Page 172 - Design of Reinforced Masonry Structures

4.36 CHAPTER FOUR

For f = 200 psi and f = 60,000 psi, the above expression yields
y
r
ρ = A s = . 0 3284 ⎛ 200 ⎞ ⎟ = . 0 001097 ≈ . 0 00011
⎜
min ⎠
bd ⎝ 60 ,000
9" The above result means that a reinforced beam,
with r = 0.0011 would have its nominal strength
equal to 1.3 times the nominal cracking moment.
Accordingly, r = 0.0011 may be considered as
the minimum reinforcement ratio for a reinforced
masonry beam. See Example 4.12.

Example 4.12 A 9- × 24-in. brick beam is rein-
20"
24" forced with a No. 4 Grade 60 bars placed at 20 in.
from the compression face of the beam (Fig. E4.12).
Calculate for this beam (a) the nominal cracking
moment, (b) nominal moment strength, and (c) check
if the beam complies with the code requirements. ′ f =
m
1500 psi.
Solution
#4
Given: b = 9 in., h = 24 in., d = 20 in. f = 200 psi
r
2
FIGURE E4.12 Beam cross sec- (MSJC-08 Table 3.1.8.2.1). A = 0.20 in. .
s
tion for Example 4.12. a. Calculate nominal cracking moment of the beam
from Eq. (4.54):
⎛ bh ⎞ ⎛ 924()( ) 2 ⎞ ⎛ 1 ⎞
2
M = f r ⎜ ⎟ = 200( ) ⎜ ⎟ ⎜ ⎟ = 14 4 . k-ft
cr ⎠ ⎝ ⎝ 0 0⎠
⎝ 6 6 ⎠ 12 00,
b. Calculate the nominal moment strength of the beam. From Eq. (4.9)
Af (. ) (
020 60)
a = sy = = 111 iin.
.
.
)
(
.
(
080 fb ′ 080 15 9)
.
m
From Eq. (4.12), the nominal strength of the beam is
⎛
.
M = A f ⎛ ⎝ d − a ⎞ ⎠ 2 = 020 60 20 − 111 ⎞ ⎛ 1 ⎞ ⎠ = 19 45 k-ft
(
.
)
(.
⎝
⎠ ⎝ 12 ⎠
n
s y
2

c. M = 19.45 k-ft > 1.3M = 1.3(14.4) = 18.72 k-ft. Therefore, the beam complies
cr
n
with the code requirement. Note that r = A /bd = 0.20/(9)(20) = 0.0011.
s
4.7.3.2 Maximum Reinforcement Requirements The code provisions for maximum
reinforcement in beams are intended to ensure that the reinforcement would yield suffi-
ciently so that the beam would exhibit a ductile behavior.
MSJC-08 Section 3.3.3.5.1 requires that for masonry members where the quantity
M / V d ≥ 1, the cross-sectional area of reinforcement shall not exceed the area required to
u u v
maintaining a strain gradient corresponding to a strain in the reinforcing bar nearest the ten-
sion face of the member equal to 1.5 times the yield strain (i.e., 1.5e ) and a maximum strain
y
in masonry specified in MSJC Section 3.3.2(c) (i.e., e = 0.0025 for concrete masonry
mu
and 0.0035 for clay masonry). This code provision is intended to ensure that masonry