Civil Engineering Reference
In-Depth Information
that there are only a few, if any, bent-up bars in a beam and that they may not be conve-
niently located for use as web reinforcement.
Diagonal cracks will occur in beams with shear reinforcing at almost the same loads
that they occur in beams of the same size without shear reinforcing. The shear reinforcing
makes its presence known only after the cracks begin to form. At that time, beams must
have sufficient shear reinforcing to resist the shear force not resisted by the concrete.
After a shear crack has developed in a beam, only a little shear can be transferred
across the crack unless web reinforcing is used to bridge the gap. When such reinforcing
is present, it keeps the pieces of concrete on the two sides of the crack from separating.
Several benefits result. These include:
1.
The steel reinforcing passing across the cracks carries shear directly.
2.
The reinforcing keeps the cracks from becoming larger, and this enables the con-
crete to transfer shear across the cracks by aggregate interlock.
3.
The stirrups wrapped around the core of concrete act like hoops and thus increase
the beam's strength and ductility. In a related fashion, the stirrups tie the longitu-
dinal bars into the concrete core of the beam and restrain them from prying off the
covering concrete.
4.
The holding together of the concrete on the two sides of the cracks helps keep the
cracks from moving into the compression zone of the beam. Remember that other
than for deformed wire fabric, the yield stress of the web reinforcing is limited to
60 ksi to limit the width of the cracks.
8.8
DESIGN FOR SHEAR
The maximum shear
V
u
in a beam must not exceed the design shear capacity of the beam
cross section
V
n
, where
is 0.75 and
V
n
is the nominal shear strength of the concrete
and the shear reinforcing.
V
u
V
n
The value of
V
n
can be broken down into the design shear strength of the concrete
V
c
is pro-
vided in the Code for different situations, and thus we are able to compute the required
value of
V
c
plus the design shear strength of the shear reinforcing
V
s
. The value of
V
s
for each situation:
V
u
V
c
V
s
For this derivation an equal sign is used:
V
u
V
c
V
s
The purpose of stirrups is to minimize the size of diagonal tension cracks or to carry the
diagonal tension stress from one side of the crack to the other. Very little tension is carried
by the stirrups until after a crack begins to form. Before the inclined cracks begin to form,
the strain in the stirrups is equal to the strain in the adjacent concrete. Because this concrete
cracks at very low diagonal tensile stresses, the stresses in the stirrups at that time are very
small, perhaps only 3 to 6 ksi. You can see that these stirrups do not prevent inclined cracks
and that they really aren't a significant factor until the cracks begin to develop.
