Structural Concrete - Hassoun

Review Problems on Concrete Building Components 949
Conditions are met. Use l d = Ψ t Ψ e f y
20λ √ d b
f c
′
Determine the multiplication factors: (ACI Code, Section 25.4.2.4)
Ψ t = 1.0 (bottom bars)
Ψ e = 1.0 (no coating)
Ψ t Ψ e < 1.7OK
Calculate l d (ACI Code, Section 25.4.2.2)
l d = Ψ t Ψ e f y
20λ √ d b =
f c
′
λ = 1.0 (normal-weight concrete)
√
f
′
c =√
5000 = 70.7psi < 100psi
(1)(1)(60, 000)
20(1) √ (1) =42.4in. = 43 in ≥ 12 in.
5000
Example 23.2
A series of reinforced concrete beams spaced at 8 ′ 10 ′′ on center is shown in Figure 23.4. The beams
have a 15 ft span and support a 5 in. thick reinforced concrete slab.
′
Given: service dead load = 2 K/ft, service live load = 0.5 K/ft, b = 10 in., d = 18 in., f c = 3ksi,
f y = 60 ksi.
a. Design the middle beam section for flexural reinforcement.
b. Design middle beam section for shear reinforcement.
c. Check for development length.
Solution:
a. Design the section for flexural reinforcement
Check for minimum thickness to satisfy the deflection criterion: (ACI Code, Section 24.2.3.1)
Minimum thickness for simply supported beams =L/16=(15 × 12)/16=11.25 in. < 18 in. (OK)
Calculate effective width of the flange b e : (ACI Code, Section 6.3.2.1)
b e = L 15 × 12
= = 45 in.
4 4
b e = 16h f + b w = 16(5)+10 = 90 in.
b e = l n + b w = 106 in.
Choose smallest: b e = 45 in.
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 21152
8
+ 1.6 w LL × L2
8
+ 1.6 0.56152
8
M u = 90K ⋅ ft = 1080K ⋅ in.