Page 61 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 53

(1) Based on Eq. (2.2):

ð
25 R u 1Þ
T 0:2 ! C 1 ¼ 1+
a
R u 1 (2.2)
0:2 < T 1 ! C 1 ¼ 1+ 2
aT
T > 1 ! C 1 ¼ 1
where:
a ¼site class factor;
¼ 130 site Class A or B according to ASCE 41-13 [2];
¼ 90 site Class C;
¼ 60 site Class D, E, or F;
T ¼fundamental period of the building in the direction under consideration,
calculated in accordance with Section 1.7 of Code 360, including modifica-
tion for Soil-Structural Interaction (SSI) effects of Section 3.2.6 of this
document; and
R u ¼ratio of elastic strength demand to yield strength coefficient calculated
in accordance with Eq. (2.3). If the elastic base shear capacity substituted V e is
available, Eq. (2.4) can be used interchangeably.

DCR max
R u ¼ C m 1 (2.3)
1:5
S a
R u ¼ C m (2.4)
V e =W
where DCR max is the largest demand to capacity ratio (DCR) computed for any
primary component of a building in the direction of response under consider-
ation, taking C 1 ¼ C 2 ¼ C m ¼1.0.
(2) Based on Eq. (2.5) when R u cannot be determined:
T s T
1 C 1 ¼ 1+ (2.5)
2T s 0:2
For the example building, the natural period of the first mode of vibration is
0.2. The coefficient C 1 is determined as:
0:7 0:2
C 1 ¼ 1+ ¼ 1:41
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 can be determined
based on either of these methods.
(1) Based on Eq. (2.6).
ð
25 R u 1Þ
T 0:7 ! C 2 ¼ 1+
a
2 (2.6)

1 R u 1

T 0:7 ! C 2 ¼ 1+
800 T