Structural Concrete - Hassoun

Summary 181
SUMMARY
Sections 4.1–4.3: Design of a Singly Reinforced Rectangular Section
Given: M u (external factored moment), f ′ c (compressive strength of concrete), and f y (yield stress
of steel).
Case 1 When b, d, and A s (or ρ) arenot given:
1. Assume ρ min ≤ ρ ≤ ρ max . Choose ρ max for a minimum concrete cross section (smallest) or
choose ρ between ρ max /2 and ρ b /2 for larger sections. For example, if f y = 60 ksi, you may
choose
ρ = 1.2% R n = 618 psi for f ′ c = 3ksi
ρ = 1.4% R n = 736 psi for f ′ c = 4ksi
ρ = 1.4% R n = 757 psi for f ′ c = 5ksi
For any other value of ρ, R n = ρf y [1 −(ρf y ∕1.7f c)], ′ andR u = φR n .
2. Calculate bd 2 = M u /φR n (φ =0.9) for tension-controlled sections.
3. Choose b and d. The ratio of d to b is approximately 1 to 3, or d/b ≈2.0.
4. Calculate A s = ρbd; then choose bars to fit in b in either one row or two rows. (Check b min
from the tables.)
5. Calculate
{ d + 2.5in. (for one row of bars)
h =
d + 3.5in. (for two rows of bars)
Here, b and h must be to the nearest higher inch. Note: Ifh is increased, calculate new d = h
−2.5 (or 3.5) and recalculate A s to get a smaller value.
Case 2 When ρ is given, d, b, and A s are required. Repeat steps 1 through 5 from Case 1.
Case 3 When b and d (or h) are given, A s is required.
1. Calculate R n = M u /φbd 2 (φ = 0.9).
2. Calculate
( 0.85f
′
) [ √
ρ = c
1 − 1 − 2R ]
n
f y
0.85f c
′
(or get ρ from tables or Eq. 4.2).
3. Calculate A s = ρbd, choose bars, and check b min .
4. Calculate h to the nearest higher inch (see note, Case 1, step 5).
Case 4 When b and ρ are given, d and A s are required.
1. Calculate
2. Calculate
(
R n = ρf y 1 − ρf )
y
1.7f c
′
√
M
d = u
φR n b
R u = φR n (φ = 0.9)