Abstract: Steel is the
most common used material in reinforced Concrete in Civil Engineering
applications. But, because of the corrosive characteristics of steel, the
durability of the concrete cannot be ensured in Alkaline medium. In order to
prevent this drawback, Glass Fibre Reinforced Polymer can be proposed as an
alternative material to steel which has excellent properties such as high
strength, light weight, flexibility, and resistance to chemical harm. Because
of its flexibility, it can be preferred in concrete beams of curved structures
such as bridges, arches, roads, Water tanks, etc. But larger deflections can be
expected because of its low modulus of elasticity. As it is a new material to
the industry, the flexural performance should be tested especially for
curvature effects. This research addresses the finite element modelling of
curvature effects on flexural performance of GFRP concrete beams.
GFRP, FRP, FEM,
Flexure, Reinforcement Bars
Fibre Reinforced Polymer (GFRP) bars have been developed in recent times as an
alternative material to steel reinforcement in Civil Engineering applications.
This material is being successfully used as internal reinforcement bars in new
concrete structures which are exposed to corrosive environment.
Fibre Reinforced polymer materials were introduced in aerospace and automotive
industries due to their superior strength and light weight. FRP is being used
as internal reinforcement in concrete structures in the forms of bars, pre
stressing tendons and rods.
a new material gets introduced to the industry, experimental testing on its
properties and failure modes should be carried out. But as it consumes more
time and cost effective simulation of a numerical model will be more effective
which can even give more results that cannot be obtained by experimental
purpose of this research is simulating a numerical model to obtain the
curvature effects on flexural performance of GFRP concrete beams. Due to the
low modulus of Elasticity of GFRP, it is possible to produce bars with large
radius curves. But this will induce bending stresses along the bar. And a
stress reduction can be also expected in the bent portion. So, when it will be
subjected to bending loads, failure modes will be more severe. Thus, the
flexural behaviour should be properly investigated.
research will utilize Finite element modelling using ABAQUS software by
implementing experimental results data for material properties.
Manufacture of GFRP Reinforcing Bars
manufacturing methods are being carried out to produce GFRP reinforcement bars
such as pultrusion, wet lay-up, pull-winding, filament winding and injection
modelling. But, Pultrusion manufacturing is the most typical method to produce
strong and light weight bars, rods and tendons. This is an automated
manufacturing method which doesn’t require much labours and is cost effective.
this method, glass fibres are pulled out from the spools through a device which
coats them polymer resin. Then, heat-treatment will be given for those fibres
and later it will be cut to the appropriate lengths. This is an ideal process
which can only produce constant cross of bars but in different shapes,
diameters, and tensile strengths. The bars which are produced in this method
will have smooth surface. Further, in order to improve the bond mechanisms,
various surface treatments will be applied between the concrete and bars.
Material Behaviour of FRP bars
When FRP bars are used for reinforcement
bars in concrete structures, the fibres are oriented parallel to the bar’s
length and also continuous. Comparing to the transverse direction, this orientation
makes FRPs highly orthotropic with high strength and stiffness. The tensile
behaviour of FRP bars are linear-elastic up to failure. Thus, FRP bars rupture
don’t shows the plastic behaviour or yielding like steel reinforcement.
Therefore, it’s more brittle than steel bars.
As steel is considered as an isotropic
material, the compressive properties can be said equal to the tensile
properties. But, FRP is an anisotropic material, where the compressive strength
is significantly lower than the tensile strength. In the literature it is said
that the compressive strength of FRP bars are 35% of its tensile strength (Kobayashi &
Fujisaki, 1995). But some other
findings show that it is 80% of its tensile strength (Chaallal & Benmokrane, 1993). Other mechanical
properties such as ultimate tensile strength, ultimate strain and tensile
modulus of elasticity will vary according to their fibre types, manufacturing
process, resin matrix type and uses of additives. But, it has been proved that
the tensile modulus of elasticity of FRP is considerably lower than the steel. (Generally
less than 100GPa, steel- 200GPa). Comparatively it has also a lower axial
stiffness. As larger deflection can be expected, the design of concrete
structures with FRP reinforcement bars should be governed by Serviceability
glass fibres, Carbon and Aramid fibres are also widely used for structural
applications. Figure 1 shows different types of FRP bars. It has been proved
that Carbon and Aramid FRPs has excellent modulus of elasticity, long term
behaviour, fatigue behaviour, alkaline resistance comparing to the GFRP. But
GFRP was found more economical comparing to the other FRPs. E-glass is the most
commonly used grade because of its low cost and modulus of elasticity ranging.
Tests on GFRP reinforced
An experimental study of flexural
behaviour of GFRP concrete beams was carried out for 24 concrete beams with
type a and type b where type a is uncrack specimen and type b is specimen with pre-crack
in mid span (Barris C. ,
Torres, Turon, Baena , & Mias, 2008). A four-point
bending load test was conducted to evaluate the short-term serviceability
behaviour. The Strain behaviours were investigated and variation in neutral
axis depth along the cracking was also observed. It was also found that the
crack width is depended on the bond coefficient.
Another experimental study was conducted
on crack width of GFRP concrete beams and the cracking behaviour of 15 beams
were observed (Barris C. ,
Torres, Vilanova, Mias, & Liorens, 2016). The Digital Image Correlation
(DIC) technique was used to measure the crack widths, over the flexural zone.
It was found that the crack width in reinforced concrete flexural members
depend on the cover, bar spacing, bond stress between concrete and rebar, ø/?eff
ratio and strain level of the reinforcement.
An investigation was carried out on
Flexure-Shear Analysis of concrete beam reinforced with GFRP bars (Ramadass &
Job Thomas, 2010).
The influence of longitudinal reinforcement ratio, vertical reinforcement
ratio, and compressive strength of concrete, and shear strength of GFRP was
analysed. The nominal shear strength (Vn) of the concrete section can
be evaluated using equation (1), and the nominal shear strength resistance (Vn*)
corresponding to the flexural capacity of the beam subjected to concentrated
load can be computed by equation (2).
Where Vf is the shear resistance, Vc is
the shear strength of concrete section without stirrups Mn refers
the nominal moment of resistance of the section and a is the shear span. It was
found that the shear strength of the beam increases with the increase of
longitudinal and vertical reinforcement. The a/d ratio at failure mode change
also increase with the increment of
concrete length and amount of vertical reinforcement.
was done to strengthen the reinforced concrete beams with CFRP and GFRP. 3
control beams, 3 CFRP strengthened beams, and 3 GFRP strengthened beams were
totally casted and magnetized apparatus with Kinear Variable differential
transformer (LVDT) was used to measure the displacements.in this study, shear
edges of the beams were wrapped twice by CFRPs and GFRPs. Both materials have
shown a successful results in yielding. Even the corner rounding was
successful, double wrapping was not given a successful results (Onal, 2014).
Behaviour of reinforced concrete beams
reinforced with GFRP bars were also investigated to compare the strength,
reinforcement deformation, displacement, and some anchorage aspects between the
GFRP & steel-reinforced beam (Giongo, Paultre,
& Tavares, 2008). A four point bending test was
conducted and found longitudinal reinforcement stiffness is the m main
parameter which controls the behaviour of the reinforced concrete beams. It was
concluded that the design procedure carried out here was not able to ensure the
flexural capacity. But it was clearly found that GFRP reinforced beams to be
designed for serviceability limit state instead of ultimate limit state. Also
CFRP has shown a higher failure reduction than GFRP.
Another experimental test study was
conducted and three point bending test was carried out for simply supported
concrete beams reinforced with longitudinal GFRP bars and GFRP stirrups. A
finite element analysis was performed for this test. The objective was to investigate the
influence of longitudinal GFRP reinforcing bar’s arrangement on the effective
strength of GFRP stirrups. The strain behaviour of the shear stirrups was also
investigated. It was observed that when the shear reinforcement ratio
increases, the crack sizes at the peak load was also increased (Stoner, 2015).
Finite Element Modelling of
Concrete Beams Reinforced with FRP
Ferreira et al (2001) has simulated a
model for the finite element analysis of concrete beams reinforced with GFRP longitudinal
reinforcement bars (Stoner, 2015). The formulated
model utilized two dimensional degenerated concrete shell elements based on a
first order shear deformation theory (Stoner, 2015). Several
experimental tests was conducted to the concrete beams and the experimental
results were analysed. A strong correlation between the experimental results
and the numerical model was found. The generated model was applicable to shells
and plates of arbitrary shapes.
Rafi et al (2007) performed a two
dimensional non-linear finite element analysis of simply supported concrete
beams reinforced with Carbon fibre reinforced polymer (CFRP) bars (Stoner, 2015). In this study, a smeared crack approach has
been modelled to analyse the tensile behaviour. The cracking criteria can be
explained by fracture energy (Gf) and Gf can be computed
using equation (3).
Where a = 80.6, n = 0.32 and ønmax
is the maximum size of aggregate. The non-linear analysis was performed by
incorporating the material models and element formation into the finite element
analysis software DIANA. An excellent numerical stability was observed and
strong correlation between the experimental results and numerical results was
Demenico et al. (2014) proposed a finite
element-based limit analysis approach to predict the peak load and failure
mechanism of concrete members reinforced with FRP bars (Stoner, 2015). The proposed
analysis consists both Elastic Compensation Method (ECM) and the Linear
Matching method (LMM). The implementation of the ECM and LMM was conducted
using the Finite element software ADINA. Even the model was able to provide the
precise upper and lower boundary on the peak load, the model has not provided
accurate predictions for under reinforced beams. This was concluded as a
rupture of FRP bars which represented a brittle failure even the proposed
methodology has focused on the plastic behaviour. Because the brittle failure
of under reinforced concrete element is not considered in practical
applications, this limitation was acceptable.
By now, many experimental studies and as
well as numerical studies has been carried out on GFRP concrete beams to
investigate their strength, flexural behaviour, shear behaviour, crack widths,
mechanical properties and comparative behaviour with other FRPs. The curvature
effects of GFRP beams have not been widely investigated till now. Even it has
been introduced to the structural applications because of its non-corrosive
behaviour, it has many limitations too. Especially, because of the low modulus
of Elasticity, excess deflections can be expected under bending. And as it is a
brittle material, it can be fail in rupture under bending.in most of the investigations,
the correlation between the experimental results and numerical model fit very
well. ABACUS, ANSYS, and ADINA were widely used Softwares for the finite
element modelling of GFRP beams in past studies.
It’s my privilege to express my
gratitude to my research supervisor Dr.J.C.P.H.Gamage for her support and
guidance for this research. I would like to extend my thanks to the instructors
who were very helpful and motivate. Also, I would like to thank my colleagues
who are doing the research with me.
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