Page 195 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.59

Calculate the factored shear (or shear demand): 9.63" (10" nominal)

2 932 15 67)
wl (. ) ( .
V = u = = 22 97 kips
.
u
2 2
Calculate the shear strength of masonry (V ) from
m
Eq. (4.96):
d = 34"
40"
.
(
.
)(
.
V = 2 25 A n f ′ = 2 25 9 63 34)( 1500)
m
nm
,
b
.
= 28 532 lb = 28 53 kips
fV = (0.8)(28.53) = 22.82 kips ≈ V = 22.97 kips
u
nm
Since fV ≈ V , shear reinforcement is theoretically
nm
u
not required for this beam. However, provide minimum
shear reinforcement for the beam, say No. 3 Grade 60
bar single-legged stirrup at 48 in. on center as discussed 2#6
in the next section to provide ductility in the beam. FIGURE E4.20 Beam cross
section for Example 4.20.
4.10.3 Shear Strength of Reinforced Masonry
Beams with Shear Reinforcement
Often, shear in flexural elements is greater than that can be resisted by masonry alone
(i.e., V ≥ fV ). In such cases, shear reinforcement must be provided to resist shear that
nm
u
may be in excess of the shear resistance of the masonry alone. Based on this premise, the
nominal shear strength of a reinforced masonry beam (V ) may be considered as a sum of
n
two strength components: (1) shear strength provided by the masonry (V ), and (2) shear
nm
strength (resistance) provided by the shear reinforcement (V ). This statement can be
ns
expressed as stated by MSJC-08 Eq. (3.19):
V = V + V (4.97)
ns
nm
n
Note that the value of V in Eq. (4.97) is limited to that given by Eq. (4.93).
n
The shear resistance to be provided by transverse reinforcement in a masonry beam can
be expressed by multiplying both sides of Eq. (4.97) with the strength reduction factor for
shear f (Table 4.1) and rearranging the terms as follows:
fV = f(V + V ) (4.98)
nm
n
ns
φV = φV − φV
ns n nm
In Eq. (4.98), the term fV accounts for shear contribution of the shear reinforce-
ns
ment provided in the beam. Note that if V exceeds fV , a need for larger beam cross
n
u
section or a higher compressive strength of masonry is indicated. This is an important
concept in the sense that the nominal shear strength of a beam with transverse rein-
forcement (fV ) is controlled by the shear strength provided by the masonry (fV ), for
n
nm
when V exceeds fV [ ≤ φ4A n m ′ f , Eq. (4.93)] no amount of shear reinforcement would
n
u
make the beam adequate for shear, and the shear strength provided by the masonry (fV )
nm
must be increased either by providing a larger effective depth (d) of beam or much
higher compressive strength of masonry (shear strength of masonry increases in proportion