Civil Engineering Reference
In-Depth Information
8.
Section 8.11.8 of the ACI Code permits a shear of 1.1
V
c
for the ribs of joist construc-
tion, as where we have closely spaced T beams with tapered webs. For the 10% increase in
V
c
,
the joist proportions must meet the provisions of ACI Section 8.11. In that section it is stated
that the ribs must be no less than 4 in. wide, must have depths not more than 3.5 times the min-
imum width of the ribs, and may not have clear spacings between the ribs greater than 30 in.
8.10
EXAMPLE SHEAR DESIGN PROBLEMS
Example 8.1 illustrates the selection of a beam with a sufficiently large cross section so that
no web reinforcing is required. The resulting beam is unusually large. It is normally consid-
ered much better practice to use appreciably smaller sections constructed with web reinforc-
ing. The reader should also realize that it is good construction practice to use some stirrups in
all reinforced concrete beams (even though they may not be required by shear) because they
enable the workers to build for each beam a cage of steel that can be conveniently handled.
EXAMPLE 8.1
Determine the minimum cross section required for a rectangular beam from a shear standpoint so
that no web reinforcing is r
eq
uired by the ACI Code if
V
u
38 k and
c
f
4000 psi. Use the con-
c
b
w
d
servative value of
V
c
2
f
.
SOLUTION
Shear strength provided by concrete is determined by the equation
V
c
(0.75)(2
4000
b
w
d
)
94.87
b
w
d
But the ACI Code 11.5.5.1 states that a minimum area of shear reinforcement is to be provided if
V
u
exceeds
V
c
:
1
2
38,000
(
2
)(94.87
b
w
d
)
b
w
d
801.1 in.
Use 24
36
beam (
d
33.5
)
The design of web reinforcing is illustrated by Examples 8.2 through 8.6. Maximum
vertical stirrup spacings have been given previously, whereas no comment has been made
about minimum spacings. Stirrups must be spaced far enough apart to permit the aggre-
gate to pass through, and, in addition, they must be reasonably few in number so as to
keep within reason the amount of labor involved in fabricating and placing them. Accord-
ingly, minimum spacings of 3 or 4 in. are normally used. Usually #3 stirrups are assumed,
and if the calculated design spacings are less than
d
/4, larger-diameter stirrups can be
used. Another alternative is to use
stirrups instead of
stirrups. Different diameter
stirrups should not be used in the same beam, or confusion will result.
As is illustrated in Examples 8.3, 8.5, and 8.6, it is quite convenient to draw the
V
u
di-
agram and carefully label it with values of such items as
V
c
/2, and
V
u
at a distance
d
from the face of the support and to show the dimensions involved.
Some designers place their first stirrup a distance
d
from the face of the support,
while others place it one-half of the end-calculated spacing requirement from the face.
The more common practice is to put the first one 2 or 3 in. from the support.
V
c
,
