Page 529 - Design of Reinforced Masonry Structures

SHEAR WALLS 7.91

and (2) the other above this region. Shear strengths of these two regions are determined
separately as follows:
1. For all cross sections within a region defined by the base of the shear wall and a plane
at a distance L (wall length) above the base, the nominal shear strength is to be deter-
w
mined from Eq. (7.76):
V = A r f (7.76)
n n n y
where V = nominal shear strength, lb (kN)
n
2
2
A = L t = net cross-sectional area of masonry, in. (mm )
n w
r = ratio of distributed shear reinforcement on plane perpendicular to plane of A
n n
f = yield strength of steel reinforcement
y
The value of r in Eq. (7.76) can be expressed as
n
w
ρ = total area horizontal shear reinforcement t = LA v /s (7.77)
n
net area of masonry Lt
w
where L = length of wall, in. (mm)
w
A = cross-sectional area of one horizontal shear reinforcement bar
v
s = spacing of horizontal shear reinforcement
Substitution for r from Eq. (7.77) into Eq. (7.76) yields
n
Lf A
V = wy v (7.78)
n
s
The total factored shear force for designing the region of plastic hinging is deter-
mined at a distance equal to the smaller of L /2 or one-half the story height above the
w
base of the shear wall.
2. For the region above that of plastic hinging, the nominal shear strength is determined
as specified in MSJC-08 Section 3.3.4.1.2 [Eqs. (3-19) through (3-22)] and is discussed
in Chap. 4. The nominal shear strength above the plastic hinge region, V , is obtained
n
as the sum of the nominal shear strengths of masonry, V , and the nominal strength of
m
reinforcement, V , as follows:
s
V = V + V (7.79)
n m s
The nominal shear strength V in Eq. (7.79) is subject to the following limitations
n
based on M /V d ratio:
u
u v
(a) Where M /V d ≤ 0.25

u
u v
V = 6 A f ′ (7.80)
n n m
(b) Where M /V d ≥ 1.0
u
u v
V = 4 A f ′ (7.81)
n n m
(c) The value of V may be interpolated for the condition: 0.25 < M /V d < 1.0
n u u v
The nominal strength of masonry, V , is determined from Eq. (7.82):
m
⎡ ⎛ M ⎞ ⎤
V = ⎢ 40 175. − . ⎜ u ⎟ ⎥ A n f ′ + 025. P (7.82)
u
m
m
⎣ ⎝ Vd ⎠
v ⎦
u