Structural Concrete - Hassoun

15.8 Torsion in Reinforced Concrete Members (ACI Code Procedure) 541
closed stirrups, and longitudinal reinforcement, A l , in the form of longitudinal bars. The ACI Code,
Section 22.7.6.1, presented the following expression to compute A t and A l :
1. Closed stirrups A t can be calculated as follows:
where
T n = 2A 0A t f yt cot θ
s
(15.24)
T n = T u
and φ = 0.75
φ
A t = area of one leg of transverse closed stirrups
f yt = yield strength of A t ≤ 60 ksi
s = spacing of stirrups
And A 0 and θ were defined in ACI Section 22.7.6.1. Equation 15.24 can be written as
follows:
A t
s =
T n
2A 0 f yt cot θ
If θ = 45 ∘ , then cot θ = 1.0, and if f yt = 60 ksi, then Eq. 15.25 becomes
A t
s =
(15.25)
T n
120A 0
(15.26)
where T n is in K ⋅ in. Spacing of stirrups, s, should not exceed the smaller of P h /8 or 12 in. For
hollow sections in torsion, the distance measured from the centerline of stirrups to the inside
face of the wall shall not be less than 0.5 A 0 h /P h .
2. The additional longitudinal reinforcement, A l , required for torsion should not be less than the
following:
( ) ( )
At fyt
A l = P
s h cot 2 θ (15.27)
f y
If θ = 45 ∘ and f yt = f y = 60 ksi for both stirrups and longitudinal bars, then Eq. 15.27
becomes
( ) ( )
At At
A l = P
s h = 2 (x
s 1 + y 1 ) (15.28)
where P h is as defined in ACI Section 22.7.6.1. Note that reinforcement required for torsion
should be added to that required for the shear, moment, and axial force that act in combination
with torsion. Other limitations for the longitudinal reinforcement, A l , are as follows:
a. The smallest bar diameter of a longitudinal bar is that of no. 3 or stirrup spacing s/24,
whichever is greater.
b. The longitudinal bars should be distributed around the perimeter of the closed stirrups with
a maximum spacing of 12 in.
c. The longitudinal bars must be inside the stirrups with at least one bar in each corner of
the stirrups. Corner bars are found to be effective in developing torsional strength and in
controlling cracking.
d. Torsional reinforcement should be provided for a distance (b t + d) beyond the point theoretically
required, where b t is the width of that part of the cross section containing the
stirrups resisting torsion.