Simplified Design for Beams and One-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 79

3.7.3 Simplified Design for Torsion Reinforcement

When required, torsion reinforcement must consist of a combination of closed stirrups and longitudinal
reinforcement (ACI 11.5.4). For spandrel beams built integrally with a floor slab system (where reduction of
torsional moment can occur due to redistribution of internal forces after cracking), a maximum torsional

⎛

A cp
p cp

⎞

moment of may be assumed for normal weight concrete (ACI 11.5.2.2). The ACI provisions

φ 4 λ ʹ f c

⎜ ⎟

⎝ ⎠

for members subjected to factored torsional moment T u and factored shear force V u for normal weight concrete
can be summarized as follows:

(1) Check if the torsion can be neglected

⎛

A cp
p cp

⎞

T cr ≤φλ ʹ f c

⎜ ⎟

(ACI 11.5.1)

⎝ ⎠

(2) If torsion cannot be neglected, for members in statically indeterminate structures where redistribution of
forces can occur, calculate the maximum factored torsional moment at the critical section to be considered
(ACI 11.5.2.2):

⎛

A cp
p cp

⎞

T cr =φ 4 λ ʹ f c ⎜ ⎟

(ACI 11.5.2.2)

⎝ ⎠

(3) Design the torsional reinforcement for a torque equal to the smaller of the factored torsional moment from
an elastic analysis or the value computed in Step 2. Consider only the spandrel beam reinforcement to resist
torsion. Ignore portion of slab framing in spandrel. If portion of slab is included, torsion reinforcement must
be included in the slab as well.

(4) Check the adequacy of the section dimensions. The cross-sectional dimensions need to be increased if:

2 2

⎛
⎜

⎞
⎟

⎛
⎜

⎞
⎟

⎛
⎜

⎞
⎟

V u
b w d

T u p h
1.7A oh

V c

+ ≥φ

b w d +

8 f c ʹ

(ACI 11.5.3)

where:

V u = factored shear force at the section, kips.
ρ h = perimeter of centerline of outermost closed stirrups, in.
A oh = area enclosed by centerline of the outermost closed stirrups, in 2
V c = nominal shear strength provided by concrete, kips
b w = web width, in.
d = distance from extreme compression fiber to centroid of tension reinforcement, in.

(5) Calculate the required area of stirrups for torsion:

A t T u

(ACI 11.5.3.6)

s =

2 φ A o f y