Structural Analysis of Bridge Gusset Plates

Structural Analysis of Bridge Gusset Plates:

Steel vs. Composite

by

Stephen Ganz

An Engineering Report Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

MASTER OF ENGINEERING IN MECHANICAL ENGINEERING

Approved:

______

Ernesto Gutierrez, Project Adviser

Rensselaer Polytechnic Institute

Hartford, Connecticut

August, 2012

© Copyright 2012

by

Stephen Ganz

All Rights Reserved

CONTENTS

LIST OF TABLES v

LIST OF FIGURES vi

TERMINOLOGY / LIST OF SYMBOLS / ACRONYMNS vii

ACKNOWLEDGMENT viii

ABSTRACT ix

1. Introduction 1

2. Methodology 2

3. Bridge Design 3

4. Loading 4

4.1 Dead Load 4

4.2 Live Load 4

4.3 Total Load 4

5. Materials 5

5.1 Carbon Steel 5

5.2 HexPly 8552 IM7 6

6. FEA Models 7

6.1 Plate Geometry 8

6.1.1 Bottom End Plates 8

6.1.2 Mid Span Plates 9

6.1.3 Upper End Plates 10

7. FEA Results 11

7.1 Carbon Steel 11

7.2 HexPly 8552 IM7 14

7.2.1 HexPly 8552 IM7 [0 90]S 14

7.2.2 HexPly 8552 IM7 [0 45 90]S 17

7.2.3 HexPly 8552 IM7 [0 45 90]S 21

7.3 Factors of Safety 29

8. Conclusions 32

9. References 33

10. Appendices 35

LIST OF TABLES

Table 1: Carbon Steel Properties xx

Table 2: HexPly 8552 IM7 Properties xx

Table 3: Composite Layup Arrangements xx

Table 4: Stresses and Tsai-Wu Criterion (All Models) xx

Table 5: Factors of Safety (All Models) xx

Table 6: Minimum Factors of Safety (All Models) xx

LIST OF FIGURES

Figure 1: Side and Plan views of the Bridge xx

Figure 2: Bridge Free Body Diagram xx

Figure 3: FEA bridge showing loads and boundary conditions xx

Figure 4: Iso view of the bridge with shell thicknesses rendered xx

Figure 5: End Plate Detail Drawing (Plates A and L) xx

Figure 6: Mid Span Plate Detail Drawings (Plates B, D, E, F, G, H, I and J) xx

Figure 7: Upper End Plate Detail Drawings (Plates C and K) xx

Figure 8: Abaqus FEA Stress results for Carbon Steel Model xx

Figure 9: Abaqus FEA Deflection results for Carbon Steel Model xx

Figure 10: Abaqus FEA Tsai-Wu results for HexPly [0 90]S Model xx

Figure 11: Abaqus FEA Deflection results for HexPly [0 90]S Model xx

Figure 12: Abaqus FEA Tsai-Wu results for HexPly [0 45 90]S Model xx

Figure 13: Abaqus FEA Deflection results for HexPly [0 45 90]S Model xx

Figure 14: Abaqus FEA Tsai-Wu results for HexPly [0 15 30 45 60 75 90]S Model xx

Figure 15: Abaqus FEA Deflection results for HexPly [0 15 30 45 60 75 90]S Model xx

TERMINOLOGY / LIST OF SYMBOLS / ACRONYMNS

FEA – Finite Element Analysis

FBD – Free Body Diagram

2D – 2 Dimensions

DOT – Department of Transportation

E – Modulus of Elasticity

G – Modulus of Rigidity

ν – Poisson’s Ratio

ρ – Density

tp – Ply Thickness

YS – Yield Strength

UTS – Ultimate Tensile Strength

σ1t – Tensile strength in the 1 (longitudinal) direction

σ1c – Compressive strength in the 1 (longitudinal) direction

σ2t – Tensile strength in the 2 (transverse) direction

σ2c – Tensile strength in the 2 (transverse) direction

τ12f – Shear Strength

[orientation number of plies]S – Laminate Layup which is characterized by ply orientation, number and symmetry about the mid-plane.

Abaqus – Computer Software used to perform modeling and FEA

ACKNOWLEDGMENT

Type the text of your acknowledgment here.

ABSTRACT

A structural comparison of bridge gusset plates was performed using Abaqus/CAE 6.9 EF-1 for different materials. The two materials chosen are structural steel and HexPly brand 8552 IM7 prepreg composite. Performance of the two materials was based on stress and deflection. Several different ply layups were considered for composite construction.

This paper will focus on performing structural analyses of gusset plates. The goal here is compare the performance differences in metallic and composite plates.

iii

1.  Introduction

Bridges play a vital role in transportation networks the world over. Spanning up to several thousand feet long and towering up to several hundred feet high, these man-made engineering marvels allow for convenient safe passage for people and their cargo. Many bridges are based on truss designs to efficiently transmit load back to their foundations. Gusset plates are integral to truss based bridge design because they serve as the attachment point for the truss members. Gusset plates have become the focal point of much research since the collapse of the I-35 Bridge over the Mississippi river in 2007, in which the National Transportation Safety Board (NTSB) reports that the probable cause is due to inadequate plate design.

For this project, a structural comparison of bridge gusset plates of different materials was performed. Loading is assumed to be in plane (2 dimensional). The gusset plates were modeled and analyzed in Finite Element Analysis (FEA) software, Abaqus/CAE 6.9-EF1. Performance criterion was based on stress and deflection.

2.  Methodology

In order to perform a comparative structural analysis for steel and composite gusset plates, a Warren truss bridge was constructed to state and federal guidelines. The model consists of plates, trusses, loads and boundary conditions. The trusses are connected to the plates with tie constraints to simulate a perfect bond. The trusses have a simple, robust geometry with a coarse mesh. This is acceptable because this project is not concerned with any analysis of the trusses and their mesh refinement has no effect on the results for the plates. Other more advanced analyses simulate the entire bridge in much greater detail such as in [Abaqus Brief], but this was an investigation into a specific bridge failure. For the purposes this project, this level of complexity is not warranted.

This eliminates any unnecessary computation involving trusses similar to [Najjar]. The size of the gusset plates are based on dimensions shown in [Najjar]. It is also important to note that the dimensions chosen for the bridge and plates may not be perfectly accurate for an actual bridge of the same size (however, they are a close approximation), but that is not the goal of this project, the goal is to perform a comparative structural analysis of the plates.

Loading will come from dead load (bridge weight) and live load (vehicles, snow) based on building requirements in accordance with DOT rules and regulations. Transverse forces (wind) will be ignored since these plates are not significantly loaded in transverse bending as well as to permit the use of shell elements for 2D analysis. This is acceptable because failure of these joints is more commonly associated with tensile and buckling failure. This will provide enough information to make a structural comparison

A mesh study summarized in Appendix B ensured accuracy of the model. Stresses and deflections resulting from the final runs were compared to draw conclusions about the different materials.

3.  Bridge Design

The bridge chosen for this project is a Warren truss style bridge. The bridge does not actually exist, but has been constructed using state and federal guidelines. The bridge is assumed to be 120' long and 20' high with angular members set at 45°. All of the vertical beams in the Warren truss and horizontal joists are assumed to have a cross section of 64in2 [J. Kinlan] and are made from steel 0.284 lb/in3 in density [Shigley's]. The clear minimum width of the roadway for a bridge maintained on a state highway in Connecticut is 28’ [BDM] and assumed to be 1’ thick. On either side of the bridge there is a 5’ wide sidwalk, 6” thick [BDM]. Therefore, total bridge width is 38’. The two sides of the bridge are connected by seven floor joists at the bottom, which also to support the roadway and five joists connect the bridge at the top.

4.  Loading

In the case of bridges, loading comes from three major components: dead load (structure), dynamic load such as wind and live load (vehicles and snow). For the purposes of this project only dead load and live load will be considered.

4.1 Dead Load

Dead load is comprised of the weight of the Warren truss section, sidewalks, asphalt, roadway and floor joists. Based on the dimensions listed in Section 3 and calculations detailed in Appendix A dead load has been determined to be 298,272 lbs.

4.2 Live Load

Live load is comprised of weight of passing vehicles and snow. Appendix A details the calculations for live load and has been determined to be 279,435 lbs.

4.3 Total Load

The combination of Dead Load and Live Load results in a Total Load (W) of 577,708 lbs. For the purposes of this project the load is assumed to be distributed evenly, so one-fifth of the total load is applied at the joints as shown below.

5.  Materials

5.1 Carbon Steel

Carbon steel was chosen as the baseline material for the gusset plates because of its widespread use in structural applications. It’s relatively low cost, machine and weld-ability make it a popular choice.

Property [Shigley’s] [ASTM A36] / Value
E (Msi) / 23.8
G (Msi) / 11.5
ν / 0.292
ρ (lb/in3) / 0.282
YS (ksi) / 36 min
UTS (ksi) / 58-80

5.2 HexPly 8552 IM7

This material was chosen as the composite of choice as determined in [J. Kinlan]. Three different layups were chosen for determine if there is a significant performance advantage that comes with varying fiber orientation (i.e. increasingly isotropic behavior). The plies were kept symmetric about the mid-plane and even in number per orientation.

Property / Value
E1 (Msi) / 23.8
E2 (Msi) / 1.7
E3 (Msi) / 1.7
ν12 / 0.32
ν13 / 0.32
ν23 / 0.0229
G12 (Msi) / 0.75
G13 (Msi) / 0.75
G23 (Msi) / 0.831
σ1t (ksi) / 395
σ1c (ksi) / -245
σ2t (ksi) / 16.1
σ2c (ksi) / -32.3
τ12f (ksi) / 17.4
ρ (lb/in3) / 0.047
tp (in) / 0.006
Layups / Thickness
[083,9083]S / 0.50 per layer
[056,4556,9056]S / 0.333 per layer
[024,1524,3024,4524,6024,7524,9024]S / 0.143 per layer

6.  FEA Models

The models used for analysis is a complete vertical side section of a Warren truss bridge consisting of plates, trusses, loads and boundary conditions. Loads were applied to partitioned sections of the plate’s surface as surface tractions which are defined as force per unit area (psi). This reduces the chance of unusually high stress concentrations commonly associated with point loads which can otherwise affect the accuracy of the model.

Since loading and the design of the bridge is symmetric only gusset plates a, b, c, d, e, f and g were analyzed. The Free Body Diagram (FBD) for the bridge is shown below.

6.1 Plate Geometry

For this bridge model there are 3 kinds of plates: the bottom ends, the top ends and the remaining plates. Also shown is the geometry for the partitions on the surfaces of the plates used for tie constraints with the truss members. All dimensions shown are in inches unless otherwise noted.

6.1.1  Bottom End Plates

These are the plates at the bottom corners on each side of the bridge.

6.1.2  Mid Span Plates

There are two sub-types of these plates, both are identical in geometry, the only difference is the number of partitioned surfaces to overlap with a corresponding number of trusses. Both plates are symmetrical about the vertical centerline.

6.1.3  Upper End Plates

These are the plates located at the upper corners at each end of the bridge.

7.  FEA Results

7.1 Carbon Steel

Performing a finite element analysis on a bridge using carbon steel gusset plates yielded the following results. Maximum Von Mises stress in any of the plates was found to be 12,697 psi. Based on yield strength of the material this correlates to a factor of safety of 2.84. Maximum deflection of the structure was 0.448 inches downward and 0.180 inches sideways.

Deflections

7.2 HexPly 8552 IM7

Performing a finite element analysis on a bridge with HexPly 8552 IM7 gusset plates yielded the following results. However unlike the steel plates, the factor of safety of the composite plates cannot be calculated using a Von Mises stress, their factors of safety are based on Tsai-Hill failure criterion. This is calculated by the CFAILURE field output request based on material properties from table XX.

7.2.1  HexPly 8552 IM7 [0 90]S

7.2.2  HexPly 8552 IM7 [0 45 90]S

7.2.3  HexPly 8552 IM7 [0 45 90]S

7.3 Factors of Safety

FEA Results
Carbon Steel / Stress
Plate A / 11068
Plate B / 7476
Plate C / 10334
Plate D / 12320
Plate E / 11190
Plate F / 12697
Plate G / 11767
Composite Models (TSAIW) / Layer 1 / Layer 2 / Layer 3 / Layer 4 / Layer 5 / Layer 6 / Layer 7
HexPly [0 90]S
Plate A / 0.226 / 0.268
Plate B / 0.107 / 0.126
Plate C / 0.271 / 0.246
Plate D / 0.242 / 0.268
Plate E / 0.165 / 0.145
Plate F / 0.172 / 0.193
Plate G / 0.171 / 0.152
HexPly [0 45 90]S
Plate A / 0.111 / 0.155 / 0.138
Plate B / 0.078 / 0.121 / 0.112
Plate C / 0.159 / 0.121 / 0.127
Plate D / 0.176 / 0.264 / 0.216
Plate E / 0.151 / 0.097 / 0.103
Plate F / 0.140 / 0.211 / 0.194
Plate G / 0.206 / 0.140 / 0.146
HexPly [0 15 30 45 60 75 90]S
Plate A / 0.118 / 0.132 / 0.155 / 0.173 / 0.184 / 0.176 / 0.155
Plate B / 0.116 / 0.133 / 0.154 / 0.169 / 0.173 / 0.163 / 0.149
Plate C / 0.210 / 0.174 / 0.151 / 0.147 / 0.147 / 0.153 / 0.178
Plate D / 0.262 / 0.303 / 0.347 / 0.375 / 0.373 / 0.343 / 0.299
Plate E / 0.202 / 0.172 / 0.144 / 0.127 / 0.125 / 0.133 / 0.153
Plate F / 0.210 / 0.241 / 0.278 / 0.303 / 0.307 / 0.286 / 0.263
Plate G / 0.283 / 0.236 / 0.200 / 0.181 / 0.176 / 0.184 / 0.212
Factors of Safety
Carbon Steel / YS / UTS
Plate A / 3.253 / 5.240
Plate B / 4.815 / 7.758
Plate C / 3.484 / 5.613
Plate D / 2.922 / 4.708
Plate E / 3.217 / 5.183
Plate F / 2.835 / 4.568
Plate G / 3.059 / 4.929
Tsai-Wu
Layer 1 / Layer 2 / Layer 3 / Layer 4 / Layer 5 / Layer 6 / Layer 7
HexPly [0 90]S
Plate A / 4.425 / 3.731
Plate B / 9.346 / 7.937
Plate C / 3.690 / 4.065
Plate D / 4.132 / 3.731
Plate E / 6.061 / 6.897
Plate F / 5.814 / 5.181
Plate G / 5.848 / 6.579
HexPly [0 45 90]S
Plate A / 9.009 / 6.452 / 7.246
Plate B / 12.821 / 8.264 / 8.929
Plate C / 6.289 / 8.264 / 7.874
Plate D / 5.682 / 3.788 / 4.630
Plate E / 6.623 / 10.309 / 9.709
Plate F / 7.143 / 4.739 / 5.155
Plate G / 4.854 / 7.143 / 6.849
HexPly [0 15 30 45 60 75 90]S
Plate A / 8.475 / 7.576 / 6.452 / 5.780 / 5.435 / 5.682 / 6.452
Plate B / 8.621 / 7.519 / 6.494 / 5.917 / 5.780 / 6.135 / 6.711
Plate C / 4.762 / 5.747 / 6.623 / 6.803 / 6.803 / 6.536 / 5.618
Plate D / 3.817 / 3.300 / 2.882 / 2.667 / 2.681 / 2.915 / 3.344
Plate E / 4.950 / 5.814 / 6.944 / 7.874 / 8.000 / 7.519 / 6.536
Plate F / 4.762 / 4.149 / 3.597 / 3.300 / 3.257 / 3.497 / 3.802
Plate G / 3.534 / 4.237 / 5.000 / 5.525 / 5.682 / 5.435 / 4.717
Min Factors of Safety
Carbon Steel / YS / UTS
Plate A / 2.835 / 4.568
Plate B
Plate C
Plate D
Plate E
Plate F
Plate G
HexPly [0 90]S
Plate A / 3.690
Plate B
Plate C
Plate D
Plate E
Plate F
Plate G
HexPly [0 45 90]S
Plate A / 3.788
Plate B
Plate C
Plate D
Plate E
Plate F
Plate G
HexPly [0 15 30 45 60 75 90]S
Plate A / 2.667
Plate B
Plate C
Plate D
Plate E
Plate F
Plate G

8.  Conclusions