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TRANSVERSE DISTRIBUTION FACTORS FOR HORIZONTALLY CURVED BRIDGES UNDER THE EFFECT OF PERMIT VEHICLES

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TRANSVERSE DISTRIBUTION FACTORS FOR HORIZONTALLY CURVED BRIDGES UNDER THE EFFECT OF PERMIT VEHICLES

ABSTRACT

Permit vehicles with non-standard gage are increasingly used to carry heavy and oversized cargos. Currently, approximate methods and evaluation of the transverse, live load, girder distribution factor (GDF) for horizontally curved, steel, I-girder bridges subjected to permit vehicles are lacking. Therefore, the effect of permit vehicles on GDFs for curved bridges needs to be determined to allow rapid and efficient evaluation for issue of permits. Four permit vehicles obtained from a Pennsylvania Department of Transportation (PennDOT) database and twenty-seven curved bridges from Kim (2007) are analyzed with CSiBridge® to conduct the parametric study. The present study evaluates the influence of key parameters (radius, span length, girder spacing, and gage) on moment GDFs, determines if GDFs for permit vehicles can be accurately predicted by modifying AASHTO approximate moment GDF equations, and establishes an approximate GDFs for the outermost girder. Two approximate moment GDF models from Kim (2007) are utilized: (1) The single GDF model (SGM); and (2) the combined GDF model (CGM) to calculate GDF for curved bridges subjected to permit vehicles. A linear regression analysis is conducted to determine the relationship between AASHTO approximate GDFs and GDFs for curved bridges subjected to permit vehicles to develop a proposed, approximate GDF equation for curved girder bridges. Based on the numerical results from FEM, SGM and CGM, the present study demonstrates that GDFs for curved bridges cannot be accurately predicted by AASHTO approximate GDFs. The present study develops a new approximate GDF equation to predict moment distribution in curved bridges with respect to radius, span length, and vehicle gage. The numerical analysis results demonstrate that span length and radius have larger effects on GDFs than girder spacing and vehicle gage. A goodness-of-fit method combined with the linear regression analysis propose two developed approximate GDF equations (SGM and CGM equations). Both two developed approximate GDF equations are demonstrated to accurately predict GDFs for curved bridges compared to FEM results and provide slightly larger results compared to FEM results. GDFs for HL-93 are also calculated and be demonstrated to have larger results than GDFs for the evaluated permit vehicles.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE OF CONTENTS

Acknowledgements …………………………………………………………………………………………………… vii

Chapter 1 INTRODUCTION ……………………………………………………………………………………… 1

1.1 Problem Statement ……………………………………………………………………………………….. 3

1.2 Scope of the Research …………………………………………………………………………………… 3 1.3 Objectives of the Research …………………………………………………………………………….. 5

1.4 Tasks ………………………………………………………………………………………………………….. 5

Chapter 2 LITERATURE REVIEW ……………………………………………………………………………. 7

2.1 Introduction …………………………………………………………………………………………………. 7

2.2 Live Load Distribution Factor Studies for Curved Bridges ………………………………… 7

2.3 AASHTO Methods for Curved Bridges …………………………………………………………… 10

2.4 AASHTO Methods for Straight Bridges ………………………………………………………….. 12

2.5 Distribution Factor Studies for Bridges Subjected to Permit Vehicles …………………. 13

2.6 The Finite Element Modeling Method for Curved Bridges ………………………………… 16

2.7 Summary …………………………………………………………………………………………………….. 20

Chapter 3 STUDY DESIGN ………………………………………………………………………………………. 21

3.1 Introduction …………………………………………………………………………………………………. 21

3.2 Procedure to Obtain GDFs for Curved Bridges ………………………………………………… 22

3.3 Determination of Parameters ………………………………………………………………………….. 23

3.4 Curved Bridge Details …………………………………………………………………………………… 24

3.4.1 Curved Bridge Details for the Parametric Study ……………………………………… 24

3.4.2 Curved Bridges for the Validation of Approximate GDF Equations ………….. 27

3.5 Permit Vehicle Information……………………………………………………………………………. 28

3.6 Bending and Warping Stresses in Curved I-girder …………………………………………….. 33

3.7 Load Cases for Curved Bridges Subjected to Permit Vehicles ……………………………. 34

3.8 AASHTO Approximate GDFs ……………………………………………………………………….. 34

3.9 Formulation of the GDF Equation ………………………………………………………………….. 35

Chapter 4 NUMERICAL MODELING ……………………………………………………………………….. 40

4.1 Introduction …………………………………………………………………………………………………. 40

4.2 3D Numerical Bridge Model ………………………………………………………………………….. 40

4.2.1 Element Types ……………………………………………………………………………………. 40 4.2.2 Boundary Conditions …………………………………………………………………………… 42

4.2.3 Description of the Bridge Model …………………………………………………………… 42

4.3 Permit Vehicle Assignment in Numerical Models …………………………………………….. 44 4.4 2D Straight Bridge Model ……………………………………………………………………………… 48

4.5 Summary …………………………………………………………………………………………………….. 48 Chapter 5 DATA PROCESSING ……………………………………………………………………………….. 50

5.1 Introduction …………………………………………………………………………………………………. 50 5.2 Single GDF Model ……………………………………………………………………………………….. 50

5.3 Combined GDF Model ………………………………………………………………………………….. 52

5.4 Torsional Moment Related to Bending Moment ……………………………………………….. 54

5.5 Summary …………………………………………………………………………………………………….. 58

Chapter 6 ANALYSIS RESULTS AND DISCUSSION ………………………………………………… 59

6.1 Introduction …………………………………………………………………………………………………. 59

6.2 Warping Effect on GDFs ………………………………………………………………………………. 59 6.3 Modification of AASHTO Approximate GDFs ………………………………………………… 66

6.4 Strength of Parameters on GDFs…………………………………………………………………….. 71 6.5 Proposed Approximate GDF (SGM) ………………………………………………………………. 78

6.6 Proposed Approximate GDF (CGM) ………………………………………………………………. 79 6.7 Accuracy of GDF Equations ………………………………………………………………………….. 82

6.8 Validation of GDF Equations…………………………………………………………………………. 84

6.9 Comparison of Approximate GDFs for Permit Vehicles and HL-93 ……………………. 85

6.10 Summary …………………………………………………………………………………………………… 86

Chapter 7 SUMMARY AND CONCLUSIONS ……………………………………………………………. 87

7.1 Summary …………………………………………………………………………………………………….. 87

7.2 Summary and Conclusions …………………………………………………………………………….. 88

7.3 Future Research ……………………………………………………………………………………………. 90

REFERENCES………………………………………………………………………………………………….. 93

APPENDIX Parameter Effect on GDFs Plots and Residual Plots of SGM and CGM …. 97

 

 

Chapter 1 

 

INTRODUCTION

Permit vehicles with non-standard configurations are increasingly used to carry heavy and oversized cargos for economic, military and other special needs. These permit vehicles must pass over highway bridges to move special loads. Highway bridges are mainly designed by considering the effect of standard vehicles with a 6 feet gage, however, the gage of permit vehicles is usually larger than 6 feet and the gross vehicle weight (GVW) is much heavier than a standard design vehicle. To design or analyze a curved or straight bridge under live loads, the maximum moment of each girder must be determined. The live load, girder distribution factor (GDF) is a convenient tool to predict the maximum moment per girder, which equals the maximum moment per girder divided by the maximum moment for the entire bridge. Hence, it is very important for bridge engineers to determine the moment GDF for horizontally curved, steel, I-girder bridges subjected to permit vehicles.

Evaluating horizontally curved, steel, I-girder bridges subjected to permit vehicles is more complicated than evaluating straight bridges. Warping normal stresses caused by bridge girder curvature influence the total girder moments for curved bridges. The most widely used method to evaluate girder moments for a curved bridge subjected to permit vehicles is a 3D finite element analysis. However, it is very time-consuming and costly to use 3D models to get maximum moments for the horizontally curved, steel, I-girder bridges subjected to permit vehicles.

The AASHTO approximate GDFs for straight bridges subjected to standard vehicles have simplified the process of evaluating girder moments in the straight bridges. This research is motivated to pursue an approximate method to predict moment GDF for curved bridges subjected to permit vehicles.

The present study is a parametric study considering key parameters including radius, span length, girder, and vehicle gage. Twenty-seven curved bridge designs from Kim (2007), and four different permit vehicles with wide gage and high GVW from a PennDOT permit vehicle database are used to develop an approximate method to predict

GDF for curved bridges under the effect of permit vehicles.

Regression analysis is used to determine the relationship between GDF for curved bridges subjected to permit vehicles and AASHTO approximate GDFs for straight bridges. The regression analysis results show that the AASHTO approximate GDFs cannot reasonably be modified to accurately predict the GDF for curved bridges subjected to permit vehicles in this parametric study. Therefore, the present study uses regression analysis to develop a new approximate GDF equation to predict moments for curved bridges subjected to permit vehicles.

The developed new approximate GDF equation can be utilized by agencies to determine whether a specific permit vehicle can pass over a curved bridge without running 3D finite element analysis, which will considerably increase the evaluation efficiency.

1.1 Problem Statement

There are several approximate methods to predict GDFs for straight bridges subjected to standard vehicles. However, the evaluation of GDFs for horizontally curved, steel, I-girder bridges subjected to permit vehicles is lacking. The analysis of curved bridges is more complex because of the warping effect. A permit vehicle has many more axles and a wider gage that may influence GDF for horizontally curved, steel, I-girder bridges. Hence, the effects of permit vehicle gage on GDF for horizontally curved, steel, I-girder bridges are evaluated in the present study.

1.2 Scope of the Research

This study is limited to the evaluation of girder moment GDF for horizontally curved, steel, I-girder bridges subjected to four different permit vehicle gages. The permit vehicle gages considered are 16 ft, 18 ft, and 18.25 ft. Two permit vehicles have the same gage but different axle spacing.

Curved bridges considered in the present study are simply supported. The geometry of twenty-seven curved bridges are taken from Kim (2007). The details of geometry of bridges is provided in Chapter 3.

The parameters considered in the present study are: radius, girder spacing, span length, and gage.  Based on these parameters, the total number of analysis cases in the present study is 108. The details of analysis cases are provided in Chapter 3. The variation range of study parameters is provided in Table 1-1.

 

Table 1-1.Study Parameter Values

 

Parameter Range (ft)
Radius 200, 350, 750
Girder Spacing 10, 11, 12
Span Length 72, 108, 144
Gage 16, 18, 18.25

 

For a 2D line analysis, three bridges with different span lengths (72 ft, 108 ft, and 144 ft) are modeled as simply supported beams. The parapet and superelevation of the concrete deck that have been demonstrated to have negligible influence on GDFs are not considered in 3D models.

Additional limitations in the present study are as follows:

  1. All materials remain in the elastic range;
  2. No dynamic effect is considered;
  3. No centrifugal force is considered;
  4. Cross-frame types are “X” type for all curved bridges;
  5. Cross-frame spacing is the same for all curved bridges;
  6. Concrete deck thickness is the same for all curved bridges; and
  7. Girder section for curved brides is composite with concrete deck.

 

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1.3 Objectives of the Research

The primary objective of the present study is to develop an approximate GDF equation, based on an extensive parametric study, to predict GDF for the outermost girder in horizontally curved, steel, I-girder bridges subjected to permit vehicles.

The developed approximate GDF equation can be used by agencies to determine the best route for a permit vehicle passing over a curved bridge and contribute to the establishment of a PennDOT permit vehicle database.

 

1.4 Tasks

Tasks to achieve the objectives of the present study are:

  1. Determine key parameters for the parametric study;
  2. Gather curved bridges and permit vehicles geometry information;
  3. Develop 3D curved bridge models to run four different permit vehicles to collect maximum total normal stress, bending stress, and warping stress in the bottom flange of the outmost exterior curved girder for each load case;
  4. Develop 2D straight bridge models to run four different permit vehicles to compute the maximum moment for the entire straight bridge;
  5. Compute maximum moment GDFs based on GDF models from Kim (2007);
  6. Compute GDFs for straight bridges based on AASHTO approximate GDF

equations;

  1. Utilize regression analysis to determine the relationship between GDF for curved bridges subjected to permit vehicles and AASHTO approximate GDFs

for a straight bridge results;

  1. Utilize regression analysis to develop a new approximate GDF equation for the outmost exterior girder in curved bridges subjected to permit vehicles;
  2. Evaluate the accuracy of developed GDF equations by comparing to 3D FEM GDF results;
  3. Evaluate the accuracy of developed GDF equations within study range of parameters; and
  4. Compare the developed approximate GDFs for the permit vehicle to GDFs for

HL-93 loading calculated from (Kim, 2007).

TRANSVERSE DISTRIBUTION FACTORS FOR HORIZONTALLY CURVED BRIDGES UNDER THE EFFECT OF PERMIT VEHICLES

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