LB/PORJ/SI /o3 
Optimum Design Of 
Plate Girders 
r 9- a v r > 
. - . w . i A T u * " V' 
Presented by 
Ms. A.N.Weeratunga 
Supervised by 
Dr. (Mrs.) M.T.P.Hettiarachchi 
Department of Civil Engineering £>£/r• 0 7 ^ . Z C S 4 S -tO 
University of Moratuwa 
Sirt T.anka 
This thesis was submitted to the department of Civil Engineering 
of the University of Moratuwa in partial fulfillment of the 
requirements for the Degree of M.Sc. in Structural Engineering. 
2003 / March 
U n i v e r s i t y o f M o r a t u w a 
78152 7 8 1 5 2 
eclatatlon 
I Arosha Narmadha W e e r a t u n g a , s i n c e r e l y a n d t r u l y 
declare that the work included in the thesis i n p a r t o r w h o l e , h a s 
not been submitted for any other a c a d e m i c q u a l i f i c a t i o n a t a n y 
inst i tut ion. 
il 111 
I - - -
: • / i\:bstract 
Steel plate girders are generally used lo span long distances and support heavy loads. 
They consist of top and bottom flanges connected to a vertical web. The flanges are 
connected to the web by fillet welds. Plate girders could be custom designed lo suit client's 
requirements. They are often used in situations where rolled steel sections of the required 
sizes are not available. The designer has the option of selecting suitable dimensions for the 
flanges and web from a vast range of possibilities. Smaller flange areas could be achieved 
with deep girders. However deep girders could suffer from shear buckling of the web; a 
problem that could be overcome by providing either a thick web or stiffening the web. Thick 
webs result in heavy sections while the thin web option though resulting in material savings 
could result in a more expensive solution due to high fabrication costs. 
The objective of this study is to assist the structural designer achieve a cost effective steel 
plate girder by providing design guidelines. The study was limited to parallel flanged steel 
plate girders made of Grade 43 steel and used in buildings. 
Optimum dimensions of flanges and webs have been obtained for both stiffened and un-
stiffened steel girders of simply supported spans ranging from 3m to 25m, subject to 
uniformly distributed loads, and point loads of varying magnitudes. The design loads used 
are those for girders supporting a reinforced concrete slab and subject to office type imposed 
loads. The girders are designed non-compositely. The design checks for the plate girder were 
carried out using software developed in-house. The optimum design is selected on the basis 
of total cost (i.e. material and fabrication costs). 
The variation of steel tonnage and the total cost of steel girders for the different parameters 
selected are presented in tabular and graphical format. 
From the results obtained optimum span-to-depth ratios were selected under 
different girder types with their relevant spans. 
This is of particular important to Sri Lanka where rolled steel sections need to be imported 
much in advance of construction and last minute modifications will thus prove to be difficult. 
This problem could be overcome by having a steel plate girder custom designed, and 
fabricated locally, which will be well cost effective. 
cknowSedgement 
First, my sincere thanks to.Dr.(Mrs.) M.T.P.Hettiarachchi, for her untiring contribution 
to the development of this project and guiding me through out the project to make it 
a memorable success. I admire her as a wonderful, understanding and amicable 
supervisor. 
A special thank to Mr. Nimal Gunawardena, General Manager, Dockyard General 
Engineering Services (Pvt.) Ltd. at Colombo 12 who arranged for me a valuable visit 
to dockyard and also, to all the officers of the Dock-yard who helped me in 
obtaining all information. 
I also thank Dr. A.D.C. Jayanandana, Dr. S.A.S. Kulathilake, Research Co-ordinator and 
Prof. A.K.W. Jayawardena, the Head, Department of Civil Engineering providing me 
help and constructive criticism in development of this project. 
Thank you to Prof.(Mrs.) N.Ratnayake, Director, Postgraduate Studies, for her valuable 
advice and also to Asian Development Bank for funding me through out the project. 
I would like to thank my friends who helped me in numerous ways to improve the 
quality of the project. 
Finally, I want to thank my family for their unflinching support and encouragement 
over the year to pursue my goals. 
Arosha Weeratunga 
March 2003 
Declaration 
Abstract 
Acknowledgement 
Contents at a Glance 
Table of Contents 
List of Tables, Figures, and Graphs 
Chapter 1 INTRODUCTION 
Chapter 2 LITERATURE REVIEW ON GIRDERS 
Chapter 3 DESIGN METHODOLOGY 
Chapter 4 COST ANALYSIS 
Chapter 5 ANALYSIS AND DISCUSSION 
Chapter 6 OPTIMUM DEAM LAYOUT 
Chapter 7 CONCLUSION AND RECOMMENDATIONS 
References 
Appendix 
_ •>• J , o i ontents 
List of tables, figures and graphs 
1 Introduction 
1.1 Background 
1.2 Girder types 
1.3 Suitability of plate girders in building floors of Sri Lanka. 
1.4 What is ' Optimum design of steel plate girders'? 
1.5 Objective 
1.5.1 How was the project planed? 
1.5.2 An overview of the project planned. 
Litorature review on girders 
2.1 Introduction 
2.2 Review on different shapes of flanges and webs 
2.3 Review on different types of loadings on flanges and webs 
2.4 Review on development of tension field theory. 
2.5 Review on introduction of stiffencrs to the girder. 
2.6 Review on design methods on girders. 
2.8 Review on typical span-to-depth ratios for different girders 
2.9 Conclusion 
Design Methodology 
3.1 Background 
3.1.1 Design load effects 
3.1.2 Variations and Limitations considered 
3.1.3 Girder types 
3.1.3.1 Unstiffened girders 
3.1.3.2 Stiffened girders 
3.2 The computer program 
3.2.1 Introduction 
3.2.2 Flow chart for girder design 
3.2.2.1 Main flow chart 
3.2.2.2 Unstiffened girder flow chart 
3.2.2.3 Stiffened girder flow chart 
S3 v " 
Cost Analysis 33 
4.1 Introduction 3 4 
4.2 Cost calculation 3 4 
4.2.1 Material cost 3 4 
4.2.2 Fabrication cost 3 6 
4.2.3 Overheads 3 6 
4.3 Cost evaluation 3X 
Analysis and Discussion 41 
5.1 Loadings on plate girders 4 2 
5.2 Secondary girder analysis 43 
5.2.1 Variations considered 4 4 
5.2.2 Optimum solutions 4 5 
5.3 IG-type plate girders 4 6 
5.3.1 Variations considered 4 7 
5.3.2 Optimum solutions 4 9 
5.4 2G-type plate girders 51 
5.4.1 Variations considered 52 
5.4.2 Optimum solutions 5 4 
5.5 3G -type plate girders 5 6 
5.5.1 Variations considered 57 
5.5.2 Optimum solutions 5 9 
5.6 4G -type plate girders 61 
5.6.1 Variations considered 6 2 
5.6.2 Optimum solutions 6 3 
Optimum Beam Layout 65 
6.1 Introduction 6 6 
6.2 Cost analysis to determine optimum b e a m l a y o u t t o r a p a n e l 6 9 
6.3 Conclusion 73 
Conclusions and Recommendations 74 
7.1 Comparison between unslilTened and stiffened girders 75 
7.2 Conclusion 79 
7.3 Recommendations XO 
V I I I 
References 82 
Appendix 84 
A Design examples 84 
A. 1.1 Plate girder design w i t h o u t u s i n g s t i l T e n e r s S4 
A. 1.2 Plate girder design u s i n g s t i l T e n e r s b u t w i t h o u t u t i l i z i n g t e n s i o n 
field action 88 
A.1.3 Plate girder design using stiffeners a n d u t i l i z i n g t e n s i o n field 
action 9 7 
8 Design tables 108 
B.l Secondary girders 109 
B.2 lG-type girders 117 
B.2.1 Unstiffened girders 117 
B.2.2 Stiffened girders 125 
B.3 2G-type girders 137 
B.3.1 Unstiffened girders 137 
B.3.2 Stiffened girders 145 
B.4 3G-type girders 157 
B.4.1 Unstiffened girders 157 
B.4.2 Stiffened girders 165 
B.5 4G-type girders 177 
B.5.1 Unstiffened girders 177 
B.5.2 Stiffened girders 1X3 
Figures 
Figure 1:1 Typical cross-section of a girder 2 
Figure 1:2 Unstiffened plate girder. 4 
Figure 1:3 Stiffened plate girder. 4 
Figure 1:4 Different types of girders & their various spans considered 7 
Figure 2:1 Sectional views and front views of the tapered plate girder. 10 
Figure 2:2 Cross-sections and the section through the web of the girder. 1 1 
Figure 2:3 Basler's assumed plastic tensile zone. 13 
A Figure 2:4 Komatsu's failure model. 13 
Figure 2:5 Variation of shear strength with web slenderness. 16 
Figure 2:6 Simplified moment/shear interaction diagram. 17 
Figure 3.1 Governing dimensions of flange, web and stiffeners of girder section 21 
Figure 3.2 Floor slab plan for girder types 21 
Figure 3.3 Floor slab plan for effective load areas 22 
Figure 3.4 Flow chart for girder unstiffened girder 23 
Figure 3.5 Simply supported beams 25 
Figure 3.6 Flange-to-web weld 25 
Figure 3.7 Girder for 2G type 2 6 
Figure 3.8 Cross-section of load bearing stiffener 2 6 
Figure 3.9 Cross-section of intermediate stiffener 2 6 
Figure 3.10 Flow chart for stiffened girder 2 7 
Figure 3.11 2 8 
* Figure 3.12 2 8 
Figure 3.13 2 9 
Figure 3.14 2 9 
Figure 4.1 Stiffened girder. 3 8 
Figure 5.1 Plan view of secondary girders. 4 3 
Figure 5.2 Line diagram of the secondary girder. 4 4 
Figure 5.3 Plan view of main girder. 4 6 
Figure 5.4 Line diagram of the main girder. 4 6 
Figure 5.5 Plan view of main girder. 51 
Figure 5.6 Line diagram of the main girder. 51 
Figure 5.7 Plan view of main girder. 5 6 
Figure 5.8 Line diagram of the main girder. 5 6 
Figure 5.9 Plan view of main girder. 61 
Figure 5.10 Line diagram of the main girder. 61 
ri v 
!! X 
Tables 
Table 2-1 Typical span-to-depth ratios for different girder types 18 
Table 3-1 Variations on spans and span / depth ratios 23 
Table 4-1 Various Material cost of steel plates. 35 
Table 4-2 Material cost of steel plates used for the analysis. 35 
Table 4-3 Number of joints required for butt-weld 37 
Table 4-4 Unit cost of cutting and welding of steel plales 37 
Table 5-1 Loadings on secondary girders. 4 3 
Table 5-2 Optimum solutions for secondary girders. 4 5 
Table 5-3 Loadings on one point load girders. 4 6 
Table 5-4 Optimum solutions for lG-type unstiffened girders. 4 9 
Table 5-5 Optimum solutions for lG-type stiffened girders. 5 0 
Table 5-6 Loadings on two point load girders. 51 
Table 5-7 Optimum solutions for 2G-type unstiffened girders. 5 4 
Table 5-8 Optimum solutions for 2G-type stiffened girders. 55 
Table 5-9 Loadings on three point load girders. 5 6 
Table 5-10 Optimum solutions for 3G-type unstiffened girders. 5 9 
Table 5-11 Optimum solutions for 3G-type stiffened girders. 6 0 
Table 5-12 Loadings on two point load girders. 61 
Table 5-13 Optimum solutions for 4G-type unstiffened girders. 6 4 
Table 5-14 Optimum solutions for 4G-type stiffened girders. 6 4 
Table 6-1 Total cost for 12m x 8m panel, by using different options 73 
Table 7-1 Variations of Load, Weight and span/depth o f secondary girders. 7 5 
Table 7-2 Variations of Load, Weight and span/depth of lG - t y p e for stiffened a n d 
unsliffened girders. 7 6 
Table 7-3 Variations of Load, Weight and span/depth of 2(i-lype For stiffened a n d 
unstiffened girders. 7 7 
Table 7-4 Variations of Load, Weight and span/depth o f 3 G - type for stiffened a n d 
unsliffened girders. 78 
Table 7-5 Variations of Load, Weight and span/depth o f 4G- t y p e for .stiffened a n d 
unstiffened girders. 78 
Table 7-6 Optimum span-to-depth ratios for different girder types. 7 9 
Table B:l Analysis for span = 3m 109 
Table B:2 Analysis for span = 4m 111 
Table B:3 Analysis for span = 5m 113 
Table B:4 Analysis for span = 6m 115 
Table B:5 Analysis for span = 6m 117 
Table B:6 Analysis for span = 8m 119 
Table B:7 Analysis for span = 10m 121 
Table B:8 Analysis for span = 12m 123 
Table B:9 Analysis for span = 6m 125 
Table B:10 Analysis for span = 8m 128 
Table B: 11 Analysis for span = 10m 131 
Table B:12 Analysis for span = 12m 134 
Table B: 13 Analysis for span = 9m 137 
Table B: 14 Analysis for span = 12m 139 
Table B: 15 Analysis for span • - 15m 141 
Table B: 16 Analysis for span = 18m 143 
Table B: 17 Analysis for span = 9m 145 
Table B:18 Analysis for span = 12m 148 
Table B: 18 Analysis for span = 15m 151 
Table B: 19 Analysis for span = 18m 154 
Table B:20 Analysis for span = 12m 157 
Table B:21 Analysis for span = 16m 159 
Table B:22 Analysis for span = 20m 161 
Table B:23 Analysis for span = 24m 163 
Table B:24 Analysis for span = 12m 165 
Table B:25 Analysis for span = 16m 168 
Table B:26 Analysis for span = 20m 171 
Table B:27 Analysis for span = 24m 174 
Table B:28 Analysis for span = 15m 177 
Table B:29 Analysis for span = 20m 179 
Table B:30 Analysis for span = 25m 181 
Table B:31 Analysis for span = 15m 183 
Table B:32 Analysis for span = 20m 186 
Table B:33 Analysis for span = 25m 189 
Graphs 
Graph 5:1 Total cost vs. Depth for secondary girders when spacing varies. 4 3 
Graph 5:2 Total cost vs. Depth for lG-type unstiffened girders when spacing varies. 4 6 
Graph 5:3 Total cost vs. Depth for lG-type stiffened girders when spacing varies. 4 7 
Graph 5:4 Total cost vs. Depth for 2G-type unstiffened girders when spacing varies. 51 
Graph 5:5 Total cost vs. Depth for 2G-type stiffened girders when spacing varies. 52 
Graph 5:6 Total cost vs. Depth for 3G-type unstiffened girders when spacing varies. 5 6 
Graph 5:7 Total cost vs. Depth for 3G-type stiffened girders when spacing varies. 57 
Graph 5:8 Total cost vs. Depth for 4G-type unstiffened girders when spacing varies. 61 
Graph 5:9 Total cost vs. Depth for 4G-type stiffened girders when spacing varies. 6 2 
4