Structural Concrete - Hassoun

954 Chapter 23 Review Problems on Concrete Building Components
Determine the design moment strength: (ACI Code, Section 5.3.1)
M u = 1.2M DL + 1.6M LL
M u = 1.2 w DL × L2
8
M u = 1.2 31252
8
+ 1.6 w LL × L2
8
+ 1.6 11252
8
M u = 406.25 K ⋅ ft = 4, 875 K ⋅ in.
Check maximum moment: (ACI Code, Section 21.2.2)
Using similar triangles from Figure 23.7
0.003
= 0.005
c max d − c max
0.003
= 0.005
c max 20 − c max
c max = 7.50 in.
a max = β 1 c max = 0.85 × 0.85 = 6.38 in.
= 3.25 in. 2
A s max = 0.85f c ′ ba max
= 0.85(3)(12)(6.38)
f y 60
(
M u max = φA s max f y d − a )
max
=(0.9)(3.25)(60)
2
= 2951.73 K ⋅ in. = 245.98 K ⋅ ft
M u max
< M u , Compression steel is needed
(
20 − 6.38
2
)
A s′
0.003
20″
Figure 23.7
A s
12″
0.005
Strain diagram for the cross section.
Find the required area of steel:
M u1 = M u max = 245.98 K ⋅ ft
A s1 = A s max = 3.25 in. 2
M u2 = M u − M u1 = 406.25 − 245.98 = 160.27 K ⋅ ft