Structural Concrete - Hassoun

Design and Analysis Flowcharts 975
Given: M u , b, d, d′, f ′ c , f y
Required: A s , A′ s
Calculate ρ min and ρ max
(1)
Calculate R u, max
R u, max = ϕρ max f y (1-ρ max f y /1.7f′ c )
Calculate ϕ M n = M u1 as singly reinforced
M u1 = R u, max bd 2
No
M u ≥ M u1
Yes
Comp. steel is not
required
A s1 = ρ max bd
Go to Flowchart 23.4
M u2 = M u - M u1
A s2 = M u2 /ϕf y (d - d′)
Total A s = A s1 + A s2
A s ≤ A s max
No
ε t = 0.003(d t - c)/c
ε t = 0.005
Yes
Check if comp. steel yields.
Let a = A s1 f y /0.85f′ c b
c = a/β 1
Calculate f ′ s = 87(c - d′)/c
Change
section
f ′ s = f y
A′ s = A s2
Yes
f ′ s ≥ f y
No
f ′ s < f y
A′ s = A s2 f y /f ′ s
End
End
Flowchart 24.5
Design of rectangular sections with compression steel.
Refer to Flowchart 24.1 to calculate ρ min and ρ max .