Structural Concrete - Hassoun

200 Chapter 5 Shear and Diagonal Tension
Table 5.1
Values of S max
= A v
f y
/50b w
= 24 in. When f yt
= 60 ksi and f
c ′ < 4500 psi
b w (in.) 10 11 12 13 14 15 16 18 20 22 24 b w
S max (in.) no. 3 stirrups 24 24 22 20.3 18.9 17.6 16.5 14.7 13.2 12 11 264/b w
S max (in.) no. 4 stirrups 24 24 24 24 24 24 24 24 24 21.8 20 480/b w
Table 5.1 gives S max based on Eqs. 5.22 and Eqs. 5.23. Final spacings should be rounded to
the lower inch. For example, S = 20.3 in. becomes 20 in.
5.6.3 Maximum Shear Carried by Web Reinforcement V s
To prevent a shear–compression failure, where the concrete may crush due to high shear and
compressive stresses in the critical region on top of a diagonal crack, the ACI Code, Section
22.5.1.2, requires that V s shall not exceed (8 √ f ′ c)b w d.IfV s exceeds this value, the section should
be increased. Based on this limitation,
If f ′ c = 3ksi, then V s ≤ 0.438b w d (kips) or V s ∕b w d ≤ 438 psi.
If f ′ c = 4ksi, then V s ≤ 0.506b w d (kips) or V s ∕b w d ≤ 506 psi.
If f ′ c = 5ksi, then V s ≤ 0.565b w d (kips) or V s ∕b w d ≤ 565 psi.
5.6.4 Maximum Spacing of Stirrups
To ensure that a diagonal crack will always be intersected by at least one stirrup, the ACI Code,
Section 9.7.6.2, requires that the spacing between stirrups shall not exceed d/2, or 24 in., provided
that V s ≤ (4 √ f c)b ′ w d. This is based on the assumption that a diagonal crack develops at 45 ∘ and
extends a horizontal distance of about d. In regions of high shear, where V s exceeds (4 √ f c)b ′ w d,
the maximum spacing between stirrups must not exceed d/4. This limitation is necessary to ensure
that the diagonal crack will be intersected by at least three stirrups. When V s exceeds the maximum
value of (8 √ f c)b ′ w d, this limitation of maximum stirrup spacing does not apply, and the dimensions
of the concrete cross section should be increased.
A second limitation for the maximum spacing of stirrups may also be obtained from the
condition of minimum area of shear reinforcement. A minimum A v is obtained when the spacing s
is maximum (Eq. 5.21).
A third limitation for maximum spacing is 24 in. when V s ≤ (4 √ f c)b ′ w d and 12 in. when V s
is greater than (4 √ f c)b ′ w d but less than or equal to (8 √ f c)b ′ w d. The least value of all maximum
spacings must be adopted. The ACI Code maximum spacing requirement ensures closely spaced
stirrups that hold the longitudinal tension steel in place within the beam, thereby increasing their
dowel capacity, V d (Fig. 5.5).
5.6.5 Yield Strength of Shear Reinforcement
The ACI Code, Section 20.2.2.4, requires that the design yield strength of shear reinforcement shall
not exceed 60 ksi (420 MPa). The reason behind this decision is to limit the crack width caused by
the diagonal tension and to ensure that the sides of the crack remain in close contact to improve the
interface shear transfer, V a (Fig. 5.5). For welded deformed wire fabric, the design yield strength
shall not exceed 80 ksi (560 MPa).