Page 177 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.41

Hence, e < 1.5e . Check if the beam is ductile, that is, r ≤ 0.75r .
y
b
s
.
ρ = A s = 127 = 0 0083.
bd (. ) (
763 20)
From Table 4.5, for concrete masonry with ′ f = 1500 psi and Grade 60 rein-
m
forcement, 0.75r = 0.0066, which is less than r provided . (= 0.0083). Therefore, the
b
beam is not ductile.
The beam design is not acceptable as it does not comply with the code
requirements.
c. Check the nominal strength of the beam reinforced with one No. 11 bar. A =
s
2
1.56 in. . Assume that the reinforcement has yielded.
a = (156 60. )( ) = 10 22 in .
.
.
080 (15. )(763. )
⎛ a ⎞
M = A f y ⎝ d − ⎠ 2
n
s y
⎛
.
)( )
.
= (156 60 20 − 10 22 ⎞
⎝ 2 ⎠
= 1393 7.k--in. = 116 14. k-ft
Verify from Eq. (4.30) that reinforcement has yielded and e ≥ 1.5e . From
s
y
Eq. (4.5),
.
.
c = a = 10 22 = 12 78 in.
.
.
08 08
.
c 12 78
>
= = 0 64 0 454 (4.34 repeated)
.
.
d 20
Hence, e < 1.5e . Check the reinforcement ratio.
s
y
.
.
ρ = A s = 156 = 0 0102 > ρ max = 0 0088
.
bd (. )(
763 20)
This beam is overreinforced and not acceptable because it does not comply
with the code requirements. It is further noted that No. 11 bar is not permit-
ted by the MSJC Code when using strength design philosophy for design of
reinforced masonry.

4.8 PROCEDURE FOR FLEXURAL
DESIGN OF BEAMS
4.8.1 General Procedure
Beam design is essentially a trial-and-error problem. Several examples that illustrate proce-
dure for designing reinforced masonry beams, such as lintels, are presented in this section.
The design process begins with certain given information. In reinforced masonry, the
beam width b is usually known because the beam is generally a part of a masonry wall