Effects of Thermal Loads on Concrete Cover of FRP...

Aiello, M.A., F. Focacci, and A. Nanni, “Effects of Thermal Loads on Concrete Cover of FRP Reinforced Elements: Theoretical and Experimental Analysis,” ACI Materials Journal, Vol. 98, No. 4, July-Aug. 2001, pp. 332-339.

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Effects of Thermal Loads on Concrete Cover of FRP Reinforced Elements:

Theoretical and Experimental Analysis

Maria A. Aiello1, Francesco Focacci2 and Antonio Nanni3

1 Department of Innovation Engineering, University of Lecce, Via per Arnesano, 73100,

Lecce, Italy

2 Dipartimento di Costruzione dell’Architettura (DCA), Istituto Universitario di Architettura

di Venezia, Campo Tolentini 191, 30135 Venice, Italy

3 Center for Infrastructure Engineering Studies, 224 Engineering Research Lab 1870 Miner

Circle, University of Missouri – Rolla, Rolla, MO 65409-0710

Abstract

The paper is devoted to the analysis of FRP reinforced concrete elements under

thermal loads. As known, non metallic rebars present high values of transverse coefficients of

the thermal expansion (CTE) with respect to concrete; as a consequence, when temperature

increases, tensile stresses take place within the concrete that may produce splitting cracks and,

eventually, the concrete cover failure if the confining action is not sufficient.

An analytical model is proposed to determine the values of temperature increase (∆T)

corresponding to the first appearance of the cracking phenomenon and to the concrete cover

failure.

An experimental investigation, carried out on concrete specimens reinforced with FRP

rebars, is described and obtained results are compared with theoretical predictions.

Keywords: Coefficient of thermal expansion, Concrete cover, Cracking, FRP, Transverse CTE, Thermal load, Spalling.


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M. A. Aiello, is an Assistant Professor in Structural Engineering, Department of Innovation

Engineering, University of Lecce, Italy. Her main research interests include the structural

analysis of FRP reinforced concrete members, the bond between FRP and concrete, the

adhesion systems between polymers and concrete and the analysis of composite laminated

structures.

F. Focacci is a Post Doctoral Researcher in the Dipartimento di Costruzione dell’Architettura

(DCA), University of Venice. His research deals with the structural behavior of FRP

reinforced concrete members, bond between FRP bars and concrete and structural

rehabilitation using FRP.

Antonio Nanni, FACI, is the V&M Jones Professor of Civil Engineering and Director of the

University Transportation Center (UTC) at the University of Missouri-Rolla. Prof. Nanni is

interested in construction materials, their structural performance, and field application. He is

an active member in the technical committees of ACI, ASCE, ASTM and TMS.

RESEARCH SIGNIFICANCE

The paper is part of a research work on the influence of thermal actions on structural

performance of FRP reinforced concrete structures. The different transverse coefficients of

thermal expansion of concrete and FRP rebars may cause splitting cracks within the concrete

and, ultimately, the spalling of the concrete cover. Such phenomena, affecting the bond

between the FRP rebars and concrete, could have a relevant influence on structural response

of the FRP reinforced concrete members both under service and ultimate conditions. The

paper presents theoretical and experimental analyses aimed at furnishing design algorithms to

avoid a degradation of the structural response caused by thermal loads and to provide

appropriate confining action.


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1. Introduction

The use of FRP rebars as reinforcement for concrete elements seems to be an effective

solution for overcoming durability problems of traditional steel reinforced concrete structures,

due to the corrosion of metallic rebars. For this reason the replacement of steel with non-

metallic rebars for constructions is gaining popularity worldwide. The numerous experimental

and theoretical studies carried out in the last years and many structural applications besides

the great effort done in many countries to establish the guidelines of practical use of FRP

reinforced concrete structures confirm the increasing interest in this field. However, in order

to gain a deeper insight in the structural behavior of such new materials and to guarantee their

safe application, further researches are needed in specific areas as that concerning the

structural performance and durability under service conditions (Conrad, Bakis, Bootby and

Nanni, 1995) and among all the effect of the temperature increases.

Unidirectional FRP rods, generally utilized in concrete, present an anysotropic

behavior. As a consequence, the coefficients of thermal expansion are different in longitudinal

and transverse directions. In particular, the longitudinal CTE, controlled by fibers, is low and

even negative (as in the case of aramidic fibers), while the transverse CTE, controlled by the

resin, is up to 3 - 6 times that of the concrete (Gentry et al., 1996). As a result, a uniform

increase in temperature produces bursting stresses within the concrete that may cause splitting

cracks. This fact involves a degradation of the bond between concrete and reinforcement

(Tepfers, 1998; Tepfers, 1979), affecting the structural response.

Recent studies have evidenced the influence of the thermal load on concrete elements

reinforced with FRP rebars (Uijl, 1995; Matthys et al., 1996; Aiello, 1999; Aiello et al. 1999)

and some technological solutions have been considered to reduce the thermal incompatibility

problems between concrete and composite rods (De Sitter and Tolman 1995; Gentry and


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Husain, 1999). However, further investigations are needed for a better understanding of the

physical phenomenon in order to develop models aiming to furnish design provisions on the

confining action needed to avoid the splitting cracks within the concrete at a given

temperature increase.

In this paper an analytical model is presented; the analysis of the thermal effects is

performed considering the concrete as a thick-walled pipe surrounding the composite rebar.

Analytical relationships are determined taking into account different states of stress within the

concrete. In particular, two stages are considered: that corresponding to the uncracked

concrete, up to ∆Tcr producing the first radial crack and that corresponding to the cracked

concrete, up to ∆Tsp producing the spalling of the concrete cover. Therefore, the model allows

to determine the thermal loads ∆Tcr and ∆Tsp for given geometrical and thermal properties.

Obtained results are compared with those from an experimental investigation resulting

in the consideration that the theoretical model presented in this study allows to determine a

relationship between the acting thermal load and the required minimum concrete cover value.

2. Analytical model

The effect of thermal loads on concrete cover is analyzed by means of a theoretical approach

based on the following assumptions.

• FRP rebars are treated independently, meaning that the clear spacing between two adjacent

bars is sufficient to avoid the occurrence of horizontally splitting cracks at the bar level

(this assumption could be easily removed).

• Absence of boundary restraints at the bar terminations, aiming to focus the analysis on the

effects of stresses interaction between FRP bars and concrete produced by thermal actions.


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• Effect of transverse reinforcement is neglected in order to evaluate the only contribution of

the concrete cover to sustain the bursting stresses produced from the temperature

variations.

• Concrete and FRP bars present a linear elastic behavior. Some non-linearity could occur

because of the presence of plastic deformations within the concrete or a viscous behavior

of both the concrete and the polymeric matrix within the bars. These non-linear phenomena

may lead to a different redistribution of stresses between concrete and reinforcement. At

present this influence is ignored.

The analytical investigation is carried out considering a cylindrical FRP bar embedded

in a concrete cylinder as thick as the concrete cover and subjected to a temperature increase

∆T (Fig. 1). Due to T∆ , a radial compression Tσ acts at the cylindrical surface dividing

concrete and bar, it is defined by the compatibility equation:

bc rr ∆=∆ (1)

where cr∆ is the variation of the radius of the cylindrical hole in concrete where the rod lies

and br∆ is the variation of the bar radius, due to T∆ and Tσ , expressed as:

( )TTTb

T00bb 1

ErTrr ν−

σ−∆α=∆ (2)

2.1 Behavior of the concrete

At the internal surface of the cylindrical concrete hole the radial compression Tσ acts to

increase the hole radius from the initial value r0 by a certain amount 1cr∆ .


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Taking into account the axial symmetry of the system, in the hypothesis of plane

elasticity, at a generic point in the concrete with distance equal to ρ from the centerline of the

bar, the following stresses can be determined:

( )

( ) T2

22

20

22

20

T2

22

20

22

20

r1rr

r

r1

rrr

σ

ρ

+−

=ρσ

σ

ρ

−−

=ρσ

θ

ρ

(3)

being ( )ρσρ the stress in the radial direction and ( )ρσθ the stress in the circumferential

direction and r2 the outer radius of the cylinder. The maximum value of the circumferential

tension in concrete, acting at 0r=ρ , is:

T2

022

20

22

max, rrrr

σ−+

=σθ (4)

At a certain ∆T, here named crT∆ , this stress reaches the concrete tensile strength and splitting

cracks take place. Therefore two cases must be considered, that is crTT ∆≤∆ and crTT ∆>∆

2.2 The case crTT ∆∆∆∆≤≤≤≤∆∆∆∆

The stresses (3

give the

following

strains:

( ) ( ) ( )

( ) ( ) ( )

ε ρρ

νρ

σ

ε ρρ

νρ

σ

ρ

θ

=−

−

−

−+

=−

+

−

−−

rE r r

r rE r r

r

rE r r

r rE r r

r

c

c

cT

c

c

cT

02

22

02

22

202

22

02

22

2

02

22

02

22

202

22

02

22

2

1 1

1 1

(5)


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As consequence the initial radius r0 of the hole, due to Tσ , increases by the amount:

ν+

−+σ

=∆ c20

22

20

22

c

T01c rr

rrE

rr (6)

2.3 The case crTT ∆∆∆∆>>>>∆∆∆∆

When the tensile strength of concrete is overcame, the formation of a circular crown of

concrete with radial cracks is expected (Fig. 2), being r0 and crr its inner and outer radius,

respectively. Inside the crown, circumferential tension is not possible.

It can be proved that the distribution of the radial compression in the cracked circular crown is

described by:

( ) T0r σρ

−=ρσρ (7)

It can be noted that in the uncracked concrete ( )ρσρ decreases proportionally to the inverse of

ρ2, while in the cracked zone it decreases as the inverse of ρ, due to the absence of the

circumferential tension.

The radial compression (7) produces the radial strain:

( ) Tc

0

Er σ

ρ−=ρερ (8)

The uncracked zone, outside the circular crown, is internally delimited by a

circumference with radius crr and externally delimited by a circumference with radius r2.


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At the interface between cracked and uncracked zone, the radial compression

(equation (7) written at crr=ρ ) is given by:

( ) Tcr

0crcr, r

rr σ−=σρ (9)

Equation (3) at crr≥ρ gives:

( )

( ) Tcr

02

22

2cr

22

2cr

Tcr

02

22

2cr

22

2cr

rrr1

rrr

,x

rrr1

rrr

σ

ρ

+−

=ρσ

σ

ρ

−−

=ρσ

θ

ρ

(10a)

(10b)

The condition ( ) ctcr fr =σϑ , that is:

( ) ctTcr

02cr

22

2cr

22

2cr f

xrr

rr1

rrr

=σ

+

− (11)

or:

0

rfr

rr

rr

rfr

rr

2ct

0T

2

cr

2

2

cr

2ct

0T

3

2

cr =σ

+

−

σ+

(12)

allows to determine crr as a function of Tσ .

In conclusion, the increase 1cr∆ of the radius 0r is the sum of two contributions: the

decrease of the cracked zone thickness (due to the radial compression (7)) and the increase of

the circle radius out of which concrete is uncracked, that is: (note that for the second

contribution equation (6) can be used in which Tσ is the compression given by equation (9)

and cr0 rr = )


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ν+

−+

+σ

=∆ c2cr

22

2cr

22

0

cr

c

T01c rr

rrrr

lnE

rr (13)

The increment of the radius of the cylindrical hole where the cable lies, due to T∆ is:

Trr 0c2c ∆α=∆ (14)

From equations (6) and (14) one obtains:

Tr

rrrr

Er

r 0cc20

22

20

22

c

T0c ∆α+

ν+

−+σ

=∆ (15)

when concrete does not crack.

From equations (13) and (14) one obtains:

Tr

rrrr

rr

lnE

rr 0cc2

cr22

2cr

22

0

cr

c

T0c ∆α+

ν+

−+

+σ

=∆ (16)

when concrete cracks.

Compatibility equation (1) can be written as:

( )TT

Tb

Tbcc2

022

20

22

c

T 1E

TTrrrr

Eν−

σ−∆α=∆α+

ν+

−+σ

(17)

when concrete does not crack and as:

( )TT

Tb

Tbcc2

cr22

2cr

22

0

cr

c

T 1E

TTrrrr

rr

lnE

ν−σ

−∆α=∆α+

ν+

−+

+σ

(18)

when concrete cracks, being rcr defined by equation (12) as a function of Tσ .


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2.4 Equilibrium configuration after radial cracking

The equilibrium equation (12) imposes the radial compression at crr=ρ to be equal to

the radial compression associated to the circumferential tension fct in the inner circumference

of the uncracked circular crown. By setting:

2ct

0T

2

cr

rfrA

rr

σ=

=β (19)

it can be written as:

0AA 23 =+β−β+β (20)

It can be proved that equation (20) has only one meaningful solution for the actual problem

when A is in the range 30.0A0 ≤≤ . No solutions can be found for 30.0A > .

The condition 30.0A > means too high radial compression σT or too small concrete cover r2

for the uncracked circular crown of concrete to be able to stop the radial cracking, as can be

seen in definition (19).

The solution corresponding to 30.0A = is 48.0=β . It’s possible to conclude that the

maximum radial compression that concrete can hold is given by:

0

2ctT r

rf30.0=σ (21)

being the outer radius of the cracked circular crown:

2cr r48.0r = (22)


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2.5 ∆∆∆∆T producing the first radial cracks and the concrete cover failure

First radial cracks appears in concrete when the circumferential tension at 0r=ρ , given by

equation (4) reaches the tensile strength of concrete, that is when:

11f

rrrrf 2

2

ct20

22

20

22

ctT +γ−γ=

+−=σ (23)

being:

0

2

rr=γ (24)

Corresponding ∆T is given by equation (17) as:

( ) ( )

ν−+

ν+γ−γ+=∆α−α TT

Tb

ct

c

ctc2

2

c

ctcrcb 1

Ef

Ef

11

Ef

T (25)

The failure of the concrete cover happens when the radial compression σT is such that the ratio

β reaches the value 0.48. By imposing this condition in equation (20), radial compression σT

is found as:

γ=σ ctT f30.0 (26)

Corresponding ∆T is given by equation (18) as:


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( ) ( )[ ] ( )TTTb

ctc

c

ctspcb 1

Ef3.0

6.148.0lnE

f30.0T ν−

γ+ν++γ

γ=∆α−α (27)

As the mechanical properties of materials and γ value are known, it is possible to find ∆T

value producing the first radial cracks in concrete and that causing the concrete cover failure,

once the difference bc α−α is specified.

3. Experimental investigation

An experimental investigation has been performed to analyze the effects of temperature

increases on concrete elements reinforced with GFRP (Glass Fiber Reinforced Polymers)

rebars. Materials properties, test apparatus and obtained results are described in the following.

3.1 Materials

The GFRP deformed rods (C-BAR™) reinforcing the tested specimens had a nominal

diameter of 13 mm and were supplied by Marshall Industries Composites, USA. Mechanical

properties of the reinforcement and the concrete utilized are reported in Table 1.

The average tensile strength fr and the average tensile elastic modulus Er of the reinforcement

were those of the manufacture’s specification, while the transverse Young’s modulus Etb and

the Poisson ratio νTT of the utilized C-BAR was determined by the inverse rule of mixtures

based on the percentage of fibers and matrix.

The average compressive strength fc of the concrete was evaluated by standard compression

tests; elastic modulus Ec and tensile strength fct were calculated according to (ACI 318).

Effects of thermal loads on FRP reinforced concrete elements are dependent on the transverse

CTE of the materials. In the performed analysis, CTE’s of the concrete (αc) and GFRP bars

(αb) were experimentally evaluated testing six GFRP rods and four concrete elements under

an increasing thermal load and recording the corresponding strains by means of a strain gage


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attached on the specimen’s surface. The average values and standard deviations were

evaluated as αb = 58 10-6 °C-1, STD = 7.8 10-7 °C-1 and αc = 12.1 10-6 °C-1,

STD = 2.5 10-6 °C-1.

The Tg (Glass Transition Temperature) of the resin utilized for making C-BAR™ has been

evaluated by the DMA technique; the obtained value is Tg = 132 °C: Taking into account that

the maximum temperature value reached during tests is almost 100 °C, it can be asserted that

properties of rebars would not have considerable changes during test procedure.

3.2 Specimens Geometry and Test Procedure

Concrete elements were reinforced with an FRP bar without transverse reinforcement. Two

shapes of cross section, circular and rectangular, were considered to analyze the influence of

the concrete confining action on the structural performance of the members under thermal

loading. In the first case, the confining action is axis-symmetric, as generally considered in

analytical models utilized for studying the thermal stress problem. For rectangular cross

sections, the axis-symmetry is removed by placing the bar closer to one side. Details of the

specimens geometry are reported in Fig. 3 and Table 2. The specimen’s codes indicate the

shape (first letter, R: rectangular, C: cylindrical) followed by the concrete cover value

expressed in millimeters.

Specimens were subjected to a thermal loading by utilizing an oven. Holes were drilled in the

concrete to place thermo-couples for detecting the temperature inside the specimen. The

oven’s temperature was increased in steps of 5 to 10°C, once the temperature in the concrete

had stabilized, up to a crack opening (Fig.4). Strain measurements were obtained with strain

gages placed as shown in Fig. 3.


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3.3 Results and Discussion

In the Figs. 5 to 12 experimental results are reported. In particular, recorded strains versus

temperature increases are drawn for each tested specimen; curves refer to the strain values

measured by each strain gage attached on the specimens and indicated by a number. In

addition, the average value of the strains is calculated and plotted in the figures. As one can

see, curves present a similar trend, characterized generally by two stages: the first stage

corresponds to the uncracked situation, while a slope variation is observed when a splitting

crack is opening.

Comparisons between experimental and theoretical results are shown in Fig. 13. In particular,

the temperature increases corresponding to the appearance of a splitting crack are reported

versus the ratio between the concrete cover value and the bar diameter (c/d).

The theoretical prediction presents an almost linear variation of the ∆Tsp, producing the

spalling of the concrete cover as a function of the ratio c/d. Experimental results are in good

agreement with the predictions.

The figure illustrates that values of c/d>2 guarantee a good performance (i.e. no splitting

cracks) of the reinforced concrete elements under temperature variations typical of service

conditions.

4. Parametric analysis

Based on equation (27) a parametric analysis has been performed in order to evaluate the

needed concrete cover for a given design value of ∆T. For the analysis, three concrete types (fc

= 30, 40 and 50 MPa) were considered; consequent concrete properties Ec and fct were

estimated. For the performed analysis key parameters characterizing the reinforcement are the

transverse elastic modulus of the rebars, ETb, and theirs transverse coefficient of thermal


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expansion, αb; therefore different values have been considered to evaluate the minimum

required concrete cover under the assigned ∆T.

Figures 14 to 16 show the minimum concrete cover (expressed by the ratio c/d) to be adopted

in order to avoid the concrete cover spalling for ∆T = 50 °C in function of the mechanical

properties of the FRP rebar and the concrete utilized.

It can be observed that either the transverse Young’s modulus of the bar and the transverse

CTE or the bar influence the spalling phenomenon, while the concrete strength, in the

considered range, does not change the order of magnitude of the results. This is because an

increasing of fc produces an increasing of fct and consequently a decreasing of c/d (∆Tsp = ∆T

= 50 °C is fixed) and at the same time an increasing of Ec and consequently an increasing of

c/d.

Diagrams similar to those reported in the figures can be drawn, with corresponding tables, for

all possible design situations. Using such curves (or tables) designer can evaluate the required

minimum concrete cover in order to avoid the splitting phenomenon once the service

temperature increases (∆T), the mechanical properties of materials (compressive strength and

CTE of concrete, radial elastic modulus and CTE of the bars) are known.

5. Conclusions

On the basis of the theoretical and experimental investigations, the following concluding

remarks can be drawn:

• Theoretical and experimental results evidence the effects of thermal loads on FRP

reinforced concrete elements, that is the presence of splitting cracks and possible concrete

cover failure when the confining action is not sufficient.


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• Results obtained confirm the need of an accurate evaluation of the concrete cover as

function of the service temperature. However, a concrete cover value greater than two

times the bar diameter seems avoid the occurrence of the splitting cracks.

• Analytical relationships have been shown to be useful for design. In fact tables and

diagrams can be drawn for an assigned thermal load varying properties of concrete and

reinforcement. Once service temperature and properties of materials are defined the

designer could easy evaluate the minimum required concrete cover to avoid the spalling

phenomenon, utilizing diagrams (or corresponding tables) similar to those reported in the

paper.

• Two shapes of cross section, circular and rectangular were considered for a concrete cover

value c = 19 mm. However, in order to analyze the influence of the concrete confining

action, axis-symmetric or not for circular and rectangular cross-section respectively, further

tests are needed. In particular, rectangular specimens with concrete cover values c=38 mm

and c=57 mm will be tested in comparison with results of cylindrical specimens.

• Radial pressure from anchored bar add stress to the stress in concrete cover caused from

thermal expansion of bar. This stress superposition may not be linear, because the diameter

of the bar decreases under tensile load due to Poisson deformation, wich counteracts the

thermal diameter increase. For bars under compression the situation is more unfavorable,

because both Poisson deformation and thermal expansion increase the bar diameter. A such

occurrence could be further investigated from a theoretical and experimental point of view.

A wider experimental investigation would allow, more correctly, to assess a theoretical model

to furnish, by simplified relationships, the minimum concrete cover that must be adopted at

design stage under a given temperature gradient, once the mechanical and geometrical

properties of the members are known.


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References

Aiello, M. A.(1999), “Concrete Cover Failure in FRP Reinforced Beams under Thermal

Loads”. Journal of Composites for Constructions, Vol. 3, no. 1, 46-52.

Aiello, M.A., Focacci, F., Huang, P.C., Nanni, A. (1999), “Cracking of Concrete Cover in

FRP Reinforced Concrete under Thermal Loads”. Fourth International Symposium on

Fiber Reinforced Polymer (FRP) for Reinforced Concrete Structures (FRPRCS-4),

Baltimore, Maryland, USA.

Conrad, J.O., Bakis C.E., Bootby, T.E. and Nanni, A. (1995), “Durability of Bond of Various

FRP Rods in Concrete”. CDCC-98, Sherbrooke, Canada, 299,310.

Den Uijl, J. A. (1995), “ Bond and fatigue properties of Arapree“. Non Metallic (FRP)

Reinforcement for concrete structures, L. Taerwe, ed., E & Spon, London, 146-153.

De Sitter, W. R., and Tolman, F. (1995), J. A., “ Uni-directional fibre pretensioned concrete

elements“. Non Metallic (FRP) Reinforcement for concrete structures, L. Taerwe, ed.,

E & Spon, London, 49-56.

Gentry, T.R. (1996). “Thermal compatibility of Plastic Composite Reinforcement and

Concrete”. Advanced Composite Materials in Bridges and Structures, M.M. El-Badry,

ed., Canadian Society for Civil Engineering, Montreal, Quebec, 149-156.

Matthys, S., De Schutter, G., and Taerwe, L. (1996). “ Influence of transverse thermal

expansion of FRP reinforcement on the critical concrete cover”. Advanced Composite

Materials in Bridges and Structures, M.M. El-Badry, ed., Canadian Society for Civil

Engineering, Montreal, Quebec, 665-672.

Gentry, R.T., and Husain, M. (1999), “Thermal compatibility of concrete and composite

reinforcements”. Journal of Composites for Constructions, Vol. 3, no. 2, 82-86.


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Tepfers, R. (1998). “Bond between FRP-Bars and Concrete”. Division of Building

Technology, Chalmers University of Technology, Göteborg, Publication no. 98:3,

Work no. 22, 1-16.

Tepfers, R. (1979). “Cracking of concrete cover along anchored deformed reinforcing bars”.

Magazine of Concrete Research, Vol. 31, no. 106, 3-12.

ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-95)

and Commentary (ACI 318R-95”, American Concrete Institute, Farmington Hills,

Mich.

Appendix Notation

The following notations are used in the paper:

c = value of the concrete cover;

Ec= Young’s modulus of the concrete;

E r = elastic tensile modulus of the reinforcement;

Etb = Young’s modulus of the bar in the transverse direction;

fc = compressive strength of the concrete;

fct = tensile strength of the concrete;

fr = tensile strength of the reinforcement;

L = specimen length;

r0 = rb = radius of the bar;

r2= rc = radius of the concrete cylinder;

rcr = radius of the cracked concrete cylinder;

αc = coefficient of thermal expansion of concrete;

αb = coefficient of thermal expansion of the bar in the transversal direction;


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ε = strain value;

∆T = temperature increase;

∆Tcr = temperature increase producing the first concrete cracking;

∆Tsp = temperature increase producing the spalling of the concrete cover;

νc = Poisson’s ratio of concrete;

νTT = Poisson ratio of the rebar in the transverse direction;

σT = stress at the interface concrete-rebar;

List of Tables

Table 1: Mechanical properties of materials

Table 2: Tested specimens

List of Figures

Fig. 1: a) Reinforcement and concrete effective area; b) Dimensions; c) radial stress acting at

the interface rebar-concrete under a temperature increase

Fig. 2: First concrete cracking and concrete spalling

Fig. 3: Specimens Geometry a) Rectangular cross-section; b) Circular cross-section

Fig. 4: Crack opening

Fig. 5: Strains versus temperature increase (Shape of the cross-section: Circular; Concrete

cover value=19 mm)


cover value=19 mm)

Fig. 7: Strains versus temperature increase (Shape of the cross-section: Rectangular; Concrete

cover value=19 mm)

Fig. 8: Strains versus temperature increase (Shape of the cross-section: Rectangular; Concrete

cover value=19 mm)


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Fig. 9: Strains versus temperature increase (Shape of the cross-section: circular; Concrete

cover value=38 mm)


cover value=38 mm)

Fig. 11: Strains versus temperature increase (Shape of the cross-section: circular; Concrete

cover value=57 mm)


cover value=57 mm)

Fig. 13: Comparison between theoretical and experimental results for GFRP rods

Fig. 14: Needed concrete cover for C50T °=∆ and MPa30fc =



Table 1: Mechanical properties of materials

Concrete C-BARTM

fc (MPa)

Ec* (MPa)

fct*

(MPa) fr

(MPa) Er

(MPa) ETb*

(MPa) νTT*

38.50 30000 3.9 770 42000 4000 0.4 *theoretically evaluated

Table 2: Tested specimens

Specimen Bar Diameter d (mm)

Concrete cover

c (mm)

Spec. LengthL (mm)

Number of

specimens R19 13 (0.51”) 19 (0.75”) 762 (30.00”) 2 C19 13 (0.51”) 19 (0.75”) 457 (18.00”) 2 C38 13 (0.51”) 38 (1.50”) 457 (18.00”) 2 C57 13 (0.51”) 57 (2.25”) 457 (18.00”) 2


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Rebar

Concrete

2r2 = c +d/2

2r0 = d

σT

a)

b) c)

∆T = ∆TcrFirst cracking

∆T = ∆TspLimit situation

∆T > ∆TspConcrete spalling

1 12

2

fct

fct

r2

r cr =

0.4

8r2

r0

11f 2

2

ctT +−=

γγσ

σθ = 0

σθ = 0

σT = 0.3fctγ

1fct

1

σρ (rcr)= 0.625fct

fct

0

2rr=γ


22

Sect A-A

1

43

21

A

A

LA

A2

76 mm

102

mm

L

c c

50 mm

a)b)

Strain gage position Strain gage position

Sect A-A


23

C1.9 Specimen 2

0200400600800

100012001400160018002000

0 10 20 30 40 50∆∆∆∆T (°C)

εε εε (m

icro

-str

ain)

1

2

34

av

∆∆∆∆Tsp

C1.9 Specimen 1

0

500

1000

1500

2000

2500

0 10 20 30 40 50∆∆∆∆T (°C)

εε εε (m

icro

-str

ain)

1

2

3

4av

∆∆∆∆Tsp


24

R1.9 Specimen 1

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60

∆∆∆∆T (°C)

εε εε (m

icro

-str

ain)

1

2

av

∆∆∆∆Tsp

R1.9 Specimen 2

0100200300400500600700800900

1000

0 10 20 30 40 50

∆∆∆∆T (°C)

εε εε (m

icro

-str

ains

)

1

2 av∆∆∆∆Tsp

C3.8 Specimen 2

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100

∆∆∆∆T(°C)

εε εε (m

icro

-str

ains

) 1

2

av

∆∆∆∆Tsp


25

C3.8 Specimen 1

0200400600800

10001200140016001800

0 20 40 60 80 100

∆∆∆∆T (°C)

ε ε ε ε (m

icro

-str

ains

) 1

2

av∆∆∆∆Tsp

C5.7 Specimen 1

0

200

400

600

800

1000

1200

0 20 40 60 80 100∆∆∆∆T (°C)

ε ε ε ε (m

icro

-str

ains

) ∆∆∆∆Tsp

1

2

av


26

20

40

60

80

1 2 3 4 5c/d

∆∆ ∆∆T

(°C

)

Analytical modelC3.8

C5.7

C1.9

R1.9

C5.7 Specimen 2

0

500

1000

1500

2000

2500

0 20 40 60 80 100

∆∆∆∆T (°C)

εε εε (m

icro

-str

ains

)

∆∆∆∆Tsp

1

2

av

40 45 50 70 75 801

2

3

6

7

8

c/d

ETb = 2 GPa

ETb = 3 GPa

ETb = 4 GPa

ETb = 5 GPaETb = 6 GPaETb = 7 GPaETb = 8 GPaETb = 9 GPaETb = 10 GPa

νTT 0.35 Ec 26 GPafc 30 MPa νc 0.18

fct 3.4 MPa αc 12⋅10-6 °C-1

∆Tsp = 50 °C

55 60 65

4

5

αb (106 °C-1)


27

40 45 50 70 75 801

2

3

6

7

8

c/d

ETb = 2 GPa

ETb = 3 GPa

ETb = 4 GPa

ETb = 5 GPaETb = 6 GPaETb = 7 GPaETb = 8 GPaETb = 9 GPaETb = 10 GPa

νTT 0.35 Ec 34 GPafc 50 MPa νc 0.18fct 4.4 MPa αc 12⋅10-6 °C-1

∆Tsp = 50 °C

55 60 65

4

5

αb (106 °C-1)

40 45 50 70 75 801

2

3

6

7

8

c/d

ETb = 2 GPa

ETb = 3 GPa

ETb = 4 GPa

ETb = 5 GPaETb = 6 GPaETb = 7 GPaETb = 8 GPaETb = 9 GPaETb = 10 GPaνTT 0.35 Ec 30 GPa

fc 40 MPa νc 0.18

fct 3.9 MPa αc 12⋅10-6 °C-1

∆Tsp = 50 °C

55 60 65

4

5

αb (106 °C-1)

Effects of Thermal Loads on Concrete Cover of FRP...

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