Torsion -Cont. - dm2_080093

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(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