Civil Engineering Reference
In-Depth Information
beam. Figure 4.4 shows the shape of the proposed σ-ε relationship used in
this analysis. The mathematical form of the σ-ε relationship is expressed as
follows:
σ
for
(
ε
≤
ε
≤
ε
)
cu
cu
c
0
E
ε
for
(
ε
≤
ε ε
≤
)
c
0
t
0
σ ε
( )
=
(4.4a)
σ
+
ψ
(
ε
−
ε
)
for
(
ε
≤ ≤
ε
ε
)
to
t
0
t
0
t
1
σ
+
λ
(
ε
−
ε
)
for
(
ε
≤ ≤
ε
ε
)
tu
t
1
t
1
tu
where:
σ
ε
cu
E
=
c
0
σ
−
−
σ
tu
t
0
ψ
=
(4.4b)
ε
ε
t
t
1
0
−
σ
tu
λ
=
ε
−
ε
tu
t
1
In Figure 4.4, σ
t
0
and ε
t
0
represent the cracking strength and the corre-
sponding elastic strain, respectively; σ
tu
and ε
t
1
represent the residual stress
and the residual strain, respectively, at a point where the slope of softening
tensile curve changes; ε
tu
is the ultimate tensile strain;
E
is Young's modulus
for the SFRC; σ
cu
and ε
c
0
are the compressive strength and the analogous
elastic strain, respectively; and ε
cu
is the ultimate compressive strain.
As mentioned in Section 4.2.1, in compression, the concrete stress-strain
relationship can be divided into ascending and descending branches. The
behavior of FRP-confined concrete for flexural members can be assumed
as similar to that of stirrup-confined concrete. Hence, confinement has no
effect on the slope of the ascending part of the stress-strain relationship, and
it is the same as for unconfined concrete, but not in the descending part in
Figure 4.2. The compressive flexural strengths for both unconfined and con-
fined concrete are the same and equal to the cylinder compressive strength.
Figure 4.5 shows the uniaxial stress-strain curve for carbon and glass FRP
composites in the fiber direction. For a more generalized expression, many
studies show that instead of maintaining constant after compressive strength
σ
cu
, the σ-ε relationship may descend and the rate of descending is depen-
dent on
V
f
l
/
d
, where
V
f
is the volume ratio of fiber to concrete,
l
is the fiber
length, and
d
is the fiber diameter (Gao 1991).
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