Structural Concrete - Hassoun

Summary 145
SUMMARY
Flowcharts for the analysis of sections are given at www.wiley.com/college/hassoun.
Sections 3.1–3.8
1. The type of failure in a reinforced concrete flexural member is based on the amount of tension
steel used, A s .
2. Load factors for dead and live loads are U = 1.2 D +1.6L. Other values are given in the text.
3. The reduction strength factor for beams φ = 0.9 for tension-controlled sections with
ε t ≥ 0.005.
4. An equivalent rectangular stress block can be assumed to calculate the design moment
strength of the beam section, φM n .
5. Design provisions are based on four conditions, Section 3.5.
Sections 3.9–3.13: Analysis of a Singly Reinforced Rectangular Section
Given: f ′ c, f y , b, d, and A s . Required: the design moment strength, φM n .
To determine the design moment strength of a singly reinforced concrete rectangular section:
1. Calculate the compressive force, C = 0.85f ′ cab and the tensile force, T = A s f y . Calculate a =
A s f y ∕(0.85f ′ cb).
2. Calculate φM n = φC(d − a/2) = φT(d − a/2) = φA s f y (d − a/2). Check ε t = 0.003(d t − c)/
c ≥ 0.005 for φ = 0.9 (tension-controlled section). (See Section 3.6.)
3. Calculate the balanced, maximum, and minimum steel ratios:
ρ b = 0.85β 1
( f
′
c
f y
)(
87
87 + f y
)
ρ min = 0.2
f y
for f ′ c ≤ 4.5ksi
ρ max = (0.003 + f y∕E s )ρ b
0.008
where f c ′ and f y are in ksi. (See Section 3.9.2.) The steel ratio in the section is ρ = A s /bd. Check
that ρ min ≤ ρ ≤ ρ max .
4. Another form of the design moment strength is
(
M n = ρf y (bd 2 ) 1 − ρf )
y
= R n bd 2
( ρfy
R n = ρf y
[1 −
1.7f c
′
1.7f c
′
)]
and
R u = φR n
5. For f y = 60 ksi and f ′ c = 3 ksi (Table 3.2), ρ max = 0.01356, ρ min = 0.00333, R n = 686 psi, and
R u = 615 psi.
For f y = 60 ksi and f ′ c = 4ksi, ρ max = 0.01806, ρ min = 0.00333, R n = 911 psi, and
R u = 820 psi.
Section 3.14: Analysis of Rectangular Section with Compression Steel
Given: b, d, d ′ , A s , f ′ c,andf y . Required: the design moment strength, φM n .