Three-Dimensional Static and Dynamic Analysis of Structures
UJX=lh.o A Physical Approach With Emphasis on Earthquake Engineering
?g5u#Q> ! t'F_1P^*/ by
! _|rVg. Edward L. Wilson
tHj |_t Professor Emeritus of Structural Engineering
>[U.P)7; University of California at Berkeley
=`oQcIkz }?vc1%w Copyright Computers and Structures, Inc., 1996-2001
dLtn,qCX0^ The CSI Logo is a trademark of Computers and Structures, Inc.
O [81nlhS0 SAP90, SAP2000, SAFE, FLOOR and ETABS are trademarks of
Q6r!=yOEY Computers and Structures, Inc.
yye( ^ ISBN 0-923907-00-9
<f'2dT@6 -}W ` Preface To Third Edition
\~YyY'J This edition of the book contains corrections and additions to the July 1998 edition.
D}| 30s?u1 Most of the new material that has been added is in response to questions and comments
6a=Y_fma from the users of SAP2000, ETABS and SAFE.
ezOZHY>|# Chapter 22 has been written on the direct use of absolute earthquake displacement
W97%12J3 loading acting at the base of the structure. Several new types of numerical errors for
o=,q4;R ' absolute displacement loading have been identified. First, the fundamental nature of
#Ang8O@y displacement loading is significantly different from the base acceleration loading
J6) &b7 traditionally used in earthquake engineering. Second, a smaller integration time step is
nO d '$q required to define the earthquake displacement and to solve the dynamic equilibrium
>;;tX3( equations. Third, a large number of modes are required for absolute displacement
EK:s# loading to obtain the same accuracy as produced when base acceleration is used as the
pNHO;N[& loading. Fourth, the 90 percent mass participation rule, intended to assure accuracy of
&Vtgh3I the analysis, does not apply for absolute displacement loading. Finally, the effective
P9RIX;A= modal damping for displacement loading is larger than when acceleration loading is
gmY*}d`
'f used.
2[*r9%W To reduce those errors associated with displacement loading, a higher order integration
LcA~ a<_ method based on a cubic variation of loads within a time step is introduced in Chapter
\*_@`1m 13. In addition, static and dynamic participation factors have been defined that allow the
l9 |x7GB structural engineer to minimize the errors associated with displacement type loading. In
PUdJ>U addition, Chapter 19 on viscous damping has been expanded to illustrate the physical
0F\ e*{gc effects of modal damping on the results of a dynamic analysis.
l u^fKQ Appendix H, on the speed of modern personal computers, has been updated. It is now
LQnkpy3A possible to purchase a personal computer for approximately $1,500 that is 25 times
Jhyb{i8RR faster than a $10,000,000 CRAY computer produced in 1974.
wM^_pah#Y5 Several other additions and modifications have been made in this printing. Please send
*$KUnd-T your comments and questions to
ed@csiberkeley.com.
g8_C|lVZi Edward L. Wilson
bYKyR}e April 2000
