Civil Engineering Reference
In-Depth Information
8.13
SHEAR STRENGTH OF MEMBERS SUBJECTED
TO AXIAL FORCES
Reinforced concrete members subjected to shear forces can at the same time be loaded
with axial compression or axial tension forces due to wind, earthquake, gravity loads ap-
plied to horizontal or inclined members, shrinkage in restrained members, and so on.
These forces can affect the shear design of our members. Compressive loads tend to pre-
vent cracks from developing. As a result, they provide members with larger compressive
areas and thus greater shear strengths. On the other hand, tensile forces exaggerate cracks
and reduce shear resistances because they will fairly well eliminate shear resistance due to
aggregate interlock.
When we have appreciable axial compression, the following equation can be used to
compute the shear carrying capacity of a concrete member:
N
u
2000
A
g
f
c
b
w
d
V
c
2
1
(ACI Equation 11-4)
For a member subjected to a significant axial tensile force, the shear capacity of the
concrete may be determined from the following expression:
f
c
b
w
d
N
u
500
A
g
V
c
2
1
(ACI Equation 11-8)
In this expression
N
u
the axial load is minus if the load is tensile. You might note that
if the computed value of for use in this equation is 500 psi or more, the concrete
will have lost its capacity to carry shear. (The value of
V
c
used may not be less than zero.)
N
u
/
A
g
The SI values for ACI Equations 11-4 and 11-8 are, respectively,
c
N
u
14
A
g
f
V
c
1
b
w
d
6
c
0.3
N
u
A
g
f
V
c
1
b
w
d
6
Instead of using ACI Equation 11-4 to compute the shear capacity of sections subject
to axial compressive loads, ACI Equation 11-5 may be used. In this equation a revised
moment,
M
m
, may be substituted for
M
u
at the section in question and
V
u
d
/
M
u
shall not be
1.0. For this case
V
c
may not be larger than the value obtained with ACI Equation 11-7.
w
V
u
d
c
c
b
w
d
(ACI Equation 11-5)
V
c
1.9
f
2500
b
w
d
3.5
f
M
u
4
h
d
(ACI Equation 11-6)
M
m
M
u
N
u
8
N
u
500
A
g
c
b
w
d
(ACI Equation 11-7)
V
c
may not be
3.5
f
1
