Structural Concrete - Hassoun

174 Chapter 4 Flexural Design of Reinforced Concrete Beams
4.6 ADDITIONAL EXAMPLES
The following design examples give some practical applications and combine structural analysis
with concrete design of beams and frames.
Example 4.10
For the precast concrete I-section shown in Fig. 4.11, calculate the reinforcement needed to support a
factored moment of 360 K⋅ft. Use f c ′ = 4ksi and f y = 60 ksi.
Solution
Determine if the force in the flange area 14 × 5 in. will be sufficient to resist a factored moment of 360
K⋅ft. Let d = 23.5 in. Force in flange (C c )=0.85 × f c ′ (flange area) = 0.85 × 4 × (14 × 5) = 238 K located
at 2.5 in. from the top fibers and a = 5in.:
(
φM n = 0.9C c d − a )
23.5 − 2.5
= 0.9 × 238 = 374.9K⋅ ft
2
12
which is greater than the applied moment of 360 K⋅ft. Therefore, a < 5in.:
(
φM n = φA s f y d − 1 )
2 a (
)
60A
360 × 12 = 0.9A s (60) 23.5 −
s
1.7 × 14 × 14
where
a =
A s f y
0.85f c ′ b
Solve to get A s = 3.79 in. 2 Or use Eq. 4.2 to get ρ = 0.01152 and A s = 0.01152 × 14 × 23.5 = 3.79 in. 2
Use three no. 10 bars in one row, as shown in Fig. 4.11.
For similar T-sections or I-sections, it is better to adopt a section with a flange size to accommodate
the compression force, C c . In this case, a is less than or equal to the flange depth. The bottom flange is
in tension and not effective.
Figure 4.11 Example 4.10.