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Material properties of fibre reinforced polymer (FRP) reinforcement
in compression – A review
Lukas Bujotzek1,*, Dominik Hiesch1, Redouan El Ghadioui2, Tilo Proske2
1. TU Darmstadt, Institute of Concrete and Masonry Structures, Darmstadt, Germany
2. Dr.-Ing., TU Darmstadt, Institute of Concrete and Masonry Structures, Darmstadt, Germany
*Corresponding author email: bujotzek@massivbau.tu-darmstadt.de
Abstract
Corrosion of steel reinforcement is the reason for a large part of damages to existing steel-reinforced
concrete structures. For this reason, alternative reinforcement materials have become an important
subject of research. As a reasonable alternative to conventional steel reinforcement, bars made of fibre-
reinforced polymers (FRP) have proven to be applicable. Tensile properties of such FRP bars have been
investigated for several decades already. Test procedures to determine the modulus of elasticity in
tension and the tensile strength are precisely specified in accepted international guidelines. Within these
guidelines and standards, the contribution of FRP reinforcement in compression is neglected.
However, current experimental investigations on FRP-reinforced concrete members under compressive
loading show a significant increase of the load-bearing capacity and a more ductile fracture behaviour
in contrast to unreinforced specimens. Due to the absence of standardised test specifications, the
experimental values for the compressive strength of FRP rebars gained by different researchers vary
widely. These deviations can not only be explained by the dependence of the compressive strength on a
wide range of material properties but also result from different failure mechanisms that occur due to
different test setups and specimen geometry. The compressive modulus is highly dependent on the fibre
properties and can therefore be estimated via the tensile modulus.
In the scope of an extensive literature research, main material parameters of the composite material FRP
are presented for fibres and matrix resin. Besides, existing test standards and analytical calculation
approaches are compared and evaluated based on a database containing compression tests on GFRP and
CFRP rebars. Finally, boundary conditions considering the design of FRP-reinforced concrete members
in compression are recommended.
Keywords: FRP, compressive strength, material testing, composite materials, structural design
1. Introduction
1.1. Background
The application of reinforcement made of fibre-reinforced polymers (FRP) is becoming increasingly
important in the construction industry. On of the great advantages of this innovative material apart from
its low weight is its high tensile strength, which exceeds that of conventional reinforcing steel by far.
Additionally, the advantageous chemical properties of the composite consisting of fibres and matrix
result in high corrosion resistance, cf. (Ehrenstein (2006)).
International standards and guidelines provide test specifications for determining the material properties
of such reinforcement in tension, cf. ACI 440:2016, which differ from those of reinforcing steel due to
the high tensile strengths. Currently, FRP contribution in compression is not subject to any of these
standards (fib bulletin 40:2007, ACI 440:2016, CSA-S806-2:2007). According to leading
standardization authorities, the use of such reinforcement in compression is not permitted, due to the
lack of knowledge and experimental experience.
1.2. Motivation
Current research programs have shown that the use of FRP reinforcement in concrete members in
compression increases the load-bearing capacity and has a positive influence on the post cracking
behaviour. Particularly in combination with appropriate transverse reinforcement, favourable effects
occur due to confinement of the concrete core, thus increasing the concrete strength. Moreover, in
contrast to steel-reinforced members, FRP-reinforced members often exhibit significantly more ductile
post-cracking behaviour. Apart from the fact that the axial load-bearing contribution of the FRP
reinforcement is lower than that of steel due to the significantly lower modulus of elasticity, a distinct
contribution of the FRP reinforcement in compression can be observed in tests, cf. e. g. Tobbi, Farghaly
and Benmokrane (2012) and Afifi, Mohamed and Benmokrane (2013). Involved researchers agree that
neglecting this contribution is too conservative. It is essential to understand the failure of fibre-
reinforced composites and to gain knowledge of the relevant mechanical properties to properly
determine this contribution in the future.
2. Material behaviour of FRP in compression
2.1. Deformation behaviour
As a result of the significantly higher stiffness of the fibres compared to the polymer matrix, the
deformation behaviour of FRP in compression as well as in tension depends predominantly on the fibre
modulus Efi, cf. Ehrenstein (2006). The mixture rule for determining the elastic modulus Ef of FRP in
fibre-parallel direction shows this relationship mathematically. The rule according to Eq. (1) is generally
regarded as valid for high fibre volume contents Vf and high ratios of Efi / Em, which are usually present
in construction practice. The matrix modulus of elasticity is represented by Em.
f fi fi fi m fi fi
(1 )E V E V E V E
(1)
The respective transverse deformation behaviour of fibres and matrix is of decisive importance for the
compressive strength of FRP reinforcements. Due to the different Poisson´s ratios of fibres and matrix
and the resulting relative deformations transverse to the fibre direction, the bond behaviour is
significantly lower in compression than in tension, cf. Ehrenstein (2006). Due to the wide range of
possible combinations of fibres and matrix, these deformation parameters vary widely.
According to Ehrenstein (2006) and fib bulletin 40:2007, the Poisson´s ratio of thermoset resins and
thermoplastics ranges between νm = 0.35 - 0.40 and νm = 0.37 - 0.40, while that of glass, carbon and
aramid fibres is νfi = 0.25; 0.28 - 0.36 and 0.38, respectively. Wu (1990) and Chaallal and Benmokrane
(1993) are the only known authors who have measured transverse strains in their tests on FRP rebars
made for concrete reinforcement in compression, revealing values of 0.27 – 0.37 and 0.29, respectively.
2.2. Failure mechanisms
Unlike the tensile strength of FRP, which mainly depends on the fibre strength, failure in compression
is more complex. Hahn (1986) describes three possible failure modes of FRP in compression, which are
schematically shown in Figure 1. The first mode, namely longitudinal splitting (a), occurs due to
transverse tensile stresses resulting from the difference in the transverse strains of fibres and matrix
described above. A distinction must be made between whether the bond between fibre and matrix fails
(in the case of stiff matrices) or the fibres in soft, ductile matrices can deform so much that they fail in
bending. This failure mechanism is also described as delamination, cf. Bazhenov et al. (1992). Due to
the lateral support of the reinforcement by the concrete, this failure mechanism can only occur after the
destruction of the surrounding concrete, e.g. by spalling of the concrete cover. The second mode is shear
crippling (b) and describes the displacement of the entire FRP cross-section due to the formation of
shear bands. These shear bands form as a function of an initial shear angle, which can be attributed to
the skewness of the fibres resulting from the production process. The third failure mechanism is
described as a compressive failure (c) and describes a progressive failure in the cross-section. The basic
mechanism occurs as a result of the failure of individual fibres, which fail due to buckling and transfer
loads to adjacent fibres, which subsequently fail in the same manner.
The difference between compressive failure and shear crippling is mainly the propagation of the failed
structure over the cross-section. Shear crippling is more likely to occur at low ultimate strains because
the progress of plasticisation into the whole cross-section is limited, e. g. in the case of carbon fibre
reinforced polymers (CFRP). In summary, it is stated that compressive failure and shear crippling are
related and that shear crippling is always a consequence of single fibre buckling, cf. Hahn and Sohi
(1986). Failure modes (b) and (c) or a combination of them are also often denoted as crushing failure.
Figure 1: Compressive failure modes of FRP according to Hahn (1986)
The failure mechanisms can vary depending on the material properties and combinations as well as on
geometric boundary conditions. To a large extent, the compressive strength of FRP is influenced by the
fibre and matrix properties concerning strength and stiffness. In particular, the shear stiffness as well as
the tensile strength of the matrix should be mentioned. Due to the characteristics of the individual fibre
buckling, the fibre stiffness affects the compressive strength. Furthermore higher compressive strengths
can be developed when appliying fibre types with a high fibre diameter. At the macro level, a high fibre
volume content has a positive effect on the compressive strength. An influence of the specimen diameter,
which can be attributed to delayed curing rates of the matrix resin, can be recognised based on test
results from Wu (1990).
2.3. Analytical approaches to determine the compressive strength of FRP reinforcement
Analytical models for determining the compressive strength ff,c of FRP are known from materials
research in the field of polymers and are available with varying degrees of complexity depending on the
type of approach. The most cited approach goes back to Rosen (1965) and is based on the shear band
theory and periodic deflection of the fibres taking the fibre volume content Vf and matrix shear modulus
Gm into account.
m
f,c
f
1
G
fV
(2)
The approach presented in Eq. (2) is questioned by different researchers. Bazhenov et al. (1992) mention
that experimental data show a linear relationship between ff,c and Vf which is not represented by the
equation. Naik and Kumar (1999) also question the approach because the type of fibre is not taken into
account, even though available test results show a decisive influence.
In addition to the model according to Eq. (2), Rosen (1965) presents another approach in which failure
in the case of aperiodic deflection of the fibres in compression is described. In addition to Vf, the yield
stress fm,y and the elastic modulus Em of the matrix is included in the model shown in Eq. (3). This makes
it possible to depict the ductility of the matrix. The failure mechanism here consists of a tensile failure
of the matrix with simultaneous buckling of the fibres.
f m m,y
f,c
f
3 (1 )
V E f
fV
(3)
Naik and Kumar (1999) state that the two models by Rosen (1965) provide an imprecise overestimation
of the actual compressive strength. Another parameter that significantly influences the compressive
strength of FRP reinforcement is the individual fibre diameter, as it influences the fibre buckling load,
c.f. Lessard and Chang (1991). Budiansky (1983) further develops Rosen's model, assuming plastic
shear behaviour by taking the plastic shear distortion γy into account and neglecting the bending
resistance of the fibres, combining it with an approach according to Argon (1972).
mf
f,c
y
/ (1 )
1/
GV
f
(4)
a) longitudinal splitting
b) shear crippling
c) compressive failure
The angle of initial fibre skewness is assumed to be φ = 2 °. For φ = 0 °, the approach corresponds to
Eq. (2).
It is apparent that a well-founded estimation of the compressive strength of FRP reinforcement is
complex and only possible with knowledge of special material properties. The knowledge gained from
the derivation of the discussed approaches should be used for a deep understanding of FRP compressive
failure. Nevertheless, it is essential to introduce a standardised procedure to experimentally determine
the material properties of FRP reinforcement in compression.
3. Material testing in compression
3.1. Introduction
The experimental determination of the compressive strength of FRP is a complex challenge. While on
the one hand global buckling and second-order effects of slender specimens must be avoided, the
specimen needs to have a certain minimum length to avoid premature failure due to end effects. Besides,
certain types of test setups may fail in applying the load due to edge stresses. These main influences are
highlighted and critically discussed in the following.
3.2. Testing length and slenderness effects
The negative influence of small test lengths on the compressive strength of FRP reinforcement can be
proven by several experimental studies. For example, tests by Wu (1990) show consistently lower
compressive strengths at a total length to diameter ratio (ltot / d) ratio of 1.0 compared to ltot / d = 2.50,
where ltot is the free testing length and d is the diameter of the tested specimen, with all other conditions
remaining unchanged. The results of the compressive strength tests by Kobayashi and Fujisaki (1995)
are consistently below the results of comparable test series. This is attributed to the very short free test
length of only 5 mm. According to Choi and Horgan (1977), the background of this negative influence
of small ltot / d ratios is due to strong edge effects for transversally isotropic materials such as FRP. St.
Venant's principle according to which non-uniformly applied stresses can be assumed to be uniformly
distributed due to load redistribution, is no longer valid. Consequently, constraint stresses from end
effects cannot be sufficiently reduced within the usual disturbance length ld for isotropic materials,
which corresponds approximately to the diameter of the tested sample. Due to the transverse isotropy of
fibre composites, the E / G ratio is significantly higher compared to isotropic materials and the
disturbance length ld is subsequently longer. A value for ld = 1.61 ∙ d is determined for usual Poisson´s
ratios (ν = 0.3) of FRP, applying an analytical approach for determining ld according to Choi and Horgan
(1977), see Figure 2. To perform adequately exact measurements, a sufficient length is required over
which the stresses are uniformly distributed. If this length is set to 2 ∙ d, the required sample length,
taking into account the disturbance lengths on both sides, is approximately 5 ∙ d.
Figure 2: Length dependence of compressive strength due to edge effects and buckling according to Carlsson and Pipes
(1989) and analytical approach according to Choi and Horgan (1977)
In Figure 2 the compressive strength ratio ff,c / ff,c,max is plotted over l / d, following the findings from
Carlsson and Pipes (1989). The negative influence of small specimen lengths becomes apparent, since
ff,c / ff,c,max is small for small ltot / d ratios. The ratio ff,c / ff,c,max increases since edge effects become less
ltot / d
ff,c /ff,c,max
1.0
10 20 30 40 50 60
(ltot / d)opt
d
E
ldG
ld
ld
ltot lf
d
influential until second-order effects dominate for higher slendernesses and the curve eventually
converges according to Euler-buckling. Following the curve, a specific maximum point can be observed
between 5 < l / d < 10, corresponding to the above mentioned order of magnitude of l / d = 5 and thus
revealing a range of ltot / d – values under which reasonable results can be expected.
3.3. Existing testing standards
Since testing FRP compressive strength is indispensable and challenging at the same time, standards
have to be set up, to specify geometrical as well as other boundary conditions. Since, with one exception,
no standards exist for the testing of FRP in structural engineering, relevant criteria from standards of the
leading polymer and aerospace industries are given below. One of the main features regarding the
evaluation of the test standards is the type of load application. While regulations in EN ISO 604:2003
and ASTM D695-15:2015 for testing unreinforced plastics specify load application via the end faces of
the specimen (a), the load is applied indirectly to the specimen’s free length via shear elements (b) when
testing FRP laminates in the aerospace sector, cf. ISO 14126:1999, ASTM D3410:2016 and DIN EN
2850:2018. This procedure also corresponds to GOST 31938:2012, the only standard for reinforcement
made of FRP, according to which the load is taken up by anchor sleeves and introduced into the specimen
by means of shear (c). The three different types of load application are shown in Figure 3.
Figure 3: Typical test set-ups to determine compressive material properties of FRP
Additionally, there is a strong dispersion when regarding the free length and the corresponding
slenderness defined by the standards evaluated. All standards indicate that stability failure must be
excluded and at the same time a sufficient free length must be available to ensure that a region
undisturbed by transverse stresses can form in which the specimen fails at best. To take influences from
second-order effects into account during the test, the strains on both sides of the specimen must be
recorded and compared with each other. This guarantees a uniaxial stress state as far as technically
possible. To avoid buckling failure, critical strains are specified in EN ISO 604:2003. When defining
specimen slenderness, the standards differ between a general test specimen length or a specification
depending on the diameter. Some standards specify different specimen geometries depending on the
material property to be measured. In some cases, the slenderness for modulus of elasticity measurements
is significantly higher than for the determination of the compressive strength.
Concerning the test interpretation, failure points in the mid-section of the specimen are favoured by all
standards. Failure in the area of the load application components is only accepted with restrictions or
not at all. Exactly defined failure modes are given in ISO 14126:1999, which are comparable to the
failure modes described in section 2.2. Displacement controlled loading with an average loading speed
of 1 mm/min is recommended by all standards, except GOST 31938:2012. The majority of the standards
examined indicate that the samples should be protected from moisture, heat and UV radiation before
(a)
(b)
specimen
w2 ∙ d;
10 –50 mm
ltot =
machine head
d
machine head
w
ltot = 5 -25 mm
Shear tabs
specimen specimen
w
ltot = 6 ∙ d
anchor sleeves
machine head
(c)
Corresponding standards:
EN ISO 604:2003
ASTM D695-15:2015
Corresponding
standards:
ISO 14126:1999
ASTM D3410:2016
DIN EN 2850:2018
Corresponding
standard:
GOST 31938:2012
testing and that the tests should be carried out in a standard climate (23 °C and 50 % RH). For a
statistically reliable evaluation, at least 5 valid tests per parameter combination must be documented.
Table 1: Comparison of FRP-standards for testing in compression
Industry sector
plastics & polymers
aerospace
structural
concrete
standard name
EN ISO
604:2003
ASTM D695-
15:2015
ISO
14126:1999
ASTM
D3410:2016
DIN EN
2850:2018
GOST
31938:2012
tested material
unreinforced
plastics
rigid plastics
FRP-
laminates
FRP-
laminates
FRP-
laminates
FRP-rebars
material property:
ff,c = compr. strength
Ef,c = compr. modulus
ν = Poisson´s ratio
Ef,c
ff,c
ff,c
Ef,c
ff,c
Ef,c
ff,c
Ef,c
ν
ff,c
Ef,c
ff,c
ff,c
Ef,c
free length ltot in mm
50
10
2 ∙ d
10 - 25
variable
10
5
6 ∙ d
load application
end faces
end faces
shear tabs
shear tabs
shear tabs
anchor sleeves
loading speed v
mm/min
1.0
1.3
1.0 ± 0.5
1.0 ± 0.5
1.0
5 - 15
number of specimens
> 5
> 5
> 5
> 5
> 5
3 - 6
A summary of the relevant values is given in Table 1. Regarding the load application, the specifications
according to GOST 31938:2012 seem to be the most reasonable for further tests on reinforcement made
of FRP. Load application via the end faces may be suitable for unreinforced plastics due to their material
isotropy but is not suitable for testing FRP because of constraint stresses due to edge effects. Similarly,
the short test length of 2 ∙ d according to ASTM D695-15:2015 is also excluded for the reasons
mentioned in section 3.2. Due to the specific dimensions of the standardised test specimens from the
aerospace sector, these values cannot be used any further, so that an orientation towards GOST
31938:2012 also appears to be appropriate here. With regard to the test length, it would be useful to
specify a upper and lower threshold in order to exclude both stability and end effects due to constraint
stresses. Only concerning the loading speed, GOST 31938:2012 must be regarded critical. Due to the
high sensitivity of the compression tests, the lower values according to the other standards appear to be
more reasonable.
4. Evaluation of literature-based material tests and analytical approaches
4.1. General
In the following, the essential conclusions that were obtained from 156 tests across 22 test series on FRP
reinforcement in compression from the literature are compiled and critically examined. Thereby, a wide
range of different approaches is found, which enhances the need for standardisation in the field of
material testing of FRP in compression. Some of the researched test series could not be taken into
account for further investigations due to e. g. premature failure of the test specimens in the area of load
application. Also, several test series contained only limited useful information on the properties of the
materials investigated or on reference tests under tensile loading, which further limited the number of
parameters that could be evaluated. The majority of the tests listed below were carried out on rods made
of GFRP (glass fibre reinforced polymers) reinforcement. Some specimens made of CFRP could also
be integrated. The theoretical findings regarding material properties and test-setup are examined based
on the results from the analysed tests. Finally, models for estimating the contribution of the FRP
reinforcement to the total load-bearing capacity of concrete members in compression are briefly
presented and evaluated.
4.2. Evaluation of compressive failure modes
A closer look at the test results reveals three different failure mechanisms after the invalid results have
been deducted. The first failure mechanism is referred to as crushing failure and occurs in particular
with very small ltot / d ratios, corresponding to mode (b) and (c), cf. Figure 1. A correlation of the
compressive strength with the tensile strength ff,t is not necessarily expected, since different mechanical
mechanisms dominate. Nevertheless, in the context of this investigation ff,c is plotted against ff,t for GFRP
and CFRP specimens in Figure 4 to provide a reference.
Concerning the comparison of the mean ratios mf = ff,c / ff,t between GFRP and CFRP, GFRP shows
higher values. This is expected due to the greater thickness of the glass fibres compared to the carbon
fibres. Thus, the ratio mf for GFRP is 73 % while a value of only 40 % can be observed for CFRP. To
relate the compressive strength ff,c to the well-known tensile strength ff,t, the correlation coefficient ρf is
calculated in addition to the mean ratio mf. The high correlation coefficient of ρf = 94 % for CFRP is
particularly remarkable. For GFRP, this value equals 59 %. A certain correlation between the two values
was to be expected since high tensile strengths are often accompanied by high stiffnesses, which in turn
have a positive effect on the compressive strength.
Figure 4: Compressive failure due to crushing of GFRP and CFRP, left and crushing vs. longitudinal splitting, right
The right part of Figure 4 shows that the strength ratio ff,c / ff,t does not differ significantly between the
two failure modes crushing and longitudinal splitting. The ratio mf equals 0.73 for crushing failure while
it is 0.67 for longitudinal splitting failure for GFRP specimens. This observation shows that the two
modes cannot be completely separated from one another, as parameters like the strength, the transverse
strain behaviour and the matrix stiffness influence both modes. The modes differ much more depending
on the load application and the specimen slenderness.
4.3. Axial load-deformation behaviour in compression
According to Eq. (1), it can be assumed that the fibre properties dominate the deformation behaviour of
FRP reinforcement in tension and compression. To investigate this hypothesis, Figure 5 shows the
moduli of elasticity in compression Ef,c and tension Ef,t plotted against each other. In addition to a mean
ratio of mE = Ef,c / Ef,t, a correlation coefficient ρE is calculated for both CFRP and GFRP. For the
evaluation of the modulus of elasticity as a decisive material property, all valid test results on GFRP and
CFRP bars are considered, regardless of the failure modes that occurred. Based on the given load-
deformation diagrams according to Wu (1990), Chaallal and Benmokrane (1993), Deitz, Harik and
Gesund (2000), Bruun (2014), Khan, Sheikh and Hadi (2015), Khorramian and Sadeghian (2019) and
Urbański (2020), it is evident that FRP shows a linear elastic material behaviour in compression,
provided that no drifting forces or eccentricities occur at high slendernesses. The monitoring of such
second-order effects is ensured by strain measurement on multiple sides of the specimen.
The assumption of a ratio of Ef,c / Ef,t ≈ 1.00 can be approximately confirmed for both GFRP and CFRP.
The corresponding ratios mE are 0.97 and 0.90 respectively. This indicates that the significantly softer
GFRP bars show a better agreement between Ef,c and Ef,t than those made of CFRP. The reason for this
deviation is the very short specimen geometry under which the CFRP specimens from Kobayashi and
Fujisaki (1995) were tested and which account for a relatively large part of the presented test results on
CFRP. Effects from second-order and buckling failure can be seen for slendernesses λ = l / d ≥ 9. The
0
400
800
1.200
1.600
0400 800 1.200 1.600
ff,c in N/mm²
ff,t in N/mm²
GFRP
CFRP
regression: GFRP
m
f= 0.73
ρf= 59 %
regression: CFRP
m
f= 0.40
ρf= 94 %
crushing
0.4 ≤ l/d≤ 8.0
0
400
800
1.200
1.600
0400 800 1.200 1.600
ff,c in N/mm²
ff,t in N/mm²
crushing
longitudinal splitting
regression: crushing
mf= 0.73
ρf= 59 %
GFRP
0.5 ≤ l/d≤ 11
regression: splitting
mf= 0.67
ρf= 88 %
right part of Figure 5 shows test results from Deitz, Harik and Gesund (2000) and Bruun (2014) on
GFRP rebars at high slendernesses, as well as an analytical approach for estimating the buckling load
according to Euler. Therefore the maximum developed compressive stress σf,c from the test results is
normalised to the corresponding compressive modulus Ef,c and plotted over λ. The critical buckling
stress fcr is calculated according to the equation given in Figure 5 as a function of the slenderness λ and
the compressive modulus Ef,c.
Figure 5: Relationship between Ef,c and Ef,t for GFRP and CFRP, left; length-dependence of fc,f for slender specimens, right
The coefficient k, which is determined depending on the geometric boundary conditions, is chosen to be
0.63 in order to match the test results as closely as possible. For stability failure, good agreement
between the experimental results and the analytical approach can be observed, indicating that FRP
buckling can be considered independently of the complex cross-sectional fracture behaviour based on
stiffness and slenderness. For slendernesses that lead to stress failure due to second-order effects, the
ultimate load is overestimated by the buckling formula, as to be expected. The determination of
adequately close stirrup spacing to avoid buckling of the longitudinal FRP reinforcement is part of
current research projects, cf. Elmessalami, Abed and El Refai (2021).
4.4. Approaches for FRP reinforcement contribution in compression
As already mentioned above, applying compressive strength of FRP reinforcement in the design of
concrete members is not recommended by international standards, (fib bulletin 40:2007, ACI 440:2016,
CSA-S806-2:2007). Several research projects are currently conducting experimental tests on small-scale
FRP-reinforced concrete columns. The following equations are used to determine the ultimate member
load NR consisting of a concrete part NR,c and an FRP reinforcement contribution. The concrete
contribution NR,c is also part of current research concerning increased concrete strength due to
confinement effects, c. f. Pantelides, Gibbons and Reaveley (2013) and Afifi, Mohamed and
Benmokrane (2014) but is not part of the investigations described in this paper.
The following two equations show two different approaches. In the first approach, the FRP contribution
is estimated via a reduction factor α for the FRP tensile strength ff,t, which can be considered as the ratio
of the compressive stress developed in the FRP rebar σf,c and the tensile strength ff,t.
R R,c f,t f
N N f A
(7)
The second approach is based on the assumption of uniformly distributed strains in the cross-section
assuming rigid bond between concrete and reinforcement. The FRP contribution is calculated as the
product of the applied strain εf,c, the corresponding compressive modulus Ef,c and the FRP reinforcement
area Af.
R R,c f,c f,c f
N N E A
(8)
Table 2 merges the referenced test series, specifying the reinforcement type, the tensile modulus and
strength Ef,t and ff,t. For comparability purposes the ratio αexp. is calculated via the experimentally derived
0
40000
80000
120000
040000 80000 120000
Ef,c in N/mm²
Ef,t in N/mm²
CFRP
GFRP
regression CFRP
m
E= 0.90
ρE= 86 %
regression GFRP
m
E= 0.97
ρE= 81 %
Elastic modulus
m
E
= E
f,cm
/ E
f,tm
0
5
10
15
20
25
010 20 30
σf,c / Ef,c in ‰
λin -
second-order
stress failure
GFRP k = 0.63
lcr =k ∙ l
2
2
c,f
1²
16
cr
f
Ek
compressive strains εf,c,exp in the rebars and compared to the of αrec, recommended by the authors in order
to fit their experimental results as close as possible.
Table 2: Evaluation of different approaches to estimate FRP contribution in concrete members in compression
Reference
reinforcement
type
Ef,t in
N/mm²
ff,t in
N/mm²
εf,c,exp
in ‰
αrec.
Tobbi, Farghaly and
Benmokrane (2012)
GFRP
47,600
728
-
-
0.35
Afifi, Mohamed and
Benmokrane (2013)
GFRP
55,400
934
1.34 - 2.52
0.08 - 0.15
0.35
Afifi, Mohamed and
Benmokrane (2014)
CFRP
140,000
1,899
1.65 - 2.55
0.12 - 0.18
0.25
Maranan et al. (2016)
GFRP
62,600
1,184
2.00
0.106
-
Hadhood, Mohamed and
Benmokrane (2017a)
GFRP
54,900
1,289
2.25 - 2.47
0.096 - 0.105
0.102 -
0.128
Hadhood, Mohamed and
Benmokrane (2017b)
CFRP
141,000
1,680
3.00
0.25
0.35
It can be seen from the comparison between column 6 and 7 that the recommended values αrec. are
consistently higher than the values obtained via the rebar strain, indicating positive effects of the FRP
reinforcement besides its axial load contribution. Overall, the approach according to Eq. (8) can be
considered more suitable for further research efforts due to the mechanical consistency based on
uniformly distributed strains. Since the developed compressive stress in the FRP rebar depends not only
on the modulus of elasticity of the reinforcement and the used concrete, but also on the ultimate strain of
the concrete as well as the amount and type of transverse reinforcement, the use of a general ratio α is not
recommended at this point. Fillmore and Sadeghian (2018) conducted tests on exclusively longitudinally
reinforced concrete cylinders in concentric compression under varying reinforcement ratios in order to
quantify the correlation between axial stiffness of GFRP reinforcement on the load contribution. A linear
correlation between the bar contribution and the reinfordement ratio is shown by the experimental
findings.
The authors mentioned above agree on the fact that neglecting the FRP reinforcement in compression
underestimates the members’ actual load-bearing capacity. This thesis is sufficiently substantiated by
numerous test results.
5. Summary and conclusions
This paper evaluates the behaviour of GFRP and CFRP reinforcement in compression for application in
concrete members. Within an extensive literature review, the basic mechanical principles, concerning
compressive deformation and failure modes are described, followed by a presentation of existing
approaches to determine FRP compressive strength analytically. The complexity as well as the
requirement of various input parameters, which are often not documented, underline the need for a
consistent test standard. Hence, various test standards according to different industrial sectors for
determining the compressive strength of FRP are described. For the most part, the boundary conditions
of GOST 31938:2012, which is compared with standards from the plastics and aerospace sector, are
considered reasonable.
To compare the theoretical findings with the material behaviour under real conditions, test data from 22
test series taken from the literature are evaluated. Regarding the modulus of elasticity, there is good
agreement with the theoretical findings. Concerning the compressive strength, initial findings were
obtained, but there is a need for further clarification about the evaluation of the actual magnitude of the
compressive strength that can be applied. This is also shown by the subsequently presented analytical
approaches for determining the ultimate load of FRP-reinforced concrete members.
The next task is to extend the number of conducted tests of FRP reinforcements in compression. Based
on this, the behaviour under monotonic long-term loading has to be evaluated. The final goal is the
development of a consistent mechanical model, that can be used to realistically and reliably estimate the
load-bearing capacity of FRP-reinforced concrete members in compression.
cf,exp.
exp.
ft ft
Ef
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