Torsion -Cont. - dm2_080094

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(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