Seismic Effects on Structures PDF
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DEVELOPMENTS IN GEOTECHNICAL ENGINEERING, 67 SEISMIC EFFECTS ON STRUCTURES EMILIA JUHÄSOVÄ Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Czechoslovakia ELSEVIER Amsterdam Oxford — New York — Tokyo 1991 Scientific Editor Ing. Gustav Martinöek, DrSc. Published in co-edition with Veda, Publishing House of the Slovak Academy of Sciences, Bratislava Distribution of this book is being handled by the following publishers for the U.S.A. and Canada Elsevier Science Publishing Company, Inc. 655 Avenue of the Americas New York, N.Y. 10010 for the East European countries, China, Northern Korea, Cuba, Vietnam and Mongolia Veda, Publishing House of the Slovak Academy of Sciences Klemensova 19, 814 30 Bratislava, Czechoslovakia for all remaining areas Elsevier Science Publishers 25 Sara Burgerhartstraat P.O. Box 211, 1000 AE Amsterdam, The Netherlands Library off Congress Cataloging-in-Publication Data Juhäsovä, Emilia. Seismic effects on structures/Emilia Juhäsovä. p. cm. (Developments in geotechnical engineering; 67) Translated from the Slovak by Daniela Kardosovä. Includes bibliographical references and index. ISBN 0-444-98743-6 1. Earthquake engineering. 2. Earthquake resistant design. 3. Buildings Earthquake effects. I. Title. II. Series. TA654.6.J84 1991 624.1762- -dc20 91-2203 CIP ISBN 0-444-98743-6 (Vol. 67) ISBN 0-444-41662-5 (Series) ISBN 80-224-0238-9 (Veda) © Emilia Juhäsovä, 1991 Translation © Daniela Kardosovä, 1991 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 prior permission of the copyright owner. Printed in Czechoslovakia Further titles in this series 1. G. SANGLERAT — THE PENETROMETER AND SOIL EXPLORATION 2. Q. ZÄRUBA AND V. MENCL — LANDSLIDES AND THEIR CONTROL 3. Ε. E. WAHLSTROM — TUNNELING IN ROCK 4. R. SILVESTER — COASTAL ENGINEERING, 1 and 2 5. R. N. YONG AND B. P. WARKENTIN — SOIL PROPERTIES AND BEHAVIOUR 6. Ε. E. WAHLSTROM — DAMS, DAM FOUNDATIONS, AND RESERVOIR SITES 7. W. F. CHEN — LIMIT ANALYSIS AND SOIL PLASTICITY 8. L N. PERSON — ROCK DYNAMICS AND GEOPHYSICAL EXPLORATION Introduction to Stress Waves in Rocks 9. M. D. GIDIGASU — LATERITE SOIL ENGINEERING 10. Q. ZÄRUBA AND V. MENCL — ENGINEERING GEOLOGY 11. Η. K. GUPTA AND Β. K. RASTOGI — DAMS AND EARTHQUAKES 12. F. H. CHEN — FOUNDATIONS ON EXPANSIVE SOILS 13. L. HOBST AND J. ZAJI'C — ANCHORING IN ROCK 14. B. VOIGHT (Editor) — ROCKSLIDES AND AVALANCHES, 1 and 2 15. C. LOMNITZ AND E. ROSENBLUETH (Editors) — SEISMIC RISK AND ENGINEERING DECI SIONS 16. C. A. BAAR — APPLIED SALT-ROCK MECHANICS, 1 The In-Situ Behavior of Salt Rocks 17. A. P. S. SELVADURAI — ELASTIC ANALYSIS OF SOIL-FOUNDATION INTERACTION 18. J. FEDA — STRESS IN SUBSOIL AND METHODS OF FINAL SETTLEMENT CALCULATION 19. A KEZDI — STABILIZED EARTH ROADS 20. E. W. BRAND AND R. P. BRENNER (Editors) — SOFT-CLAY ENGINEERING 21. A. MYSLIVEC AND Z. KYSELA — THE BEARING CAPACITY OF BUILDING FOUNDATIONS 22. R. N. CHOWDHURY — SLOPE ANALYSIS 23. P. BRUUN — STABILITY OF TIDAL INLETS Theory and Engineering 24. Ζ. BA2ANT — METHODS OF FOUNDATION ENGINEERING 25. Ä. KEZDI — SOIL PHYSICS Selected Topics 26. H. L. JESSBERGER (Editor) — GROUND FREEZING 27. D. STEPHENSON — ROCKFILL IN HYDRAULIC ENGINEERING 28. P. E. FRIVIK, N. JANBU, R. SAETERSDAL AND L I. FINBORUD (Editors) — GROUND FREEZING 1980 29. P. PETER — CANALS AND RIVER LEVIES 30. J. FEDA — MECHANICS OF PARTICULATE MATERIALS The Principles 31. Q. ZÄRUBA AND V. MENCL — LANDSLIDES AND THEIR CONTROL Second, completely revised edition 32. I. W. FARMER (Editor) — STRATA MECHANICS 33. L. HOBST AND J. ZAJIC — ANCHORING IN ROCK AND SOIL Second, completely revised edition 34. G. SANGLERAT, G. OLIVARI AND B. CAMBOU — PRACTICAL PROBLEMS IN SOIL ME CHANICS AND FOUNDATION ENGINEERING, 1 and 2 35. L. RfiTHÄTI — GROUNDWATER IN CIVIL ENGINEERING 36. S. S. VYALOV — RHEOLOGICAL FUNDAMENTALS OF SOIL MECHANICS 37. P. BRUUN (Editor) — DESIGN AND CONSTRUCTION OF MOUNDS FOR BREAKWATERS AND COASTAL PROTECTION 38. W. K. CHEN AND G. Y. BALADI — SOIL PLASTICITY Theory and Implementation 39. Ε. T. HANRAHAN — THE GEOTECHNICS OF REAL MATERIALS The e, e method g k 40. J. ALDORF AND K. EXNER — MINE OPENINGS Stability and Support 41. J. E. GILLOTT — CLAY IN ENGINEERING GEOLOGY 42. A. S. CAKMAK (Editor) — SOIL DYNAMICS AND LIQUEFACTION 43. A. S. CAKMAN (Editor) — SOIL-STRUCTURE INTERACTION 44. A. S. CAKMAK (Editor) — GROUND MOTION AND ENGINEERING SEISMOLOGY 45. A. S. CAKMAK (Editor) — STRUCTURES, UNDERGROUND STRUCTURES, DAMS AND STOCHASTIC METHODS 46. L. RETHÄTI — PROBABILISTIC SOLUTIONS IN GEOTECHNICS 47. Β. M. DAS — THEORETICAL FOUNDATION ENGINEERING 48. W. DERSKI, R. IZBICKI, I. KISIEL AND Z. MROZ — ROCK AND SOIL MECHANICS 49. T. ARIMAN, H. HAMADA, A. C. SINGHAL, M. A. HAROUN AND A. S. CAKMAK (Editors) — RECENT ADVANCES IN LIFELINE EARTHQUAKE ENGINEERING 50. Β. M. DAS — EARTH ANCHORS 51. K. THIEL — ROCK MECHANICS IN HYDROENGINEERING 52. W. F. CHEN AND X. L. LIU — LIMIT ANALYSIS IN SOIL MECHANICS Second, completely revised edition 53. W. F. CHEN AND E. MIZUNO — NONLINEAR ANALYSIS IN SOIL MECHANICS 54. F. H. CHEN — FOUNDATIONS ON EXPANSIVE SOILS Second, completely revised edition 55. J. VERFEL — ROCK GROUTING AND DIAPHRAGM WALL CONSTRUCTION 56. Β. N. WHITTAKER AND D. J. REDDISH — SUBSIDENCE Occurrence, Prediction and Control 57. E. NONVEILLER — GROUTING Theory and Practice 58. V. KOLÄR AND I. NEMEC — MODELLING OF SOIL-STRUCTURE INTERACTION 59A. R. S. SINHA — UNDERGROUND STRUCTURES Design and Instrumentation 59B. R. S. SINHA AND L ÖZDEMIR — UNDERGROUND STRUCTURES Instrumentation and Constructions 60. R. L. HARLAN, K. E. KOLM AND E. D. GUTENTAG — WATER-WELL DESIGN AND CONSTRUC TION 61. I. KAZDA — FINITE ELEMENT TECHNIQUES IN GROUNDWATER FLOW STUDIES with applications in hydraulic and geotechnical engineering 62. L. FIALOVSZKY — SURVEYING INSTRUMENTS AND THEIR OPERATIONAL PRINCIPLES 63. H. GIL — THE THEORY OF STRATA MECHANICS 64. Η. K. GUPTA — RESERVOIR INDUCED EARTHQUAKES 65. V. J. LUNARDINI — HEAT TRANSFER WITH FREEZING AND THAWING 66. T. S. NAGARAJ — PRINCIPLES OF TESTING SOILS, ROCKS AND CONCRETE 67. E. JUHÄSOVÄ — SEISMIC EFFECTS ON STRUCTURES PREFACE Earthquake engineering solves a very wide variety of problems of structural dynamics. The most important of them are how to analyse the behaviour of engineering structures under the effects of dynamic motions in subsoil, how to work out and apply suitable computation methods for the seismic response solution and how to protect the structures against undesirable seismic effects. This relatively young branch of science has originated at the boundaries of structural mechanics, engineering seismology, random process theory and other related sciences. Theory and practice of earthquake engineering have been growing very rapidly in the last decades. This is connected with the possibilities of powerful computers which are exploited for the solution of exacting problems of non-linear and non-stationary seismic response and also with the progress in laboratory equipments and simulation techniques using electrohydraulically controlled loading systems and seismic shaking tables. Interest in the methods of earthquake engineering is increasing also in the countries with lower occur rence of strong seismic motions, and this is connected with the construction of modern nuclear power plants and with the protection of their mechanical and electrical equipment against extraordinary loading events. Natural tectonic earthquakes have a wide variety of origins and occurrences. They are random with short-time duration and with variable frequency and amplitude, and are non-stationary. Therefore, it is very important to obtain the largest amount of information about the potential seismic motions in the given region or building site and for the given geological-tectonic conditions. The basic information about the seismic response to the actual seismic motion can be obtained from seismic response spectra. It is advantageous to complete the basic spectral characteristics by the computation of other comple menting quantities and by multi-mode seismic response spectra for represen tative computation dynamic models. All knowledge about seismicity including weak earthquakes and microtremor of soils from technical seismic sources is important. Also methods of synthetic seismic accelerogram simulations give some possibility of spreading knowledge about potential future seismic motions in the investigated site region. If we want to forecast and calculate the seismic response of structures viii satisfactorily we must first know the dynamic properties of different types of structures. Such knowledge can be obtained by the application of dynamic excitation methods on full-scale structures with measurement of response to obtain natural frequencies and modes of vibration together with damping parameters. Methods of natural frequencies and modes computation as well as those of seismic response analysis should be verified by the dynamic behaviour of full-scale structures, or by the response of models, structural elements or their parts in laboratory conditions using shaking table loading. The more detailed analysis of torsional seismic effects and seismic response of column elements with higher axial compression has resulted from experience of failure development in new modern structural systems caused by strong seismic motion. There still remain the questions of non-linear seismic response while taking into account the peculiarities of stiffness and damping non-lineari ties and the demands of proper seismic design and the protecting of structures against unfavourable seismic effects. When the seismic motions are too strong there is a need to protect the structures by the help of special devices such as spring-dashpot systems, elas- tomeric bearing systems, sliding systems or other response reduction systems. Different types of protection systems are mainly necessary to preserve at least the most important parts of significant structures. The concept of the book is intended to serve both readers who are acquainted with the problems of earthquake engineering and also for the beginners in this field. It is essential in proper seismic design to understand the principles of the seismic response of the structure in order to avoid in the design any weak places in the structure, and depending on the importance of the structure to include a sufficient degree of seismic resistance. One of the aims of this book is to provide help in this field. Emilia Juhäsovä LIST OF SYMBOLS a a — increment coefficients of seismic acceleration 71 ? a A — amplitude of deflection of harmonic seismic motion; auxiliary mode coefficient A, — cross-section area of the i-th element AF{u) — absolute distribution function A,(t, τ) — autocorrelation function of non-stationary process b — width of cross-section Κ — thickness of the web of I cross-section Β — amplitude of deflection of harmonic seismic motion B, B — dimensions of building in plan x y Ci\-> ca — increment coefficients of seismic velocity c — Love wave velocity L Cp — longitudinal wave velocity C — Rayleigh wave velocity R C — shear wave velocity s Cov(x, y) — correlation moment (covariance) d i — distance of the i-th element from the axis of prin cipal carrying element e — eccentricity in asymmetric systems in jc-direction χ e e — eccentricity in asymmetric systems in ^-direction y y Ε — modulus of elasticity E(x) — mean value E(x y) — mixed moment of the 2nd order 9 f — frequency — y'-th natural frequency fj fx — first natural frequency m — probability density F(x) — distribution function F(S) — standard seismic force 'J FS ω — Fourier amplitude spectrum G — shear modulus of elasticity h — height of section XU κ height of the web of I cross-section Η height of the building Η(ϊω) frequency characteristic I inertial modulus of mass [Ι\ unit diagonal matrix j subscript of natural mode J, inertial moment of the i-th element J inertial moment of the girder in walls with openings l J inertial moment of the frame girder P J inertial moment of the frame column s Λ, sectional moment of inertia in torsion-bending k damping coefficient D [k] damping matrix D k increment coefficients of seismic deflection a Κ stiffness [Κ] stiffness matrix Κ, stiffness of the i-th element in simple torsion Κ base standard seismic coefficient s κ stiffness in χ-, ^-directions y κ stiffness in displacement of the base 3 Κ torsional stiffness Θ stiffness in tilting of the base K. r 1 height of the element l, height of the i-th storey of building l. height of the base m concentrated mass Μ mass matrix Μ bending moment Μ limit elastic bending moment el Μ plastic bending moment pl η number of storeys number of cycles with extreme amplitude c N mode coefficient J j Ν IS, N2S generalized multi-mode standard spectra Ρ(Α) probability q (0, qqjj{{tt)),, qq))((tt)) generalized time-histories of the y'-th mode when j solving in relative coordinates ϊϊ;;((ίί)),, ??,,(('')),, ##((00 generalized time-histories of the y'-th mode when solving in absolute coordinates weight force of the i-th storey ß, critical axial force ßcr r radius of the i-th circular element I r 1/5 r 2i external, internal radius of the circular tube element R epicentral distance xiii R correlation function of the stationary process ΕΞ autocorrelation function of the stationary process JCJC S static moment 5 5 seismic response spectrum of acceleration, deflec a? d> ν tion and velocity S pseudovelocity seismic response spectrum pv s reduced rest spectrum of seismic response dr Ss r»s os os os multi-mode (s-mode) seismic response spectrum of D, OV, OA, OS, O W deflection, velocity, acceleration, shear force and bending moment ue resulting standard force or deformation seismic max, ι effect S((o), S (<o) power spectral density xy xx S (tf) power spectral density of a non-stationary Xl 9 process S(z t) shear force at level z, in time t h t time arrival time of m-th wave mode trim Τ period of vibration 7: y-th natural period of vibration j Ά first natural period of vibration U amplitude of steady harmonic motion Μ deflection matrix ο vector of y-th natural mode of a discrete system 7 limit elastic deflection "el ultimate deflection 1/ m resonant amplitude «R amplitude of free damped vibration "ο, U(t), !i(0, ö(0 time-history of relative deflection, velocity and acce leration of single mass system in x-direction {«(OK {ώ(0}, [w vectors of relative deflections, velocities and acce lerations of discrete systems in the x-direction relative deflection, velocity and acceleration of con u(z, t\ u(z, t), u(z, t) tinuous mass systems in the x-direction y-th natural mode of a continuous system u?(z) group velocity for the m-th wave mode U(co) m n external horizontal forces acting on a frame system Κ, Κ V ν v time-history of relative deflection, velocity and acce leration of a single mass system in the ^-direction elastic sectional modulus el v(t% v(t\ v(t) plastic sectional modulus coordinate axis in asymmetrical systems x, y, x y 9 coordinate of the i-th element of asymmetrical sys X ι' I tem xiv χ (ή, χ (ή, χ (ή — time-history of deflection, velocity and acceleration of seismic motion in x-direction x(t) — stationary random process s X(t) — random process ζ — coordinate axis in the vertical direction a — moment of the 3rd degree x3 a — moment of the 4th degree xA Sj — dynamic standard coefficient for-the y-th mode of vibration Af — increment of frequency At — time increment Δω — increment of angular frequency £, — limit elastic strain e €j — y-th damped angular frequency e — ultimate strain m ε — first damped angular frequency χ ζ — damping ratio Ό ζ — damping ratio for elastic region Ό ζ — equivalent damping ratio for the non-linear region Ό η — standard modal coefficient υ 9 — logarithmic decrement of damping Θ — parameter of Wilson method 0(0, (Ο, (Ο — time history of torsional angle, angular velocity and angular acceleration of asymmetrical systems Xj — shape coefficient of shear deformation of the i-th element A — frequency ratio Ay — y-th frequency number μ — mass of unit length of element v, — damping degree ξξ{ (ί)Ο, , ξ((ΐΟ),, ξ (t) — time-history of absolute deflection, velocity and acceleration of a single mass system in the x-direc- tion { ξ (Ο { ζ ((Ο0} — vectors of absolute deflections, velocities and acce 9 lerations of a discrete system in the x-direction ξ(ζ, /), ξ (ζ, t), ξ (ζ, ή — absolute deflection, velocity and acceleration of a continuous system in the x-direction ρ — density, unit volume mass σ, — limit elastic stress 6 σ — root mean square deviation χ σ — mean square deviation χ τ — parameter of time <pi — rotation of frame node Φ„, (pj — phase shift
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