Page 116 - Advanced Design Examples of Seismic Retrofit of Structures

108 Advanced Design Examples of Seismic Retrofit of Structures

f y and A v ¼yield strength of reinforcement steel and area of each shear rein-
forcement element in steel grid, respectively;
H ¼wall’s height;
S ¼distance of the horizontal reinforcement;
P u ¼vertical loads on the wall according to a proper load combination; and
α ¼coefficient which takes into account the effects of reinforcement on the
shear strength of masonry as Eq. (2.54):
(2.54)
α ¼ Φ 1 Φ 2
15nd b
Φ 1 ¼ 1 (2.55)
L w
7:5qd b
Φ 2 ¼ 1 (2.56)
t m
where:
n ¼total number of shear reinforcement bars in the section;
d b ¼diameter of the reinforcement elements in steel grid;
q ¼factor which is 1.0 for one-sided shotcrete and 2.0 for two-sided
shotcrete; and
t m ¼thickness of masonry.

Sliding Based on Ghiassi et al. [50], the relation for determination of sliding
failure of shotcreted masonry walls which is an adaptation of FEMA306 [53]
relation for determination of sliding failure capacity of reinforced masonry
walls is based on Eq. (2.57). This equation includes the terms related to masonry
friction and concrete friction; the assumed values of the frictional coefficient for
masonry and concrete are 0.7 and 0.9, respectively.
(2.57)
V sliding ¼ 0:7P u +0:9A v f y

m-Factors for Linear Static Analysis
As previously stated, design codes are silent about the shotcreted URM walls in
terms of introducing their failure modes, providing relations for determination
of their strength, and their deformation capacity and acceptance criteria. By
studying the results of several previously performed test data, Ghiassi et al.
[50] proposed m-factors for linear static analysis. In this example, these pro-
posed factors shown in Table 2.14 for various failure modes and performance
levels are taken into account.

2.8.4.4 Results
The vulnerability of the walls (unretrofitted and shotcreted) of the example
building in the two stories under various diaphragm conditions are shown in
Figs. 2.56–2.58. In these figures, the vulnerable walls are shown in blue.