Structural Concrete - Hassoun

378 Chapter 11 Members in Compression and Bending
(a)
(b)
Figure 11.12 Side bars in rectangular sections: (a) six side bars and (b) two side bars
(may be neglected).
Example 11.7
Determine the balanced load, P b moment, M b ,ande b for the section shown in Fig. 11.13. Use f c ′ = 4ksi
and f y = 60 ksi.
Solution
The balanced section is similar to Example 11.2. Given: b = h = 22 in., d = 19.5 in., d ′ = 2.5in., A s =
A ′ s = 6.35 in.2 (five no. 10 bars), and six no. 10 side bars (three on each side).
1. Calculate the distance to the neutral axis:
( ) (
87
c b = d
87 + f t =
y
a b = 0.85(11.54) =9.81 in.
87
87 + 60
)
19.5 = 11.54 in.
2. Calculate the forces in concrete and steel bars; refer to Fig. 11.13a. In the compression zone,
C c = 0.85f c ′ ab = 0.85(4)(9.81)(22) =733.8K.
( )
f s ′ c − d = 87 ′ ( )
11.54 − 2.5
= 87
= 68.15 ksi > 60 ksi
c
11.54
Then f s ′ = 60 ksi. C s1 = A ′ s (f y − 0.85f c ′ )=6.35(60 − 0.85 × 4) =359.4 K
( )
11.54 − 2.5 − 4.25
f s2 = 87
= 36.11 ksi
11.54
C s2 = 2(1.27)(36.11 − 0.85 × 4) =83.1K
Similarly, f s3 = 4.07 ksi and C s3 = 2(1.27)(4.07 − 0.85 × 4) = 1.7 K.
In the tension zone,
ε s4 = 964.50 × 10 −6
T 1 = 2(1.27)(28) =71 K
f s4 = 28 ksi
T 2 = A s f y = 6.35(60) =381 K