Page 197 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.61

b. Higher compressive strength of masonry: Calculate the required value of ′ f
m
from Eq. (4.93) by substituting fV = V .
n
u
)
φV = (0 8 4.( ) A n f ′ = 24 000, lb
m
n
,
f ′ = 24 000 = 49 15
.
m
08)(4 7 63 20)( . )(
(. 4 )
whence ′ f = 2416 psi. Therefore, increase the compressive strength of masonry
m
to 2500 psi (rounded-off figure).
63
7
V
φ( ) = φ A f ′ = ( . )( )( . )(20 ) 2500
4
4
0
8
n max n m
= 24 ,4416 lb = 24 42 kips > V = 24 kips OK
.
u
Therefore, the beam section is acceptable. Calculate fV , shear strength pro-
nm
vided by the masonry.
=
φV = φ2 25 A f ′ = 0 8 2 25 7 63 20)( 2500) = 13 734 lb = 13 73 kips
)
.
.
.
(
.
(
.
(
)
)
(
,
nm n m
fV = 13.73 kips < V = 24 kips; shear reinforcement required.
u
nm
Commentary: The two options presented above would result in a satisfactory beam
design. Alternative (a) does not require shear reinforcement as the masonry alone in
the larger beam size would be able to resist the entire shear in the beam. In alternative
(b), if the masonry strength is increased to 2500 psi, the nominal 8- × 24-in. beam can
be used if shear reinforcement is provided. See Example 4.22.
4.10.4 Determination of Shear Reinforcement for Masonry Beams
For design purposes, we can substitute V (the factored shear or shear demand) for fV in
u n
Eq. (4.98) resulting in the following expression:
V = f (V + V ) (4.99)
u
ns
n
The shear strength required to be provided by shear reinforcement (V ) can be expressed
ns
by rearranging Eq. (4.99) as follows:
V = V −φ V nm (4.100)
u
φ
s
The shear reinforcement in masonry beams is provided typically in the form of single
transverse bars placed in the grouted cells of masonry beams and hooked around horizon-
tal reinforcement. Inclined stirrups, which sometimes are provided in reinforced concrete
beams, are not practical for masonry which is built from precast units. The relationship
between the nominal shear strength provided by shear reinforcement and the area of shear
reinforcement is given by Eq. (4.101) [MSJC-08 Eq. (3-23)]:
⎛ A ⎞
V = 05. ⎜ v ⎟ fd (4.101)
ns ⎝ s ⎠ y