Structural Concrete - Hassoun

19.5 Design of Flexural Members 761
If this condition is not met, then compression steel does not yield. In this case, A ′ s may be neglected
(let A ′ s = 0), or alternatively, the stress in A ′ s may be determined by general analysis, as explained
in Chapter 3.
When prestressed and nonprestressed reinforcement are used in the same section, Eq. Eq.
19.39 should read as follows:
[
f ps = f pu 1 − γ (
p f pu
ρ
β p
1 f c
′ + d ( ))] ω − ω
′
(19.47)
d p
(ACI Code, Section 20.3.2.3.1). If any compression reinforcement is taken into account when calculating
f ps ,theterm
ρ p
f pu
f ′ c
+ d d p
(ω − ω ′ )
must be greater than or equal to 0.17 and d ′ must be less than or equal to 0.15d p ,whered, d ′ ,andd p
are the distances from the extreme compression fibers to the centroid of the nonprestressed tension
steel, compression steel, and prestressed reinforcement, respectively,
γ p = factorfortype of prestressing tendon
⎧
⎪ 0.55 for f py
not less than0.8
⎪ f pu
⎪
= ⎨0.40 for f py
not less than0.85
⎪
f pu
⎪
⎪0.28 for f py
not less than0.90
⎩ f pu
β 1 = 0.85 forf ′ c ≤ 4ksiless0.05 foreach1ksiincreaseinf ′ c, but β 1 ≥ 0.65.
1. For rectangular sections, the ACI Code, Section 21.2.2.2, limits the reinforcement ratio as
follows (ε t ≥ 0.005 for tension-controlled sections):
where
( ) fps
ω p = ρ p
ω = ρ
f c
′
( fy
f ′ c
)
ω p + d d p
ω ≤ 0.32β 1
and
and
ρ p = A ps
bd
ρ = A s
bd
(prestressed steel)
(nonprestressed steel)
2. If ordinary reinforcing bars A ′ s are used in the compression zone, then the condition becomes
ω p + d d p
(ω − ω ′ ) ≤ 0.32β 1
where ω ′ = ρ ′ ( f y ∕f ′ c) and ρ ′ = A ′ s∕bd. This reinforcement limitation is necessary to ensure
a plastic failure of underreinforced concrete beams.