Page 237 - Advanced Design Examples of Seismic Retrofit of Structures

230 Advanced Design Examples of Seismic Retrofit of Structures

(2) Based on Eq. (4.21) when R u cannot be determined:

T s T
1 C 1 ¼ 1+ (4.21)
2T s 0:2
where T s is the natural period at the intersection of the acceleration-sensitive
and velocity-sensitive regions, which for soil type III is 0.7 according to Stan-
dard 2800 [13].
0:7 0:346
C 1 ¼ 1+ ¼ 1:295
2 0:7 0:2

where C 2 ¼modification factor to represent the effect of pinched hysteresis
shape, cyclic stiffness degradation, and strength deterioration on maximum dis-
placement response. Based on Code 360 [10], this parameter is can be deter-
mined based on either of these methods.
(1) Based on Eq. (4.22):

ð
25 R u 1Þ
T 0:7 ! C 2 ¼ 1+
a
2 (4.22)

1 R u 1
T 0:7 ! C 2 ¼ 1+
800 T
(2) In the absence of precise calculations, C 2 can be taken as 1.0.
For the example building, it was assumed that C 2 ¼1.
C m ¼effective mass factor to account for higher modal mass participation
effects obtained from Table 3.4 of Code 360 [10]. C m is 1.0 for the example
building in the transverse direction which is a steel unbraced frame, categorized
as “Other” structural systems in this table. This coefficient is 0.9 for the building
in the longitudinal direction as a three-story braced building.
The design base shear of the example building in the two longitudinal (X)
and transverse (Y) directions are as follows:
V x ¼ 1:295 1:0 1:0 0:9 0:35 2:75 W ¼ 1:12W

V y ¼ 1:295 1:0 1:0 1:0 0:35 2:75 W ¼ 1:25W
The seismic force F x applied at any floor level x shall be determined in
accordance with Eqs. (4.23) and (4.24) [10]:

F x ¼ C vx V (4.23)

w x h k x
C vx ¼ (4.24)
n
X k
w i h
i
i¼1