Optimal Performance- Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 181

S
V W C

pushover analysis, the capacity curve, to usable
data as of nonlinear dynamic analysis.

R =

a

(8)

m

y

The Coefficient Method

V y is yield strength calculated using nonlinear
static pushover analysis.

In the coefficient method that is recommended by
FEMA273, FEMA356 and ASCE41, the target
displacement, δ t at roof level, shall be calcu-
lated in accordance with an equation similar to
Eq. (6). The internal forces and deformation of
every component will be accordingly obtained.
The coefficients C i and S a , have slightly differ-
ent definitions in these references, but they are
essentially the same. According to ASCE41, that
is believed to provide better results compared to
FEMA356, the target displacement is obtained
from the following equation.

W is effective seismic weight.

C m is effective mass factor and is given in a
table in ASCE41.

S a is the response spectrum acceleration, at the
effective fundamental period and damping ratio of
the building in the direction under consideration.
It is shown graphically in Figure 1 in which Ts
is characteristic period of response spectrum and
B1 is obtained from B1 = 4/[5.6 - ln(100β)] and
β is effective viscose damping ratio.
C 2 is the adjustment factor to represent the
effect of pinched hysteretic shape, cyclic stiffness
degradation and strength deterioration on maxi-
mum displacement response. For T e >0.7 sec,
C2= 1.

T

2

δ = C C C S

e

g (6)

t a

0 1 2

π

2

4

where:
T e is the effective fundamental period of build-
ing in the direction under consideration. (clause
3.3.3.2.6)
C 0 is the modification factor to relate spectral
displacement of an equivalent SDOF system to the
roof displacement of the MDOF building system.
C 1 is modification factor to relate expected
maximum inelastic displacements to displace-
ments calculated for linear elastic response. It is
calculated from the following equation. According
to ASCE41, some limitations apply.

2

R
T e

− 1

800

1

C = + (9)

1

2

Figure 1. General horizontal response spectrum

( R − 1 )

C = + 1 (7)

1 2

α T e

α is site class factor given by ASCE41.

R is the ratio of elastic strength demand to cal-
culated yield strength.