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
Af = area of flange plate
a = stiffener spacing
Pyw = characteristic strength of web
Pyf = characteristic strength of flange
M = bending Moment
h = overall depth
tf = flange thickness
fy = yield strength of steel
ᵞmo = partial safety factor (resistance of class 1, 2, 3 cross-sections)
Mf = bending moment of flange
Rd = diagonal resistance
b = breadth
bf = section flange width
tf = section flange thickness
dw = depth of web
D = depth of section
tw = web thickness
Py = steel design strength
Ag = gross sectional area
Fv = design shear force
Fc = design axial compression
Mb = buckling resistance moment
MA = moment at section A
Mmax = maximum moment
MD = moment at section D
Pb = buckling strength
PV = shear strength
γfd =dead load factor
γfi = live load feactor
w = self-weight (UDL)
W = concentrated load
Mx = maximum major axis moment in the segment length Lx governing Pcx
MLT = maximum major axis moment in the segment length L governing Mb
Pcy = compression resistance considering buckling about minor axis only
λy = slenderness ratio about the minor axis.
VA = reaction force at section A
VB = reaction force at section B
VC = reaction force at section C
VD = reaction force at section D
VE = reaction force at section E
Vcr = critical shear buckling resistance
Fv = maximum shear force;
Vw = simple shear buckling resistance.
Mu = maximum applied moment
L = length of girder
