Global Structural Analysis of Buildings © 2000 Karoly A. Zalka Global Structural Analysis of Buildings Karoly A.Zalka London and New York © 2000 Karoly A. Zalka First published 2000 by E & FN Spon 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by E & FN Spon 29 West 35th Street, New York, NY 10001 E & FN Spon is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2002. © 2000 Karoly A.Zalka All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Publisher´s Note This book has been prepared from camera-ready copy provided by the author. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Zalka, K.A. Global structural analysis of buildings/Karoly A.Zalka. p. cm. Includes bibliographical references and index. 1. Structural analysis (Engineering) 2. Global analysis (Mathematics) I. Title. TA645 .Z35 2000 690´.21–dc21 00–026451 ISBN 0-203-18429-7 Master e-book ISBN ISBN 0-203-18456-4 (Adobe eReader Format) ISBN 0-415-23483-2 (Print Edition) © 2000 Karoly A. Zalka Contents Preface Notations 1 Introduction 1.1 Background 1.2 General asumptions 1.3 The structure of the bok 2 Spatial behaviour 2.1 Basic principles 2.2 The equivalent column and its characteristics 2.3 The spatial behaviour of the equivalent column 3 Stability and frequency analyses 3.1 Stability analysis 3.1.1 Doubly symetrical systems—basic critical loads 3.1.2 Coupling of the basic modes; combined sway- torsional buckling 3.1.3 Concentrated top load; single-storey buildings 3.1.4 Shear mode situations 3.1.5 Soil-structure interaction 3.1.6 Individual beam-columns 3.2 Frequency analysis 3.2.1 Doubly symmetrical systems—basic natural frequen- cies 3.2.2 Coupling of the basic modes; combined lateral- torsional vibrations 3.2.3 Concentrated mas at top level; single-storey buildings 3.2.4 Soil-structure interaction 3.2.5 Suplementary remarks © 2000 Karoly A. Zalka 4 Stres analysis: an elementary aproach 4.1 Horizontal load 4.1.1 Wind 4.1.2 Seismic load 4.1.3 Construction misalignment 4.1.4 Comparisons 4.2 Buildings braced by paralel wals 4.2.1 Basic principles 4.2.2 Load distribution 4.2.3 Deformations 4.3 Buildings braced by perpendicular wals 4.3.1 Load distribution 4.3.2 Deformations 4.4 Buildings braced by frameworks 4.4.1 Frameworks in a symetrical arangement 4.4.2 Frameworks in an asymetrical arangement 4.5 Maximum bending moments in the bracing elements 4.6 Worked examples 4.6.1 Example 1: building braced by paralel wals 4.6.2 Example 2: building braced by perpendicular wals 4.6.3 Comparison 4.6.4 Example 3: building braced by frameworks and a single wal 4.7 Discusion 5 Stres analysis: an advanced aproach 5.1 The equivalent column and its load 5.2 Deformations of the equivalent column 5.2.1 Horizontal displacements 5.2.2 Rotations 5.3 Deformations of the building 5.4 Load distribution among the bracing elements 5.4.1 Shear forces and bending moments 5.4.2 Torsional moments 5.5 Streses in the bracing elements 5.6 Concentrated force at top level; single-storey buildings 5.7 Buildings with I =0, subjected to uniformly distributed xy horizontal load 5.8 Worked example: a 6-storey building in London 5.8.1 Model: individual shear wals 5.8.2 Model: built-up shear wals and cores © 2000 Karoly A. Zalka 5.9 Suplementary remarks 5.9.1 Frameworks and coupled shear wals 5.9.2 Bracing systems with shear or a mixture of shear and bending deformations 5.9.3 Special cases—scope for simplification 5.9.4 Second-order efects 5.9.5 Soil-structure interaction 6 Ilustrative example; Qualitative and quantitative evaluation 6.1 Case 1 6.1.1 Critical load 6.1.2 Fundamental frequency 6.1.3 Maximum streses and deformations 6.2 Case 2 6.2.1 Critical load 6.2.2 Fundamental frequency 6.2.3 Maximum streses and deformations 6.3 Case 3 6.3.1 Critical load 6.3.2 Fundamental frequency 6.3.3 Maximum streses and deformations 6.4 Evaluation 7 Global critical load ratio 7.1 Global critical load ratio—Global safety factor 7.2 Global critical load ratio—Performance indicator 7.3 Further aplications 8 Use of frequency measurements for the global analysis 8.1 Stifneses 8.2 Critical loads 8.2.1 Multistorey buildings under uniformly distributed floor load 8.2.2 Concentrated top load; single-storey buildings 8.3 Deformations 8.3.1 Multistorey buildings subjected to horizontal load of trapezoidal distribution 8.3.2 Concentrated force at top level; single-storey buildings 8.3.3 Deformations of the building © 2000 Karoly A. Zalka 9 Equivalent wall for frameworks; Buckling analysis of planar structures 9.1 Introduction 9.2 Characteristic deformations, stiffnesses and part critical loads 9.3 Frameworks on fixed suports 9.3.1 The aplication of sumation theorems 9.3.2 The continum model 9.3.3 The sandwich model 9.3.4 Design formulae 9.4 Frameworks on pined suports 9.4.1 Frameworks without ground flor beams 9.4.2 Frameworks with ground flor beams 9.5 Frameworks with ground flor columns of diferent height 9.6 Analysis of coupled shear wals by the frame model 9.7 Frameworks with cros-bracing 9.7.1 Shear stifnes and shear critical load 9.7.2 Critical loads 9.7.3 Structures with global regularity 9.8 Infiled frameworks 9.9 Equivalent wal for 3-dimensional analysis 9.10 Shear wals 9.1 Symetrical cros-wal system buildings 9.12 Planar bracing elements: a comparison 9.13 Suplementary remarks 10 Test results and acuracy analysis 10.1 Description of the models 10.2 Horizontal load on Model ‘M1’ 10.3 Horizontal load on Model ‘M2’ 10.4 Comparative analysis of the formulae for horizontal load 10.5 Dynamic tests 10.6 Stability tests 10.6.1 Model ‘M1’ 10.6.2 Model ‘M2’ 10.6.3 Deformation of the bracing elements 1 Evaluation; design guidelines 1.1 Spatial behaviour 1.2 Stability analysis 1.3 Frequency analysis © 2000 Karoly A. Zalka 1.4 Streses and deformations 1.5 Structural performance of the bracing system 1.6 Stability of planar structures 1.6.1 Low-rise to medium-rise (4–25-storey) structures 1.6.2 Tal (over 25-storey) structures 1.6.3 Structural performance of planar bracing elements Apendix A Cros-sectional characteristics for bracing elements Appendix B The generalized power series method for eigenvalue problems Apendix C Mode coupling parameter κ References Further reading © 2000 Karoly A. Zalka Preface A shift in emphasis can be seen in the approach to structural design. More often structures are looked at ‘globally’, as whole structural units, rather than a group of individual elements. The investigation of this global behaviour, also described as ‘holistic’ or ‘whole building’ behaviour has been made possible by new theoretical achievements and the spectacular advance in computer technology during the last decades. The global structural analysis of buildings can be carried out following two routes. First, sophisticated and complex computer packages based on the finite element method offer endless facilities and can handle even huge structures with a great number of elements. Second, analytical methods can also deal with whole structures leading to simple closed-form solutions, with the additional benefit of providing fast checking facilities for the computer-based methods. This book follows the latter route and, after describing and solving the complex theoretical problems of bracing systems covering many practical cases, intends to achieve the following three objectives: • To present simple procedures and closed-form formulae which make it possible for the practising structural engineer to carry out a general structural analysis of the bracing system of building structures in minutes. • To show that the main areas of structural design (stability, stress and frequency analyses) are not independent; indeed they can be linked by the global critical load ratio which can be used to achieve optimum structural solutions with high performance and adequate safety. • To help to understand global behaviour better and to develop structural engineering common sense through the introduction of the most representative stiffness characteristics for the stability, stress and frequency analyses. © 2000 Karoly A. Zalka Notations CAPITAL LETTERS A cross-sectional area; area of the plan of the building; floor area Aa area of lower flange Ab cross-section of beams Ac cross-section of columns Ad cross-section of diagonal bars in cross-bracing Ah cross-section of horizontal bars in cross-bracing Af area of upper flange; contact area between foundation and soil Ag area of web Ai cross-sectional area of the ith bracing element Aj incremental area Ao area of closed cross-section defined by the middle line of the walls Aref reference area for the force coefficient B plan breadth of the building (in direction y) C centre of vertical load; centroid C1, C2, C3, C4 constants of integration E modulus of elasticity Eb modulus of elasticity of beams Ec modulus of elasticity of columns Ed modulus of elasticity of diagonal bars in cross-bracing Eh modulus of elasticity of horizontal bars in cross-bracing F concentrated load (on top floor level); horizontal force Fcr critical concentrated load Fcr,X, Fcr,Y critical concentrated load in directions X and Y Fcr, ϕ critical concentrated load for pure torsional buckling Fg full-height (global) bending critical concentrated load Fi vertical load on the ith bracing element/framework; vertical force at xi, yi Fl local bending critical concentrated load Fm total horizontal load due to misalignment Fx, Fy components of the resultant of the horizontal load in directions x and y Fw global wind force Fw,x,F w,y wind force in directions x and y FWj global wind force for height/width>2 G modulus of elasticity in shear H height of building/frame/coupled shear walls; horizontal force I second moment of area Ib second moment of area of beams © 2000 Karoly A. Zalka