OPTIMUM DESIGN OF WELDED PLATE GIRDER

ABSTRACT

The Project work presents an Optimum design of welded plate girder. A simply supported plate girder with span of 15meters was chosen for the case study. The girder was subjected to a self-weight of 50KN/m and concentrated loads of 1000KN at 5m and 10m from the left support. The plate girder was analysed to get the design moments and shear forces. An initial manual design was carried out for the plate girder in accordance with BS 5950-2000. From the design, initial section parameters comprising flange breadth, flange thickness, web depth and web thickness were assigned to the plate girder. The initial section parameters were then subjected to an optimisation process using Generalised Reduced Gradient (GRG) in Excel solver Add-in. From the optimisation process there was 19.34% reduction in the area of the plate girder which translates to 19.34% reduction in weight. This shows that optimisation process can be an effective tool in the search for solution into real world problems.

TABLE OF CONTENTS

Title Page   

Certification

Approval

Dedication

Acknowledgment

Abstract     

Table of Contents

List of Figures               

List of Tables                

List of Notations           

CHAPTER ONE: INTRODUCTION

1.1. Background of study

1.2. Statement of Problem

1.3. Aim and Objectives of Study

1.4. Scope of Study

1.5. Significance of Study

CHAPTER TWO: LITERATURE REVIEW

2.1. Definition of plate girder

2.2. Types of plate girder

2.3. Different shapes of flanges and webs

2.3.1, Load bearing stiffeners

2.3.2. Longitudinal stiffeners

2.3.3. Transverse Stiffeners

2.4 Introduction of weld and stiffness to girder

2.5 Design methods of girders

2.6 Typical span-to-depth ratio for different girders

2.6.1. Span configuration

2.6.2. Girder Spacing

2.6.3. Spacing

2.6.4. Section Proportion

CHAPTER THREE: DESIGN METHODOLOGY

3.1. Introduction

3.2. Design Problem

3.3. Design Considerations

3.4. Design Procedure   

3.4.1. Determination of section parameters        

3.4.2. Dimension/sizing of plate girder element

3.4.3. Section classification/proportional limitation

3.4.4. Moment Resistance      

3.4.5. Choice of Optimum depth

3.5. Optimisation programme

3.5.1. Design Parameters        

3.5.2. Assumptions

3.5.3. Optimisation Process

3.5.4. Optimizer (Excel solver) settings

3.6. The Investigations

3.6.1. Selection of Numerical problem      

3.6.2. The pilot design and search for pattern

3.6.3. Detailed Investigations

CHAPTER FOUR: RESULTS AND DISCUSSION

4.1. Design Brief 

4.2. Loading        

4.3. Design shear forces and moments                

4.4. Initial sizing of plate girder

4.5. Section Classification

4.6. Dimension of web and flanges  

4.7. Moment Resistance

4.8. Shear buckling resistance of web        

4.9. Shear buckling resistance of end panel AB  

4.10. Optimisation Result Analysis

4.11. Discussion of Results

CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS

5.1. Conclusion

5.2. Recommendations

REFERENCES

LIST OF FIGURES

Fig. 1.1; Plate girder composed of three plates   

Figure 2.2; plate girder configurations                

Figure 2.3; Plate girder with splice and variable cross-section                  

Figure 2.4; Plate girder with haunches, tapers and cranks               

Figure 2.5; Plate girder with hole for service       

Figure 2.6; Plate girder proportions 

Figure 2.7; Typical diaphragm and cross-sections of plate girders  

Figure 2.8: Components of Typical I-Girder Bridge     

Figure 2.9; Typical plate girder                 

Figure 2.10; End panel strengthened by longitudinal stiffener

Figure 3.1 Optimisation process

Figure 3.2 Symmetrical girder section       

Figure 4.1; Plate girder span and loading  

Figure 4.2; Load diagram of the plate girder       

Figure 4.3; Shear force diagram of the plate girder       

Figure 4.4; Moment diagram of the plate girder  

Figure 4.5; Final plate girder section details

Figure 4.6; Variation of flange thickness with web depth      

Figure 4.7; Variation of plate girder area with web depth      

Figure 4.8; Variation of % increase in weight with web depth         

Figure 4.9; Variation of web thickness with web depth

Figure 4.10; Variation of flange breadth with web depth

Figure 4.11; Variation of flange thickness with web thickness        

LIST OF TABLES

Table 3.1; Typical span/effective depth ratios    

Table 4.1; Initial and optimised section results   

Table 4.2; Variation of flange thickness with web depth        

Table 4.3; Variation of area of plate girder with web depth   

Table 4.4; Variation %reduction in weight with web depth   

Table 4.5; Variation of web thickness with web depth 

Table 4.6; Variation of flange breadth with web depth 

Table 4.7; Variation of flange thickness with web thickness  

LIST OF NOTATIONS

A_f = area of flange plate

a = stiffener spacing

P_yw = characteristic strength of web

P_yf = characteristic strength of flange

M = bending Moment

h = overall depth

t_f = flange thickness

f_y = yield strength of steel

ᵞ_mo = partial safety factor (resistance of class 1, 2, 3 cross-sections)

M_f = bending moment of flange

R_d = diagonal resistance

b = breadth

b_f = section flange width

t_f = section flange thickness

d_w = depth of web

D = depth of section

t_w = web thickness

P_y = steel design strength

A_g = gross sectional area

F_v = design shear force

F_c = design axial compression

M_b = buckling resistance moment

M_A = moment at section A

M_max = maximum moment

M_D = moment at section D

P_b = buckling strength

P_V = shear strength

γ_fd  =dead load factor

γ_fi = live load feactor

w = self-weight (UDL)

W = concentrated load

M_x = maximum major axis moment in the segment length L_x governing P_cx

M_LT = maximum major axis moment in the segment length L governing M_b

P_cy = compression resistance considering buckling about minor axis only

λ_y = slenderness ratio about the minor axis.

V_A = reaction force at section A

V_B = reaction force at section B

V_C = reaction force at section C

V_D = reaction force at section D

V_E = reaction force at section E

V_cr = critical shear buckling resistance

F_v = maximum shear force;

V_w = simple shear buckling resistance.

M_u = maximum applied moment

L = length of girder