Civil Engineering Reference
In-Depth Information
3.3.11 Effect of Fibers on Characteristic Length (L
r
)
The characteristic length (
L
r
) is the key parameter linking strains (
) and crack
opening (
w
), [
49
]. In an analytical model,
L
r
is an indication of the crack spacing
considered in calculations.
L
r
is in
ε
fl
uenced by several parameters: type and volume
of
bers, matrix strength, cross-section geometry, presence of conventional rein-
forcement (longitudinal or transverse), load level (service, ultimate), etc., therefore
no consensus has yet been achieved to determine it.
Figure
3.7
shows the in
uence of
L
r
on a member response, where
L
r
varies
from
h
/4 to 2
h
for a 150 mm deep and 400 mm wide SFRC beam. The parametric
analysis done by De-Montaignac et al. [
49
] showed that increasing
L
r
reduces the
bending strength and thus estimates wider cracks for a given bending moment.
De-Montaignac et al. [
49
] ensured that it is more conservative to adopt a larger
L
r
for
predicting crack width in service conditions or for predicting ultimate strength [
49
].
For FRC members, some researchers have proposed the utilization of a constant
value for
L
r
(Table
3.2
) while other researchers suggest that this value should vary
depending on load.
De-Montaignac et al. [
49
] concluded that:
Fibers in a high amount (0.75
fl
1.25 %) confers to concrete a better structural
behavior, proving a hardening behavior in bending, limiting crack opening in SLS
and giving a ductile behavior in ULS [
49
].
If the structural behavior is governed by the maximum crack width the use of a
single value of
L
r
in a section analysis gives good correlation with experimental
values [
49
].
De-Montaignac et al. [
49
] recommends the use of
L
r
=
2h
for FRC members
without conventional reinforcement and
L
r
= min(h, s
m
) for members with con-
ventional reinforcement [
49
].
-
Table 3.2 Proposed values for L
r
[
49
]
Reinforcement
Past studies for deflection,
average curvature and crack width
This study for maximum
crack width
Rule
References
SFRC
h/2
RILEM [
77
],
Massicotte [
117
],
Ultkjaer et al. [
118
],
Kooiman [
119
],
Iyengar et al. [
120
],
Pedersen [
121
]
2h
2h/3
AFGC [
122
]
h
b [
2
], CNR [
123
]
2h
Strack [
124
]
Min [s
m
; h/2]
a
Min [s
m
;h]
a
SFRC and
reinforcing bars
Massicotte [
117
]
Min [s
m
;y]
a
b [
2
], CNR [
123
]
a
s
m
is estimated with the Eurocode 2 [
125
]
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