Structural Concrete - Hassoun

3.11 Adequacy of Sections 111
2. Check ε t :
Also,
a =
A s f y
0.85f c ′ b
c =
(
dt − c
ε t =
c
1.8 × 60
= = 3.97 in.
0.85 × 4 × 8
a
0.85 = 4.67 in. d t = d = 15.5in. c
= 0.3 < 0.375
d t
)
0.003 =
( )
15.5 − 4.67
0.003 = 0.007 > 0.005, φ = 0.9
4.67
or check
ρ = A s
bd = 1.8
8 × 15.5 = 0.0145 M
2
u
Then the section is adequate.
Example 3.5
A simply supported beam has a span of 20 ft. If the cross section of the beam is as shown in Fig. 3.18,
f c ′ = 3ksi,andf y = 60 ksi, determine the allowable uniformly distributed service live load on the beam
assuming the dead load is that due to beam weight. Given: b = 12 in., d = 17 in., total depth h = 20 in.,
and reinforced with three no. 8 bars (A s = 2.37 in. 2 ).
17"
3"
3 # 8
20' 0"
12"
Solution
Figure 3.18 Example 3.5.
1. Determine the design moment strength:
ρ = A s
bd = 3 × 0.79
12 × 17 = 0.0116
ρ max = 0.01356 (Table 3.2)
ρ