Page 304 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Steel Frame Building Retrofitted Chapter 5 293

T s T
1 C 1 ¼ 1+ (5.9)
2T s 0:2
C 2 ¼Modification factor to represent the effect of pinched hysteresis shape,
cyclic stiffness degradation, and strength deterioration on maximum displace-
ment response. Based on Code 360 [5], this parameter is can be determined
based on either of these methods.
(1) Based on Eq. (5.10)

ð
25 R u 1Þ
T 0:7 ! C 2 ¼ 1+
a
2
1 R u 1
T 0:7 ! C 2 ¼ 1+ (5.10)
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. C m is 1.0 for the steel frames with
concentric braces and also the main buildings (simple frame with masonry
infill) which is categorized as “Other” structural systems in this table.
For determination of the buildings natural period, the recommended relation
in Eq. (5.11) in Standard 2800 is used which is categorized as “Other” structural
systems.
3
T ¼ 0:05 HðÞ 4 (5.11)

where H is the total height of the building.
3
4 0:75
T ¼ 0:05 HðÞ ¼ 0:05 7:1Þ ¼ 0:21 sðÞ For the main building
ð
3
4 0:75
T ¼ 0:05 HðÞ ¼ 0:05 5:55Þ ¼ 0:18 sðÞ For the sports building
ð
Based on the derived natural periods from the model, we have:
- For the main building
0:7 0:49 0:7 0:42
C 1 xðÞ ¼ 1+ ¼ 1:17, C 1 yðÞ ¼ 1+ ¼ 1:23
1:4 0:2 1:4 0:2
C 2 ¼ 1:0
C m ¼ 1:0
S axðÞ ¼ S ayðÞ ¼ 0:3 2:75 ¼ 0:825

V XðÞ ¼ 0:965 W
)
V YðÞ ¼ 1:02 W