Page 79 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 71

K y X
(2.21)
T xy ¼ M x X X
2
K x Y + K y X 2
K x Y
(2.22)
T yx ¼ M y X X
2
K x Y + K y X 2
K y X
(2.23)
T yy ¼ M y X X
2
K x Y + K y X 2
where:
The calculations of shear force demand due to torsion for Wall#1 are as
follows:
2,986,473 0 8:92Þ
ð
T xx ¼ 2,375,496 ¼ 342kg
184,952,682,631
T xy ¼ 0
ð
2,986,473 0 8:92Þ
T yx ¼ 625,852 ¼ 902kg
184,952,682,631
T yy ¼ 0
The generated demand force in each wall depends on the relative stiffness of
that particular wall with respect to that of the other walls in that story which are
parallel to this wall. The participation factor of each wall in masonry buildings
with rigid diaphragm from the shear force demand is calculated according to
Eq. (2.24).
K i
PF ¼ X n (2.24)
K i
i¼1
where:
K i is the wall’s stiffness. The walls’ participation factors and also demand
forces are presented in Appendix-A Table A-C-2-5 and Table A-C-2-6,
respectively.
As an example, the generated demand forces in Wall#1 are determined as
follows:
2,986,473
PF ¼ ¼ 0:39%
760,987,984
f U i ¼ PF F U
f UD 1 ¼ 0:39% 2156 ¼ 8:4 Ton
f UF 1 ¼ 0:39% 765 ¼ 3:0 Ton

Q UD ¼ Max f UD , f UD + T xx + T yx