one or two

interior diaphragms are provided. then they must be equally spaced).

The flange transverse bending moments must be amplified (to account for

second order effects) in the following manner for compression flanges:

()M,

,\I, AW = \I1__'_"_

STtFcr

..,..,

(Eq. 2.21)

where, (Mt)AMP is the amplified flange transverse bending moment, Mu is the factored

overall bending moment, and Sxe is the section modulus to the compression flange. Fer

is calculated using the equation below:

(Eq.2.22)

where, E is the modulus of elasticity of steel, Lb is the girder unbraced length, and rt is

the radius of gyration of the flange about a vertical axis through its midpoint.

The design criteria developed by Sause et a1. (2003) describe, in detail, the

method in which to incorporate the effects of flange transverse bending moments into

corrugated web girder designs. The key concepts will be summarized here. The

stresses created by flange transverse bending moments are to be superimposed with

the stresses from overall bending moments. This is to be done in both compression

and tension flanges. When the compression flange is composite with the deck, the

flange transverse bending moments in the compression flange can be neglected. For

situations where the girder is designed to be linear elastic, the stress superposition is

straight forward. When the plastic strength of a girder is considered, flange transverse

bending moments created by the corrugated web are treated similarly to flange

transverse bending moments from wind loads (AASHTO LRFD 1999). Under plastic

conditions. the flange transverse bending moments will create fully yielded regions at

the flange tips. The flange force due to overall bending must then be placed on the

remaining section. discounting the yielded regions. The \\idth of the yielded region.'- -.,'..... -' '-

b". at each edge of the flange is:

(Eq.2.23)

where, br is the width of the flange, tf is the thickness of the flange, and Fyr is the yield

stress of the flange.

2.6 AASHTO LRFD Bridge Design Specifications

The designs developed in this research were based on the AASHTO LRFD

Bridge Design Specifications (1999) for I-sections in flexure, with the modifications

discussed in Sections 2.2 through 2.5. This section presents an overview of the

general design equation, limit states, loads, load combinations, and important

calculations involved in the girder designs presented in this thesis.

General Design Equation

The general design equation of the AASHTO LRFD specifications is:

(Eq.2.24)

where Qi refers to force effects from various loads, and Rn refers to the resistance of

the specific bridge component. Yi is a statistically based load factor that generally

increases the value on the left side of Equation 2.24. and ~ is a statistically based

resistance factor that generally reduces the value on the right side of Equation 2.24. 11

is a load modifier based on the ductility. redundancy, and importance. Equation 2.24

states that the factored loads must be less than or equal to the factored resistance.

24

Limit States and Load Combinations

The AASHTO LRFD specifications require four limit states be considered for

steel I-girders. These are the Strength limit state for flexural resistance, the Service

limit state, the Fatigue and Fracture limit state, and the Strength limit state for shear

resistance. The investigation of Constructability is also required, though this is not

specifically identified as a limit state. These limit states can be reached under

different loading conditions, and each loading condition is identified by a Roman

numeral after the limit state name. The limit states that were investigated for the

designs generated in this thesis are Strength I, Strength III, Strength V, Service II,

Fatigue, and Constructability.

Strength I is the set ofloading conditions that relate to the normal use of the

bridge without wind. Flexural strength and shear strength are investigated under

Strength I. Strength III is the set of loading conditions for a bridge exposed to winds

exceeding 55 mph (90 km/hr), with a reduced live load. Strength V is the set of

loading conditions for normal use of a bridge with 55 mph (90 km/hr) winds. Flexural

strength is investigated under Strength III and Strength V. Service II is the set of

loading conditions under which yielding and permanent deformation of the steel

structure is prevented. Fatigue is the set ofloading conditions investigated to prevent

failure from repetitive load cycles. Constructability, which is termed "Construction"

in this thesis. relates to the loads to be considered in investigating the incomplete

bridge under construction.

25

The AASHTO LRFD specifications use 2-letter symbols to refer to different

loads. The loads considered in this thesis are DC, OW, LL, 1M, and WS. DC is the

dead load of the structural components and attachments. OW is the superimposed

dead load of wearing surfaces and utilities. LL is the live load created by specified

combinations of a Design Truck, Design Tandem, and Design Lane loads. 1M is a

dynamic load allowance applied to LL. WS is the wind load on the bridge.

The girder designs presented in this thesis are based on the four-girder

prototype bridges with composite tubular flange girders developed by Smith (200 I).

The bending moments and shears used to design girders in the present research are

those calculated by Smith (200 I) for girders with circular tubular flanges and flat

webs. Due to the different girder geometry, these load effects are only approximately

accurate (but sufficiently accurate) for the designs developed in this thesis.

The AASHTO LRFD specifications describe a set of loads and load factors to

create the load combination that should be considered for each limit state. These load

combinations are listed below.

Strength I

1.25DC + 1.50DW + 1.75(LL + 1M)

Strength III

I.25DC + I.50DW+ I.40WS

Strength V

I.25DC + I.50DW + 1.35(LL + 1M) + OAOWS

26

(Eq.2.25)

(Eq.2.26)

(Eq.2.27)

Service II

I.OODC + I.OODW + I.30(LL + 1M)

Fatigue

0.75(LL + 1M)

(Eq.2.28)

(Eq.2.29)

In addition, AASHTO LRFD specifications require the bridge design engineer to

investigate the Constructability of a design. For this purpose, a load combination was

established called the "Construction" load combination, given below.

I.5DC (Eq.2.30)

Strength I Limit State - Flexure

As discussed further in Chapter 3, composite and non-composite designs were

investigated in this thesis. For composite designs, the girders and an effective width

of the deck contribute to the moment carrying capacity. For non-composite designs,

the girders alone carry the moment, but they are assumed to be laterally braced by the

deck. In either case, lateral torsional buckling is not a flexural limit state to be

considered under the Strength I loading conditions. The compression flange (concrete

filled tube) was deemed compact by satisfying the tube slenderness limit given in

Section 2.3. The flat web was deemed compact by satisfying the AASHTO LRFD

specifications for web compactness. This web compactness specification was not

applied to corrugated web girders because the corrugated web will not experience web

buckling under bending stresses due to the "accordion effect" mentioned in Section

2.5.

27

A compact section should be able to develop the full plastic moment.

However, for composite sections the AASHTO LRFD specifications require a

concrete ductility check that reduces the ultimate flexural strength below the plastic

moment, based on empirical equations. For tubular flange girders, the ultimate

flexural strength is calculated using a strain compatibility analysis (Smith 2001). The

flexural strength from this analysis is less than the full plastic moment. The concrete

ductility check of the AASHTO LRFD specifications is not required. In the strain

compatibility analysis, the concrete is represented by an equivalent rectangular stress

block and the steel exhibits elastic-perfectly plastic behavior. Ultimate strength is

reached when the strain is 0.003 at the top of the deck for composite sections, or at the

top of the tube concrete for non-composite sections.

Strength III and Strength V Limit States - Flexure

The Strength III and Strength V limit states include wind load. The wind load

is applied laterally to the bridge, and it is assumed that the load on the lower half of

the exterior girder is carried by the bottom flange, creating a transverse bending

moment in the flange between bearings or benveen diaphragms. Wind load on the

upper half of the girder is carried by the deck to the end diaphragms and bearings. For

compact sections. the AASHTO LRFD specifications allow the transverse flange

moment to be carried by yielded portions at the bottom flange tips. The equation to

calculate the \\idth of these yielded portions was presented in Section 2.5. The flange

28

force due to overall bending must then be placed on the remaining section, discounting

the yielded regions.

Strength I Limit State - Shear

The Strength I limit state for shear was investigated using either the flat web or

corrugated web shear strength design criteria discussed in Section 2.4.

Constructability

For Constructability, lateral torsional buckling of a girder before the girder was

composite with the deck was investigated using design equations discussed in Section

2.2. The Construction load combination (1.5 DC) was used in this investigation. In

all cases investigated in this thesis, the unbraced length was greater than Lp, and

therefore, lateral torsional buckling controlled. Equations presented in Section 2.2

were used to calculate the lateral torsional buckling strength.

Service II

Calculations of the elastic section properties were perfonned using a

transfom1ed section for concrete filled tubular flange girders, in the composite and

non-composite conditions. In these calculations, the concrete was transfom1ed to an

equivalent area of steel using the modular ratio. For the Service II limit state check.

stresses on a composite section due to the Service II load combination were calculated

using a three-step process. The factored DC moment was applied to the steel girder

29

and tube concrete. The factored DW moment was applied to the long term composite

section and the factored LL moment was applied to the short term composite section.

The long term composite section -is based on an increased modular ratio (by a factor of

3) to account for creep that will occur over time in the concrete. The tube concrete is

neglected for both the short and long term composite section calculations because it is

assumed that the tube concrete is fully stressed by the DC moment (Smith 2001). The

purpose of this limit state check is to confirm that yielding will not occur in the

flanges under the Service II load combination.

Fatigue

AASHTO LRFD specifies two types of Fatigue limit states: load induced

fatigue and distortion induced fatigue. The load induced fatigue is investigated using

Equation 2.19. The constants used in the equation were based on whether the girder

is a corrugated web girder or a flat web girder. The values to be used for a corrugated

web girder were discussed in Section 2.5, and those for a flat web girder with

stiffeners are provided in the AASHTO LRFD specifications. The corrugated and flat

web girders with interior diaphragms have diaphragm connection plates at midspan

only, as discussed in Chapter 4. Distortion induced fatigue was not directly

considered after it was detemlined that it would not control the designs.

30

3. Prototype Bridge Design Study

3.1 Introduction

Chapter 2 introduced previous research on tubular flange girders and

corrugated web girders. Lateral torsional buckling of conventional I-shaped girders

and tubular flange girders was discussed. Shear strength of conventional I-shaped

girders and corrugated web girders was discussed. Corrugated webs create transverse

bending moments in the flanges of corrugated web girders, which must be taken into

account in design. The relevant AASHTO LRFD Bridge Design Specifications (1999)

were briefly discussed, as well as the modifications that must be applied to the

AASHTO LRFD specifications in order to design rectangular tubular flange girders

with corrugated webs. In this chapter, a prototype bridge is introduced, and the design

process used in conjunction with the modified AASHTO LRFD specifications is

discussed. To facilitate this design process, MathCAD files were developed to

evaluate a girder design according to these modified AASHTO LRFD specifications.

All of the designs generated for the study are described and compared in detail. Also,

the efficiencies of corrugated webs are investigated.

3.2 Prototype Bridge

The prototype bridge is the full scale bridge for which all designs in this study

are generated. The prototype bridge is 131.23 ft. (40000 mm) long, simply supported,

and a single span. It has a 50 ft. (15240 mm) wide, 10 in. (254 mm) thick concrete

31

deck. There are four girders, equally spaced at 12.5 ft (3810 mm). The deck

overhangs are 6.25 ft. (1905 mm) wide. The bridge carries two 12 ft. (3658 mm)

traffic lanes, and has 13 ft. (3962 mm) on either side for a shoulder and parapet. The

loads, however, were generated assuming four 11.5 ft. (3505 mm) design lanes with 2

ft. (610 mm) on either side for a shoulder and parapet. This resulted in more

conservative designs, which would be adequate for a future change in use. Figure 3.1

shows the prototype bridge. The geometry of this prototype bridge has been used in

other recent research at Lehigh University (Smith 2001, Kim 2004a). Therefore, the

results of the present study can be compared with those of the other studies. More

importantly, testing has been perfonned on 0.45 scale girders designed for this

prototype bridge (Kim 2004a). Thus, for testing purposes, two prototype designs from

the present research were scaled to 0.45 offull size so that the same footings, deck,

and loading procedure could be used, as discussed in Chapter 4. The prototype girders

have concrete filled rectangular tubular compression flanges. The tube and deck

concrete have an ultimate compressive strength of 6 ksi (40 MPa).

3.3 Limit State Ratios

As mentioned in the chapter introduction (Section 3.1), MathCAD files were

developed and used to generate the designs in this study. The MathCAD files were

based on the modified AASHTO LRFD specifications (Chapter 2). In the files, limit

state ratios were used as indicators of whether certain design criteria were satisfied. A

limit state ratio is calculated by dividing factored loads by factored resistance for a

32

specific limit state. Thus, a ratio less than 1.0 indicates that the design criterion for

this limit state is satisfied. The limit state ratios used in this design study, and the

design criteria that they refer to, are listed below.

Ratiolnexure - Strength I limit state for flexure

RatioIIInexure - Strength III limit state for flexure

RatioVflexure - Strength V limit state for flexure

Ratioshear - Strength I limit state for shear

Ratiowebslendemess - AASHTO LRFD proportion limit for web slenderness

Ratiotensionflange - AASHTO LRFD proportion limit for tension flange

Ratioflangebracing - ratio of Lbto Lp (a ratio over 1.0 requires a check oflateral

torsional buckling strength)

Ratioltbresistance - Constructability considering lateral torsional buckling under

the Construction load combination

RatioserviccIl - Service II limit state for prevention of yield

RatiofatigucCW - Fatigue limit state for corrugated web-to-tension flange detail

Ratiofatigucconnplatc - Fatigue limit state for transverse stiffener-to-tension flange

detail

Ratiotubcthickncss - compactness check for tube

3.4 Design Process

The design process involved choosing a section depth. choosing a web depth

and thickness. choosing the tube size. and choosing a bottom flange width and

thickness. The design decisions were made in that order. These design decisions are

discussed below.

Section Depth

Generally, bridge girder length-to-depth ratios are kept between twenty and

thirty. Making the corrugated web deep and thin made it more economically efficient

(Sect. 3.8). With this in mind, a length-to-depth ratio close to twenty was appealing.

It was decided to use a combined tube and web depth of70 in. (1778 mm), which gave

a length-to-depth ratio for the steel section of approximately 22. This fixed depth

reduced the extensive number of designs that could have been generated.

Web Depth and Thickness

The tube depth dictated the web depth. The three tube depths considered are 4

in. (101.6 mm), 6 in. (152.4 mm), and 8 in. (203.2 mm). It was desired to obtain a

minimum weight design, so the design process was iterated three times, once using

each tube depth. The iteration that provided the minimum weight was selected as the

final design. The web depth changed for each iteration so that the combined tube and

web depth remained consistent at 70 in. (1778 mm). Once the web depth was decided,

a web thickness was chosen in order to satisfy the necessary shear strength criteria for

the Strength I limit state. The web thickness was varied by 1/16 in. (1.6 mm).

All web designs generated in the design study were unstiffened flat webs. This

allowed for a direct comparison of weight between corrugated web and flat web

34

designs. Also, the webs of tubular flange girders are required to be stocky so that the

girders benefit from the torsional stiffness of the tube, as discussed in Chapter 2.

Thus, flat webs could not have the large depth-to-thickness ratio that is necessary for

the inclusion of transverse stiffeners to significantly increase the shear strength.

Tube Size

Before selecting the tube size, an approximate tension flange size was

specified so that the tube could be designed. With the tube depth already selected,

only the tube width and thickness had to be selected. The tube width was chosen so

that the girder would satisfy the criteria for lateral torsional buckling. The tube

thickness was chosen to satisfy Equation 2.8, which made the tube compact. Tube

thicknesses of3/8 in. (9.5 mm), 1/2 in. (12.7 mm), and 5/8 in. (15.9 mm) were

investigated. The tube sizes used in the designs were selected from a list of tubes

suggested by industry advisors to the project, and will be referred to as "suggested"

tube sizes.

Tension Flange Width and Thickness

The tension flange was designed last. The tension flange was likely to be

governed by the Fatigue or Service II limit states. The thickness was varied by 1/4 in.

(6.4 mm). and the width was varied by I in. (25.4 mm). A maximum of2 in. (50.8

mm) was set for the flange thickness. and the maximum width was governed by the

AASHTO LRFD tension flange proportion limit. In most cases. several combinations

35

of width and thickness satisfied the limit states. Thus, the minimum weight/minimum

area tension flange was chosen.

Other Checks

After all of the cross-section dimensions were selected, the final design was

then checked to make sure that it satisfied all remaining limit states. This included a

check to make sure that Strength III and Strength V were satisfied.

It was of interest to determine how much the initial approximation of the

tension flange size would affect the selected tube size. For several cases, a large initial

flange size and a small initial flange size were tried in order to observe the effect.

This never caused a change in the tube size, and therefore the initial approximation of

the tension flange size had little effect on the design.

3.5 Types of Designs

At the earliest stages of the design study, certain important design conditions

were uncertain. These design conditions governed the types of girders that were

designed. These design conditions are discussed here, followed by a detailed

discussion of the hybrid girder considerations.

Design Conditions

One design condition is the use of composite or non-composite conditions for

designing the bridge for service conditions. A composite design uses shear connectors

36

attached to the top flange that allow the concrete deck to act compositely with the

girders. An effective width of the concrete deck thus contributes to the load carrying

capacity of the cross-section. For a non-composite design, the loads are carried by the

girders alone. For tubular flange girders, shear connectors must be attached to the

tube.

A second design condition is the use of homogeneous or hybrid girder sections.

A homogeneous cross-section employs a single strength steel in the section whereas a

hybrid section uses different strength steels.

A third design condition is the diaphragm arrangement. Diaphragms ·provide

torsional bracing to the girders. As mentioned in Section 1.1, a primary advantage of

the tubular compression flange is the added torsional stiffness, which increases the

lateral torsional buckling strength. By increasing the lateral torsional buckling

strength, the number of necessary interior diaphragms is decreased.

Given these uncertain design conditions, a range of different designs were

developed. This included composite and non-composite, and homogeneous and

hybrid designs. Designs with and without interior diaphragms at midspan were

developed. Also, as mentioned in Chapter 1, both corrugated web and unstiffened flat

web designs were generated. Considering several important combinations of the

design conditions discussed above, twelve total types of designs were studied.

37

Homogeneous and Hybrid Designs

The homogeneous designs use ASTM A709 Grade 50W steel with a minimum

yield stress of 50 ksi (345 MPa), which is the most commonly used steel strength in

bridge design. The hybrid arrangement that was considered incorporates a tube made

of ASTM A588 steel, with a minimum yield stress of 50 ksi (345 MPa), coupled with

a web and bottom flange made from ASTM A709 Grade HPS 70W steel with a yield

stress of 70 ksi (485 MPa). The higher strength steel allowed the bottom flange to be

smaller and the web to be thinner, thus resulting in a lower weight design. It is

difficult to obtain tubes with 70 ksi (485 MPa) strength, so the complete 70 ksi (485

MPa) design was not considered. In addition, the tube design was controlled by lateral

torsional buckling. For the comparatively large unbraced lengths (i.e., 65.62 ft.

(20000 mm) and 131.23 ft. (40000 mm» used in this study, lateral torsional buckling

is more affected by the tube geometry than the steel strength.

The 70 ksi (485 MPa) web was not efficient for the hybrid unstiffened flat web

designs because the depth-to-thickness ratio for the flat webs caused them to be

governed by elastic shear buckling. In the elastic shear buckling range, the buckling

strengths of a 70 ksi (485 MPa) flat web and a 50 ksi (345 MPa) flat web are the same,

because the elastic buckling strength depends only on the web dimensions. Figure 3.2

illustrates the unstiffened shear strength ('tnu) of 50 ksi (345 MPa) and 70 ksi (485

MPa) flat webs versus the web depth-to-thickness ratio (D/t\\). Note that the curves

converge in the clastic shear buckling range.

38

3.6 Selection of Corrugated Web Geometric Parameters

Before corrugated web designs were generated, the corrugated web geometric

parameters for the 50 ksi (345 MPa) and 70 ksi (485 MPa) webs were established.

The parameters are the corrugation shape, corrugation angle (a), and corrugation fold

width (w). Figure 3.3 illustrates the shape and parameters chosen for this study. The

parameters are discussed below.

Corrugation Shape

The decision to use a triangular shape was based on work performed by Abbas

(2003). In deriving a C-Factor Correction Method for calculating flange transverse

bending moments caused by vertical shear acting on the corrugated web, C was

defined as the ratio of the area under one-half wave of a corrugation shape to the area

under one-half wave of an equivalent sinusoidal corrugation shape. Equivalent

corrugation shapes have the same wavelength (q) and corrugation depth (hr). Abbas

(2003) detennined that flange transverse bending moments for a specific corrugation

shape could be calculated by multiplying the C factor by the flange transverse bending

moments calculated for the equivalent sinusoidal corrugation. It was evident that a

triangular shape would minimize the flange transverse bending moments, thus

prompting the choice for this design study.

39

Corrugation Angle

It was observed during preliminary studies of corrugated webs that the global

buckling capacity of a corrugated web is increased by increasing the angle change

between two successive corrugation folds. However, the fatigue life of a girder may

be shortened when the angle is large (Abbas 2003). A value between 30 and 45

degrees is often used for the angle change between two successive corrugation folds,

and a value of 40 degrees was selected for this study. a, defined here for a triangular

shape as halfthe angle change between the successive folds, is 20 degrees.

Corrugation Fold Width

Given a prescribed tube and web depth of 70 in. (1778 mm), and a minimum

tube depth of 4 in. (101.6 mm), the maximum depth of the web is 66 in. (1676 mm). It

was assumed that the web will be proportioned such that the global and local shear

strength will be shear yielding. In this case, 0.707 times the shear yield stress and web

area must be greater than or equal to the factored shear force for the Strength I limit

state. This means that the minimum web thicknesses for the 50 ksi (345 MPa) and 70

ksi (485 MPa) webs are 7/16 in. (11.1 mm) and 5/16 in. (7.9 mm), respectively. Using

Equation 2.15 with AL equal to 2.586, the maximum corrugation fold width for the 50

ksi (345 MPa) and 70 ksi (485 MPa) webs are 27.25 in. (692.2 mm) and 16.45 in.

(417.8 mm). respectively.

To reduce fabrication effort. the maximum allowable fold width should be

used. In order to have an even number of half wavelengths (Section 2.5) in the

40

predetermined specimen of 131.23 ft. (40000 nun), the actual maximum fold width

was not used. However, the corrugation folds were sized very close to maximum

width, such that an even number of half wavelengths could be used. The web shape

and dimensions are shown in Figure 3.3. One corrugation geometry was used for all

50 ksi (345 MPa) webs, and one geometry was used for all 70 ksi (485 MPa) webs.

Calculations were performed, and Equation 2.14 was checked to confirm that

the global shear strength of these webs was shear yielding. The use of Equation 2.15

to calculate maximum fold width mandated that the local shear strength of the webs

was also shear yielding. The resulting corrugated webs are as efficient as possible.

3.7 Discussion of Designs

Tables 3.1 through 3.3 provide the geometry and limit state ratios for each

type of girder designed for the prototype bridge. Three types of designs were

generated: corrugated web girders designed without considering flange transverse

bending (Designs 1 through 6 shown in Table 3.1), conventional flat web girders

(Designs 7 through 12 shown in Table 3.2), and corrugated web girders designed

considering flange transverse bending (Designs 13 through 18 shown in Table 3.3).

These designs are discussed in the following sections.

Designs 1 through 6

Design 1 is a composite. corrugated web design. and the girder is

homogeneous. There are two end diaphragms. and no interior diaphragm. The first

41

two design iterations were performed with a 4 in. (101.6 mm) deep tube and a 6 in.

(152.4 rom) deep tube, respectively. It was determined that designs using the

suggested tubes with these depths could not provide sufficient lateral torsional

buckling strength. The third iteration was performed with an 8 in. (203.2 rom) deep

tube, which results in a 62 in. (1575 rom) deep web. A 7/16 in. (11.1 rom) thick web

was required to satisfy the shear strength criteria. A 20x8x5/8 in. (508x203.2x15.9

rom) tube satisfies the lateral torsional buckling criteria and a 27xl-3/4 in. (685.8x44.5

mm) tension flange satisfies the remaining limit states.

Design 2 is a composite, corrugated web design, and the girder is

homogeneous. There are three diaphragms, one at each end and one at midspan. The

interior diaphragm provides torsional bracing to the girder, and reduces the unbraced

length of the girders, therefore a smaller tube can be used. In this design, therefore,

either a 4 in. (101.6 mm) deep tube or a 6 in. (152.4 mm) deep tube can satisfy the

lateral torsional buckling criteria. These were the first and second iterations,

respectively. An 8 in. (203.2 mm) deep tube, however, led to the minimum weight

design. Once again, the 8 in. (203.2 mm) deep tube led to a 62 in. (1575 mm) deep

web, and the required web thickness of 7/16 in. (11.1 mm) is the same as for Design 1.

This time, however, a smaller tube satisfies the lateral torsional buckling criteria. The

required tube size is 16x8x3/8 in. (406.4x203.2x9.5 mm). A 27x 1-3/4 in. (685.8x44.5

mm) tension flange satisfies the rest of the limit states. It is interesting to note that the

only change to the design conditions from Design 1 to Design 2 was the addition of an

interior diaphragm. and this change affects only the size of the tubular flange.

42

Design 3 is a composite, corrugated web design, and the girder is hybrid. The

tube has a yield stress of 50 ksi (345 MPa), and the web and bottom flange both have a

yield stress of70 ksi (485 MPa). There are two end diaphragms, and no interior

diaphragm. The suggested 4 in. (101.6 mm) and 6 in. (152.4 mm) deep tubes could

not satisfy the lateral torsional buckling criteria. An 8 in. (203.2 mm) deep tube was

investigated. The web depth is 62 in. (1575 mm), and a 5/16 in. (7.9 mm) web

thickness is required to satisfy the shear criteria. A 20x8x5/8 in. (508x203.2x15.9

mm) tube satisfies the lateral torsional buckling criteria and a 22xl-l/2 in. (558.8x38.1

mm) tension flange satisfies the rest of the limit states. Notice that the use of a 70 ksi

(485 MPa) web allowed the thickness to decrease from 7/16 in. (11.1 mm) to 5/16 in.

(7.9 mm) when comparing Designs 1 and 3. Also notice that the use of a 70 ksi (485

MPa) tension flange allowed the cross-sectional area of the tension flange to decrease

from 47.25 in.2 (30484 mm2) to 33 in? (21290 mm2

).

Design 4 is similar to Design 3, the only difference being the addition of an

interior diaphragm. Design 4 is a composite, corrugated web design, and the girder is

hybrid. As seen previously, when an intermediate diaphragm was added, either a 4 in.

(101.6 mm) deep tube or a 6 in. (152.4 mm) deep tube can satisfy the lateral torsional

buckling criteria in the first and second iterations, respectively. An 8 in. (203.2 mm)

deep tube, however, led to the minimum weight design. The 62 in. (1575 mm) web

depth requires a 5/16 in. (7.9 mm) thickness to satisfy the shear criteria. The tube

required to satisfy the lateral torsional buckling criteria is smaller than in Design 3

because of the addition of the interior diaphragm. The required tube size is l6x8x3/8

43

in. (406.4x203.2x9.5 mm). A 25xl-l/2 in. (635x38.1 mm) tension flange satisfies the

rest of the limit states. Design 4 can be compared with both Designs 3 and 2. The

introduction of the interior diaphragm from Design 3 to 4 allows for the smaller tube.

The use of a hybrid girder rather than homogeneous girder when going from Design 2

to 4 allows for a thinner web and a smaller tension flange.

One of the possible design permutations is a homogeneous non-composite

design. However, the non-composite design must satisfy the Strength limit states

using only the girder and concrete within the tube. Preliminary studies showed the

size of the girder tension flange would be extremely large to satisfy all limit states.

Therefore, only the hybrid non-composite case was considered.

Design 5 is a non-composite, corrugated web design, and the girder is hybrid.

Just as in the composite hybrid designs, the tube has a yield stress of 50 ksi (345 MPa)

and the web and tension flange both have a yield stress of 70 ksi (485 MPa). There

are two end diaphragms, and no interior diaphragm. The suggested 4 in. (101.6 mm),

6 in. (152.4 mm), and 8 in. (203.2 mm) deep tubes could not satisfy the lateral

torsional buckling criteria. It seems that an 8 in. (203.2 mm) deep tube should be able

to satisfy the lateral torsional buckling criteria, just as in the previous designs. The

lateral torsional buckling strength under the Construction loading conditions is

independent of whether the bridge will be composite or non-composite in service.

However. the suggested 8 in. (203.2 mm) tubes do not satisfy the lateral torsional

buckling criteria because the estimated girder dead loads are higher for non-composite

designs since non-composite girders are generally heavier than composite girders.

44

Thus, it was necessary to use a deeper tube for Design 5. However, deeper

tubes were not on the list of suggested tubes provided by industry advisors to the

project. Therefore, the decision was made to use a tube size that, when scaled down

for testing, would be a tube on the list of suggested tubes (so that it could be used in

the test specimen). As mentioned earlier, the scale factor to be used for testing was

predetermined to be 0.45 to take advantage of an existing test setup. Three design

iterations were performed with 4 in. (101.6 mm), 6 in. (152.4 mm), and 8 in. (203.2

mm) tubes each scaled by 1/0.45. The 8.89 in. (225.8 mm) deep tube yielded the

lowest weight. The web was, therefore, 61.11 in. (1552 mm) deep, and a web

thickness of 3/8 in. (9.5 mm) was needed to satisfy the shear criteria. A tube size of

31.11 x8.89xO.83 in. (790.2x225.8x21.1 mm) satisfies the lateral torsional buckling

criteria and a 26xl-3/4 in. (660.4x44.5 mm) tension flange satisfies the rest of the limit

states.

Design 6 is a non-composite, corrugated web design, and the girder is hybrid.

The difference from Design 5 is the addition of an interior diaphragm. Suggested 4 in.

(101.6 mm), 6 in. (152.4 mm), and 8 in. (203.2 mm) tubes satisfied the lateral

torsional buckling criteria. However, none of them could satisfy the Strength I and

Service II flexural limit states. In non-composite design. increasing the tension flange

size decreases the demand on the compression flange only to a certain extent because

the corrugated web does not contribute to overall bending. Therefore. the size of the

compression and tension flanges need to be balanced for the Strength I limit state.

45

Once again, it was necessary to use tube depths other than those originally

suggested by the industry advisors to the project. The 8.89 in. (225.8 mm) deep tube

provided the minimum weight design. Interestingly, both Designs 5 and 6 have low

lateral torsional buckling limit state ratios because Strength I and·Service II control the

compression flange design. Since lateral torsional buckling was not a critical limit

state, the fact that one design has an interior diaphragm was of no consequence, and

the two designs were the same. For Design 6, the web depth and thickness are 61.11

in. (1552 mm) and 3/8 in. (9.5 mm), respectively. The tube size is 31.11x8.89xO.83

in. (790.2x225.8x21.1 mm) and the tension flange is 26x1 3/4 in. (660Ax44.5 mm).

Designs 7 through 12

Design 7 is a composite, unstiffened flat web design, and the girder is

homogeneous. There are two end diaphragms. The first two design iterations were

performed with a 4 in. (101.6 mm) deep tube and a 6 in. (15204 mm) deep tube,

respectively. Similar to the corrugated web designs, it was determined that none of

the suggested tubes with these depths could provide sufficient lateral torsional

buckling strength. The third iteration was successful, using an 8 in. (203.2 mm) deep

tube. The web depth of 62 in. (1575 mm) requires a thickness of 11/16 in. (17.5 mm)

to satisfy the shear strength criteria. A tube size of 20x8x5/8 in. (508x203.2x15.9

mm) satisfies the lateral torsional buckling criteria. A 24x1-1/2 in. (609.6x38.1 mm)

tension flange satisfies the rest of the limit states. This design can be directly

compared to Design 1. the only difference being the switch from corrugated web to

46

flat web. The flat web must be thicker than the corrugated web to carry the shear.

The thickness of the corrugated web is 7/16 in. (II.! mm), whereas the thickness of

the flat web is 11/16 in. (17.5 mm). On the other hand, the corrugated web girder

needed a bigger tension flange than the flat web girder because the corrugated web

does not carry overall bending stresses. The tension flange size for the corrugated web

girder is 47.25 in.2 (30483.8 mm2), whereas the tension flange size for the flat web

girder is 36 in.2 (23225.8 mm2).

Design 8 is also a composite, unstiffened flat web design, and the girder is

homogeneous. This design has three diaphragms, one at each end and one at midspan.

An interior diaphragm allowed successful designs to be generated using 4 in. (101.6),

6 in. (152.4), and 8 in. (203.2) deep tubes. The 8 in. (203.2 mm) deep tube provided

the minimum weight design. An 11/16 in. (17.5 mm) thick web is required to satisfy

the shear strength criteria. However, the 16x8x3/8 in. (406.4x203.2x9.5 mm) tube

required to satisfy the lateral torsional buckling criteria is smaller than used in Design

7 because of the shorter unbraced length. A 25xl-l/2 in. (635x38.1 mm) tension

flange is required to satisfy the rest of the limit states. Design 8 can be directly

compared to Design 2, to illustrate the differences between a corrugated web design

and a flat web design with all other design conditions held constant. The web

thickness is larger for the flat web design than for the corrugated web design, and the

tension flange area is larger for the corrugated web design than for the flat web design.

Design 9 is a composite, unstiffened flat web design, and is hybrid. Design 9

has two end diaphragms. The only successful design iteration was for a tube depth of

47

8 in. (203.2 mm). The web depth and thickness are 62 in. (1575 mm) and 11/16 in.

(17.5 nun), respectively. Note that the web is the same thickness as in the

homogeneous Design 7, because the shear strength was governed by elastic buckling.

The elastic buckling strengths of a 70 ksi (485 MPa) web and a 50 ksi (345 MPa) web

are the same. A 20x8x5/8 in. (508x203.2xI5.9 nun) tube satisfies the lateral torsional

buckling criteria, and a 21xl in. (533.4x25.4 mm) tension flange satisfies the rest of

the limit state ratios. The transition to hybrid did allow Design 9 to have a smaller

tension flange than Design 7. The differences between the corrugated web and flat

web designs are illustrated once more by comparing Designs 3 and 9. Design 9

requires a thicker web to carry the shear, but Design 3 requires a larger tension flange

to carry bending.

Design 10 is also a composite, unstiffened flat web design, and is hybrid. It is

different from Design 9 in that an interior diaphragm has been introduced. The web

depth and thickness are 62 in. (1575 mm) and 11/16 in. (17.5 mm), respectively. A

16x8x3/8 in. (406.4x203.2x9.5 mm) tube satisfies the lateral torsional buckling

criteria. This tube is smaller than the tube used in Design 9. The tension flange that

satisfies the rest of the limit states is 18x1-1 /4 in. (457.2x31.8 mm). Once again, the

web thickness of the hybrid Design 10 is the same as that of its homogeneous

counterpart, Design 8. The flange is smaller than that of Design 8, as would be

expected. Designs 4 and 10 again illustrate the differences between corrugated web

designs and flat web designs.

48

Design 11 is a non-composite, unstiffened flat web design, and is hybrid.

There are two end diaphragms. The first three design iterations were performed with 4

in. (101.6 mm), 6 in. (152.4 mm), and 8 in. (203.2 mm) deep tubes, respectively.

None of the suggested tubes with these depths could provide sufficient lateral torsional

buckling strength. Tube sizes that would scale by 0.45 to suggested tube sizes were

considered. The minimum weight design used an 8.89 in. (225.8 mm) deep tube. The

web depth and thickness are 61.11 in. (1552 mm) and 11/16 in. (17.5 mm)

respectively. The tube that satisfies the lateral torsional buckling criteria is

31.1 Ix8.89xO.83 in. (790.2x225.8x21.1 mm). A 28xI-l/4 in. (7I1.2x31.75 mm)

tension flange satisfies the rest of the limit states.

Design 12 is exactly the same as Design 11. This situation occurred before

with the non-composite corrugated web designs, Designs 5 and 6.

Designs 13 through 18

For the first set of twelve designs, the corrugated web flange transverse

bending moments were neglected. At this point, however, a second set of six

corrugated web designs that includes the effects of flange transverse bending moments

will be briefly discussed (see Table 3.3). The detailed geometry of the new designs

will not be discussed because there is very little change from the previous set of

corrugated web girder designs. The only change between Designs 1 through 6 and

Designs 13 through 18 is the size of the tension flange. The increased stresses in the

compression flange due to the Construction loading conditions were not significant

49

enough to require a larger tube. However, the increased stresses in the tension flange

due to Service II loading did require an increase in size.

Discussion of the Weights of the Designs

It is important to discuss the weights of the designs in more detail. For this

discussion, refer again to Tables 3.1 through 3.3. The girder designs are lighter when

an interior diaphragm is added, because the tube required to satisfy the lateral torsional

buckling criteria is smaller. For example, Design 14 is approximately 13% lighter

than Design 13. However, although the girder is lighter, the fabrication effort and cost

are increased by the necessary interior diaphragm.

In addition, the hybrid girders are lighter than the homogeneous girders. For

example, Design 15 is approximately 19% lighter than Design 13. However, the

weight savings must offset the cost of more expensive steel if the hybrid girders are to

be more economical. The non-composite designs are generally much heavier than the

composite designs because the girders alone carry the Strength I, Service II, and

Fatigue load combinations. The weight savings from using composite girders must

offset the cost and effort involved in making the girders composite with the deck if the

composite girders are to be more economical.

All of the corrugated web girders are lighter than their flat web counterparts.

This \vas one of the goals in setting the length-to-depth ratio close to 20. However.

some of the corrugated web girders are only slightly lighter than their flat web

counterparts. This is particularly evident when comparing Designs 13 and 7 or

50

Designs 14 and 8. The difference between Designs 13 and 7 is only 0.2% and the

difference between Designs 14 and 8 is only 0.5%. The savings in weight for these

designs do not seem to justify the added expense of forming and welding a corrugated

web. However, it is well known that corrugated web girders become more efficient

for deeper girders because the web depth-to-thickness ratio (D/tw) is not a controlling

factor as it is with flat web girders. This is discussed in more detail in Section 3.8.

Therefore, the corrugated web should prove to be more efficient for deeper designs.

The length-to-depth ratio of bridge girders is between 20 and 30, 20 being the deepest

practical design. Thus, to generate deeper designs, the prototype bridge must be

longer. The 131.23 ft. (40000 mm) prototype bridge was chosen because it had been

used for previous studies. The findings of this study, however, support a future design

study using a longer (e.g., 196.85 ft. (60000 mm)) prototype bridge.

3.8 Efficiency of Corrugated Web

As mentioned in Section 3.7, efficient design of corrugated web girders

(relative to flat web girders) was investigated. When the girder web is not deep

enough, a flat web of the same thickness as a corrugated web may have equal or

greater shear strength. It would be inefficient to corrugate a web in this situation. In

addition. since a corrugated web does not contribute to overall bending, corrugated

web girders require more steel in the tension flange than a similar flat web girder.

These issues are discussed below.

51

Efficiency of Corrugated Webs in Shear

The maximum design shear stress resistance of a corrugated web is 0.707 times

the shear yield stress of the web steel (Section 2.4). However, the maximum shear

stress capacity for an unstiffened flat web is the full shear yield stress. Therefore,

there is a clear range over which an unstiffened flat web has equal or greater strength

than a corrugated web. Though stated in Section 2.4, the AASHTO LRFD shear

strength specifications for flat webs are briefly reviewed here for convenience. The

nominal shear resistance of an unstiffened flat web is:

(Eq.3.1)

where, C is the ratio of the shear buckling stress to the shear yield stress. Vp is the

plastic shear force, or shear yield force, given by:

(Eq.3.2)

where Fyw is the yield stress of the web, D is the web depth, and tw is the web

thickness. The web depth-to-thickness ratio (Dltw) is used to calculate C, which in

tum, will detennine whether the web will yield in shear, buckle in the inelastic range,

or buckle in the elastic range. As mentioned earlier, given the appropriate web depth-

to-thickness ratio, C can have a value of one, thus giving the unstiffened flat web the

full shear yield strength.

Given the strength of the web steel. and the modulus of elasticity. the shear

strength can be plotted as a function of the web depth-to-thickness ratio. At a specific

depth-to-thickness ratio. the shear strength of an unstiffened flat web \\ill fall below

0.707 multiplied by the shear yield stress of the web. This is illustrated in Figure 3.4.52

If it is assumed that the corrugated web is designed as discussed in Section 3.6, with

AL less than or equal to 2.586, then for any web with a depth-to-thickness ratio larger

than the specific ratio mentioned above, the corrugated web will be stronger than the

unstiffened flat web. As stated earlier, two web steels with different yield stresses

were investigated in this research. These yield stresses were 50 ksi (345 MPa) and 70

ksi (485 MPa). For a 50 ksi (345 MPa) web, the depth-to-thickness ratio at which a

corrugated web becomes stronger than an unstiffened flat web is approximately 79.

For a 70 ksi (485 MPa) web, the depth-to-thickness ratio is approximately 67. Thus,

all corrugated web designs were checked to confirm that their depth-to-thickness ratios

were above the appropriate value.

Note that the results of this simple analysis do not imply that the web depth-to

thickness ratio of corrugated web girders can increase without consequence.

Depending on the corrugated web geometry, there is a maximum web depth-to

thickness ratio that can not be exceeded without the shear resistance being limited by

global web buckling. This ratio is quite large, however, and is not considered in

Figure 3.4. When considering only local buckling, as in Figure 3.4, the corrugated

web can have any depth-to-thickness ratio without a loss of strength.

Although the flat webs designed for the tubular flange girders described in

Section 3.7 were designed as unstiffened webs. a flat web which uses the minimum

amount of stiffeners is relatively easy to fabricate. The small number of stiffeners is

often considered negligible in tenns of cost. Often. stiffeners must be placed on webs

simply for the use of diaphragm connection plates. Thus. it should be detennined

53

when a corrugated web design is stronger than a flat web with a minimum number of

stiffeners. The AASHTO LRFD specifications provide the shear resistance of a

stiffened flat web. The nominal shear resistance is:

(Eq. 3.3)

where, Vp, C, and D are as defined earlier, and do is the stiffener spacing. The first

term in parentheses addresses shear buckling or yield, whereas the second term

addresses tension-field-action developed after shear buckling. Equation 3.3 may also

include a reduction factor based on the maximum moment within the shear panel,

however, for the present discussion, this factor is neglected.

The minimum number of stiffeners occurs when the stiffeners are spaced at the

AASHTO LRFD specified maximum stiffener spacing of three times the depth of the

web (i.e., dofD equal to 3). For this case, the shear strength can be plotted as a

function of the web depth-to-thickness ratio, and the depth-to-thickness ratio at which

the strength of a flat web with minimum stiffeners falls below the strength of a

corrugated web can be determined. For a 50 ksi (345 MPa) web, this depth-to-

thickness ratio is approximately 91. The 70 ksi (485 MPa) web is part of a hybrid

girder design. and the AASHTO LRFD specifications do not permit the use of tension-

field-action in the design of hybrid girders. and thus the shear strength of hybrid

girders is limited to that of an unstiffened flat web. Therefore. the results for an

54

unstiffened flat web and a flat web with stiffeners are the same. Figure 3.5 illustrates

these results.

Efficiency of Corrugated Webs, Considering the Tension Flange

The above discussions of corrugated web efficiency are not comprehensive in

making corrugated web girders efficient. They are simply a first check to eliminate

inefficient designs. Another step in the check of efficiency is to consider that

corrugated webs do not contribute to bending strength of a girder. Due to this lack of

bending strength contribution, a corrugated web girder must have a larger tension

flange than a girder with a flat web. Efficient corrugated web girder designs, relative

to flat web girder designs, will trade off steel from the web to the tension flange.

However, the reduction of steel in the web must be greater than the steel put back into

the tension flange. Otherwise, the corrugated web girder will be heavier and therefore

more expensive. Specific criteria have not been developed to address this issue.

55

Table 3.1 Prototype Corrugated Web Girder Designs (Neglecting Flange TransverseBending Moments)

DesiQn 1 2 3 4 5 6

Corruaated Web yes yes yes yes yes yes

Composite yes yes yes yes no no

Hybrid no no yes yes yes yes

Interior Diaphraam no yes no yes no yes

Dweb (in.l 62 62 62 62 61.11 61.11

Tweb (in.) 7/16 7/16 5/16 5/16 3/8 3/8

Tube Size (in.) 20x8x5/8 16x8x3/8 20x8x5/8 16x8x3/8 31.11 x8.89xO.83 31.11 x8.89xO.83

Bbf (in.) 27 27 22 25 26 26

Tbf(in.l 1-3/4 1-3/4 1-1/2 1-1/2 1-3/4 1-3/4

Ratioll\exuJl! 0.95 0.99 0.97 0.90 0.98 0.98

RatiolilnexuJl! 0.52 0.55 0.57 0.50 0.54 0.54

RatioVl\exuJl! 0.87 0.91 0.90 0.83 0.89 0.89

Ratio'he., 0.95 0.95 0.97 0.97 0.84 0.84

Ratio...b'Ie""eme.. NA NA NA NA NA NA

Ratio,en,oonflanne 0.64 0.64 0.61 0.69 0.62 0.62

Ratioflanaeb<3c>n" 5.71 3.60 5.71 3.60 3.76 1.88

RatioftbJ1!'~I.nce 0.93 0.88 0.95 0.89 0.49 0.46

Ratio,eMOOIl 0.99 0.99 1.00 0.95 1.00 1.00

Ratio,.,nueCw 0.68 0.67 0.96 0.84 0.82 0.82

Ratio,"",uP'COnnol.'e NA 0.78 NA 0.98 NA 0.95

Ratio,ube<hd.ne.. 0.72 0.98 0.72 0.98 0.85 0.85

WeiQhl (kips) 48.92 41.78 38.88 33.74 59.63 59.63NA =Not Applicable

56

Table 3.2 Prototype Conventional Flat Web Girder Designs

DeslQn 7 8 9 10 11 12

Corrugated Web no no no no no no

Composite yes yes yes yes no no

Hvbrid no no yes yes yes yes

Interior Diaphraqm no yes no yes no yes

Dv-Ieb (in.) 62 62 62 62 61.11 61.11

Tweb (in.) 11/16 11/16 11/16 11/16 11/16 11/16

Tube Size (in.) 20x8x5/8 16x8x3/8 20x8x5/8 16x8x3/8 31.11x8.89xO.83 31.11x8.89x0.83

Bbf (in.) 24 25 21 18 28 28

Tbf(in.) 1-1/2 1-1/2 1 1-1/4 1-1/4 1-1/4

Ratioln.xure 0.76 0.77 0.73 0.73 0.84 0.84

Ratiollln.xure 0.42 0.42 0.41 0.43 0.45 0.45

RatioVn.xure 0.70 0.70 0.67 0.67 0.76 0.76

Ratioshe., 0.79 0.79 0.79 0.79 0.81 0.81

Ratio...'bslendeme.. 0.35 0.50 0.30 0.44 0.20 0.20

Ratio,ensionnanne 0.67 0.69 0.88 0.60 0.93 0.93

Ration'noebn>ano 5.71 3.55 5.71 3.55 3.76 1.88

Ratio't><eSislance 0.94 0.88 0.95 0.91 0.48 0.46

RatioseMcell 0.99 0.99 0.98 0.98 1.00 1.00

Ratiof"",,ueCw NA NA NA NA NA NA

Ratio,at"",econnpl.te NA 0.72 NA 0.99 NA 0.96

Ratio,ube1hidn... 0.72 0.98 0.72 0.98 0.85 0.85

Weiqht (kips) 50.05 43.57 43.35 36.87 62.82 62.82NA = Not Applicable

57

Table 3.3 Prototype Corrugated Web Girder Designs (Incorporating FlangeTransverse Bending Moments)

Design 13 14 15 16 17 18

Corruqated Web yes yes yes yes yes yes

Comoosite yes yes yes yes no no

Hybrid no no yes yes yes yes

Interior Diaphraqm no yes no yes no yes

Dweb (in.) 62 62 62 62 61.11 61.11

Tweb (in.) 7/16 7/16 5/16 5/16 3/8 3/8

Tube Size (in.) 20x8x5/8 16x8x3/8 20x8x5/8 16x8x3/8 31.11 x8.89xO.83 31.11 x8.89xO.83

Bbf (in.) 33 29 24 19 32 32

Tbf (in.) 1-1/2 1-3/4 1-1/2 2 1-112 1-1/2

Ratiol tlexure 0.93 0.95 0.92 0.92 0.95 0.95

Ratioili tlerure 0.49 0.51 0.51 0.54 0.50 0.50

RatioVtlerure 0.84 0.87 0.85 0.86 0.86 0.86

Ratio'h... 0.95 0.95 0.97 0.97 0.84 0.84

RatiOw.bslond.m... NA NA NA NA NA NA

Ratio..n'ion',no. 0.92 0.69 0.67 0.40 0.89 0.89

Ratianann.tncono 5.77 3.60 5.77 3.60 3.79 1.89

Ratio'tn,"'.n", 0.98 0.99 0.98 0.99 0.49 0.46

Ratio,.",,,," 1.00 0.99 0.99 0.96 1.00 1.00

Ratio'a'"uoCW 0.64 0.63 0.88 0.83 0.78 0.78

Ratio'''"u.connol'''. NA 0.73 NA 0.97 NA 0.91

Ratio.UtlO'\hidnm 0.72 0.98 0.72 0.98 0.85 0.85

Weight (kips) 49.93 43.34 40.22 33.97 60.75 60.75NA =Not Applicable

58

50' (15240 rll'1)

2' (610 l'1l'1) 46' (14021 MM) 2' (610 rlrl)

hi 1rt;:J t:;:l l:';:l t;:l

-... -... -... -...6'-3' (1905 l'1l'1) 12'-6' (3810 l'1l'1) 12'-6' (3810 l'1rl) 12'-6' (3810 rlrl) 6'-3' 0905 l'1l'1)

Figure 3.1 Prototype Bridge

I

- ---J

--_._-----

- FW-unstiffened 50 ksi (345 MPa) I;I'I'

- FW-unstiffened 70 ksi (485 MPa) I!I

15.0 i~--------- ----,----------- ------~-------~~

10.0 ~--~--------- .......

5.0 ~

O.O:-~-"--~--·-- .~-~.---.--~--.~~-.-- ------"~-----.-. -

o 50 100 150 200 250

30.0 L -- ----

45.0

40.0 ~L====\

35.0 ~f- \ _

,~ 25.0 L .~ _~ ~-- ,~ 20.0:----------\

D/tw

Figure 3.2 Shear Strength of 50 ksi (345 MPa) and 70 ksi (485 MPa) Flat Webs

59

q=50.80' 0290 I'll'l)

(a) 50 ksi (345 MPa) Corrugated Web

q=30.88' 084.4 MI'l)

(b) 70 ksi (485 MPa) Corrugated Web

Figure 3.3 Prototype Bridge Corrugated Webs

_FW-unstiffened 50 ksi (345 MPa) i

--FW-unstiffened 70 ksi (485 MPa) .

35.0 -~------\----------i _CW 50 ksi (345 MPa),t _ CW 70 ksi (485 MPa)

30.0 -;'~;;;;;;;;;;~~::;::;===:::::::::::::~~:::::::~~-.

45.0 -;:-------- .------ ..-~.~===========,

f40.0 t:

f~'::!::!:::!::!::"~,

~ 25.0 -{-----------''''\------~ .

15.0

10.0 L __

5.0 ~------~----------~----~~---

0.0 .:- .--..--.-~--.-.--~.-~.-~--~-.~~-.-.~.. _.. ~~.~.__ L __ .--~.--.~

o 50 100 150 200 250D/tw

Figure 3.4 Comparison of Corrugated Web Shear Strength to Unstiffened Flat WebShear Strength for 50 ksi (345 MPa) and 70 ksi (485 MPa) Webs

60

25020015010050

__ FW-stiffened 50 ksi (345 MPa) I:

~~~'::!:::!~.-------J __ FW-unstiffened 70 ksi (485 MPa) 11

+------\-------1 _CW50ksi(345MPa) i~

- CW 70 ksi (485 MPa) iiII

45.0

40.0

35.0

30.0

~ 25.0:.

c 20.0l"

15.0

10.0

5.0

0.0

0D/tw

Figure 3.5 Comparison of Corrugated Web Shear Strength to Stiffened Flat WebShear Strength for 50 ksi (345 MPa) and 70 ksi (485 MPa) Webs

61

4. Test Specimen and Test Procedure

4.1 Introduction

In the previous chapter, the prototype bridge was described, and the results of a

design study were discussed. This design study investigated twelve different tubular

flange girder designs, which used various combinations of corrugated or flat web,

composite or non-composite, homogeneous or hybrid, and braced or unbraced

conditions. The tubular flange girder design process and the method used to establish

the corrugation geometry of the designs with corrugated webs were also discussed.

Also, design considerations for an economically efficient corrugated web were

discussed.

This chapter discusses the development of the test specimen and the testing

procedures used in this research. The first topic is the choice of prototype girder

designs to be scaled down into the test girders. A new corrugated web design is

introduced in order to make fabrication of the test specimen easier. The detailed

design of the test specimen is described, including stiffeners, welds, and shear studs.

The diaphragms used for the test specimen are those used previously by Kim (2004a).

These diaphragm designs were checked to make sure that they were adequate for the

test specimen. The loading conditions and instrumentation used in the tests are

discussed so that the reader can more fully understand the results provided in Chapter

5. Finally. the stress-strain properties of the materials used in the test girders. the

62

measured cross-section dimensions, and selected geometric imperfections of the test

girders are presented.

4.2 Choice of Test Girders

As mentioned in Section 4.1, the first task was to decide which prototype

girder designs to scale down into test girders. Composite designs were selected

because they are viewed as more economically efficient in practice. The deck

contributes to the load carrying capacity, and therefore composite girders are lighter

than non-composite girders. Tests that are valuable from an engineering practice

standpoint will encourage the future use of these types of girders. It was also decided

that a prototype girder design without an interior diaphragm should be used to provide

a good representation of the advantages of tubular flange girders.

For the composite designs with no interior diaphragm, estimated costs of the

homogeneous and hybrid designs were compared. It was determined that

homogeneous designs would be less expensive to fabricate because of the lower price

of the 50 ksi (345 MPa) steel. Fabrication of the test girders was performed by High

Steel Structures, Inc., located in Lancaster, Pennsylvania.

Industry advisors to the project from High Steel Structures and other

companies and agencies have some reservations about the economic efficiency of

corrugated web girders. The initial scope of this research project, however, was to

design and test concrete filled rectangular tubular flange girders with corrugated webs.

Thus. a compromise was reached in which the two test girders would consist of one

63

corrugated web girder and one flat web girder. Given all of the considerations

discussed above, it was decided that Designs 13 and 7 would be scaled down into test

girders, and these two test girders would be used in the test specimen.

4.3 Scaling Process

Scaling the Moment and Shear

Bending moment and shear were scaled to create the same stress levels in the

test girders as in the prototype girders. Flexural stress is calculated as follows:

MU=-

S(Eq.4.1)

where, cr is the flexural stress, M is the moment in the cross-section, and S is the

section modulus of the cross-section. The section modulus incorporates the

dimensional scale factor cubed, so the moment is multiplied by the dimensional scale

factor cubed. The shear stress is calculated as follows:

VQT=-

/1(Eq.4.2)

where, 't is the shear stress, V is the shear in the cross-section, and Q is the first

moment of the area, above or below the point in question, about the neutral axis. I is

the moment of inertia of the cross-section and t is the thickness of the cross-section at

the point in question. It is evident that using the scale factor on all girder dimensions

will create a net factor equivalent to the dimensional scale factor squared in the

denominator. TIms, the shear is multiplied by the dimensional scale factor squared.

64

Scaling the Prototype Girders

Initially, each girder dimension for prototype girder Designs 13 and 7 was

scaled by 0.45, and input along with the scaled moment and shear into the MathCAD

files which were used for design, in order to verify the scaling process. It was

observed that all limit state ratios were the same as they were for the corresponding

prototype girders. Simply scaling all girder dimensions by 0.45, however, does not

provide available tube sizes and plate thicknesses. It was therefore decided to choose

available tube sizes and plate thicknesses so that fabrication of the test specimen was

feasible. Some scaled dimensions were rounded up and others were rounded down in

order to keep limit state ratios similar to those of the prototype designs. Depths and

widths were chosen in 1/2 in. (12.7 mm) increments. Thicknesses were chosen in 1/16

in. (1.6 mm) increments. Also, the tube dimensions were chosen using input from

High Steel Structures regarding tube costs. A low cost tube was chosen over one that

provided limit state ratios closer to those ofthe prototype designs. This low cost tube

was slightly larger than necessary, and led to lower limit state ratios for lateral

torsional buckling. The scaled dimensions and limit state ratios are shown in Table

4.1. The scaled test girder cross-sections are shown with the corresponding prototype

girders in Figure 4.1.

When scaling the corrugated web, a (20 degrees) was not changed. but the

plate \\'idth (w) was multiplied by the 0.45 scale factor. The scaled webs are shO\\'TI in

Figure 4.2. Note that the shear limit state ratio for the 3/16 in. (4.8 mm) thick web of

scaled Design 13 is 1.02. If the web is incrementally increased in size by 1/16 in. (1.6

65

nun), then the shear limit state ratio falls to 0.75. The value of 1.02, though too large,

more closely matches the shear limit state ratio of the prototype Design 13, and since

the shear limit state would not be approached during testing, the 3/16 in. (4.8 mm)

web was maintained.

4.4 New Corrugated Web for Test Specimen

Due to the limited funding available for the project, it was desired to mitigate

fabrication effort and expense for the corrugated web test girder, and alternative ways

to obtain a corrugated web were considered. Six trapezoidal corrugated web girders

had been tested in fatigue at Lehigh University by Abbas (2003), and webs from these

girders were available for re-use. The corrugated web shape of these girders is shown

in Figure 4.3. a is the corrugation angle, b is the width of the longitudinal fold, c is

the width of the inclined fold, pis the ratio of the longitudinal fold width to the

inclined fold width, d is the projection of the inclined fold in the longitudinal

direction, hr is the corrugation centerline depth, q is the corrugation wavelength, and tw

is the thickness of the web. These webs were fabricated using steel with a 70 ksi (485

MPa) yield stress.

Several important design criteria were considered before these webs were re

used. As stated earlier, the corrugated web used in the test girder should have global

and local shear strength equal to the shear yield stress. In other words. neither global

nor local buckling could occur before the web yielded in shear. Shear strength design

criteria developed by Sause et al. (2003) show the follo\\ing modified version of

66

Equation 2.13, which guarantees that the global buckling shear strength of a

trapezoidal corrugated web is shear yielding:

(Eq.4.3)

where, D is the depth of the web, E is the modulus of elasticity of steel, Fyw is the

yield stress of the web material, and F(a,~) is:

F(a,[3)= (1+[3)sin3a{ 3[3+1 }3/4

[3 + cosa ,82 ([J +1)(Eq.4.4)

It was determined that the inequality of Equation 4.3 was satisfied. Also, it was

determined that AL:S 2.586 (Sect. 2.4), which guarantees that the local buckling shear

strength of a corrugated web is shear yielding. The test girder with the re-used web

was treated as a homogeneous design, even though the web material has a 70 ksi (485

MPa) yield stress. When assuming that the web has a yield stress of 50 ksi (345

MPa), the previous two inequalities are still satisfied.

The re-used trapezoidal corrugated web was incorporated into the MathCAD

files used for girder design, and new limit state ratios were obtained. These limit state

ratios are given in Table 4.2. The scaled Design 13 with the trapezoidal corrugated

web is hence forth called scaled Design 19. The deck thickness used in obtaining

these limit state ratios was 6 in. (152.4 mm) rather than the lOin. (254 mm) scaled by

0.45. for reasons that \..ill be discussed later. Therefore. new limit state ratios are also

provided in Table 4.2 for scaled Design 7 \\ith a 6 in. (254 mm) thick deck.

67

RatioIIIflexure and RatioVflexure were not reevaluated because the extra effort was not

justified.

The re-used corrugated web of scaled Design 19 was overstrength for shear, as

illustrated by the shear limit state ratio of 0.79. Note that the lateral torsional buckling

limit state ratio for scaled Design 19 was 0.93 with the re-used corrugated web. This

is because the flange transverse bending moments were increased by using a

trapezoidal web. The trapezoidal shape has an accumulated area under one half

corrugation (See Sect. 3.6) that is 3.9 times as large as that of the triangular shape.

Note that the Service II limit state ratio is 1.11 for scaled Design 19. Obviously, this

should be a concern for a girder that will be put in service, but is of little consequence

for the scaled Design 19. As described later in this chapter, the Service II load was not

a specific load condition applied during testing. As mentioned above, scaled Design

19 was treated as homogeneous, with the web yield stress assumed to be 50 ksi (345

MPa). No benefit was obtained from the actually greater web strength during testing.

Under the Strength I loading conditions, the girder was uniformly loaded to create a

moment of approximately 18500 kip-in (2.1 x109 N-mm) at midspan. This

corresponds to a maximum shear of approximately 104 kip (4.63x I05 N). The shear

strength of the corrugated \veb is approximately 135 kip (6.00xI05 N) when a 50 ksi

(345 MPa) yield stress is assumed for the web.

To re-use the trapezoidal webs from the previously tested girders. web pieces

were cut from three of the fatigue test girders and spliced together to provide the

necessary length of web. Webs from girders G3A. GSA. and G6A (Abbas. 2003)

68

were re-used for the scaled Design 19 test girder. Girders G3A and GSA had been

fatigue tested until cracking occurred. They were repaired and then tested without

further failure. G6A had failed early, and was never repaired. One of the girders had

a crack in the web at the end of a partial stiffener, and it can be viewed in Figure 4.4.

This crack was repaired by the fabricator. Figure 4.5 illustrates how the web pieces

were cut from the three girders and spliced together to provide a continuous

corrugated web. The dashed lines in the figure represent the cuts that were made.

Each corrugation wavelength is numbered and the N and S refer to North and South

longitudinal folds, respectively.

4.5 Design Details

4.5.1 Stiffener Designs

For scaled Designs 19 and 7, bearing stiffeners were required at the ends, and

diaphragm connection plates were required at midspan. Even though the prototype

girder Designs 13 and 7 were designed under the Construction loading conditions

without interior diaphragms, tests of scaled Designs 19 and 7 were planned both with

and without a midspan diaphragm present. Recall that scaled Design 19 has a

trapezoidal corrugated web and scaled Design 7 utilizes a flat web that was designed

without stiffeners (for shear). The flat web. however, was provided with additional

stiffeners at the midspan and quarter points. These were to prevent web distortion

(Kim 2004a). not to develop tension field action after shear buckling. Web distortion

69

is not considered to be an issue with the corrugated web. It was decided to design

these intermediate stiffeners to be the same as the bearing stiffeners.

The AASHTO LRFD specifications require that bearing stiffeners are

connected to both sides of the web, extend to the full depth of the web, and extend as

closely as practical to the outer edges of the flanges. In order to prevent local buckling

of the bearing stiffener plates, the following inequality must be satisfied:

b, S 0.48/pJ EF"'j

(Eq.4.5)

where, bl is the width of the stiffener, tp is the thickness of the stiffener, E is the

modulus of elasticity of steel, and Fys is the yield stress of the stiffener steel. It was

decided to use 50 ksi (345 MPa) steel for the stiffeners. Using Equation 4.5, with bl

chosen so that the stiffeners extend to the outer edge of the tubular flange, a stiffener

thickness of 0.50 in. (12.7 mm) was found to be satisfactory for both scaled Designs

19 and 7.

It is also necessary to verify that bearing stiffeners have the bearing resistance

to carry the reaction force at the bearing. In these calculations, the scaled maximum

shear in the test girders under the Strength I loading conditions was used as the

maximum value of the end reaction. The factored bearing resistance, Br• is:

(Eq.4.6)

where. Qb is the resistance factor for bearing (1.00) and Apn is the net area of the

stiffeners. taking into account the portion of stiffener that must be clipped to fit around

the flange-to-web fillet welds. This clip length was assumed to be 1 in. (25.4 mm).

70

Using Equation 4.6, it was determined that the stiffeners had satisfactory bearing

resistance.

Finally, the pair of bearing stiffeners was evaluated as part of an axial

compression member. This axial compression member consists of the stiffeners and a

portion of the web that extends nine times the thickness of the web on each side of the

stiffeners. The effective length of the axial compression member is 0.75 times the

web depth, due to buckling restraint provided by the flanges. The factored axial

compression resistance, Phis:

(Eq.4.7)

where, ~c is the resistance factor for compression (0.9), and Pn is the nominal axial

compression resistance. Note that the corrugated web bearing stiffeners were treated

as part of an asymmetric axial compression member because the stiffeners are attached

to an inclined fold. The stiffener geometry for scaled Designs 19 and 7 is presented in

Figures 4.6 and 4.7, respectively. St1 is a set of stiffeners located at a quarterpoint,

St2 is a set of midspan stiffeners, and St3 is a set of bearing stiffeners. St2 and St3

have bolt holes because they function as diaphragm connection plates. St I is located

on the flat web of scaled Design 7 to prevent web distortion. The stiffener locations,

as well as other information about scaled Designs 19 and 7. are illustrated in Figure

4.8.

71

4.5.2 Fillet Weld Designs

Tube Flange-to-Web Fillet Welds

The first welds considered were the tube flange-to-web and the bottom flange-

to-web fillet welds. Figure 4.9 provides illustrations for the discussion of these welds.

The design process is essentially the same for both flanges, but only the tube flange-

to-web fillet welds are shown in the figure. A unit longitudinal dimension of the

girder was considered for design.

The fillet welds were designed to resist web out-of plane bending along with

the horizontal shear transferred between the flange and web, and overall bending

stresses. The web was assumed fully plastified in plate bending, as shown in the

figure. The dimension, a, is the size of the fillet weld, and yielding of the weld is

assumed to occur along the throat. A tensile force, T, is developed on the throat of

one fillet weld, whereas a compressive force, C, is developed on the throat of the

other. Shear forces, Vz, also develop along the throat of the two fillet welds. The

shear and normal forces provide a vertical force resultant, F. The plastic moment of

the web, Mp, is a known quantity. The distance between forces, d, can be expressed as

a function of a. F is calculated using the following expression:

M"F=-d

(Eq.4.8)

Considering the tension side fillet weld. T and Vz can be expressed in terms of F. The

stresses, cry and 'tyz, are calculated by dividing force by the area.

The horizontal shear force carried by one fillet weld. Vx. is the lesser of one

half the fully yielded concrete filled tubular flange force or one half the fully yielded

72

web and bottom flange force. In the case of the corrugated web girder, the web was

not included in this calculation for reasons discussed previously. 'txy is calculated by

dividing Vx by the area. The stress calculations are:

T T(j =--=----

y area 0.707a(1)

v. V.T - • - •

>= - area - 0.707a(1)

Vx VxT ------.::.......,..-

" - area - O.707a(~J

(Eq.4.9)

(Eq. 4.1 0)

(Eq.4.11)

where, L is the span length of the girder. The stresses are substituted into Von Mises

yield criterion:

2 ( \2 ( )2 (2 2 2) 2((jx - (j y ) + (j y - (Y: J + (j: - (y x + 6 T X)' + T y: + Tr. = 2(j>p (Eq.4.12)

az and 'txz are assumed zero, so the only unknown is the contribution from overall

bending, ax. The yield criterion can be written as a function of ax, equal to the left

side minus the right side of Equation 4.12. For values of ax for which the function

remains negative, the distortion energy per unit volume in the state of combined stress

is less than that associated with yielding in a simple tension test, and therefore the

weld does not yield. An example of the function plotted versus ax is shown in Figure

4.10. The weld size was chosen so that the function ofax is negative over the overall

bending stress range that will be experienced by the girder at the weld location.

Figure 4.10 shows the function being negative for ax ranging from approximately -50

ksi (-345 :MPa) to 50 ksi (345 MPa). so the girder steel will yield in bending before the

73

weld metal does. The compression side of the tube flange-to-web fillet weld was

investigated in the same manner discussed above, but the tension side was determined

to be more critical. The calculations required the tube flange-to-web fillet welds to be

3/16 in. (4.8 mm), and the bottom flange-to-web fillet welds to be 1/4 in. (6.4 mm).

Tube Flange-to-Stiffener Fillet Welds

Next, the tube flange-to-stiffener fillet welds were investigated. Figure 4.11

provides illustration for the discussion of these welds. These welds are designed to

allow the stiffeners to develop their in-plane plastic moment, as shown in the figure.

This moment can develop as the stiffener helps the tube develop torsional moments to

restrain lateral torsional buckling of the girder (Kim 2004a). Based on the plastic

moment of the stiffeners, the force per unit length along the stiffener on the welds,

Fys·tp, was determined. Fys is the yield stress of the stiffener steel and tp is the

thickness of the stiffener. Three possible failure modes are shovm in Figure 4.11. In

Case I, there is tensile yielding due to normal stress on the horizontal faces of the

welds. The force per unit length required along the stiffener to cause this yielding, R1,

IS:

(Eq.4.13)

where, CJywcld is the yield stress of the weld and a is the size of the weld. Case 3

illustrates the situation where shear yielding occurs on the vertical faces of the welds.

The force per unit length required along the stiffener to cause this yielding. R3• is:

74

(Eq.4.14)

where, tyweld is the shear yield stress of the weld. Case 2 is combined shear and tensile

yielding on the weld throat, and can be analyzed using virtial work. A diagram of the

virtual displacements is also shown in Figure 4.11. Observing the virtual

displacements, it is evident that the force per unit length, R2, is:

R2 ·Li= 2(a(O.707a)Li a +r(O.707a)Lib)

After substitution for Lia and Lib, the following is obtained:

(Eq.4.15)

(Eq.4.16)

Using the Von Mises yield criterion, the following relationship between cr and t is

obtained:

(Eq.4.17)

Substitution of Equation 4.17 into Equation 4.16 yields:

(Eq.4.18)

R2 is a function of t, so the derivative is taken to find the minimum value of R2. This

is determined to be:

(Eq.4.19)

Therefore, Cases 2 and 3 provide the same resistance. and are the critical cases. A

weld size was chosen so that the resistance. R, was greater than the load. Fys·tp• The

calculations required the tube flange-to-stiffener welds to be 9/16 in. (14.3 mm). The

75

remainder of the weld designs were not complicated, and do not require extensive

explanation.

4.5.3 Selection of Deck

Initially a composite cast-in-place deck was considered for the test specimen.

Shear studs could be mounted to the tubular flanges, and then the deck could be

poured. However, this created some difficulties in testing the test specimen under

Construction loading conditions. As will be discussed in Section 4.6, the tests

performed under the Construction loading conditions required the girders to be loaded

in the non-composite state. If the deck was cast-in-place, the cast-in-place deck would

have to be thick enough for the concrete to provide the full Construction loading

conditions. After investigating this possibility, it was detennined that, due to

dimensional scaling and other factors, the deck would have to be 20 in. (508 mm)

thick. The prototype bridge deck thickness is only lOin. (254 mm) and the scaled

deck thickness should only be 4.50 in. (114.3 mm). Obviously, the excessive

thickness required did not seem practical.

Therefore, it was decided to re-use the pre-cast deck previously used by Kim

(2004a) for similar sized test specimens. Similar to the present research, the previous

research by Kim (2004a) used a 0.45 scale test specimen based on a 131.23 ft. (40000

mm) bridge, so the pre-cast deck was the correct length. The deck concrete had an

ultimate strength of 6 ksi (41.4 MPa). as assumed for the designs in the present

76

research. In addition, the pre-cast deck design was determined to be adequate for the

loading applied in the present research.

The existing deck consisted of six panels, 6 in. (152.4 rnm) thick by 156 in.

(3962 rnm) wide by 120 in. (3048 rnm) long. The panels are post-tensioned

longitudinally. The post-tensioning strands used by Kim (2004a) were 0.60 in. (15.2

rom) diameter seven-wire strand, with an ultimate tensile strength of 270 ksi (1862

MPa). A post-tensioning stress of 187 ksi (1289 MPa) was applied to each tendon.

Kim (2004a) used nine post-tensioning strands, but for reasons discussed in Section

4.5.5, only seven strands were used in the present study. Calculations were made to

verify that the lower number of post-tensioning strands would be adequate. The steps

taken to make this pre-cast deck composite with the girders are discussed in Section

4.5.4.

4.5.4 Deck Construction

As mentioned in the previous section, the deck was pre-cast, and therefore

steps were taken to make it composite with the girders. The first step was to core

holes in the deck panels so that shear studs could be placed through the holes and

welded to the girders. The hole size and location were determined based on the shear

stud design discussed in the next section. The second step was to make the deck level.

A laser level was used to establish a level plane. and the deck was shimmed to parallel

with this level plane. The third step was to post-tension the deck. The fourth step was

to place and weld the shear studs to the top of the tubular flange through the core

77

holes. Then, wood forms were built along the sides of the test girder tubes to form a

haunch, and grout was poured through the core holes to fill the haunch and the core

holes up to the top surface of the deck. Photographs ofa core hole and shear studs are

provided in Figures 4.12 and 4.13, respectively.

4.5.5 Shear Stud Design

The AASHTO LRFD specifications outline the design requirements for shear

studs. The ratio of the height to the diameter of the shear stud must not be less than

4.0. Also, the clear depth of concrete cover over the top of the shear stud must be at

least 2 in. (50.8 mm) and the shear stud must penetrate into the deck at least 2 in. (50.8

mm). Both 5 in. (127 mm) and 6 in. (152.4 mm) long shear studs were used, based on

the girder deflections under the weight of the pre-cast deck panels and requirements

for clearance and penetration. Shear studs must not be closer than four stud diameters

center-to-center transverse to the longitudinal axis of the girder, and the clear distance

between the edge of the top flange and the edge of the nearest shear stud must not be

less than I in. (25.4 mm). Given these requirements, as well as the fact that the studs

had to fit within a core hole, it was decided to use the four stud diamond shaped shear

stud arrangement illustrated in Figure 4.14. A 0.75 in. (19.1 mm) stud diameter was

chosen.

After the shear stud diameter and arrangement were chosen. the pitch of the

shear studs. p. was determined based on the fatigue limit state:

J!"Q < ll RZr

I - p

78

(Eq.4.20)

where, Vsr is the shear force range under live load plus impact for the fatigue limit

state, Q is the first moment of the transformed area of the slab about the neutral axis of

the short-term composite section, I is the moment of inertia of the short term

composite section, ng is the number of shear studs in a group (ng=4), and Zr is the

shear fatigue resistance of an individual shear stud determined from the AASHTO

LRFD specifications. All of the values used in Equation 4.20 were scaled values.

The inequality expressed in Equation 4.20 states that the shear flow at the de~k-to-

girder interface under the fatigue loading must be less than or equal to the resistance of

a stud group divided by the pitch. In addition to Equation 4.20, the center-to-center

pitch of the shear studs is not allowed to exceed 24 in. (609.6 mm) by the AASHTO

LRFD specifications. It was determined from Equation 4.20 that the pitch must be

less than 22.08 in. (560.8 mm).

The number of shear studs required by the strength limit state was investigated.

This number, n, is:

Vn=_hQ,

(Eq.4.21)

where, Vh is the nominal horizontal shear force, equal to the lesser of the plastic

strength of the deck or the girder, and Qr is the factored shear resistance of one stud

from the AASHTO LRFD specifications. Thus, Equation 4.21 states that the number

of studs required is the total shear divided by the shear strength of one stud. These

calculations showed that 39 shear studs were required between the points of zero and

ma..ximum moment. The pitch detemlined from the fatigue limit state was determined

to be more critical.

79

The pitch of the shear studs was not a flexible design choice because the core

hole locations were limited. There were various reinforcement bars in the pre-cast

deck panels that needed to be avoided. A core hole pattern was established, however,

that satisfies the strength limit state requirement (44 shear studs were used). The core

hole spacing is not constant, and does not always satisfy the fatigue limit state pitch

requirement. However, fatigue loading was not part of the test program (see Section

4.6). The core hole pattern is illustrated in Figure 4.15. The transverse reinforcing is

the prestressed strands and the longitudinal reinforcing is the post-tensioning strands.

The core holes interfered with two of the post-tensioning strands used previously by

Kim (2004a), so only seven strands were used, as noted earlier. Note that the shear

stud design was generated for the scaled Design 19 test girder, and the web was not

included in calculating the plastic strength of the girder. The shear stud design is not

conservative for scaled Design 7, which requires 52 shear studs between the points of

zero and maximum moment. However, scaled Design 7 was taken to only 67% of its

plastic moment during the testing.

4.6 Test Procedures

The third objective stated in Section 1.2 was to test the scaled girders to

investigate their ability to carry their design loads. The tests were performed outdoors.

due to the size of the test specimen and lack of space on the lab floor. The load was

applied by placing 24 x 24 x 72 in. (609.6 x 609.6 x 1829 mm) concrete blocks.

having an average weight of 3.3 7 kip (15.0 kN). on the deck of the test specimen

80

(Figure 4.16). The blocks were placed two across on the deck so that the weight of

one block could be assumed to act on each girder of the test specimen. The blocks

were placed onto the deck by a crane.

Two loading conditions are of particular interest in this research. The first was

the Construction loading condition. The test loading condition which simulates this

loading condition will be referred to as the Simulated Construction loading condition.

The tests under this loading condition investigated the lateral torsional buckling

strength of the tubular flange girders before they were composite with the deck. The

second loading condition of importance was the Strength I loading condition, which

investigated the flexural strength of the composite girder and deck. The test loading

condition which simulates this loading condition will be referred to as the Simulated

Strength I loading condition.

An additional consideration was the stress in the test girders when the girders

were made composite with the deck. The test specimen was loaded with blocks at the

time the test girders were made composite with the deck to create the scaled moment

at midspan that produced the correct stresses in the test girders at midspan for the

beginning of the composite condition. This loading condition is called the Simulated

Mdc loading condition. After the girders were made composite with the deck, blocks

from the Simulated Mdc loading condition were augmented with the additional blocks

to reach the Simulated Strength I loading condition.

The number and spacing of concrete blocks was calculated such that the

moment at midspan was the same as the moment under the corresponding loading

81

condition in the AASHTO LRFD specifications. The moment diagram across the

simply supported span simulated the moment diagram from a uniform distributed load.

The moment created by the girder steel, concrete within the rectangular tube

compression flange, deck, and details such as stiffeners and instrumentation cables

was considered. A number and spacing of blocks was determined for the Simulated

Construction loading condition and the Simulated Strength I loading condition. The

scaled midspan moment levels that were to be reached in the Simulated Construction,

Simulated Mdc, and Simulated Strength I loading condition tests were 7946 kip-in

(9.0x108 N-mm), 5297 kip-in (6.0x108 N-mm), and 18500 kip-in (2.1 X 109 N-mm),

respectively. Figure 4.16 shows the corresponding block arrangements.

The order that the blocks were placed on the test specimen was also important.

The loading was intended to be similar to an increasing uniform load, even though the

loading was applied by a number of concentrated loads. This was achieved by

determining the new moment diagram after each block was placed. This moment

diagram was compared to the moment diagram from a uniform distributed load equal

to the weight of the blocks divided by the length of the test specimen. Block

placement sequences were determined to make the two diagrams very similar. The

midspan moments calculated from the block arrangements for the Simulated

Construction. Simulated Mdc • and Simulated Strength I loading condition tests were

7962 kip-in (9.0x108 N-mm). 5870 kip-in (6.6xl08 N-mm). and 18711 kip-in (2.1x109

N-mm). respectively.

82

The block arrangements are illustrated in Figure 4.16. The Simulated Mdc

loading condition arrangement illustrated in Figure 4.16 (b) was adjusted slightly

before the blocks of the Simulated Strength I loading condition were added. The

Simulated Mdc loading condition blocks are shaded in the Simulated Strength I loading

condition arrangement (Figure 4.16 (c». Note that each block illustrated in the figure

represents two blocks, the one shown and one directly behind it.

Blocks were placed on wood cribbing that in turn transferred the load down to

the deck. Figure 4.17 shows the wood cribbing. The longitudinal members were

parallel to the girders. Two longitudinal members transferred load to a single girder,

and were spaced equidistantly from the girder. The cribbing included transverse wood

pieces which created the proper block spacing. During the non-composite stages

(Simulated Construction and Simulated Mdc loading conditions), each block applied

two loads to each girder through the shims that the deck panels sat on. The bottom of

the wood shims had a layer ofTeflon. An additional layer ofTeflon was placed on the

top flange of the test girders, at the shim locations, creating a Teflon-on-Teflon

interface. Figure 4.18 shows a picture of a wood shim. For some of the non

composite testing stages, rollers oriented to roll in the transverse direction of the test

specimen were placed between the deck and scaled Design 7 (see Sect. 5.2). For

stability purposes, the deck still sat on wood shims on scaled Design 19 during this

time. Figure 4.19 shows a picture of a roller. During the composite stage (Simulated

Strength I loading condition). each block applied a single load to the composite

83

section because the deck sat on a continuous haunch. Figure 4.20 shows a picture of

the haunch.

4.7 Test Instrumentation and Data Acquisition System

The instrumentation used during the tests included 127, 120 ohm, uniaxial

strain gages, sixteen +/- 2 in. linear variable differential transformers (LVDT), twelve

+/- 3 in. LVDT, and eight string potentiometers with various ranges from lOin. to 25

in. Thus, 163 total channels were monitored during testing. The strain gages were

conditioned by Vishay signal conditioners. Each channel was run to one of four

analog-to-digital boards, where the signals were converted and read by a PC. The PC

was equipped with the TestPoint data acquisition software. The TestPoint program

was written to save data to an output file, and to plot selected vertical deflections and

lateral displacements of the test girders during the tests.

Figures 4.21 through 4.25 illustrate the locations of the instrumentation. The

small rectangles represent strain gages, whereas the small circles indicate locations

where a displacement transducer is attached. Figure 4.21 shows the profile view of

the instrumentation located on scaled Design 7, and Figure 4.22 provides the details

of the instrumentation. The purpose of the instrumentation shown in each drawing

detail is discussed in this paragraph. Detail A shows a set of vertically oriented web

strain gages used to measure web distortion in the flat web. Detail B shows a set of

longitudinally oriented web strain gages used to detem1ine the location of the neutral

a.xis. Detail C shows a set of longitudinally oriented flange strain gages used along

84

with those in Detail B to locate the neutral axis, and observe bending behavior. It was

determined through calculation that the cross-section labeled by G in Figure 4.21 and

depicted in Detail G in Figure 4.22 would remain elastic throughout testing, and thus

could be used as an "Elastic" section for monitoring the load level. Flange strain

gages shown in Detail C were also located at these Elastic sections. Detail D shows

the flange strain gages used to check first yield due to bending and the transducers

used to measure vertical deflection at midspan. Detail E shows the transducers used to

measure vertical deflection at other cross-sections, and Detail F shows the transducers

used to measure longitudinal displacement and twist of the tension flange.

Figure 4.23 shows the profile view of the instrumentation located on scaled

Design 19, and Figure 4.24 provides the details of the instrumentation. Details A and

J show the vertically oriented web strain gages used to measure web distortion in the

corrugated web. Detail D shows the transducers used to measure vertical deflection at

midspan, and Detail E shows the transducers used to measure vertical deflection at

other cross-sections. Detail F shows the transducers used to measure longitudinal

displacement and twist of the tension flange. Detail I shows the strain gages used to

differentiate between overall, plate, and flange transverse bending, as well as to

measure strain on an Elastic section.

Detail K shows strain gages used to measure flange transverse bending in the

tube and bottom flange. The C-Factor Correction Method (Abbas 2003) was used to

deternline the flange transverse bending moments. and it was determined that the

ma.ximum flange transverse bending moment would occur in the first inclined fold.

85

followed by a zero flange transverse bending moment in the second inclined fold. The

strain gages shown in Detail K were used to measure strains from these bending

moments. The C-Factor Correction Method also revealed that flange transverse

bending moment stresses would combine with overall bending moment stresses to

create a more critical point than midspan. Hence, the strain gages shown in Detail L

were used to observe first yield. Figure 4.25 shows Detail H, which shows the

transducers used to measure lateral displacements of the two test girders.

4.8 Stress-Strain Properties of Test Specimen Materials

Steel tension coupon tests and concrete cylinder compression tests were

conducted on the test specimen materials. The tension coupon tests were performed

according to ASTM E8-00. The coupons were standard 8 in. (203.2 mm) gage length

coupons. Coupons were tested using a bracket with linear displacement

potentiometers mounted to each side. The average displacement from the two linear

displacement potentiometers was divided by the gage length to provide the strain data.

Also, some of the coupons were instrumented with uniaxial strain gages on both sides

at the midpoint of the gage length. The tensile force ofthe test machine was divided

by an average of three cross-sectional area measurements, within the gage length, to

provide the stress value. The yield stress was determined using the 0.2% offset

method.

Figure 4.26 illustrates the identifiers used for the material. The letters before

the hyphen (CW of FW) refer to whether the material is from the corrugated web

86

girder (scaled Design 19) or the flat web girder (scaled Design 7). The letters after the

hyphen represent the tube (T), concrete (C), web (W), or flange (F). Scaled Design 19

was made using two tubes spliced together from different heats. One is approximately

48 ft. (14630 mm) long, whereas·the other is approximately 12 ft. (3658 mm) long.

Coupons were taken from both tubes. Whenever coupons were taken from a tube,

they were taken at six places around the cross-section, including two from each of the

long tube sides, and one from each of the short tube sides.

Scaled Design 7 was also made using two tubes, but both were from the same

heat. Therefore, only one set of coupons was tested. For scaled Design 7, the coupons

were not flat, and had a large curvature after being cut from the tube. The curvature

created approximately I in. (25.4 mm) of out-of-flatness from the endpoints to the

midpoint of the coupons, which had a length of26 in. (660.4 mm). During the tension

tests, the linear displacement potentiometers did not provide accurate results for small

values of strain, because of the interaction of the transducer bracket and the curved

coupons. For this reason, only the results from the coupon with strain gages were used

in determining the yield stress and strain. The strain gage data showed early softening

of the steel. Calculations supported this by showing that an out-of-flatness of

approximately I in. (25.4 mm) at the midpoint of the coupon will cause one side of the

coupon plate to reach the yield strain as the coupon becomes straight under the tensile

load.

The web for scaled Design 19 is the web used by Abbas (2003). Recall that

the web was created from three of the girders tested by Abbas. Tension coupon data

87

for the web material of Abbas' girder G6A, which provided the web plate for the

midspan area of scaled Design 19 was used in the present study. Scaled Design 7 has

several splices in the web, but the web came from a single plate. The tension flange

steel for both test girders came from the same plate, so a single set of four coupons

was taken from this plate.

Tables 4.3 through 4.9 provide tension test data from the coupons. alp and Elp

are the proportional limits of stress and strain, ayand Ey are the yield stress and strain,

and au and Eu are the ultimate stress and strain. The tables also include a stress-strain

point which corresponds to a stress equal to the average of the yield stress and ultimate

stress. Data is provided for each coupon, and the average of the set of coupons, for

each type of material. In most cases where strain gages and linear displacement

potentiometers were used in the test, the data was nearly identical, and only the linear

displacement potentiometer data is presented. For the FW-T coupons, it was noted

earlier that the linear displacement potentiometer data was not accurate for small

values of strain, so the data for small values of strain is from the strain gages on one

coupon.

A "Material Model" row is included for each set of coupons. The Material

Model row was used as input for finite element analyses discussed in Section 5.6. In

most cases. the Material Model is a quadra-linear curve based on the data sho"t'TI in

this row of the tables. The data sho"t'TI in this row is the average data for CW-T (48

ft.). CW-T (12 ft.). CW-W. CW-F. FW-W. and FW-F materials. For the FW-T

material. the Material Model row uses the data from the single coupon tested \\;th

88

strain gages for the linear proportional limit and yield properties. The linear

displacement potentiometers provided accurate results for large values of strain, so

averages were used for the ultimate strain. The strain corresponding to the average of

the yield stress and ultimate stress was beyond the range of the strain gages, but less

than the point when the linear displacement potentiometers started providing accurate

results. Therefore, this strain had to be approximated. Figures 4.27 through 4.33

provide illustrations of the stress-strain curves from the tests, as well as the

corresponding quadra-linear curves. It is evident that the quadra-linear curves provide

a good representation of the test data. For the FW-T case shown in Figure 4.31,

several additional points were added to the Material Model curve so that it would

better represent the early softening of the material.

The concrete within the two tubes came from the same pour. At the time ofthe

pour, fifteen 6 in. (152.4 mm) by 12 in. (304.8 mm) cylinders were made. The

concrete cylinder compression tests were performed according to ASTM C 39/C 39M

01. The cylinders were tested at 7, 14,21, and 28 days for the ultimate strength. At a

time close to testing of the test specimen, a stress-strain test was performed on the

remaining three cylinders. A bracket was placed on the cylinders, and an LVOT was

mounted to each side. Strain was calculated by dividing the average displacement of

the LVOTs by the gage length. Stress was calculated by dividing the compressive

force in the test machine by the cross-sectional area of the cylinder. All three

cylinders provided similar results. and one of the stress-strain curves is illustrated in

89

Figure 4.34. The average ultimate strength of the three cylinders was 7.8 ksi (53.8

MPa).

4.9 Measured Girder Cross-Section Dimensions and Initial Tube

Imperfection

Measured Girder Cross-Section Dimensions

The actual cross-section dimensions of the test girders were measured and the

averages are presented in Table 4.10. The tension flange width and thickness was

measured at 10 places along the test girder spans. The tube was assumed to have its

nominal outer dimensions of lOin. x 4 in. The tube thickness was measured from the

tension test coupons. The web thickness was measured at three places on each end

and the web depth was measured once at each end.

Test Girder Initial Imperfection

The initial imperfection (out-of-straightness or sweep) of the tube was

measured for both test girders. Table 4.11 provides the initial tube imperfection of

scaled Designs 7 and 19. In Table 4.11, x represents the longitudinal distance along

the test girder measured from the west bearing. A more detailed coordinate system is

provided in Section 5.3. The maximum amplitude of the initial tube imperfections

was equal to Ll945 and Ll1512 for scaled Designs 7 and 19. respectively. where Lis

the test girder span. Initial imperfection was considered positive in the south

direction. Thus. it is evident that the scaled Design 7 initial tube imperfections were to

90

the south, whereas the scaled Design 13 initial tube imperfections were to the north.

At the time, it was thought that the tube out-of-straightness was the critical

imperfection. As discussed in Chapter 5, however, it was observed that experimental

results did not agree well with Finite Element Method (FEM) simulation results, and

various tension flange imperfections were studied using FEM simulations.

91

Table 4.1 Scaled Girder Designs 13 and 7

Scaled Girder Design 13 7CorruQated Web yes noComposite yes yesHybrid no noInterior DiaphraQm no noDweb (in.) 28 28Tweb (in.) 3/16 5/16Tube Size (in.) 10x4x1/4 10x4x1/4Bbf (in.) 14 10Tbf (in.) 3/4 3/4

Ratiolnexure 0.88 0.74

Ratioilinexure 0.46 0.41

RatioVnexure 0.80 0.67

Ratioshear 1.02 0.77

RatiOwebslendemess NA 0.30

RatiOtensionnanoe 0.78 0.56

Rationanoebracinn 5.22 5.22

Rationbresistance 0.75 0.73

Ratioservicell 0.95 0.94

RatiOtatioueCW 0.61 NA

Ratiotatioueconnniate NA NA

RatiOtubethickness 0.91 0.91NA=Not Applicable

92

Table 4.2 Scaled Girder Designs 19 and 7 (6 in. (152.4 nun) thick deck)

Scaled Girder DesiQn 19 7Corrugated Web yes noComposite yes yesHybrid no noInterior Diaphragm no noDweb (in.) 28 28Tweb (in.) 1/4 5/16Tube Size (in.) 10x4x1/4 10x4x1/4Bbf (in.) 14 10Tbf (in.) 3/4 3/4

Ratiolnexure 0.88 0.67

Ratioilinexure NA NA

RatioVnexure NA NA

Ratioshear 0.79 0.77

Ratiowebslendemess NA 0.30

RatiOtensionnanne 0.78 0.56

RatiOnanaebracina 5.22 5.22

Ratio"bresistance 0.93 0.73

Ratioservicell 1.11 0.91

RatiofatiaueCW 0.58 NA

Ratiofatiaueconnolate NA NA

RatiOtubethicl<ness 0.91 0.91NA=Not Applicable

93

Table 4.3 CW-T (48 ft.) Stress-Strain Properties

alp a y au (ay+au)/2 Eat (ay+au)/2CW-T (48 tt) (ksi) EJD (ksi) (ksi) Ev (ksi) (ksl) &u (ksi) (ksi) (ksll

Coupon 1 40 0.001379 54.7 0.003927 65.8 0.143637 60.3 0.018800

Coupon 2 40 0.001379 55.1 0.004231 65.0 0.152312 60.1 0.019601

Coupon 3 35 0.001207 54.6 0.003882 64.9 0.140590 59.8 0.017889

Coupon 4 40 0.001379 56.9 0.003973 66.8 0.110591 61.9 0.015905

Coupon 5 40 0.001379 60.7 0.004040 68.7 0.047456 64.7 0.011781

Coupon 6 40 0.001379 52.7 0.003937 63.5 0.153025 58.1 0.025269

Average 39.2 0.001351 55.8 0.003998 65.8 0.124602 60.8 0.018208MaterialModel 39.2 0.001351 55.8 0.003998 65.8 0.124602 60.8 0.018208

Table 4.4 CW-T (12 ft.) Stress-Strain Properties

alp ay au (ay+au)/2 Eat (ay+au)/2CW-T (12 tt) (ksi) EJD(ksl) (ksi) Ev (ksi) (ksi) &u (ksi) (ksi) (ksi)

Coupon 1 40.0 0.001379 59.3 0.004024 62.5 0.019689 60.9 0.006577

Coupon 2 45.0 0.001552 64.9 0.004410 67.6 0.020228 66.3 0.006902

Coupon 3 40.0 0.001379 61.3 0.004238 64.0 0.025915 62.7 0.007472

Coupon 4 45.0 0.001552 60.1 0.004175 63.3 0.023300 61.7 0.010360

Coupon 5 50.0 0.001724 61.1 0.003998 64.5 0.028545 62.8 0.010743

Coupon 6 45.0 0.001552 62.1 0.003916 64.4 0.020650 63.3 0.010386

Averaqe 44.2 0.001523 61.5 0.004127 64.4 0.023055 62.9 0.008740MaterialModel 44.2 0.001523 61.5 0.004127 64.4 0.023055 62.9 0.008740

Table 4.5 CW-W Stress-Strain Properties

alp cry au (ay+au)/2 Eat (ay+au)/2CW-W (ksi) EJD (ksi) (ksi) Ev (ksi) Iksi) &u Iksi) (ksl) (ksil

Coupon 1 40.0 0.001379 69.1 0.004488 97.8 0.118143 83.5 0.021833MaterialModel 40.0 0.001379 69.1 0.004488 97.8 0.118143 83.5 0.021833

94

Table 4.6 CW-F Stress-Strain Properties

alp a, au (a,+a.)/2 Eat (a,+a.)/2CW·F (ksil E!D(ksil (ksil Ev (ksil (ksil Eu lksil iksil (ksi)

Coupon 1 61.3 0.002114 61.4 0.010560 85.0 0.124452 73.2 0.030316

Coupon 2 60.8 0.002097 60.9 0.010547 84.6 0.124977 72.8 0.030637

Coupon 3 60.2 0.002076 60.3 0.011512 83.6 0.129828 72.0 0.031206

Coupon 4 60.4 0.002083 60.5 0.011922 83.7 0.123372 72.1 0.031626


Table 4.7 FW-T Stress-Strain Properties

alp a, au (a,+a.)/2 E at (a,+a.)/2FW·T (ksi) E!D(ksl) (ksi) Ev (ksl) (ksi) Eu (ksi) (ksl) (ksl)

Coupon 1 10.0 0.000345 54.4 0.003881 68.9 0.151539 61.7 NA

Coupon 2 NA NA NA NA 65.3 0.174318 59.9 NA




Average NA NA NA NA 69.1 0.153806 61.7 NAMaterialModel 10.0 0.000345 54.4 0.003881 69.1 0.153806 61.7 0.007000

NA=Not Applicable

Table 4.8 FW-W Stress-Strain Properties

alp a, a. (a,+a.)/2 Eat (a,+a.)/2FW·W (ksi) CtD (ksl) (ksl) Ev (ksi) (ksl) Eu (ksl) (ksl) (ksl)

Coupon 1 35.0 0.001207 57.9 0.004371 71.5 0.106899 64.7 0.027839

Coupon 2 40.0 0.001379 59.9 0.004329 73.9 0.129492 66.9 0.029496

Coupon 3 45.0 0.001552 60.6 0.004627 74.3 0.118111 67.5 0.030119

Coupon 4 40.0 0.001379 62.1 0.004911 75.7 0.130339 68.9 0.029743

Averaae 40.0 0.001379 60.1 0.004560 73.9 0.121210 67.0 0.029299MaterialModel 40.0 0.001379 60.1 0.004560 73.9 0.121210 67.0 0.029299

95

Table 4.9 FW-F Stress-Strain Properties

alp a y au (ay+au)/2 Eat (ay+au)/2FW-F (ksil £JD (ksil (ksil &, (ksl) (ksl) Eu (ksil (ksi) (ksi)

Coupon 1 61.3 0.002114 61.4 0.010560 85.0 0.124452 73.2 0.030316

Coupon 2 60.8 0.002097 60.9 0.010547 84.6 0.124977 72.8 0.030637

Coupon 3 60.2 0.002076 60.3 0.011512 83.6 0.129828 72.0 0.031206

Coupon 4 60.4 0.002083 60.5 0.011922 83.7 0.123372 72.1 0.031626


Table 4.10 Average Measured Girder Dimensions

TensionTube Tension Flange Web Web

Thickness Flange Thickness Depth ThicknessTest Girder (in.) Width (in.) (in.) (in.) (in.)

Scaled Design 19 0.23 13.99 0.76 28.09 0.25Scaled Design 7 0.24 9.95 0.75 28.00 0.32

Table 4.11 Initial Imperfection (Sweep) of Tubes

Scaled Design 7 Scaled Design 19x location (in.) Imperfection (in.) x location (in.) Imperfection (in.)

708.66 0.00000 708.66 0.00000648.66 0.18750 648.66 -0.15625588.66 0.56250 588.66 -0.21875528.66 0.65625 528.66 -0.28125468.66 0.75000 468.66 -0.31250408.66 0.71875 408.66 -0.25000354.33 0.75000 354.33 -0.31250348.66 0.71875 348.66 -0.37500288.66 0.62500 288.66 -0.46875228.66 0.53125 228.66 -0.43750168.66 0.50000 168.66 -0.37500108.66 0.28125 108.66 -0.2187548.66 0.09375 48.66 0.03125

0 0.00000 0 0.00000

96

20x8x~ in.

10x4x! In.

52' (1 75 rUT)

28' Oil. MM)

33' (838.2 fTlfTl)3, <19.1 MM)4 14' (355.5 MfTl)

(a) Design 13

2Dx8xa In.

JOx4x~ In.

62' 0575 fTlfTl)

ft,' <17.5 nM)

28' 011.2 MM)

5, (7.9 MM)fb

1~' (38.1 nn) 34

, 09.124' (609.6 rlrI)

(b) Design 7

Figure 4.1 Prototype and Scaled Versions of Designs 13 and 7

97

q=22.8£>' (580.£> PH'))

(a) 50 ksi (345 MPa) Corrugated Web

q=13.90' (353.1 MM)

(b) 70 ksi (485 MPa) Corrugated Web

Figure 4.2 Scaled Corrugated Webs

8.66' (220 I'll'l)

hr=5.91' <150 ",,) R=4.72' (120 ,.,,.,)

d=7.87' (200 ,.,,.,) d=7.87' 200 I'll'l)b=Il.81' (300 I'l")

q=39.37· <1000 I'l")

Figure 4.3 Trapezoidal Corrugated Web

98

Figure 4.4 Fatigue Crack

99

INTENTIONAL SECOND EXPOSURE

Figure ..L-t Fatiguc Crack

llll

G3A

1'-9~' (547.7 1'1I'I) 1'-5it;· (449.3 /1/1)

2B' OIL

I I

I - I'- 1- - l- I- . - ~ - I- I- ... 1- r1/1/1) I 1 S I N 2 S 2 N 3 S 3 N 4 S 4 N 5 S 5 N 6 S 6 N 71 5

- '- I- . - ~ ~ . - -I- "'" - I-- I- I- - Hr

t I

South [jJ,.de,., No,.th f ltee ~lt,.tiltl Stirfene,.~

G6A

IB'-O~' (5501 /I,.,)

2B' OIL

I lr - - - - ~ - ..- ,- r- - p.- I- . 11

. ,.,,.,) 7Js 7 f~ 8 S 8 N 9 S 9 N 10 S 10 f 11 S 11 N 12 l~ ~

I- "'" - - -I- - - - I- I- - 1-0 - -I- 1r

I t

South Gir"de,., fjo,.th fltce ~Q,.tiQIStiffene,.~G5A

21'-O~' (6402 nn) 1'-9~' (547.7 nn)

2B' (711

II

,- . - - ~ 1- - -t- - - .. --- ... -If• /1/1) I~t 13 13 t 14 < 14 r 15 15 r 16 16 r 17 17 r IB 18 , I

L I-- . - - i- I- .1- - .. ~ - - . ... - 100- -~,I II

South Glr"der, North fltce ~ortlolStlrrener~

Noteo The end beltrlng stlHeners have been rel'loved ;rol'l G6A.The p:lrtlol stltrenl'rS sha~n In the dl':lwlng h:l ve been

rel'loved to below the cut

Figure 4.5 Web cuts and Splicing Arrangement

100

28.00' (

~ IIn

V

~ ~00

00

o 0

11.2 r'lr'I)00

00

00

00

00

----

.50' <12.7 r'lr'I) thickness

4.19' Cl06.4 MM)

Cross section with InterMedlo. te stiffener (St2)and beo.rlng stiffener (St3)

Plan View

1'- -+-"-'0.""50"--'-.:<12.7 Mn)

Figure 4.6 Stiffener Geometry for Scaled Design 19

101

28.00' (

II n

n

~/

~

11.2 1'11'1)

..,j~

"---

50' <12.7 1'11'1) thicKness

4.20' <106.7 1'11'1)

Cross section with Interl'ledlate stiffener CStD

28,00' C

II n

n

I~V

~o 0g g

o g

11.2 1'11'1)o 0o 0o g

o 0o 0

-

.50' 02,7 1'11'1) thickness

4.20' Cl06J nn)\

Cross section with internedia te stiffener CSt2)and bearing stiffener CSt3)

Figure 4.7 Stiffener Geometry for Scaled Design 7

102

Scoled Design 19 (CorrugQtlons not shown for dorlty)

6' U52A 1'1II)

xl' <254xIOl.6x6.4 m) TUb~ Veb Spl1c~a' (4,8 Ml

Veb Spl1c~ E70 I r1' (4.8 "I'll v \

GJA G6A 14'x3/4' (3~~ K!9.1 rn) Botto" r

\:.t 3 28',1' <711.2><6,4 ""I veb~ ,d' (6A "ft) f\~t 2 E70 /,' (6A nn) v \ St

-6' (~2.4 I'tll

10'x4'

South Girdl1r, North rOell

Scoled Dl'Slgn 7

14'-94' (4500 Ml G' <152.4 on)14'-94' (4500 M)

'xl' <254xIOL6x6,4 m) TUb~ .a' (4.8 Ml f\

E70/ d' (4,8 I'IIIl v \

2B'xa C71L2x7,9 I'JI) \leb~ .,1' (6,4 nnl f\St 3 St 1 St 2 E70 /1, (1;,4 III'Il \ St 3

10'x3/4' (2 .19.1 ""I Bottoft n~g\ St 1

.....6' <152.4 m) 14'-94' (4500 on)

10'x4

tJorth Girder, North race

Figure 4.8 Scaled Designs 19 and 7

103

x--- ~---<

a.

z

I..F

web

ax

d

F

a.

0.707a. (throQ t of weld)

Figure 4.9 Illustrations for Tube Flange-to-Web Fillet Welds

104

20 40 60 80 100o

10000 --r---'-~~~-~-~-i

8000 -'-:-~~~~-~--

I6000 -T----~_4.--~-~-~-------~-----1I

4000 -r--2000 -:--~-----'l.~-~-~~~-~~~--J'-~---j

!

- Ib 0 _I------~~-~~~~~-~ I

1

-2000 ~--~---'"I

-4000 ~II

-6000 .,'~-~---~-~------------

-8000 ~I-----_----~I

-10000 -1------~~---,---'-~~-~~-~

-100 -80 -60 -40 -20

Figure 4.10 Example of f(ax) versus ax (Used for Tube-to-Web Fillet Weld Design)

105

<J

"\ V.J

Case 1

II1III1 Fys1111111~

Mp

Case 2 Case 3

O"ywcld O"ywcld 0" 't

R2

't 0"

'tywcld'a 1 stlrr. I 'tywcld'a

RJ

A:iO'

Figure 4.11 Illustrations for Tube Flange-to-Stiffener Fillet Welds

106

Figure 4.12 Core Hole in Pre-Cast Deck

.. -' ,,

.,';

...

Figure 4.13 Shear Studs Mounted in Core Hole

107

INTENTIONAL SECOND EXPOSURE

Figure 4.12 Core Hole in Pre-Cast Deck

Figure 4.13 Shear Studs Mounted in Core Hole

107

9" (228.6 M[Y))

0.75" C19.l [Y)[Y) DIA. TYP.

Figure 4.14 Shear Stud Arrangement

Figure 4.15 Core Hole Pattern

108

3 15 II 7 1 13 9 5 b 10 14 2 8 12 16 4

:--r-30.33' 070.4 11M) 11 spes @ 60' USe4 I'lIll = 660' (16764 "1'1) 30.33' 070.4 nl'l):r-

(a) Simulated Construction Loading Condition

120' (3048 "'" 120' (3048 I'IMl

(b) Simulated Mdc Loading Condition

19.38' ( 923.38' .3n 19 (492 l'1l'i) 25 spes @ 27.25' (692.2 M) = 681.25' (J7~5 MI'I) Ll'II'Ilr

51 45 39 35 29 49 43 37 33 27 47 41 31 32 42 49 29 34 39 44 50 30 3. 40 46 52

25 19 13 9 ~ 23 17 II I ~ 21 15 I 8 16 22 I ~ 12 18 24 I 10 14 20 26~. ';Wij ~

I I

(c) Simulated Strength I Loading Condition

Figure 4.16 Loading Arrangements

109

Figure 4.17 Wood Cribbing

Figure 4.18 Wood Shim

110

Figure 4.19 Rollers

Figure 4.20 Haunch

111

6(152.4 I'm) (2249 m)

1-;-;---;4'-~'-----'3'

(4501 1'lII) (2249 n~) (152.4 I'ln)

'-------i4·-9a·'----ol.----i4.-9~··---"'-----l4·-9a··---ol.--;

(4501 0") (4501 "0) (45l1 0.,)

EottoM of bOttg~ OgoeF

Figure 4.21 Profile View of Scaled Design 7 Instrumentation

112

l' (25.4 I'lM)

l' <25.4 I'lr'l)

2' <50.8 r'lf,) • 2' (50.8 I'lM)

6" 052.4 MM) 6' (152.4 riM)

•6' <152.4 MI'l) 6' (152.4 I'lM)

•5" <152.4 MI'l) 5' <152.4 MM)

• •6" 052.4 f'lf'l) 6' (152.4 I'lf'l)

2' (50.8 MM) • 2" (50.8 r'lM) •

Detail A: strain oat;Jes Detail B: strain t;Jat;Jes

Detail DI strain gagesood strimJ pots

l' (25.4 I'IM)

•4' (101.5 MI'l)

• l' (25.4 I'll'l)4' <101.6 I'lr'l)

•

Detail C, strain gages

2' (50.8 r'lM).-J-+--I2' (50.8 I'lM)2' (50.8 MM)

2' (50.8 I'lM)

l' (25.4 I'lr'l)

l' (25.4 MM)

l' (25.4 r'lr'l)

5' (127 MMlEtj5' Cl27 I'lM) 1' (25.4 I'IM)

Detail [I string potsand LVDrS

-4' ClO1.6 I'lM)

>-- •10' <254 MM)

i) i)

w • <10' <254 MM)

I-- •4' Cl01.6 nn)

~

De-tail G' strain oaoes

Figure ....22 Details of Scaled Design 7 Instrumentation

113

!'-71f<-l.......-..;.

(50~! Ml........-.........>-i··-7M·

CSO~I M)

!'-7U........l.--......r'-I0G;' l'-7/t'-l.o......"-i'-7/t(50~1 "I'll (874.7 m) (500.1 m) (50~1 "N

. .l....-,..L.----\4·-9aL-----'-~·

(4~01 N'll

E.llcn of bgUQ'! fltJ';.

Figure 4.23 Profile View of Scaled Design 19 Instrumentation

114

-4' (101.6 I'll'l)

I-- •

I) [)

20' (508 rll'!) ( <2' (50.8 MM)

10' (254 MI'l)

2' (50.8 MM)

o

o

DE'toil AI strain oooes Detail P, strin';! pots

7' 077.8

7' 077.8

Detail (, string potsand LVPIS

I' <25.4 MM)

l' (25.4 MM) l' <25.4 MM)

Detail F'

l' <25.4 I'lM)

I' (25.4 /'1M)

l' (25.4 1'11'1)...-........_ ...

6' (152.4 1'11'1) o' 052.4 MM)

De tail II stl'aln Qooes

2' <50.8 MM)

~' (9.5 1'1,,)

I

Dotall ~;, strain <;0<;:;0;l'

Detail J' strain caoes

I' (25.4 Mr-I) l' (25.4 1'10)

'--........~~1· (25.4 M)

r,n) 6' 052.4 1'1,,)

Detail LI st·'o'o oo.ors

Figure 4.24 Details of Scaled Design 19 Instrumentation

115

7~' 0461 M) between tube sj' (14l0 ~~) between botto~ fl sides

7'-lO~"~'"----l4'-9~"-----'-

(24ll2 ml (4~1 n~)

.-"-----i4·-9~··---'""'---7'-l~'

(4~01 ml C24ll2 ml

Top Vi•• of Grdrr' forI gtecp,t PSMrenen1 I YDTs

Figure 4.25 Details of Lateral Displacement Instrumentation

116

r'W-T ~'W-C,

\ .r -C IW -~

I~'<

VJ-F

VJ- T 'W-C

r'W-\JVJ-F

Figure 4.26 Material Test Identifiers

117

70 ~f----------

60 h~~:::::======:::=:======-=-=-==--C>..----JI 1

50jf~---I

:::- !! 40 ~

UlUl

~ 30 -1------------------------------'en

20 -1------------------------

0.2 0.25

"

'"I',I-.....Material Modelil

,I

0.150.1

o ~--------~----,- ----o 0.05

--Test Data10 ------------------------~

Strain (in./in.)

Figure 4.27 CW-T (48 ft.) Coupon 1

70 --,---- ------~----~~----------~--------------.,

601-1---- ----~----------

50 -1---------------\----- --~---~-----.

-~ 40 -- --- - --------------------------~---------------

--Test Data

. -..... Material Model

UlUlCl)

30...-en

20

10 -

00 0.05 0.1 0.15

Strain (in.lin.)0.2 0.25

Figure 4.28 CW-T (12 ft.) Coupon 5118

-

~~-

----- ::::--- r ~r--- ,

/-

~

-

,

-Test Data

i-.-Material Model

120

110

100

90

80-'iii 70:.lZ 60een 50

40

30

20

10

oo 0.05 0.1 0.15

Strain (in.lin.)

Figure 4.29 CW-W Coupon 1

0.2 0.25

90----

80-'-----~

60 '

----- ~---------~-1

!

-- -~ ~-- -~ ------

'iii .:. 50 -: --~~--------~- ~----~----- -~-~~----~---~~~-~----

CIlCIle 40 - --------- --- - -- ----~-------~~ ~-~----~--------en

30 ~ -- --------

20

10 ___~ ~_~ __~_____ _ --Test Data

-r-Material Modelo

o 0.05 0.1 0.15Strain (in.lin.)

Figure 4.30 CW-F Coupon-+119

0.2 0.25

80 -,--------------------------____,

0.30.250.20.1 0.15Strain (in.lin.)

0.05o

~ .---.~ I-f r

~ 'I~

IrrLI

i

~~,~

rL i--Test Data (Lin. Disp. Pot.)

t i --Test Data (Strain Gages)1- I, I-+--Material Modelfo

-0.05

10

60

20

70

&l40e....

CJ) 30

__ 50

~--

Figure 4.31 FW-T Coupon 1

80 -,-----

60 -'r----- ------~

-- ----~----------------------------~----

__ 50"iii~

&l 40e....

CJ) 30 ~ ~ ~ ~ .

20 ------- -------- -~--~-------

10 t~---------~-------~----------~------~. --Test Data

oo 0.05 0.1 0.15

Strain (in.lin.)

-+-- Material Model

0.2 0.25

Figure 4.32 FW-W Coupon 2120

90 ~------~-~---------

80 -----~-=---____=_~~------= ......

70

60 ..;po..------------------

-~ 50-enen~ 40 -1-------------------en

30 -I-------~ ----------------~

20-1-----

_______--.;' --Test Data

-.-Material Model

10 -1----

o ...-~o 0.05 0.1 0.15

Strain (in.lin.)0.2 0.25

Figure 4.33 FW-F Coupon 4

9000 -:----~~~---- ---- -------------

8000 i---~----- ---.-----------

7000 ~----~,,

6000 .:-~- .·iii i.e: 5000 -:-------~----- --------------en •en '~ 4000 ~------~---- -----------------------. ---. -----.-- --------- .-en

3000 ~-- ------- -- --

2000:- --- ---~--

1000 :~--.

o '-.---~~---------.-.. -.---. ----.--~-.---.--.-- -. -. .-.------- ---.--.-.-o 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004

Strain (in.lin.)

Figure 4.34 CW-C and FW-C121

5. Experimental Results and Comparison with Analytical Results

5.1 Introduction

In the previous chapter, the development of the test specimen was discussed.

The choice of the prototype girders to scale and test, and detail designs, such as

stiffeners, welds, and shear studs were discussed. The load conditions to be developed

during testing were described in detail. The data acquisition system and

instrumentation were presented. Finally, the stress-strain properties of the materials

used in the test girders, the measured cross-section dimensions, and selected geometric

imperfections of the test girders were presented.

This chapter presents the experimental results. The specific stages of testing,

and a set of coordinate axes to facilitate understanding of the experimental results are

presented first. Then, data from strain gages is presented. Next, the vertical deflection

of the test girders, and lateral displacements of the test girders are presented.

Comparisons are made between experimental results and analytical results. Other

results that are only summarized are the web distortion for both test girders, and tube

and tension flange lateral curvatures, and tension flange plate bending for scaled

Design 19.

5.2 Test Stages

Each stage of the testing progranl is explained in this section. A stage of

testing is considered to be any period of time when data was continuously obtained

122

from the instrumentation. An identification scheme is provided so the reader will

know the test stage corresponding to given experimental results.

Deck Placement

The first stage of testing was the Deck Placement stage. This stage involves

the placement of the six deck panels on the test girders. The panels sat on wood

shims. The bottom of the wood shims had a layer ofTeflon. An additional layer of

Teflon was placed on the top flange of the test girders, at the shim locations, creating a

Teflon-on-Teflon interface. This was an attempt to minimize friction between the

deck panels and girders for the Simulated Construction loading condition.

Stages 1, 2, and Mdc

The next stage of testing was referred to as Stage 1. This stage used the

Simulated Construction loading condition with a single interior diaphragm located at

midspan (and end diaphragms at the bearings). The test girders were non-composite

with the deck panels, and the deck panels were supported by shims with a Teflon-on

Teflon interface to the girders. Stage 2 was a repeat of Stage 1, with the exception that

the interior diaphragm was removed. After Stage 1 and Stage 2, the Simulated Mdc

loading condition was applied to the non-composite test girders. As mentioned in

Chapter 4, the purpose of the Simulated Mdc loading condition was to create the san1e

stress levels in the non-composite test girders as in the non-composite prototype

123

girders, at the time the girders are made composite with the deck. This stage is

referred to as the Mdc stage.

Roller Placement

As discussed later in Section 5.6, the lateral displacements of the test girders

during Stage 2 were much smaller than expected from analytical results. Friction was

thought to have caused the test girders to be braced by the deck and/or the adjacent

test girder. Therefore, to reduce this friction, rollers oriented to roll in the transverse

direction of the test specimen were placed between the deck and scaled Design 7. For

stability purposes, the deck still sat on wood shims with Teflon-on-Teflon interface to

scaled Design 19. The stage in which the wood shims on scaled Design 7 were

replaced with rollers is referred to as the Roller stage.

Stage 2-2, Mdc-2, and Stage 3

Stage 2 was repeated, and then the Simulated Mdc loading condition was again

placed on the test specimen. These stages were referred to as Stage 2-2 and Mdc-2,

respectively. With the Simulated Mdc loading condition in place, the work was

performed to make the test girders composite with the deck. Then, the Simulated

Strength I loading condition was applied to the test specimen in a final test stage

referred to as Stage 3.

124

Stage Identification

The data recorded from the instrumentation was balanced (set to zero) at the

beginning of each stage. For some of the stages, it is convenient to present

experimental results from only that stage. For other stages, it makes more sense to

present the total results. This can be explained by considering moment versus vertical

deflection for Stage 3. If the data zeroed at the beginning of Stage 3 is presented,

moment versus vertical deflection will include only the effects of the blocks placed in

Stage 3. If the total results are presented, then the moment versus vertical deflection

plot will include the girder self-weight, Deck Placement, Simulated Mdc loading

condition, and the effects of the other test stages. It is thus important to be able to

differentiate between the test stage results and total results, and the subscripts of

Table 5.1 are placed on symbols to indicate that these results are for an individual test

stage. If none of the subscripts of Table 5.1 are used, then the results are total results.

5.3 Coordinate Axes and Instrumentation Identification

Coordinate axes for the test girders and instrumentation identifiers are given in

this section to aid in interpreting experimental results. Figure 5.1 illustrates the

coordinate axes of the test girders. The origin is at the west bearing, at the center of

the bottom of the tension flange. x is positive in the eastward direction, y is positive in

the vertical direction, and z is positive in the southward direction.

Identifiers for the test instrumentation on scaled Designs 19 and 7 are sho\'m in

Figures 5.2 through 5.4. The letter before the hyphen (C or F) refers to whether the

125

instrumentation was located on the corrugated web girder (scaled Design 19) or the

flat web girder (scaled Design 7). The letter after the hyphen (S or D) refers to

whether the instrumentation was a strain gage or a displacement transducer. The letter

after the hyphen is followed by a number. Scaled Design 19 had 69 strain gages and

18 displacement transducers, whereas scaled Design 7 had 58 strain gages and 18

displacement transducers. Note also that each cross-section, at which strain gages

have been placed, has been given an identifier. The identifier is located at the top of

the list of strain gages for that cross-section. Each cross-section at which a vertical

deflection transducer is located is also given an identifier.

5.4 Strain Gage Data

Moment versus strain graphs were generated for each stage at the "Elastic"

sections shown in Figures 5.2 and 5.3. According to beam theory, strain through the

height of a cross-section varies linearly from zero at the neutral axis. In addition, the

strain at a specific point in a cross-section increases linearly with moment in the cross-

section according to the following equation:

(Eq.5.1)

where M is the moment in the cross-section, E is the modulus of elasticity of steel, I is

the moment of inertia of the cross-section, y' is the distance from the neutral axis to

the point in question, and E is the strain at the point in question. However, strain at a

point \\;thin the cross-section may not increase linearly with moment on the cross-

section if a nonlinearity. such as the effect of residual stresses. is present. Eq. 5.1 is

126

only true while Hooke's Law is valid on the entire cross-section. The moment will not

be linearly related to strain after residual stresses have caused partial yielding of the

material in the cross-section. After some initial study, the strain data was thought to

include nonlinearity, even at sections expected to remain linear elastic. To verify this,

the bending moment was calculated from static equilibrium, using the measured

weights of the individual loading blocks (Kim 2004b), and the bending moment was

compared to the strain data.

Figures 5.5 through 5.16 illustrate moment versus strain graphs for Stage 1,

Stage 2, and Stage 3 at the Elastic sections. The strain value graphed for scaled

Design 19 is the average of the four comer strain gages of the tension flange at each

Elastic section. This average eliminates lateral curvature or plate bending of the

tension flange (see Sect. 5.9). The strain value graphed for scaled Design 7 is the

average of the three gages on the tension flange of the Elastic section. This average

eliminates lateral curvature of the tension flange. The strain gage identifiers are

provided on the graphs, and can be compared against Figures 5.2 through 5.4.

Stage 1 Elastic Sections

The Stage 1 graphs (Figures 5.5-5.8) show nonlinearity on the loading branch

of the curves. Linear regression lines were developed using the unloading branches of

each curve, because cross-sections that yield will unload elastically. These regression

lines were plotted along the loading branches of the curves to further illustrate the

nonlinearity in the data. Note that the nonlinearity creates pemlanent strain at the end

127

of Stage 1. The nonlinearity and resulting pennanent strain are believed to be from

local yielding on the cross-section due to residual stresses.


In the case where residual stresses exist in a steel girder, loading and unloading

within a selected load range will eventually nearly eliminate the residual stresses.

This effect is often referred to as the "shakedown" of residual stresses. The

elimination of residual stresses is illustrated in the Stage 2 graphs (Figures 5.9-5.12).

Notice that the loading and unloading portions of the curves are identical, and do not

show serious nonlinearity. The same load level is used in Stages 1 and 2, so in Stage 2

the test girders are being loaded along the unloading branch from Stage 1. The graphs

for Stage 2-2 are not shown because they are similar to Stage 2, and do not provide

any additional infonnation.


The Stage 3 graphs (Figures 5.13-5.16) appear to be linear in the initial portion

of the moment versus strain curves. After the stresses become larger than those in

Stages 1 and 2, the curves become nonlinear.

Summarv of Results from Elastic Sections

From the graphs discussed above, it is obvious that Equation 5.1 cannot be

used to calculate moment from strain on the Elastic sections. Therefore. the bending

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moments for the various test stages were determined from static equilibrium. Only

tension flange strain gage results were presented in the above discussion, but

nonlinearity was observed in all strain gages at the Elastic sections. The residual

stresses that cause local yielding and the related nonlinearity are not observed in the

tension tests of the web and tension flange material. The residual stresses are likely

introduced into the flanges by web-to-flange welding. Residual stresses appear to be

present in the tubes, especially FW-T, as discussed in Section 4.8. These stresses

would contribute to the observed nonlinearity.

Midspan Section

Moment versus strain graphs for Stages 1, 2, and 3 were also generated at the

"Midspan" sections. These results are presented in Figures 5.17 through 5.22. The

strain gage identifiers are provided on the graphs, and can be compared against

Figures 5.2 through 5.4. These graphs display similar behavior to that shown in

Figures 5.5 through 5.16. As expected, the nonlinearity is larger at midspan because

of the larger moment levels.

Investigation of Stresses

The stresses in the steel and concrete during the various loading stages were

estimated assuming linear elastic behavior of the cross-section. For scaled Designs 19

and 7. the steel cross-section and the concrete in the tube as well as the deck were

modeled as an equivalent transfonned section. The stresses were estimated and

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compared to the material strengths to verify that the observed nonlinearity in the

moment versus strain curves was not from gross yielding of the steel in the cross

section, or stresses exceeding the linear elastic range of the concrete. The midspan

stresses were studied. During the tests under the Simulated Construction loading

condition (Stage 1, Stage 2, and Stage 2-2), the stress in the top of the tube concrete

reached 3.8 ksi (26 MPa) and 3.6 ksi (25 MPa) for scaled Designs 19 and 7,

respectively. The stress at the top of the tube reached 25 ksi (173 MPa) and 24 ksi

(168 MPa) for scaled Designs 19 and 7, respectively. The stress at the bottom of the

tension flange reached 25 ksi (175 MPa) and 28 ksi (196 MPa) for scaled Designs 19

and 7, respectively.

During the Simulated Strength I loading condition test (Stage 3), the stress in

the top of the tube concrete reached 2.6 ksi (18 MPa) for both test girders. The stress

in the top of the deck concrete reached 1.3 ksi (9 MPa). The stress at the top of the

tube reached 17 ksi (120 MPa) for both test girders. The stress at the bottom of the

tension flange reached 51 ksi (350 MPa) and 52 ksi (357 MPa) for scaled Designs 19

and 7, respectively.

As mentioned in Section 4.8, the ultimate strength of the concrete was 7.8 ksi

(54 MPa), and the linear elastic limit can be estimated as 3.9 ksi (27 MPa). The

stresses in the tube concrete and in the deck did not exceed this value, so concrete

material nonlinearity does not appear to contribute to the nonlinearity in the moment

versus strain curves. The steel used in the test specimen, except for the FW-T

material, had a proportional limit of at least 40 ksi (276 MPa). as shO\\11 in Section

130

4.8. Some of the steel stresses presented above exceed 40 ksi (276 MPa), however,

the moment at which the Midspan sections started to exhibit nonlinearity was

estimated from Figures 5.17 through 5.22, and the stress levels corresponding to the

onset of nonlinearity were calculated assuming linear elastic behavior. The stress

levels at which the two test girders started to show nonlinearity in the midspan

moment-strain curves was approximately 18 ksi (124 MPa) for scaled Design 7 and 10

ksi (69 MPa) for scaled Design 19. Therefore, since the midspan moment-strain

graphs exhibit nonlinearity of stresses well below 40 ksi (276 MPa), the nonlinearity is

most likely due to residual stresses in the steel.

Strain Jumps

Two jumps in strain at the "East Elastic" sections of the test girders, caused by

placing block number four of the Simulated Construction loading condition

arrangement are observed in Figures 5.5 and 5.7. This is observed as ajump forward

in the strains of scaled Design 7 (Figure 5.5), and a jump backward in the strains of

scaled Design 19 (Figure 5.7). It is speculated that the non-composite deck panels

were not in contact with the scaled Design 7 test girder near the East Elastic section

until after block number four was placed. In Figure 5.5, the slope ofthe data for

scaled Design 7, before block number four is placed, is approximately 7% steeper than

the linear regression line. In Figure 5.7, the slope of the data for scaled Design 19,

before block number four is placed. is approximately 9% flatter than the linear

regression line. In other words, scaled Design 7 was not being fully loaded and scaled

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Design 19 was being overloaded, before block number four was placed. This strain

jump is not observed for the Stage 3 test after the girders are composite with the deck.

In the composite case, the deck is supported by a continuous haunch, and therefore

makes contact everywhere along the test girders.

Neutral Axis Location

Plots were made to determine the experimental location of the neutral axis in

the test girders during the unloading phase of each test stage. This was done by

plotting strains at the Elastic sections. Longitudinal strains were plotted at the

different heights over the cross-section, and a linear regression line was fit to the data.

The intersection of the linear regression line with the zero strain axis was the location

of the neutral axis. This was performed after each block was removed. The fully

loaded condition was taken as the initial point for the longitudinal strain values. Thus,

the neutral axis location could be plotted throughout the unloading phase ofeach test

stage.

Figures 5.23 through 5.30 display the location of the neutral axis for each test

stage. The neutral axis location does not change in Stages I, 2, and 2-2. However, in

Stage 3, the neutral axis dropped over the course of unloading from slightly above the

analytically calculated location (discussed later) to slightly below. The reason may be

as follows. When the deck panels were post-tensioned, a compressive force in the test

girders was introduced by friction between the wood shims and the girders. This

condition existed when the instrumentation was balanced for Stage 3. As the test

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specimen was loaded, the deck panels were compressed more closely together, and

some of the compression in the girders was lost. This caused the neutral axis to be

above predicted at the beginning of unloading. As the test specimen was unloaded,

gaps may have opened at the deck panel joints. This would cause the compression

area to become less effective, and the neutral axis to drop.

Comparison of Experimental and Analytical Results

Table 5.2 presents analytical results for the slope of the moment-strain plots

(stiffness) and the neutral axis location, measured from the bottom ofthe tension

flange. The actual, measured girder dimensions were used along with transformed

sections to calculate these values of the stiffness and neutral axis location. The

analytical calculations are shown for both the East Elastic sections and West Elastic

sections of the test girders because the haunch thickness was slightly different at these

two locations.

Table 5.3 presents a comparison of the experimental results and analytical

results. The experimental stiffnesses range from approximately the same as the

analytical, to 11% more stiff. No comprehensive reason for the discrepancy has been

detemlined. However, the two possible causes for difference in stiffness are suggested

here. During the test stages using the Simulated Construction loading condition when

the deck is non-composite. the deck may assist in carrying load. A net tension may

develop in the girder and a net compression in the deck. This \\ill cause the test

girders to appear stiffer. and also push the neutral a,is position upward. The

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corrugated web may also contribute slightly to the moment carrying capacity of scaled

Design 19, even though it was neglected in the analytical calculations. The

combination of the corrugated web and deck contributions could cause the neutral axis

to move upward or downward, depending on the size of the individual contributions.

5.5 Vertical Deflection Results

Experimental Measurements

Vertical deflections were monitored at five cross-sections along the bottom of

the tension flange of each test girder. These cross-sections were Section A, Section B,

Section C, Section D, and Section E. Refer to Figures 5.2 and 5.3 for details about

these section locations. Midspan moment versus vertical deflection graphs were

generated for each of these sections. Sections A and E were plotted on the same graph

to show the symmetry of the test girder deflections. Likewise, Sections Band D were

plotted on the same graph. The two vertical deflection transducers at Section C were

plotted on the same graph to show twisting of the tension flange at midspan of the test

girders.

Analytical Calculations

Graphs were generated to compare the experimental results \vith analytical

results. The analytical results were calculated using transfomled sections for the

girders. Vertical deflections due to bending defonnations and shear deformations~ ~

were considered in the analytical calculations. In calculating vertical deflections due

134

to shear, an effective shear area must be determined. In the non-composite case, the

effective shear area is assumed to be the area of the web. In the composite case, the

effective shear area contributed by the haunch and the deck are included. The total

effective shear area ofa composite section is calculated by dividing the transformed

section cross-sectional area by a form factor, fs, calculated as follows:

(Eq.5.2)

where, A is the cross-sectional area, I is the cross-sectional moment of inertia, Qis the

first moment of the area above or below the point in question about the neutral axis,

and b is the width of the cross-section at the point in question. One important note

concerning the shear deformation calculations is that the shear stiffness of a

corrugated web must be multiplied by the following term (Abbas, 2003):

f3 + cosa

f3 + 1(Eq.5.3)

where Pis the ratio of the longitudinal fold width, b, to the inclined fold width, c, and

a is the corrugation angle for a trapezoidal corrugation shape. This factor decreases

the shear stiffness of a corrugated web, when compared to a flat web with the same

effective shear area.

Comparison of Experimental Results and Anah1ical Results

Figures 5.31 through 5.66 show the midspan moment versus vertical

deflection graphs. as well as the comparisons between experimental results and

analytical results. The experimental results for midspan moment versus vertical

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deflection are similar to the results for moment versus strain. The results are nonlinear

for Stage 1, and linear for Stage 2. The results of Stage 3 are linear until the stress

levels of the previous stages are exceeded, and then the results become nonlinear. In

Stages 1 and 3, the analytical results are compared to the unloading branch of the

experimental data because the loading branch is nonlinear. In Stage 2, the analytical

results are compared to the loading branch of the test data. In the non-composite

stages (Stages 1 and 2), the comparison between experimental and analytical is shown

after block number four was placed, so that the contact issue discussed in Section 5.4

does not influence the comparison.

It is important to note that the experimental and analytical data are not linear

for moment versus vertical deflection, even after the shakedown of residual stresses.

If the loading were proportional, then the moment and curvature of a linear elastic

girder would increase linearly, and the vertical deflections along the span would also

increase linearly. However, the loading used in the experimental program only

approximates a uniformly distributed loading (i.e., a proportional loading), as

discussed in Section 4.6, and therefore the graphs are only approximately linear.

Tables 5.4 and 5.5 present comparisons of experimental results and analytical

results for stiffness of the midspan moment versus vertical deflection plots. Table 5.4

includes only bending deformations in the analytical vertical deflection calculations.

whereas Table 5.5 includes bending and shear defom1ations. TI1e inclusion of shear

defom1ations increases the ratios by approximately 5% for scaled Design 19 and 3%

for scaled Design 7. TI1e difference is due to the fact that corrugated webs are not as

136

stiff in shear, as discussed above. The results are similar to those obtained for the

moment versus strain graphs, in that the experimental results are stiffer than the

analytical results. The reader may refer to Section 5.4, where possible reasons for the

increased stiffness are discussed.

Total Vertical Deflections

The vertical deflection results presented thus far have been for individual test

stages only. It is equally important to look at total vertical deflection throughout all

testing. Figures 5.67 through 5.72 present total midspan moment versus total vertical

deflection at the five sections for each girder. These results are presented for all test

stages through the end of Stage 3. Horizontal offsets have been added between stages

to make viewing easier. The figures include calculated girder self-weight effects,

measured Deck Placement effects, measured Stage 1 effects, measured Stage 2 effects,

measured Roller Placement effects, measured Stage 2-2 effects, measured Mdc-2

effects, calculated haunch weight effects, and measured Stage 3 effects. The girder

self-weight and haunch weight effects had to be calculated because no data was taken

to measure these effects. The Mdc stage was assumed to unload elastically before the

Roller Placement stage, and is not shown in Figures 5.67 through 5.72.

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5.6 Lateral Displacement Results

Finite Element Simulations

Numerous simulations were generated by Kim (2004b) using the Finite

Element Method (FEM). The FEM models used by Kim for these simulations were

similar to those used in his Ph.D. dissertation (Kim 2004a), but the models used in this

study had rectangular tubular flanges. The FEM simulations were performed to

understand the lateral displacement results obtained from testing. As discussed in

Chapter 4, only the tube flange imperfections (sweep) were measured before testing.

FEM simulation results were used to investigate how the imperfection in the tension

flange could affect the lateral displacements of the test girders. Numerous

imperfection shapes were investigated in the FEM models. Six initial imperfection

shapes, illustrated in Figure 5.73, were considered in the simulations. The

displacements shown in the figure are the midspan displacements. The value of Ux is

an amplitude that was defined for each FEM model. The shapes of the imperfections

along the lengths of the tube and tension flange are half sine waves. The midspan

displacements are positive in the south direction. Table 5.6 provides descriptions for

the different FEM models that were investigated. SD7 and SO 19 stand for scaled

Designs 7 and 19, respectively. The shape column refers to the shape number in

Figure 5.73. The amplitude column indicates the value ofux, where L is the span of

the test girders. The material column refers to the stress-strain models that were used

in the FEM simulations.

138

The material stress-strain models presented in Section 4.8 were used

consistently in the FEM simulations except for the model used to represent the tube

steel in scaled Design 7. Recall that the accuracy of the stress-strain data for the tube

steel (FW-T) for scaled Design 7 was questionable (see Sect. 4.8). The original

quadra-linear curve was initially used for the stress-strain model in the FEM

simulations. However, the early softening observed in the tension tests led to a poor

fit between the stress-strain model and the actual stress-strain data, and the simulation

results showed a lateral torsional buckling strength less than the Simulated

Construction loading condition applied during the Stage 1 and Stage 2 tests. The use

of this stress-strain model for the scaled Design 7 tube steel, along with all other

stress-strain models from Section 4.8, is referred to as MaW in Table 5.6. More points

were added to the FW-T stress-strain model, as shown in Figure 4.27. This led to a

better fit between the stress-strain model and the actual stress-strain data, but the FEM

simulation results still showed that the lateral torsional buckling strength of scaled

Design 7 was less than that required for the Simulated Construction loading condition.

The use of this stress-strain model, along with all other stress-strain models from

Section 4.8, is referred to as MatI in Table 5.6. Finally, the stress-strain model for the

tube of scaled Design 19 (CW-T) was used for that of scaled Design 7. The use of this

stress-strain model, along with all other stress-strain models from Section 4.8, is

referred to as Mat2.

139

Scaled Design 7 FEM Simulation Results

For all the FEM simulations, it was assumed that the girders had their specified

initial imperfections at zero load. Figures 5.74 through 5.94 illustrate the midspan

moment versus midspan lateral displacement results obtained from the FEM models

described in Table 5.6. The midspan lateral displacement shown in these figures does

not include the initial displacement due to the initial imperfection. Figures 5.74

through 5.79 (for models SD7-1 through SD7-6) provide good qualitative information.

The second three of these models have larger initial imperfections than the first three.

It is observed that larger initial imperfections cause larger lateral displacements during

loading and a lower lateral torsional buckling strength. Also, it is observed that initial

lateral displacement of the girder, with no twist (Figures 5.74 and 5.77), will lead to

twist in the same direction (i.e., with the top flange displacement greater than the

bottom flange displacement). Initial lateral displacement accompanied by initial twist

in the same direction, however, is more critical. For instance, compare Figures 5.74

and 5.75. Model SD7-1 has the same tube imperfection as model SD7-2, but model

SD7-2 has initial twist. The initial twist causes the lateral displacements of model

SD7-2 to be larger, and lateral torsional buckling strength to be smaller.

Figures 5.76 and 5.79 (for models SD7-3 and SD7-6) introduce an interesting

situation where the initial twist is in the opposite direction of the initial lateral

displacements (i.e., with the top flange displacement less than the bottom flange

displacement). It is observed in these figures that the lateral displacement occurs in

the direction of the initial twist. not the initial lateral displacement. For these cases.

140

the initial twist dominates the movement during loading. It should be noted for these

girders that the tension flange initially displaces more than the tube, thus reducing the

twist. This issue was investigated further using the FEM models generated for scaled

Design 19. The remaining figures for scaled Design 7 (Figures 5.80 through 5.85)

show the results of changing the tube steel properties, as discussed above.

Scaled Design 19 FEM Simulation Results

A discussion similar to the one above could be presented for Figures 5.86

through 5.91 (for models SD19-1 through SD19-6), but is not necessary. Models

SD 19-3 and SD19-6 were generated to investigate the situation where initial twist is in

the opposite direction of initial lateral displacements. This was done with the tension

flange being initially displaced 1.5 times the initial displacement of the tube. Models

SD 19-7 through SD19-9 investigated additional initial displacement factors of 1.25,

1.375, and 1.3125 (see Figure 5.73), and Figures 5.92 through 5.94 show the results.

While Figures 5.92 through 5.94 provide a good view of the early behavior ofFEM

models SD19-7 through SD19-9, Figures 5.95 through 5.97 illustrate the post-peak

behavior of FEM models SD19-7 through SD19-9. Consider the post-peak behavior

first. It can be seen that at a certain point, when the initial displacement factor is

between 1.3125 and 1.375, scaled Design 19 will switch from failing in the same

direction as the initial lateral displacements to failing in the opposite direction of the

initial lateral displacements. If the initial 1\\ist is large enough (in the opposite

141

direction of the initial lateral displacements), then it dominates the motion, causing the

girder to fail in the opposite direction of the initial lateral displacements.

The early behavior is similar for all magnitudes of initial displacement used in

the tension flange. The girder displaces in the direction of the twist, and the twist is

reduced. At some point, the girder becomes vertical. The rest of the behavior depends

on the size of the initial twist. The complete behavior is best explained using two

graphs and two schematics. Figures 5.98 and 5.99 are the same as Figures 5.93 and

5.94, except that the initial imperfections have been added in. Figures 5.100 and

5.101 show schematics of the initial imperfection (1), the vertical position (2), and the

behavior after the vertical position is reached (3). SD19-8 reaches vertical with tube

and flange lateral displacements to the north, and then displaces and twists to the

north. SD19-9 reaches vertical with tube and flange lateral displacements to the south,

and then displaces and twists to the south.

Comparison of Experimental Results with Analytical Results for Scaled Design 7

Figures 5.102 and 5.103 compare the scaled Design 7 experimental results for

the tube and tension flange lateral displacement during Stages 2 and 2-2 with selected

FEM simulation results. In the figures, ST2 and ST22 represent the experimental

results from Stage 2 and 2-2, respectively. The remaining curves are FEM simulation

results identified by the model nanles from Table 5.6. For both stages, the

experimental results show the tube displacing more than the tension flange. It was

therefore speculated that the imperfection shape did not include an initial t"ist in the

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opposite direction of initial lateral displacements. The experimental results also show

much smaller lateral displacements than analytical results. The analytical results

chosen for comparison were from FEM models that had initial imperfections with

lateral displacement, but without twist, because they compared the best with the

experimental results. The figures show that the material models MatO and MatI for

the scaled Design 7 tube steel (used in models SD-l, SD-4, and SD-7) are probably

inaccurate. Even the results from model SD7-lOusing the Mat2 material model do

not compare well with the experimental results.

Recall that the Stage 2-2 test was conducted after rollers were placed between

the scaled Design 7 girder and the precast deck to eliminate friction that could restrain

lateral displacement of the girder. A further attempt to allow more lateral

displacement in the test girders was made during Stage 2-2, shown by the plateau at

the end of the curve ST22. At this point, the test specimen was fully loaded with the

Simulated Construction loading condition. The deck panels were unconnected during

this stage, but it was suspected that wood spacers between panels were causing a

certain amount of friction between panels, allowing the deck to act to some extent as a

large lateral beam, which inhibited lateral displacements of the girders. Cuts were

made through the wood shims to try to separate the deck panels. This process allowed

the movements shO\m in the plateau, and these movements suggest that the

unconnected deck panels were inhibiting lateral displacement of the test girders.

It is possible that the imperfection shape was quite different than those used in

the FEl\'1 models. As stated earlier. the initial imperfection shapes in the FEM models

143

were assumed to be at zero load. The tube imperfection in the test girders was

measured under the self weight of the girders. Also, placement of the panels caused

some lateral displacement of the test girders, but these lateral displacements do not

necessarily correspond to the FEM simulation results for the corresponding added

load, because the girders may be pushed laterally unintentionally during placement of

the panels. It is also possible that there is some lateral bracing being applied to scaled

Design 7 by the deck and/or scaled Design 19. Any of these factors could be the

source of the discrepancy in the comparison.

Comparison of Experimental with Analytical Results for Scaled Design 19

Figures 5.104 and 5.105 compare the scaled Design 19 experimental results

for the tube and tension flange lateral displacement during Stages 2 and 2-2 with

selected FEM simulation results. In the figures, ST2 and ST22 represent the

experimental results from Stages 2 and 2-2, respectively. The remaining curves are

FEM simulation results identified by the model names from Table 5.6. Note that

these names are preceded by a negative sign, because the initial imperfections and the

lateral displacement results are in the opposite direction to that used in the FEM

model. This change in direction was for comparison purposes because the initial

imperfection of the tube of scaled Design 19 was to the north.

For both stages. the experimental results show the tension flange moving more

than the tube. but both in the south direction. It is therefore believed that the initial

imperfection shape of scaled Design 19 included a twist in the opposite direction to

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the tube flange displacement. Therefore, the analytical results chosen for comparison

were from FEM models with initial imperfections of this type. The comparison

between experimental and analytical results is acceptable.

Once again, it is possible that the imperfection shape is something other than

what was used in the FEM models. It could be that the initial imperfection

incorporates lateral displacement and twist in the same direction. The scaled Design

19 girder could have been pushed southward by the scaled Design 7 girder. The

possibilities for discrepancy discussed for scaled Design 7 are also possible.

Lateral Displacement Shape Plots

Figures 5.106 through 5.113 show the lateral displacements of the tube and

tension flange for Stages 2 and 2-2, along the entire length ofscaled Designs 7 and 19.

The individual curves in each figure represent different load levels during testing

(refer to Figure 4.16). The curve entitled "Wood Spacers Cut" refers to data taken

after the cutting of wood spacers between deck panels in Stage 2-2.

5.7 Web Distortion

As stated in Section 4.7, gages were placed on the \vebs of the test girders to

measure the distortion. As the web distorts, the tubular flange will become less

effective in supplying torsional stiffness to the girder (Kim 2004a). The test girders

were the most susceptible to web distortion during Stage 2 and Stage 2-2. and results

for these stages are discussed here.

145

Web Distortion of Scaled Design 7

Sections 1 and 2 were used to measure web distortion on scaled Design 7, and

Section 2 was observed to be the most critical. The gages on either side of the web

allowed curvature to be calculated at the gage locations over the depth of the web.

Positive curvature corresponds to a radius of curvature in the positive z direction.

Figures 5.114 and 5.115 show the curvatures at Section 2 plotted over the depth of the

web for Stages 2 and 2-2, respectively. These are the curvatures when the test

specimen is fully loaded with the Simulated Construction loading condition. The

figures show that the curvature is somewhat linear over the depth of the web, with

positive curvature at the bottom and negative curvature at the top. Figure 5.116

shows a schematic view of the web distortion as the girder twists and displaces

laterally. This distortion correlates well with the measured lateral displacements.

Take note, however, that the curvature is very small. The largest curvature (0.000244

in:') corresponds to a radius of curvature of approximately 4098 in. (104089 mm).

Web Distortion of Scaled Design 19

Before testing. it was thought that web distortion of a corrugated \veb girder

would occur as vertical tension only or vertical compression only in adjacent

longitudinal folds. depending which side of the girder they were on. However. this

was not observed in Sections 3. 4. 6. 7. 9 and 10 of scaled Design 19. There was web

plate distortion \\ithin the individual folds. but no clear trends were observed.

146

However, curvatures were quite small. The maximum observed value was 0.000352

in.-I, corresponding to a radius of curvature of 2841 in. (72161 mm).

5.8 Tension Flange Transverse Curvature of Scaled Design 19

The C-Factor Correction Method (Abbas 2003) was used to calculate the

flange transverse bending moments due to vertical shear acting on the corrugated web

of scaled Design 19, under the Simulated Construction loading condition. These

transverse bending moments were then converted to transverse curvature in the

flanges. These analytical calculations were compared to experimental results.

However, the flanges experienced additional transverse bending during loading, due to

initial imperfections in the form of flange out-of-straightness. This resulted in

combined effects of transverse curvature from transverse bending due to the

corrugated web and transverse bending due to initial imperfections. Figures 5.117

and 5.118 show the experimental transverse curvature in the tension flange (using

Sections 1, 2, West Elastic, 5, Midspan, 8, East Elastic, 11, and 12) from Stage 2 and

Stage 2-2, compared to the analytically calculated transverse curvature that would be

present due to the corrugated web. The curvature is taken as positive when the radius

of curvature is measured in the positive z direction. The figures show curvature in the

tension flange only, because two failed gages created incomplete results for the tube.

Close to the ends of the simple span, the vertical shear is high. which causes

the flange transverse bending moments due to the corrugated web to be large as well.

Also. the transverse curvature in the flanges caused by initial imperfections is small at

147

the ends. Therefore, in Figures 5.117 and 5.118, the experimental results closely

match the analytical results near the ends. Out near midspan, the vertical shear is low

and the flange transverse bending moments due to the corrugated web are also small.

The transverse curvature is dominated by the effects of the initial imperfections. Thus,

the experimental results do not match the analytical results in this region.

5.9 Plate Bending in Tension Flange of Scaled Design 19

From beam theory, strains are expected to vary linearly from the neutral axis,

and to increase with distance from the neutral axis when a cross-section is subjected to

bending. Behavior contradictory to this was observed in the tension flange of scaled

Design 19 during testing. The Elastic sections and the Midspan section were used to

look at this behavior more closely. As shown in Figure 4.20, these sections have four

strain gages on the tube and five strain gages on the tension flange. Results from the

four gages on the tube and the four comer gages on the tension flange were studied.

Curvature Calculations using Experimental Data

The strain gages were used to calculate the overall curvature of the cross

section and the local curvature of the tension flange. The curvatures that were studied

are vertical curvatures. Figure 5.119 illustrates the eight gages that were studied. The

upper and lower tube gages on the north side are referred to as UTGN and LTGN.

respectively. The UTGN and LTGN are equidistant from the mid-surface of the tube.

In a similar manner. the upper and lower tension flange gages on the north side are

148

referred to as UFGN and LFGN, respectively. The UFGN and LFGN are equidistant

from the mid-surface of the flange. Similar strain gages are on the south side of the

girder. The strains at the mid-surface of the tube and mid-surface of the tension flange

were obtained by averaging the upper and lower values. In order to eliminate the

effects of lateral bending, averages obtained on the north side were averaged with

those obtained on the south side. Using these average strains (at the centroids of the

tube and flange), the overall curvature of the cross-section was determined by taking

the difference in strains divided by the distance between the two centroids. The local

(plate bending) curvature of the north and south tips of the tension flange was

determined by taking the difference between the upper and lower tension flange

strains divided by the thickness of the flange.

Comparison of Overall Cross-Section Curvature to Tension Flange Curvature

Table 5.7 shows comparisons between the overall cross-section curvature and

the local curvature of the tension flange. The specific sections are identified using

their section names. The table was generated using data from Stages 2 and 2-2 under

the full Simulated Construction loading condition. The local curvature in the tension

flange is given for both the north and south flange tips. When the flange local

curvature is opposite to the overall cross-section curvature, it will be referred to as

reverse curvature. The relationship between the section locations and the corrugation

folds can be observed in Figure 5.2. It can be seen that all of the studied sections are

located close to bend regions at the ends of longitudinal folds. The curvature in the

149

tension flange at these sections is reverse curvature, and is somewhat consistent for the

flange tip closest to the longitudinal fold. The curvature on the flange tip opposite to

the side with the longitudinal fold is not consistent. In all but two cases, the flange

local curvatures are larger than the overall cross-section curvatures. These local

curvatures are due to flange plate bending. This plate bending was also observed by

Abbas (2003) in the tension flanges of corrugated web test girders.

150

Table 5.1 Stage Identification Subscripts

Stage SubscriptDeck Placement DP

Stage 1 ST1Stage 2 ST2

Mdc MDCRoller Placement RP

Stage 2-2 ST22

Mdc-2 MDC2Stage 3 ST3

Table 5.2 Analytical Values for Stiffness and Neutral Axis Location

Girder and ConditionAnalytical Results

Stiffness (kip-in.) NA (in.)

Scaled Design 19, Noncomposite 9.41 16.43Scaled Design 7, Noncomposite 8.12 17.66

Scaled Design 19, Composite, East Elastic Section 11.99 33.01Scaled Design 19, Composite, West Elastic Section 12.04 33.11Scaled Design 7, Composite, East Elastic Section 12.24 32.37Scaled Design 7, Composite, West Elastic Section 12.39 32.60

Table 5.3 Comparison of Experimental Results and Analytical Results for Stiffnessand Neutral Axis Location

Experimental Results I Analytical Results

Test Scaled Design 19 Scaled Design 7

Stage East Elastic West Elastic East Elastic West ElasticSection Section Section Section

Stiff. NA Stiff. NA Stiff. NA Stiff. NAStage 1 1.11 1.00 1.08 0.99 1.05 1.03 1.07 1.03Stage 2 1.10 1.00 1.08 0.99 1.02 1.01 1.04 1.01

Stage 2-2 1.10 1.00 1.05 1.00 1.01 1.00 1.05 1.00Stage 3 1.09 0.96 1.10 0.99 0.99 1.00 0.99 1.02

151

Table 5.4 Comparison of Experimental Results and Analytical Results for Stiffness,Including Only Bending Deformation in Analytical Calculation

Test Experimental I AnalyticalStage C-D5 C-D8 C-D11 F-D5 F-D8 F-D11

Staqe 1 1.06 1.02 1.02 1.04 1.00 1.00Staqe 2 1.02 1.05 1.05 1.01 1.04 1.06

Stage 2-2 1.01 1.00 1.02 1.02 1.04 1.04Staqe 3 1.03 1.07 1.09 1.00 1.04 1.02

Table 5.5 Comparison of Experimental Results and Analytical Results for Stiffness,Including Bending and Shear Deformations in Analytical Calculation

Test Experimental I AnalvticalStage C-D5 C-D8 C-D11 F-D5 F-D8 F-D11

Staqe 1 1.10 1.06 1.06 1.07 1.03 1.02Staqe 2 1.07 1.10 1.09 1.04 1.07 1.09

Stage 2-2 1.06 1.04 1.06 1.06 1.07 1.06Stage 3 1.09 1.12 1.14 1.04 1.08 1.06

152

Table 5.6 Description of FEM Models

FEM Model Id. Shape Amplitude Materials807-1 1 U1000 MatO

807-2 2 U1000 MatO

807-3 3 U1000 MatO

807-4 1 U500 MatO

807-5 2 U500 MatO

807-6 3 U500 MatO

807-7 1 U1000 Mat1

807-8 2 U1000 Mat1

807-9 3 U1000 Mat1

807-10 1 U1000 Mat2

807-11 2 U1000 Mat2

807-12 3 U1000 Mat28019-1 1 U1500 MatO8019-2 2 U1500 MatO8019-3 3 U1500 Mato

8019-4 1 U1000 MatO8019-5 2 U1000 MatO

8019-6 3 U1000 Mato8019-7 4 U1000 Mato

8D19-8 5 U1000 MatO

8D19-9 6 U1000 MatO

Table 5.7 Curvatures Observed to Study Plate Bending in Tension Flange of ScaledDesign 19

Flange, North Flange, SouthSection Id. Stage Total ell (in:1

) ell (in:1) ell (in:1

)

EastElasticSection Stage 2 1.71x10·s -2.64x10-s -4.88x10·s

Midspan3.09x1O·s -4.75x10·s 2.98x10-4Section StaQe 2

WestElasticSection Stage 2 1.81x1O·s -3.70x10·s 5.54x10·s

EastElasticSection 8tage 2-2 1.73x10·s -1.32x1O-s -5.81x10·s

Midspan2.97x10·s -3.83x10·s 1.21x10-4Section Stage 2-2

WestElasticSection 8tage 2-2 1.84x10·s -3.17x10·s 6.34x10·s

153

\Jest

y Vertico.l Direction

~---- x Eo.stwo.rd Direction

2 Southwo.rd Direction

Figure 5.1 Coordinate Axes for Test Girders

154

Sectl2 Sect.1!C-Sl C-S5C-S2 C-S6(C-S3) (C-S7l(C-S4) (C-S8)

K K

EllstElQstlc MidspilnSection SectionC-S9 C-S31C-SIO Sect.IO C-S32C-SI1 C-SI8 " t 9 Sect.7 C-S33 Sect.6(C-SI2) C-:19 ~=~22 C-S29 (C=S34) C-S:O(C-SI3) (C S20) (C-S23) (C-S30) (C S35) (C-.AD(C-SI4) (C-S2D (C-S36)

I A J Sect.8C-S24( -

................-4·-7M·(~OOJ "I'll

VestEillsticSt'ctlonC-S53

Sed.3 C-S54 Sed.2 Sect.1SectA C-S49 C-S55 C-S62 C-S66C-S47 C-S5O (C-S56) C-S63 C-S67(C-S48) (C-S51)(C-S57) (C-S64) (C-S68)

(C-S52)(C-S58) (C-S65) (C-S69)J A I K K

/T'-'-........"-!.-7M'(~OOJ "I'll

C-S59C-S60 Sect.AC-S61 C-Dl8

I

+....J..----l4·-stt'----J..--:

(4~0l ""I

C-SI5Sect.E C-SI6C-D5 C-SI7

E I

7·-10Ji<--..J-----i4·-Srt'----J--l-eo(2402 "") (4~C1 N'll

C-DlC-D2

Botten of betic., Qg,npg

SCllled Design 19South Girder, North Side( ) Denotes Opposite Sidt'

Figure 5.2 Scaled Design 19 Instrumentation Identifiers

155

MidspanSectionF-S20F-S2lF-S22

Sect.2 F-S23 Sect.!F-S!O F-S24 F-S49

East F-SIl F-S25 Vest F-S50Elastic F-S!2 F-S26 Elastic F-S51S!C'etion F-S!3 (F-S27) Section F-S52F-S! F-SI4 (F-S28) F-S40 F-S53F-S2 (F-SIS) (F-S29) F-S4! (F-S54)F-S3 (F-SI6) (F-S30) F-S42 (F-S55)(F-S4) (F-S17) (F-S3D (F-S43) (F-S56)(F-S5) (F-SIB) (F-S32) (F-S44) (F-S571(F-S6) (F-SI9) (F-S33) (F-S45) (F -S58)

G G

'-10 """"".----i4·-9a:'---....[2lJ97 M) (J~2.4 IVI) (4~0l N'Il

EleYJl1kln

Sect.CF-S37F-DlI

F-57 F-S34 F-S38 F-S46F-Dl SectE F-58 SectD F-S35 r -Dl2 Sect.B F-S47 Seci.A

F-~ F-~ F~_9 'f__F-_sr_s3_9__F_I_15 F_-~8 F~_8 _

=t=7'-IOIt' p 14'-9tt:....·------i-----J14.-9tt··---i.......----114.-9f.. g 7'-lojt;](2402 ,,") (4SH "I'll (4501 N'Il (4501 MJ (2402 ""J

!ct1on cf bQ1100 £IMPR

Scaled Design 7North Girder. North Side( ) Denotl?s Opposite Side

Figure 5.3 Scaled Design 7 Instrumentation Identifiers

156

Scaled Design 7

C-Dl6(C-D17)

C-Dl3 C-D9(C-D14) (C-DlO)

C-D(j(C-D7)

C-D3(C-D4)

<2402 ",,)

No ( ) DE'notE's Top rlangE'( ) DE'notE's Boti:on rlangE'

<--.......-----14·-9i/;-------'--'(~501 rnJ

IQQ VIp ... of Gl"'d§'f'5 ferLot!'es! D:mtpcrcrnt Lyor,

Figure 5.4 Lateral Displacement Instrumentation Identifiers

157

3500 -------

----I

--+-A\9. (F-S7, F-S8, F-S9) II

--- Linear Regression of Unload IiI!

i -1- ~-

.-1'-'- '

o~~~-.~~--~--o 50 100 150 200 250 300 350 400 450 500

~SsT1 (in,/in. x106)

Figure 5.5 Moment at East Elastic Section versus Strain for Stage 1(Scaled Design 7)

2500 +--------

rr

3000 +------ ---

-C i" 2000 +------------ ""-=~/----------~-~----,~ !

~I-rn'" 1500 -,-_~Placement of __~__::!: BlOCK#4----."rf"---r------

1000 +------fl---~-"J

3500 ---~------- -~--._-----~~~-------------- ---

_____-J

--1

_ --+-A\9. (F-S46, F-S47, F-S48) II

--- Linear Regression of Unload II

-.... -_._.~~ - ~-_ .. - ....- ._--_.__.~-- ,_ .. ~-~_.. --.--._.. "'~..,.--.-..,-:-::-:--~~~:--,---:- -~ -.,.---:;:---.,.- -..,.- .,,_ .. ..,.--:;-~._..,.-~.-'.-::._--~

50

oo 100 150 200 250 300 350 400 450 500

~SsT1 (in.lin. x106)

Figure 5.6 t\loment at West Elastic Section ycrsus Strain for Stage 1(Scaled Design 7)

158

500

2500'------------- ---~- --

1000

3000 l ~,

~ 1500:'- -- --::!:

- 'C '" 2000 -- -.-- -~ ,

~

3500 -,-----------

i-----JlI------- .....---,

----------_._--I

I

I--.'v.,.t~-------------____,

I

100 150 200 250 300 350 400 450 500~SsT1 (in./in. x106

)

50

o~~~~~.~.o ",,-0_-

o

~------------,i

i -+-A\g. (C-511, C-514, C-515, C-517)i!500 +--+--'......-'111.---- _.--~ - I'

1 Linear Regression of Unload !:il

3000 -'--------

1000 +---

2500 +--------

~ 1500 +---=-o--.-,-;-;---..yrc/·

~

-c"j 2000 +------Co:i-

Figure 5.7 Moment at East Elastic Section versus Strain for Stage I(Scaled Design 19)

3500 ,---' - .----. --.- ---_._.-_._---_._._._----_... _ .._~-._-_._--- ---_.._--_._-,

____ Linear Regression of Unload

-+-A\g_ (C-5SS, C-5S8, C-5S9. C-561)

2500 ~---_.-

500 :.---

1000 ..-.

3000 .:--...--

oo SO 100 1S0 200 2S0 300 3S0 400 4S0 SOO

~SsTl (in.lin. x106)

Figure 5.8 l\Ioment at West Elastic Section yersus Strain for Stage 1(Scaled Design 19)

159

- .c .OJ" 2000 ..---.Co •

;g.~ 1500;'-·~

3500 ~------

3000 -T----------

- --I------~-----~-_l

250 300 350 400 450 500

I/------------------------4

I

-+-A'll. (FoS7. FoSS, FoS9) I

--Linear Regression of Unload I~ ~ ==r=:

150 20010050

+----f --l-------lII

o ~-'---"-L-+-"-~---~~

o

i

2500 +---------- -------------~------~

,-c"j 2000 +------C.~Nlll)

:E

J1SsT2 (in./in. x106)


3500 ------- ----------- ------- ----III

_ Linear Regression of Unload

--+--A\g. (F-S46, F-S47, F-S48)

50o

o 100 150 200 250 300 350 400 450 500

J1SsT2 (in.lin. x106)

Figure 5.10 Moment at 'West Elastic Section yersus Strain for Stage 2(Scaled Design 7)

160

.1000 ---------

f2500 L~ _

l

3000 -'---------

N •

t; 1500,-------:E

-C lI 2000 ~'----------C. L

~

3S00 ---------

SOO4S04003S0

I

I: Linear Regression of Unload

Iu---------------------j

II

Ii

100soo __.L-.L-'--t--~--~~~---.~l.-=- =:;====;========;====1

o 1S0 200 2S0 300

IlSsn (in.lin. x106)


SOO +-.-----+-41L:--f--------f -+-A\9. (C-511, C-514, C-51S, C-S17)

1000 +-.------

2S00 +---------

3000 +-.-----------

3S00 ------_._------ -----

___ Linear Regression of Unload

-+-A\9. (C-5SS, C-SS8, C-5S9, C-5S1)

o ~-.-'---- ..--.-------------o 50 100 1S0 200 250 300 3S0 400 450 SOO

IlSsn (in.lin. x106)

Figure 5.12 Moment at West Elastic Section yersus Strain for Stage 2(Scaled Design 19)

161

1000 ~---

SOO

3000 -'------

2S00:- ----------- --- --

--c ." 2000 ~- ~-----Co .

~N ~

~ 1S00 ~-------- - -- --:!:

9000

!~

I,

~------------~-i

300200100

a --~-¥-~--+--~------.

a 400 500 600 700 800 900 1000

~SsT3 (in./in. x106)


,,!

2000 -+----.r"--~----_,-----------~--I-+-A\9. (F-57, F-S8, F-59) Ii

ii--- Linear Regression of Unload Ii

1000 -r---c*--~------ I

6000 ~'--------- -~"'.r--

7000

8000 ~-------~,

t:! 4000 ~------~III

:!:3000 -,---------=~-_T'_----------------~--'

--c"6. 5000 -,------------,..---.-------~~----___,~ !--

800 900 1000700


-+-A\9. (F-546, F-547, F-548)

a '--a 100 200 300 400 500 600


Figure 5.14 Moment at West Elastic Section yersus Strain for Stage 3(Scaled Design 7)

162

3000:----- - --

2000~-~------

1000 ~-

7000 -'~---------------~----l

9000 -,~-------~-------------- --------~----~------~

8000 -'----~---~---~-----~--------~ ~---.-----------'

__ 6000 ~-------.--c"6. :~ 5000 ------------ ---~------ ....I- •

:E 4000 ~-- - ----

9000 .~---~---

8000 ----~-------.-----.~,..~~~~-

,JP------~~----~-_____,

100 200 300 400 500 SOO 700 800 900 1000

J1SsT3 (in./in. x106)


2000 -'--~~-/'-~-f'-------,---------------------i

-+-A\9. (C-S11, e-S14, C-S1S, C-S17) I____ Linear Regression of Unload j1000 -i

r

o ...t~'-t-~--~o

7000 r

3000 +---------:cr--=-=---------------

SOOO ~_._---------r.~ -..---------'2 .•- rC. 5000 ,--------------- w--*----------

g ~~ 4000 -j-----------;r.7FIn

:!:

9000 ---- .-._-------------- --.------------- ------..---------.--

8000 -:--~--------- --~---------------- .....--------- --~-..

-+-A\9. (C-SSS, C-SS8, C-SS9, C-SS1) I

--- Linear Regression of Unload Io

o 100 200 300 400 500 SOO 700 800 900 1000J1SsT3 (in.lin. x106)

Figure 5.16 Moment at West Elastic Section versus Strain for Stage 3(Scaled Design 19)

163

1000~-

SOOO~----- ------------/-M'

7000 .:...----------------r-

.....l: .

'6. 5000 .:-~-------.g .~ 4000:---- ---CIl •

:!:3000 ~--~-----

2000 .:- -----

6000 ~---------- ------ ---------


-+-A\9. (F-534, F-535, F-536)

---/-------------

I/--------------11000 +----/-

4000 ~--------

5000

o -~~-~

o 100 200 300 400 500 600 700 800 900 1000

~SsT1 (in.lin, x106)

Figure 5.17 Moment at Midspan Section versus Strain for Stage 1(Scaled Design 7)

j:III

:!:2000 +------,-F--::/--------------------'

-c:'"iCo

;g, 3000 +------------,£-/'-----,-,1'--------------------- --.

6000------

/----------_.


-+-A\9. (C-533, C-536, C-537, C-539)

-/----/--/--------------

300200100o

o 400 500 600 700 800 900 1000


Figure 5.18 Moment at Midspan Section yersus Strain for Stage 1(Scaled Design 19)

164

1000 --

4000 +----_.-------

5000

j:III

:!:2000-------- . -- --

'"iCo ,

;g, 3000 -"--------- -

-c:

6000 ----------~--- -- --


-+-A\g. (F-534, F-535, F-536)

.---~:========-=---:..:~ ..----:-=:....

100 200 300 400 500 600 700 800 900 1000



rrI

2000 -~-------/".=------

1000 +---h'-----

4000 ~--------- -~------------------~

5000 +---------

NIUI

:!:

-c"Q.

g 3000 -'---------h"----

6000


--+-A\g. (C-533, C-536, G-s37, C-539)

oo 100 200 300 400 500 600 700 800 900 1000



165

1000 .----

2000 ~-

,4000· --- -- -----------

5000

"

.~ .:. 3000 ~-------g

NI<Il

:!:

-c

14001200

4f-----------

400

~---------~I

~ ~ -+-A\g. (F-S34, F-535, F-536) I~

, Linear Regression of Unload i!"

__----++---'"~-+____~---~~----.,....._-----,..__....L

600 800 1000

J.1SsT3 (in.lin. x106)


14000

12000

10000 ~

- rl:

8000 -t-----"iCog I

M[

I- 6000 ~III

:!: ,I

r4000 ~----

2000

00 200

1200 1400


________ .-+-A\g. (C-533. C-536. C-537. C-539).

400200o

o 600 800 1000

J.1SsT3 (in./in. x106)

Figure 5.22 Moment at Midspan Section yersus Strain for Stage 3(Scaled Design 19)

166

2000

4000 ---

10000 ----------------

12000 -- ------------- ---------- -- -- ---

14000

-.!i= 8000'---------Cog

M

lii 6000:!:

, ,I'

9

___ West Elastic Section

,-----------1-+- East Elastic Section !i

-----------------

5 7Block Removal

3

,o -:

1

"30,-Ee... --"C C "Q) ._ 25 +------------------------... ...... ,;::, Q) "

CIl Cl 'met~ ~ 20 +l-----------------------.~ c ••---I.---~.------I•.-----I•._-__tl.l__-__tl.l__- .I---_tt.~.~ f- :g 15 ,f _~ Q).... 1-;::, ...~ 0... E 10 ,-----------o 0c:t:lo 0... m~ 5o.J

Figure 5.23 Neutral Axis During Unloading of Scaled Design 7 in Stage 1

--------- -------- -------

9

--- -------- -


-+- East Elastic Section

------------------

5 7Block Removal

3

5 ----

o --1

E 30e... .-."C. ,Q) .: 25 -----... ...... .;::, ellCIl ClIII CQ) III ':!: - 20 --------~--------------------------CIl U. •'- c)( a<'iii· • • • , • " • •ia c 15 ~-------------------- --------- --------------.. Q) •.... 1-;::, ...~ a... E 10o 0c:t:lo 0... 0)IIIoo.J


167

~ East Elastic Section .[I

____ West Elastic Section : i

30Ee.... --g .~ 25 -y---------------... -:::J Q)1/1 ClCIS C

~ ~ 20 +--------------------------

.~ ~ .~~==lat==--lI.....-===*~=-_t.t_-~~~---.---l,t_-__•~ .* t~ ; 15 --t----------------------------.... 1:::J ....~ 0.... E 10 -t---- ----------

o 0c~o 0~a:l

~ 5--1--.-------------o

...J

3 5 7Block Removal

9


r--- ----------------_._--- _._-

----------- -.

~ East Elastic Section


-----------

5

o

,30 +------------

rEo....... 't:J •Q) _: 25 --I--.-------.---.-.--.-,,-~--~----------... -:::J Q)1/1 C)CIS CQ) CIS:E iL 20.~ c)( 0ct u; ••---t......- ........,---t.t----4I.f--....~==~~~==1t~===*~~ ; 15-"--.... 1:::J ...~ 0... E 10 ~--- ------o 0c~o 0~a:lCIS(.)

o...J

3 5 7Block Removal

9


168

,I

--4,

95 7Block Removal

3

_30 +----------'0 .11l .=.. -~ ~25 +------------Q) C

:!:~ ,.~ C 20 f _

~ .~ 1;:::==~l:=:::="-.---..,--..,1--~~,F===l,t===t,===4,!'O C ~ • == ,; ~ 15 +r---------------Q) .... rZ 0 t I

'0 ~ 10 t iC :::: +[--------- I

o 0 ~ 1,1;Om L

~ E +t ----:-------;=-::-:-:-;::::-;-:-::::-:--;::~~IIo 0 5 I -+- East Elastic Section Ii..J .:: t

r

!I___ West Elastic SectionIIo -t------+----

1

Figure 5.27 Neutral Axis During Unloading of Scaled Design 7 in Stage 2-2

i--------------------_._-_ ..__ . -

---, -+- East Elastic Section-

---West Elastic Section

5 ------- ------

Ee... " .CD .: 25 ~----------... -~ CDIII C)

~ C ,-= ~ 20 ----II: U. ~

.~ c~ .~ ~~---t.I-----.,I-----j,IJ---4,l---.......---i.....- .......I-----.E; 15 -------I~ ...~ 0 .... E 10 -----------------o 0 -c:S:::o 0~mcooo-J

o -- ---- -- ----- ---.-----1 3 579

Block Removal

Figure 5.28 Neutral Axis During Unloading of Scaled Design 19 in Stage 2-2

169

40 ------------------------

-----,I



o

5+-----------

~ 35~:: :: ~r-~=:::::::j,t::::::::::t,====l,t::::::::::::t.==~~:::::!"' ... ~ • = ::::~ ::. 30 -r------------------------:::s CIlen C)III c::E ~ 25 -r------------

u. "o~ c: ~>< 0 r< °iii 20.,--- c: rE Q) t.... I- ':::s It- 15 "~ 0It- E~ ~ 10 -t------------o 0.. mIIICJo...J

3 5 7Block Removal

9


40 -----------------------


___ West Elastic Section5

,E 35 1 _

i ~ 30 t~=-=--~-:=~==~=:=~:==:;:==::::;::::;::::-=:::---- ---,:::s CIl ~

~ C) ~Q) ; 25 ~------------:!:u: .o~ c: .~ ~ 20-:en •iii c:... CIl •:; I- .Q) It- 15---- -- - ----z 0It- Eo 0c: ~ 10 ~--- --. ---- ---o 0.. mIIICJo

...J

o -3 5 7

Block Removal9


170

~~~'Wt-~~---~~

5000 ,~r~

4500 rr

;:-:E 2000 +-~~~~~~~~~~~~~~~~~~~-"\~~--

rr

1500 -,-~~~~~~~----,~~~~

ti1000 +-1 -+- F-D5

ri500 f _F-D18 ,-----.-------\-\,-;

,I Io -~---·=---==~=f==~===-==+T~-'--.,--~~~

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1Vertical Deflection 5T1 (in,)

Figure 5.31 Midspan Moment versus Vertical Deflection at Sections A and E forStage 1 (Scaled Design 7)

-c: 3000 -i-----~--------------~:L-\\::___-

r4000 -'-~--~~~~~~~~~~-------'l,-\\-----____.

f3500 -:------------------".~----

r

"Co;g. 2500 +--~----------~------~c_\\::__-___,

--------- ~---- ._---_ ..

;:-:E 2000 ~-------------------. --.------

------_ .._._----~

--,._-~~._.__._-----------_.__ . -Deflections after--~--- .

. ~__ J:@cement~ .Block #4

1500:-------

1000 ~. -+- F-D5

5000 r--.------4500 ~~-------

4000 l--_

3S00 ~ ---,

-:- 3000 .c ,-. ~Co ';g, 2500 ~----

SOO ~- --.-Analytical F-DS---·------

O:..······~-···~-·-·c ~.~. -.- --.------ .. -..~ -' ..-..-.. - -.-~. ~ -- ..--- .

-2.5 -2.3 -2.1 -1.9 -1.7 -1.S -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1

Vertical Deflection 5T1 (in.)

Figure 5.32 Comparison of Experimental and Anal)tical Results at Section E forStage I (Scaled Design 7)

171

5000 -r~--- ------------------~f

4500 -,--'-------"111!,,~!.----------------

4000 -~--~------~------""..--------------r

3500 +------------~~..----------~

-c: 3000 +--------------'~-__y...______-------",c.:i: 2500 -+-------------~---''rt___------___i- !~ I:E 2000 !

1500 Tr=,======~-------____\.\.____"\->, __--~, I

1000 lJ -+-F-D8r I

t I,

500 ~: -If- F-D15r IO~~-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1

Vertical Deflection ST1 (in.)

Figure 5.33 Midspan Moment versus Vertical Deflection at Sections B and D forStage 1 (Scaled Design 7)

5000 -~----~

Deflections after __~: Elacemenl of ~

Block #4500 ~~; -If- Analytical F-D8-~---~~ --~------ ------- ---- ----

o -:----------~-~~ -----~--.- ---.-~ .-~--- --.-~- .. --~ .. -~.~ --" ._.-. --- -.-.--~--

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1

1500:-~-~-------

1000 ~. -+- F-D8

-c: 3000 .---",c.~ 2500 ~:----------------

,4500 -:--------------'".

t4000 -',---------------~

3500


Figure 5.34 Comparison of Experimental and Analytical Results at Section D forStage 1 (Scaled Design 7)

172

5000 ,-----------------------~

4500 ~-------~-~---------------__1

4000 +---------""""",,------',--------------

3500 +----------~___"\;;,_____---------____i

-C 3000 -'--------------"-------'~--------_______i''jCo;g. 2500 ~-----------____"\:--,-----~:___------

~CIl 2000 -+-r--------------....~-,,~----_____1~ ~

1500 t--~ .~u.u •• -. __ u-. I

1000] --+-F-Dl1 i

500 T F-D12 I·----------~,-----"

oL-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.35 Midspan Moment versus Vertical Deflection at Section C forStage 1 (Scaled Design 7)

5000 -,---------

4500 .4-- _

4000 ,--------------~,

3500 ~-

~ 3000 .:I ,

Co •;g. 2500 ~--_.

~ tCIl 2000 ,--~--~--~--~- -.--~-----.-. ---- -.-~ l

1500!--·-~---··..-·~··~---·-~--~ ..-Defieaionsafter·- ~

1OOO~- -+- F-D11 Pla_c~eme-'ltof_~_. __.: Block #4

500 .~ _Analytical F-D11 .-------- .. ---~--~-----.

0:------··---·---- ~-~~~-..~....~--.-.-.-,-.-.-,- ...... -- ...-...~.--- ..

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.36 Comparison of Experimental and Analytical Results at Section C forStage 1 (Scaled Design 7)

173

5000

4500

4000 ct

3500 ~~- f

l: 3000~'j" r

Co >-

;g 2500 rf..

I-:E 2000 +--------------------\\--\\

~1500 If---~ ---1000 i -+- C-D5

500 ~~ -ll-C-D18

o -j".'-"---,-----r---,L~-~~~"~>-----..-.~~~--'-+-~---,--'---'-'-.~.

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1



------ -----------=\'\

5000 --,---f

4500 ~f__

4000 --'-------------"

t3500:-~--------

~ 3000 ~----~-~-------'j"Co;g 2500:-----------

t=:E 2000 -:---------

1500>-~--------------- ----Deflections after-------~ "

~ -+---- C-DS Placement of1000 .:: --- ---------~----~-------Block #4

500 .:~ __ Analytical C-DS---- - ------~-- -------~------

--o ~-"-~~~~=~.~c,~-~~=_._.__~ • • • ._._. __ L • - -

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.38 Comparison of Experimental and Ana1)tical Results at Section E forStage 1 (Scaled Design 19)

174

___ G-015

-+-G-08

5000 -~

4500 +-------~"'"--------------1

4000 +--------~_A:__~c__---------______!

3500 -t------------'~~=--------__1

-C 3000 +------------~----'~-------'j"c.:i: 2500 +--------------~:--~._____----____1.......~ 2000 +----------------".,-"<--"'-,,----------i

1500 -t-F~~~~~~,___---------'\'\_-----\."':____---j

1000

1500 1o -.jL----,-----,-----r---f---'-'-'--+~__+~'----t--"-~_r"_~. ~--<--L~---'-+_.-_'___+_••

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.39 Midspan Moment versus Vertical Deflection at Sections Band D forStage 1 (Scaled Design 19)

----Deflections after__--.'.Placement of

----~-------~.-_._._-------

Block #4

5000 -,-------------.-----------------c

4500 +------------------.;:"<-----------'

4000 -t---------------,'\.-------

3500 +--------

~ 3000 i _.- ,I ,

C. f:i: 2500 -!------------ t;: t~ 2000

1500 .

1000 ~. -+-- G-08

500 + Analytical C-08 ,------ - ----- --- -- -------- ~---

o ~-.~__ ~-'~-~----'---... -_..._.- ... -.~ 4 " ....• ---- .• ------.-.-- ..-- ..-.-~.-------- .... -

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.40 Comparison of Experimental and AnaI}1ical Results at Section D forStage I (Scaled Design 19)

175

5000r----

4500 +-------~.....__"',--------------__i

4000 +f-------~o--~-----------__i

3500 +----------=~~c_=_---------_1

'';Q.:i: 2500 +--------------~~---"\o;o_-------i=.;. 2000 -j----------------""------"....----------i::::r: ~D-11-

500 1 -II- G-D12

o +---, _ .-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1



-C 3000 +-----------~;_o_____'\.;;.____-------_1

5000 -rl--------------------------,rr

4500 {--------------..,,------------'

4000 -j--------------,,-------_____,

3500 -;-----------------~,_,__----_____,

Deflections after _---.._________elacementof ~

Block #4

--------------------"'-0------'

.1500:---

1OOO~- -+- G-D11

i=.;. 2000

-C 3000 -----------------'u....----~'';Q.

;g, 2500 ~---

500 ~. _Analytical C-D11 -------

o-'------------0·--·-- .. --.-"-.. ---"-.-"-----~-"--~.---"-.. "-~-.

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5042 Comparison of Experimental and Ana1)tical Results at Section C forStage 1 (Scaled Design 19)

176

5000 14500 i-------------------'IIIll'------!

4000 i-----.------------~~------J

3500 +------

-C 3000 +------------------~~----!"Q,

;g. 2500 +--------------------\lI~----iN

~ 2000 t1500 ,-------~-------------___\~\-_.j

~ -+-F-D5 I

1::: +.'_---~ F-D18 1=,============~==========:===: ...-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1



--------------------~-C 3000 ~-~"Q,

;g. 2500 ~------ ..----------------l.

NI-

.;, 2000 ~-----~--

1500~·-_------_.---------- .. --.- ----------;;;-----:-;------:;:-----y

Deflections after ~~ -+--- F-DS

1000 ~- elacemenLof _Block #4

5000 t4500 _f__.__. . ~-----i,

~

t4000 -~---.--------------,3500 +-[-------------.--------~---

500 ~- Analytical F-DS-----------

o -~ .---.- ._---- .-....-.-...-.-.---.-------- -....-....--2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.44 Comparison of Experimental and Anal)tical Results at Section E forStage 2 (Scaled Design 7)

177

5000 -,------

4500 +--------- ~t..--------~--------'

4000 +------------',,"'''<----------------.,

3500 +----------~~----------______;

c: 3000 +----------------'\''\\'\-------------.,'"jCo;g, 2500 +--------NI-~ 2000 +---------------.>.".",----------i

1500 +ri,======-

1000 j -+- F-D8q

500 ~ F-D15

~o -;---- =~.=.=='-"--'--"_T___~>---------"-~~----.-'~----;--~+__ • .._~,__'____'__1

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5

Vertcal Deflection ST2 (in.)


--~--~-----------

Deflections after ---1'-_________Placementot ~

Block #4

------------------l

. -+-F-D8

5000 -r--------------~--~~------,

NI-

~ 2000

1500

1000

3500 -:------~------~---------~---------',~---------<

.-.C 3000·------- -- -------------"j

c.;g, 2500~-------

4500 -:--~------------ - -------

4000 -:-----~~--~---------------"'\.------,

500 - ___ Analytical F-D8

o .~~ -- -~-- ---~--- -- ---- --- -- --~-~- -. ~-------------.~~-~-- --- ~- -- --- --2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1

Vertcal Deflection ST2 (in.)

Figure 5,46 Comparison of Experimental and Analytical Results at Section D forStage 2 (Scaled Design 7)

178

5000 14500 -j--------~------

~4000 +-r ------'-'"~-__

3500 -j----------~~---

-C 3000 +-----------~",____-

___ F-D12500

1000

1500 ~~~~~~-------~ \.'\..~------~

-+-F-D11

o~ I -~.~ ~ ..•~~

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5



"'j"Q,

~ 2500 +-----------------""N...~ 2000 +---------------'\.'\c

Deflections after ----J'*_.. EJacemenloL _

Block #4

---- -------------.5000 t

4500 +f---L

4000 ~:-----f,

3500 ~~----~---------

N...~ 2000:------------ - - --~-.-.. -.-.---.

1500 :

1ooo~. -+- F-D11

,- ..~ 3000 t------------------~-Q, ,

~ 2500 +-----

500 ~. Analytical F-D11 .----- -.-. -

O~---------- - .--~---- - - ... '- -. ------"-"------.....--.---- ..

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.48 Comparison of Experimental and Anal)1ical Results at Section C forStage 2 (Scaled Design 7)

179

--+-C-D5

-ll-C-D18

5000 -,-------------------~------~

4500 +---------------------'~----__i

4000 +----~-----------

3500 +----------------~---=m:---__i

-C 3000 +-----------------------,ill.---__i"j'Co;g. 2500 +-------------- -----.:-----j

N....:E 2000 ~--------------------~\_-_it

1500 !~_-~~~~~~"_"=;-------- -------\\r

1000 ~1500 i

o }I-I-------,----~~~~~~____,-~~~---r--~'1-1~-'----'-i~.

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1



5000 --,---~---~-

,4500 {------------------~------------\\---~

4000 -"----

3500 ----

-C 3000 ,----------------.j"

Co;g. 2500 r--- -----------------------~---- --_.-

N.... .:E 2000 -:------

1500~,--------·~----------------·--------nelle-dions afte--r------ ,

1000~. --+-C-D5 PlacementJ2L ~: Block #4

500 -~ Analytical C-D5-- -

o -~ ,~-.-~'.'~ -~-._'~-o_~~,,~=_"_..__• •__ .__ ,-.----,-.-0-.-.. ---.--

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.50 Comparison of Experimental and Anal}tical Results at Section E forStage 2 (Scaled Design 19)

180

-------------"'\.'.\----------;

NI-

~ 2000 +-----

1500 -f~I-~~[:

1000] -+- C-D8

500 ti C-D15ilflo +---L.-..-.--=-~:-::-"1'1=~---+--~ ~.......---~t---'-"--'-t

f4500 -f--

f

4000 -'-~--

5000 ~---

3500 +-----_ c

c: 3000 +-----~----------~~---------_i-. ~Co f~ 2500 -,-----

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5



Deflections after---J~, ~Iacemenlof , __ ~ .

Block #4

NI-

~ 2000

1500

1000 ~- -+- C-D8

3500 ~------ ---------

; 3000 ~;---.- .I •

Co •

~ 2500 ~

5000 ~,----

4500 i -....'"r

4000 L-__ ~ " ,----------r

500 .:. ---------------------------~- -- ~---------~--"

: Analytical C-D8

o .:. --- ---2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.52 Comparison of Experimental and Anal)tical Results at Section D forStage 2 (Scaled Design 19)

181

5000 -,--------~-----------------_____,

4500 -t---------""'li~-----F

4000 -[----~---_'..,,"----------____i

~ :::: t----------~--------------1Co ,;g. 2500 +'---------------"'__----------1

NI-~ 2000 +--------------~,-------------1

1500 +r=~~~--~--~---~--~--,--------~~-----__I

___ C-D12

-+-C-D111000

500~

o r' , I '

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5



=-2'------~--J

-~--------"

Deflections after ----f•••__________E18_cemeotof, _

Block #4

1500: _-= -_~-_-- _

1000 ~ -+-C-D11

5000 -,--~----,4500 {------------~- .....--------__1

~4000

3500---

NI-~ 2000 -:------- -----------------

-C 3000 -:-----------------------~~--.. ~Co ,

;g. 2500 -,-.:----------- ---------~----~--------"lo""'----

500 ...:: Analytical C-D11

O~---------------~·--_·-·-·--·---·~~

-2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1


Figure 5.54 Comparison of Experimental and Anal)1ical Results at Section C forStage 2 (Scaled Design 19)

182

___ F-D18

-+-F-D5

-2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0


14000 -~

13000 I

12000 -~11000 -~

10000

- 9000c

8000'j'c.;g. 7000..,

6000I-CIl

:!: 50004000

3000

20001000

0-3


-----.- -.---~---.-----.lI:

14000 }13000 +,~~~~~~-

12000 -r-~-----

11000 +L---10000 ~ .~--- ~~~~--~--~-.

- 9000 -~~,~ 8000 4--~~~~~~ __~~~~~_C.;g. 7000 -c--------

~ 6000 -~~~~~:!: 5000~

4000 ~------------- - - -------- ----- ------------

3000 ~ -+- F-D5 -- --2000 ,-------------- ------

1000, Analytical F-D5 --.- -----o -----.-----.-----.. -..-- -'" -- -.- -.- -.-.. - .

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

Vertical Deflection ST3 (in,)

Figure 5.56 Comparison of Experimental and Analytical Results at Section E forStage 3 (Scaled Design 7)

183

14000 -,-------------------------,

13000 +--------__,.-----------------

12000 111000 +---------------"'1..=__-------------1

10000 +----------~-~------------I

_ 9000 +---------------"It:=---~,.___------_____1.~ 8000 +------------ - -------_____1

Co;g, 7000 +1-------------.~-I.__----------1~ 6000 +------------------'__-~----_____1

::E 5000 +--------------------'''I<--......r----_____1

4000 ~~~~~~~~-----------"Il,.--~---___l

3000 -+- F-D8

20001000 F-D15

o _so=;===t==p==r===\~'__j__"__'__"_t~'_t_'_"_"_+~~~"_'_+~-+-'-"_'_+"....__;__'_"___

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0



14000 -,--------------------------,

13000 +-j---------w ~------------O

12000 +-r-----------...-)r,,.---------------~

11000 -t-----------""II"i.._------------'

10000 +-1---------------l~----------

; 9000 {----------'6. 8000 1--------·------.----·;g, 70001---~-------------; ..-------.., ,Iii 6000 +-~-----

:!: '5000 1---------- .-4000i===~~==- 0

3000 -+- F-D82000

1000 _ Analytical F-D8 --o --~~- -- -__ - ...-~......--.-....~~-~.-_. ~.---- ~~ -~ -~- .----~ .0- - ...... _ ..... ~ • --

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0


Figure 5.58 Comparison of Experimental and Anal)1ical Results at Section D forStage 3 (Scaled Design 7)

184

14000 113000 +!---~----.. t----------------J

12000 t----~--~.---------------~11000 +--------~

10000 +1------------'~ .._411(1...~---------~

_ 9000 +--------------=.

.~ 8000 +-----------~t_~I-------Co;g. 7000 +------------__l-~II___------

~ 6000 +-------------~,-~.-----

:!: 5000 +--------------~r__---!II .....---

4000 TFr--~-~,-'~~~~~~-------_"'l~-_..----

3000 i -+- F-D11

2000 l1000 1 --- F-D12

o ....,--,----,--,----,----l.t--.-p---'--1f-'-L-+-"-'-'-1'~'__t__-----4~'-o--L_'_'_t......"+_'_~.-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0



"-~"~----------~---~

14000 -,----------------------------.

13000 -L'---~-----'_.--------------i

12000 J-- ..... ~ ____',11000 ~-------------.:~r------------'

10000 -L--------------.l--------------'

_ 9000 ------

.~ 8000 -----------------'11~-----,--~Co;g. 7000~'----------------~.

~ 6000·~------------------.

:!: 5000 --~----

4000 .3000 . -+- F-D11

2000 ,1000 . Analytical F-D11----~---~--------,--~----~,-----

o - .--.~.,~~~--.-----~~~-.--~~~,., ...-~.. ~~--3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0


Figure 5.60 Comparison of Experimental and Anal)tical Results at Section C forStage 3 (Scaled Design 7)

185

14000 113000 1--12000 -

1100010000 +1---

_ 9000~r -.~ 8000 -------------~--------jCo:i: 7000 ---------------4.-..---1-~ 6000 -~

:i!: 5000 +---------------------......-----1

4000 +-------l-----------~~'________i

3000 1 ,: C-DS2000

1OO~ --- C_-_D,-18_---,----lt-~~..Lf_'_____'____'____'~'_t_'_'___'____r~t__"_'_-Y--"-_'_'__i~'+tIf--J-.-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0



----.---------------........

14000 --,---- !

13000 +----- -------J11

12000 .:.---------------~~------!If ,

11000 1---10000 ~--------------------I~----~!

_ 9000 -:-------------- -------------.:~--~

.~ 8000 --,----Co ";g, 7000.,;..'---------------------a

~ 6000 -;-:i!: 5000 ~----------- -----

4000 =-_c,_=cccc~c=c,==-_==__-------------------"

3000 . -+- C-D52000 - ~--------------

1000 . Analytical C-D5--------------------------- ;o ~- ---- --- ------------, -~.-"~--~~-.-.-.-.-.------.--.-~-~~"-.-.---.--~-.-.~

-3 -2.8-2.6-2.4-2.2 -2 -1.8-1.6-1.4-1.2 -1 -0.8-0.6-0.4-0.2 0


Figure 5.62 Comparison of Experimental and Analytical Results at Section E forStage 3 (Scaled Design 19)

186

___ C-D15

-+-C-D8

+------~~-- ----------

14000

13000

12000

11000

10000

- 9000c

8000"c.g 7000...

6000 Il-ll)

:!i: 5000

4000

3000

2000

1000

o -;-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0



-----='"11 ,.--.. -----

-----_.__.~----~_._----,

._--_.._----..

4000 -"-------------~--.

I3000 J -+- C-D8,,2000 ~

1000 1 Analytical C-D8-o 1 .-- -~ - -0·· , ·-0 • ,_._o~~~__ •__ .~. __ .__ .o ,_. ._•••_~_ •••••_0" 0_

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

14000 ~

13000 +!,-----f

12000 i----11000 -"--!---

10000 -"-----l

_ 9000 ~---~---

.~ 8000 -:----c. ,g 7000 ~.~~-----~ 6000 ~-----_._._-~-_._._---_.~ ---------lI)

:!i: 5000------ ---~----~---------~--


Figure 5.64 Comparison of Experimental and Analytical Results at Section D forStage 3 (Scaled Design 19)

187

14000 -~

13000 1----12000 -~

11000 t-----------9Il;:-.~---------1

10000 +----------......---.~---------______1

_ 9000 +-----------..-__..--------______1

.~ 8000 +------------ -'._------______1Co;g. 7000 +-------------It----._-----______1

~ 6000 +----------------"'1It---~ __----______1

::E 5000 +-------------------lII..----'~---___j

4000I3000 -+-C-D11

2000

100~ ] C-D12

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0



14000 -,--------

13000 +----------_--..-----------~

12000 -'-----------'.

11000 -'-----------'CJ1

10000 -'-------------......

_ 9000 -'--------------..~,-------__i

.~ 8000 -;.----Co ,

;g. 7000 ~

~ 6000 J

::E 5000~----~.-.-

4000 ---

3000 . -+-C-D11

2000 .1000 . Analytical C-D11-·-·--···_··--··· ----.--------.--- -.

o --_. __~_.~-- -- _-. -- ---0---- ..-.-----~------.-----

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0Vertical Deflection ST3 (in.)

Figure 5.66 Comparison of Experimental and Analytical Results at Section C forStage 3 (Scaled Design 19)

188

o-1-2

20000

18000

16000

14000

-:- 12000c:

~" r.90 10000:. r~ 8000 ~

~6000 ]

~. -+-F-D54000 II

2000 ]_F-D18rlr!

o+i-9 -8 -7 -B -5 -4 -3

Vertical Deflection (in.)

Figure 5.67 Midspan Moment versus Vertical Deflection at Sections A and E(Scaled Design 7)

o-1-2

_F-D15

-+-F-D8

-7-8

-,------~ '!t.------------~---------

-9

2000

o .:_~_.~.~_"_~~_~._~~ __."_~._~~_u_~~. __...-.--~••~ ... '-' .-... -. -..._- _.- .~-

4000 ----

6000 -.-------~--- • .._ ___

~ 8000~---------- -.-.---~ ...

20000

18000

16000,

14000 L

- 12000c:

"Co 10000~

-B -5 -4 -3Vertical Deflection (in.)

Figure 5.68 Midspan Moment yersus Vertical Deflection at Sections B and D(Scaled Design 7)

189

o-1-2

___ F-D12

-6 -5 -4 -3Vertical Deflection (in.)

Figure 5.69 Midspan Moment versus Vertical Deflection at Section C(Scaled Design 7)

20000 -f18000

16000

14000

-:- 12000c:.;-

.~ 10000:.:E 8000

6000

4000

2000

o I

-9 -8 -7

o-1-2-7

___ C-D18

o ..::--~-~-... --------..- ... -.-.. ~-.. ,.-..~.-.._~-,.~. '-."~"'~-_.'--'---"'-".'--

-9 -8

2000 ..::

14000 ~------------

20000 J18000 +-,----~---------;K:

16000 +-~------------l..-------_

:E 8000 .~--

6000 ~.-.------~

-+-C-D54000 ~

-6 -5 -4 -3

Vertical Deflection (in.)

Figure 5.70 Midspan Moment versus Vertical Deflection at Sections A and E(Scaled Design 19)

190

-:- 12000 -L- ~ _

c:...~ 10000 ~--:.

20000 ~------

o-1-2

____ C-D15

--+-C-D8

-8

16000 +----....--14000 +I---~'a_-~

18000 +---~---

-7 -6 -5 -4 -3Vertical Deflection (in.)

Figure 5.71 Midspan Moment versus Vertical Deflection at Sections B and D(Scaled Design 19)

'"":' 12000 -i------...=._-c

"'j

"~ 10000 +--------------~-------------.:.:-

11,

IIIiiJiiIr

!~

____ C-D12

--+-C-D11

._- ----- ----------

~ 8000 .:------~tL

6000 --'----

4000 l: 1 " offset typo

2000 -~---~-----------

O:,~~,~~~--~~-- ---- ---- .-~-.- ....-.. ,-,-., ~~.~~".--- '-' .~.---.-~.'--.-~'"~~ .... ----

-9 -8 -7 -6 -5 -4 -3 -2 -1 0Vertical Deflection (in.)

Figure 5.72 Midspan Moment \"ersus Vertical Deflection at Section C(Scaled Design 19)

191

20000 ~

180001--oz.---

16000 {---It...------------- ",L

14000 L!---'1.......---

f'"":' 12000 1----C i-, t.~ 10000 -1'----..:.: '- '

Ux

Ux

Shupe

Ux

1.25 Ux

Shope 4

Ux

0.67 Ux

Shape 2

Ux

1.375 Ux

ShupE' 5

Ux

1.5 Ux

Shope 3

1.3125 Ux

Shope 6

Note: Ux is positive in the South direction.

Figure 5.73 Initial Imperfections at Midspan

192

32.50.5 1 1.5 2Midspan Lateral Displ. (in.)

o

-,k----.----.- ...........-..-. .tr-.~

-~~___Ir

.,--

~/'//'

1/i(IJi

Maximum Moment=6955 kip-in.I4i,

--ux(top)

1--..- ux(bot.),o

-0.5

1000

2000

7000

8000

.j"

~

~ 5000

1 6000

c:CI>E 4000o~

; 3000~Ul'C

~

Figure 5.74 FEM Simulation Results for Model SD7-1

8000 -.------------------------

7000 j------------------------i

2.5 321.5

Maximum Moment=6594 kip-in.

.-----------------._----' --ux(top)

--.,\- ux(bot.)

0.5o

./-----/.. r-------/

o -l---_-t'- .-_-_---_--_--_-_--_---.J--

-0.5

1000

16000 -j ~---.. .... ---,t-.--.----•..-- ... --, _...'~-,-_..a.-----~--~ -~~ 5000 -1---------"'-·--~r-----------1

./-c:CI>g 4000~

; 3000~Ul'C~ 2000

Midspan Lateral DispJ. (in.)


0.5o-2 -1.5 -1 ~.5

Midspan Lateral Displ. (in.)-2.5

-.A-----..- __A-__

~'~'J._,.~

'"",-

~

""~'~\~

Maximum Moment=7288 kip-in. \\--ux(top)

\-,0- ux(bot.)o

-3

1000

7000

8000

~ 6000''jc.;g. 5000....c:CIl

E 4000o~

lij 3000c.III'C~ 2000


8000 ,--------------------------,

7000 -I----------~--------

----~- --ux(top)

- .. - ux(bot.)


______-----Jo._-~,-----------

1000

....c:CIl

~ 4000:!:lij 3000c.III'C

~ 2000

-1~-----------~_._.-I<---~-'--.--~_" __ "'- --.--~6000 .''jc.;g.5000

2.5 30.5 1 1.5 2Midspan Lateral Displ. (in.)

oo l-__-A- ---'--=-=-=-..=..-=-.=--=::..J--

-0.5

Figure 5.77 FEM Simulation Results for I\lodel SD7-4194

32.50.5 1 1.5 2Midspan Lateral Displ. (in.)

o

,._~ .......___----t:;---

_--A---«-----~----.//J>---/~

/1>'/

/

,ft'

,1/II Maximum Moment=6115 kip-in.

--ux(top)

f -..- ux(bot.)o-0.5

1000

7000

8000

'''jCo

;g. 5000....I:Q)

~ 4000::i!:~ 3000CoUl'C~ 2000

1 6000


8000 -,----------------------------,

7000 ~---------~----------------------------j

0.5o

~_._-_._-~_ .. - ---------~-~-_ .._-

-2 -1.5 -1 -0.5Midspan Lateral Displ. (in.)

-2.5

1000 - --ux(top) -------------------------

--. -- ux(bot. )o -'---'--""==-----'---0..----'-'---'-'-.;;..:-- -"-__----'

-3

....~,

E 4000 -I~--~--------- --~-~------' ..-,- ~---------lo '-= --~.:: \

~ 3000~----------------------------'\- -------~-----CoUl'C~ 2000 -1--- ---


1 6000 ~_----=-tI"""-"

'''jCo

;g. 5000 -j~----

Figure 5.79 FEM Simulation Results for Model S07-6195

32.50.5 1 1.5 2

Midspan Lateral Displ. (in.)

o

k_~--.-*----l:.··~ k-~·-'

~,..-g- "

)(/,/Lr'''-

--

////f(11,


I. l-ux(toP)

I - .. -- ux(bot.)o-0.5

1000

7000

8000

~ 6000'j"Q.

;g. 5000...c:Q)

5 4000~

; 3000Q.en"0i 2000


3

- 1.----.1.- --.-

2.5

---------------


--------- ---------------- . - ux(top)

-----..- ux(bot. )

0.5 1 1.5 2Midspan Lateral Displ. (in.)

j----------:.<-=-.....-------

8000

7000 -

~6000..Q.

;g.5000 -...c:CIl

54000~

; 3000Q.en

"0i 2000

1000

0-

-0.5 0

Figure 5.81 FEM Simulation Results for Model SD7-S196

0.5a-2 -1.5 -1 -0.5Midspan Lateral Displ. (in.)

-2.5

1::-"'-'.40---.- -a --&----.---:.;::...................'-

~.........'''"'i.,

"'~"'-,

".~~

\:~

\\\\

Maximum Moment=7749 kip-in. \--ux(top)

\.....,- ux(bot.)..o

-3

1000

7000

8000

;6000'j'Co

;g,5000...cQ)

54000~

; 3000CoIII

"C:1E 2000


10000 ,--------------------------,

9000 -t~--------------------------..., _ __=:=- __ - ·'k·-}r-

8000".-~j .

.~ 7000 l~ ;._k_·__

Co~~ 6000 l~ /_:/~A_/./------.~..--.-.-----------.-

i ::::.1

1-_-_----------,?-.(.-./----.-(-----~-.~~---....-.

!3000 !/-.. ------..-·~-M-a-x-im..·u·-m-M-o-m-e-n-t=--8-87·-3-k-ip-in.

2000 -t~---Icl-------·-·---·----- ----.---.-

30.5 1 1.5 2 2.5


a

___ ....~_ --ux(top)

- •.- ux(bot.)a J.........__-4' -J

-0.5

1000 I~---I---"- '-"--"-

Figure 5.83 FEM Simulation Results for Model SD7-IO197

~--~---

-b-~:":'~-- ....- -,,-_-"----.1-~ ----..--.-'",r'

/~~~/A/--

///'//II

II Maximum Moment=8501 kip-in.

tl I~UX(IOP)i

/ ------T-- ux(bot.)l _.. _.. __._ •

10000

9000

8000-c7000'j"

Q.;g.

6000....cQ)

E 50000:!:c 4000nlQ.til 3000'0

:!:2000

1000

o-0.5 o 0.5 1 1.5 2

Midspan Lateral Displ. (in.)2.5 3


10000 ,------------------------,

9000 ~ .- +--'---..~~~

8000 ~t-------~'_--_-l_--_-~.._---_--_"'-'-~- ..,.~~_.---~-------i

0.5o-2 -1.5 -1 -0,5


1000 :-- ux(top) .------------ ----------~------ --

: .- ux(bot. )o --~ -- - --3 -2.5

c", 7000 -f~----------~------------"-\,--------Q.:i:::6000 f~--cQ)

~ 5000:!:c 4000nlQ.~ 3000 -f-------~----------~--~------~-- --1, --~-~-- ---~-~~~-

:!: Maximum Moment=9203 kip-in.2000 -1-----------..----------.------ .-..---.-.--.--.---.-~._-~ ..-- -;~ .----------------

Figure 5.85 FEM Simulation Results for ~todel SD7-12198

._._ -Ix·· ...-..--j;

//'~

IiIIIIt~ Maximum Moment=12428 kip-in.

I i-- ux(top) I1--..-- ux(bot.) I

14000

12000

-.~ 10000Co

~..8000c

Q)

E0:E 6000c111CoIII

4000'tl

:E

2000

o-0.5 o 0.5 1.5 2 2.5 3


Figure 5.86 FEM Simulation Results for Model SO19-1

14000

12000

.~ 10000Co

~..8000c

Q)

E0:E 6000c111CoIII

4000'tl

:E

2000

• io~il-·-.-·---

A._.-~'...l·_---"""---_· .------.---~.....::..--.:......- .-:---=-----1,..l ,.-

/4'--,-r>..~-_~--------------i

....

------f=---"r--------~--------------- -

ii.

._----~ ..~-_._--------~-----_._---~----_.._---

-------~---- --------------


-------------------- -- ux(top)

-.--- ux(bot.)

2.5 30.5 1 1.5 2


oo .L-__--"- .. _--_--_.---_-~.:::.__-_J

-0.5


- - ,_......'. -I.-

~-...~

'\\'\~

Maximum Moment=12796 kip-in. \1~UX(IOP) i

,

\I"· ux(bot. )

14000

12000

-.~ 10000Co

~.... 8000cQ)

E0~ 6000cI1lCoen

4000'0

~

2000

o-3 -2.5 -2 -1.5 -1 -0.5 o 0.5


Figure 5.88 FEM Simulation Results for Model SO 19-3

32.521.5


----- n:_ ~:::\ 1

0.5

I~----,.-I--------~~--------------~--~-- --

,/.x/

i-------,.~?~---------

A"/

A

14000

12000

-.~ 10000Co

~....8000c

al

E0~ 6000 -CI1lCoen

4000 .'0

~

2000

0

-0.5 0



_K__-Ir--...---:a---·-'-'··- ir--"

.....--------------."'.41·'-·......--

--

~//'

///1

/I Maximum Moment=11760 kip-in.

j --ux(top)

~ux(bot.)

14000

12000

.~ 10000Q.:i:-... 8000cCI)

E0:E 6000cIIIQ.lJl

4000'C

~

2000

o-0.5 o 0.5 1 1.5 2


2.5 3


14000 ,---------------------------,

0.5-2 -1.5 -1 -0.5 0


-2.5


------------_.._-._.... ~.~---_--'..

\L------- .__~ . ~.__•...._. ._

--ux(top)

--. .. ux(bot.)o

-3

2000

- ...--.-......---...'-'-I~=.:::;;;-±.-- -:::.,-··~i..>'+.-----1

12000 -1-----------=-<-....:

C 8000 -1-------~------~----_______'t\-----___1CI)

Eo:E 6000 j--------

CIIIQ.lJl'C 4000:E

.~ 10000 j----------------,'------Q.:i:-


~'_'-A-" -....__'.-1-- -' .....-....._----,.,.--_.. -...---.0 ~

//I

ff111

t...~ Maximum Moment=12754 kip-in..~\~

l~ux(IOp)•.-,r,- ux(bot.)

14000

12000

--.~ 10000c.:i:--.. 8000cQ)

E0:!: 6000cI1lC.III

4000't:l

:!:

2000

o-D.5 o 0.5 1 1.5 2


2.5 3


14000 -,....-----------------------,

0.5o-2 -1.5 -1 -D.5Midspan Lateral Displ. (in.)

-2.5

------------------._.~----._~ -------\-----~

4000 i-------------------------- -----------. ~~----1

2000~ax~::\anent=13183 ~i~~____ . ~\---Ol--~_~_~ __'A_______J

-3

.~--*.~.~

12000 1---------------- t~~

"

---------------------~_____.:-__----iI

~

~C 8000 -t----------------------:-~ -1-----Q) \

E •o i:!: 6000cI1lC.III

't:l

:!:

.~ 10000c.~

Figure 5.93 FEM Simulation Results for Model SD 19-8202

J<----*-,4t------ - - ... -. --iii···· ~

.".---~

(~(

t T

tt+~4I

!

~

.l.I Maximum Moment=12977 kip-in.~\t

~~UX(toP)J0,

:t -1>- ux(bot)

14000

12000

.~ 10000Q.

:i:-C 8000Q)

Eo~ 6000cIVQ.

~ 4000~

2000

o-0.5 o 0.5 1 1.5 2 2.5 3


Figure 5.94 FEM Simulation Results for Model SO19-9

4 5 6 7 8 9 10 11 12 13 14 15Midspan Lateral Displ. (in.)

32o

-1------ ------------------------------ -----

:!-.t------------------------------- --

A Maximum Moment=12754 kip-in.

-1---------------- -------------------------~-;(t~p)-

1 ~=_:..u~(b_ot.)o_L-_------------------~-------J

-1

14000

12000

.~ 10000Q.

~.. 8000cQ)

E0~ 6000cIVQ.en

4000'C

~

2000

Figure 5.95 FEi\1 Simulation Results for Model SO 19-7 (Including Post-Peak)203

-.-..:~~1f;!}:.L!J1................" ..<JoU.....,

........tL".... ..........'

i,I

i.,,.


\M-- ux(top) I

1---- ux(bot.) I r:Io

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0Midspan Lateral Displ. (in.)

14000

12000

-.; 10000Co:i:-... 8000r::(I)

E0:!: 6000r::IIICoII)

4000'C

:!:

2000

Figure 5.96 FEM Simulation Results for Model SO 19-8 (Including Post-Peak)

--1------ ------ --- ..--.---------------

-.I-----.------.--------~---~-------_.-


------ ------- -----~------ .. - . -- ux(top)

-*- ux(bot.)

:!.!!---.i------- --~.\

-~~------ ----

I--j----------

J

14000

12000

-~ 10000Cog... 8000r::(I)

E0:!: 6000r::IIICoII)

4000'C

:!:

2000

2 3 4 5 6 7 8 9 10 11 12 13 14 15


o .L- -======_...-1 0

Figure 5.97 FEM Simulation Results for Model SO 19-9 (Including Post-Peak)204

0.5-2.5

~-lk-'.-Q .~ '" ""~-'-a-4-- -''- ._--~ -~

.,,~\

.-..+

-ofi..\..I

t\

~I

it~I

~lI

Maximum Moment=13183 kip-in. ~~\

--ux(top) \ ~

-a- ux(bot.) ~o

-3 -2 -1.5 -1 -0.5 0Midspan Lateral Displ. (in.)

Figure 5.98 FEM Simulation Results for Model SD19-8 (Including InitialImperfections)

14000

12000

-.~ 10000Q.~-- 8000cQ)

E0~ 6000cnsQ.Ul

4000't:l

~

2000

14000 -r-------------------------,.... -- •• 'f'-~--'-""-""'~r

120004---------~ .


------------- --------- --------~------.•

•i.

.~ 10000 I-~~~~~~~~--.I,"i---~~~-~~--~~~-Q. Ig 4

•1: 8000 4-~-~~~----J_+'~~-~--~--------- -...._-Q) ..

E ..o 1~ 6000cnsQ.

~ 4000~

32.521.5

__ __ _~.4. .__ , ~ . .._..__----~ ---- ._-------ux(top)

• ux(bot.)

0.5o-0.5

\ .Ol....--------~--<~.....----------'='-'---.;..;;:"--'=....:.=....J

-1

2000


Figure 5.99 FE~1 Simulation Results for Model SD19-9 (Including InitialImperfections)

205

3

N

2

o s

1

Figure 5.100 Schematic ofFEM Simulation Results for Model SD19-8

N o s

2 1 3

Figure 5.101 Schematic ofFEM Simulation Results for Model SD19-9

206

___ S07-1

-.-S07-4---:X- S07-7~S07-10

--+-S12___ S122[

o ~f~.-~~~~~~'_j__~--

5000 Tt---------------------------,f

4500 +----r-~hF=::::::~------~;;;;o-o~=-------_____j

4000 L--~--I--==--==~~-'--='=~~------------;. ~

.~ 3500 f---,..'---~----~'-----------__=__4

~ 1:: 3000 +-i--I

lii tE 2500 +f----JI---I---Y----"""7"""---'-----=::;~~-------~__:"o:E[ 2000 ~

~ 1500 r--f-f--'---r'--;T"'---------:;;,,~-----_I

~ ~1000 -r-- -lo~!Y'-----....--------------1

f

500 -t--ILI'-/"-------------------1

-0.10 0.10 0.30 0.50 0.70 0.90 1.10


1.30 1.50

Figure 5.102 Comparison of Experimental and Analytical Midspan Moment versusLateral Displacements (Scaled Design 7, Tube)

1.501.30

___ S07-1

-.-S07-4-"i;- S07-7

~S07-10

--+-S12___ S122

1.100.300.10

0':

-0.10

1000 -~-

500 -:-

r

f4500 ~.----ir~F:::+t-----~,--:--------------j

t4000 ~---j~-~~-=-

-- fC :'6, 3500 -,---....----/-'------~.:i ::: 3000 ~:--,c

5000

0.50 0.70 0.90


Figure 5.103 Comparison of Experimental and Anal)1ical Midspan Moment yersusLateral Displacements (Scaled Design 7. Tension Flange)

207

__-{SD19-3)

......... -(SD19-B)

-+-S12____ S122

5000 ~,-----.----1---[---------------

~4500 +--~-~

4000 -l-t-- --4/--J./-----L.Cl

; ,~"j 3500 +--..-------:H--,..-------------------1Co:i:;:; 3000 -;----1C

E2500 +f 1.•-.I. --;

o fi 200011~ 1500 ~

:E 1000 +----flT.l----------~~500 +,--/IL'----------------<!

f !o ~r---.-----,--.-----t-~-~_~_~JL__---_~"

-0.10 0.10 0.30 0.50 0.70 0.90

Midspan Lateral Displ. ST2 (in.)

Figure 5.104 Comparison of Experimental and Analytical Midspan Moment versusLateral Displacements (Scaled Design 19, Tube)

__-{SD19-3)

--.--{SD19-6)

-+-S12____ S122

0.70 0.90

---------------

~----- ---_.

0.30 0.50

500:--

O~--c--

-0.10 0.10

4500~-------T-- -- 94 .1_L-'~LDisQI. Fro"-'-m'-'- ----'

Cutting Wood Spacers

CfaCo~ 1500~-- ---- .

:E 1000~----IlTt

,4000 .L-----.l

- IC ~" 3500 -'---- - -1,-·------------------Co ':i: :;:; 3000 -:-' -.--.-- -J--I/------c .Cl) •

E 2500 -'-----•..ij.,------------.-o ::E

2000 ~------


Figure 5.105 Comparison of Experimental and Analytical Midspan Moment \"ersusLateral Displacements (Scaled Design 19. Tension Flange)

208

....III

~E.g"CE::::IIll'"':"111 cQ) .-

~;... CQ)w

"EGcoco;

111(J

o...J

r-800~~~~~~~~~~~~1~~~~~~~_

I

' [-+- Before Load Block 1

r-70u---¥--------------------'I --- Before Load Block 6

i -.-Before Load Block 10

r O -..-After Load Block 16I

~Ou-Hr-\.----".,----------------i

hOO-t---t--\-----'r----------------II

~300-f---+--f----J--------------Ir-200-f-I-----I-----/--------------

~100-LJI-<;;/__-------------_iI~-El'-'-~~-r"-"-~~- .~~---'--'-t~~'---'--"--t~~~~~~+-L-L-~~

-0.1 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Lateral Displacement 512 (in.)

Figure 5.106 Lateral Displacements of Scaled Design 7 (Tube, Stage 2)

~'-600-

·----100-

:------400-·- - --- ------- --------.-------------------- -------------

,--800-,---------- -, ~ ! -+- Before Load Block 1 ii

f---700-¥----------------~--j --- Before Load Block 6 :;i Iii-.-Before Load Block 10(!

------------' -#-After Load Block 16 1i

coco;III(J

o...J

....III

~E.g"CE::::IIll'"':"111 CCll .-~;... CCllW"E

0.70.60.50.2 0.3 0.4

Lateral Displacement 512 (in.)

. ------. O· -------------.-------.-

-0.1 0 0.1

Figure 5.107 Lateral Displacements of Scaled Design 7 (Tension Flange. Stage 2)209

..III

~E,g'0~:::J1Il'-;'l'lI l:Q) .-:E-

'0... l:Q)W

'EC>l:ol:o;;l'lIUo.J

~800f----r--------------,,---------

I i~ Before Load Block 1

L70~~--------------i: --- Before Load Block 6 I

II 1-.-Before Load Block 10 i1 I

~OlJ-l\----""------------11 "",*-After Load Block 16 I

1

f--50Q--I--\--\.-----'.....----------1

i:---400-1--+--1,---\.------------------1

~ 30u-+~\--'r-----\.----\-------------II

~200iI-I-100-hU----o'----------------------iI

-0.1 a 0.1 0.2 0.3 0.4 0.5

Lateral Displacement ST2 (in.)

0.6 0.7

Figure 5.108 Lateral Displacements of Scaled Design 19 (Tube, Stage 2)

-100-1--..J-J-~'"

----200--'

I~ Before Load Block 1I i

'---700-~------------' --- Before Load Block 61

I-.-Before Load Block 101

-----~! ~After Load Block 16 I

--800-,r

., 0-- ..~. __"_.~""_~ c._c _L ----- •••_0 •••_. __._~.~.__• •• _ -.~ -----.__ ••••

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


..III

~E,g'0~:::J1Il'-;'l'lI l:(I) .-:E-

'0... l:(l)W'EC>l:ol:o;;l'lIUo.J

Figure 5.109 Lateral Displacements of Scaled Design 19 (Tension Flange. Stage 2)210

....l/l

~E,g"Ce~l/l-:11l c:Q) .-:a;... c:Q)w

'EC)

c:oc:o

+::11luo

...J

~OO---,-----------~· .~~~--"'::-~.~-~.--~-~--~-....~-~-~--~-Ii--+-Before Load Block 1

~t'Ou-'l~=----------------1! ---- Before Load Block 6i-.-Before Load Block 10i I

i I ->f-After Load Block 16~600---i ~Wood Spacers Cutit

~OU---+l--'\------"--~--------"""""""----------i

~OO----H----+-----------"-~L 300-t------I1

I

t 200

iL100~t

I

-0.1 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Figure 5.110 Lateral Displacements of Scaled Design 7 (Tube, Stage 2-2)

0.70.5 0.60.40.3

-------_._------------,-=. - --_ .._...~=-=~'"'._' •

. --+- Before Load Block 1

I ---- Before Load Block 6. -.-Before Load Block 10 1

i ->f-After Load Block 16__J

-r-Wood Spacers Cut

0.2

,------------''''''---- ------ ----------- ----~ --

0.1o

o

100-

~-800------

·---200-- --

:-600~

~700-~-----------

!

1-500- - --'1.----,

-0.1

....1Il

~E,g"CCl)...::J1Il-:l1l c:

:E~... c:~w...ac:oc:o

+::l1luo

...J


Figure 5.111 Lateral Displacements of Scaled Design 7 (Tension Flange. Stage 2-2)211

.----800-~-

! I -+- Before Load Block 1 Ir----+0u-'l~-----------------1; Before Load Block 6

1

I-Al.-Before Load Block 10I I """,*-After Load Block 16~O I! t -*-Wood Spacers Cut !I

~Ol}--l'-t----\------'\--------"'."-------':--""'~---------------I

Iroo ~r--300-!r 200- -- -I----/---~.._L

i~100-

-0. 1 a 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Figure 5.112 Lateral Displacements of Scaled Design 19 (Tube, Stage 2-2)

0.70.3 0.4 0.5 0.60.20.1

[-800-r-----~--~------~----- i -+-Before Load Block 1 :

I ~ : Before Load Block 6 i~OO-""~---------------l -AI.- Before Load Block 101

•~After Load Block 16 j

~c-----~I -*-Wood Spacers Cut !

--100- - -

··· .. ·0

-0.1 0

...III

~E.g'Cl!!~--:-III CCIl .-:i::;... CCIlw

"EC)

CoCo;IIIoo

...J


Figure 5.113 Lateral Displacements of Scaled Design 19 (Tension Flange. Stage 2-2)212

-----.--- .-- -------- -------------1

5.E-Q4

--~

3.E-Q4

+

+

+

+

-1.E-Q4 1.E-Q4

cPsT2 (in:1)

----+,-----------------0

-3.E-Q4

+---- ~~-------

30 -f

~

25 ftr- fc:

::;.. 20 r.0 ~Q) I

~,,Ic: 15 r

0 [c: I0

~..III0 100 t

-l ,I f>-

5

0

-5.E-Q4

Figure 5.114 Curvature throughout Web Depth for Stage 2

30 ---~~----

, +f

25 +-~-------

:§. 20 +---- ---- ----- -+---.0

~

+10 ~- - -- -- ------ -----

c: •o 15 -"------~- ----- ---------------------+--------- -- -.- .---- - -.---------.

c:o..IIIoo-l.>-

5

+

o ..-5.E-Q4 -3.E-Q4 -1.E-Q4 1.E-Q4

C>sm (in:1)

3.E-Q4 5.E-Q4

Figure 5.115 Cur\'3ture throughout Web Depth for Stage 2-2

213

-----I..~ S

Figure 5.116 Web Distortion

S.OE-QS ,-------------------------- -----

~4.0E-QS -t------

t3.0E-QS -t--------~

l,2.0E-QS +',-------

.-. 1.oE-Qs l-";' "c- O.OE+OO -

N >I- ,

~ -1.0E-QS ~--

-2.0E-QS +--------------------------3.0E-QS ~--------- ---- ---~~===--==~_:....==__ ==: _

: -+- Stage 2 Experimental-4.0E-QS ~-----~----

--Analytical-S.OE-QS -~----~----.- --- --<----.--- --- -~-.---~c~.-.-~c-~~c~--=~-- ------~- --- -----~

o 100 200 300 400 sao 600 700

x Location on scaled Design 19 (in.)

Figure 5.117 Trans\'erse Curvature Comparison (Tension Flange. Stage 2)

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700600SOO400300200100

S f~ -1.0E-QS -~

-2.0E-QS +-,------------

~-3.0E-QS -f--------------------------i

l!

-+- Stage 2-2 Experimental I'

-4.0E-QS +c------------, 11

f __Analytical !it Ii

-S.OE-QS +-1-~--r-----;------:==r===========,===--,=i-

o

S.OE-QS

4.0E-QS

3.0E-QS

2.0E-QS -----

f"' 1.0E-QSt:- O.OE+OO

x Location on scaled Design 19 (in.)

Figure 5.118 Transverse Curvature Comparison (Tension Flange, Stage 2-2)

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UTGN

LTGN

North Side ofSeo.led Design 19

UFGN

LFGN

Figure 5.119 Strain Gages Used to Study Plate Bending in Tension Flange of ScaledDesign 19

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6. Summary, Conclusions, and Recommendations for Future Work

6.1 Summary

Two different innovations to steel I-shaped highway bridge girders were

investigated in this thesis: (1) concrete filled tubular flanges and (2) corrugated webs.

The objectives of this research were: (1) to conduct a design study of tubular flange

girders with corrugated webs and with flat webs for a four girder, 131.23 ft. (40000

nun) prototype bridge, (2) to design 0.45 scale test girders based on the results of this

design study, (3) to test the scaled girders to investigate their ability to carry their

design loads, and (4) to compare experimental and analytical results to verify the

adequacy of the analytical models and tools.

A design study investigated twelve different tubular flange girder designs,

which used various combinations of corrugated or flat web, composite or non

composite, homogeneous or hybrid, and braced or unbraced conditions. Six additional

designs were generated to incorporate flange transverse bending effects into the

original six corrugated web designs. The designs were generated based on modified

AASHTO LRFD Bridge Design Specifications (1999). Elastic section calculations

were perfomled using equivalent transfomled sections to include the concrete in the

tube and deck with the steel in the girder cross-section properties.

One corrugated web girder design and one flat web girder design were scaled

down by 0.45. re-designed and fabricated for use in a two-girder test specimen. The

re-dcsign involvcd small modifications of the dimensions to make fabrication of thc

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scaled girders feasible, and design of the test girder welds, stiffeners, shear studs, and

deck construction. The test specimen was instrumented with 163 channels, consisting

of strain gages and displacement transducers, and connected to a data acquisition

system. The test specimen was then loaded to simulate various design loading

conditions while data was recorded. Numerous analytical calculations and FEM

simulations were performed so that experimental results could be compared with

analytical results.

6.2 Conclusions

Design Study

The eighteen design study combinations (Sect. 3.7) supported the following

conclusions: (l) tubular flanges allow for the use oflarge girder unbraced lengths by

increasing the torsional stiffness of the girder; (2) corrugated webs create lighter

weight designs than unstiffened flat webs because the corrugated web is thinner,

although the flanges are slightly larger; (3) composite designs are lighter weight than

non-composite designs because the deck contributes to the load carrying capacity in a

composite design; (4) hybrid designs create lighter weight designs than homogeneous

designs because of the increased steel yield stress; (5) the presence of interior

diaphragms provides torsional bracing to a girder, increases its lateral torsional

buckling strength, and allows for the use of a slightly smaller tubular compression

flange.

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Although each of the conclusions above suggests that certain designs are more

advantageous, other issues should be considered. Composite designs require the

added cost and effort of making bridge girders composite with the deck. Hybrid

designs may cost more than homogeneous designs if the weight savings do not make

up for the cost of the higher strength steel. Interior diaphragms are costly to fabricate

and connect to the girders, and these costs may offset the benefits of the lighter weight

girders.

The design study showed corrugated web girders to be only slightly lighter

than their flat web counterparts for a 131.23 ft. (40000 mm) bridge, with a girder

length-to-depth ratio of approximately 22. As the depth-to-thickness ratio of the web

increases (for deeper girders), the corrugated web retains the same shear strength but

the flat web shear strength decreases (Sect. 3.8). Also, a corrugated web requires

more steel in the tension flange because the web does not contribute to overall bending

strength. A deeper section will help reduce the need for this excess tension flange

steel, and therefore, corrugated webs will be more advantageous for deeper girders.

Since the girder length-to-depth ratio should not be too small (say, less than 20),

deeper girders are practical only for bridges longer than the prototype bridge.

Transformed Section Calculations for Concrete Filled Tubular Flange Girders

The use of an elastic transformed section for the combined properties of the

steel tubular flange girder and the concrete in the tube and deck is a valid method for

analysis ofa tubular flange girder. As discussed in Section 5.4. the experimental

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results compare quite well with the analytical results based on elastic transformed

sections. There was a small increased stiffness observed in experimental results

compared to the analytical results, but this increased stiffness was not necessarily due

to the use of elastic transformed sections.

Strain Nonlinearity

As discussed in Section 5.4, nonlinearity was observed in the loading branch of

Stage 1 and Stage 3 moment versus strain and moment versus vertical deflection

experimental results. It was shown that this nonlinearity was due to the existence of

residual stresses within the steel. The nonlinearity due to residual stresses prevented

the use of strains for determining the bending moment, even at sections expected to be

linear elastic during the tests. Stage 1 of the tests eliminated the residual stresses for

the Simulated Construction loading condition, and therefore Stage 2 and Stage 2-2

provided linear results.

Ability to Carry Design Loads

During the Simulated Construction loading condition, a moment equal to 0.51

times the yield moment was placed on scaled Design 19 and a moment equal to 0.57

times the yield moment was placed on scaled Design 7. Flange transverse bending

moments caused the Construction loading condition stress to equal 0.67 times the

yield stress for scaled Design 19. The increase in stress due to flange transverse

bending moments was calculated using maximum shear in the span, as assumed in the

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design of the prototype corrugated web girders. Also during the Simulated

Construction loading condition, a moment equal to 0.70 times the lateral torsional

buckling moment capacity was placed on scaled Design 19 and a moment equal to

0.73 times the lateral torsional buckling moment capacity was placed on scaled Design

7. Flange transverse bending moment effects caused the Simulated Construction

loading condition stress to equal 0.93 times the lateral torsional buckling stress in the

compression flange for scaled Design 19.

During the Simulated Strength I loading condition, a moment equal to 1.01

times the yield moment and 0.88 times the plastic moment was placed on scaled

Design 19. A moment equal to 1.03 times the yield moment and 0.67 times the plastic

moment was placed on scaled Design 7.

It was shown through these tests that the test specimen could effectively carry

the loads for which it was designed. The loads placed on the test girders closely

simulated the Construction and Strength I loading conditions for the prototype bridge

and the test specimen generally behaved as expected. The presence of the residual

stresses increased the experimental vertical deflections, but once the residual stresses

were taken into account, very good comparisons existed between experimental and

analytical results.

The experimental lateral displacements were generally less than those

predicted by FEM simulations, so it is difficult to comment on the latcral torsional

buckling strength of the test girders. It is kno\\l1. howevcr, that the lateral torsional

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buckling strength of the test girders was greater than the moment created by the

Simulated Construction loading condition.

6.3 Recommendations for Future Work

Longer Prototype Bridge

As discussed in Sections 3.7 and 3.8, a prototype bridge with a longer span

would require deeper girders that would more efficiently use a corrugated web. This

research showed that the 131.23 ft. (40000 rom) prototype bridge resulted in

corrugated web designs that were only slightly lighter than flat web designs. It is

suggested that a design study be performed for a longer (e.g., a 196.85 ft. (60000 rom)

span prototype bridge.

Lateral Torsional Buckling Test

As discussed in Section 5.6, the experimental lateral displacement results did

not compare well with the FEM simulation results. It is recommended that a

laboratory experiment be performed in order to study the lateral displacements and

lateral torsional buckling strength of tubular flange girders more thoroughly. The load

should be purely vertical, without accidental lateral loading, something that was not

necessarily achieved in the tests performed in this research. The recommended test

should use a single girder, with no unintentional bracing at the ends or within the span.

In addition, a detailed set of initial imperfection measurements of the tube. web. and

tension flange should be made.

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Tube Compactness Requirement

The tube compactness requirement (Eq. 2.7) discussed in Section 2.3 only

prevents elastic buckling of the tube before yielding. It does not guarantee that the

section can be fully plastified before inelastic buckling occurs in the tube. This was

not an issue in this research because the stresses in the tube stayed below yield for the

tests. As discussed in Section 2.6, the plastic moment was calculated based on strain

compatibility, which does not assume the section to be fully plastified. In order to

calculate the plastic moment based on full plastification of the section, an appropriate

compactness limit is needed.

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References

AASHTO, "AASHTO LRFD Bridge Design Specifications," Second Edition, 1999.

Abbas, H.H., "Analysis and Design of Corrugated Web I-Girders for Bridges usingHigh Perfonnance Steel," Ph.D. Dissertation, Department of Civil and EnvironmentalEngineering, Lehigh University, 2003.

Easley, IT., "Buckling Fonnulas for Corrugated Metal Shear Diaphragms," ASCEJournal of the Structural Division, Vol. 101, No. ST7 (July), pp. 1403-1417, 1975.

Elgaaly, M., R.W. Hamilton, A. Seshadri, "Shear Strength of Beams with CorrugatedWebs," ASCE Journal of Structural Engineering, Vol. 122, No.4 (April), pp. 390-398,1996.

Kim, B.G., "HPS Bridge Girders with Tubular Flanges," Ph.D. Dissertation,Department of Civil and Environmental Engineering, Lehigh University, 2004a.

Kim, B.G., Personal Communication, Department of Civil and EnvironmentalEngineering, Lehigh University, 2004b.

Sause, R., H.H. Abbas, W.G. Wassef, R.G. Driver, M. Elgaaly, "Corrugated WebGirder Shape and Strength Criteria," Report No. 03-18, pp. 51-58, Center forAdvanced Technology for Large Structural Systems, Lehigh University, 2003.

Smith, A. "Design ofHPS Bridge Girders with Tubular Flanges," M.S. Thesis,Department of Civil and Environmental Engineering, Lehigh University, 2001.

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Vita

Mark Robert Wimer was born in Wooster, Ohio on November 22, 1978. His

parents' names are Robert and Betheny Wimer, and he has a younger sister, Stacy. He

graduated from Waynedale High School in 1997. He went on to study Civil

Engineering at Ohio Northern University. He was married to his wife, Brandi, in

2000. He graduated first in his class with a Bachelor of Science in 2002. He is

currently attending Lehigh University, and this thesis is partial fulfillment ofa Master

of Science.

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