Continuous
concrete beam
s
strengthened with fibre
reinforced polymer
Lander Vasseur
1
Supervisors:
Stijn Matthys
2
, Luc
Taerwe
3
Abstract
:
The capacity of concrete members can be increased
by applying FRP EBR (Fibre Reinforced Polymer

Externally
Bonded Rei
nfor
cement
).
Though
t
he structural behaviour of
reinforced concrete beams strengthened
in flexure
with FRP
EBR has been extensively investigated
for
isostatic beams
, limited
information on the behaviour of
FRP strengthened
continuous
(hyperstatic) beams is
available. In the
following
,
some specific
aspects of
strengthened continuous beams are investigated.
Because continuous beams have a moment redistribution, a
moment line with different signs and a different moment/shear

force ratio, debonding mechanisms
,
which cause
bond failure
of
the laminate,
can appear at an earlier or later stage or can be
even avoided.
Keywords
:
Concrete,
FRP EBR,
Flexural strengthening,
Hyperstatic beam,
Debonding Mechanism
,
Non

linear behaviour
I.
I
NTRODUCTION
Structures may need to
be strengthened for many different
reasons
, such as
change in function
and durability issues
.
There are different str
engthening techniques available, among
which
the use of
FRP EBR
(Fibre Reinforced Polymer

Externally Bonded Reinforcement)
.
Herewith,
adv
anced
continuous fibre based compo
sit
s
are glued in the tension zone
of concrete beams.
The use of FRP EBR will increase the
capacity of the member, but additional mechanisms of failure
(debonding mechanisms)
may govern the
ultimate state,
among which bond
failure between the laminate and the
concrete.
This
study focuses on
the flexural strengthening
of
continuous
beams
with FRP EBR
.
Typically for continuous beams
is the
non

linear behaviour
,
which is characterized by the moment
redistribution. This moment
redistribution
influences the
above mentioned debonding mechanisms.
In addition
the
moment line of continuous beams and isostatic beams differs
in such a way,
that different debonding mechanisms may
govern.
Figure
1
: Hyperstatic beam used in study
1
PhD

Student,
Magnel Laboratory for
C
oncrete
R
ese
arch,
Dept. of Structural En
g
.
(IR 14)
, Ghent University, Belgium, Lander.Vasseur@UGent.be
2
Prof. Dr. Ir.,
Magnel Laboratory for
Concrete Research
,
Dept. of Structural Eng
.
(
IR
14)
, Ghent University, Belgium, Stijn.Matthys@UGent.be
2
Prof. Dr. Ir.,
Magnel Laboratory for
Concrete Research
,
Dept. of Structural Eng.
(IR
14)
, Ghent University, Belgium, Luc.Taerwe@UGent.be
In the
framework of this PhD research,
an analytical and
experimental study is
performed
, both based on symmetrical
two span beams with
three supports and two
point
loads
(figure 1).
This article focuses on the analytical study with
respect to debonding
II.
N
ON LINE
AR BEHAVIOUR OF CONT
INUOUS BEAMS
First a short introduction will be given about the non

linear
behaviour of continuous beams.
Because of the
indeterminateness
of a hyperstatic construction, this
construction can be calculated both following the linear elas
tic
theory and following the more complex but realistic non

linear
theory.
Using the linear theory
, the relationship between the
acting load and the internal moment is linear, as
in the case of
isostatic beams. While
calculat
ions
following the non

linear
t
heory
results in a
non

linear relationship between acting load
and internal moment
, which is
relate
d
to the variable stiffness
along the length of the beam (and which also depends on the
load level). This
can involve
, in the case of hyperstatic beams,
a si
gnificant redistribution of moments with respect to the
linear situation.
For this study, a simplified model is used
based on
[1]
. Herewith
two zones with each a constant flexural
stiffness over the length of the zone
s are assumed
. The first
zone
is located around the middle support
(with stiffness
K
sup
)
and the se
cond one is located in the span (with stiffness
K
span
)
(figure
1
).
To illustrate the non

linear behaviour of continuous beams,
figure 2 represents the moment redistribution of a two span
beam (figure 1) with a height of 400
mm and a width of 200
mm. For internal steel r
einforcement two bars (diam 12)
and
one bar (diam 20) are considered in the spans and two bars
(diam 12) and one bar (diam 18) at the mid

support. The
corresponding reinfor
cement ratio’s are
s
,span
= 0
,
75 % and
s
,
sup
= 0
,
67 %. As external reinforcement CFRP
(Carbon
Fibre Reinforced Polymer)
laminates are glued at the soffit of
the spans with corresponding reinforcement ratio
f,span
=
0
,
17
%. In the
figure 2
the field span
moment M
span
and t
he
support cracks
span cracks
support yields
span yields
support
collapses
0
40
80
120
160
200
240
200
160
120
80
40
0
40
80
120
160
200
240
F [kN]
Nonlinear moment
distribution
(with FRP EBR)
Linear elastic
moment distribution
M
span
[kNm]  span moment
M
support
[kNm]  support moment
Figure 2: Moment redistribution of 2 span beam
mid

support moment M
support
at the
critical section
(where
the
moment
is maximum)
is given
in function of the acting point
load
F. Herewith it is remarkable that the moment the internal
steel reinforcemen
t at the support start to yield, a considerable
redistribution of moments is noticed. This effect is called the
moment redistribution.
III.
L
OS OF COMPOSITE ACTI
ON
As mentioned in the introduction, b
ond failure in case of
FRP EBR implies the loss of composite a
ction between the
concrete and the FRP
reinforcement
.
This phenomenon
appears once the
transfer
red
stresses in the bond interface
exceed a maximum transferable bond stress
.
This type of
failure
is
often
very sudden and
brittle.
In figure 3 an example
of a
debonded laminate from experimental testing is given.
Figure 3:
Debonding which results in
loss of composite action
According to Matthys
[2]
different
bond
failure aspects
can
be
distinguished
.
First there is
debonding by c
rack bridging
,
caused by a combination of peeling effect and local
fluctuations in the interfacial shear stresses at a flexural and/or
shear crack. Secondly ther
e is
debonding by f
orce transfer
.
This debonding mechanism appears once the overall
distribution of interfacial shear stresses, caused by the acting
shear force, exceeds the bond strength between the concrete
and the FRP reinforcement. Next there is
debond
ing by
curtailment or restricted
anchorage length
. Similar to internal
steel reinforcement, the remaining force in FRP has to be
anchored due to a certain anchorage length. By applying a too
short anchorage length, debonding will occur. And at last there
i
s
debonding by e
nd shear failure
, which occurs i
f a shear
crack appears at the
laminate

end and
propagate
s
at the
level
of the intern
al steel reinforcement
. In this case the laminate as
well as a thick layer of concrete will rip off.
IV.
S
PECIFIC DEBONDING AS
P
ECTS RELATED TO
CONTINUOUS BEAMS
AND CONCLUSIONS
T
he
re is a
difference between
the moment line of
isostatic
beams and continuous beams, which may influence the
debonding mechanisms
. More
specific, the moment line
of
Figure 4:
Moments with opposite signs in continuous beams and
anchoring laminates into compression zones
continuous beams is one with opposite signs.
Whereas the
moment in the span is positive, the moment at the mid

support
is negative. As a result, the compression
zones in the spans are
situated at the top of the beam, at the mid

support the
compression zone is situated at the soffit of the beam (shaded
zones in
f
igure
4
). This allows in contrast to reinforced
isostatic beams, to anchor the CFRP laminates in the
co
mpression zones (except for the outer supports). By
extending a laminate into these compression zones, two
out of
the four differ
ent debonding mechanisms will be avoided:
debonding by a limited anchorage length and debonding by
end shear failure (concrete
rip

off)
, which is a big advantage
in comparison with isostatic beams
.
To evaluate the effect of the moment redistribution
on the
different debonding mechanisms
,
a comparison is made with
respect to the linear elastic theory by an analytical
study
.
Herewit
h a
beam configuration
is used following figure 1, with
similar internal reinforcement ratios mentioned in paragraph
II. As FRP EBR, variable
sections of laminates are used
.
Herewith laminates are applied at the soffit of the spans and/or
on top of the bea
m at the
middle support
. The lengths of the
laminates are chosen in such a way, they are not anchored into
the compression zones, with the aim
to
not
avoid
certain
debonding mechanisms.
Herewith the length of the laminate at
the soffit of the span equals 2
000 mm and is applied so that
the centre of the laminate is just beneath the point load. The
laminate at the top of the beam above the mid

support equals
1600 mm
.
During the analytical study all different debonding
mechanisms are investigated at three diff
erent locations along
the length of the beam (case A, case B and case C in figure 4).
Figure 5 gives the effect of the moment redistribution on the
different debonding mechanisms calculated following
[3]
at
different locations in comparison with the linear
elastic theory.
Herewith it can be noticed that following this research project
differences can be found for th
e
particular
configuration
of
46
% later debonding (
debonding by restricted anchorage
length in case A
) until 26 % earlier debonding (
debonding b
y
restricted anchorage length in case B
), which is a considerable
difference.
Hence
it
can be recommended to do calculations of
strengthened hyperstatic constructions following the non

linear theory.
Figure 5:
Effect of non

linear behaviour on the debond
ing load
R
EFERENCES
[1]
Taerwe, L. and B. Espion.
Serviceability and the Nonlinear Design of
Concrete Structures
. in
IABSE PERIODICA 2/1989
. 1989.
[2]
Matthys, S.,
Structural behaviour and design of concrete members
strengthened with externally
bonded FRP reinforcement
, 2000, Ghent
University: Ghent. p. 345.
[3]
fib bulletin 14, Externally bonded FRP reinforcement for RC
structures
. 2001, International federation for structural concrete,
Lausanne.
Case A
Case B
Case C
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