Page 156 - Design of Reinforced Masonry Structures

4.20 CHAPTER FOUR

Verify from Eq. (4.30) that reinforcement has yielded. From Eq. (4.5)

.
.
.
c = a = 30 = 375 in
.
08 08
.
c 375
.
= = 0 188 < 0 454 (4.30 repeated)
.
.
.
d 20 0
Hence, the reinforcement has yielded, and e ≥ 1.5e . Use f = 0.9.
s
y
f M = 50.78 k-ft
n
Example 4.4 Determine the design moment strength, fM , of the beam described
n
in Example 4.3 if Grade 40 reinforcing bar were to be used instead of Grade 60 bar
(Fig. E4.4). All other data are the same.
7.63'' (8'' nominal) Solution
2
Given: A = 0.61 in. (one No. 7 bar), b = 7.63 in. (8 in.
s
nominal), ′ f = 2000 psi, f = 40 ksi.
y
m
Assume that the reinforcement has yielded. This
would be verified later. Calculate the depth of compres-
sion block, a, from Eq. (4.9):
d = 20''
24''
Af
1#7 a = sy (4.9 repeated)
.
080 fb ′ m
FIGURE E4.4 Beam cross
section for Example 4.4. (061 40. )( )
a = = 20 in
.
.
.
080 (20. )(763. )
From Eq. (4.13)
φM = φA f ⎛ d − a ⎞
n s y ⎝ ⎠ 2
⎛
)( )
.
= 09 . (061 40 20 − 20 . ⎞
⎝ 2 ⎠
= 4417 24 k-in. = 34 77 k-ft
.
.
Verify from Eq. (4.32) that reinforcement has yielded. From Eq. (4.5)
.
.
.
c = a = 20 = 25 in
.
08 08
.
c 25
.
= = 0 125 < 0 547 (4.32 repeated)
.
.
d 20 0
.
Hence, the reinforcement has yielded, and e ≥ 1.5e .
s
y
fM = 34.77 k-ft
n