Design and Optimization of Metal Structures

By J Farkas and K Jarmai

An industrial book that analyses various theoretical problems, optimizes numerical applications and addresses industrial problems such as belt-conveyor bridge, pipeline, wind turbine power, large-span suspended roof and offshore jacket member. Multi-storey frames and pressure vessel-supporting frames are discussed in detail. The book’s emphasis is on economy and cost calculation, making it possible to compare costs and make significant savings in the design stages, by, for example, comparing the costs of stiffened and un-stiffened structural versions of plates and shells. In this respect, this book will be an invaluable aid for designers, students, researchers and manufacturers to find better, optimal, competitive structural solutions.

• Emphasis is placed on economy and cost calculation, making it possible to compare costs and make significant savings in the design stages of metal structures
• Optimizes numerical applications and analyses various theoretical and industrial problems, such as belt-conveyor bridge, pipeline, wind turbine power, large-span suspended roof and offshore jacket member
• An invaluable aid for designers, students, researchers and manufacturers to find better, optimal, competitive structural solutions

• Language: English
• Publisher: Elsevier Science
• Release date: Apr 1, 2008
• ISBN: 9781782420477

J Farkas

Jozsef Farkas, University of Miskolc, Hungary

Book preview

DESIGN AND OPTIMIZATION OF METAL STRUCTURES

Dr. József Farkas

Professor Emeritus of Metal Structures, University of Miskolc, Hungary

Dr. Károly Jármai

Professor of Mechanical Engineering, University of Miskolc, Hungary

Table of Contents

Cover image

Title page

ABOUT THE AUTHORS

Copyright

About the Authors

List of Symbols

Preface

Acknowledgements

Chapter 1: Newer Mathematical Optimization Methods

Publisher Summary

1.1 INTRODUCTION

1.2 THE SNYMAN-FATTI METHOD

1.3 THE PARTICLE SWARM OPTIMIZATION ALGORITHM

1.4 MULTIOBJECTIVE OPTIMIZATION

Chapter 2: Cost Calculations

Publisher Summary

2.1 INTRODUCTION

2.2 THE COST FUNCTION

Chapter 3: Seismic Resistant Design

Publisher Summary

3.1 INTRODUCTION

3.2 GROUND CONDITIONS AND SEISMIC ACTION

3.3 DESIGN OF BUILDINGS

3.4 SPECIFIC RULES FOR STEEL BUILDINGS

Chapter 4: Fire Resistant Design

Publisher Summary

4.1 INTRODUCTION

4.2 CALCULATION OF THE STEEL MECHANICAL PROPERTIES AT ELEVATED TEMPERATURES

4.3 CALCULATION OF THE ACTIONS FOR THE FIRE SITUATION

4.4 STEEL TEMPERATURE DEVELOPMENT

Chapter 5: Large-span Suspended Roof Members

Publisher Summary

5.1 INTRODUCTION

5.2 THE SUSPENDED ROOF MEMBERS

5.3 DESCRIPTION OF ANALYTICAL MODEL

5.4 OPTIMIZATION

5.5 NUMERICAL DATA (Figure 5.2)

5.6 PARAMETRIC EVALUATION

5.7 CONCLUSIONS

Chapter 6: Frames

Publisher Summary

6.1 INTRODUCTION

6.2 SIMPLE FRAME WITH WELDED OR BOLTED CORNER JOINTS

6.3 OPTIMUM SEISMIC DESIGN OF A MULTI-STOREY FRAME

6.4 FIRE-RESISTANT OPTIMUM DESIGN OF A MULTI-STOREY FRAME

6.5 EARTHQUAKE-RESISTANT OPTIMUM DESIGN OF A TUBULAR FRAME

6.6 FIRE-RESISTANT OPTIMUM DESIGN OF A TUBULAR FRAME

Chapter 7: Stiffened Plates

Publisher Summary

7.1 MINIMUM COST DESIGN OF A WELDED STIFFENED SQUARE PLATE LOADED BY BIAXIAL COMPRESSION

7.2 OPTIMUM DESIGN AND COST COMPARISON OF A WELDED PLATE STIFFENED ON ONE SIDE AND A CELLULAR PLATE BOTH LOADED BY UNIAXIAL COMPRESSION

7.3 ECONOMIC ORTHOGONALLY WELDED STIFFENING OF A UNIAXIALLY COMPRESSED STEEL PLATE

7.4 ECONOMIC WELDED STIFFENING OF A STEEL PLATE LOADED BY BENDING

7.5 MINIMUM COST DESIGN OF A WELDED SQUARE STIFFENED PLATE SUPPORTED AT FOUR CORNERS

7.6 MINIMUM COST DESIGN OF A WELDED STEEL SQUARE CELLULAR PLATE SUPPORTED AT FOUR CORNERS

Chapter 8: Welded Stiffened Cylindrical and Conical Shells

Publisher Summary

8.1 RING-STIFFENED CYLINDRICAL SHELLS SUBJECT TO AXIAL COMPRESSION AND EXTERNAL PRESSURE

8.2 A RING-STIFFENED SHELL SUBJECT TO BENDING

8.3 A STRINGER-STIFFENED SHELL SUBJECT TO BENDING

8.4 A STRINGER-STIFFENED SHELL SUBJECT TO AXIAL COMPRESSION AND BENDING

8.5 A WELDED ORTHOGONALLY STIFFENED CYLINDRICAL SHELL SUBJECT TO AXIAL COMPRESSION AND EXTERNAL PRESSURE

8.6 A STRINGER-STIFFENED STEEL CYLINDRICAL SHELL OF VARIABLE DIAMETER SUBJECT TO AXIAL COMPRESSION AND BENDING

8.7 A RING-STIFFENED CONICAL SHELL LOADED BY EXTERNAL PRESSURE

Chapter 9: Tubular Structures

Publisher Summary

9.1 COST COMPARISON OF A RING-STIFFENED SHELL AND A TUBULAR TRUSS STRUCTURE FOR A WIND TURBINE TOWER

9.2 MINIMUM COST DESIGN OF A COLUMN-SUPPORTED OIL PIPELINE STRENGTHENED BY A TUBULAR TRUSS

Chapter 10: Square Box Column Composed from Welded Cellular Plates

Publisher Summary

10.1 INTRODUCTION

10.2 CONSTRAINTS

10.3 NUMERICAL DATA (Fig. 1)

10.4 COST FUNCTION

10.5 OPTIMIZATION AND RESULTS

10.6 CONCLUSIONS

Appendixes

References

Name Index

Subject index

ABOUT THE AUTHORS

Dr József Farkas is Professor Emeritus of metal structures at the University of Miskolc, Hungary. He graduated from the Faculty of Civil Engineering at the Technical University of Budapest and moved to the University of Miskolc where he became an assistant professor in 1950, an associate professor in 1966 and a university professor in 1975. He obtained degrees as a Candidate of Technical Science in 1966 and Doctor of Technical Science in 1978. Dr. Farkas’s research field is the optimum design of metal structures, residual welding stresses and distortions, tubular structures, stiffened plates, vibration damping of sandwich structures. He has written expert opinions for many industrial problems, especially on storage tanks, cranes, welded press frames and other metal structures. He is the author of a Hungarian university textbook on metal structures, a book in English Optimum Design of Metal Structures (Ellis Horwood Ltd, Chichester 1984), the first author of two books in English Analysis and Optimum Design of Metal Structures (Balkema, Rotterdam-Brookfield 1997), Economic Design of Metal Structures (Millpress, Rotterdam 2003) and about 260 scientific articles in journals and conference proceedings. He is a Hungarian delegate of the International Institute of Welding (IIW), member of the International Society for Structural and Multidisciplinary Optimization (ISSMO) and honorary member of the Hungarian Scientific Society of Mechanical Engineers (GTE). The University of Miskolc has also honoured him as doctor honoris causa.

Dr Károly Jármai is a professor at the Faculty of Mechanical Engineering at the University of Miskolc, where he graduated as a mechanical engineer and received his doctorate (dr.univ.) in 1979. He teaches design of steel structures, welded structures, composite structures and optimization in Hungarian and in the English language for foreign students. His research interests include structural optimization, mathematical programming techniques and expert systems. Dr. Jármai wrote his C.Sc. (Ph.D.) dissertation at the Hungarian Academy of Science in 1988, became a European Engineer (Eur. Ing. FEANI, Paris) in 1990 and did his habilitation (dr.habil.) at Miskolc in 1995. Having successfully defended his doctor of technical science thesis (D.Sc.) in 1995, he subsequently received awards from the Engineering for Peace Foundation in 1997 and a scholarship as Széchenyi professor between the years 1997-2000 He is the co-author (with Farkas) of two books in English Analysis and Optimum Design of Metal Structures, Economic Design of Metal Structures and one in Hungarian, and has published over 300 professional papers, lecture notes, textbook chapters and conference papers. He is a founding member of ISSMO, a Hungarian delegate, vice chairman of commission XV and a sub-commission chairman XV-F of IIW. He has held several leading positions in GTE and has been the president of this society at the University of Miskolc since 1991. He was a visiting researcher at Chalmers University of Technology in Sweden in 1991, visiting professor at Osaka University in 1996-97, at the National University of Singapore in 1998 and at the University of Pretoria several times between 2000-2005.

Copyright

HORWOOD PUBLISHING LIMITED

International Publishers in Science and Technology

Coll House, Westergate, Chichester, West Sussex, PO20 3QL, England

First published in 2008.

COPYRIGHT NOTICE

All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the permission of Horwood Publishing Limited, Coll House, Westergate, Chichester, West Sussex, PO20 3QL, England.

© Horwood Publishing Limited, 2008.

British Library Cataloguing in Publication Data

A catalogue record of this book is available from the British Library

ISBN: 978-1-904275-29-9

Cover design by Jim Wilkie.

Printed and bound in the UK by Antony Rowe Limited.

About the Authors

Dr József Farkas is a professor emeritus of metal structures at the University of Miskolc, Hungary. He graduated in 1950 at the Faculty of Civil Engineering of the Technical University of Budapest. He has been an assistant professor of the University of Miskolc since 1950, an associate professor since 1966, a university professor since 1975. His scientific degrees are candidate of technical science 1966, doctor of technical science 1978. His research field is the optimum design of metal structures, residual welding stresses and distortions, tubular structures, stiffened plates, vibration damping of sandwich structures. He has written expert opinions for many industrial problems, especially on storage tanks, cranes, welded press frames and other metal structures. He is the author of a university textbook about metal structures, a book in English Optimum Design of Metal Structures (Ellis Horwood, Chichester 1984), the first author of two books in English Analysis and Optimum Design of Metal Structures (Balkema, Rotterdam-Brookfield 1997), Economic Design of Metal Structures (Millpress, Rotterdam 2003) and about 260 scientific articles in journals and conference proceedings. He is a Hungarian delegate of the International Institute of Welding (IIW), member of the International Society for Structural and Multidisciplinary Optimization (ISSMO) and honorary member of the Hungarian Scientific Society of Mechanical Engineers (GTE). He is doctor honoris causa of the University of Miskolc.

Dr Károly Jármai is a professor at the Faculty of Mechanical Engineering at the University of Miskolc. He graduated as a mechanical engineer and received his doctorate (dr.univ.) in 1979 at the University of Miskolc. He teaches design of steel structures, welded structures, composite structures and optimization in Hungarian and in the English language for foreign students. His research interests include structural optimization, mathematical programming techniques and expert systems. He wrote his C.Sc. (Ph.D.) dissertation at the Hungarian Academy of Science in 1988. He became a European Engineer (Eur. Ing. FEANI, Paris) in 1990. He did his habilitation (dr.habil.) at the University of Miskolc in 1995. He defended his doctor of technical science thesis (D.Sc.) in 1995. He was awarded a Széchenyi professor scholarship in the years 1997-2000 and an award of the Engineering for Peace Foundation in 1997. He is the co-author of two books in English Analysis and Optimum Design of Metal Structures (Balkema, Rotterdam-Brookfield 1997), Economic Design of Metal Structures (Millpress, Rotterdam 2003) and one in Hungarian (Műegyetemi Kiadó 2001). He has published over 300 professional papers, lecture notes, textbook chapters and conference papers. He is a founding member of ISSMO, a Hungarian delegate, vice chairman of commission XV and a subcommission chairman XV-F of IIW. He has held several leading positions in GTE and has been the president of this society at the University of Miskolc since 1991. He was a visiting researcher at Chalmers University of Technology in Sweden in 1991, visiting professor at Osaka University in 1996-97, at the National University of Singapore in 1998 and at University of Pretoria in several times between 2000-2005.

List of Symbols

Preface

Structural optimization is a design system for searching better solutions, which better fulfil engineering requirements. The main requirements of a modern load-carrying structure are the safety, fitness for production and economy. The safety and producibility are guaranteed by design and fabrication constraints, and economy can be achieved by minimization of a cost function.

The main aim of this book is to give designers and fabricators aspects for selection of the best structural solution. A lot of structural versions fulfil the design and fabrication constraints and designers should select from these possibilities the best ones. A suitable cost function helps this selection, since a modern structure should be not only safe and fit for production but also economic.

A simple numerical example illustrates this aspect. In Table 1 three cross-sections of a bent box beam are shown. Their bending moment capacity (or section modulus) is nearly equal, but their cross-sectional areas (or mass) and costs (for a beam length of 20 m) are different.

Table 1

Characteristics of three different bent box beam cross-sections

Furthermore, their safeties against plate buckling (or plate slendernesses) are also near equal. The limiting plate slenderness in the case of a steel of yield stress 235 MPa for webs is 69 and for compression flange is 42. The cost includes material cost and welding cost of four longitudinal fillet welds. It can be seen that, to select the most suitable version, the beam of the minimum mass or cost should be selected, since this structural version is safe and economic.

This simple calculation is made by varying only few parameters. In most cases, treated in this book, much more unknowns should be varied to find the best solution. In these cases one needs special mathematical methods, some of them are treated in this book as well.

The optimum design procedure can be formulated mathematically as follows: the objective function should be minimized

subject to constraints

where n is the number of unknowns and p is the number of constraints.

The solution of this constrained function minimization problem needs effective mathematical methods.

The above description shows that the structural optimization has four main components:

(1) design constraints relate to stress, stability, deformation, eigenfrequency, damping,

(2) fabrication constraints formulate the limitation of residual welding distortions, requirements for welding technology, limitations of plate thicknesses and main structural dimensions, definition of available profile series,

(3) a cost function is formulated according to the fabrication sequence and contains the cost of materials, assembly, welding, cutting and painting,

(4) mathematical methods.

In our systematic research we have developed suitable means for these main components. Design constraints are formulated according to relevant Eurocodes or design rules of American Petroleum Institute (API), Det Norske Veritas (DNV) and European Convention for Constructional Steelwork (ECCS).

We have worked out a calculation method for residual welding stresses and distortions, for the cost function we have created a calculation method mainly for welded structures and we use several effective mathematical algorithms.

We have solved a lot of structural optimization problems for various structural models. Since these models are the main components of industrial structures, designers can use them in their work. The cost estimation in design stage is a good basis for the comparison of candidate structural versions.

Our structural models of welded I- and box-beams, tubular trusses, steel frames, stiffened plates and shells can be used in all industrial applications i.e. in bridges, buildings, roofs, columns, towers, ships, cranes, offshore structures, belt-conveyor bridges, machine structures, vehicles, etc.

Some special structural models are involved as follows: cellular plates, suspended beams for roofs, wind turbine towers, a tubular member of a truss tower of a fixed offshore platform.

Since the functions are highly nonlinear only numerical problems can be treated. Therefore, the conclusions are not completely general. In spite of this the solutions give valuable aspects for optimum design, because the numerical data are selected realistically.

The first step of the optimization procedure is the selection of variables. For this selection we need to know the main characteristics of a typical structure as follows: materials, loads, geometry, topology, profiles, fabrication technology, joints, costs. The better solutions can be obtained by changing these characteristics.

The new design aspects of our book to be emphasized are as follows. Seismic- and fire-resistant design methods are treated in special chapters and their applications are worked out in the chapter for frames. In the case of welded stiffened plates and cylindrical shells the problem of economy of stiffening is systematically investigated.

A question arises whether a thicker unstiffened or a thinner stiffened plate or