Civil Engineering Reference
In-Depth Information
And for a bent-up bar or a group of bent-up bars at the same distance from the sup-
port, we have
c
b
w
d
V
s
A
v
f
y
sin
3
f
(ACI Equation 11-17)
8.9
ACI CODE REQUIREMENTS
This section presents a detailed list of the Code requirements controlling the design of web
reinforcing, even though some of these items have been previously mentioned in this chapter:
V
c
, the
Co
de
(11.5.5.1) requires the use of web reinforcing. The value of
V
c
is normally taken as
, but the Code (11.3.2.1) permits the use of the following less conservative value:
1.
When the factored shear
V
u
exceeds one-half the shear design strength
c
b
w
d
2
f
c
2500
w
V
u
d
M
u
c
b
w
d
V
c
1.9
f
b
w
d
3.5
f
(ACI Equation 11-5)
As previously mentioned,
M
u
is the moment occurring simultaneously with
V
u
at the
section in question. The value of
V
u
d
/
M
u
must not be taken greater than 1.0 in calculating
V
c
, according to the Code.
2.
When shear reinforcing is required, the Code states that the amount provided must
fall between certain clearly specified lower and upper limits. If the amount of reinforcing
is too low, it may yield or even snap immediately after the formation of an inclined crack.
As soon as a diagonal crack develops, the tension previously carried by the concrete is
transferred to the web reinforcing. To prevent the stirrups (or other web reinforcing) from
snapping at that time, their area is limited to the minimum value provided at the end of the
next paragraph.
ACI Section 11.5.5.3 specifies a minimu
m a
mount of web reinforcing such as to provide
an ultimate shear strength no less than . Using this provision of the Code should
prevent a sudden shear failure of the beam when inclined cracks occ
ur
. The shear strength
calculated with this expression may not be less than 50
b
w
s
. If a psi strength is avail-
able for a web width
b
w
and a length of beam
s
equal to the stirrup spacing, we will have
c
b
w
s
0.75
f
c
0.75
f
c
b
w
s
A
v
f
y
0.75
f
c
b
w
s
0.75
f
A
v
minimum
(ACI Equation 11-13)
f
y
but not le
ss
than the value obtained with a 50 psi strength
50
b
w
s
/
f
y
.
c
If
f
is gre
at
er than 4444 psi, the minimum value of
A
v
is controlled by the
c
b
w
s
/
f
y
c
expression
0.75
f
. Should
f
be less than 4444 psi, the minimum
A
v
value will
be controlled by the
50
b
w
s
/
f
y
expression.
In SI units
c
b
w
s
0.33
b
w
s
f
y
A
v
, min
1
16
f
f
y
This expression from ACI Section 11.5.5.3 provides the minimum area of web rein-
forcing
A
v
which is to be used as long as the factored torsional moment
T
u
does not exceed
