(6) whenever the nominal shear stress, vu, exceeds the shear

capacity, vc, of the concrete, shear reinforcement must be provided to

carry the excess. This quantity of shear reinforcement is calculated using

Equation (45) except the value of vc shall be obtained from Equation (48)

which includes the effects of torsion.

(7) whenever the nominal torsion stress, vtu, exceeds the maximum

torsion capacity of the concrete, torsion reinforcement in the shape of

closed ties, shall be provided to carry the excess. The required area of

the vertical leg of the closed ties is given by:

[v(tu)V - vtc] b2hs

EQUATION:

A(t)V =

(51)

3[phi][alpha]tbthtfy

and the required area of the horizontal leg of the closed ties is given by:

(v(tu)H-vtc) bh2s

EQUATION:

A(t)H =

(52)

3[phi][alpha]tbthtfy

where,

At

= area of one leg of a closed stirrup resisting

torsion within a distance s, sq in

s

= spacing of torsion reinforcement in a direction

parallel to the longitudinal reinforcement, in

[phi]

= capacity reduction factor equal to 0.85

bt

= center-to-center dimension of a closed rectangular tie

along b, in

ht

= center-to-center dimension of a closed rectangular tie

along h, in

[alpha]t

= 0.66 + 0.33 (ht/bt) < /= 1.50 for ht >/= bt

[alpha]t

= 0.66 + 0.33 (bt/ht) < /= 1.50 for ht < /= bt

The size of the closed tie provided to resist torsion must be the greater of

that required for the vertical (along h) and horizontal (along b)

directions. For the case of b less than h, the torsion stress in the

vertical direction is maximum and the horizontal direction need not be

considered. However, for b greater than h, the torsion stress in the

horizontal direction is maximum. In this case, the required At for the

vertical and horizontal directions must be obtained and the greater value

used to select the closed stirrup. It should be noted that in the

horizontal direction, the beam is not subjected to lateral shear (slab

resists lateral loads) and the value of vtc used in Equation (52) is

calculated from Equation (50) which does not include the effect of shear.

2.08-77