Page 192 - Design of Reinforced Masonry Structures

4.56 CHAPTER FOUR

4.10 DESIGN FOR SHEAR IN REINFORCED
MASONRY BEAMS

4.10.1 MSJC Provisions for Estimating Shear Strength of a Masonry Beam
The provisions for shear strength of reinforced masonry beams are covered by MSJC-08
Section 3.3.4.1.2, which are discussed in this section.
Masonry beams without any shear reinforcement are capable of providing a certain
amount of resistance to shear in beams caused by transverse loads. Tests indicate that the
shear resistance of masonry depends on the following parameters:
′
1. Compressive strength of masonry (varies with f )
m
2. Net cross-sectional area of masonry
3. Shear span-to-depth ratio (a dimensionless parameter), M /V d
u v
u
4. Axial force, if any, in the member
The beneficial effect due to the presence of axial load occurs because of the resulting
improved aggregate interlock. This benefit does not apply to transversely loaded members
such as beams and lintels, however, because those members are subjected to negligible
axial loads.
Accordingly, the nominal shear resistance V of masonry alone is given by Eq. (4.91)
nm
[MSJC-08 Eq. (3.22)]:
⎡ ⎛ M ⎞ ⎤
V = ⎢ 40 175. − . ⎜ u ⎟ ⎥ A f ′ + 025. P (4.91)
nm ⎝ Vd ⎠ n m u
⎣ u v ⎦
where V = nominal shear strength of the masonry (alone)
nm
M = factored moment in the beam
u
V = shear due to factored loads
u
d = depth of the beam in the direction of the shear considered
v
A = net cross-sectional area of masonry member
n
P = factored axial load (if present)
u
Equation (4.91) is based the on research. The value of shear-span to depth ratio, M /V d ,
u v
u
is to be taken as a positive number and need not be taken greater than 1.0 (MSJC-08
Section 3.3.4.1.2.1).
Equation (4.91) shows that increasing the ratio M /V d has an adverse influence on
u
u v
the nominal shear strength of a masonry beam. Regardless of the amount of transverse
reinforcement provided in the beam, the maximum value of its nominal shear strength V

n
is limited by MSJC-08 Eqs. (3-19) and (3-20) as follows:
1. Where M / V d ≤ 0.25,
u v
u
V ≤ 6 A n f ′ m (4.92)
n
2. Where M / V d ≥ 1.00,
u u v
V ≤ 4 A n f ′ m (4.93)
n
3. Values of V given by Eqs. (4.92) and (4.93) are the maximum values of V for the speci-
n
n
fied limits of M /V d ratios. For M /V d ratios between 0.25 and 1.0, the value of V is
n
u v
u
u
u v