(8) When torsion reinforcement is required, it must be provided in

addition to reinforcement required to resist shear. The closed ties

required for torsion may be combined with those required for shear.

However, the area furnished must be the sum of the individually required

areas and the most restrictive requirements for spacing and placement must

be met. Figure 33a shows several ways to arrange web reinforcement. For

low torsion and shear, it is convenient to combine shear and torsional web

reinforcement in the form of a single closed stirrup whose area is equal to

At + Av/2. For high torsion and shear, it would be economical to

provide torsional and shear reinforcement separately. Torsional web

reinforcement consists of closed stirrups along the periphery, while the

shear web reinforcement is in the form of closed stirrups distributed along

the width of the member. For very high torsion, two closed stirrups along

the periphery may be used. The combined area of the stirrups must equal

At and they must be located as close as possible to each other, i.e., the

minimum separation of the flexural reinforcement. In computing the required

area of stirrups using Equation (51), the value of bt should be equal to

the average center-to-center dimension of the closed stirrups as shown in

Figure 33a.

(9) In the design of closed ties for beams subjected to both shear

and torsion, the following limitations must be considered: a) the minimum

quantity of closed ties provided in a beam subjected to both shear and

torsion shall not be less than that required for a beam subjected to shear

alone; b) the maximum nominal shear stress, vu, must not exceed 10 [phi]

(f'c)1/2; c) the maximum nominal torsional stress, max vtu, shall not

exceed the following;

12 [phi] (f'c)1/2

EQUATION:

max vtu

< /=

(53)

[1 + (1.2vu/vtu)2]1/2

d) the required spacing of closed stirrups shall not exceed (bt + ht)/4,

or 12 inches nor the maximum spacing required for closed ties in beams

subjected to shear only; e) the required areas Av and At shall be

determined at the critical section and this quantity of reinforcement shall

be uniformly distributed throughout the member; and f) to insure the full

development of the ties, they shall be closed using 135-degree hooks.

(10) In addition to closed stirrups, longitudinal reinforcement must

be provided to resist the longitudinal tension caused by the torsion. The

required area of longitudinal bars A*l shall be computed by:

bt + ht

EQUATION:

A*l = 2At

(54a)

s

or by

400bs

vtu

bt + ht

EQUATION:

A*l =

-2At

(54b)

fy

vtu + vu

s

2.08-78