Table Of ContentDEVELOPMENTS 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
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for all remaining areas
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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
