Direct Shear

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EQUATION:
vc = [phi][1.9(f'c)1/2 + 2500 p] < /=
(44)
2.28[phi](f'c)1/2
where,
vc = maximum shear capacity of an unreinforced web, psi
p = reinforcement ratio of the tension reinforcement at the
support
[phi] = capacity reduction factor equal to 0.85
(3) whenever the nominal shear stress, vu, exceeds the shear
capacity, vc, of the concrete, shear reinforcement must be provided to
carry the excess.  Closed ties placed perpendicular to the flexural
reinforcement must be used to furnish the additional shear capacity.  Open
stirrups, either single or double leg, are not permitted.  The required area
of shear reinforcement is calculated using:
EQUATION:
Av = [(vu - vc) b ss]/[phi]fy
(45)
where,
Av = total area of stirrups, sq in
vu-vc = excess shear stress, psi
ss = spacing of stirrups in the direction parallel to the
longitudinal reinforcement, in
[phi] = capacity reduction factor equal to 0.85
(4) In order to insure the full development of the flexural
reinforcement in a beam, a premature shear failure must be prevented.  The
following limitations must be considered in the design of the closed ties:
a) the design shear stress (excess shear stress vu - vc) used in
Equation (45) shall be equal to, or greater than, the shear capacity of
unreinforced concrete, vc, as obtained from Equation (44); b) the nominal
shear stress, vu, must not exceed 10 [phi] (f'c)1/2; c) the area,
Av, of closed ties should not be less than 0.0015bss; d) the required
area, Av, of closed ties shall be determined at the critical section, and
this quantity of reinforcement shall be uniformly distributed throughout the
member; and e) the maximum spacing of closed ties is limited to d/2 when
vu - vc is less than 4 [phi] (f'c)1/2 but is further limited to d/4
when vu - vc is greater than 4 [phi] (f'c)1/2.
e.
Direct Shear.
(1) Direct shear failure of a member is characterized by the rapid
propagation of a vertical crack through the depth of the member.  This crack
is usually located at the supports where the maximum shear stresses occur.
Failure of this type is possible even in members reinforced for diagonal
tension.
2.08-74