Building Design and Construction Handbook - Merritt - Ventech!

CONCRETE CONSTRUCTION 9.99
tored shear force Vu is less than half the design shear strength �Vc of the concrete
alone. Torsion should be combined with shear when the factored loads cause a
torsional moment Tu larger than
2 Acp for nonprestressed beams (see Art.
��ƒ�� c �
pcp 9.48).
Shear strength should be computed at critical sections in a beam from Eq. (9.38).
Open or closed stirrups may be used as reinforcement for shear in beams; but closed
stirrups are required for torsion. The minimum area for open or closed stirrups for
vertical shear only, to be used where 0.5�Vc � Vu � �Vc and the factored torsional
moment Tu can be neglected, should be calculated from
50bws A � (9.81)
v
where A v � area of all vertical legs in the spacing s, in parallel to flexural reinforcement,
in 2
b w � thickness of beam web, in 2
ƒ y � yield strength of reinforcing steel, psi
Note that this minimum area provides a capacity for 50-psi shear on the cross
section b ws.
Where V u exceeds V c, the cross-sectional area A v of the legs of open or closed
vertical stirrups at each spacing s should be calculated from Eq. (9.40a). A v is the
total area of vertical legs, two legs for a common open U stirrup or the total of all
legs for a transverse multiple U. Note that there are three zones in which the
required A v may be supplied by various combinations of size and spacing of stirrups
(Fig. 9.37):
1. Beginning 1 or 2 in from the face of supports and extending over a distance
d from each support, where d is the depth from extreme compression surface to
centroid of tension steel (A v is based on V u at d from support).
2. Between distance d from each support and the point where �V s � V u � �V c
� 50b ws (required A v decreases from maximum to minimum).
3. Distance over which minimum reinforcement is required (minimum A v extends
from the point where �V s � 50b ws to the point where V u � 0.5�V c).
FIGURE 9.37 Required shear reinforcement in three zones of a beam
between supports and midspan is determined by cross-hatched areas.
ƒ y