Civil Engineering Reference
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M
nx
M
ny
1 - β
M
ny
M
noy
+
=1
M
nox
M
noy
β
log 0.5/log β
log 0.5/log β
M
nx
M
nox
M
ny
M
noy
=1
+
1.0
M
nx
β
M
ny
M
nx
+
=1
M
ny
1 - β
+
=1
M
noy
M
nox
M
noy
M
nox
β
45 deg
M
nx
M
nox
0
β
1.0
Figure 5.11
Adimensional load contour at a constant
P
n
.
5.9.1 Concrete contribution,
V
c
,
for
rectangular sections
According to ACI 440.1R-06, the concrete shear capacity,
V
c
,
of flexural
members using FRP as main reinforcement can be evaluated as
(5.55)
Vkfbd
c
=
′
c
w
2
Vkfbd
[or
=
′
for SI Units]
c
c
w
where
k
is the ratio of depth of neutral axis to reinforcement depth,
d.
For
members with only one layer of tensile reinforcement,
k
is calculated according
to ACI 440.1R-06 as
(
) (
)
(
)
2
(5.56)
k
=ρ+ρ
2
n
n
-
ρ
n
ff
ff
ff
where ρ
f
is the ratio of the longitudinal FRP bars and
n
f
is the modular
ratio:
n
f
=
E
f
/
E
c
.
For columns, however, multiple layers of longitudinal reinforcement ren-
der Equation (5.56) inaccurate. To generalize the
V
c
formulation for rect-
angular columns, the location of the neutral axis in a cracked section can
be calculated by equalizing the first moments of area of the compressive
and transformed tensile portions of the cross section around a separating
neutral axis located at
x
=
kd.
This equation can be written as
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