Investigations on behaviour of flexural deficient and CFRP strengthened reinforced concrete beams under static and fatigue loading

Construction and Building Materials 201 (2019) 746–762

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Investigations on behaviour of flexural deficient and CFRP strengthened reinforced concrete beams under static and fatigue loading Nawal Kishor Banjara a,b,⇑, K. Ramanjaneyulu a,b a b

Academy of Scientific and Innovative Research, CSIR Campus, Taramani, Chennai 600113, India CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India

h i g h l i g h t s
Experimental investigations on flexural deficient and CFRP strengthened RC beams under monotonic and fatigue loading.
Analytical Formulations for CFRP retrofit of flexural deficient RC beams.
S-N expression which integrates the degree of deficiency for evaluating the fatigue life of flexural deficient RC beams.
Inexpensive numerical models to supplement expensive and time consuming experimental investigations.
Numerical simulations of flexural deficient and CFRP strengthened RC beams under monotonic and fatigue loading.

a r t i c l e

i n f o

Article history: Received 28 August 2018 Received in revised form 28 December 2018 Accepted 2 January 2019

Keywords: Flexural deficient Monotonic and fatigue loading CFRP strengthening Numerical simulations S-N expression

a b s t r a c t In this study, experimental investigations are carried out on control (without flexural deficiency) and flexural deficient reinforced concrete (RC) beams with two levels (FD1-20% and FD2-30% deficient) of deficiency, under monotonic as well as fatigue loading. After confirming the load carrying capacities under monotonic loading, studies are carried out on flexural deficient RC beams under fatigue loading by considering four load ranges (20–55%, 20–65%, 20–75% and 20–85% of load carrying capacity of control beam, Puc). It is found that load carrying capacities of FD1 and FD2 RC beams are around 8% and 20% respectively less than that of control beam. But, the fatigue lives of flexural deficient RC beams FD1 and FD2 are drastically less than that of control beam. Fatigue lives of FD1 and FD2 beams under fatigue with load range of 20–75% of Puc are respectively only 4840 and 292 cycles compared with 1.07387 cycles for control beam. Flexural deficient RC beams are strengthened with CFRP fabric to attain the required moment carrying capacity and are tested under monotonic and fatigue loading. The fatigue lives of flexural deficient RC beams strengthened with one layer of CFRP fabric (SFD1 and SFD2) are increased beyond that of control beam. Further, numerical models are also developed to evaluate the performance of control, deficient and CFRP strengthened flexural deficient RC beams. The fatigue life evaluated by numerical simulations, based on the maximum fracturing strain comprising of contributions from the static loading, stress cycling and cyclic crack opening, corroborated well with that evaluated from experimental investigations. Numerical approach presented in this study would provide inexpensive means for assessing the fatigue life of deficient as well as CFRP strengthened flexural deficient RC beams and would help to devise an appropriate strengthening strategy to attain the required fatigue life. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Reinforced concrete structures undergo deterioration due to aging, environmental effects, increase in loads and errors during design and construction phases. When a material is stressed to

⇑ Corresponding author at: CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India. E-mail address: [email protected] (N.K. Banjara). https://doi.org/10.1016/j.conbuildmat.2019.01.010 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

its strength limit, micro crack initiation and propagation leads to excessive deformation and finally gets fractured. Many civil structures such as airport pavements, highway and railway bridges and offshore elements are continuously subjected to cyclic loads. Performance of these structures under fatigue loading has to be considered for ensuring their safety. Ultimate load carrying capacity of structure under fatigue load is far lesser than that under nonrepetitive type of load. Reinforced concrete structures often exhibit cracking caused by the action of corrosion of reinforcements.

N.K. Banjara, K. Ramanjaneyulu / Construction and Building Materials 201 (2019) 746–762

Material ageing and deterioration, in adequate reinforcements, change in usage, and overloading of structures lead to deficiency in flexural capacity of reinforced concrete structural elements and therefore require immediate attention. There are several methods, such as shotcrete jacketing, steel plates bonding, Fibrereinforced polymer (FRP) and external post-tensioning [26,8,29,4] for strengthening of deficient RC beams. Among these techniques, strengthening by FRP fabric/laminates is one of the most widely used method. Fibre-reinforced polymer (FRP), an advanced composite material that was first used in aerospace applications, is being applied in retrofit of civil structures. Due to its high strength-to-weight ratio, FRP material is being used specifically for strengthening of flexural members of concrete structures [22]. Rehabilitation of deteriorated reinforced concrete structures using carbon fibre reinforced polymers (CFRP) is gaining popularity due to high corrosion resistance, high strength, lightweight, durability, flexibility in application and low thermal conductivity. FRP sheets or plates are generally bonded to the tension faces of flexural elements to increase their bending capacity, or to their side faces to increase the shear capacity. The reinforced concrete beams strengthened with various types of FRP laminates were experimentally investigated by Grace et al. [18]. It was found that, in addition to the longitudinal layers, the fibers oriented in the vertical direction forming a U-shape around the beam cross section significantly reduce beam deflections and increase beam load carrying capacity. An analytical study on the flexural behaviour of reinforced concrete beams strengthened with externally bonded CFRP laminates was carried out by Ng and Lee [24]. Direct analytical procedure was developed to evaluate the flexural capacity of concrete beams strengthened with CFRP and to predict their failure modes. Kim and Aboutaha [21] investigated the effect of different variables, such as amount of CFRP and end CFRP anchorage system on the flexural capacity and ductility of CFRP strengthened beams. End CFRP diagonal anchorage system was found to enhance the flexural ductility. Ekenel et al. [13] carried out studies on the flexural strengthening of reinforced concrete (RC) beams with two FRP systems. Use of anchor spikes in fabric strengthening was found to increase ultimate strength, and use of mechanical fasteners can be an alternative to epoxy bonded pre-cured laminate systems. Six reinforced concrete beams strengthened using CFRP laminates were tested under different sustaining loads by Wenwei and Guo [31]. Results of the study shown that sustaining load levels at the time of strengthening have important influence on the ultimate strength of strengthened reinforced concrete beams. Flexural behaviour of reinforced concrete beams strengthened using Carbon Fibre Reinforced Polymer (CFRP) sheets was investigated by Esfahani et al. [15]. The effect of reinforcing bar ratio on the flexural strength of the strengthened beams was examined. The flexural strength and stiffness of the strengthened beams were found to be increased compared with that of control specimens. Obaidat et al. [25] developed a finite element model to analyse RC beams retrofitted with CFRP. From finite element analyses, the load-deflection behaviour, failure modes and crack patterns were obtained and compared with the experimental results. It was observed that behaviour of the retrofitted beams, significantly influenced by the length of CFRP. A study to determine the effectiveness of carbon fiber reinforced polymer (CFRP) sheets as a flexural repair system for Reinforced Concrete (RC) beams was carried out by Fayyadh and Razak [16]. CFRP sheets found to increase the flexural stiffness and the ultimate load capacity of damaged beams. The experimental tests were conducted on RC beams retrofitted by unconventionally arranged CFRP strips and on a reference (not retrofitted) one by Bocciarelli et al. [5]. The experimental outcomes proven that CFRP strips can improve the load carrying capacity of the retrofitted beams. An experimental and analytical study to investigate the

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flexural behaviour of reinforced concrete beams strengthened using carbon-fibre reinforced polymer (CFRP) laminate was carried out by Boukhezar et al. [6]. The experimental and analytical results indicated that the flexural capacity and stiffness of strengthened and repaired beams using CFRP laminates were increased compared with those of control beams. El-Gamal et al. [14] carried out experimental investigations on the flexural behaviour of reinforced concrete (RC) beams strengthened by using glass and carbon fibre reinforced polymers. All strengthened beams showed an increase in the load carrying capacity compared with the reference beams. Experimental and analytical studies on the flexural behaviour of fully composite steel-concrete I-girders strengthened by externally bonded carbon fibre reinforced polymer (EB-CFRP) sheets were conducted by Afefy et al. [2]. An analytical design procedure was proposed in order to obtain the moment of resistance of the composite girders. Extensive experimental studies were conducted and proved the efficiency of bonding fibre-reinforced polymers (FRPs) systems on reinforced concrete (RC) beams by Gheorghiu et al. [17]. Smallscale beams were loaded in fatigue for different number of cycles and subsequently tested monotonically upto failure. It was found that CFRP-concrete joint was altered by the fatigue loading without affecting the ultimate capacity of the beams. Carbon and glass fibre-reinforced polymers (CFRP and GFRP) were used to enhance the service load-carrying capacity of reinforced concrete bridge T-sectional girders by Wang et al. [30]. The results shown that an FRP-strengthened T-beam subjected to fatigue loading demonstrated excellent behaviour. To investigate the fatigue damage behavior of reinforced concrete (RC) beams strengthened with prestressed fiber reinforced polymer (FRP), a series of experiments were conducted by Xie et al. [32]. Based on the results, fatigue failure mechanism of the strengthened beams and an empirical formula was developed to predict the fatigue lives of such members. Dong et al. [12] conducted a study on the behaviour of RC beams strengthened with FRP sheets. The results showed that the FRP sheets can be used to significantly enhance the fatigue resistance of the beams strengthened. Hojatkashani and Kabir [19] carried out a study to investigate the effect of CFRP composites on the fatigue response of reinforced concrete beams. Out of six reinforced concrete (RC) beams, three were retrofitted with CFRP sheets and subjected to fatigue load cycles. Song and Yu [28] examined the fatigue performance of corroded reinforced concrete (RC) beams strengthened with CFRP sheets by carrying out experimental and analytical studies. Strengthening with one and two layers of CFRP sheets at low and medium corrosion levels, were found to be sufficient to increase the fatigue life, fatigue strength, and ultimate strength of the beam. Peng et al. [27] studied seven RC beams to examine the effects of different strengthening methods on the flexural fatigue performance of the beams. It is evident from the experimental results that strengthening with prestressed CFRP plates significantly enhanced the monotonic and fatigue performances of reinforced concrete beams. Al-Saadi and Al-Mahaidi [3] carried out experimental study of NSM carbon FRP bonded to concrete with adhesive under fatigue loading tests. Specimens were tested under different fatigue load ranges, finally equations were developed to predict fatigue lives. Response of carbon-fiber-reinforced polymer (CFRP) strengthened reinforced concrete (RC) beams under fatigue loading were experimentally investigated by Charalambidi et al. [9]. Two different amplitudes of cycles were investigated. Beams subjected to the low loading range, sustained more than 2 million cycles. Whereas beams subjected to the high loading range, sustained less number of cycles. Study on comprehensive prediction and design model for the fatigue life of reinforced concrete beams strengthened with NSM FRP composites was conducted by Chen and Cheng [10] and evaluated the effects of various important design parameters on

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the fatigue performance. The effects of corrosion on the fatigue behavior of reinforced concrete beams were experimentally investigated by Ma et al. [23]. Based on the fatigue studies, the loaddeflection, fatigue crack propagation, fatigue life and the failure modes of RC beams were discussed. A model for flexural stiffness calculation for the corroded beams was proposed. 1.1. Research significance From the review of existing literature, it is found that though many discrete works were carried out on response of CFRP strengthened flexural deficient RC structural members, the following issues are still open and require attention: (i) influence of different levels of flexural deficiency on fatigue behaviour of RC beams, (ii) effect of CFRP strengthening on fatigue life of flexural deficient RC beams, (iii) S-N expression for fatigue life estimation of flexural deficient RC beams with different levels of deficiency and (iv) numerical simulation of flexural deficient and CFRP strengthened RC beams under fatigue loading. In the present study, experimental and numerical investigations are carried out to understand the behaviour of flexural deficient and CFRP strengthened RC beams subjected to fatigue loading. Numerical models are also developed for carrying out numerical simulations to evaluate static and fatigue behaviour of control, flexural deficient and CFRP strengthened flexural deficient RC beams to complement the experimental investigations. 2. Experimental investigations on flexural deficient RC beams To assess the static and fatigue behaviour of flexural deficient reinforced concrete (RC) rectangular beams, experimental investigations are carried out on five control (C) and fourteen flexural deficient rectangular RC beams. Control beam is designed as per Indian Standard IS 456:2000 [20] as a balanced section. Specimens of 1800 mm overall length and cross section dimensions of 150 mm  200 mm are chosen for the study. The effective span of the beam is considered as 1500 mm as shown

in Fig. 1(a). Fe500 steel reinforcement bars are used. For control beam, three numbers of 12 mm diameter steel bars as beam bottom main reinforcement, two numbers of 8 mm diameter steel bars as hanger bars at beam top and 8 mm diameter two legged stirrups at 120 mm spacing are provided. Clear cover to reinforcement bar is 25 mm. Two levels of flexural deficiency, viz., 20% (designated as FD1) and 30% (designated as FD2) are considered in this study. Flexural deficiency is simulated by reducing the area of main reinforcement bars with respect to that of control beam. In practical applications, flexural deficiency due to insufficient reinforcement could happen due to an error in design or omission of steel bars during construction or uniform corrosion damage or due to overloading during service. The reinforcement details of control, flexural deficient (FD1 and FD2) beam specimens are shown in Fig. 1(b). To obtain strain in the reinforcement during testing, electrical resistance strain gages of 5 mm gauge length are affixed on main reinforcement bars. For casting of RC beams, concrete mix is designed with ordinary Portland cement, river sand and coarse aggregate of 10 mm and 20 mm size (60% is 10 mm size and 40% is 20 mm size) as constituents. Water cement ratio of 0.5 is adopted. Concrete with mix proportions of cement (1.0): fine aggregate (2.25): coarse aggregate (2.35) is used. In addition to the beam specimens, six cubes of size 150 mm  150 mm  150 mm and six cylinders of size 150 mm  300 mm, are cast to evaluate the material properties, such as compressive strength, split tensile strength and modulus of elasticity of concrete. For evaluating fracture energy, three concrete prism specimens of size 100 mm  100 mm  500 mm are cast and a central notch of 5 mm  20 mm is created after curing of 28 days. From the material test data, the average values of compressive strength, modulus of elasticity and split tensile strength of the concrete used in the present study are found to be 44.7 MPa, 31,500 MPa and 3.2 MPa, respectively. Notched prisms are tested under three-point bending. From the load versus crack mouth opening displacement (CMOD) curves, fracture energy is evaluated and found to be 126 N/m.

Fig. 1. (a) Geometry with cross section and (b) reinforcement [i) control, ii) FD1 (20% flexural deficiency) and iii) FD2 (30% flexural deficiency)] details of the RC beams.

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2.1. Behaviour of flexural deficient RC beams under monotonic loading Test setup used for experimental investigations is shown in Fig. 2(a). Four-point bending tests on six (two of each type) simply supported RC beams are carried out under monotonic loading using hydraulic actuator of 500 kN capacity. Rate of loading used in the study is 0.2 mm/min. With gradual increase in loading, flexural as well as shear cracks are formed initially. With further increase in loading, flexural cracks are dominated and beams are failed in flexural mode with excessive deformation. Load versus deflection plots of control, flexural deficient (FD1 and FD2) RC beams are shown in Fig. 2(b). First crack load, ultimate load, and deflection at failure of control and flexural deficient RC beams are presented in Table 1. Average load carrying capacity of control (C) beam and flexure deficient RC beam specimens FD1 and FD2 are found to be 99.68 kN, 91.83 kN and 79.19 kN, respectively. Load carrying capacities of flexural deficient RC beams (FD1 and FD2) are reduced when compared with that of control beam due to reduction in the moment carrying capacity of the beam with flexural deficiency. 2.2. Behaviour of flexural deficient RC beams under fatigue loading Based on ultimate load carrying capacity, Puc, of the control beam, ranges of fatigue loading are fixed. Control beams (C) are tested under fatigue loading with three load ranges i.e., with maximum load of 65%, 75% and 85% of Puc. Minimum load is chosen as 20% of Puc. The minimum load represented the non-varying permanent load such as dead load. The minimum fatigue load also ensures stability of test set-up. The flexural deficient RC beams FD1 and FD2 are tested under fatigue loading with four load ranges i.e., with maximum load of 55%, 65%, 75% and 85% of Puc and minimum load of 20% of Puc. The four-point bending test set up and the instrumentation as used during static testing are employed for fatigue tests also. Pre-programmed fatigue protocols with load ranges

described above are setup to run the servo-hydraulic actuator at loading frequency of 4 Hz. During fatigue testing, initially the load is applied monotonically up to the mean load of predetermined load range. The cyclic load is then applied using sinusoidal wave between the maximum and minimum loads. Due to fatigue load, strength and stiffness of the beam are degraded progressively. Under fatigue loading, flexural as well as shear cracks are formed initially. With further increase in number of cycles, flexural cracks are propagated and beams are failed in flexural mode. The failure in all the beams is due to fatigue fracturing of longitudinal tensile reinforcement bars. It is also observed that once the cracked are formed, no significant change in the crack pattern is observed with increase in number of cycles. The load versus displacement, strain in reinforcement bar and stiffness degradation with increase in number of cycles under fatigue with load range of 20–65% of Puc for control beam and flexural deficient RC beams FD1 and FD2 are shown in Fig. 3(a)–(c) respectively. Stiffness degradation under fatigue loading is evaluated. Stiffness is calculated as ratio of load range (Pmax  Pmin) to displacement range (dmax  dmin), at different cycles. 100% stiffness is assumed at first cycle. With increase in number of cycles, stiffness decreases and degradation in stiffness is evaluated with respect to that of first cycle. It is observed that stiffness degradation is faster in deficient beams compared with that in control beam. The fatigue life of deficient beam is much lesser than that of control beam. It is noted that flexural deficient RC beam FD2 failed faster than the flexural deficient RC beam FD1. Stiffness degradation in deficient beam FD2 is much faster than that in beam FD1. Number of cycles to fatigue failure of control and flexural deficient RC beams FD1 and FD2 under different load ranges are presented in Table 2. From Table 2, it is observed that the control beam did not fail even after one million cycles, under fatigue with load range of 20–65% of Puc. Large number of cycles and enormous time is required to complete a single fatigue test under lower range of loading. If there is reduction in reinforcement area due to uniform corrosion or omission of

120

Load, kN

100 80 60 40 20 0 0

(a)

5

Control Beam FD1 FD2 10 15 20 25 30 Deflection, mm

35

(b)

Fig. 2. (a) Schematic test set up (b) Load versus displacement plots of control and flexural deficient RC beams.

Table 1 First crack load, ultimate load, and deflection at failure of control and flexural deficient RC beams. Type of beam

Deficiency of the type (%)

First Crack Load (kN)

Ultimate Load (kN)

Average Load (kN)

Deflection at failure (mm)

Control-0%-1 Control-0%-2 FD1-20%-1 FD1-20%-2 FD2-30%-1 FD2-30%-2

0

18.34 18.71 18.50 17.86 17.62 16.54

97.62 101.74 90.54 93.12 78.03 80.36

99.68

32.52 34.18 30.25 31.13 29.50 31.42

20 20 30 30

91.83 79.19

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80

1 500000

70

1000 750000

80

100000 1000000

60

1000 750000

100000 1000000

60 Load, kN

Load, kN

1 500000

70

50

40

50 40

30

30

20

20

10

10

0

1

2 3 4 5 Displacement, mm

6

500

7

1000 1500 2000 Strain in reinforcement ( )

70 Stiffness Degradation (%)

750

2500

60 50 40 30

20 10 0

0

0.2

0.4 0.6 0.8 1 Number of Cycles, N x106

1.2

(a) Fatigue behaviour of control beam 1 100000

70

1000 161400

10000 161475

1 100000

70

1000 161400

10000 161475

60

Load, kN

Load, kN

60

80

50

50

40

40

30

30

20

20

10

10

1

2

3 4 5 6 Displacement, mm

7

60 50 40 30

20 10 0

500

8

70

Stiffness Degradation (%)

80

1000 1500 2000 2500 3000 Strain in reinforcement ( )

0

3500

45000 90000 135000 180000 Number of Cycles, N

(b) Fatigue behaviour of flexure deficient beam FD1 (20% deficiency)

1 50000

70

1000 69600

80

25000

1000 69600

Load, kN

50 40

50 40

30

30

20

20

10

10

1

2

3 4 5 6 Displacement, mm

7

8

70

25000

60

60 Load, kN

1 50000

70

Stiffness Degradation (%)

80

60 50

40 30 20 10 0

300

800 1300 1800 2300 2800 3300 Displacement, mm

0

20000 40000 60000 Number of Cycles, N

80000

(c) Fatigue behaviour of flexure deficient beam FD2 (30% deficiency) Fig. 3. Load versus displacement, strain in reinforcement bar and stiffness degradation behaviour under fatigue loading with load range of 20–65% of Puc.

Table 2 Comparison of number of cycles to fatigue failure of control (C) and flexural deficient (FD1 and FD2) RC beams obtained from experimental studies. Designation of the Specimen

Control Beam (C) Puc = 99.68 kN

FD1 Pu = 91.83 kN

FD2 Pu = 79.19 kN

Load Range

C-0%-20-65 C-0%-20-75 C-0%-20-85 FD1-20%-20-55 FD1-20%-20-65 FD1-20%-20-75 FD1-20%-20-85 FD2-30%-20-55 FD2-30%-20-65 FD2-30%-20-75 FD2-30%-20-85

Load

Min. % Puc

Max. % Puc

Min. kN

Max. kN

20 20 20 20 20 20 20 20 20 20 20

65 75 85 55 65 75 85 55 65 75 85

19.94 19.94 19.94 19.94 19.94 19.94 19.94 19.94 19.94 19.94 19.94

64.80 74.76 84.73 54.82 64.80 74.76 84.73 54.82 64.80 74.76 84.73

Number of cycles to fatigue failure (Nf) (Experimental) >10,00,000* 1,07,387 5750 7,97,298 1,61,482 4940 72 7,08,443 69,660 292 **

Note:– *After 1 Million cycles, test is stopped, Pmin – minimum load; Pmax – maximum load; **FD2 beams are not tested under this load range as maximum load of load range is higher than the beam capacity.

751

0.8 0.7 0.6

Control

500

FD1

400

FD2

Stress Range,

Normalized Load Range, ∆P/Puc

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0.5 0.4

0.3 0.2 0

0.5

1 1.5 2 Number of cycles, N x106

300 200 Control FD1 FD2

100

0

2.5

1

(a) Normalized load range Vs no. of cycles

2

3

4 5 Log (N)

6

7

(b) ∆σ in steel reinforcement Vs log (N)

Fig. 4. Fatigue life of control and flexural deficient (FD1 and FD2) RC beams.

reinforcement bar, fatigue life at the same load level reduces drastically with respect to that of control beam. Plots of normalized load range (defined as ratio of load range – DP (i.e. Pmax  Pmin) to ultimate load of control beam– Puc) versus number of cycles to fatigue failure (Nf) of control beam and flexure deficient RC beams FD1 and FD2 are presented in Fig. 4(a). The strain data acquired from strain gages affixed on reinforcement bars during fatigue testing is used to determine the stresses in steel reinforcement bars. Fig. 4(b) shows the relationship between the stress range in the steel bar at the centre of beams and total number of cycles to fatigue failure. These plots can be used for evaluation of fatigue life of control beam and deficient RC beams. If level of flexural deficiency is known, Fig. 4(a) can be used or if stress range is known, Fig. 4(b) can be used to evaluate fatigue life of RC beams.

are presented in Table 3. The average value of ‘b’ is found to be 0.031.

f ðxÞ ¼ a  0:031lnðxÞ

Step 2:– By fitting fatigue data of control and flexural deficient RC beams FD1 and FD2 to Eq. (2), the value of coefficient ‘a’ is evaluated for each deficiency ratio (bFD) namely, 0.2 and 0.3. The values of coefficient ‘a’ are found to be 0.7973 and 0.7827 for bFD values of 0.2 and 0.3 respectively. For obtaining the relation between bFD and coefficient ‘a’, linear relation (ax + b) is arrived and is given in Eq. (3).

a ¼ 0:9098  0:4664bFD

where Pn ¼ For arriving at S-N expression which is dependent on the level of flexural deficiency, multilevel linear regression analysis is carried out using the procedure proposed in the following. Step 1:– Logarithmic fit of experimental fatigue data of control (C) and flexural deficient (FD1 and FD2) RC beams are carried out individually using the following expression.

f ðxÞ ¼ a þ b lnðxÞ

ð1Þ

ð3Þ

Step 3:– From Eqs. (2) and (3), a unified S-N expression is arrived for flexural deficient RC beams as given in Eq. (4).

ln N ¼ 29:35  32:26Pn  15:05 bFD

3. S-N expression for fatigue life of deficient RC beams

ð2Þ

DP P uc

ð4Þ

is normalized load range with respect to ultimate

load of control beam, ‘N’ is the number of cycles to fatigue failure and ‘bFD’ is the flexural deficiency ratio. In this study, ‘bFD’ is taken as 0.2 and 0.3. By using Eq. (4) which is dependent on the level of flexural deficiency, fatigue life of RC beam/girder can be evaluated for normalized load range and for the known deficiency level. Using this equation, the number of cycles to failure of a specimen under fati-

where ‘a’, ‘b’ are constants. The coefficients of regression for control and flexural deficient (FD1 and FD2) RC beams are evaluated. However, in order to determine the dependence of the regression parameter on flexural deficiency, value of coefficient ‘b’ is fixed at first. In the present study, the value of ‘b’ is taken as average of the three regression coefficients (from logarithmic fit of fatigue data of control and flexural deficient RC beams FD1 and FD2). The value of coefficient ‘b’ obtained from fitting of individual fatigue data of control and deficient specimens are evaluated and

Table 3 Coefficient ‘b’ from fitting of individual fatigue data of control and deficient specimens. Specimen Name

Coefficient

Value

Control FD1 FD2 Average, b

b1 b2 b3

0.034 0.031 0.029 0.031

Fig. 5. S-N curves for control (C) and flexure deficient (FD1 and FD2) RC beams.

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gue with different load ranges are obtained for control and flexural deficient (FD1 and FD2) RC beams. S-N curves developed based on the proposed S-N expression, for flexural deficient RC beam as given in Eq. (4), are presented in Fig. 5. S-N plots can also be generated for other levels of flexural deficiency using the proposed S-N expression integrated with level of flexural deficiency. If the flexural deficiency is known, fatigue life of a structure can be evaluated using Eq. (4). The integrated S-N expression will be useful to evaluate the number of cycles to fatigue failure of RC beams with known flexural deficiency and to plan for appropriate retrofit strategy.

4. Methodology for CFRP strengthening of flexural deficient RC beams Carbon fibre reinforced polymer (CFRP) fabric is chosen for strengthening of flexural deficient RC beams. Fig. 6 shows strains and corresponding stresses in conventional reinforcement and CFRP fabric reinforcement of RC beam of rectangular cross section under flexure at ultimate limit state as per ACI 440 [1]. Methodology to evaluate the number of CFRP layers required for strengthening of flexural deficient RC beams is presented in the form of flowchart in Fig. 7.

Fig. 6. Internal strain and stress distribution in CFRP strengthened RC beam of rectangular section under flexure at ultimate limit state (ACI 440).

Area of reinforcement (Ast), Area of CFRP (Af) = n wf tf n =no. of CFRP layers, wf = width of CFRP, tf = thickness of CFRP Assume neutral axis depth, c

Check adequacy of assumed CFRP layers Revise no. of layers, if required Calculate moment carrying capacit

The strain in steel reinforcement,

Effective strain in CFRP reinforcement,

Calculate strain in steel and composite matrix based on strain compatibility

Revise neutral axis depth, c No

Effective stress in CFRP, Effective stress in steel,

Calculate stress level in respective material

Whether, Fc = FT

Calculate internal forces; Compressive force: Tensile forces: force in steel bar, Fs = Force in CFRP, Ffe= Total tensile force, Fig. 7. Procedure for CFRP strengthening of RC beams.

Yes

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Based on procedure presented in flow-chart, a single layer of CFRP fabric is found to be sufficient for the moment carrying capacity of flexural deficient RC beams FD1 and FD2 to reach upto that of the control beam. Hence, one layer of CFRP fabric is used for strengthening of the flexural deficient RC beams FD1 and FD2.

adhesive material. Material properties of Sikadur-330 and CFRP fabric are obtained from manufacturer’s catalogue and are given in Table 4. Strengthening of flexural deficient RC beams FD1 and FD2 is carried out using one layer of CFRP fabric as shown in Fig. 8(d).

5. Experimental investigations on CFRP strengthened flexural deficient RC beams

5.1. Behaviour of CFRP strengthened flexural deficient RC beams under monotonic loading

Before starting of the CFRP strengthening, soffit of the deficient RC beam is prepared properly and adhesive material is mixed properly as shown in Fig. 8(a) and (b) respectively. CFRP fabric (Sika wrap 450C) which is used for strengthening of flexural deficient RC beams is shown in Fig. 8(c). Sikadur-330 is used as

After curing CFRP fabric impregnated with epoxy for seven days, CFRP strengthened flexural deficient beams, labelled as SFD1 and SFD2 are tested under monotonic loading. Strengthened RC beams are failed due to tearing of the CFRP fabric into small strips followed by yielding of reinforcement bars. Load deflection plots of

Fig. 8. (a) Surface preparation, (b) mixing of adhesive material, (c) CFRP fabric and (d) CFRP strengthened beams.

Table 4 Material Properties of CFRP Fabric and Epoxy. FRP Composite

Modulus of Elasticity (N/mm2)

Tensile Strength (N/mm2)

Elongation at Break (%)

Layer Thickness (mm)

Epoxy (Sikadur-330) Dry Fibre (Sikawrap-450C)

3800 230,000

30 4000

0.9 1.7

0.8–1.0 0.255

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Fig. 9. (a) Load displacement plots of control (C), flexural deficient (FD1 and FD2) and CFRP strengthened flexural deficient (SFD1 and SFD2) RC beams, (b) typical failure pattern of strengthened RC beam SFD1 and (c) typical failure pattern of strengthened RC beam SFD2.

control, flexural deficient (FD1 and FD2) and CFRP strengthened flexural deficient (SFD1 and SFD2) RC beams are presented in Fig. 9(a). Typical failure patterns of CFRP strengthened RC beams (SFD1 and SFD2) are shown in Fig. 9(b) and (c). From Fig. 9(a), it may be seen that load carrying capacity of CFRP strengthened flexural deficient (SFD1 and SFD2) RC beams reached closer to that of control beam. Hence, it is observed that one layer of CFRP fabric is found to be sufficient for strengthening of flexural deficient (FD1 and FD2) RC beams considered in this study. 5.2. Behaviour of CFRP strengthened flexural deficient RC beams under fatigue loading After confirming load carrying capacities of CFRP strengthened RC beams under monotonic loading, experimental investigations

are carried out on fatigue behavior of CFRP strengthened flexural deficient RC beams (SFD1 and SFD2) for four load ranges, viz., 20–55%, 20–65%, 20–75% and 20–85% of Puc. Under fatigue loading also, beams are failed by tearing of CFRP fabric into small strips followed by yielding and fracturing of reinforcement bars. Initially, shear and flexural cracks are developed and with increased loading flexural cracks are propagated upto compression zone and finally beams are failed in flexural mode. The fatigue failure in all the beams is due to fracturing of longitudinal tensile reinforcement bars. It is also observed that once cracks are formed, no significant changes in crack pattern is observed with increase in number of cycles. Fig. 10 shows failure pattern of SFD1 RC beam under fatigue loading. Fig. 11(a)–(c) respectively show the load versus displacement, load versus strain in reinforcement bar and stiffness degradation versus number of cycles of SFD1 under fatigue loading with load range of 20–65% of Puc. Similarly, Fig. 11(d) and (e)

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3D nonlinear cementitious material is used for modelling of concrete. The nonlinear behavior of concrete in the biaxial stress

(a) Overall failure pattern

(b) Fracturing of reinforcement bar Fig. 10. Failure pattern of SFD1 RC beam under fatigue loading.

respectively show the load versus displacement and stiffness degradation versus number of cycles of SFD2 due to fatigue loading with load range of 20–65% of Puc. Due to continuous fatigue loading, stiffness of the beam is degraded which resulted in increased crack growth and deformation and causing finally the failure of the beam. Results of fatigue investigations carried out on CFRP strengthened flexural deficient RC beams are presented in Table 5. From the results presented, in Table 2 for control and flexural deficient beams; in Table 5 for CFRP strengthened flexural deficient beams, it may be observed that the fatigue lives of flexural deficient RC beams strengthened with one layer of CFRP fabric are increased. Stress versus number of cycles to fatigue failure of 20% and 30% flexural deficient beams along with that of the corresponding CFRP strengthened flexural deficient RC beams are compared in Fig. 12 (a) and (b) respectively. 6. Numerical investigations on flexural deficient (FD) and CFRP strengthened flexural deficient (SFD) RC beams It is observed that the time required to conduct fatigue experiments under lower load range is enormous. Though the computational studies can not be claimed as substitutes for experimental investigations, experimentally validated numerical models can complement the experimental investigations and can effectively help in acquiring insight into the problem domain. Hence, numerical models of control, flexural deficient and CFRP strengthened flexural deficient RC beams are developed for carrying out numerical investigations. The details are presented in the following sections. 6.1. Numerical simulations of control and flexural deficient RC beams Numerical investigations are carried out on control (C) and flexural deficient (FD1 and FD2) RC beams using finite element software ATENA. Macro models of concrete beams are generated by first creating key points followed by lines, surfaces and volumes. Further, steel plates at loading and supporting points are created by volume elements. Macro model of control beam with steel plates at loading points and supports is shown in Fig. 13(a). Master and slave criteria are assigned between the beam and steel plates. Loading and monitoring points are also assigned. Main reinforcements, hanger bars and stirrups are created at the respective positions as per details of reinforcements furnished in Fig. 1. In this study, reinforcements are modelled as discrete bars. Numerical model of reinforcement bars of control beam is shown in Fig. 13 (b). Bilinear stress strain law is assumed for all the reinforcements.

state is described by effective stress ref c and the equivalent uniaxial strain, eeq . The equivalent uniaxial stress-strain diagram for concrete is as shown in Fig. 13(c). Trial analyses are carried out by varying the mesh size in order to obtain the optimum mesh density. Tetrahedral elements with 4 to 10 nodes are used for modelling of concrete. An optimum mesh size of 25 mm is adopted for further numerical investigations in this study. Finite element model of control beam with plates at loading points and supports is shown in Fig. 13(d). Similar models with appropriate reinforcement details of flexural deficient RC beams are also developed. Load is applied at one-third span points. The load is applied in steps/increments as required by Newton Raphson method, in order to predict the nonlinear behaviour. 6.1.1. Validation of numerical models of control and flexural deficient RC beams under monotonic loading Numerical models of control (C) and flexural deficient RC beams (FD1 and FD2) are validated by comparing the results of numerical investigations with the experimental results as shown in Fig. 14 (a)–(c), respectively. Load carrying capacity and deflection of the RC beams obtained from the numerical simulation are found to be within the ±5% variation with respect to the results of experimental study, except for specimen FD1. The crack formations observed in experimental and numerical investigations carried out on control beam specimen are shown in Fig. 14(d) and (e), respectively. Upon validation of the numerical models of control and flexural deficient RC beams under monotonic loading, further numerical studies are carried out under fatigue loading using the validated numerical models. 6.1.2. Numerical simulations of control and flexural deficient RC beams under fatigue loading The formulation for simulation of response under high-cycle fatigue was proposed by Dobromil et al. [11]. In the fractureplastic material model proposed by Cervenka and Papanikolaou [7], crack growth is controlled by the maximum fracturing strain, f f (emax ). The maximum fracturing strain (emax Þis composed of contris butions from the static loading (emax Þ, stress cycling (erfat Þand cyclic

crack opening (eCOD fat Þ.

f emax ¼ esmax þ erfat þ eCOD fat

ð5Þ

Fatigue damage is caused by increase in the maximum fracturing strain due to (i) cycling of tensile stresses and (ii) crack opening and closing in each cycle. The former is dominant before cracking occurs and controls the crack initiation. The latter is dominant in cracked material and controls growth of existing cracks. The strain due to cycling of tensile stress is obtained by

erfat ¼

wfat Lt

ð6Þ

where wfat is fatigue fracturing displacement for the given stress and is to be determined from softening law shown in Fig. 15. Lt is the crack band size. The strain due to crack opening and closing is obtained by

eCOD fat ¼

wCOD fat Lt

and wCOD fat ¼ n  nfat  Dw

ð7Þ ð8Þ

where ‘n’ is number of cycles applied, ‘Dw’ denotes the difference between the maximum and minimum crack opening during a cycle.

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75

1 100000

75

10000 515000

55 45

1 100000

65 Load, kN

Load, kN

65

1000 250000

10000 515000

55 45

35

35

25

25

15

15 1

2

3

4 5 6 7 Displacement, mm

8

500

9

1500 2500 3500 4500 Strain in reinforcement bar

(a) SFD1

5500

(b) SFD1 75

50

1 100000

1000 250000

10000 485000

65

40

55 Load, kN

Stiffness Degradation (%)

1000 250000

30

20

45 35

10

25

0

15

0

150000 300000 450000 Number of Cycles, N

600000

1

(c) SFD1

3

5 7 Displacement, mm

9

11

(d) SFD2

Stiffness Degradation (%)

60

50 40 30

20 10 0 0

150000 300000 450000 Number of Cycles, N

600000

(e) SFD2 Fig. 11. (a) Load versus displacement of SFD1, (b) load versus strain in reinforcement bar of SFD1, (c) Stiffness degradation versus number of cycles of SFD1, (d) Load versus displacement of SFD2 and (e) Stiffness degradation versus number of cycles of SFD2 under fatigue loading with load range of 20–65% of Puc.

The material parameter nfat scales the damage contribution from cyclic crack opening and closing. f The maximum fracturing strain (emax ) as calculated above is incorporated in the material model. For fatigue analysis, number of cycles (N) are applied in increments and levels of damage are evaluated. In first step, minimum load is applied. In second step, load is applied upto maximum load.

In third step, load is applied in reverse cycle upto minimum load and then in fourth step, damage is calculated. Steps two to four are repeated till the specimen is failed. From numerical analysis, fatigue lives of control and flexural deficient (FD1 and FD2) RC beams are evaluated and are presented in Table 6. Good correlation is observed between the results of numerical and experimental fatigue investigations.

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N.K. Banjara, K. Ramanjaneyulu / Construction and Building Materials 201 (2019) 746–762 Table 5 Number of cycles to fatigue failure of CFRP strengthened flexural deficient RC beams (SFD1 and SFD2) for different load ranges obtained from experimental studies. Designation of the Specimen

SFD1

Load Range

SFD1-20%-20-55 SFD1-20%-20-65 SFD1-20%-20-75 SFD1-20%-20-85 SFD2-30%-20-55 SFD2-30%-20-65 SFD2-30%-20-75 SFD2-30%-20-85

SFD2

Load

Min. %Puc

Max. %Puc

Min. kN

Max. kN

20 20 20 20 20 20 20 20

55 65 75 85 55 65 75 85

19.94 19.94 19.94 19.94 19.94 19.94 19.94 19.94

54.82 64.80 74.76 84.73 54.82 64.80 74.76 84.73

Number of cycles to fatigue failure (Nf) (Experimental) >10,00,000* 515,472 364,153 12,528 >10,00,000* 485,520 163,500 6472

0.8

FD1

0.7

SFD1

0.6 0.5

0.4 0.3 0.2

Normalized Load Range, (∆P/Puc)

Normalized Load Range, (∆P/Puc)

Note:- *After one million of cycles, test is stopped.

0 0.5 1 1.5 2 2.5 3 Number of Cycles, N x106

0.8

FD2

0.7

SFD2

0.6 0.5 0.4 0.3 0.2

0

(a) FD1, SFD1

0.4 0.8 1.2 1.6 2 Number of Cycles, N x106

(b) FD2, SFD2

Fig. 12. Normalized load range versus number of cycles to fatigue failure of (a) 20% flexural deficient (FD1) and CFRP strengthened (SFD1) beams and (b) 30% flexural deficient (FD2) and CFRP strengthened (SFD2) beams.

6.2. Numerical simulations of CFRP strengthened flexural deficient RC beams

tangential stiffness are evaluated based on the stiffness of the adjacent finite elements using Eq. (10).

Geometry of CFRP strengthening system is generated by creating points, lines and surfaces. After creating surface of CFRP system, volume is created by extruding 1 mm in the normal direction. After this, it is necessary to model epoxy resin, CFRP fabric reinforcement, and connection between CFRP system and RC beam. Proper material properties as given in Table 4, are assigned. CFRP reinforcement is modelled as 2D quadrilateral membrane elements which behaves like composite material to capture orthotropic behavior. Epoxy resin is modelled as matrix and CFRP fabric is modelled as a smeared reinforcement. Smeared reinforcement is specified only in one direction (i.e. fibre direction) and orthotropy is included in the material model. This modelling requires input for the material parameters of epoxy resin (matrix) and input for the parameters of CFRP fabric (reinforcement). Interface material model is used to simulate interface between CFRP system and RC beam. The interface is modelled based on Mohr-Coulomb criterion with tension cut-off. The constitutive relation for a general threedimensional case is given in terms of tractions on interface planes and relative sliding and opening displacements. Linear bond-slip relationship for the interface is assumed in both tangential and normal directions as given in Eq. (9).

K¼

8 9 > < s1 > =

2

ktt s2 ¼ 6 4 0 > : > ; r 0

0 ktt 0

9 38 > < Dv 1 > = 7 0 5 Dv 2 > > : ; Du knn 0

ð9Þ

where (s) is the shear stress and (r) is the normal stress. The Knn and Ktt denote the initial elastic normal and shear stiffness, respectively. Friction coefficient of 0.3 is used in this study. Normal and

Econcrete  10 element size

ð10Þ

Using Eq. (10) interface stiffness is evaluated and is found to be 12.6  106 MN/m3. Numerical model of CFRP strengthened flexural deficient beam is as shown in Fig. 16(a). 6.2.1. Validation of numerical models of CFRP strengthened flexural deficient RC beams under monotonic loading Results obtained from finite element analysis of numerical models of CFRP strengthened flexural deficient RC beams SFD1 and SFD2 with single layer of CFRP fabric are validated with the experimental results as shown in Fig. 16(b) and (c), respectively. Load carrying capacity and maximum deflection of the CFRP strengthened deficient RC beams obtained from the numerical simulations are found to be within the ±5% variation with respect to results of the experimental study. Further, numerical models are also developed for flexural deficient beams strengthened with two, and three layers of CFRP fabric and are designated as SFD11L, SFD1-2L and SFD1-3L; SFD2-1L, SFD2-2L and SFD2-3L. Load versus deflection plots for CFRP strengthened flexural deficient RC beams SFD1 and SFD2 with different number of CFRP fabric layers are shown in Fig. 17(a) and (b) respectively. From the results of the study on flexural deficient beams strengthened with two or three layers of CFRP fabric, it is noted that load carrying capacities of SFD1-2L and SFD1-3L are respectively 24% and 30% higher than that of the control beam. Similarly, load carrying capacities of SFD2-2L and SFD2-3L are respectively 18% and 22% higher than that of the control beam. The enhancement in load carrying capacity of flexural deficient RC beam when strengthened with three layers of CFRP fabric is not much compared with that

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Fig. 13. (a) Macro model of beam (b) reinforcement details of concrete beam (c) uniaxial stress-strain law for concrete and (d) finite element model with loading and reactions.

when two layers of CFRP fabric are used for strengthening. Also, when three layers of CFRP fabric are used, ductility is reduced. It may be due to concrete crushing. Hence, it is concluded that, maximum improvement in the load carrying capacity for the cases considered in this study is achieved when two layers of CFRP fabric are used for strengthening.

6.2.2. Numerical simulations of CFRP strengthened flexural deficient RC beams under fatigue loading Numerical simulations are carried out on RC beams strengthened with one layer of CFRP fabric (SFD1 and SFD2) subjected to fatigue loading with load ranges of 20–55%, 20–65%, 20–75% and 20–85% of Puc. The minimum load is kept constant at 20% of Puc

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100

100

80

Load, kN

Load, kN

80

60

60

Experimental Study

40

40

Numerical Study

20

Experimental Study

20

0 0

5

10

15 20 25 Deflection, mm

30

Numerical Study

0

35

0

5

10 15 20 Deflection, mm

(a) Control

25

30

(b) FD1 100

Load, kN

80 60

40

Experimental Study

20

Numerical Study

0 0

5

10

15

20

25

30

35

Deflection, mm

(c) FD2

(d) Crack patterns of control beam (Experimental)

(e) Crack patterns of control beam (Numerical) Fig. 14. Validation of (a) Control beam (b) Flexural deficient beam –FD1 and (c) Flexural deficient beam –FD2, (d) crack patterns in control beam (experimental) and (e) crack patterns in control beam (numerical).

Fig. 15. Softening law and fatigue damage.

for all the cases. The maximum load is set as 55%, 65%, 75% and 85% of Puc for different cases. Load cycles (N) are applied in increments and levels of damage are evaluated. Number of cycles to fatigue failure of SFD1 and SFD2 beams are evaluated for all the load ranges considered in this study. A typical fatigue behaviour of SFD1 beam under the load range of 20–65% of Puc is shown in Fig. 18. Comparison of number of cycles to fatigue failure of flexural deficient RC beams strengthened with one layer of CFRP fabric is presented in Table 7. From the numerical investigations, it is found that fatigue lives of deficient RC beams strengthened with one layer of CFRP fabric are increased and could sustain more cycles compared with control beam. Best fit of normalized load range (Pn = DP/Puc) versus number of cycles

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Table 6 Comparison of fatigue lives of control and flexural deficient (FD1 and FD2) RC beams as obtained from experimental and numerical studies. Designation of the Specimen Control

C-0%-20-55 C-0%-20-65 C-0%-20-75 C-0%-20-85 FD1-20%-20-55 FD1-20%-20-65 FD1-20%-20-75 FD1-20%-20-85 FD2-30%-20-55 FD2-30%-20-65 FD2-30%-20-75 FD2-30%-20-85

FD1 (20% deficient)

FD2 (30% deficient)

Number of cycles to fatigue failure (Nf) (Experimental)

Number of cycles to fatigue failure (Nf) (Numerical)

**

>10,00,000* 1,07,387 5750 7,97,298 1,61,482 4940 72 7,08,443 69,660 292

28,65,000 21,45,000 1,49,300 9700 6,50,000 1,90,400 4200 50 6,22,100 50,500 200

***

***

Note: * After 1 Million cycles, test is stopped. ** Beam are not tested under this load range. *** Load carrying capacity of RC beam is lower than the maximum load of load range

(a)

100

100

80

80

Load, kN

120

Load, kN

120

60 40 Experimental Study Numerical Study

20 0 0

10

20 30 Deflection, mm

60 40

Experimental Study Numerical Study

20 0

40

0

(b) SFD1

10

20 30 Deflection, mm

40

(c) SFD2

Fig. 16. (a) Numerical model of CFRP strengthened beam, (b) validation of numerical model SFD1beam and (c) validation of numerical model SFD2 beam.

to fatigue failure of control beam and CFRP strengthened flexural deficient RC beams (SFD1 and SFD2) is presented in Fig. 19. S-N expression for CFRP strengthened flexural deficient RC beams is proposed as given in Eq. (11).

ln N ¼ 23:03  21:27P n

ð11Þ

Further, numerical simulations are also carried out by modelling deficient RC beams strengthened with two layers of CFRP fabric. Number of cycles to fatigue failure of deficient RC beams strengthened with two layers of CFRP fabric are presented in Table 7. It is found that strengthening with two layers of CFRP fabric has further increased fatigue life of the beams. It can be

concluded that the numerical models developed in present study can be adopted for evaluating the fatigue behaviour of CFRP strengthened flexural deficient RC beams of real structures with different levels of flexural deficiency, under different load ranges.

7. Conclusions Experimental and numerical investigations are carried out on control, flexural deficient (FD1 – 20% deficiency; FD2 – 30% deficiency) and CFRP strengthened flexural deficient (SFD1 and SFD2)

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120

100

100

Load, kN

140

Load, kN

140 120

80 60

SFD1-1L-Exp SFD1-1L-Num SFD1-2L-Num SFD1-3L-Num

40 20 10

20 30 Deflection, mm

60 SFD2-1L-Exp SFD2-1L-Num SFD2-2L-Num SFD2-3L-Num

40 20

0 0

80

40

0

0

10

(a) SFD1

20 30 Deflection, mm

40

(b) SFD2

Fig. 17. Load versus deflection plots of flexural deficient RC beams strengthened with one, two and three number of CFRP fabric layers (a) SFD1 and (b) SFD2.

0.8

60

Load, kN

50 40 30 20

10 0 0

5

10 15 Deflection, mm

20

Normalized Load Range, (∆P/Puc)

70

Control

SFD1

SFD2

0.7 0.6 Best fit line 0.5 0.4 0.3

ln N = 23.03 - 21.28 Pn

0.2 0

1 2 Number of Cycles, N x 106

3

Fig. 18. Fatigue behaviour of CFRP strengthened flexural deficient RC beam (SFD1) under the load range of 20–65% of Puc.

Fig. 19. S-N plots for control beam and flexural deficient RC beams strengthened with one layer of CFRP fabric (SFD1 and SFD2) based on numerical study.

RC beams under monotonic and fatigue loading. Based on the study, the following conclusions are drawn:

(iii) To improve the load carrying capacity and fatigue life, flexural deficient RC beams are strengthened with CFRP fabric to attain the required moment carrying capacity. The load carrying capacity of flexural deficient RC beams strengthened with one layer of CFRP reached closer to that of control beam. One layer of CFRP fabric has improved the load carrying capacities of flexural deficient RC beams FD1 and FD2 by 17.27% and 31.77% respectively. (iv) The fatigue lives of flexural deficient RC beams strengthened with one layer of CFRP fabric (SFD1 and SFD2) are increased beyond that of control beam. Under fatigue with load range of 20–75% of ultimate load carrying capacity of control beam (Puc), fatigue lives of SFD1 and SFD2 are 3,64,153 and 1,63,500 cycles compared with 1,07,387 cycles for control beam.

(i) From the experimental investigations carried out on control and flexural deficient (FD1 – 20% deficiency; FD2 – 30% deficiency) RC beams under monotonic loading, it is found that load carrying capacities of 20% and 30% flexural deficient RC beams are around 8% and 20% respectively less than that of control beam. (ii) The fatigue lives of flexural deficient RC beams FD1 and FD2 are alarmingly far less than that of control beam. For example, under fatigue with load range of 20–75% of ultimate load carrying capacity of control beam (Puc), fatigue lives of FD1 and FD2 beams are respectively 4840 and 292 cycles compared with 1.07387 cycles for control beam.

Table 7 Comparison of fatigue lives of CFRP strengthened deficient RC beams SFD1 and SFD2 as obtained from experimental and numerical studies. Designation of the Specimen

Number of cycles to fatigue failure (Nf) (Experimental) with one layer of CFRP

Number of cycles to fatigue failure (Nf) (Numerical) One Layer

Two Layers

SFD1

>10,00,000* 6,15,472 3,64,153 12,528 >10,00,000* 4,85,520 1,63,500 6472

20,30,000 7,25,800 2,50,600 8200 16,70,000 5,90,600 2,10,400 5100

>20,00,000 11,80,500 4,35,650 15,800 >20,00,000 8,25,400 3,85,300 11,500

SFD2

SFD1-20%-20-55 SFD1-20%-20-65 SFD1-20%-20-75 SFD1-20%-20-85 SFD2-30%-20-55 SFD2-30%-20-65 SFD2-30%-20-75 SFD2-30%-20-85

Note:- *After one million of cycles, test is stopped.

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(v) Numerical investigations on control, flexural deficient beams (FD1, FD2) and flexural deficient RC beam strengthened with single, double and triple layered CFRP fabric (SFD1-1L, SFD1-2L and SFD1-3L; SFD2-1L, SFD2-2L and SFD2-3L) are carried out. It is found that load carrying capacities of SFD1-2L and SFD1-3L are respectively 24% and 30% higher than that of the control beam. Similarly, load carrying capacities of SFD2-2L and SFD2-3L are respectively 18% and 22% higher than that of the control beam. The enhancement in load carrying capacity of flexural deficient RC beam when strengthened with three layers of CFRP fabric is not much compared with that when two layers of CFRP fabric are used for strengthening. (vi) The fatigue life evaluated by numerical simulations based on the maximum fracturing strain comprising of contributions from the static loading, stress cycling and cyclic crack opening, corroborates well with that evaluated from experimental investigations. Fatigue lives under load range of 20–75% of ultimate load carrying capacity of control beam (Puc), for control, flexural deficient beams FD1 and FD2 from experimental study are respectively 1,07,387, 4940 and 292 cycles; whereas from numerical study these are respectively 1,49,300, 4200 and 200 cycles. (vii) Fatigue lives under load range of 20–75% of ultimate load carrying capacity of control beam (Puc), for flexural deficient RC beams strengthened with one CFRP layer (SFD1 and SFD2) from experimental study are respectively 3,64,153 and 1,63,500 cycles; whereas from numerical study they are respectively 2,50,600 and 2,10,400 cycles. (viii) It can be stated that the validated numerical models can provide alternate means for evaluating the fatigue life of RC beams with different levels of flexural deficiencies and different load ranges and help in minimizing the need for resorting to the costly and time consuming experimental investigations.

Acknowledgement Authors express acknowledgements to the staff of Structural Testing Laboratory at CSIR-Structural Engineering Research Centre for the help during the experimental study. Funding No funding. Conflict of interest No conflict of interest. References [1] ACI 440.2R-08, Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures, American Concrete Institute, USA, 2008. [2] H.M. Afefy, K. Sennah, H. Akhlagh-Nejat, Experimental and analytical investigations on the flexural behavior of CFRP-strengthened composite girders, J. Constr. Steel Res. 120 (2016) 94–105. [3] N.T.K. Al-Saadi, R. Al-Mahaidi, Fatigue performance of NSM CFRP strips embedded in concrete using epoxy adhesive, Compos. Struct. 154 (2016) 419–432.

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