Structural Concrete - Hassoun

15.9 Summary of ACI Code Procedures 543
3. Design for shear:
a. Calculate the nominal shearing strength provided by the concrete, V c . Determine the shear
to be carried by web reinforcement:
V u = φV c + φV s or V s = V u − φV c
φ
b. Compare the calculated V s with maximum permitted value of (8 √ f ′ cb w d) according to the
ACI Code, Section 22.5.1.2. If calculated V s is less, proceed with the design; if not, increase
the dimensions of the concrete section.
c. The shear web reinforcement is calculated as follows:
A v = V ss
f ytd
where
A v = area of two legs of the stirrup
s = spacing of stirrups
The shear reinforcement per unit length of beam is
A v
s = V s
f ytd
d. Check A v /s calculated with the minimum A v /s:
(min) A v
s = 0.75√ f ′ c
(
bw
f yt
)
≥ 50
(
bw
f yt
)
The minimum Av, specified by the code under the combined action of shear and torsion,
isgiveninstep5.
4. Design for torsion:
a. Check if the factored torsional moment, T u , causes equilibrium or compatibility torsion.
For equilibrium torsion, use T u . For compatibility torsion, the design torsional moment is
the smaller of T u from factored load and
T u2 = φ4λ √ ( )
A
2
f c
′ cp
(Eq. 15.29)
P cp
b. Check that the size of the section is adequate. This is achieved by checking either Eq. 15.21
for solid sections or Eq. 15.22 for hollow sections. If the left-hand-side value is greater than
φ(V c ∕b w d + 8 √ f ′ c), then increase the cross-section. If it is less than that value, proceed. For
hollow sections, check if the wall thickness t is less than A 0 h /P h . If it is less, use Eq. 15.23
instead of Eq. 15.22; otherwise, use Eq. 15.25.
c. Determine the closed stirrups required from Eq. 15.25:
A t
s =
T n
2A 0 f yt cot θ
(Eq. 15.25)
and A t /s should not be less than 25 b w /f yt . Also, the angle θ may be assumed to be 45 ∘ ,
T n = T u ∕φ, andφ = 0.75.