Structural Concrete - Hassoun

Review Problems on Concrete Building Components 959
Allowable soil pressure = 4ksf
γ soil = 130 pcf
Solution:
Note: All moments and shear values are calculated using ADAPT-BUILDER software.
a. Design the Slab
1. Assume a slab thickness. For f y = 60 ksi, the minimum depth to control deflection is L/20 =
11(12)/20 = 6.6 in. Assume a total depth of h = 7 in. and assume d = 6 in. (to be checked later).
2. Calculate A s : For M u = 3K⋅ ft, b = 12 in., and d = 6in., R u = M u 3(12, 000)
=
bd2 (12)(6)2 =
83.33 psi. From tables in Appendix A, ρ = 0.0023 < ρ max = 0.01806, φ= 0.9.
∴ A s = ρbd = 0.0023(12)(6) =0.17 in. 2
Choose no. 4 bars, A b = 0.2in. 2 , and S = 12A b
= 12(0.2) = 14.12 in.
A s 0.17
Check actual d = 7 − 3 − 4 = 6 in. (acceptable)
4 16
Let S = 14 in. and A s = 0.17 in. 2
3. Check the moment capacity of the final section.
A s = 12 (0.2) =0.1714 in.2
14
a =
A s f y
0.85f c ′ b = 0.1714(60) = 0.2521 in.
(0.85)(4)(12)
(
φM n = φA s f y d − a )
(
=(0.9)(0.1714)(60) 6 − 0.2521 )
= 54.37 K ⋅ in.
2
2
= 4.53 K ⋅ ft > M u = 3K⋅ ft
4. Check main reinforcement maximum spacing. (ACI Code, Section 7.7.2.3)
s = 3h = 3 ∗ 7 = 21 in.
s = 18 in.
Use no. 4 bars spaced at 14 in.
5. Calculate the shrinkage reinforcement normal to the main steel.
For f y = 60 ksi,ρ min = 0.0018 (ACI Code, Section 7.6.1.1)
A sh = ρbh = 0.0018(12)(7) =0.15 in. 2
Choose no. 4 bars, A b = 0.2in. 2 , and S = 12A b
= 12(0.2)
A s 0.1512 = 15.9in.
Let S = 15 in. and A s = 0.15 in. 2
6. Check the shrinkage reinforcement maximum spacing (ACI Code, Section 7.7.6.2)
s = 5h = 5 ∗ 7 = 35 in.
s = 18 in.
Use no. 4 bars spaced at 15 in.