THE LOAD-CARRYING CAPACITY OF REINFORCED …

8
818 THE LOAD-CARRYING CAPACITY OF REINFORCED CONCRETE BEAMS STRENGTHENED WITH CARBON FIBRE COMPOSITE IN THE TENSION ZONE SUBJECTED TO TEMPORARY OR SUSTAINED LOADING Juozas Valivonis 1 , Tomas Skuturna 2 , Mykolas Daugevičius 3 Vilnius Gediminas Technical University, Saulėtekio ave. 11, LT-10223 Vilnius, Lithuania E-mail: 1 [email protected], 2 [email protected], 3 [email protected] Abstract. The article presents the results of the research carried out on the reinforced concrete beams under bending strengthened in the tensile zone with carbon fibre composite. The beams under bending were subjected to short-term and sustained static loading. The duration of sustained loading was 400 and 863 days. A total of four series of beams with different reinforcement ratio and loading duration were tested. Experimental research showed that sustained loading reduces the load-carrying capacity of the beams. Prior to long-term testing of the beams, the load-carrying capacity of control beams subjected to short-term static loading was measured. The decrease of the strength of the beams was caused by a long-term creep effect of concrete in the compression zone as well as plastic shear deforma- tions in the bond of concrete and carbon fibre. To calculate the bending capacity, the built-up bar theory enabling es- timation of short and long-term deformation capacity in the bond of concrete and carbon fibre was applied. Keywords: bending capacity, bond shear stiffness, long-term load, creep effect, distribution of deformations. 1. Introduction Methods enabling calculation of the load-carrying capacity of a beam are based on the balance of resultant forces caused by internal effects and external actions. Therefore, two methods can be distinguished that are most frequently used: the method of balance of internal and external forces (An et al. 1991; GangaRao 1998; Toutanji 2006; Alagusundaramoorthy et al. 2003; Pham 2004; Lu 2007; Bencardino et al. 2007; Capozucca 2002) and the method based on the theory of built-up bars (Va- livonis 2007; Marčiukaitis et al. 2007; Skuturna et al. 2008; Benyoucef et al. 2006, 2007). If the first method is applied to determine the load- carrying capacity, according to ACI 440.2R-08 it is measured by creating balance of forces in respect to the weight centre of the compression zone cross-section (Fig 1): 1 1 1 2 2 R s yd f f f x x M A f d A f h β β = - - . (1) If calculations are made according to Fib biulletin 14, the condition for balance of forces is: ( ) ( ) ( ) 1 2 2 2 R s yd G f f f G s s s G s M A f d x AE h x A E x a = + + ε + ε δ - , (2) where: A f , A s1 , A s2 – the area of carbon fibre reinforce- ment, steel bar reinforcement in tension and compression; f f , f y – strengths of carbon fibre and tensile steel rein- forcement; x the height of the compression zone; h – the height of strengthened beam; d – the effective depth of reinforced concrete beam; ε f , ε s2 – deformations carbon fibre composite and compressed steel reinforcement; E f , E s2 the elasticity modulus of carbon fibre composite and compressed steel reinforcement; β 1 , δ G – reduction coef- ficients of the compression zone β 1 =0.65–0.85 and δ G =0.4). Fig 1. The design scheme

Transcript of THE LOAD-CARRYING CAPACITY OF REINFORCED …

Page 1: THE LOAD-CARRYING CAPACITY OF REINFORCED …

818

THE LOAD-CARRYING CAPACITY OF REINFORCED CONCRETE BEAMS STRENGTHENED WITH CARBON FIBRE COMPOSITE IN THE TENSION

ZONE SUBJECTED TO TEMPORARY OR SUSTAINED LOADING

Juozas Valivonis1, Tomas Skuturna2, Mykolas Daugevičius3

Vilnius Gediminas Technical University, Saulėtekio ave. 11, LT-10223 Vilnius, Lithuania E-mail: [email protected], [email protected], [email protected]

Abstract. The article presents the results of the research carried out on the reinforced concrete beams under bending strengthened in the tensile zone with carbon fibre composite. The beams under bending were subjected to short-term and sustained static loading. The duration of sustained loading was 400 and 863 days. A total of four series of beams with different reinforcement ratio and loading duration were tested. Experimental research showed that sustained loading reduces the load-carrying capacity of the beams. Prior to long-term testing of the beams, the load-carrying capacity of control beams subjected to short-term static loading was measured. The decrease of the strength of the beams was caused by a long-term creep effect of concrete in the compression zone as well as plastic shear deforma-tions in the bond of concrete and carbon fibre. To calculate the bending capacity, the built-up bar theory enabling es-timation of short and long-term deformation capacity in the bond of concrete and carbon fibre was applied. Keywords: bending capacity, bond shear stiffness, long-term load, creep effect, distribution of deformations.

1. Introduction

Methods enabling calculation of the load-carrying capacity of a beam are based on the balance of resultant forces caused by internal effects and external actions. Therefore, two methods can be distinguished that are most frequently used: the method of balance of internal and external forces (An et al. 1991; GangaRao 1998; Toutanji 2006; Alagusundaramoorthy et al. 2003; Pham 2004; Lu 2007; Bencardino et al. 2007; Capozucca 2002) and the method based on the theory of built-up bars (Va-livonis 2007; Marčiukaitis et al. 2007; Skuturna et al. 2008; Benyoucef et al. 2006, 2007).

If the first method is applied to determine the load-carrying capacity, according to ACI 440.2R-08 it is measured by creating balance of forces in respect to the weight centre of the compression zone cross-section (Fig 1):

1 11 2 2R s yd f f f

x xM A f d A f hβ β = − +ψ − . (1)

If calculations are made according to Fib biulletin 14, the condition for balance of forces is: ( )

( ) ( )1

2 2 2

R s yd Gf f f G s s s G s

M A f d xA E h x A E x a

= − δ ++ ε − δ + ε δ −

, (2)

where: Af, As1, As2 – the area of carbon fibre reinforce-ment, steel bar reinforcement in tension and compression; ff, fy – strengths of carbon fibre and tensile steel rein-forcement; x – the height of the compression zone; h – the height of strengthened beam; d – the effective depth of reinforced concrete beam; εf, εs2 – deformations carbon fibre composite and compressed steel reinforcement; Ef, Es2 – the elasticity modulus of carbon fibre composite and compressed steel reinforcement; β1, δG – reduction coef-ficients of the compression zone β1 =0.65–0.85 and δG =0.4).

Fig 1. The design scheme

Page 2: THE LOAD-CARRYING CAPACITY OF REINFORCED …

819

The analyses of research related to the load-carrying capacity of flexural members shows that strengthened beams can fail in the compression zone, in the horizontal section by peeling off a strip of carbon fibre together with a layer of concrete or when carbon fibre composite rup-ture in the middle of the beam span when the limit stresses of carbon fibre composite are reached (Bulavs et al. 2005; Leung 2003; Maalej 2005; Marčiukaitis 2009; Ramos et al. 2006; Saxena et al. 2008; Thomsen et al. 2004). As research of other investigators shows, strength-ened beams fail in the compression zone when the ratio of the width and height of the beam is close to 1 (Gao et al. 2007).

The bond of carbon fibre composite and concrete in strengthened structures is not stiff. When subjected to loading, due to shear deformations, the composite in the bond moves in respect to concrete. Due to this, the effi-ciency of strengthening reduces (Skuturna et al. 2008). Therefore, the guide for the design ACI 440.2R-08 indi-cates that the force of carbon fibre composite is reduced by multiplying by coefficient 0.85fψ = .

Fig 2. Shear deformations in tension zone of beam

In order to evaluate the influence of the shear on the

load-carrying capacity of the composite layer without using the reduction coefficients, it is suggested to apply the built-up bar theory. This theory reflects the real work of strengthened structures since it takes into account slip of the composite layer caused by shear stresses due to which the load-carrying capacity of strengthened ele-ments decreases. Besides, it is not necessary to take into account the reduction coefficients when the structures are subjected to short-term and sustained loading.

2. A method of calculation of the load-carrying capac-ity of strengthened beams

According to the built-up bar theory, in order to make calculations the cross-section of the beam is di-vided into two separate members (Fig 3).

The bending moment:

0R cM M T a= + ⋅ , (3)

Fig 3. The design scheme

where: M0 – sum total of bending moments of separate members when the bond is stiff; Tc – bond shear force is calculated according to the formula (Ржаницын 1986):

( )

( )

sinh1

( ) cosh 0.5

ppc

c p

lP a lT

t EI l l

⎡ ⎤λ ⋅⋅ ⋅⎢ ⎥= −

γ ⎢ λ ⋅ ⋅ λ ⋅ ⎥⎣ ⎦∑

. (4)

The value λ, assessing the stiffness of the bond is calculated:

( )c c tλ = ξ ⋅ γ , (5)

( ), ,

2

, ,

1 1

( )

,( )

cc eff c eff fe fe

c eff c eff

tE t A E A

a

E t I

γ = + +⋅ ⋅

+⋅

(6)

( ),( ) c eff

c

b G tt

a

⋅ξ = , (7)

where: Ac,eff, Ec,eff (t), Ic,eff – the area of effective rein-forced concrete cross section, the effective elasticity modulus, the effective moment of inertia; b – the width of cross section.

The characteristic of the bond shear stiffness Gc,eff (t) can be calculated according to the formula:

( ).

1

( )110 2

4 460 ,

cc eff

cm

s crc

fe R a

E tG t

E

M

M k

= + −

ρ− −

ρ ⋅

(8)

where: Ec(t) – the elasticity modulus of concrete is calcu-lated according to EC2; Ecm – the secant modulus of con-crete; ρfe – reinforcement ratio of carbon fibre composite; ρs1 – reinforcement ratio of steel reinforcement in tension zone; Mcrc – the cracking moment; MR – the load-carrying capacity of the beams with external carbon fibre rein-forcement when the bond between carbon fibre composite and concrete is stiff is calculated according to the formula 9; ka – coefficient which evaluates the type of anchorage of external reinforcement (when external reinforcement over supports ka =1; when carbon fibre reinforcement is not additionally anchored).

Page 3: THE LOAD-CARRYING CAPACITY OF REINFORCED …

820

( )

( )2 2 2 2

0.5.

R cd

s s s s f f f f

M f b x d xE A d a A E a

= ⋅ ⋅ − ⋅ +

+ ε − + ⋅ ⋅ ε ⋅ (9)

where: fcd – strengths of concrete under compression; as2 – distance to centroid of compressive steel reinforce-ment; af – distance to centroid of carbon fibre composite.

3. Specimens and methodology of the experimental research

4 series of beams were produced for experimental research. The project size of the samples was 100×200×1500 mm. The compression and tension zones of the first series of beams were reinforced with 2Ø6 reinforcing steel bars. The compression zone of the sec-ond series was reinforced with 2Ø6 reinforcing bars and the tension zone was reinforced with 2Ø8 reinforcing bars. The compression and tension zones of the third series of beams were respectively reinforced with 2Ø8 and 2Ø12 reinforcing steel bars. The compression zone of the fourth series of beams was reinforced with 2Ø6 rein-forcing bars and the tension zone was reinforced with 2Ø14 reinforcing bars.

Carbon fibre of B8C and B12C series beams was glued up the supports. Carbon fibre in B6C and B14C series beams overlapped the supports. The cross-section area of carbon fibre reinforcement in all series of beams was the same.

The characteristics of beam concrete, steel bars and composite carbon fibre reinforcement are given in Ta-ble 1.

Experimental research on the second series of beams was carried out under short-term loading. Beams of all other series were tested under both short-term and sus-tained loading.

The reinforced concrete beams were tested on the testing stand (Fig 4). The length of the beam span was 1200 mm. One hydraulic jack was used to create loading. The loading was increased by stages. The beam testing scheme is show in Fig 5.

Fig 4. Overview of test setup for short-term loading

Table 1. Material properties

Series Beam code

fc, (MPa)

Ec, (GPa)

ff, (MPa)

Ef, (GPa)

fy, (MPa)

fyu, (MPa)

Af, (cm2)

As, (cm2)

Asc, (cm2)

B6.1C

B6.2C

B6.3Ct

B6.4Ct

4800 231 0.167 1

B6.5

38.27 34.1

– –

358 460

0.6784 0.6784

B8.1C

B8.2C 4800 231 0.167

2

B8.3

35 31.3

– –

557 638

1.038 0.57

B12.1C

B12.2C

B12.3Ct

B12.4Ct

32.1 32.27 4800 231 0.167

B12.5

3

B12.6 – –

318 456

2.26 1.01

B14.1C

B14.2C

B14.3Ct

38.27 34.1

B14.4Ct 32.87 31.45

4800 231 0.167 4

B14.5 – –

358 460

3.08 0.6784

Page 4: THE LOAD-CARRYING CAPACITY OF REINFORCED …

821

Fig 5. Testing scheme of short-term loading

During the testing the following measurements were

made: beam deflection and displacement of carbon fibre composite in respect to concrete, deformations of the external carbon fibre reinforcement, deformations of concrete in the compression and tension zones, the crack-ing moment, the character and the width of the increase of cracks were also recorded.

For sustained bending of beams the equipment (Figs 6, 7) which ensured a stable level of loading during the whole period of the research was used. The places of concentrated forces were the same as in control beams. To achieve the effect of sustained loading the beams were loaded up to the level of 0.6MR of the load-carrying ca-pacity. During the testing, similarly as with beams under short-term loading, deformations and beam deflection were measured here. At the end of sustained testing the beams are unloaded and each sample is subjected to short-term loading until it reaches the capacity loading.

Beams

25.0 25.0 25.025.0 25.0

25.0 25.025.0 25.0

Weight pallet

Bearing supportLoad transfer beam

CFRP

layers

A

A-AA

Beams

Bearing support

Fig 6. Testing scheme of sustained loading test

Fig 7. Test setup for sustained loading

4. Results of experimental research

Nineteen reinforced concrete beams were tested in order to define the influence of short-term and sustained loading on the work of strengthened beams.

Characteristic points of the work of beams can be distinguished in the charts of the bending moment and deformations of the beams subjected to short-term load-ing. The research shows that the modulus of elasticity of carbon fibre under tension is ~ 7 times bigger than the modulus of elasticity of concrete. Therefore, external carbon fibre reinforcement in a reinforced concrete mem-ber restricts deformations of concrete under tension. This means that the cracking moment significantly increases in a reinforced concrete member with a restricted tension zone in comparison with non-strengthened beams. The first refraction point of the graph (Fig 8) characterises appearance of vertical cracks.

Fig 8. Distribution of deformations in beam B12-1C: ε-1 composite layer under tension; ε-2 the layer with steel bar reinforcement under tension; ε-3 concrete in the compression zone

It has also been found out that carbon fibre rein-

forcement in the tension zone influences increase of cracks, limits the development of cracks, therefore, the width and height of cracks do not increase. Carbon fibre is glued to reinforced concrete beams with epoxy adhe-sive. When adhesive deforms, carbon fibre composite slips horizontally and causes stresses in concrete. Due to these stresses, additionally to vertical cracks, horizontal cracks appear in concrete (Fig 9). Research shows that these cracks interconnect and in separate zones damage the bond between carbon fibre composite and concrete. When the bond is damaged, increase in steel bar deforma-tion significantly grows (Fig 8 refraction of the graph).

Later, depending on how carbon fibre composite was anchored, beams failed by peeling off carbon fibre composite (Fig 10) or carbon fibre rupture (Fig 11).

The research conducted shows that the load-carrying capacity of the strengthened beams subjected to short-term loading compared to the beams without external reinforcement increases. The load-carrying capacity of B6С series beams increases more than 3 times; the load-carrying capacity of B8С series beams increases more than 70 %; the load-carrying capacity of B12С series beams increases more than 50 % in comparison with the beams that were not strengthened (Table 3).

0

2

4

6

8

10

12

14

16

18

20

-0.2 -0.1 0 0.1 0.2 0.3 0.4

Deformations [ε·10²]

Ben

ding

mom

ent

[kN

·m]

ε-1

ε-2

ε-3

Page 5: THE LOAD-CARRYING CAPACITY OF REINFORCED …

822

Fig 9. Distribution of leaning cracks along the beam at the site of bond of carbon fibre and concrete in the tension zone

Fig 10. Failure mode of beams by peeling off carbon fibre composite

Fig 11. Rupture of carbon fibre in the middle of beam

Experimental research revealed that the higher rein-

forcement ratio of steel bar reinforcing, the lower the strengthening effect of carbon fibre composite. The maximum strengthening effect is reached when steel bars reinforcement ratio is low. Experimental research showed that the best strengthening effect was reached in B6C beams since the strength qualities of concrete and com-posite were more used because higher deformations were reached (Figs 12, 13). Research also showed that when members are considerably reinforced, carbon fibre fixed in the tension zone is not fully used (Figs 12, 13).

The sustained bending tests revealed that the inten-sity of creep deformations in the compression zone of concrete is higher than in the tension zone. It has also been found out that under sustained loading deformations in the tension zone at the steel bar reinforcing level are bigger than the composite layer deformations (Figs 14, 15). This enables us to make a conclusion that the com-posite layer under tension displaces in respect to rein-

forced concrete beam. Therefore, when repeatedly loaded ultimate deformations at which the load-carrying capacity is lost are reached faster.

0

5

10

15

20

25

-0.25 -0.20 -0.15 -0.10 -0.05 0.00

Deformations [ε·10²]

Ben

ding

mom

ent

[kN

·m]

B6.1C

B12.1C

B14.1C

Fig 12. Distribution of deformations of compression zone of concrete

0

5

10

15

20

25

0.00 0.20 0.40 0.60 0.80 1.00

Deformations [ε·10²]

Ben

ding

mom

ent

[kN

·m]

B6.1C

B12.1C

B14.1C

Fig 13. Distribution of deformations of carbon fibre composite layer under tension

0.16

0.17

0.18

0.19

0.20

0.21

0.22

0 50 100 150 200 250 300 350 400

Days

Def

orm

atio

ns [

%]

ε-1

ε-2

Fig 14. Distribution of creep deformations in the lay-ers under tension in the beam B12-3Ct: ε-1 composite layer under tension; ε-2 the layer with steel bar rein-forcement under tension

The intensity of deformations reached when loading

was 0.6MR depended on reinforcement ratio of steel bar reinforcing. When beams B 6.3Ct and B6.4Ct are loaded until the level of permanent load is reached, the steel reinforcement under tension reaches yield stresses. When beams are unloaded, residual deformations in the layers under tension are measured (Fig 16, Table 2).

Page 6: THE LOAD-CARRYING CAPACITY OF REINFORCED …

823

0.10

0.20

0.30

0.40

0 200 400 600 800Days

Def

orm

atio

ns [

%]

ε-1

ε-2

Fig 15. Distribution of creep deformations in the lay-ers under tension in the beam B14-3Ct: ε-1 composite layer under tension; ε-2 the layer with steel bar rein-forcement under tension

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Deformations [ε·10²]

Ben

ding

mom

ent

[kN

·m]

ε-1

ε-2

Fig 16. Distribution of relative deformations in beam B6.3Ct: ε-1 composite layer under tension; ε-2 the layer with steel bar reinforcement under tension

0

2

4

6

8

10

12

14

16

18

20

0.0 0.1 0.2 0.3 0.4 0.5 0.6Deformations [ε·10²]

Ben

ding

mom

ent

[kN

·m]

ε-1ε-2Series7

Fig 17. Distribution of relative deformations in beam B12.3Ct: ε-1 composite layer under tension; ε-2 the layer with steel bar reinforcement under tension The residual deformations of beams B6.Ct and

B12.Ct are higher than creep deformations (Fig 17, Ta-ble 2). The size of residual deformations of beams B14.Ct is similar to creep deformations since increase of defor-mations developed proportionally until the permanent load was reached and when it was being unloaded, pro-portionally decreased (Fig 18, Table 2). Whereas, the increase of deformations in beams B6.Ct was also caused by yield deformations of tensile reinforcement due to which residual deformations were significantly bigger than creep deformations.

0

5

10

15

20

25

30

0.0 0.1 0.2 0.3 0.4 0.5

Deformations [ε·10²]

Ben

ding

mom

ent

[kN

·m]

ε-1ε-2Series2

Fig 18. Distribution of relative deformations in beam B14.3Ct: ε-1 composite layer under tension; ε-2 the layer with steel bar reinforcement under tension

Table 2. Creep and residual deformations of layers under tension

Beam code εcr,cs ⋅102

εres,cs ⋅102 εcr,f ⋅102 εres,f ⋅102

B6.3Ct 0.2845 0.51763 0.0884 0.3137

B12.3Ct 0.034 0.06375 0.02575 0.0465

B12.4Ct 0.02275 0.01975 0.03275 0.05675

B14.3Ct 0.232 0.2335 0.0412 0.04182

B14.4Ct 0.2575 0.261 0.0326 0.042514

where: εcr,cs , εres,cs – creep and residual deformations of layer with steel bar reinforcement under tension; εcr,f , εres,f – creep and residual deformations of composite layer under tension.

Experimental research showed that the load-carrying

capacity of beams after sustained loading decreased. The biggest decrease in load-carrying capacity was displayed in the beams which were the least reinforced and it reached up to 28 %. The decrease of load-carrying capac-ity in the beams reinforced with ∅12 and ∅14 longitudi-nal reinforcement reached from 4 % to 7 %. This can be explained by creep deformations of concrete in the com-pression zone and shear creep deformations of carbon fibre composite under tension. When the strengthened beams are unloaded, residual deformations remain in the tensile and compressed layers. Deformations of speci-mens increase starting from the residual value when sus-tained loading test is over and beams are subjected to short-term loading. Deformations in the layers at each loading stage are bigger than in control beams at the same level of loading. Therefore, failure of beams subjected to sustained loading occurs earlier than that of the beams tested by applying only short-term loading. The results of the load-carrying capacity of the beams are presented in Table 3.

Calculation of the load-carrying capacity of strengthened beams under temporary and sustained load-ing was made according to the suggested methodology which evaluates the stiffness of bond of concrete and carbon fibre composite (Formula 8) as well as the influ-ence of sustained loading. The results of calculation are given in Table 3.

Page 7: THE LOAD-CARRYING CAPACITY OF REINFORCED …

824

Table 3. Experimental and calculated load-carrying capacity Se

ries

Code 0, ,expR tM

(kN·m) 0, ,R t calcM

(kN·m) 1, ,expR tM

(kN·m) 1, ,R t calcM

(kN·m) 0 0, , , ,expR t calc R tM M

1 1, , , ,expR t calc R tM M

B6.1C 15.50 15.40 0.99

B6.2C 18.00 15.40

0.86

B6.3Ct 10.61 14.6 1.38

B6.4Ct

14.76 14.6 0.99

1

B6.5 5.20 B8.1C 15.82 17.57 1.11

B8.2C 15.63 17.57

1.12 2

B8.3 9.10

B12.1C 18.0 17.34 0.96

B12.2C 18.0 17.34

0.96

B12.3Ct 17.22 17.07 0.99

B12.4Ct

17.55 17.07

0.97

B12.5 11.62

3

B12.6 11.78

B14.1C 23.00 27.70 1.2

B14.2C 28.00 27.70

0.99

B14.3Ct 24.00 1.12

B14.4Ct 24.00

1.12

4

B14.5 28.50

Calculation results show that if the suggested calcu-

lation method is used, the load-carrying capacity of strengthened beams can be measured quite precisely. Analysis of results shows that calculation exactness mainly depends on reinforcement ratio. Calculations of load-carrying capacity of beams whose reinforcement ratio is very low or big are not so exact (1–38 %) than of beams where reinforcement ratio is normal (1–12 %).

Conclusions

Research showed that carbon fibre composite sig-nificantly increases the load-carrying capacity of strengthened members. The effect of strengthening de-pends on reinforcement ratio of steel bar reinforcement in the specimens. The lower the ratio of this reinforcement, the higher the strengthening effect since the strength of carbon fibre composite is better used. The higher rein-forcement ratio of steel bar reinforcement, the lower the effect of strengthening.

It has been defined that sustained loading influences the load-carrying capacity of strengthened beams. Under sustained loading creep deformations of concrete in the compression zone as well as carbon fibre composite oc-cur and they remain when specimens are unloaded. When beams are again subjected to short-term loading, defor-mations increase starting from the residual values. As a result, the load-carrying capacity of the specimens de-creases in comparison with the load-carrying capacity of the beams loaded only short-term.

A calculation method that evaluates the stiffness of bond carbon fibre composite and concrete as well as the influence of sustained loading has been suggested. The

load-carrying capacity calculation results quite precisely coincide with the experimental values.

References

An, W.; Saadatmanesh, H.; Ehsani, M. R. 1991. RC beams strengthened with FRP plates. II analysis and parametric study, Journal of Structural Engineering 117(11): 3434–3455. doi:10.1061/(ASCE)0733-9445(1991)117:11(3434)

Alagusundaramoorthy, P.; Harik, I. E.; Choo, C. C. 2003. Flex-ural behaviour of RC beams strengthened with carbon fi-ber reinforced polymer sheets or fabric, Journal of Com-posites for Construction 7(4): 292–301. doi:10.1061/(ASCE)1090-0268(2003)7:4(292)

American Concrete Institute (ACI). 2008. Guide for the Design and Construction of Externally bonded FRP systems for Strengthening Concrete Structures (ACI 440.2R-08). Farmington Hills, Mich.

Bencardino, F.; Spadea, G.; Swamy, R. N. 2007. The problem of shear in RC beams strengthened with CFRP laminates, Construction and Building Materials 21(11): 1997–2006. doi:10.1016/j.conbuildmat.2006.05.056

Benyoucef, S.; Tounsi, A.; Adda Bedia, E. A.; Meftah, S. A. 2006. Creep and shrinkage effect on adhesive stresses in RC beams strengthened with composite laminates, Com-posite science and technology 67: 933–942.

Benyoucef, S.; Tounsi, A.; Benrahou, K. H.; Adda Bedia, E. A. 2007. Time-dependent behavior of RC beams strength-ened with externally bonded FPR plates: interfacial stresses analysis, Mechanics of Time-Dependent Material 11(3-4): 231–248. doi:10.1007/s11043-007-9045-2

Bulavs, F.; Radinsh, I.; Tirans, N. 2005. Improvement of capac-ity in bending by the use of FRP layers on RC beams, Journal of Civil Engineering and Management 11(3): 169–174.

Page 8: THE LOAD-CARRYING CAPACITY OF REINFORCED …

825

Capozucca, R.; Cerri, M. N. 2002. Static and dynamic behav-iour of RC beam model strengthened by CFRP-sheets, Construction and Building Materials 16(2): 91–99. doi:10.1016/S0950-0618(01)00036-8

Fib Task Group 9.3. 2001. Externally Bonded FRP Reinforce-ment for RC Structures. Fib bulletin 14, Lausanne, Swit-zerland. 130 p.

GangaRao, H. V. S.; Vijay, P. V. 1998. Bending behavior of concrete beams wrapped with carbon fiber, Journal of Structural Engineering 124(1): 3–10. doi:10.1061/(ASCE)0733-9445(1998)124:1(3)

Gao, B.; Leung, C. K. Y; Kim, J. K. 2007. Failure diagrams of FRP strengthened RC beams, Composite Structures 77(4): 493–508. doi:10.1016/j.compstruct.2005.08.003

Leung, H. Y.; Balendran, R. V. 2003. Effect of using external GFRP plates on structurally deficient RC beams, Journal of Civil Engineering and Management 9(1): 36–44.

Lu, S.; Xie, H. 2007. Strengthen and real-time monitoring of RC beam using „intelligent“ CFRP with embedded FBG sensors, Construction and Building Materials 21(9): 1839–1845. doi:10.1016/j.conbuildmat.2006.05.062

Maalej, M.; Leong, K. S. 2005. Effect of beam size and FRP thickness on interfacial shear stress concentration and fail-ure mode of FRP-strengthened beams, Composite Science and Technology 65(7-8): 1148–1158. doi:10.1016/j.compscitech.2004.11.010

Marčiukaitis, G.; Valivonis, J.; Bareišis, J. 2007. An analysis of the joint operation of a CFRP concrete in flexural ele-ments, Mechanics of Composite Materials 43(5): 467–478. doi:10.1007/s11029-007-0044-9

Marčiukaitis, G.; Balevičius, R. 2009. Stress, Strain and Creep Analysis of the Layered Composite Structures under Sus-tained Loading, Engineering structures and technologies 1(3): 123–134.

Pham, H.; Al-Mahaidi, R.; 2004. Assessment of available pre-diction models for the strength of FRP retrofitted RC beams, Composite Structures 66(1-4): 601–610. doi:10.1016/j.compstruct.2004.05.008

Ramos, G.; Casas, J. R.; Alarcon, A. 2006. Normalized test for prediction of debonding failure in concrete elements strengthened with CFRP, Journal of Composites for Con-struction 10(6): 509–519.

doi:10.1061/(ASCE)1090-0268(2006)10:6(509)

Saxena, P.; Toutanji, H.; Noumowe, A. 2008. Failure analysis of FRP strengthened RC beams, Journal of Composites for Construction 12(1): 2–14.

doi:10.1061/(ASCE)1090-0268(2008)12:1(2)

Skuturna, T.; Valivonis, J.; Vainiūnas, P.; Marčiukaitis, G.; Daugevičius, M. 2008. Analysis of deflections of bridge girders strengthened by carbon fiber reinforcement, The Baltic Journal of Road and Bridge Engineering 3(3): 145–151. doi:10.3846/1822-427X.2008.3.145-151

Thomsen, H.; Spacone, E.; Limkatanyu, S.; Camata, G. 2004. Failure mode analyses of reinforced concrete beams strengthened in flexure with externally bonded fiber-reinforced polymers, Journal of Composites for Construc-tion 8(2): 123–131.

doi:10.1061/(ASCE)1090-0268(2004)8:2(123)

Toutanji, H.; Zhao, L. 2006. Verifications of design equations of beams externally strengthened with FRP composites, Journal of Composites for Construction 10(3): 254–264. doi:10.1061/(ASCE)1090-0268(2006)10:3(254)

Valivonis, J.; Skuturna, T. 2007. Cracking and strength of rein-forced concrete structures in flexure strengthened with carbon fibre laminates, Journal of Civil Engineering and Management 13(4): 317–323.

Ржаницын, А. Р. 1986. Составные стержни и пластинки [Built-up bars and plates]. Moscow: Stroiizdat. 316 p.