Structural Concrete - Hassoun

762 Chapter 19 Introduction to Prestressed Concrete
3. For flanged sections, the steel area required to develop the strength of the web (A pw )isused
to check the reinforcement index.
( ) fps
ω pw (web) =ρ pw ≤ 0.32β 1
where
ρ pw = A pw
b w d d
If nonprestressed reinforcement is used, then the reinforcement limitations are
where
ω pw +
ω w = A s
b w d
f ′ c
d
d pw
(ω w − ω ′ w) ≤ 0.32β 1
( fy
f ′ c
)
ω ′ w = A′ s
b w d
When compression steel A ′ s is not used, then ω ′ w = 0. The preceding reinforcement conditions
must be met in the analysis and design of partially prestressed concrete members.
For class C of prestressed concrete flexural members, where f t > 12 √ f c ′ (cracked section),
crack control provisions should be used as explained in Section 6.7 of this textbook. When
using Eq. 6.18 for the maximum spacing s, the ACI Code, Section 24.3.2, specifies the following:
a. For tendons, use 2 of the spacing s.
3
b. For a combination of nonprestressed reinforcement and tendons, use 5 of the spacing s.
6
c. For tendons, use Δf ps in place of f s ,whereΔf ps is the difference between the stress computed
in the prestressing tendons at service load based on a cracked section and the decompression
stress, f dc , in the prestressing tendons, which may be taken conservatively, to be equal
to the effective prestress, f se . Note that Δf ps should not exceed 36 ksi. If it is less than or
equal to 20 ksi, the spacing requirement will not apply. Equation 6.17 can be written as
follows:
( ) [ ( ) ]
2 40
s = 15 − 2.5C
3 Δ f c
ps
( fy
f ′ c
)
19.6 CRACKING MOMENT
Cracks may develop in a prestressed concrete beam when the tensile stress at the extreme fibers
of the critical section equals or exceeds the modulus of rupture of concrete, f r . The value of f r
for normal-weight concrete may be assumed to be equal to 7.5λ √ f ′ c where λ = 1.0. The stress at
the bottom fibers of a simply supported beam produced by the prestressing force and the cracking
moment is
σ b =− F A − (Fe)y b
I
+ M cry b
I
When σ b = f r = 7.5λ √ f c, ′ then the cracking moment is
M cr = I
(
7.5λ √ f c ′ + F y b A + (Fe) y )
b
I
(19.48)