Bending and time-dependent responses of RC beams strengthened with bonded carbon fiber composite laminates

Construction and Building Materials 29 (2012) 597–611

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Bending and time-dependent responses of RC beams strengthened with bonded carbon fiber composite laminates Habibur Rahman Sobuz a,⇑, Ehsan Ahmed a, Norsuzailina Mohamed Sutan a, Noor Md. Sadiqul Hasan b, Md. Alhaz Uddin c, Md. Jahir Uddin d a

Department of Civil Engineering, Faculty of Engineering, Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia School of Civil Engineering, Linton University College, Legenda Education Group, 71700 Mantin, Negeri Sembilan, Malaysia Department of Civil Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia d Department of Civil Engineering, Khulna University of Engineering and Technology (KUET), Khulna 9203, Bangladesh b c

a r t i c l e

i n f o

Article history: Received 18 August 2011 Received in revised form 4 November 2011 Accepted 16 November 2011 Available online 19 December 2011 Keywords: Time-dependent performance Flexural response RC beams Composites laminates Creep Tension stiffening

a b s t r a c t Externally bonded carbon fiber reinforced polymer (CFRP) sheet has shown excellent performance to repair, restore and increase the load-carrying capacity of RC structures. In this paper results of an experimental test are presented in which fourteen RC beams strengthened with CFRP epoxy bonded sheets in flexure and time-dependent tests are subjected to four-point bending and sustained load respectively. The test variables included different degrees of strengthening scheme and two types of sustained load for both uncracked and cracked beams. For flexural strengthening, the increase of ultimate strength provided by CFRP was assessed by varying the layers of laminates and incorporating end anchorage. In time-dependent test, deflection reduction coefficient in concrete tension stiffening model is proposed to evaluate the stiffness of the section after cracking for RC beams. It is found that the analytical values based on effective modulus method (EMM) are in general gives conservative estimates of the experimental results. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction One of the main driving forces for the development of external bonding of high-strength fiber reinforced polymer (FRP) composites is the potential of a viable alternative technique over the traditional steel plate in structural strengthening and upgrades of damaged or deteriorated members, without significantly altering the appearance of the member. Before the introduction of fiber reinforced polymer strengthening technologies, one popular technique for upgrading reinforced concrete beams was the use of external epoxy-bonded steel plates [1–3]. However, this method suffers deterioration problem caused by the corrosion of the steel. There is currently a wide range of techniques available to repair or strengthen structurally deficient and functionally obsolete structures. One such technique is adding FRP as external bonded reinforcement to the surface of concrete beams or slabs. Fiber reinforced polymer composites are thin laminates that are externally bonded to structural elements using an epoxy adhesive to increase their load-carrying capacity. FRP materials are lightweight, durable and non-corrosive and can be installed quickly, offering economically and structurally sound alternative in most applications. Comprehensive experimental studies conducted in the past ⇑ Corresponding author. E-mail address: [email protected] (H.R. Sobuz). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.11.006

have shown that this strengthening system has several advantages over the traditional ones. Carbon FRP laminate in strengthening reinforced concrete structures provides a more practical and cost-effective solution than traditional steel plates for improving structural performance [4,5]. Much published research has been carried out to investigate the flexural response of either steel plate or FRP sheet strengthened RC beams over the last few decades [6–11]. The use of CFRP laminates has shown considerable improvement in flexural performance, although premature de-bonding failure of plates was still a concern in some of numerous experimental studies to date [12–15]. Debonding problems in FRP bonded RC members are a priority for mechanics and design issues, due to their premature brittle nature. In the last two decades, there has been a concentration of research efforts into characterisation and modelling of de-bonding failures that lead to a significant progress in understanding the modes and mechanisms of premature de-bonding failures of FRP. End anchorage can prevent the premature failure of CFRP laminates from the concrete tension side. In fact, proper anchoring systems may help a CFRP pre-cured laminate develop higher stresses throughout its length, decreasing stress concentrations and increasing bond strength. Alam and Jumaat [16] tested on full-scale reinforced concrete beams strengthened with single layer CFRP laminates with U-shaped end anchorage. It was reported that the end anchorage eliminated premature end peeling and it had

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Nomenclature As A0s Af Ct d0 d df D Ect Epe e

fr l

total cross section area of tension steel total cross section area of compression steel area of FRP coefficient for creep at times t (days) compression effective depth effective depth of beam section (tension steel) effective depth of beam in FRP (tension FRP) overall depth of the section age-adjusted modulus of elasticity age adjusted modulus of FRP laminates eccentricity of the steel reinforcement and FRP laminate measured from the centroid of the cracked transformed concrete section modulus of rupture of the concrete span length of simply supported beam

significant effects on the failure mode, ultimate strength, deflections and strain characteristics of the strengthened beams. Siddiqui [17] carried out an experimental test program on U-shaped CFRP end anchorage strengthened reinforced concrete beams for the flexural strengthening. It was concluded that tension side bonding of CFRP laminates with U-shaped end anchorages is very efficient in flexural strengthening. Serviceability of concrete can be defined as satisfactory performance under service load conditions which in turn can be described in terms of two basic parameters namely cracking and deflection. Deflections constitute one of the important serviceability criteria in the design of reinforced concrete (RC) structures. Creep and shrinkage effect are the most dominating factors affecting time-dependent deformations of reinforced concrete beams. Due to these effects deformation of reinforced concrete beams increases with time by a significant amount. The deflection due to the time dependent effect is more critical for cracked beams. In cases where deflection control is critical, it is important to accurately predict the long-term time dependent deflections. A critical review of the abundance of research which occurred around this time is provided by Ghali [18]. He presented a summary of the key research that was performed on the deflection behaviour of reinforced concrete structures; the fiber reinforced polymer as externally bonded reinforcement being of most interest for the maintenance, rehabilitation and upgrading of existing or newly build RC structures. Numerous research work has been carried out on the instantaneous deflection of reinforced concrete (RC) beams externally bonded with different types of FRP systems [19– 22]. It was observed from these studies that an increase in the flexural strength and stiffness of the beams results, due to the strengthening effect of FRP laminates. Additionally, several researches of long-term behaviour of FRP strengthened reinforced concrete beams were provided by a number of researchers [23– 28] and they received a considerable attention from the research community. Only a small amount of information on long-term studies has been published on RC beams with externally bonded FRP sheets under sustained loading. Masia et al. [27] conducted an experimental investigation on creep performance of RC beams strengthened with externally bonded FRP strips. The test results indicate that for the epoxy adhesive used, creep in the adhesive is minimal. Al Chami et al. [24] studied a series of experiment on the long-term performance of CFRP strengthened concrete beams. They applied sustained loads varied from 59% to 78% of the ultimate static capacities of the un-strengthened beams. They concluded that FRP strengthening is effective for increasing the ultimate capacities of the beams;

Mcr Mu Ma T

jr /pt

jsh

ush esh ðt; t0 Þ eshu

cracking moment of the RC beam ultimate moment capacity of the RC beam maximum applied moment fictitious compressive force induced in the steel reinforcement and FRP laminate factor depends on the quantity and location of the bonded reinforcement creep coefficient of FRP laminate shrinkage induced curvature of a reinforced or prestressed concrete curvature due to shrinkage of concrete shrinkage strain at time t ultimate shrinkage strain

however, there is virtually no improvement in performance with regard to the long-term deflections. Pelvris and Triantafillou [22] have investigated the timedependent (creep and shrinkage) behaviour of reinforced concrete members strengthened with FRP sheets. It was observed that composites material plays a favourable role in the long-term response of strengthened elements. They also reported that increasing the CFRP area fraction decreased both the immediate and the creep deflections. Arockiasamy et al. [25] developed an analytical method and proposed a simplified equation to predict the long-term behaviour of CFRP internally reinforced concrete beams. The ageadjusted elastic modulus method based on the ACI approach [29] used to calculate the time-dependent curvature, strains and deflections induced by the creep and shrinkage of concrete. This conclusion is in contradiction with the findings of Pelvris and Triantafillou [22], which indicated that increasing the CFRP area fraction decreased the instantaneous and creep deflections. Presently, along with ACI 435R (American Concrete Institute) approach [30], some analytical methods [31–35] are available to compute the long-term deflections in RC members. These are mainly based on strain compatibility and equilibrium of forces with different models to account for the curvature due to creep and shrinkage. The accurate prediction of deflections is, therefore, critical which requires the use of non-linear and time-dependent analytical methods. However, at the design stage, simplified methods which take into account the most important parameters influencing the long-term behaviour may be very useful to adequately design the structure. The long-term increase in deflection function of member geometry (reinforcement area), load characteristics (age of concrete at the time of loading, magnitude and duration of sustained load), material characteristics (creep and shrinkage of concrete, mix proportions), curing conditions, relative humidity, and temperature. For the cracked beam section, beside the creep and shrinkage strain, another factor which can influence the theoretical result is the tension stiffening. In the case of serviceability, and specifically for deflections, ACI 318 [36] proposed bond dependent coefficients to modify Branson’s equation in concrete tension stiffening model for FRP strengthened RC beams, while only one author Zou [34] proposed a tension stiffening model for prestressed RC beams using second moment of inertia by including material parameters. In this paper, attention is paid to the gaining of a proper understanding of the structural behaviour of reinforced concrete beams strengthened with multi-layered carbon fiber composite laminates. The paper focuses on two main stages. Firstly, it evaluates the flexural response of RC beams bonded with CFRP sheets. The

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effectiveness of transverse edge strips in preventing the de-bonding failure of FRP laminates is also discussed. Secondly, an experimental investigation on the time-dependent response of CFRP bonded reinforced concrete cracked and un-cracked beams are carried out under the sustained uniform load. The experimental results are used to verify the analytical values based on ACI recommended effective modulus method (EMM) approach. Factors affecting the long-term deflection and cracking performance of CFRP strengthened RC beam are identified in this study. Finally, a deflection reduction coefficient in concrete tension stiffening model is proposed to get better accuracy in the time-dependent deflection calculation of CFRP strengthened cracked RC beams.

beam is calculated using equivalent rectangular stress block of the beam cross section following the BS code of practice BS 8110-1 [37]. Then, the first cracking (Pcr) and ultimate loads (Pult) are calculated from the cracking and ultimate moment capacity.

2. Analytical consideration

where Ec is the modulus of elasticity of concrete; and Ie is the effective moment of inertia, which evaluated from the well-known Branson [38] formula and is given by

2.2. Time-dependent deflection response The equation of instantaneous deflection of a simply supported beam of spans length l, under the uniformly distributed loading w (refer to Fig. 2a) can be expressed as 4

dðto Þ ¼

2.1. Flexural response

ð2Þ

"  3  3 # M cr M cr Icr 6 Ig Ie ¼ Ig þ 1  Ma Ma

Analytical approach to evaluate the contribution of FRP composites laminates to concrete structures in flexural behaviour is described in the code BS 8110-1 [37]. The code uses a rectangular stress block to determine the equilibrium forces which are acting on the reinforced concrete beams. In this codes, it adopts the traditional sectional analysis called ‘‘plane sections remain plane’’ for strain compatibility, and the stress strain relationships of concrete, steel and FRP laminates are used for equilibrium equations (refer to Fig. 1). The theoretical cracking moment Mcr of the RC beam is computed using the flexural formula as given below

fr Ig M cr ¼ yt

5 wl 384 Ec Ie

ð3Þ

where Mcr is the cracking moment; Ma the maximum applied moment; and Ig and Icr is the moment of inertia of a gross and a cracked section respectively. For an un-cracked FRP-bonded beam with a rectangular cross section, moment of inertia can be evaluated based on gross section (Ig) using transformed area for both steel and CFRP, that is (refer to Fig. 2b)

Ig ¼

ð1Þ

 2 3 bh h þ bh x  þ ðn  1ÞAs ðd  xÞ2 þ ðn  1ÞA0s ðx 12 2 0

 d Þ2 þ np bp t p ðdf  xÞ2

where yt is the neutral axis to the tension face of the beam, fr the modulus of rupture of the concrete and I is the second moment of inertia of the cross section. The ultimate moment capacity of the

where b is the beam width; h the beam height; x the neutral axis depth for un-cracked section; the modular ratio of steel to concrete,

b

0.45fcu

0.0035

Fsc

d'

s=0.9x

x=d/2

As'

Fcc

N. A h

d

df

ð4Þ

z εs

As

Fst

εf

d''

d'' Ff

εs

Section

Strain distribution

Rectangular Stress block

Fig. 1. Linear strain variation over the depth of the section and BS 8110-1 rectangular stress block.

(a)

(b)

(c)

Fig. 2. (a) Uniformly distributed loaded (UDL) beam, (b) un-cracked section, and (c) cracked section details.

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n the Es/Ec; modular ratio of CFRP laminate to concrete; np the Ep/Ec; As the total area of tensile steel reinforcement; d the distance from the top compressive face to the centroid of tensile steel; df the distance from the top compressive face to the centroid of CFRP laminate; bp the width of CFRP laminate and tp is the thickness of CFRP. For a cracked rectangular section, moment of inertia (Icr) can be expressed as (refer to Fig. 2c)

Finally, the deflection due to shrinkage for a simply supported beam can be expressed as:

1 2 Dsh ¼ ush l 8

ð13Þ

This shrinkage deformation will be added to the previously determined deflection considering creep effects to get the total deflection.

3

Icr ¼

bh 0 þ nAs ðd  xÞ2 þ ðn  1ÞA0s ðx  d Þ2 þ np bp t p ðdf  xÞ2 3

ð5Þ

A0s

where x is the neutral axis depth for a cracked section; the total area of compressive steel reinforcement; and d0 is the distance form top compressive face to the centroid of compressive reinforcement. The coefficient for creep at times td (days) after load application is given by the following expression recommended by ACI 435R [30]

/cðtÞ ¼

t 0:6 d /uc 10 þ t0:6 d

ð6Þ

where /uc is the ultimate creep coefficient and depends on conditions of concrete. The age-adjusted modulus of elasticity is given by the following expression

Ect ¼

Ec ðt o Þ 1 þ v/cðtÞ ðt; t o Þ

ð7Þ

where v is the aging coefficient of concrete and varies between the values of 0.7 and 0.9 with the average value of 0.8. Similarly, the age adjusted modulus of CFRP laminates can be expressed as [23]

EFRPðtÞ ¼

EFRP ðt o Þ 1 þ /FRPðtÞ 

th tho

n

1

ð9Þ

Te Ee Icr;t

ð10Þ

where T is the fictitious compressive force induced in the steel and CFRP laminate, considered in total; and e is the eccentricity of the steel reinforcement and CFRP laminate measured from the centroid of the cracked transformed concrete section. For a CFRP-bonded section [23] 0 Te ¼ ½As Es ðd  xÞ  A0s Es ðx  d Þ þ bp t p EFRP ðtÞðh  xÞesh ðt; t 0 Þ

ð11Þ

0

where esh ðt; t Þ = shrinkage strain at time t, with drying commencing at time t0 . The shrinkage strain at any time t (in days) can be expressed recommended by ACI 435R [30]

esh ðt; t0 Þ ¼

t

aþt

eshu

where a is an experimental constant, strain.

"  3  3 # Mcr Mcr Icr 6 Ig Ie ¼ bd I g þ 1  Ma Ma

ð12Þ

ð14Þ

where bd is the reduction coefficient used in calculating deflection and expressed as

bd ¼ ab

Here t is the time in hours and tho is 1 h, n is the gradient of the curve which has to be determined from the experimental results. The values of Ect and EFRP(t) are then used in the transformed section analysis to get Icrt. This is then used in Eq. (3) to determine Iet. Then, replacing Ec and Ie by Ect and EFRP(t), respectively, in Eq. (2). Finally, the deflection considering creep effects can be calculated. The curvature (ush ) due to shrinkage of concrete in an asymmetrically RC member can be found by the fictitious tensile force method by Branson [38] as

ush ¼

Concrete has the ability to carry tensile stress between cracks in the tension zone due to the bond between the steel and concrete, a tension stiffening model is only applicable for the analysis of cracked cross-section of the reinforced concrete beams. A model proposed by Gilbert [39] for reinforced concrete members with steel reinforcement or FRP is involved in this study as shown in Fig. 3. The model specified in ACI 440 [40] for concrete tension stiffening was originally developed for conventional RC beams reinforced by steel round bars or deformed bars. In this study, this model has been modified for RC beams externally bonded with CFRP laminates by the modification factor bd with the accurately predicted bond-dependent coefficient value of ab. Then, a modified tension stiffening model may be expressed as below

ð8Þ

where /pt is the creep coefficient and is given by

/FRPðtÞ ¼

2.3. Concrete tension stiffening



Ef þ1 Es

 ð15Þ

3. Description of experimental investigation 3.1. Test program The experimental study consists of casting fourteen reinforced concrete beams. The beams were divided into two groups; the specimens of first group were used for flexural strengthening by CFRP laminates whereas second group specimens were employed time-dependent strengthening for un-cracked and cracked section. These beams were fabricated and tested based on the test program given in Tables 1 and 2. For first group, a total of six beams having different level of strengthening scheme were fabricated for the flexural test in the laboratory. First beam (designated as CBF) was not bonded with CFRP laminates, three beams (FBF-1L, FBF-2L and FBF3L) were bonded with different layers of CFRP laminates (1, 2 and 3-layers respectively) and the other two beams (designated as FBF-1LU and FBF-1LW) were bonded with one layer CFRP laminates and having one U-shaped and two W-shaped edge strip respectively. In the second group, a total of eight reinforced concrete beams having different degrees of strengthening schemes with carbon fiber laminates, and these beams are subjected to sustained loads that corresponds to un-cracked and cracked section were fabricated in the laboratory. Two beams

b

dn NA As

bw bw

ds

Act

eshu = ultimate shrinkage Fig. 3. Tension stiffening model by Gilbert [39].

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H.R. Sobuz et al. / Construction and Building Materials 29 (2012) 597–611 Table 1 Test program for flexural test. Flexural strengthening scheme FRP ratio, qFRP (%)

Beam designation

0 Control (not bonded)

0.4 1-layer bonded

0.8 2-layers bonded

1.2 3-layers bonded

0.4 1-layer U-strip bonded

0.4 1-layer W-strip bonded

CBF

FBF-1L

FBF-2L

FBF-3L

FBF-1LU

FBF-1LW

Table 2 Test program for time-dependent test. Section type and sustained load

Beam designation

FRP ratio, qFRP (%)

Service load

Time-dependent strengthening schemea

Cracked (22.56 kN)

CBC FBC-1L

0 0.4

0.56 P a0

A B

FBC-2L FBC-3L

0.8 1.2

CBU FBU-1L

0 0.4

FBU-2L FBU-3L

0.8 1.2

Un-cracked (15.31 kN)

0.36 P b1 0.33P c2 0.30 P d3 0.38 P a0 0.25 P b1 0.22P c2 0.21

P d3

C D A B C D

Flexural capacity of un-strengthened (control) beam, P a0 = 40.3 kN. Flexural capacity of 1-layer CFRP strengthened concrete beam, P b1 = 62.0 kN. Flexural capacity of 2-layers CFRP strengthened concrete beam, P c2 = 69.75 kN. Flexural capacity of 3-layers CFRP strengthened concrete beam, P d3 = 74.4 kN. a Strengthening scheme: (A) un-strengthened (control) beam, (B) one layer of CFRP sheets bonded beam, (C) two layers of CFRP sheets bonded beam, (D) triple layers of CFRP sheets bonded beam.

(designated as CBU and CBC) were not strengthened with CFRP laminates and considered as control or reference beams, three beams (FBU-1L, FBU-2L and FBU-3L) for un-cracked and the remaining three beams (FBC-1L, FBC-2L and FBC-3L) for cracked were strengthened with different layers of CFRP laminates (1, 2 and 3-layers respectively). In the time-dependent specimens, the main parameters are the two types of sustained load and different FRP ratios for both cracked and un-cracked sections of beams. Different CFRP ratios were chosen such as to facilitate comparison among these beams with the same sustained loads. The flexural capacities of different layered CFRP-bonded beams have been investigated from the static test in the laboratory.

[41] standard test method for creep of concrete in compression. Three cylinders were tested to determine the ultimate compressive strength; three were stacked and loaded together 0.40 times the cylinder ultimate compressive strength on a creep rig. The creep strain was used to determine the average strain value of the three specimens. The creep coefficient is calculated by taking the ratio of creep strain of the concrete at the testing age to the instantaneous elastic strain of the concrete. The result of the concrete creep test over a period of 6 months is shown in Fig. 4. It was observed that the curve of the experimental result for concrete creep coefficient did not fully stabilize after 6 months period. Therefore, to carry out the theoretical calculation of this paper, the experimental value of creep coefficient is used instead of the ACI recommended creep model as mentioned earlier in section 2. 3.2.1.2. Drying shrinkage test. The drying shrinkage was performed on 100 mm  100 mm  285 mm prisms in accordance with the ASTM C157-92 [42]. Three specimens were cast in steel moulds. The shrinkage strain for each specimen was the average value of three specimens. Fig. 5 shows the experimental results for the shrinkage strain of concrete over a period of 6 months. Similar to the creep results, the shrinkage strain of concrete did not stabilize fully after the 6 months period. Again, instead of ACI recommended shrinkage model, the experimental result will be used to carry out the theoretical calculation to get better accuracy in the results. 3.2.2. Properties of steel reinforcement Two types of longitudinal reinforcement bars were used in this study. High yield deformed bars of 6 mm and 10 mm (T6 and T10) were used as compression and tension reinforcement for the beam specimens. Six millimetre diameter (R6) plain round mild steel bar was used as transverse shear reinforcement in this study. Tensile tests were conducted in the laboratory on the reinforcing bars to obtain the modulus of elasticity and yield strength values of the steel reinforcing bars and these values were used for theoretical predictions. Table 4 shows the details of steel reinforcement properties.

3.2. Material properties 3.2.1. Properties of concrete All the beams were cast from the same batch in this current investigation. For concrete, crushed granite aggregate of 20 mm nominal size was used. The mix proportions were set at 1:1.65:2.45:0.45 by weight of ordinary Portland cement, locally available natural sand, and crushed granite aggregate and water to achieve a 28-day concrete strength of 36.0 MPa. The water–cement ratio was maintained at 0.5 for casting all of the beams. A total of ten cubes (150  150  150 mm), two cylinders (150 mm in diameter and 300 mm in height), six cylinders (150 mm in diameter and 300 mm in height), three prisms (100  100  500 mm) and three prisms (100  100  285 mm) were tested in the laboratory for evaluating the concrete compressive strength, modulus of elasticity, coefficient of concrete creep, modulus of rupture and shrinkage strain of the concrete at 28 days. These characteristics of the concrete’s basic properties, as obtained from laboratory tests, are shown in Table 3. Some of these concrete properties are used to carry out the theoretical calculation in this study.

Fig. 4. Concrete creep coefficient versus time plot.

3.2.1.1. Compressive creep test. A total of six cylinders measuring 150 mm in diameter and 300 mm in height were cast in the laboratory and cured into the curing tank for 28 days. The test was conducted in compliance to the ASTM C512-87

Table 3 Concrete properties. Properties

Values found in the laboratory

Concrete cube strength (MPa) Modulus of elasticity (GPa) Modulus of rupture (MPa)

36.0 28.6 3.7

Fig. 5. Concrete shrinkage strain versus time plot.

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H.R. Sobuz et al. / Construction and Building Materials 29 (2012) 597–611

Table 4 Steel properties. Reinforcement type

Yield strength (MPa)

Modulus of elasticity (GPa)

Tension, T10 Compression, T6 Shear, R6

482 470 215

195 186 200

of the span, carbon fiber of U and W-wrapped CFRP laminates were attached transversely to prevent any type of premature de-bonding of CFRP laminates from the beam soffit.

3.4. Surface treatment phase

Table 5 CFRP laminates and epoxy adhesive properties. Materials

Property

Values

CFRP laminate

Sheet form Yield strength (MPa) Modulus of elasticity (GPa) Elongation at ultimate (%) Tensile strength (MPa) Density (g/cm3)

Uni-directional roving 1315 165 2.15 1685 1600

Epoxy adhesive

Modulus of elasticity (GPa) Elongation at ultimate (%) Tensile strength (MPa)

3 2.6 55

3.2.3. Properties of CFRP laminates and epoxy adhesive The carbon fiber reinforced polymer (CFRP) laminates are commercially available with unidirectional plain roving form. CFRP composites laminate of 1.2 mm thickness and 100 mm wide were used for the strengthening purposes of the beams and they were cut from the Sika Carbodur S1012/160 [43] roving laminate. They contain 68% volumetric fraction of high strength carbon fibers and 32% of epoxy resin. The CFRP composite laminate was tested in the laboratory to get the tensile strength, yield strength, modulus of elasticity and the percentage of ultimate elongation at failure. The other properties of the carbon fibers and epoxy adhesive as supplied by the manufacturer are shown in Table 5.

3.3. Specimen fabrication The preparation of the beam specimens first involved cutting, fabricating and installing the steel reinforcement according to the configuration as shown in Fig. 6. The dimensions of all the specimens were identical. All the beam specimens are 150  200 mm in cross section and 1900 mm in span length on a simply supported span. R6 (6 mm in diameter) stirrups were placed at a constant spacing of 125 mm throughout the entire length of the beams so as to prevent the beams from failing in shear. The tensile reinforcements were placed at a depth of 168 mm, while the compressive reinforcement was placed at 30 mm from the top surface. Small rectangular concrete blocks were cast, which were used to maintain the clear cover throughout the length of the beams. The control beam was designed to fail in flexure following the BS 8110-1 [37]. After at least 1 month of casting, a 100 mm wide and 1.2 mm thickness CFRP laminates were precisely cut and then bonded on the tension face of the beam. In addition, CFRP transverse edge strips were used for flexural strengthening to prevent the premature de-bonding failures of carbon fiber laminates. No transverse edge strips were used for time-dependent strengthening. The schematic diagram of single, double and triple layers strengthening schemes of the reinforced concrete beams are depicted in Fig. 7a–c respectively. The detail of the specimens FB-1LU and FB-1LW strengthening schemes are shown in Fig. 7d and e respectively. In these cases, at the CFRP cut-off points near the end

In the fabrication of beams, it was needed to prepare the substrate before the composite sheets were bonded to the tensile face of the concrete beams. Prior to the bonding of the CFRP laminates to the beams, the required region of the concrete surface was made rough using a coarse sand paper texture and cleaned with an air blower to remove all dirt. Once the beam surface was prepared to the required standard, the epoxy resin was mixed at a proportion of 1:3 using a two-part cold curing epoxy resin Sikadur-30 (Part-A and Part-B) in accordance with manufacture’s instruction. Mixing was carried out in a rectangular thin plastic plate until the uniform colour appears. A uniform mid-grey colour indicates adequate mixing of the white resin and the black hardener. A nominal thickness of the epoxy adhesive has been controlled for the CFRP surface. Sikadur-30 adhesive was applied on cleaned and prepared substrate components and then, the CFRP laminates were placed onto the prepared concrete surface. The composite laminate was attached starting at one end and applying enough pressure by rubber roller. During hardening of the epoxy, a constant uniform pressure was applied on the laminates surface in order to extrude the excess epoxy resin to ensure good contact between the epoxy, the concrete and the laminate. All the excess epoxy was removed from the sides of the laminates. The same procedure has been applied for second and third layer laminates attachment on the beam surface. To ensure a proper bonding, a minimum of 3 days curing of the externally applied adhesive was maintained for all the specimens. Fig. 8a–d shows the photographic view of the strengthening procedure of carbon fiber laminates on the beam soffit level by using epoxy adhesive.

3.5. Test set up and loading procedure All the specimens were tested in the ‘‘Heavy Structure Laboratory’’ of Universiti Malaysia Sarawak, Malaysia. After the curing period of 28 days was over the beam as washed and its surface was cleaned for clear visibility of cracks. Two different setups were made in the laboratory for the flexural and time-dependent deflection performance tests. All the specimens’ support were placed 50 mm away from the end points. In both cases the beams were tested simply supported on a span of 1900 mm. The most commonly used load arrangement for flexural testing of beams consisted of four-point loads whereas the long-term test consists of a two-point loading system.

3.5.1. Four-point bending test In the four-point bending test, beams were subjected to symmetric loading composed of two concentrated loads placed at equal distance 250 mm from the beams centreline and loading was under displacement control. An experimental four-point loading arrangement was performed in the laboratory as shown in Fig. 9a. The specimen was checked dimensionally before the test carry out, and a detailed visual inspection made with all information carefully recorded. Load was applied monotonically by two hydraulic jacks, which are attached to a pressure gauge. Load was transmitted through a load cell and a spreader steel beam on the tested beam. Three linear variable displacement transducers (LVDTs) were used to monitor the vertical deflections at the mid-span and under the loading points by means of quarter span locators. A portable electronic data logger was used to record the reading of deflections. After a regular increase of loading, the loading values and the corresponding deflections were recorded. The static load was applied until failure occurred in the beam. The load and the corresponding deflection taken from the test were then used to investigate the behaviour of the beams. The quarter span

Fig. 6. Longitudinal and cross section detail of the experimental beams.

(a)

150mm

H.R. Sobuz et al. / Construction and Building Materials 29 (2012) 597–611

603

100mm 1500mm

(b)

150mm

2000mm

100mm 100mm

(c)

150mm

1300mm 1500mm

100mm 1100mm 1300mm

(d)

250mm

100mm A 200mm A

50mm 300mm

(e)

50mm 250mm

400mm

500mm

400mm

50mm 300mm

100mm U- Strip laminate Longitudinal laminate Section A -A

50mm 100mm B

B 50mm 250mm

450mm

500mm

450mm

50mm 250mm

100mm W- Strip Longitudinal laminate laminate Section B -B

Fig. 7. Strengthening schemes of RC beams: CFRP laminates of (a) single, (b) double and (c) triple layers (d) strengthened beam with one U-shaped strip (e) with two Wshaped edge strips.

LVDTs were used mainly to check the symmetrical nature of the loaded beams. Cracks were visually detected using a magnifying glass and its propagation was traced and the corresponding loads were recorded on the beam.

capacity of the un-strengthened beams as mentioned in Table 2 that corresponds to the un-cracked and cracked sections are simulated by giving equivalent uniformly distributed loading.

3.5.2. Time-dependent test Time-dependent deflection performance of multi-layered CFRP strengthened cracked and un-cracked beams have been performed in the laboratory subjected to distribution of sustained loads as shown in Fig. 9b. In this situation, loads were applied using concrete blocks and steel beams along the length of the beam to simulate uniformly distributed loading. The mid-span deflection of each beam relative to the self-weight value was recorded immediately after loading. During the testing, the deflections of all beams were measured at mid span and quarter span of the beams using digital dial gauges. Also, two digital dial gauges were placed at midspan at 20 mm from the front and back sides of the beam, to check for any unintentional rotation of the beams due to sustained loading. The average of the two dial gauge readings was taken as the mid-span deflection. The quarter span dial gauges were used to check the symmetrical nature of the long-term loaded beams. Readings were noted at regular intervals from 1, 3, 5, 10, 14, 21 days, weekly up to 3 months and every 15 days thereafter up to 6 months for the experimental beams. In time-dependent tests, two different service load levels obtained from the static

4. Test results and discussion 4.1. Four-point bending test 4.1.1. Load–deflection responses The load-mid span deflection behaviour of the control beam and beam strengthened with different layers of CFRP laminates are shown in Fig. 10. It is observed from Fig. 10, that initially all the strengthened beams behave like the control beam with the internal steel reinforcing bars carrying the majority of the tensile force in the section. When the internal steel yields, the additional tensile force is carried by the FRP system and an increase of the load capacity of the member is obtained. Eventually, the FRP

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Fig. 8. Strengthening procedure of carbon fiber laminates: (a) cleaning beam surface, (b) cleaning CFRP surface, (c) attaching epoxy on CFRP, (d) pressing CFRP laminate.

Fig. 9. Four-point bending test setup, (b) time-dependent deflection test setup.

strengthened beams fail. The failure modes which are observed on the CFRP strengthened beams are different from that of the classical reinforced concrete control beam. CFRP reinforced beams behave in a linear elastic fashion nearly up-to the failure. This brittle mode of failure is considered as a drawback for this system of reinforcement. The displacement ductility index (displacement at failure divided by displacement at yield) can give an estimation of the lack of ductility of these beams (refer to Table 6). It was also observed that un-strengthened beams showed more displacement or ductility as compared to that of concrete beams of different CFRP configurations. The maximum deflection prior to the final failure of the CFRP strengthened beams was found to be about 8.72 mm and it indicates that the strengthened beams are less ductile compared to the un-strengthened beams. It was also observed that un-strengthened beams showed more displacement or ductility as compared to that of concrete beams of different CFRP configurations. The ductility of the beams FBF-1L, FBF-2L and FBF-3L

decreased significantly as compared to the control beam, due to brittle failure caused by de-bonding failure between the concrete and CFRP laminate. This drawback is improved by applying transverse strips into the each end of the beam in order to avoid the end de-bonding of the CFRP laminate (FBF-1LU and FBF-1LW). The lower value of ductility index for the CFRP strengthened beams (FBF1L, FBF-2L and FBF-3L) indicate the lacking of ductility of such strengthened beams. Fig. 11 plots the load–deflection response of beams strengthened with single layer of CFRP laminate with different degrees of restrain at the edges against premature de-bonding. This figures illustrate that, compare to the response of un-wrapped strengthened beam, the transverse edge strips strengthened beams achieved a substantial gain in the flexural strength. The load deflection plots of strengthened beams with U and W-edge strips show similar response to that of strengthened beam without transverse edge strips. However, a significant increase in the ultimate

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Fig. 10. Load–deflection responses of control beam and multi-layer CFRP strengthened beams.

load carrying capacity was noted in these two beams, although it still showed signs of de-bonding just before final failure. For the beam strengthened with W-wrapped strips, the observed load carrying capacity measured in terms of ultimate displacement was substantially higher than the beam strengthened with U-wrapped strips. It is concluded that tension side bonding of CFRP sheets with end anchorages is very effective in flexural strengthening of RC beams as this scheme not only increases the flexural capacity substantially, but also maintains sufficient deformation capacity until failure. 4.1.2. First cracking and ultimate loads Table 6 shows the experimental results of controlled and strengthened beams in terms of the first cracking load and ultimate load. It also includes the theoretical prediction of first cracking loads and ultimate loading capacity of the test beams. Theoretical predictions of the first cracking load is calculated from the equivalent transformed section analysis of the beam cross-section and ultimate capacity is predicted using equivalent stress block of the

Fig. 11. Load–deflection response of single layer strengthened beam with different edge restraint beams.

cracked cross section in accordance to the provision mentioned in BS 8110-1 [37]. The yield load of a reinforced concrete beam is the load causing yielding of the tension steel reinforcement. From the experimental investigation, it can be observed that the control beam had a yield load at around 37.2 kN when the tensile reinforcing steel yielded with a mid-span deflection of 23.5 mm. The ultimate load is defined as the maximum applied load resisted by a beam or the load just before a sudden drop in the load if this occurs. Table 6 clearly shows that for the beam strengthened with carbon fiber laminates; load capacity was increased substantially compared to the control beam. For the control beam, the failure occurred in flexure due to the crushing of extreme compression zone concrete by yielding of the tension steel reinforcement. The ultimate load was 40.3 kN at a maximum mid-span deflection of 19.86 mm. It is also seen that the deflections are reduced significantly thereby increasing the stiffness for the strengthened beams. At ultimate load level of the specimens, the strengthened beams exhibit a maximum decrease of deflection up to 56% of that of the control beam. Comparing the

Table 6 Experimental and theoretical results. Experimental load (kN)

Theoretical load (kN)

Beam design-nation

P a cr

P

P c cr

P

CBF FBF-1L FBF-2L FBF-3L FBF-1LU FBF-1LW

12.4 15.5 18.6 21.7 17.05 18.6

40.3 62.0 69.75 74.4 75.95 82.15

11.3 12.3 13.4 14.4 12.3 12.3

b ut

Maximum

ult

P ultðThe:Þ PultðexpÞ

crack spacing (mm)

Ductility index

Failure modea

31.5 82.6 98.8 106.8 82.6 82.6

0.78 1.33 1.41 1.43 1.09 1.00

105 126 138 149 156 162

3.81 1.65 1.48 1.29 2.28 2.42

1 2 2 2 3 3

d

P a cr = experimental first cracking load. P b ut = experimental ultimate load. P c cr = theoretical first cracking load. P dult = theoretical ultimate load. a Failure mode (1) Flexural failure by crushing of the compression concrete which could happen before or after yielding of tensile steel reinforcement; Mode (2) De-bonding of the FRP laminate from the concrete surface induced by flexural shear crack; Mode (3) Rupture of the FRP laminate after yielding of the steel in tension with crushing of the compression concrete.

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ultimate load of the strengthened beam to the control beam, an increase of 54%, 73% and 85% was achieved for 1, 2 and 3-layers CFRP strengthened beams respectively. The use of transverse U and W shaped wrap strips gives an increase of 88% for U-shaped case and double the flexural capacity for W-shaped case as compared to that of control beam. When compared to that of 1-layer unwrapped beam, these increases in flexural capacity were 23% and 33% respectively. The ultimate load for the U-wrapped edge strip beam was 75.95 kN whereas W-wrapped strip beam the ultimate load was 82.15 kN. The observed change in the ultimate strength of the beam with W-edge strips was 8% higher than the U-edge strips strengthened beam. An important character to be noticed about the usage of CFRP sheets is the high ductile behaviour of the beams. But the ductile behaviour by the use of CFRP can give us enough warning before the ultimate failure. In general, different layers of CFRP strengthened RC beams (FBF-1L, FBF-2L, and FBF-3L) showed significant increases in flexural stiffness and ultimate capacity compared to that of the control beam. Consequently, it has been seen that prevention of de-bonding failure and improvement of strengthening performance of beams FBF-1LU and FBF1LW can be achieved by adding U and W-wrapped edge strips in the beam. The layered strengthened beams could not reach their theoretical ultimate capacities given in Table 6 due to the occurrence of premature failure either due to the separation of CFRP sheets or diagonal cracks. The average ultimate capacity achieved for beams repaired with third layered CFRP laminate was 74.4 kN with a reduction of 30% as compared to the theoretical ultimate capacity (Ptheo. = 106.8 kN). Furthermore, in the case of first and second layered CFRP laminates, the achieved ultimate capacities were also less than their corresponding theoretical ultimate capacity. This is because the shear in the interface reached its maximum shear stress before any remarkable yielding of the CFRP sheet, leading to less composite action and sheet separation. This did not enable the beams to achieve their full theoretical capacity. The results also indicate that beams FBF-1LU and FBF-1LW showed more ductile behaviour than the 1-layer un-wrapped beams. These end anchorage beams failed due to the rupture of the CFRP laminate and crushing of concrete simultaneously. The beam FBF-1LU could not reach its full ultimate theoretical capacity whereas the beam FBF-1LW reached its full ultimate theoretical capacity. This implies that the beam FBF-1LW is stiffer than the beam FBF-1LU. Thus, it is concluded that the FRP laminate thickness and transverse edge strips significantly influence the structural performance of the strengthened RC beams. A comparison between experimental and theoretical results shows that the theoretical calculation gives a conservative estimation of the first cracking load but underestimates the ultimate capacity of the strengthened beams. It has been seen that the beam using transverse edge strips gives a very good prediction from its theoretical results, compared to the different layered strengthened specimens. In general, the experimental results are in very good agreement with the theoretical predictions, especially those for the control and end anchorage strengthened beams. 4.1.3. Crack spacing and distribution Generally, in beams cracks occur when the stress in the tensile zone reaches the modulus of rupture of the concrete beam. Table 6 shows the summarised values of ultimate loading stage maximum crack spacing. It was observed that the first crack always appears in the middle third part of the beam. The cracks forming on the surface of the beams were mostly vertical, suggesting failure in flexure. The maximum crack spacing has been measured in the central part of the beam, where the bending moment is constant. It can be seen from Table 6, crack spacing of un-strengthened beam was lower than the different level of CFRP strengthened reinforced

concrete beam. It was also observed that the increase in CFRP layers on reinforced concrete beams increased crack spacing. Moreover, closed spaced cracks or more cracks, leads to a smaller crack width. The reason for this behaviour is that the crack spacing is a function of both the tensile strength and the bond strength of the concrete, reinforcing steel and CFRP laminates. The increase in the tensile strength of concrete is due to the increase in its strength from the contribution of CFRP laminates rather than the increase in the bond strength of concrete. When the multi-layered CFRP laminates are attached on the soffit of the beams, a longer distance is required for the tensile force in the steel reinforcement and CFRP laminates to be retransferred to the surrounding concrete, which implies larger crack spacing. 4.2. Time-dependent deflection test 4.2.1. Effect of carbon fiber ratio under the same sustained loads The total deflections, time-dependent deflection and the ratio of the time-dependent to instantaneous deflections of un-cracked and cracked beams with different CFRP ratios under the same sustained loads are compared as shown in Figs. 12a–c and 13a–c respectively. The level of the applied sustained load is presented in terms of ultimate capacity (Puc) of un-strengthened (control) beam for un-cracked and cracked section. It is clear that the higher the FRP ratio, the smaller is the instantaneous and time-dependent deflections for un-cracked and cracked section due to the corresponding sustained loads. Thus, the FRP laminate seems to be effective in decreasing the instantaneous deflections and also its influence on the long-term deflections under sustained load. The time-dependent deflections of beams FBU-1L, FBU-2L and FBU-3L are 20%, 28% and 35% less than the un-cracked control beam (CBU) under the service loads (0.38P0) whereas for the cracked beams FBC-1L, FBC-2L and FBC-3L, it is 37%, 46% and 56% less respectively, than the control beams (CBC) under the service loads (0.56P0). It is also observed that the instantaneous deflections for un-cracked and cracked beams with different FRP configurations are significantly lower than the comparable unstrengthened beams. The sustained load intensity of all un-cracked beams is smaller than that of cracked beams and hence un-cracked beams exhibits smaller long-term defections than those of cracked beams. In general, the higher the FRP ratio, the lower is the longterm deflection of the CFRP strengthened beams. Hence, CFRP ratio is affecting the time-dependent performance of the strengthened beams. At the lower sustained load (un-cracked beams), the greater the CFRP reinforcement ratio, the greater is the ratio of the timedependent to instantaneous deflections. In this case, the reduction in time-dependent deflection is not obvious because smaller amount of concrete and FRP creep enhance the deflection. Consequently, the greater the CFRP reinforcement ratio, the lower is the ratio of the time-dependent to instantaneous deflections observed in the higher sustained load level (cracked beams). 4.2.2. Instantaneous and time-dependent deflections The measured instantaneous and long-term deflections under sustained loads at the end of 6 months for un-cracked and cracked beams are summarised in Table 7. In all cases, the long-term deflections are obtained by subtracting the instantaneous deflection from the total deflection. It is seen that the Instantaneous deflections for CFRP strengthened beams (FBU-1L, FBU-2L, FBU-3L, FBC-1L, FBC-2L and FBC-3L) are significantly lower than the comparable un-strengthened (control) beams. The reduction of time-dependent deflection is less for un-cracked section as compared to that of cracked sections. From the experimental investigation, it is identified that the long-term deflection after a period of 180 days was on average 42% and

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Fig. 12. RC beams with different CFRP ratios for un-cracked section: (a) total deflection, (b) time-dependent deflection, (c) ratios of time-dependent to instantaneous deflection.

46% higher than that of Instantaneous deflection for CFRP strengthened beams while the long-term deflection of control beam was 64% and 65% higher to that of Instantaneous deflection for the un-cracked and cracked section respectively. For CFRP strengthened beams, the long-term deflection at 6 months period was on average 1.41 and 1.45 times the instantaneous deflection for un-cracked and cracked section respectively. This is significantly lower than the un-strengthened reinforced concrete beams under service loads in which the deflection of control beams at the same period had been measured to be about 1.64 and 1.65 times the instantaneous deflection for un-cracked and cracked section respectively. Long-term deflections of CFRP strengthened beams are occurred on average 72% and 73% within 70 days for un-cracked and cracked section from the time when the sustained load was applied, while it is occurred about 76% and 83% over a period 70 days for un-strengthened beams. Thus, it is concluded that attachment of FRP sheet not only reduces the Instantaneous deflection but it is also more effective in controlling the longterm deflection under sustained load.

607

Fig. 13. RC beams with different CFRP ratios for cracked section: (a) total deflection, (b) time-dependent deflection, (c) ratios of time-dependent to instantaneous deflection.

4.2.3. Comparison of test results with analytical predictions Effective modulus approach based on the recommendation of ACI committee 435R-95 [32] was used to compute the instantaneous and long-term deflections of CFRP strengthened reinforced concrete beams. The instantaneous and long-term deflections were predicted based on the applied sustained loads by including the beam self-weight using this method. ACI recommended creep and shrinkage model are adopted in this study in evaluating time dependent deformation. The experimental deflections at the midspan are compared with the analytically predicted behaviour. In the analysis for the predictions of long-term deflections, the creep coefficient obtained earlier from the compressive tests and the shrinkage strains measured from the drying shrinkage tests were used to get the close comparison with the experimental results. The creep strain of the FRP composite laminate also needs to be evaluated. Unidirectional carbon fiber is considered to behave as linear elastic materials and it was showed by Plevris and Triantafillou [22] that carbon fiber laminates are practically creep free. Based on the outcome of that study, the creep coefficient of CFRP laminates is considered as zero for the long-term analysis of the

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Table 7 Deflection of RC beams strengthened with CFRP laminates.

a

Beam

FRP ratio, qfrp (%)

Instantaneous deflection (mm)

Time-dependent deflection (mm)

Total deflectiona (mm)

Time-dependent/ instantaneous deflection

CBU FBU-1L FBU-2L FBU-3L CBC FBC-1L FBC-2L FBC-3L

0 0.4 0.8 1.2 0 0.4 0.8 1.2

0.42 0.38 0.35 0.33 1.38 0.99 0.84 0.69

0.27 0.17 0.15 0.12 0.9 0.45 0.38 0.31

0.69 0.55 0.5 0.45 2.28 1.44 1.22 1.00

0.642 0.447 0.428 0.363 0.652 0.454 0.452 0.449

Total deflection = instantaneous deflection (after load application) + time-dependent deflection (at the end of 6 months period).

section. Once the concrete creep coefficient, shrinkage strains and CFRP laminates creep coefficient are known, and then the instantaneous and long-term deflections are calculated using the effective modulus approach. Test results were collected up to 180 days after the sustained loading as mentioned in Table 2 were imposed on the experimental beams. Transformed gross sectional properties were used in the calculation. Deflection predictions were made for all the period of time at which experimental reading were also recorded at the same time due to the same sustained load. The total deflections are the sum of the instantaneous deflection and the deflections due to the inclusion of creep and shrinkage effects. The predicted mid-span deflections are compared to the experimental results in Fig. 14a–d under sustained loading for un-cracked beams with different CFRP configurations. In the case of un-cracked beams CBU, FBU-1L, FBU-2L and FBU-3L, a reasonable prediction of the deflection is achieved using the effective modulus method for the beams strengthened with CFRP laminates, and this includes instantaneous deflection instantaneously after loading throughout the entire loading period. Due to the unequal reinforcement at the top and

bottom faces, along with the creep, the shrinkage deformation will also occur in these beams. Thus, it can be seen that the total deflection predicted using effective modulus approach is slightly overestimated compared with the experimental results. However, a close fit is observed between the predictions of the EMM approach and the experimental results for the un-cracked beams especially for the control specimen. As can be seen from Fig. 14a–d, long-term deflection using effective modulus method gives better predictions at the initial period while it shows slight difference at the end of 6 months. In general, the analytical results give conservative estimations for the long-term deformation of the test beams. Beam with crack section compares the theoretical prediction of deflections at mid-span to the experimental results of the beams subjected to a sustained load greater than their cracking load. Typical comparison of experimental deflections for beams CBC, FBC-1L, FBC-2L and FBC-3L with the predictions of the analytical method are presented in Fig. 15a–d. The figures show that the method based on effective modulus method predicts the long-term deflection of the test beams very well for the cracked beam. Difference between the predicted and experimental results of the cracked

Fig. 14. Long-term deflection of un-cracked beam: (a) un-strengthened (CBU), (b) single (FBU-1L), (c) double (FBU-2L), and (d) triple layers (FBU-3L).

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609

Fig. 15. Long-term deflection of cracked beam: (a) un-strengthened (CBC), (b) single (FBC-1L), (c) double (FBC-2L), and (d) triple layers (FBC-3L).

beams is observed because the beams behave in a rather inelastic manner, contrary to the assumed elastic behaviour. The creep that occur immediately following load application may also cause the experimental curve to concave slightly downward. It can be seen that the experimental deflection is slightly lower than the theoretical predicted deflection. It is observed that the experimental results of the beams reinforced with carbon fiber laminate are in reasonable agreement with the predicted values. The rate of increase of long-term deflection changes with time. This is particularly evident when compared to the predicted long-term deflection with the test results. From Fig. 15a–d, analytical method based on EMM approach provides a closer fit to the experimental results for the cracked beams especially for the control specimen. In general, it is seen that the long-term deflection of the cracked beams using analytical approach mentioned in this study again gives conservative estimate of the experimental results. This can be attributed to the proper accounting of the effects of carbon fiber laminates in the tensile zone of the beams. Under the sustained loads, concrete in the compression zone undergoes creep, and the curvature of a cross section increases, leading to increased deflection of the beam. It is also observed that the addition of carbon fiber resulted in a higher load at which yielding of the tensile reinforcement occurs. This is due to the CFRP composite laminates carrying stresses across the tensile zone in the cracked section. Plevris and Triantafillou [22] showed that the analytical predictions which overestimated the experimentally measured timedependent deflections for reinforced concrete beams with externally bonded FRP strips. Plevris and Triantafillou assumed a fully cracked cross section wherever the beam moment exceeded the cracking moment. That is, tension stiffening was not accounted for. It can be seen that, the predicted long-term deflections overestimated with the experimental values those which take account without tension stiffening. Calculations without concrete tension stiffening overestimate the deflection. The tension stiffening model

used in this study is based on Branson formula (refer to analytical study section). This model is presented in the following section for FRP bonded sections. Inclusion of a material parameter in the tension stiffening model can give closer estimation of the experimental results. 4.2.4. Modified concrete tension stiffening For the cracked beam section, in addition to the creep coefficient and ultimate shrinkage strain, another factor which can influence the analytical result is the tension stiffening, noting that concrete has the ability to carry tensile stress between cracks in the tension zone due to the bond between the steel and concrete. The tension stiffening model used in this study was similar to that mentioned in ACI 440 [40] model. It is noted that most of the research was conducted before using GFRP as reinforcement in reinforced concrete. There was no value specified for ab when using CFRP. In the present study, this model has been modified by the CFRP bond-dependent coefficient (ab) to get a closer estimation of the experimental results in calculating long-term deflection for CFRP strengthened RC beams. The predicted mid-span deflections of RC beams (with and without tension stiffening) are compared to the experimental results in Fig. 16a–c for the cracked beams FBC-1LC, FBC-2L and FBC-3L respectively. The importance of including the effect of tension stiffening in the deflection calculation based on modified model through the CFRP bond-dependent coefficient is showed in these Fig. 16a–c. It is clear from these results that the calculation without the concrete tension stiffening effect overestimates the long-term deflection of the beams. However, if the concrete tension stiffening is taken into account, the predicted values are comparable to the experimental results. Moreover, the calculated instantaneous and time-dependent deflection were achieved best-fit by changing the value of CFRP bond-dependent coefficient (ab = 0.1) for the CFRP strengthened cracked RC beams. Finally, it is concluded that modified tension

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Fig. 16. Long-term deflection of cracked beams with and without tension stiffening effects: CFRP laminates of (a) single (FBC-1L), (b) double (FBC-2L), and (c) triple layers (FBC-3L).

stiffening model gives better prediction for the long-term deflection calculation of CFRP strengthened cracked RC beams. 5. Conclusions Both the bending and time-dependent performance of carbon fiber strengthened RC beams are experimentally investigated and compared with the analytical results. Based on experimental and theoretical investigations the following conclusions are made: 5.1. Flexural behaviour 1. The result of the experimental study indicates that externally bonded CFRP laminates is an effective method to strengthen the reinforced concrete beams and improve the structural load carrying capacity. 2. Regarding the effect of number of layers, an increase in flexural stiffness, yield load, and ultimate load is achieved with the increase of carbon fiber laminate layers. It seems that the beam behaves as if the plate was thicker and no inter-layer de-lamination is observed in all cases. Nevertheless, the possible brittle failure of the strengthened beams still needs to be considered. 3. Regarding the effect of transverse edge strip, significant improvement in flexural strength was noted and the de-bonding of laminates occurred just before or at the final failure. The use of transverse edge strips increased the flexural capacity of strengthened beams by as much as 33% when compared to strengthened beams without edge strips. The W-wrapped CFRP edge strips arrest the propagating cracks more effectively than the U-shaped CFRP edge strips. 4. Beams strengthened with different CFRP layered have not reached their ultimate flexural capacity due to the effect of peeling and premature de-bonding failure of the laminates.

When the beams were strengthened with transverse CFRP edge strips, the mode of failure changed from flexural failure (yielding of steel reinforcement) to sudden rupture of the CFRP laminates. The use of the CFRP edge strips is more prominent since the full flexural capacity for the strengthened beams can be achieved in terms of end anchoring scheme. 5. It was also observed that the ultimate load carrying capacity cannot be increased uniformly by simply adding the number of CFRP laminates layers. This suggests that the gain in the ultimate flexural strength was more significant in beams with lower FRP reinforcement ratios with end anchoring scheme. From the experimental results it is clear that minimum one layer of CFRP sheets with end anchorage can give the desired results. 6. In general, theoretical flexural strength based on strain compatibility in the concrete, steel and CFRP reinforcement gave a reasonable prediction of the experimental results. A closer agreement for the ultimate load achieved provided the premature de-bonding of CFRP laminates can be prevented by using the transverse edge strips in the beam. 5.2. Time-dependent behaviour 1. The contribution of externally bonded carbon fiber reinforced polymer (CFRP) laminates to time-dependent deflection control of RC beams is distinctly proven. 2. From the experimental investigation, it is seen that the longterm deflection after a 6 month period was 64% and 65% higher to that of instantaneous deflection for the controlled un-cracked and cracked beams; whereas, it was on average 42% and 46% higher for the strengthened un-cracked and cracked beams respectively. This indicates attachment of FRP sheet not only reduces the instantaneous deflection but it is also effective in controlling the long-term deflection.

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3. The effectiveness of carbon fiber beams in reducing timedependent deflections is not to the same extent as in providing flexural strength, especially for beams subjected to lower sustained load levels. 4. Carbon fiber laminates attachment has considerable effects on the time-dependent deflection of reinforced concrete beams. In general, the larger the CFRP reinforcement ratio, the smaller was the long-term deflection. For the same sustained loading, a maximum reduction of 35% in deflection was observed in uncracked 3-layers strengthened beam (FBU-3L) as compared to the control one (CBU). Whereas for the cracked section (FBC3L), the corresponding reduction in deflection was 56% as compared to the un-strengthened beam (CBC). 5. In all cases, the theoretical predictions are giving conservative estimates of the experimental results for the test CFRP strengthened and un-strengthened RC beams. 6. In this study, the modified tension stiffening model based on ACI 440 approach is, in general, conservative; yielding an average difference of 18% with the experimental deflection at the end of 6 months. Finally, it is concluded that ACI 440 approach incorporating modified tension stiffening model was found to predict the time-dependent deflections of the test reinforced concrete beams very well.

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