Page 354 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch08.qxd 9/29/05 5:21 PM Page 8.8

LATERAL-FORCE DESIGN

8.8 CHAPTER EIGHT

predicted for a building for a given earthquake acceleration. The structure is initially elastic, and so
the linear-elastic force-deflection behavior is plotted in the figure. Large infrequent earthquakes
require large seismic design forces for the elastic condition, and it is more economical to design a
building that provides reasonable ductility but significantly reduced building resistance. This nominal
building performance is plotted as a pushover force–deflection curve in the figure. The equal-
displacement hypothesis postulates that the maximum inelastic displacement will be no larger than
the maximum displacement expected if the structure remains elastic. This hypothesis has been examined
by numerous research studies, and it has been shown to be generally valid if the building is not exces-
sively weak, does not have a very short period, and does not exhibit poor inelastic performance. As a
consequence of this observation, seismic design provisions establish reduced seismic design forces and
ductile detailing requirements. The design procedure gives all appearances of being a force-based design
method, but it is really an inelastic deformation design method based on the equal-displacement
hypothesis combined with the detailing requirements of the AISC Seismic Design Provisions.

Seismic Base Shear. The equivalent static force method is the more commonly used method and
is described here. The dynamic method is discussed in greater detail in Art. 8.5. The equivalent sta-
tic force method defines the static shear, V, at the base of the building as
V = C s W (8.6)
2
where W is the total dead load, including permanent equipment, plus a minimum of 10 lb/ft for par-
2
tition loads, snow loads exceeding 30 lb/ft , and at least 25% of floor live loads in storage and ware-
house occupancies. The base is the level at which seismic motions are imparted to the building. The
seismic response coefficient, C S , is
C = SI (8.7a)
DS
s
R
but C S need not exceed
C = SI (8.7b)
D1
s
TR
and C S should not be less than
(8.7c)
C S = 0.044IS DS
In these equations, I is the importance factor for the building, T is the fundamental period of the
building, and R is the response modification factor, which is assigned based on the perceived ductil-
ity of the structural system. Steel structural systems can offer significant ductility, and therefore
R values between 5 and 8 are common. S D1 and S DS are the design spectral response acceleration
at 1-s period and in the short-period range, respectively. Equations (8.7a) and (8.7b) combine to
provide a basic design spectrum as shown in Fig. 8.4. However, the design spectrum may be reduced
for very-short-period structures as shown in the figure. The NEHRP provisions divide structures into
Seismic Design Categories A through E. The division is based on the importance factor of the build-
ing and the severity of the design earthquake ground motion at the site. For structures in Seismic
Design Categories E and F, C S should not be less than

C = 05 . SI (8.7d)
1
s
R
The fundamental period of the structure, T, may be computed by a dynamic analysis or by
approximate equations such as
x
T a = C r h n (8.8)

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