Civil Engineering Reference
In-Depth Information
The design values in table 3-8 are valid for › = 4000 psi:
Table 3-8 Concrete Shear Strength Design Values for
›
= 4000 psi
Equation
Design Value
ACI Section
0.095
b
w
d
ACI 11.2.1.1
V
c
= 2
f
c
ʹ
b
w
d
0.048
b
w
d
ACI 11.4.6.1
0.50 V
c
=
f
c
ʹ
b
w
d
0.48
b
w
d
ACI 11.4.7.9
b
w
d
Maximum ( V
c
+ V
s
) = 10
f
c
ʹ
Joists defined by ACI 8.13
V
c
= 2.2
0.104
b
w
d
ACI 8.13.8
b
w
d
f
c
ʹ
* b
w
and d are in inches and the resulting shear in kips
The selection and spacing of stirrups can be simplified if the spacing is expressed as a function of the effective depth
d (see Reference 3.3). According to ACI 11.4.5.1 and ACI 11.4.5.3, the practical limits of stirrup spacing vary
from s = d/2 to s = d/4, since spacing closer than d/4 is not economical. With one intermediate spacing at d/3, the
calculation and selection of stirrup spacing is greatly simplified. Using the three standard stirrup spacings noted
above (d/2, d/3, and d/4), a specific value of
φ
V
s
can be derived for each stirrup size and spacing as follows:
For vertical stirrups:
V
s
=
φ
A
v
f
y
d
s
φ
ACI Eq. (11.15)
By substituting d/n for s (where n = 2, 3, or 4), the above equation can be rewritten as:
φ
V
s
=φ
A
v
f
y
n
Thus, for No.3 U-stirrups @ s = d/2 with f
y
= 60,000 psi and
φ
= 0.75
φ
V
s
= 0.75(0.22)60
2 = 19.8 kips, say 20 kips
The values
φ
V
s
given in Table 3-9 may be used to select shear reinforcement with Grade 60 rebars.
Table 3-9 Values of
φ
V
s
(f
y
= 60 ksi)
s #3 U-stirrups #4 U-stirrups #5 U-stirrups
d/2 20 kips 36 kips 56 kips
d/3 30 kips 54 kips 84 kips
d/4 40 kips 72 kips 112 kips
*
Valid for stirrups with 2 legs (double the tabulated values for 4 legs, etc.)
It should be noted that these values of
φ
V
s
are not dependent on the member size nor on the concrete strength.
In the above equations, b
w
and d are in inches and the resulting shears are in kips.
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