Structural Concrete - Hassoun

112 Chapter 3 Flexural Analysis of Reinforced Concrete Beams
Therefore, it is a tension-controlled section and φ = 0.9.
Also, ρ>ρ min = 200 = 0.00333.
f y
(
2. φM n = φA s f y d −
A s f )
y
1.7f c ′ b
(
)
2.37 × 60
= 0.9 × 2.37 × 60 17 − = 1878 K ⋅ in. = 156.5K⋅ ft
1.7 × 3 × 12
3. The dead load acting on the beam is self-weight (assumed):
12 × 20
w D = × 150 = 250 lb∕ft = 0.25 K∕ft
144
where 150 is the weight of reinforced concrete in pcf.
4. The external factored moment is
M u = 1.2M D + 1.6M L
( ( 0.25
= 1.2
8 × 202) wL
+ 1.6
8 × 202) = 15.0 + 80w L
where w L is the uniform service live load on the beam in K/ft.
5. Internal design moment equals the external factored moment:
156.5 = 15.0 + 80w L and w L = 1.77 K∕ft
The allowable uniform service live load on the beam is 1.77 K/ft.
Example 3.6 Minimum Steel Reinforcement
Check the design adequacy of the section shown in Fig. 3.19 to resist a factored moment M u = 30 K ⋅ ft,
using f ′ c = 3ksiandf y = 40 ksi. Figure 3.19 Example 3.6.
Solution
1. Check ρ provided in the section:
ρ = A s
bd = 3 × 0.2
10 × 18 = 0.00333