Table Of ContentGlobal Optimization of Design Parameters of Network Arch Bridges
by
Nazrul Islam
MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)
Department of Civil Engineering
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
September, 2010
Global Optimization of Design Parameters of Network Arch Bridges
by
Nazrul Islam
A thesis submitted to the Department of Civil Engineering of Bangladesh University
of Engineering and Technology, Dhaka, in partial fulfilment of the requirements for
the degree of
MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)
Department of Civil Engineering
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
September, 2010
The thesis titled “Global Optimization of Design Parameters of Network Arch
Bridges” submitted by Nazrul Islam, Roll No.: 100704335, Session: October 2007
has been accepted as satisfactory in partial fulfilment of the requirement for the
degree of M.Sc. Engineering (Civil and Structural) on 5th September, 2010.
BOARD OF EXAMINERS
______________________________________
Dr. Raquib Ahsan Chairman
Associate Professor (Supervisor)
Department of Civil Engineering
BUET, Dhaka.
______________________________________
Dr. Md. Zoynul Abedin Member
Professor and Head (Ex-officio)
Department of Civil Engineering
BUET, Dhaka.
______________________________________
Dr. Abdur Rouf Member
Professor
Department of Civil Engineering
BUET, Dhaka.
______________________________________
Mr. Sabbir Siddiquee Member
Director, Building and Structural Engineering (External)
DPM Consultant Ltd
Dhaka
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DEDICATION
To Those
Who Are Praised
By
Allah
iii
DECLARATION
It is hereby declared that except for the contents where specific reference have been
made to the work of others, the studies contained in this thesis is the result of
investigation carried out by the author. No part of this thesis has been submitted to
any other university or other educational establishment for a Degree, Diploma or
other qualification (except for publication).
_________________________________
Nazrul Islam
iv
ACKNOWLEDGEMENT
IN THE NAME OF ALLAH, MOST GRACIOUS, MOST MERCIFUL
All praises to the Sustainer of the worlds, and grace, honour and salutations on the
Chief of Apostles and Seal of Prophets, Muhammad Sallallahu Alaihissalam, his
family, companions and those who followed him in an excellent manner and invited
mankind towards Allah, till the Day of Resurrection.
I would like to thank Allah Subha’nahu Wa Ta’ala the Exalted for His blessing that
allowed me to complete this thesis and I pray that He accepts it as a work of sincerity
and benefit.
I would like to express my deep and sincere gratitude to my thesis supervisor, Dr.
Raquib Ahsan, Associate Professor of Civil Engineering Department of BUET for his
dynamic supervision, continuous guidance, invaluable suggestion, and enthusiastic
encouragement throughout various stages of this research. His active interest in this
topic and valuable advice was the source of author’s inspiration. I am also grateful to
Professor Dr. Abdur Rouf of Civil Engineering Department of BUET for his help and
valuable suggestions regarding this work.
During this work I have collaborated with many colleagues for whom I have great
regard, and I wish to extend my warmest thanks to all those who have helped me with
my work in the Department of Civil Engineering of BUET.
Finally, I extend my acknowledgement and heartfelt love to my family members who
are always a constant source of inspiration throughout my life.
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ABSTRACT
Structural optimization of network arch bridges is performed in this study.
Optimization has been achieved through execution of a simulator, evaluation of a
constrained objective function and adjustment of system parameters in an iterative
and directed way. Objective is to minimize the total material cost required for hanger,
arch concrete and arch reinforcement of network arch bridges. The optimization
problem is characterized by having mixed design variables. Structural analysis of
network arch bridges is performed by a finite element simulator, ANSYS.
Optimization of structural design of the bridge is performed through a global
optimization algorithm EVOP. An interfacing environment has been developed by
integrating ANSYS with EVOP. The interfacing has been verified through some
benchmark problems of optimization. Finally parameters of a tied arch bridge are
invoked in the optimization process as the initial design and after completion of
optimization process, optimal design variables i.e. hanger arrangement, no of hangers,
cross section required for hanger, arch section and rise to span ratio of arch, are
obtained within a range of design constant parameters. Response parameters of the
arch bridge with optimum design variables are analyzed regarding hanger stress,
bending moment, axial force and influence line for bending moment in arch and
amount of reinforcement required in the arch. Results are compared with the initially
designed arch. Results show that arch bridges with optimal design variables using
global optimization technique shows significant improvement over the arch bridges
designed initially. Optimal design variables confirm significant reduction of bending
moment in arch than the arch bridges with vertical hangers. Based on optimum design
criteria it is found that circular arch geometry requires shallower arch than that
required for parabolic arch. In addition, within the range of design constant
parameters it is observed that 36% to 40% of total cost can be saved for circular and
parabolic arches if design is optimized. Results also show that parabolic arch with
optimum design variables is more economic than the optimal arch bridges with
circular arch geometry. The interfacing environment developed in the study opens the
door for simulation driven most economical design of any type of structure.
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TABLE OF CONTENTS
Page
No.
DEDICATION iii
DECLARATION iv
ACKNOWLEDGEMENT v
ABSTRACT vi
LIST OF FIGURES xi
LIST OF TABLES xvii
LIST OF ABBREVIATION xix
LIST OF NOTATION xx
CHAPTER 1 INTRODUCTION
1.1 Background 1
1.2 Objectives of the Present Study 3
1.3 Scope and Methodology of the Study 3
1.4 Organization of the Thesis 3
CHAPTER 2 LITERATURE REVIEW
2.1 General 5
2.2 Arch Bridges 5
2.3 Network Arch Bridges 7
2.4 Global Optimization Method 12
2.4.1 Classification of Global Optimization Methods 12
2.5 Simulation Driven Optimization 15
2.6 Conclusion 19
CHAPTER 3 FORMULATION OF OPTIMIZATION PROBLEM
3.1 General 21
3.2 Optimal Design Problem Statement 21
3.3 Objective Function 22
3.4 Design Variables and Design Constant Parameters 22
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3.5 Explicit Constraints 25
3.5.1 Explicit Constraints for Hanger Arrangement 25
3.5.2 Explicit Constraints for Number of Hangers 26
3.5.3 Explicit Constraints for Cable Section of Hanger 26
3.5.4 Explicit Constraints for Arch Section 26
3.5.5 Explicit Constraints for Arch Rise 27
3.6 Implicit Constraints 27
3.6.1 Implicit Constraints Regarding Design of Hangers 28
3.6.2 Implicit Constraints Regarding Design of Arch 29
3.6.3 Implicit Constraints Regarding Hanger Position 31
3.6.4 Constraints Regarding in Plane Stability of Arch 32
3.7 Conclusion 33
CHAPTER 4 INTERFACING GLOBAL OPTIMIZATION
ALGORITHM, EVOP WITH FINITE ELEMENT
SOFTWARE, ANSYS
4.1 General 34
4.2 Advantage of FEA Software, ANSYS for Interfacing with 34
EVOP
4.3 Interfacing ANSYS with EVOP in the Optimization 35
Process
4.4 Verification of Interfacing 37
4.4.1 Test Case 1 for Structural Shape Optimization 37
4.4.2 Test Case 2 for Structural Shape Optimization 42
4.5 Conclusion 48
CHAPTER 5 FINITE ELEMENT MODELING AND ANALYSIS
OF NETWORK ARCH BRIDGES
5.1 General 49
5.2 Network Arch Bridge 49
5.3 Finite Element Model of Network Arch Bridges 51
5.3.1 Element types 52
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5.3.2 Material Properties 53
5.3.3 Geometrical Parameters 54
5.3.4 Finite Element Meshing and Node Connectivity 55
5.3.5 Boundary Conditions 56
5.4 Vehicle Modelling 57
5.4.1 Standard Vehicle 57
5.5 Loading 59
5.5.1 Influence Line Generation 60
5.5.2 Multistep Load Generation 60
5.6 Load Cases and Load Combinations 62
5.7 Validation of the Finite Element Model of Arch Bridge 63
5.7.1 Validation of Finite Element Model for Parabolic 63
Geometry of Arch
5.7.2 Validation of Finite Element Model for Circular 69
Geometry of Arch
5.8 Finite Element Analysis 70
5.9 Design and Post Processing for Optimization 74
5.9.1 Design of Arch 74
5.9.2 Postprocessing of Arch Design 75
5.9.3 Postprocessing of Hanger Design 75
5.10 Conclusion 75
CHAPTER 6 RESULT OF OPTIMIZATION
6.1 General 77
6.2 Optimum Design 77
6.3 Optimum Design for Circular Geometry of Arch 77
6.3.1 Comparison of Influence Lines for Circular Arch 80
6.3.2 Comparison of Results for Bending Moment, Axial 84
Force, Strength Criteria and Reinforcement Percentage for
Circular Arch
6.3.3 Comparison Optimum Values of Objective Function 92
6.4 Optimum Design for Parabolic Arch 94
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Description:It is hereby declared that except for the contents where specific reference Chief of Apostles and Seal of Prophets, Muhammad Sallallahu Alaihissalam, his network arch bridges is performed by a finite element simulator, ANSYS. In other industries dealing with civil, mechanical, and automotive.
