Page 65 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 57

from the adjacent stories contribute to the center of mass of each story. The
details of each wall in calculation of the center of mass are found in
Appendix-A in Table A-C-2-2 and it is not mentioned here for the sake of brev-
ity. As an example, for wall#1 we have:

W Wall ¼ L W H W Ms Wall
W Wall 1 ¼ 0:93 3 740 ¼ 2065kg

M Wi d xi ¼ W Wall i d xi
M W 1 d x1 ¼ 2065 0:46 ¼ 950kgm

M Wi d yi ¼ W Wall i d yi
M W1 d y1 ¼ 2065 0:00 ¼ 0:00kgm
Similarly, the center of mass of the diaphragms based on the information
from Table 2.3 can be determined according to Table 2.6. The coordinates of
the center of mass (COM) for each story taking into account the effects of dia-
phragms and the walls are presented in Table 2.7.
As an example, the calculations for Panel#1 is presented below.

W Diaphragm ¼ L Diaphragm W Diaphragm Ms Diaphragm
W Diaphragm 1 ¼ 22:40 6:5 550 ¼ 80,080kg
M Di d xi ¼ W Diaphragm i d xi
M D 1 d x1 ¼ 80,080 11:025 ¼ 882,882kgm

M Di d yi ¼ W Diaphragm i d yi
M D1 d y1 ¼ 80,080 3:075 ¼ 246,246kgm
Finally, the coordinates of the center of mass of each story are determined.

X X
M Wi d xi + M Di d xi
X CM ¼ X X
W Wall i + W Diaphgragm i
11,492,781 + 8,737,619
X CM 1 ¼ ¼ 22:03m
523,861 + 394,595
12,266,833 + 11,786,888
X CM 2 ¼ ¼ 22:84m
570,237 + 530,991
X X
M Wi d Yi + M Di d Yi
Y CM ¼ X X
W Wall i + W Diaphgragm i
4,623,895 + 3,416,691
Y CM 1 ¼ ¼ 8:75m
523,861 + 394,595
5,054,931 + 4,539,196
Y CM 2 ¼ ¼ 8:71m
570,237 + 530,991