Page 165 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.29

8" Solution
For a nominal 8- × 24-in. clay brick beam, b = 8.0 in.,
h = 24 in. From Eq. (4.53) the nominal cracking moment
of the beam is
⎛ bh ⎞
2
M = f r ⎜ ⎟ (4.53 repeated)
cr
⎝ 6 ⎠
2
The modulus of rupture, f = 200 lb/in. for solid
r
20" grouted masonry in running bond laid in Type S portland
24"
cement mortar (MSJC Table 3.1.8.2.1). Therefore,
80
(. )(24 ) 2
.
M = (.020 ) = 153 .6 k-in = 12 .8 k-ft
cr
6
1.3M = 1.3(12.8) = 16.64 k-ft
cr
The nominal strength of this beam, φM , of this
n
1#8 beam was calculated to be 65.83 kip-ft in Example 4.5
(calculations not repeated here). Therefore,
FIGURE E4.10 Beam cross sec-
.
tion for Example 4.10. φ M 65 83
M = n = = 73 14. k-ft > 1 3. M = 16 64. k-fft
φ 09
n cr
.
The nominal strength of the beam (73.14 k-ft) is greater than 1.3 times the nomi-
nal cracking moment of the beam (16.64 k-ft). Therefore, this beam satisfies the code
requirements for nominal cracking moment strength of the beam.
Example 4.11 Check if the beam described in Example 4.10 would satisfy the
code requirements for cracking moment if it were reinforced with (a) one No. 3
Grade 60 bar instead of one No. 8 bar, (b) one No. 4 bar instead of one No. 8
Grade 60 bar. ′ f = 2500 psi, f = 60 ksi.
m
y
Solution
The cracking moment of the beam, M , remains the same as calculated in Example 4.10
cr
as its value is independent of the amount of tensile reinforcement, M = 12.8 k-ft.
cr
1.3M = 1.3(12.8) = 16.64 k-ft
cr
Calculate the nominal strength of the beam, φM .
n

a. Beam reinforced with one No. 3 Grade 60 bar.
2
b = 8 in., d = 20 in., A = 0.11 in. (one No. 3 bar) ′ f = 2500 psi, f = 60 ksi.
m
y
s
Assume that the tension reinforcement has yielded (to be verified later). Calculate
from Eq. (4.9) the depth a of the compression block.
Af
a = sy (4.9 repeated)
080 fb ′
.
m
01
1
a = (. )(60 ) = .041 in
.
25
. 080 ( . )( .800 )