Debonding failure modes of flexural FRP-strengthened RC beams

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Composites: Part B 39 (2008) 826–841 www.elsevier.com/locate/compositesb

Debonding failure modes of flexural FRP-strengthened RC beams Mohammad Reza Aram a,b, Christoph Czaderski b,*, Masoud Motavalli a,b b

a Faculty of Civil Engineering, University of Tehran, Tehran, Iran Empa, Structural Engineering Research Laboratory, 8600 Du¨bendorf, Switzerland

Received 8 June 2005; received in revised form 2 October 2007; accepted 8 October 2007 Available online 5 November 2007

Abstract In this paper, different types of debonding failure modes are described. Then, experimental results of four-point bending tests on FRP strengthened RC beams are presented and debonding failure mechanisms of strengthened beams are investigated using analytical and finite element solutions. Reasonable results could be obtained for modelling of debonding failure load of tested beams. Existing international codes and guidelines from organizations such as ACI, fib, ISIS, JSCE, SIA, TR55, etc. are presented and compared with the results from the experiments and calculations. A discrepancy of up to 250% was seen between different codes and guidelines for predicting the debonding load. Furthermore, a new recommendation for debonding control is given. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Carbon fibre; B. Debonding; Flexural strengthening; C. Analytical modelling; C. Finite element analysis

1. Introduction Post-strengthening of reinforced concrete structures with fibre reinforced plastic (FRP) plates, fabrics and similar products is prevalent today. FRP has high tensile strength and, in contrast to steel plates, has the advantage of being substantially lighter. Furthermore, FRP products are corrosion-resistant and exhibit excellent fatigue strength. They can be used for the strengthening of concrete members in bending, shear or torsion as well as confinement. Concrete is unable to resist high tensile stresses, therefore making the delamination or debonding of FRP from the substrate a highly probable failure mode for strengthened concrete elements. Generally, there are two debonding failure types. The first type is midspan debonding, which initiates at flexural or shear cracks in the midspan of a concrete element and propagates towards the ends of the plate. This failure mode has been investigated experi-

*

Corresponding author. Tel.: +41 44 823 55 11; fax: +41 44 823 44 55. E-mail address: [email protected] (C. Czaderski).

1359-8368/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2007.10.006

mentally and analytically e.g. by Arduini and Nanni [1] and Wendel [2], who studied the behaviour of precracked RC beams strengthened with FRP plates. The second debonding failure type is plate end debonding which starts at the ends of the plate and propagates along the beam. There has been a significant amount of research on this failure mode, which has resulted in closed-form elastic solutions for interfacial stresses [3–6], analytical design guidelines for end anchorage [7,8] and nonlinear finite element modelling [9,10]. A complete bond model has been proposed by Neubauer and Rostasy [11,31] in order to check debonding at all vulnerable locations of the strengthened beam. This was followed by another detailed method given by Niedermeier [12]. Neubauer’s and Niedermeier’s methods are based on the fact that the maximum increase in tensile stress in the plate between two cracks depends on the tensile stress in the plate and is determined by modelling the bond behaviour at a concrete tooth between two cracks. Even with the substantial amount of research that has been carried out, debonding failure mechanisms are nevertheless complicated processes and still not fully understood, therefore making it difficult to predict the failure load. In this paper, different debonding failure modes will

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

(1) Plate end shear failure

(4) Flexural crack debonding (3) Shear crack debonding

827

(2) Anchorage failure at last crack

Fig. 1. Possible debonding failure modes.

be described and some of existing international codes and guidelines such as ACI, fib, ISIS, JSCE, SIA, TR55, etc. [13–20] are surveyed. Experimental results will be compared with analytical and FE calculations and different types of debonding criteria presented in the guidelines. 2. Debonding failure modes Possible failure modes of FRP strengthened RC beams include shear failure, flexural failure (concrete crushing and FRP rupture) and FRP debonding. The most common failure mode of flexural beams strengthened with FRP is debonding of the FRP reinforcement. When a reinforced concrete beam with an externally bonded FRP plate is subjected to flexural loading, high tensile and bond shear stresses develop in the concrete near the adhesive layer. In general, debonding of the FRP plate from the concrete is due to these high stresses. The weakest part in the bond surface is the concrete layer close to the surface. Cover delamination or FRP debonding can thus occur if the interfacial stresses cannot be sustained by the concrete. Debonding initiation generally takes place in a region of high stress concentration at the concrete-FRP interface. These regions include the ends of the FRP reinforcement and those around the shear and flexural cracks. Therefore codes and guidelines concentrate on two debonding failure modes: plate end debonding and midspan debonding. The first mode is the failure that originates near the plate end and propagates in the concrete either at the cut-off point of the plate ((1) plate end shear failure) or at the last crack ((2) anchorage failure at last crack). The second mode is the failure that is caused at a

Cover=20 mm 3φ8

3. Experimental work and results Experimental work was carried out at the Swiss Federal Laboratories for Materials Testing and Research (Empa) on four short span beams. The tests were commissioned by Stesalit AG, Switzerland, the producer of the CFRP plates and performed in 1996. One of the four beams, B1, was used as the reference beam and the remaining three beams were strengthened using three different CFRP plates. The geometry, test setup and material properties are shown in Fig. 2 and Table 1 [21]. Three 8 mm diameter bars were provided as both tensile and compression reinforcement. The steel reinforcement had a yield stress of 485 MPa and ultimate strength of 623 MPa. Shear reinforcement consisted of 6 mm diameter closed stirrups at a spacing of 150 mm. A usual concrete with maximum aggregate size of 32 mm was used. The specimens were simply supported at the ends and were loaded using two concentrated loads with a 667 mm spacing. Deflection was measured using a dial gauge positioned at midspan. The strain at the top and bottom side of the midspan was measured with a mechanical strain gauge (D1, D2). The reference beam failed by concrete crushing, whereas the strengthened beams failed by plate rupture or debonding depending on the material properties of the CFRP plates. Due to the low CFRP strength and high elastic modulus, the failure mode of B2 was rupture of the CFRP

667

667

667

dial gauge

D1 y

150

x φ6@150

shear or flexural crack and then propagates from such a crack towards the plate end (Fig. 1).

250

200

D2 2000 2400 mm

Fig. 2. Geometry and cross-sectional properties of tested beams [21].

200

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M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

Table 1 Material properties of test beams [21]

4. Analytical, finite element and design models

Beam

fy (MPa)

fu (MPa)

fcu (MPa)

CFRP plate

ffa (MPa)

Efa (GPa)

4.1. Analytical models

B1 B2 B3 B4

485 485 485 485

623 623 623 623

49 49 49 52

– 50  1.2 mm 50  1.2 mm 50  1.2 mm

– 1300 2000 2700

– 305 214 155

Various analytical methods are available to analyze beams strengthened with bonded FRP plates. Analytical calculations are used below to model the behaviour of strengthened beams and to predict the debonding failure load.

a

Specified by producer, efu is calculated from ff and Ef.

with little ductility. Others failure modes involved debonding of the CFRP plate (Fig. 3). A comparison of the load–deflection diagrams is shown in Fig. 4. Two changes of slope are evident. The first is due to concrete cracking. The second occurs when the reinforcing steel begins to yield. The failure load is about the same for all three beams. The load capacity of the strengthened beams is up to 100% greater than the reference beam. B2 with the stiffest plate (highest elastic modulus) has the lowest deformation. However, B3 exhibited the largest deflection at failure as compared with the other strengthened beams.

4.1.1. Cross-section analysis (CSA) An analytical approach based on a cross-section analysis is presented in order to calculate the failure load of the strengthened beam. By assuming full composite action between the concrete and the FRP plate, it is possible to calculate the behaviour of a cracked concrete beam and to develop a simplified nonlinear solution. As done in [22], the load–deflection curve of the beam is calculated by using a moment–curvature diagram for the cross-section. Using results from this approach and design models, three types of failure modes (numbers 2, 3, 4) can be predicted (see Fig. 1). In order to obtain the moment–curvature relationship, the bending moment capacity of the cross-section is calculated by increasing the curvature from zero to ultimate capacity. The compatibility condition states that the strain varies linearly along the cross-section from top to bottom (Fig. 5). The neutral axis depth of cross section (x) is calculated by using the equilibrium and compatibility conditions of cross section: F c þ F s2 ¼ F s1 þ F t þ F f ;

ð1Þ

where Fc, Fs2, Fs1, Ft and Ff are, respectively, the total force in the compressive part of concrete, compression reinforcement, tensile reinforcement, tensile part of uncracked concrete and plate. The compressive behaviour of the concrete can be defined by a parabolic function proposed by Hognestad [23]: 8 < Ec e ð0 6 e 6 et ; tensileÞ;  2 rc ðeÞ ¼ : fc 2  ee0  ee0 ð0 6 jej 6 2e0c ; compressiveÞ:

Fig. 3. Debonding failure of beam B4.

c

c

ð2Þ

40 B1: reference beam B2: plate with E=305 GPa

30

Load F [kN]

B3: plate with E=214 GPa B4: plate with E=155 GPa

20

10

0 0

10

20

30

40

Deflection at midspan [mm]

Fig. 4. Load–deflection diagrams of tested beams [21].

50

The moment–curvature diagram comprises pre-cracking, post-cracking and post-yielding stages. The first stage extends to the onset of flexural cracking in the cross-section. The second stage follows up to first yield of the tensile steel. The third stage continues to the limit of concrete crushing or FRP rupture or debonding, depending on the failure mode involved. In these calculations, it is assumed that full composite action is maintained until failure. The bending moment capacity is determined by   2x1 M n ¼ F s1 ðd  cx Þ þ F s2 ðcx  d 0 Þ þ F t x  cx þ 3 þ F f ðh  cx Þ;

ð3Þ

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

829

Fs2

x

d0

εc εs2

d-x

h-x

d

A s2

As1

εs1

Af

εf

Fs1 Ff

Fig. 5. Stress and strain distribution in cross-section.

where x1 ¼ Efctexc and cx is the depth of Fc from top of the cross-section. The related curvature is calculated as follows:  jec;top j þ jec;bot j ec þ ec hx x ¼ : ð4Þ /¼ h h For simplification, the moment–curvature diagram can be represented by a trilinear function (Fig. 6). Using the above mentioned moment–curvature analysis, the moment, curvature and bending stiffness (EI) can be calculated for the end of each stage. Beam deflection is obtained by integrating twice the beam curvature. The first integration of beam curvature gives the inclination of the beam; the second integration results in the deflection of the beam: R hðxÞ ¼ y 0ðxÞ ¼ /ðxÞ dx; R ð5Þ y ðxÞ ¼ hðxÞ dx:

a certain length of beam is equal to the difference of the FRP force between two cross-sections divided by the bonding area between them: sb ¼

DT : bf Dx

ð6Þ

Eq. (6) defines a mean global value for shear stress that results from a change in bending moment along the beam. It has to be noted that this is a simplification, because in reality the shear stress is not constant between the cracks.

M

Figure 6

The top (ec,top) and bottom (ec,bot) strains of the beam are found using a similar approach as that used to calculate the curvature. The steps required for the analytical calculations of a FRP reinforced beam are illustrated in Fig. 7. Calculation of bond shear stress between the FRP and concrete is very important in order to check the debonding failure mode. This can be done by calculating the change of the force in the FRP (Fig. 8). That is, the shear stress along

θ = φdx y = θdx

εc,top εc,bot

τb =

Mn

stage3

My

φ

Δεc,bot Ef Af

bf Δx

EIn

Fig. 7. Steps for analytical calculation of FRP reinforced beam. stage2

Mcr

EIy

stage1

b EIg

φcr

Curvature φy

T

T+ΔT

φn

Fig. 6. Moment–curvature diagram of cross section.

Fig. 8. Shear stress between FRP and concrete.

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

4.1.2. Interfacial stresses at plate end In order to predict the plate end shear failure (see Fig. 1), the interfacial stresses at the plate end must be calculated. Eq. (6) is not valid at the plate end because of different boundary conditions at the free edges of the plate, that cause interfacial normal and shear stress concentrations at the end of the plate. The interfacial stresses at the plate end have been calculated by various people such as Roberts and HajiKazemi [3], Taljsten [24], Malek et al. [25] and Smith and Teng [26]. A combination of shear and normal stresses at the plate end may lead to premature failure of the strengthened beam by debonding of the plate from the concrete surface. An appropriate failure criterion for concrete must therefore be introduced to determine the failure load. To this end, the Kupfer–Gerstle or Mohr–Coulomb failure criterion can be used. According to the Kupfer–Gerstle model, the strength of concrete under a tension–tension combination of stresses is approximated by [7]: r2 ¼ ftu ¼ 0:295ðfcu Þ2=3 ;

ð7Þ

where r2 is the maximum principal stress. The Mohr–Coulomb relation between s and r can be expressed as [27]: s2 ¼ Qfc fctm  Qðfc  fctm Þry  Qr2y ;

ð8Þ

c fctm where Q ¼ ðf fþf . Þ2 c

ctm

Using Eqs. (7) and (8) debonding failure mode is controlled as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r  r 2 rx þ ry x y 2=3 þ r2 ¼ þ s2 6 ftu ¼ 0:295ðfcu Þ 2 2 ! no debonding; s2  Qfc fctm þ Qðfc  fctm Þry þ Qr2y 6 0 ! no debonding:

4.2. Nonlinear finite element analysis (FEA) Nonlinear finite element analysis using the commercial finite element package ATENA [28] has been used to predict the behaviour of the externally bonded FRP reinforced RC beams described in Section 3. 4.2.1. FE model 1 (FEM1) The nonlinear behaviour of the strengthened beams was examined by FEA using a smeared crack model for the concrete and a bond slip model for the FRP-concrete interface. The internal reinforcement and FRP plate were modelled with bar reinforcement elements. For the FRP, this assumption was deemed sufficiently accurate since the FRP plate externally strengthens the bottom face of the beam in the tensile direction. The SBeta material property of ATENA [28] was used for the quadrilateral concrete elements and includes 20 material parameters. SBeta is a special material property for concrete, covering all nonlinear properties including its softening behaviour. The complete equivalent uniaxial

stress–strain diagram and biaxial stress failure criterion according to Kupfer et al. were used. From the cube strength of concrete fcu the compressive strength, tensile strength, elastic modulus and fracture energy were determined by the program using formulas from the CEB-FIP Model Code 90 and VOS 1983 [28]. In order to model the debonding phenomenon accurately, an appropriate bond model for the interface between the FRP plate and concrete must be incorporated. The behaviour of the FRP-concrete interface was defined according to the bond-slip relationship given by Ulaga et al. [29]. This behaviour is represented by a bilinear relationship as shown in Fig. 9, where the variables are calculated as follows: 4f ctm ; 3 Ga S f0 ¼ sf0 ; ta S f1 ¼ S f0 þ 0:225: sf0 ¼

ð9Þ

Steel reinforcement was assumed to behave in an elastic– plastic manner with strain hardening effects, while the FRP reinforcement was assumed to behave linear-elastically with brittle fracture in tension. 4.2.2. FE model 2 (FEM2) A nonlinear FE model 2 was created in an attempt to predict the complicated stress states in the anchorage zone between the FRP plate and the concrete beam. In this model, the FRP plate and the adhesive layer were modelled by 2D quadrilateral elements to achieve more accurate results. The FRP plate was modelled by elastic plane stress elements and the adhesive layer was modelled using the SBeta nonlinear material property described above. A Young’s modulus of 12,800 MPa was taken for the adhesive and its Poisson’s ratio was 0.3. The tensile and compressive strength of the adhesive were taken as 30 and 90 MPa respectively [30]. 4.3. Codes, guidelines and other references 4.3.1. Plate end debonding To prevent plate end debonding at the last crack (see Fig. 1), the anchorage force existing at the last crack should be checked with a design limitation. Numerous codes, guidelines and other references that present this type of design limitation are summarised in Table 2. For

Bond shear stress

830

τf0

S

S

Slip (mm)

Fig. 9. Bond slip relationship for FRP–concrete interface.

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

831

Table 2 Design limitations to prevent plate end debonding Codes and guidelines

Debonding criteria

ACI440 [13]

(1) Vend 6 0.67Vc (2) The plate should extend a distance d past the point corresponding to the Mcr rffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2bcf E f tf T f;max ¼ 0:64ak c k b bf Ef tf fctm ; lb;max ¼ 2f ; k b ¼ 1:06 bf P 1

fib1 [14]

fib2 [14] ISIS [15] SIA166 [17] TR55 [18]

1þ400

ctm

where bf/bc P 0.33, generally kc = 1 but for FRP bonded to concrete face with low compaction kc = 0.67. Approximately a = 0.9 but for beams with sufficient internal and external shear reinforcement a = 1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffi Ef fc fctm f tf ffi ; lb;max ¼ 1:44 pEffiffiffiffiffiffiffiffi T f;max ¼ 0:23bf tf tf fc fctm pffiffiffiffi bf tf lf ¼ ffu sbu bc ; sbu ¼ 0:307 fc qffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4f ctH Ef t f T f;max ¼ bf  2GFb Ef tf ; lb P lb;max ¼ p2 2GFb ; GFb ¼ fctH 8 ; sf0 ¼ 3 s2f0 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T f;max ¼ 0:5k b bf Ef tf fctm ; lb;max ¼ 0:7 ðEf tf =fctm Þ

Ref. [19]

V end 6 1:4V c ; V c ¼ ½1:4  ðd=2000Þbc d½qs fc 1=3 ; qs ¼ bAc sd ; rffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi Efffiffiffiffi tf ffi T f;max ¼ 0:3bp bL fcu bf lb;max ; lb;max ¼ 2: p fcu ( rffiffiffiffiffiffiffi b 1 lbP lb;max 2bcf  bp ¼ b ; bL ¼ b lb < lb;max sin 2lpl 1þbcf b;max

Ref. [20]

The anchorage length lA (see Table 3) satisfies the end anchorage qffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T f;max ¼ 0:5bf k b Ef tf fctm ; lb;max ¼ 2fEf tf ; 1:0 6 k b 6 1:3

Ref. [31]

M end Mu

6 0:67; 1:4  ðd=2000Þ P 1:1

ctm

comparison purposes, the safety factors have generally been excluded and a uniform system of notation has been adopted. All references include Ef, tf, bf and fctm. fib1 [14] proposes the most expanded equation for Tf,max which includes various parameters such as FRP properties, concrete tensile strength, concrete surface condition, internal shear reinforcement and geometry. It is worth noting that the ACI code and Ref. [19] limit the shear load at the plate end. ISIS defines a different type of anchorage length with a uniform bond strength along this anchorage length and the assumption is that midspan debonding can be avoided by using this anchorage length.

4.3.2. Midspan debonding In order to prevent midspan debonding of the plate, the codes and guidelines give two different approaches. Generally, a design limitation is placed on the bond shear stress or the FRP tensile strain (or stress). Design limitations for numerous codes and guidelines as well as other references are given in Table 3. fib [14] gives two different approaches based on the calculation of the maximum possible increase in tensile FRP stress that can lead to the calculation of a maximum interfacial bond stress. A general diagram of the maximum possible increase in FRP tensile stress is shown in Fig. 10 (approach 2 of fib). The strain (stress) limitations of fib2, JSCE and Ref. [19] depend on

Table 3 Design limitations to prevent midspan debonding Codes and guidelines ACI440 [13] strain limitation

Debonding criteria ( ef 6 jm efu ; jm ¼

fib1 [14] strain limitation fib2 [14] shear stress limitation





nEf tf 1 60efu 1  360000 6 0:9 for nEf tf 6 180; 000 90;000 1 60efu ð nEf tf Þ 6 0:9 for nE f t f > 180; 000

The FRP strain limitation has a range from 0.65% to 0.85% rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi S cr 0:053Ef fc fctm ðBÞ ðBÞ ðBÞ ðBÞ 0:185Ef rf ¼ S cr  0:285 fc fctm 4tf ; max Drf ¼ þ ðrf Þ2  rf tf "rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # ffi p ffiffiffiffiffiffiffiffiffiffi ðAÞ ðBÞ 0:053Ef fck fctm ðmax Drf max Drf Þ ð1Þ ðAÞ ð2Þ 1 2 max Drf ¼ max Drf  rf ; max Drf ¼ c þ rf  rf ðBÞ tf ð3Þ

rf

c

max Drf ¼ ffu  rf (see Fig. 10) fib3 [14] shear stress limitation

f 6 1:8f ctk sb ¼ bDT f Dx

ISIS [15]

Debonding qffiffiffiffiffiffiffiffiffi can be avoided by using sufficient anchorage of Table 2 N rf 6 2GnfftEf f ; Gf  0:5 mm pffiffiffiffi ef 6 0:8%; sb 6 2:5scd ; scd ¼ 0:3 fc (Ref. [32]) 2 sb 6 0.8 N/mm ef 6 0.8% rffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi Ef fcu rdb ¼ 0:38bp bL tf f ef 6 0:65%; sb;avr ¼ 1:6 MPa; lA ¼ bf sTb;avr V sb;B ¼ bc zm 6 sB;DB (see Table 9)

JSCE [16] stress limitation SIA166 [17] strain limitation shear stress limitation TR55 [18] strain limitation shear stress limitation Ref. [19] stress limitation Ref. [20] strain limitation Ref. [31] shear stress limitation

832

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

only for the plate end calculations and other FE results are obtained from FEM1. (3)

max Δ f

5.1. Deflections, strains and failure loads (A)

(B)

(1)

(2) (C)

σf Fig. 10. Diagram of the maximum possible increase in FRP tensile stress (see Table 3, fib2 approach for the definition of numbers and letters).

the stiffness of the FRP (Eftf) and on the concrete properties but ACI uses Eftf and the rupture strain of the FRP (efu). Others recommend a constant value for it. Furthermore, the bond shear stress limitation of fib3 and SIA is related to the tensile and shear strength of the concrete, respectively. Ref. [20] recommends that for the maximum existing plate force, Tf, midspan and plate end debonding can be prevented by ensuring a certain anchorage length, lA (see Table 3). 5. Comparison of experiments, calculations and guidelines Comparisons between experiments, calculations and guidelines are useful to determine the credibility of the design models. In this section, results from FEM2 are used

Using a cross-section analysis (Section 4.1.1) and FEA, the load–deflection behaviour of the experimental beams presented in Section 3 were calculated. All specimens failed after yielding of the steel reinforcement. The load–deflection, top strain and bottom strain relationships of the beams are shown in Figs. 11 and 12. The Figures show a good agreement between the test results, cross-section analysis and FEA. It can be seen in the Figures that under increasing load, a strengthened beam (B2–4) passes from the uncracked state to the cracked state, which is generally followed by yielding of the internal steel reinforcement before failure occurs. By using the proposed analytical cross-section solution, only two main failure modes, concrete crushing or FRP rupture, can be predicted. The analytical calculations were continued up to concrete crushing or FRP rupture failure modes; therefore it is observed that the cross-section analysis for beam B4 gives a much larger deflection than the experiments and the FEA. It should also be noted that experimental strains were not measured up to failure. From cross-section analysis, the top and bottom strains along beams B3 and B4 are shown in Fig. 13 at maximum load. The slope of the strain line increases at the points of concrete cracking and steel yielding. Fig. 13 shows that the strain is constant between point loads indicating a constant bending moment along this length.

40

40

B1

B2

32

Load F (kN)

Load F (kN)

32 24 16

24 16 8

8

0

0 0

10

20

30

40

50

0

60

10

40

30

40

50

60

40

B3

B4

32

Load F (kN)

32

Load F (kN)

20

Deflection at midspan (mm)

Deflection at midspan (mm)

24 16 8

24 16

CSA Exp FEM1

8

0 0

10

20

30

40

Deflection at midspan (mm)

50

60

0 0

10

20

30

40

Deflection at midspan (mm)

Fig. 11. Load–deflection diagrams of the beams.

50

60

40 36 32 28 24 20 16 12 8 4 0 -0.3

B1 Load F (kN)

Load F (kN)

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

40 36 32 28 24 20 16 12 8 4 0 -0.3

B2

0

0.3

0.6

B3

0

0.3

0.6

0.9

1.2

1.5

1.8

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

Strain at midspan (%)

Load F (kN)

Load F (kN)

Strain at midspan (%) 40 36 32 28 24 20 16 12 8 4 0 -0.3

833

2.1

2.4

2.7

3

40 36 32 28 24 20 16 12 8 4 0 -0.3

B4 D1(Exp) D2(Exp) D1(CSA) D2(CSA) D1(FEA1) D2(FEA1)

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

Strain at midspan (%)

Strain at midspan (%)

Fig. 12. Top strain (D1) and bottom strain (D2) at midspan (see Fig. 2).

1

1

top strain

B3

0.8

bottom strain

0.6

Top and bottom strain (%)

Top and bottom strain (%)

top strain

steel yielding

0.4 0.2 0 0

500

1000

1500

-0.2

2000

B4

0.8

bottom strain

0.6

steel yielding

0.4 0.2 0 0

500

1000

1500

-0.2

crack onset

2000

crack onset

-0.4

-0.4

Beam length (mm)

Beam length (mm)

Fig. 13. Distribution of top and bottom strain along B3 and B4 for maximum load.

40

Load F (kN)

Load F (kN)

B2

32 24

steel yielding

16 8 0

40

B3

32

Load F (kN)

40

24 16

steel yielding

crack onset 1 2

3

4

5

Maximum shear stress (Mpa)

6

24 16 steel yielding 8

8 0

B4

32

crack onset

0 0

1

0 2

3

4

5

Maximum shear stress (MPa)

6

0

crack onset 1 2

3

4

5

6

Maximum shear stress (MPa)

Fig. 14. Maximum shear stress between FRP and concrete using cross-section analysis and Eq. (6).

5.2. Bond shear stress Load versus maximum shear stress values were calculated for beams B2–4 using Eq. (6) and are shown in Fig. 14. It can be seen that there are two large increases

in the maximum shear stress; the first occurs due to concrete cracking while the second occurs at the onset of steel yielding. A summary of the FE analysis as well as the cross-section analysis is shown in Table 4. It is worth noting that

834

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

Table 4 Results from FEA compared to analytical analysis (DB: debonding, FR: FRP rupture, CC: concrete crushing) Beam

B1 B2 B3 B4

Failure load (kN)

Failure mode

FRP strain at failure (%)

Shear stress at failure load (MPa)

Exp.

CSA

FEA

Exp.

CSA

FEA

FEA

CSA

FEA

15.6 30 31.4 29.2

14.3 27.8 36.9 38.1

17.5 29.0 27.3 25.8

CC FR DB DB

CC FR FR CC

CC FR DB DB

– 0.43 0.53 0.63

– 3.96 4.74 4.16

– 4.1 4.2 4.5

Shear stress (Mpa)

6 Fmax =27 kN

Analytical

4

B3

FEA

2 0 -2

0

500

1000

1500

2000

-4 -6

Beam length (mm)

Shear stress (Mpa)

6 Analytical

4

Fmax =25.5 kN

B4

FEA1

2 0 -2

0

500

1000

1500

2000

-4 -6

Beam length (mm) Fig. 15. Shear stress distribution along B3 and B4 at maximum load.

the predicted failure modes using the FEA are the same as those seen during the experiments. The bond shear stress distribution along B3 and B4 from the cross-section analysis (Eq. (6)) and FEA are shown in Fig. 15 at maximum load. The bond shear stress is seen to increase where a change in the section properties occurs, at locations of concrete cracking and steel yielding. At the location along the beam where the steel reinforcement yields, the bond shear stress increases dramatically, because the steel reinforcement no longer contributes to the flexural stiffness of the section and any increase in bending moment must be carried by the FRP plate. Fig. 15 shows that the first shear stress peak along beam B3 occurs at about 200 mm. Up to this point the cross section is uncracked and at approximately 500 mm the reinforcement steel yields and there is the second shear stress increase. In Fig. 15 results from the cross-section analysis show the mean global value of the bond shear stress along the beams. There is a difference in the FEA results as compared with the cross-section analysis, because of shear stress concentrations at the cracks caused by local effects. Generally, bond stresses are required for a moment gradient (equilibrium bond) or strain compatibility (compatibility bond) between two cracks [11,12]. In Fig. 15 at midspan where the bending moment is constant, the bond stresses are exclusively induced by tension stiffening, i.e. for strain compatibility, and are not needed for equilibrium [31].

5.3. Plate end For the behaviour of the beams at the FRP plate end, the results from the two different finite element models are compared with the results from closed-form solution proposed by Smith and Teng [26] in Fig. 16. For FEM2, nonlinear and linear material properties were used for the concrete and adhesive. Comparison of the results reveals that the shear and normal stresses in the vicinity of the plate end are generally similar except for FEM1. Furthermore, FEM1 is not capable of calculating the normal stresses because of using one dimensional bar elements for the CFRP reinforcement. Closed-form and finite element solutions do not fulfil the boundary condition of zero shear stress at the plate end (Fig. 16); however FEM2 could fulfil this boundary condition if a much finer mesh was chosen at the plate end. Using results from nonlinear FEM2 and the two failure criteria presented in Section 4.1.2, the probability of plate end shear failure for beams B2–4 is summarized in Table 5. This table shows that the tested beams do not fail in plate end shear failure. This fact can not be compared with the experiments, because the type of debonding failure mode (midspan or plate end) was not determined. Table 5 shows also that the normal and shear stresses are dependent on the FRP type and have different values for the beams.

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841 1.4

Shear stress (MPa)

Closed-form solution[26] FEA2(nonlinear) FEA2(linear) FEA1

B4

1.2

T f;a ¼ T f;max

1

0.6 0.4 0.2 0 10

20

30

40

Distance from plate end (mm) 0.60 Closed-form solution[26]

B4

Normal stress (MPa)

0.50

FEA2(nonlinear) FEA2(linear)

0.40



lb;max

2

lb



lb;max

ð10Þ

:

The calculations of maximum anchorage force according to fib1 and SIA are shown in 6a and 6b, where Fmax is the experimental failure load. There is a sizeable discrepancy between the predicted values for Tf,max. The reason is that SIA does not include the geometry factor (kb). Comparing the existing tensile FRP force, Texist, with Tf,a, it is observed that this failure mode is not critical for all beams except B2 according to SIA. Similar equations to determine the maximum anchorage force and length of the FRP plates can be found in codes, guidelines and references. The values of design limitations for the anchorage force and length are shown in Table 7 for B4. In Table 7 the maximum anchorage force varies from 11.5 to 32.6 kN, Ref. [19] being the most conservative.

0.8

0

lb

835

0.30

5.5. Midspan debonding

0.20 0.10 0.00 -0.10

0

10

20

30

40

-0.20

Distance from plate end (mm) Fig. 16. Comparison of interfacial shear and normal stresses at plate end for beam B4 (F = 25.5 kN).

5.4. Anchorage force at last crack The second type of plate end debonding, anchorage failure at last crack (failure mode 2 in Fig. 1), can be verified by calculation of the anchorage force. According to fib [14] and SIA [17], the maximum FRP force which can be anchored is calculated considering the available bond length, lb, which is the length of the plate glued on the uncracked part of beam (i.e. the uncracked length of beam minus the unplated length). If lb is smaller than lb,max given by the guidelines, then the maximum force must be reduced using e.g. Eq. (10) [14]:

Design limitation values for midspan debonding are shown in Table 8. There is a large discrepancy between the JSCE code and Ref. [19] with other guidelines. Comparing this table with the numerical results presented in Table 4, it is noted that ACI440 proposes more accurate limitation values. Furthermore, the maximum bond shear stress measured by other references varies from 0.9 to 5 MPa [9,33,34]. So it could be concluded that the bond shear stress limitations proposed by fib3 and SIA are on the unsafe side and TR55 is very conservative. Existing studies show that the maximum transferable load from FRP to concrete depends strongly on the strength of concrete. Therefore it seems that FRP strain limitations given by codes and guidelines are not sufficient to predict the midspan debonding. Midspan debonding occurs when the interfacial shear or normal stresses cannot be sustained by the concrete even if the existing FRP strain is lower than the design strain limitations, as in beam B3 in which the FRP strain at debonding was 0.74%. Neubauer and Rostasy [31] proposed a detailed method for the estimation of debonding failure. This method is

Table 5 Plate end debonding control considering combination of normal and shear stresses, from FEM2 Beam

F (kN)

smax (MPa)

ry,max (MPa)

rx,max (MPa)

Kupfer–Gerstle equation (7)

Mohr–Coulomb equation (8)

B2 B3 B4

30 32 29

1.55 1.3 1.01

0.78 0.71 0.56

1.81 1.84 1.63

No debonding No debonding No debonding

No debonding No debonding No debonding

Table 6a Calculation of end anchorage according to fib Beam

Mcr (kN m)

Fmax (kN)

lb (mm)

Ef (MPa)

lb,max (mm)

Tf,max (kN)

Tf,a (kN)

Texist (kN)

B2 B3 B4

2.997 2.976 3.106

30 31.4 29.2

50 45 56

305,000 214,000 155,000

239 200 167

44.8 37.5 32.6

16.8 14.9 18.3

12.5 10.5 9.2

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M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

Table 6b Calculation of end anchorage according to SIA Beam

Mcr (kN m)

Fmax (kN)

lb (mm)

Ef (MPa)

lb,max (mm)

Tf,max (kN)

Tf,a (kN)

Texist (kN)

B2 B3 B4

2.997 2.976 3.106

30 31.4 29.2

50 45 56

305,000 214,000 155,000

199 167 139

27.1 22.7 19.7

11.9 10.6 12.8

12.5 10.5 9.2

Table 7 Design limitations for anchorage failure of beam B4 Limitations

ACI440

fib1

fib2

ISIS

SIA166

TR55

Ref. [19]

Ref. [31]

Maximum anchorage force (kN) Maximum anchorage length (mm)

– –

32.6 167

17.3 178

– –

19.7 139

25.4 165

11.5 331

25.6 167

Table 8 Design limitations for midspan debonding Beam

Limits

ACI440

fib2

fib3

JSCE

SIA166

TR55

Ref. [19]

Ref. [20]

B2

FRP strain (%) Shear stress (MPa) FRP strain (%) Shear stress (MPa) FRP strain (%) Shear stress (MPa)

0.41 – 0.58 – 0.8 –

– 0.0–3.2 – 0.0–2.6 – 0.0–2.3

– 5.8 – 5.8 – 5.9

0.17 – 0.20 – 0.23 –

0.8 4.8 0.8 4.8 0.8 5.0

0.8 0.8 0.8 0.8 0.8 0.8

0.20 – 0.24 – 0.29 –

0.65 – 0.65 – 0.65 –

B3 B4

based on the calculation of the maximum possible increase in tensile FRP stress between two cracks (concrete tooth, Fig. 17) in which the differential equations at a concrete tooth are solved. The probability of debonding between two cracks is then estimated by comparing the existing shear stress at the bottom line of the concrete tooth (sB) with the shear stress at the initiation of debonding (sB,DB). In this approach, the existing shear stress is expressed by Eq. (11). In order to simplify the solution in this example,

Scr

1 A

2

3

4

5

B

aQ

Fig. 17. Crack pattern of strengthened beam as recommended by Neubauer [31].

Table 9 Summary of Neubauer and Rostasy method for beam B4 at failure load of 26.7 kN  Crack aQ (mm) D ¼ bc aQ þ z2m Scr,max KF,y sB,y (MPa) KF,el

Scr,max,y (mm)

sB,DB (MPa)

sB (MPa)

1 2 3 4 5

79 62 50 36

1.609 1.125 0.882 0.819

0.883 0.883 0.883 0.0

116 266 416 566 667

44,203 81,703 119,203 156,703 181,875

0.848 0.459 0.315 0.239

46 35 29 26

3.13 1.69 1.02 0.50

1.221 0.837 0.637 0.549

Table 10 Predicted midspan debonding load (kN) using cross-section analysis and the limitations according to the guidelines without using safety factors compared to maximum loads achieved in experiments Beam

ACI440 FRP strain

fib2 bond stress

fib3 bond stress

JSCE FRP strain

SIA166 bond stress

SIA166 FRP strain

TR55 FRP strain

TR55 bond stress

Ref. [19] FRP strain

Ref. [20] FRP strain

Ref. [31] bond stress

Exp.

B2 B3 B4

27.1 27.2 27.8

13.1 13.1 13.4

FR (27.8) CC (36.9) CC (38.1)

14.4 14.1 14.2

FR (27.8) 34.1 35.7

FR (27.8) 33.2 27.6

FR (27.8) 33.2 27.6

8.9 10.5 12.4

16.2 16.2 16.8

FR (27.8) 29.1 24.6

33.9 29.8 26.7

30 31.4 29.2

CC: debonding will not occur before concrete crushing. FR: debonding will not occur before FRP rupture.

Table 11 Predicted loads (kN) of the beams calculated using cross-section analysis (chapter 4.1.1) and finite element analysis (chapter 4.2.1) versus experimental results (DB: debonding, FR: FRP rupture, CC: Concrete crushing) Beam

– – – – 8 8 8 8 8 8 8 8 8 8 8 9 9 33 33 1 1 1 1 34 34 34

No. of layers

tf

1 1 1 1 1 1 2 2 3 3 2 2 1 1 1 6 6 6 2 1 2 1 2 2 3 4

1.2 1.2 1.2 1.2 0.16 0.16 0.32 0.32 0.48 0.48 0.32 0.32 0.16 0.16 1.2 1.2 1.2 0.78 0.26 1.0 2.0 1.0 2.0 0.22 0.33 0.44

bf

50 50 50 50 51 51 51 51 51 51 76 76 102 102 51 150 150 100 100 300 300 150 150 115 115 115

Analytical loads (kN)

New recommendation

FEA

Exp.

Concrete crack

Steel yield

Concrete crush

FRP rupture

ACI

Error (%)

SIA

Error (%)

Shear stress limit (MPa)

Strain limit (–)

Failure load (kN)

Error (%)

Failure load (kN)

Error (%)

Failure load (kN)

4.4 4.5 4.5 4.7 1.9 2.2 1.9 2.2 2.5 2.6 2.3 2.6 2.3 2.6 2.2 3.8 3.8 9.2 8.3 9.9 11.5 9.5 9.8 2.9 2.9 2.9

12.0 23.7 20.2 17.9 8.6 15.6 9.9 16.9 16.9 18.2 11.2 18.2 10.0 16.9 16.7 28.1 28.1 65.4 53.2 – – 90.7 127.0 30.7 33.8 37.0

14.3 – – 38.1 15.8 21.9 20.1 26.2 27.8 31.4 25.3 31.4 21.9 27.8 32.5 46.6 46.6 104.5 73.2 140.8 176.7 128.8 158.2 32.6 35.2 37.3

– 27.8 36.9 – – – – – – – – – – – – – – – – – – – – – – –

– – 27.2 27.8 14.8 CC CC CC 25.6 CC CC CC 21.8 CC 28 CC CC 98 CC CC 154 120.5 112 CC CC CC

– – 13.4 4.8 +5.7 N.A. N.A. N.A. +31.3 N.A. N.A. N.A. +23.9 N.A. +60.9 N.A. N.A. +38.6 N.A. N.A. +94.9 +56.5 14.5 N.A. N.A. N.A.

– – 33.2 27.6 11.7 18.7 15.9 22.8 20.1 27.1 20.1 27 16 23.1 27.6 45.2 45.2 92 63 CC CC CC CC CC CC CC

8 7 +5.7 5.5 16.4 7.0 +1.3 +2.2 +3.1 +12.9 +9.2 +2.7 9.1 5.7 +58.6 +28.0 +29.9 +30.1 14.6 N.A. N.A. N.A. N.A. N.A. N.A. N.A.

– – 3.21 3.34 3.24 3.24 3.24 3.24 3.79 3.79 3.79 3.79 3.79 3.79 3.52 3.00 3.00 3.81 3.52 2.70 2.70 2.70 2.70 2.96 2.96 2.96

– – 0.0080 0.0080 0.0080 0.0049 0.0076 0.0035 0.0066 0.0030 0.0080 0.0078 0.0080 0.0080 0.0035 0.0080 0.0080 0.0079 0.0080 0.0045 0.0023 0.0059 0.0037 0.0080 0.0080 0.0080

– – 22.6 23.9 11.7 16.9 15.4 17.9 17.9 18.9 20.1 26.9 16 23.1 16.2 45.2 45.2 91.8 63 126 110.4 101 126.1 CC CC CC

– – 28.0 18.2 16.4 15.9 1.9 19.7 8.2 21.3 +9.2 +2.3 9.1 5.7 6.9 +28.0 +29.9 +29.8 14.6 +60.5 +39.7 +31.2 3.7 N.A. N.A. N.A.

17.5 (CC) 29.0 (FR) 27.3 (DB) 25.8 (DB) 15 (DB) 21 (DB) 18 (DB) 23 (DB) 19 (DB) 26 (DB) 25 (DB) 31 (DB) 23 (DB) 29 (DB) 23 (DB) 44 (DB) 45 (DB) 90 (DB) 68 (DB) 118 (DB) 94 (DB) 110 (DB) 114 (DB) 35 (DB) 37 (DB) 39 (DB)

+12 3 13 11 +7 +4 +15 +3 3 +8 +36 +18 +31 +18 +32 +25 +29 +27 8 +50 +19 +43 13 19 10 1

15.6 (CC) 30.0 (FR) 31.4 (DB) 29.2 (DB) 14.0 (DB) 20.1 (DB) 15.7 (DB) 22.3 (DB) 19.5 (DB) 24.0 (DB) 18.4 (DB) 26.3 (DB) 17.6 (DB) 24.5 (DB) 17.4 (DB) 35.3 (DB) 34.8 (DB) 70.7 (DB) 73.8 (DB) 78.5 (DB) 79.0 (DB) 77.0 (DB) 131 (DB) 43.0 (DB) 41.0 (DB) 39.5 (DB)

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

B1 B2 B3 B4 A1-1 A1-2 A2-1 A2-2 A3-1 A3-2 A4-1 A4-2 A5-1 A5-2 A6-1 A6 B6 E1a S1a SM4 SM6 MM2 MM5 3 4 5

Ref.

837

838

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

the crack spacing Scr is assumed constant and equal to the stirrup spacing (150 mm). VB : bc z m

ð11Þ

It is important to note that this shear stress is calculated by assuming the width of the FRP plate equal to the concrete width, so that an equivalent thickness of the plate is considered in the calculation. A summary of calculations for beam B4 using the Neubauer and Rostasy method is shown in Table 9 in which KF is the ratio DTf/Tf between two cracks and sB,y is the shear stress at the beginning of steel yielding. Scr,max is the maximum crack spacing that corresponds to KF. For Scr > Scr,max, stable debonding starting at the second crack (B) of the concrete tooth is possible. In this case after initiation of debonding, the plate force at crack B still can be increased along with the stable growth of the bond crack from B towards A. For Scr 6 Scr,max, unstable debonding starts instantaneously at the initiation of debonding since no potential for stable debonding exists. The calculations show that stable debonding initiates from somewhere between crack 3 and 4 at failure load of 26.7 kN (Fig. 17). In Table 9, the following equations were used: 8 < K F;el KK f;A1 for sA 6 K Df;A fy ; S cr bc f;A A K F;el ¼ ; K F;y ¼ K f;A fy : S cr bc DA for sA > DA ; DA fy =sA sffiffiffiffiffiffiffiffiffiffiffi ar coshðK F þ 1Þ 8f ctm E f A f zf ; x¼ : S cr;max ¼ ; Kf ¼ 1 þ x Ef tf E s As z s ð12Þ

Table 10 shows the comparison between midspan debonding failure loads according to different codes and guidelines and other references. The strain and shear stress limitations given in Table 8 are used in combination with cross-section analysis to predict these failure loads. A discrepancy of up to 250% can be found between predicted debonding failure loads using the different approaches. Furthermore, for comparison the experimentally derived failure loads are given in Table 10, although the types of debonding (midspan or plate end) were not determined during the tests. Neubauer and Rostasy’s approach agrees best with the experimental results. Also, it can be seen that the strain limitation of the ACI and TR55 codes provide appropriate values for the debonding load, while the JSCE, fib2 and Ref. [19] propose very conservative values. The predicted failure loads according to the shear stress limitation of SIA166 and fib3 are on the unsafe side. 5.7. Comparison with tests from the literature Selected experimental results for debonding failure of FRP-flexural-strengthening tests carried out by other authors are summarized in Table 11 [1,8,9,33,34]. Results are taken from test specimens with different configurations in geometry, materials and FRP layers. For comparison, the failure loads from the cross-section analysis, FEA and experiments are shown in the table. Although the

Brena-Macri2004 Rahimi-Hutchinson2001 Pham-Al Mahaidi2004 Arduini-Nanni1997 Maalej-Bian2001 FEA

17 16 15 14 13 12 11

9 TR55, SIA

8 7

Ref[20]

6 5 4 3 2 1

Specimen Names

Fig. 18. Maximum measured FRP strain at failure.

5

4

3

MM5

MM4

MM3

MM2

SM6

SM3

E1a

SM2

A7

S1a

B6

A6-1

A5-2

A5-1

A4-2

A4-1

A3-2

A3-1

A2-2

A2-1

A1-2

0 A1-1

Strain(‰)

10

A6

sB ¼

5.6. Comparison of failure loads calculated using different limitations

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

FEA results are in a good agreement with experiments for some specimens; the predictions are higher for others for the following reasons:  Uncertainty of material properties such as fctm, Ec, Ga, ta in the references.  Effects of number of FRP layers and FRP width on the failure load that can not be considered in FEA model. The measured and calculated maximum FRP strains of the specimens are given in Fig. 18, which shows that the maximum design value for FRP strain can not be a constant value and depends on the material characteristics of the FRP and concrete such as Ef, tf, bf, fct, beam geometry and loading configuration. In Table 11 the strain limitations of ACI and SIA are used in combination with cross-section analysis to predict analytical failure loads. The assumption is that all beams have no anchorage failure. It is observed that SIA strain limitation (0.008) has better agreement with experiments. However it is not applicable for some specimens. The reason may be due to the fact that the strain limitation is not accurate when the failure mode is debonding due to high shear stresses. The 0.008 strain limitation is more accurate when the failure is debonding at flexural cracks. So the 0.008 strain limitation should be combined with a suitable shear stress limitation to give a better correlation. The calculations showed that the tensile strength of concrete (fct) is a convenient shear stress limitation. The predicted failure loads according to this combined recommended criterion are shown in Table 11. Bold numbers show which strain limitation (0.008) or shear stress limitation (fct) governs for the predicted failure load. The discrepancy between predicted failure load and test results varies between 28% and +60% which is due to uncertain material properties and model simplifications. However for design purposes these discrepancies can be covered by reasonable safety factors. 6. Summary and conclusions Nonlinear analyses of flexurally strengthened RC beams have been carried out and compared to experimental results. Calculation (analytical and FE) of different types of debonding failure modes have been reviewed and compared with experimental results. In order to prevent midspan debonding of the FRP plate, a limitation can be placed on the bond shear stress or the FRP strain. Large discrepancies in these limitations were seen in existing codes and guidelines. From analytical and FE calculations and experiments it seems that FRP strain limitations given by codes and guidelines are not sufficient to predict the midspan debonding which occurs in high shear stress zones even if the existing FRP strain is lower than the design strain limitations. So a combined strain and shear stress limitation is recommended.

839

The following conclusions can be drawn from the work that has been presented here: 1. The values of the limiting bond shear stress of SIA166 and fib3, which are related to the tensile and shear strength of the concrete, were on the unsafe side for the test beams considered. On the other hand, the values given by TR55 and fib2 were too conservative. 2. The strain (stress) limitation of fib2, JSCE and Ref. [19] depends on the stiffness of the FRP (Eftf) and concrete properties but ACI uses Eftf and the ultimate strain of the FRP (efu). Others recommend a constant value for it. 3. A combined strain and shear stress limitation is recommended although it has not been completely developed yet. At this state, the use of a strain limitation of 0.008 and a shear stress limitation of sb = fct is recommended. 4. Plate end debonding can be avoided by limiting the FRP force at the last crack. However, formulations in existing codes, guidelines and references resulted in a large range of the maximum FRP anchorage force. All references include Ef, tf, bf and fctm in the formula. fib1 proposes the most expanded equation for Tf,max which includes various parameters such as FRP properties, concrete tensile strength, surface condition of concrete, internal shear reinforcement and geometry. For this failure mode TR55 is recommended. 5. A combination of shear and normal stresses at the cutoff point of the plate may lead to premature failure of the strengthened beam by plate end shear failure or concrete cover delamination. An appropriate failure criterion must therefore be introduced into the codes and guidelines in order to include this failure mode. This failure mode was not critical for the investigated test beams B2–B4. 6. A discrepancy of up to 250% was found between predicted debonding failure loads using various codes and guidelines. 7. A complete bond model proposed by Neubauer and Rostasy that can check debonding at all the vulnerable locations along the strengthened beam was seen to have the best agreement with the experimental results of B2– B4. However, the method is very complex and perhaps not feasible in practice.

7. Summary of new recommendation To avoid debonding, the following limitations in combination with cross-section analysis are recommended: 1. Plate end debonding can be avoided by limiting the FRP force at the last crack. All formulations for this force in references include Ef, tf, bf and fctm. For this failure mode the formulation in TR55 is recommended (see Table 2).

840

M.R. Aram et al. / Composites: Part B 39 (2008) 826–841

2. In order to prevent debonding of the plate in zones with high shear loads, the use of shear stress limitation equal to the tensile strength of the concrete (fct) is recommended. 3. In order to prevent debonding at flexural cracks, a strain limitation of 0.008 is recommended.

Acknowledgements The research work presented in this paper is part of a collaborative Ph.D. thesis between the University of Tehran, Iran, and Empa, Switzerland. The authors wish to acknowledge the company Stesalit AG, commissioner of the laboratory tests. Appendix 1. Notation The Ef Ga Gf Mcr Mend Mu Sf0 Tf, max VB Vc Vend bc bf fctk fctH fctm fcu ffu fu fy Ic Ics If lb lb, n tf ta yc yf zm zf zs bp bL

max

following symbols are used in this paper: modulus of elasticity of FRP shear modulus of adhesive fracture energy of concrete cracking moment bending moment at plate end bending moment capacity of strengthened cross section ultimate slip where debonding occurs maximum FRP force which can be anchored shear force at crack B concrete shear strength shear force at plate end width of concrete cross section width of FRP plate characteristic value of concrete tensile strength surface tensile strength of concrete mean value of concrete tensile strength cube concrete strength tensile strength of FRP ultimate tensile strength of reinforcement yielding stress of steel reinforcement moment of inertia of concrete cross section second moment of area of strengthened concrete equivalent cracked section moment of inertia of FRP cross section available bond length maximum anchorage length number of plate layers thickness of FRP plate thickness of adhesive distance from the bottom of concrete to its centroid distance from the top of FRP plate to its centroid average internal lever arm lever arm of plate lever arm of steel width coefficient bond length coefficient

e0c ef efu rdb rf rx, max ry, max maxDrf sb sbu sB,DB scd

ultimate concrete strain in compression FRP strain rupture strain of FRP ultimate plate stress FRP stress at the location of flexural crack maximum axial stress maximum normal stress maximum anchorable FRP tensile stress bond shear stress mean bond strength of the FRP to concrete shear stress at initiation of debonding design shear strength of concrete

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