Structural Concrete - Hassoun

5.8 Design Summary 205
5.8 DESIGN SUMMARY
The design procedure for shear using vertical stirrups according to the ACI Code can be summarized
as follows:
1. Calculate the factored shearing force, V u , from the applied forces acting on the structural
member. The critical design shear value is at a section located at a distance d from the face
of the support.
2. Calculate φV c = φ2λ √ f cb ′ w d,or
[
φV c = φ 1.9λ √ ]
f c ′ V
+ 2500ρ u d
w b
M w d ≤ φ3.5λ √ f cb ′ w d
u
Then calculate 1 φV 2 c.
3. a. If V u < 1 φV 2 c, no shear reinforcement is needed.
b. If 1 φV 2 c < V u ≤ φV c , minimum shear reinforcement is required. Use no. 3 U-stirrups
spaced at maximum spacings, as explained in step 7.
c. If V u >φV c , shear reinforcement must be provided according to steps 4 through 8.
4. If V u >φV c , calculate the shear to be carried by shear reinforcement:
V u = φV c + φV s or V s = V u − φV c
φ
5. Calculate V c1
=(4 √ f c)b ′ w d and V c2
=(8 √ f c)b ′ w d = 2V c1
. Compare the calculated V s with the
maximum permissible value of V c2
=(8 √ f c)b ′ w d.IfV s < V c2
proceed in the design; if not,
increase the dimensions of the section.
6. Calculate the stirrups spacing based on the calculated S 1 = A v f yt d/V s or use Figs. 5.10 and
5.11 or Tables 5.2 and 5.3.
7. Determine the maximum spacing allowed by the ACI Code. The maximum spacing is the
least of S 2 and S 3 :
a. S 2 = d∕2 ≤ 24 in. if V s ≤ V c1
=(4 √ f c)b ′ w d.
b. S 3 = A v f yt ∕50b w ≥ A v f yt ∕(0.75 √ f cb ′ w ).
Thus, S max is the smaller of S 2 and S 3 . Values of S 3 are shown in Table 5.1.
8. If S 1 calculated in step 6 is less than S max (the smaller of S 2 and S 3 ), then use S 1 to the nearest
smaller 1 in. If S 2 1 > S max ,thenuseS max as the adopted S.
9. The ACI Code did not specify a minimum spacing. Under normal conditions, a practical
minimum S maybeassumedtobeequalto3in.ford ≤ 20 in. and 4 in. for deeper beams.
If S is considered small, either increase the stirrup bar number or use multiple-leg stirrups
(Fig. 5.8).
10. For circular sections, the area used to compute V c is the diameter times the effective depth d,
where d = 0.8 times the diameter, ACI Code, Section 22.5.2.2.