Page 176 - Design of Reinforced Masonry Structures

4.40 CHAPTER FOUR

Verify from Eq. (4.30) that the tension reinforcement has yielded and that e ≥
s
1.5e . From Eq. (4.5),
y
.
.
.
c = a = 655 = 819 in
.
08 08
.
c 819
.
<
= = 0 41 0 454 (4.30 repeated)
.
.
d 20
Hence, steel has yielded and e ≥ 1.5e . Check if the beam is ductile, that is,
s
y
r ≤ 0.75r .
b
.
A 10
ρ = s = = 0 0066.
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 exactly equal to r provided .
b
Therefore,
f = 0.9,
and
φM = (0.9)(83.63) =75.27 k-ft > M = 72 k-ft.
n u
Check that M 1.3M .
n cr
⎛ bh ⎞ ⎛ 763 24(. )( ) 2 ⎞
2
.
M = f r ⎜ ⎟ = 200 ⎜ ⎟ = 146,4496 in-lb = 12 21 k-ft
cr ⎠ ⎝ ⎠
⎝ 6 6
1.3M = 1.3(12.21) = 15.87 k-ft
cr
M = 100.6 k-ft > 1.3M = 15.87 k-ft OK
n cr
The beam is adequate to carry the imposed loads.
b. Check the nominal strength of the beam reinforced with one No. 10 bar. A =
s
2
1.27 in. . Assume that the reinforcement has yielded.
)( )
.
a = (127 60 = 832 in .
.
.
080 (15 . )(763 )
.
M = A f ⎛ ⎝ d d − a ⎞ ⎠ 2
n
s y
⎛ ⎞
.
)( )
.
= (127 60 20 − 832
⎝ 2 ⎠
=
.
.
= 1207 k-in = 100 58 k-ft
Verify from Eq. (4.30) that reinforcement has yielded and e ≥ 1.5e . From Eq. (4.5),
s
y
.
.
c = a = 832 = 10 4 in.
08 08
.
.
.
c 10 4
>
= = 0 52 0 454 (4.30 repeated)
.
.
d 20