Structural Concrete - Hassoun

114 Chapter 3 Flexural Analysis of Reinforced Concrete Beams
Summary: Singly Reinforced Rectangular Section
The procedure for determining the design moment of a singly reinforced rectangular section according
to the ACI Code limitations can be summarized as follows:
1. Calculate the steel ratio in the section, ρ = A s /bd.
2. Calculate the balanced and maximum steel ratios, Eqs. 3.18 and Eqs. 3.31 or Table 3.2, for
tension-controlled section. Also, calculate ρ min = 200/f y when f c ′ < 4500 psi (f c ′ and f y are in
√
psi units) and ρ min = 3 f c∕f ′ y when f c ′ ≥ 4500 psi.
3. If ρ min ≤ ρ ≤ ρ max , then the section meets the ACI Code limitations for tension-controlled
section. If ρ ≤ ρ min , the section is not acceptable (unless a steel ratio ρ ≥ ρ min is used). If ρ ≤
ρ max , φ = 0.9 (ε s ≤ 0.005); otherwise use Fig. 3.6.
4. Calculate a = A s f y ∕0.85f cb, ′ c, ε t ,andφ.
5. Calculate φ M n = φ A s f y (d − a/2).
Flowcharts representing this section and other sections are given at www.wiley.com/college/
hassoun.
3.13 SECTIONS IN THE TRANSITION REGION (φ