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Descripción: MEMORIAS CAPACITACION ELECTRICIDAD FIAT
CONTENTS
ABSTRACT
i
CONTENTS
ii
ACKNOWLEDGEMENTS
vii
NOTATION
viii
CHAPTER I: INTRODUCTION 1.1 1.2 1.3 1.4 1.5
Main advantages of steel structures Problems associated with the analysis and design of steel frame structures The need for design optimization Main features of a design optimization problem Literature review of steelwork design optimization 1.5.1 Mathematical programming 1.5.2 Optimality criteria method 1.5.3 Evolutionary algorithms 1.6 Goals of research 1.7 Organisation of the thesis
1 2 4 5 9 10 14 18 21 22
CHAPTER II: DESIGN PROCEDURE FOR STEEL FRAME STRUCTURES ACCORDING TO BS 5950 2.1 Introduction 2.2 Limit state concept and partial safety factors 2.3 Loads and load combinations 2.3.1 Dead load 2.3.2 Live load 2.3.3 Wind load 2.3.4 Load combinations 2.4 Serviceability limit states 2.4.1 Deflection limits
26 27 30 30 31 31 39 40 40
Contents
2.5
2.6
2.7 2.8
2.9
iii
2.4.2 Durability limits Strength requirements 2.5.1 Shear strength 2.5.2 Tension members with moments 2.5.2.1 Local capacity check 2.5.2.2 Lateral torsional buckling check 2.5.3 Compression members with moments 2.5.3.1 Local capacity check 2.5.3.2 Overall buckling check Stability limits 2.6.1 Stability against overturning 2.6.2 Stability against sway 2.6.2.1 Classification into sway /non-sway frame 2.6.2.2 Determination of the effective length factor Flowchart of design procedure Computer based techniques for the determination of the effective length factor 2.8.1 Technique 1: Digitizing the charts 2.8.2 Technique 2: Analytical descriptions of the charts 2.8.2.1 Regression analysis 2.8.2.2 Genetic programming (GP) Concluding remarks
CHAPTER III: THEORY AND METHODS FOR EVALUATING OF CRITICAL BUCKLING LOAD 3.1 3.2 3.3 3.4 3.5
Introduction Stability concept The concept of buckling in idealized framework models Historical background Methods for evaluation of elastic critical load 3.5.1 Differential equation method 3.5.2 Energy method 3.5.3 Modified slope deflection method 3.5.4 Direct method 3.5.5 Finite element method 3.6 Verification of the developed code for stability analysis 3.7 Concluding remarks
72 74 75 78 83 83 84 86 87 92 94 99
CHAPTER IV: EFFECTIVE BUCKLING LENGTH OF COLUMNS IN SWAY FRAMEWORKS: COMPARISONS 4.1 Objectives 4.2 Comparisons between the factors
Code Leff, X , ncmem
Lnmem and c
DM Leff, X , ncmem
Lnmem c
100 101
Contents
4.2.1 Example 1: Single–bay single–storey framework 4.2.2 Example 2: Two–bay single–storey framework 4.2.3 Example 3: Three–bay single–storey framework 4.2.4 Example 4: Four–bay single–storey framework 4.2.5 Example 5: Five–bay single–storey framework 4.3 Concluding remarks
iv
101 108 113 117 121 126
CHAPTER V: OPTIMIZATION PROBLEM FORMULATION AND SOLUTION TECHNIQUES 5.1 Introduction 5.2 Minimum weight via optimization techniques 5.3 Why minimum weight design for steel structures? 5.3.1 Client brief 5.3.2 Cost considerations 5.4 Optimization problem formulation 5.4.1 Design variables 5.4.2 Objective function 5.4.3 Constraint 5.4.4 Standard formulation 5.5 Features of design optimization problem 5.6 Discrete optimization techniques review 5.6.1 Branch and bound method 5.6.2 Simulated annealing 5.6.3 Genetic algorithms 5.6.3.1 Background 5.6.3.2 Survival of the fittest 5.6.3.3 Encoding the design variables 5.6.3.4 Why bit string encoding? 5.6.3.5 The anatomy of a simple GA 5.6.3.6 Constraints management 5.6.3.7 Convergence criteria and termination conditions
CHAPTER VI: MODIFICATIONS, TUNING OF GA PARAMETERS AND TESTING OF THE ALGORITHM 6.1 6.2 6.3 6.4
Introduction Description of the development GA Modifications Example 1: Tuning of GA parameters and testing of crossover operators 6.4.1 Formulation of the problem 6.4.2 Domain of each parameter and operator tested 6.4.3 Description of the test 6.4.4 Results of testing
155 156 158 160 161 162 163 165
Contents
v
6.4.5 Discussion of the results of testing 6.4.5.1 Setting of GA parameters and crossover operators 6.4.5.2 Convergence history 6.5 Example 2: Comparisons of the obtained results 6.5.1 Definition and formulation of the problem 6.5.2 Discussion of results 6.6 Example 3: A comparison of different development techniques 6.6.1 Optimization methods and tools within ANSYS 6.6.2 Problem definition and obtained results 6.7 Concluding remarks
179 179 181 181 182 183 187 187 193 195
CHAPTER VII: MAXIMIZATION OF THE DIFFERENCE IN THE EFFECTIVE BUCKLING LENGTHS EVALUATED BY FEM AND BS 5950 7.1 Objectives 7.2 Maximization of
Leff, FE X , ncmem
Leff, Code X , ncmem
7.2.1 Problem definition and solution technique 7.2.2 Example 1: Two–bay two–storey framework 7.2.3 Example 2: Five–bay five–storey framework 7.3 Maximization of Leff, FE Leff, Code mem mem subject to design criteria X , nc
196 197 197 203 208 213
X , nc
7.3.1 Formulation of the problem 7.3.2 Example 1: Two–bay two–storey framework 7.3.3 Example 2: Five–bay five–storey framework 7.4 Maximization of Leff, Code Leff, FE mem mem subject to design criteria
213 221 225 230
7.4.1 Formulation of the problem 7.4.2 Example 1: Two–bay two–storey framework 7.4.3 Example 2: Five–bay five–storey framework 7.5 Discussion of results and concluding remarks
Objectives Design procedure to bs 5950 Problem formulation and solution technique Benchmark examples 8.4.1 Example 1: Two–bay two–storey framework 8.4.2 Example 2: Five–bay five–storey framework 8.4.3 Example 3: Four–bay ten–storey framework 8.5 Validation of the optimum design 8.6 Concluding remarks
238 239 247 250 250 255 260 267 271
Contents
vi
CHAPTER IX: DESIGN OPTIMIZATION OF 3D STEEL FRAME STRUCTURES 9.1 9.2 9.3 9.4
Objectives Design procedure to BS 5950 Problem formulation and solution technique Benchmark examples 9.4.1 Example 1: Two–bay by two–bay by two–storey structure 9.4.2 Example 2: Three–bay by four–bay by four–storey structure 9.5 Validation of the optimum design 9.6 Concluding remarks
273 274 284 287 289 295 302 306
CHAPTER X: CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK 10.1 10.2 10.3 10.4
Introduction Main achievements Conclusions Suggestions for further work
308 308 310 312
Appendix A. Stability functions Appendix B. Sample of a data file for the stability analysis Appendix C. Description of the developed program for the design optimization of steel frame structures
