Structural Concrete - Hassoun

770 Chapter 19 Introduction to Prestressed Concrete
where
V p = vertical component of effective prestress force at section considered
f pc = compressive stress (psi) in concrete (after allowance for prestress losses) at centroid of section
resisting applied loads or at junction of web and flange when centroid lies within flange
Alternatively, V cw may be determined as the shear force that produces a principal tensile stress
of 4λ √ f c ′ at the centroidal axis of the member or at the intersection of the flange and web when
the centroid lies within the flange. The equation for the principal stresses may be expressed as
follows:
or
f t = 4λ √ f ′ c =
√
v 2 cw +
( 1
2 f pc
) 2
−
1
2 f pc
V cw = f t
⎛
⎜⎜⎝
√
1 + f pc
f t
⎞
⎟⎟⎠ b w d p (19.54)
where f t = 4λ √ f ′ c. When applying Eqs. 19.51 and Eqs. 19.53 or 19.54, the value of d is taken as
the distance between the compression fibers and the centroid of the prestressing tendons but is not
less than 0.8h.
The critical section for maximum shear is to be taken at h/2 from the face of the support.
The same shear reinforcement must be used at sections between the support and the section
at h/2.
19.8.3 Shear Reinforcement
The value of V s must be calculated to determine the required area of shear reinforcement.
V u = φ(V c + V s ) (Eq. 19.49)
For vertical stirrups,
and
V s = 1 φ (V u − φV c ) (Eq. 19.55)
V s = A v f y d
s
(Eq. 19.56)
A v = V ss
f y d p
or s = A v f y d p
V s
(Eq. 19.57)
where A v is the area of vertical stirrups and s is the spacing of stirrups. Equations for inclined
stirrups are the same as those discussed in Chapter 8.
19.8.4 Limitations
1. Maximum spacing, s max , of the stirrups must not exceed 0.75h or 24 in. If V s exceeds
4 √ f ′ cb w d p , the maximum spacing must be reduced to half the preceding values (ACI Code,
Section 9.7.6.2.2).
2. Maximum shear, V s , must not exceed 8 √ f ′ cb w d p ; otherwise, increase the dimensions of the
section (ACI Code, Section 22.5.1.2).