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Hindawi Advances in Civil Engineering Volume 2019, Article ID 4981750, 17 pages https://doi.org/10.1155/2019/4981750 Research Article FlexuralStrengtheningandRehabilitationofReinforcedConcrete Beam Using BFRP Composites: Finite Element Approach 1 2 1 Asaad M. H. Kadhim , Hesham A. Numan, and Mustafa Ozakça Civil Engineering Department, University of Gaziantep, Gaziantep 27310, Turkey Civil Engineering Department, Faculty of Engineering, Al-Mustansiriayah University, Baghdad 10052, Iraq Correspondence should be addressed to Asaad M. H. Kadhim; ak23674@mail2.gantep.edu.tr Received 17 November 2018; Revised 7 January 2019; Accepted 22 January 2019; Published 4 March 2019 Academic Editor: Giovanni Minafo` Copyright © 2019 Asaad M. H. Kadhim et al. /is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Basalt ﬁber-reinforced polymer (BFRP) is adopted widely in recent years in many countries to rehabilitate or strengthen structural elements such as reinforced concrete (RC) beams because it is cheap and it has stellar mechanical performance. By activating the ﬁnite element (FE) simulation, the present research submits an extensive study on the strengthening and rehabilitation of damaged full-scale RC beams due to corrosions in the main reinforcement caused by BFRP sheets. Diﬀerent parameters were taken into consideration such as corrosion grade, BFRP wrapping schemes, and the number of layers. /e ﬂexural performance of the models that build up as the control model and the damaged and the repaired methodologies by BFRP that are adopted and tested by others under the eﬀects of four-point static loadings were also underwent examination. /e full interaction at BFRP-concrete interface and the full bonding between sheets presupposed were investigated for all models. /e numerical analysis ﬁndings were compared with the experimental measurements and found to be in good agreement. /e current numerical analysis proved that the ultimate load rised by 14.8% in spite of 20% corrosion in the ﬂexural steel rebar under eight layers of BFRP composite and bottom wrapping mode. In addition, under all strategies of wrapping schemes, the ﬁndings also indicated that the deﬂection ductility index noticeably reduced for RC beams with BFRP composites compared to the control beam. Finally, all the results of midspan deﬂection, crack patterns, and strain response of the composite system were analysed and discussed brieﬂy. with the CFRP reinforcement to raise the performance of 1. Introduction ductility which has been carried out by Rezazadeh et al. [3]. Since the cost of rehabilitation for RC beams is roughly less Garyfalia et al. [4] studied the strength capacity of reinforced than that of rebuilding them, the engineers therefore used concrete beams that corroded rebars by reviewing the an- diﬀerent practical strategies to retroﬁt the existing RC beams alytical and experimental approaches that focused within with poor structural features. One of the most widespread this limit, then proposed a model to predict the ﬂexural strategies employed is ﬁber-reinforced polymer (FRP) capacity of the beams at yield load, and veriﬁed the model by family, for example, glass FRP (GFRP), carbon FRP (CFRP), comparing the results with the available experimental data and basalt FRP (BFRP). /e FRP family has some advantages that showed closeness. such as light weight, low cost, ease in ﬁxing, superior Ma et al. [5] proposed a model for computing the thermomechanical properties, and high resistance to cor- stiﬀness of corroded beams after fatigue using ﬂexural stiﬀness computation. /is model mainly comprises the rosion as compared to other families [1]. GFRP that is used in RC beams as conﬁned materials can minimize the amount inﬂuences both of corrosion-induced cracking and fatigue. of cracks and also increase the ﬂexural capacity of beams [2]. Elghazy et al. [6] performed 3D FE modelling of corrosion- A developed three-dimensional (3D) FE model is used with damaged RC beams strengthened in ﬂexure with externally the near-surface-mounted strategy of strengthened slabs and bonded composites. /ey used three parameters in the 2 Advances in Civil Engineering Under repeated loading, Attari et al. [23] studied the investigation which are corrosion levels, type of composite, and the number of composite layers. Good agreement was cost-eﬀectiveness of twin stratum carbon-glass FRP fabric as a strengthening arrangement of RC structures. According to achieved between the analytical and experimental outcomes; therefore, they conﬁrmed that the FE models were able to long-term cyclic loadings, Zhao et al. [24] observed that the emulate the nonlinear demeanor of the strengthened beams. presence of BFRP resisted more cyclic stresses without fa- Ye et al. [7] studied the shear performance of corroded tigue happening. Long-term tests on RC beams that reinforced concrete beams in which the numerical results strengthened by BFRP were conducted by Atutis et al. [25]; indicated that FRP strengthening as the wrapping or the results of this study pointed out that the BFRP has U-shaped bonding of FRP sheets was eﬀective to improve resistance to creep. Micelli et al. [26] studied the predamage status of concrete cylinders with 100 mm in diameter and the shear strength of RC beams. /e results of the study accomplished by Huang et al. 200 mm in length at the diﬀerent preloading levels with the existence unidirectional FRP sheets. [8] pointed out the inﬂuence of strengthening RC by BFRP is insigniﬁcant on precracks of concrete. /e GFRP that is /e failure modes of tested walls strengthened by BFRP sheets were diﬀerent in a reference wall (without the used in the RC beams as conﬁned materials can minimize the amount of cracks and also increase the ﬂexural capacity presence of BFRP sheets) based on the experimental study of beams [9]. Fiore et al. [10] pointed out that the load submitted by Zhou et al. [27]. Daghash and Ozbulut [28] capacity of the structural member increased based on the investigated the ﬂexural behaviour of RC beams reinforced mechanical properties of BFRP. According to the exper- with near-surface-mounted BFRP bars. /e outcomes of this imental work accomplished by Duic et al. [11] and Chen study indicated that the existence of BFRP bars worked to et al. [12], the eﬀective method to increase the ﬂexural restore the original beam strength capacity and gave a more ductile behaviour. Garyfalia et al. [29] investigated the be- strength of RC beams is by bounding the RC beams with external BFRP sheets. Garyfalia et al. [13] investigated the haviour and failure modes of the corroded rebars of rein- forced concrete beams with experimental tests indicating eﬀectiveness of patch repair and FRP-bonded laminates to retroﬁt reinforced concrete beams with corrosion damage that the presence of the FRP-laminated sheet enhanced the strength and behaviour of the corroded beams. and concluded from experimental test data that the shear strengthening improved the bond performance. Diﬀerent BFRP ratios were used as the main re- /e main conclusions by Shen et al. [14] were the RC box inforcement by Tomlinson and Fam [30] to investigate the beam repaired by BFRP worked to conﬁne the development eﬀects of these ratios on the behaviour and strength capacity crack of concrete, besides the increased stiﬀness and the of the RC beams. /e test results proved that the ultimate natural frequency of the repaired beam at the rate of 16.6% and yield loads were increased with the ﬂexural re- and 8.0% as compared with the beam without repair, re- inforcement ratio. Under static and dynamic loadings, the test results of mechanical properties of BFRP showed that spectively. Due to the mechanical properties of the BFRP, the experiential ﬁndings proved that the RC beam strengthened the dynamic strength of BFRP was around twice than that under static loading based on the investigation submitted by by BFRP behaved as linear up to failure based on the study conducted by Pawłowski and Szumigała [15]. Chen et al. [31]. /e mechanical properties of the BFRP indicated that After exposing the pullout specimens to accelerated they have durable, high-temperature resistance as in- conditioning environments and under direct tensile load, troduced by Sim et al. [16]. Furthermore, at elevated tem- Altalmas et al. [32] observed that the GFRP bars showed perature, Lu et al. [17] observed that the pultruded GFRP lower adhesion and bond strengths to concrete than the plates and glass ﬁber rovings and the basalt-ﬁber roving and BFRP bars. Dong et al. [33] investigated the bond durability BFRP plates showed much better mechanical tensile prop- of BFRP bars, and steel-ﬁber-reinforced composite bars erties and temperature resistance. under the eﬀects of the ocean environment for a long-term period. In the damaged cylinder strengthened by BFRP, Ma Under seismic loading, Jiang et al. [18] pointed out that the repaired RC columns by using BFRP restored the et al. [34] observed that the initial elastic modulus and the ultimate compressive strength of the BFRP-conﬁned con- ﬂexural capacity more than the original columns. Ibrahim et al. [19] performed the experimental test on concrete crete tended to minimize with an increase in the level of the columns reinforced by steel basalt-ﬁber composite bars, predamage. and the test results showed that the failures of all four Al-Saidy and Al-Jabri [35] noticed that the eﬀect of columns were ﬂexural. Cascardi et al. [20] studied three replacing the damaged concrete cover of corroded beams by full-reversible FRP-conﬁnement innovative techniques of using CFRP worked to increase the yield and ultimate load heritage masonry columns. Minafo` et al. [21] explored the capacities of damaged beams. Besides that, the U-shaped strips had a similar eﬀect on the ultimate capacity and compressive behaviour of eccentrically loaded slender masonry columns conﬁned by FRP and found that the ductility as replacing the concrete cover because it was successful in preventing debonding failure. /e test results of eﬀects of conﬁnement vanished in case of length greater than 20. Rousakis [22] observed the reinforced concrete the study introduced by Choi et al. [36] conﬁrmed that the strengthened T-beams prestressed by CFRP (near-surface- columns that were reinforced by nonbonded composite ropes subjected to seismic loadings that focused on the mounted technique) worked to enhance both the service- damage buildup and control at member level that may ability performance and the ultimate load-carrying capacity prevent the collapse. as compared with the unstrengthened beam. Minafo et al. Advances in Civil Engineering 3 [37] analysed the stress-strain behaviour as a literature re- /e relationship connection between the re- view of masonry conﬁned by FRP and compared the analysis inforcements (main and stirrups) with concrete is the perfect interaction, besides the concrete nodes at the in- results with available experimental data. Monaco et al. [38] analysed masonry panels strengthened by FRP using ﬁnite teraction with the same nodes of reinforcements. /e elements method and suggested simpliﬁed analytical for- connection between BFRP and concrete interface is under mulations and compared the analysis results with experi- the full degree of interaction though embodiment of the mental data from literatures. coating epoxy layer is more than enough at the interface zone (rigid regions and kinematic constraints) so that no slip and strain slip occur between them and to complete the 2. Aim and Significance of Research bonding achieved between BFRP layers. /e concrete was /e main aim of this article is to assess and emulate in- modelled as a homogeneous and isotropic material. On the ﬂuences of green substance (BFRP sheets) on a performance contrary, the assumed plane sections remain plane after of corroded RC beams when subjected to four-point static deformation and that matched with consideration of the Bernoulli–Euler hypothesis. /e stress-strain for re- loadings. To achieve this aim, a series of numerical analyzes were performed by using the commercial FE package inforcements is elastic-full plastic, and for BFRP, it is of ANSYS [39]. linear relationship. Full interactions were found between Based on the literature survey of this study, besides a main and secondary reinforcements with surrounding thorough deep seeking, to the best of the published re- concrete and no interactions between reinforcements and searches that accomplished by the authors, really scarce BFRP. studies simulated the inﬂuence of the hybrid action BFRP /e tolerance (convergence) of the solution found using composite on the demeanour and trend of RC beams using the Newton–Raphson iterative method was 5%, while it was FE approach. /erefore, it has become necessary to ﬁll this considered inﬁnite with displacement control. /e applied hiatus of researches through activating FE simulation in load was divided into substeps, and the model mesh was ANSYS package [39] to solve this issue. Hence, eight full- selected to reduce solution time and obtain an accurate solution, in which the maximum substeps is 150, substeps scale beam models are submitted and simulated in this research. On the contrary, the present study gives us an 100, and minimum substeps 1, and the number of steps for opportunity to visualize about the actual structural per- convergence occurred within this limits is shown in Table 1. formance of RC beams that are strengthened and re- Loadings, boundary condition, RC beam conﬁguration, habilitated by external BFRP layers without restoring to the distribution of BFRP layers, and mechanical properties of experimental tests that always need more time and some- the components of the composite system were all adopted what costly. from the study of Duic et al. [11] to verify the validity of the outcomes of the current study. 3. Finite Element Approach 4. Mechanical Properties of Materials In the current study, the numerical analyses are conducted based on the FE approach by using commercial ANSYS According to the mechanical properties for each of the software [39] to simulate all arrangement patterns of BFRP concrete, reinforcements with no hardening, and BFRP in the RC beam models. Diﬀerent elements are accurately reported by Duic et al. [11], these properties were adopted in selected from this program to emulate the behaviour of the current study as the required inputs in the ANSYS strengthening and rehabilitation of corroded RC beams by package [39]. Table 2 shows the mechanical properties of all BFRP layers. /e main elected elements are SOLID65, components present in the technical sheet of BFRP from LINK180, SOLID185, and SHELL181. SOLID65 is acti- suppliers. vated to represent the concrete component because this element is capable of emulating both cracking in tension 5. Configuration of Finite Element Models and crushing in compression; this element has eight nodes, and at each node, it has three degrees of freedom (DOFs). /e current model of beam was built with dimensions Due to the discussion of the uniaxial tension-compression 275 × 500 × 3200 mm with simply supported boundary situation in LINK180, this element is selected to emulate conditions as illustrated in Figure 1. /e main re- the demeanor, both main and stirrups reinforcements in all inforcements at the bottom face were 5ϕ10 and 5ϕ15 mm, models. LINK180 is composed of two nodes with three while at the top face, it was 2ϕ10 mm, and the stirrups were DOF at each node. On the contrary, SOLID185 is applied ϕ10 at 250 mm center to center. Each rebar of 10 mm in 2 2 to simulate the supports and the plates under the applied diameter has 100 mm , while 15 mm has 200 mm , as loads. SOLID185 has stress stiﬀening, plasticity, large calculated by Duic et al. [11], the cross-sectional area so deﬂection, and large strain susceptibilities, and it con- that the reinforcement ratios were 0.41 and 0.83%, tained eight nodes with three DOFs. To emulate the BFRP respectively. layers, SHELL181 is activated because it is suitable for Two techniques were introduced for BFRP wrapping of analysing thin to moderately thick shell components. RC beams that are midspan and bottom. /e midspan SHELL181 is composed of four nodes, and at each node, it technique contained A and B schemes, while the bottom has six DOFs. technique composed of C and D schemes. /e scheme A is 4 Advances in Civil Engineering Table 1: Number of steps for each model. 6. Comparison of Experimental and Numerical Results Model B1 B2 B3 B4 B5 B6 B7 B8 Number of steps for 13 13 15 16 13 14 16 13 Table 4 and bar charts in Figures 6 and 7 illustrate the convergence comparison of the yield and maximum deﬂections gathered from the experimental study [11] and the present numerical analysis (the deﬂections at yield load that is the load which Table 2: Mechanical properties of the composite system. caused the ﬁrst crack at the yield loadings within 40% of the Properties Concrete Reinforcement BFRP ultimate load and the maximum deﬂection that occurred at Compressive strength (MPa) 37 430 — the ultimate applied load). /ree principle statistical con- Splitting tensile strength (MPa) 3.62 — — cepts were carried out to investigate the degree of agreement Modulus of rupture (MPa) 4.11 — — between the experimental and the numerical results. /e ﬁrst Modulus of elasticity (MPa) 28600 200000 20400 one was the arithmetic mean which is a result of the division Poisson’s ratio 0.15 0.30 0.30 the summation of observations by the number of observa- Tensile strength (MPa) — 420 1684 tions. /e second concept was the standard deviation, and it /ickness (mm) — — 0.33 refers to the square root of the arithmetic mean of the squares of deviations of observations from their mean value. composed of one layer with 100 mm width and 400 mm /e third concept was the variance which is the square of height of wrapping, while scheme B contained three or eight standard deviation. If the ﬁrst concept achieved unity, layers of BFRP composite with a full width of the cross smaller values of the standard deviations and variance ob- section. On the contrary, scheme C contained three layers of tained would signify that the degree of agreement between BFRP wrapping with a height of 150 mm and length of the experimental and the numerical outcomes is excellent. 2600 mm, while scheme D contained eight layers of BFRP To validate yield and maximum deﬂection of ﬁndings composite with a full width of cross section and length of that obtained from the current FE analysis, these ﬁndings 2600 mm. /e locations and dimensions of all schemes are were compared with those gathered from experimental illustrated clearly in Figure 2 in which the direction of the measurements [11]. Figure 6 depicts the comparison be- ﬁbers is horizontal (i.e., along the beam axis). /e direction tween numerical and experimental deﬂections at the yield of ﬁbers in all scheme cases is along the beam axis except A stage of loading, while Figure 7 illustrates the comparison of that is parallel to the stirrups that is shown in Figure 2. numerical and experimental deﬂections at the maximum Table 3 lists the models with descriptions in detail for each stage of loading. From the outcomes in Figures 6 and 7, the model. Twenty percent of the total cross-sectional area on computed arithmetic mean values of yield and maximum the tension steel in the lower three bars was taken away to deﬂections were 0.9941 and 1.003, respectively. Moreover, simulate the corrosion. the calculated standard deviations at the yield and maximum As described in Table 3, models B1 and B2 were deﬂections were 0.0327 and 0.0178, respectively, while the employed as control beams; and the percentages of main calculated variance ranged from 0.001 to 0.0003 of yield and reinforcement ratio of these models were 0.41 and 0.83%, maximum deﬂections. From the results of statistical con- respectively. Both the models B3 and B4 represented the cepts, it can be said that the FE results matched well with the RC beam strengthened using the midspan wrapping experimental ones. Hence, the present FE simulation proved technique, and diﬀerent percentages of ratios of main the ability to eﬀectively analyse the structural response of the reinforcement were used for each model, while B5 and B6 RC beams under externally strengthening or rehabilitating represented the RC beams strengthened using the midspan them by BFRP sheets. and bottom wrapping techniques, respectively, and also diﬀerent percentages of ratios of main reinforcement were 7. Results of Analysis and Discussions employed for each model. On the contrary, both B7 and B8 models have the same percentage of main reinforcement 7.1. Load-Deﬂection Performance. Figure 8 shows the be- ratio, that is, 0.66, but the B7 model is built with a loss of haviour and trend of load-deﬂection curves at midspan for all 20% of the main reinforcement area in the tension zone proposed models. /is ﬁgure represents the midspan de- without any wrapping technique, while B8 is modelled ﬂections for each model due to the incremental loadings up to with strengthening using the bottom wrapping technique the ultimate load. In all models, the slope behaviour of the and a lose of 20% of main reinforcement area in the load-deﬂection started from zero up to the elastic limit (in- tension zone. Figure 3 illustrates the 3D view of the RC ﬂection point) is the same but has diﬀerent values. /ese slopes beam, mesh density, elevation of the reinforcement, and represent the stiﬀness of the beam that becomes less in the case 3D of the reinforcement’s conﬁguration, while Figure 4 of lower strength loading capacity. In the case of less main represents the models B3, B4, and B5 and the BFRP strips, reinforcement, the load strength capacity of the model became and Figure 5 shows the models B6 and B8 and the BFRP less as compared with that of the model having a higher main strips. /e closed and open shear cracks coeﬃcients for reinforcement ratio. /e inﬂection point represents the load concrete assumed as 0.7 and 0.2 respectively that were producing cracks and the behaviour of the model transformed adopted to complete the requirements input for concrete from linear to nonlinear. /erefore, the change in load in ANSYS. strength capacity and the slope became less because the Advances in Civil Engineering 5 3200 mm 275 mm Top ϕ10 mm 3000 mm 250 mm Stirrups ϕ10 mm 500 mm @ 250 mm c/c 500 mm Bottom reinforcement ϕ10 mm or ϕ15 mm Figure 1: Beam conﬁguration and cross section [11]. 400 mm 500 mm 400 mm 100 mm (a) 150 mm 150 mm 500 mm 2600 mm (b) (c) B A (d) Figure 2: Wrapping techniques and sections: (a) midspan scheme, (b) bottom scheme, and (c) sections and (d) directions of BFRP along the beam axis for A, B, C, and D [11]. Table 3: Model descriptions. Model Main reinforcement ratio Number of BFRP Status Schemes mark at tension zone (%) layers B1 0.41 — Control — B2 0.83 — Control — B3 0.41 3 Strengthened Midspan B4 0.83 3 Strengthened Midspan B5 0.41 8 Strengthened Midspan B6 0.83 8 Strengthened Bottom B7 0.66 0 Loss of 20% of main reinforcement area — B8 0.66 8 Strengthened and loss of 20% of main reinforcement area Bottom Innovative model. 6 Advances in Civil Engineering (a) (b) (c) Figure 3: 3D view of the (a) RC beam model and (b) mesh model and (c) 3D conﬁguration of reinforcements. (a) (b) Figure 4: (a) Models B3, B4, and B5 using the midspan wrapping technique and (b) the BFRP strips. stiﬀness of the beam became less up to failure. /e experi- were near the line so that the numerical results can show mental beams from the experimental test [11] are drawn closeness with experimental and conservatives. separately and are compared with the models B1, B2, B3, B4, As shown in Figure 8(a), the maximum percentage was B7, and B8 in Figures 8(d) to 8(i), and they showed a closeness diﬀerent at the failure load occurred between B8 and B1 in behaviour and the results with some divergence. Table 5 lists models and was 57.14%, while the maximum diﬀerence of the comparisons between the test results as deﬂection at yield displacements at the failure took place between B1 and B6 and maximum for all models with that of the experimental test models and was 43.54 mm. /e outcomes of Figure 8 proved [11]. /e mean values of deﬂections at yield and maximum are that the stiﬀness of strengthening or rehabilitating models by rounded to unity which means very close results between the BFRP layers was more than that of two control models. In experimental and numerical analysis. /e standard deviations this ﬁgure, the numerical result of deﬂection at the yield and and variance were also very small which means that all points maximum stage for all models was compared with that are rounded near the mean values. Figures 8(b) and 8(c) gathered from the experimental study. Additionally, the full represent the comparisons between experimental and nu- behaviour of some models is drawn to compare with ex- merical analysis results that are drawn with line 45 . All results perimental results. In spite of losing 20% of ﬂexural steel Advances in Civil Engineering 7 (a) (b) Figure 5: (a) Models B6 and B8 using the bottom wrapping technique and (b) the BFRP strips. Table 4: Comparison of experimental and current FE approach (the yield and maximum deﬂections). Deﬂection (mm) Loadings (experimental)- Deﬂection (mm) (experimental) numerical (kN) (numerical) Model mark Yield Ultimate Yield Ultimate Yield Ultimate B1 6.80 61.80 (165)-165 (247)-247 6.63 61.80 B2 10.70 40.20 (265)-265 (397)-397 11.27 40.72 B3 7.50 40.10 (209)-215 (313)-313 7.18 40.00 B4 13.10 39.40 (324)-318 (487)-487 12.67 39.61 B5 NA NA NA -293 NA-375 6.26 22.54 B6 NA NA NA-335 NA-425 8.97 17.94 B7 10.50 50.00 (241)-251 (362)-362 10.67 50.40 B8 9.70 22.90 (301)- 321 (452)-452 9.66 22.67 NA: not applicable. 14 70 12 60 10 50 8 40 6 30 4 20 2 10 0 0 B1 B2 B3 B4 B7 B8 B1 B2 B3 B4 B7 B8 Model mark Model mark Maximum deflection (mm) (experimental) Yield deflection (mm) (experimental) Maximum deflection (mm) (numerical) Yield deflection (mm) (numerical) Figure 7: /e experimental and numerical maximum deﬂection vs. Figure 6: /e experimental and numerical yield deﬂection vs. model. model. rebar in the B8 model, it is noticed that the tendency curve of where L is the center to center span of the simply supported the B6 model was similar to the tendency curve of the B8 beam so that the deﬂection criteria at midspan are equal to model to a great extent. Moreover, the percentage diﬀerence 8.33 and 16.66 mm. /e second criterion adopted by some between these models at the failure load did not exceed researchers was the yield load which is Pu/1.5, in which Pu is 3.39%. /is is because of using the same wrapping technique the maximum sustained load that adopted here. /e 3D and the number of BFRP layers on these models. views of yield and maximum deﬂections for all beam models /e yield load and the load corresponding to the de- shown in Figures 9–16 represent the full performance of the ﬂection are equal to the two criteria such as L/360 and L/180, analysis results by ANSYS for whole models with all Yield deflection (mm) Maximum deflection (mm) 8 Advances in Civil Engineering 500 14 0 0 0 10203040506070 0 2 4 6 8 10 12 14 Displacement (mm) Experimental deﬂection at yield (mm) B1 B5 B8 B2 B6 L/360 B3 B7 L/180 B4 (a) (b) 60 500 0 0 0 102030405060 0 10203040506070 Experimental deﬂection at maximum (mm) Displacement (mm) B1 Experimental-B1 (c) (d) 500 500 450 450 0 1020304050 010 20 30 40 50 Displacement (mm) Displacement (mm) B2 B3 Experimental-B2 Experimental-B3 (e) (f) Figure 8: Continued. Load (kN) Numerical deﬂection at maximum (mm) Load (kN) Load (kN) Load (kN) Numerical deﬂection at yield (mm) Advances in Civil Engineering 9 450 450 350 350 300 300 250 250 200 200 150 150 100 100 50 50 0 0 0 1020304050 0 102030405060 Displacement (mm) Displacement (mm) B4 B7 Experimental-B4 Experimental-B7 (g) (h) 0 5 10 15 20 25 Displacement (mm) B8 Experimental-B8 (i) Figure 8: (a) Load-deﬂection performances at the midspan for all models. Deﬂection comparisons between experimental and numeri- cal analysis at the (b) yield stage and (c) maximum stage. Load-deﬂection compression for models (d) B1, (e) B2, (f) B3, (g) B4, (h) B7, and (i) B8. Table 5: Statistical comparison of experimental and current FE approach (the yield and maximum deﬂections). Deﬂection (mm) (experimental) Deﬂection (mm) (numerical) Ratio (numerical/experimental) Model mark Yield Ultimate Yield Ultimate Yield Ultimate B1 6.80 61.80 6.63 61.80 0.975 1.000 B2 10.70 40.20 11.27 40.72 1.053 1.013 B3 7.50 40.10 7.18 40.00 0.957 0.997 B4 13.10 39.40 12.67 39.61 0.967 1.005 B5 NA NA 6.26 22.54 NA NA B6 NA NA 8.97 17.94 NA NA B7 10.50 50.00 10.67 50.40 1.020 1.008 B8 9.70 22.90 9.66 22.67 0.996 0.989 Mean 0.994 1.002 Standard 0.035 0.008 deviation Variance 0.001 0.0001 Load (kN) Load (kN) Load (kN) 10 Advances in Civil Engineering –6.63809 –5.02127 –3.40446 –1.78765 –0.170837 –60.5554 –45.7964 –31.0374 –16.2784 –1.51944 –5.82968 –4.21287 –2.59606 –0.979243 0.637569 –53.1759 –38.4169 –23.6579 –8.89894 5.86005 (a) (b) Figure 9: 3D views of deﬂections in the B1 model at (a) the yield load stage and (b) the maximum load stage. –11.3766 –8.60463 –5.83267 –3.06071 –0.28875 –41.7142 –31.5503 –21.3865 –11.2226 –1.05875 –9.99061 –7.21865 –4.44669 –1.67473 1.09723 –36.6322 –26.4684 –16.3045 –6.14068 4.02318 (a) (b) Figure 10: 3D views of deﬂections in the B2 model at (a) the yield load stage and (b) the maximum load stage. –7.15898 –5.41748 –3.67599 –1.9345 –0.193009 –40.8351 –30.9137 –20.9923 –11.0709 –1.14951 –6.28823 –4.54674 –2.80525 –1.06375 0.677737 –35.8744 –25.953 –16.0316 –6.11021 3.81118 (a) (b) Figure 11: 3D views of deﬂections in the B3 model at (a) the yield load stage and (b) the maximum load stage. Advances in Civil Engineering 11 –12.5752 –9.51561 –6.45605 –3.39649 –0.336927 –39.6118 –29.9742 –20.3365 –10.6989 –1.06132 –11.0454 –7.98583 –4.92627 –1.86671 1.19285 –34.793 –25.1554 –15.5177 –5.88013 3.75749 (a) (b) Figure 12: 3D views of deﬂections in the B4 model at (a) the yield load stage and (b) the maximum load stage. –6.16517 –4.67231 –3.17945 –1.68658 –0.19372 –26.4222 –20.0242 –13.6262 –7.22821 –0.830227 –5.41874 –3.92588 –2.43301 –0.940151 0.552712 –23.2232 –16.8252 –10.4272 –4.02922 2.36876 (a) (b) Figure 13: 3D views of deﬂections in the B5 model at (a) the yield load stage and (b) the maximum load stage. deﬂection values along the span of the beam models. reinforcement ratio at the tension zone was 0.41. Table 6 lists Figures 9–16 represent the whole performance of the models the comparisons between numerical analysis and experi- under the eﬀects of yield and at maximum load stage that has mental data from test for ductility, and they showed been converted to the curve shown in Figure 8 that reads the closeness. results at the node that gave maximum deﬂection (at the Another important note recorded on the results in Ta- ble 6 is that the peak percentage of reduction in the de- center of bottom face for each model). ﬂection ductility index was determined when the model transferred from B1 to B6 and was about 78%. On the 7.2. Ductility. /e deﬂection ductility index for each model contrary, the minimal percentage of reduction in the de- is listed in Table 6, and the ratio between the midspan ﬂection ductility index was registered between B2 and B4 deﬂections at ultimate load to the midspan deﬂection at yield models and was 15.63%. /ese reasonable results were be- load was calculated. From Table 6, it is clear that the cause of the presence of BFRP sheets. /e absolute diﬀer- maximum deﬂection ductility index was 9.15 and took place ences of deﬂection values at the ultimate loading stage were at control beam B1 model when the percentage main somewhat huge compared to the absolute diﬀerences of 12 Advances in Civil Engineering –8.96979 –6.80084 –4.6319 –2.46295 –0.294004 –17.9396 –13.6017 –9.26379 –4.9259 –0.588008 –7.88531 –5.71637 –3.54742 –1.37848 0.790469 –15.7706 –11.4327 –7.09485 –2.75695 1.58094 (a) (b) Figure 14: 3D views of deﬂections in the B6 model at (a) the yield load stage and (b) the maximum load stage. –50.404 –38.1203 –25.8367 –13.553 –1.26941 –10.6693 –8.06876 –5.46825 –2.86774 –0.267238 –9.36901 –6.76851 –4.168 –1.56749 1.03302 –44.2621 –31.9785 –19.6949 –7.41123 4.87241 (a) (b) Figure 15: 3D views of deﬂections in the B7 model at (a) the yield load stage and (b) the maximum load stage. deﬂections at the yield loading stage, as clearly depicted in trend of such members under a diﬀerent strategy of BFRP Figure 8. /e increase of BFRP sheets number in the RC composites. beam was inversely aﬀected by the value of the deﬂection ductility index as clearly depicted when compared to the values at B3 model with B5 model (the same percentage 7.3.CrackMoment,ResistingMoment,andUltimateMoment. reinforcement ratio and wrapping strength technique). A For all proposed models, Table 7 illustrates the values of load at ultimate load in [11], besides the applied load, similar behaviour of the deﬂection ductility index was also diagnosed by Rezazadeh et al. [3], Attari et al. [23], and Choi yield load, crack moment, resisting moment (internal et al. [36], who used GFRP-CFRP hybrid fabrics, CFRP, and moments rely on the plastic analysis of the beam), and GFRP for the rehabilitation of samples. Duic et al. [11] and ultimate moment from the current numerical analysis. Attari et al. [23] also diagnosed that all strengthened From this table, it is clear that the maximum value of specimens showed less ductility than did the control sam- crack moment was recorded on the B8 model and was ples. From these considerations, it is possible to say that all 45.82 kN m. /e maximum crack moment was decreased the models implemented in the ANSYS program [39] of the by about 5.70%, 5.43%, 5.15%, and 5.65% when the present work are capable of eﬀectively simulating the actual analysis transformed from model B8 to control beams, Advances in Civil Engineering 13 –22.6777 –17.1033 –11.5288 –5.95428 –0.379789 –9.6501 –7.27798 –4.90586 –2.53373 –0.161612 –8.46404 –6.09192 –3.7198 –1.34767 1.02445 –19.8905 –14.316 –8.74152 –3.16703 2.40745 (a) (b) Figure 16: 3D views of deﬂections in the B8 model at (a) the yield load stage and (b) the maximum load stage. Table 6: Ductility index. Deﬂection (mm) (numerical) Ductility index Ductility index Ratio of ductility index Model mark (numerical) (experimental) [11] (numerical/experimental) Yield Ultimate B1 6.63 61.80 9.32 9.10 1.02 B2 11.27 40.72 3.61 3.80 0.95 B3 7.18 40.00 5.57 5.30 1.05 B4 12.67 39.61 3.13 3.00 1.04 B5 6.26 22.54 3.61 NA NA B6 8.97 17.94 2.00 NA NA B7 10.67 50.40 4.72 4.80 0.98 B8 9.66 22.67 2.35 2.80 0.84 Mean 0.98 Standard deviation 0.078 Variance 0.006 Table 7: Load stages, crack moment, resisting moment, and ultimate moment. Model P ultimate [11] P applied ANSYS P yield ANSYS Crack moment Resisting moment Ultimate moment mark (kN) (kN) (kN) (kN·m) (kN·m) (kN·m) B1 247 247 165 43.21 90.24 123.50 B2 397 397 265 43.21 177.29 195.00 B3 313 313 215 43.33 114.71 156.50 B4 397 397 318 43.33 201.45 243.50 B5 380 380 375 43.46 157.32 175.00 B6 435 435 425 43.46 239.79 200.00 B7 362 362 251 43.23 143.54 181.00 B8 452 452 321 45.82 204.87 226.00 models B3 and B4, models B5 and B6, and model B7, 243.50 kN m. /ese outcomes demonstrated that the ﬂexural respectively. /is is because there are eight layers of BFRP capacity of RC beams noticeably increased under the ex- in the model B8 that contributed to increasing the mo- ternally strengthened RC by BFRP sheets. ment of inertia for the model; besides these layers worked to restrict the tension zone. Another ﬁnding that is worthy to be mentioned can be 7.4. Strain Response. Figures 17–19 show the load strain shown in Table 6 which is the peak resisting moment reg- at the top ﬁber of concrete beam models longitudinally istered on the B6 model and was 239.79 kN m, whereas the to check out if there is exceeding in the values on the ultimate moment was recorded at the B4 model and was concrete strain or not. /e strain in the concrete of models 14 Advances in Civil Engineering 500 500 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 Strain 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 B1 B3 Strain B2 B5 B1 B7 Figure 17: Load strain in concrete performances for models B1, B2, B2 B8 B3, and B5. Figure 19: Load strain in concrete performances for models B1, B2, B7, and B8. for all models. From this ﬁgure, it can be clearly noticed that the number of cracks was larger at the control beam model (B1) than did those other models. /is is because B1 has the lowest reinforcement ratio and is without any strengthening technique. As expected, the crack spacing and the number of cracks in the B3 model were largely similar to those of B7 model (strengthened by the lowest number of BFRP layer 200 model and the corroded model). In general, two modes of failure were diagnosed for all proposed models during the loading stages, and they are ﬂexural tension exhibiting ﬁrstly resulting from yielding of steel rebar and when approaching to the ﬁnal stage of loading, the ﬂexural compression failure appeared. 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Strain 8. Conclusions B1 B4 B2 B6 BFRP is considered as a green material and has illustrated to Figure 18: Load strain in concrete performances for models B1, B2, be a promising material for developing the infrastructure B4, and B6. sustainability in RC members. In this paper, eight 3D FEs of strengthening and rehabilitating full-scale RC beams using B2, B4, B5, B6, and B8 increased because the amount of BFRP strips were built under the theory of full-composite reinforcement in the tension zone is more. /e maximum action and entire bonding between these strips as layers and strain at the compression zone based on American Con- the full interaction with concrete. Based on the analysis crete Institute (ACI-318-2016) [40] is 0.003 at the top ﬁber results for the proposed models, the main conclusions can be of the concrete beam. All strain values in the case of control drawn as follows: models were within the range. /e slope of load strain of (i) /e arithmetic mean values of percentage of de- the composite systems was more than the control models ﬂections at yield and ultimate comparisons be- because the modulus of elasticity for these systems was tween numerical and experimental test results greater than the modulus of elasticity of concrete. Hence, ratios were rounded to unity, besides that the these systems have more strength and less deﬂection standard deviations and variances for these ratios compared to control models. were small enough. From these results of statistical basis, it can be deduced that the outcomes of the 7.5. Pattern of Crack and Mode of Failure. Figure 20 shows present analyses were very close and matched with the crack patterns and the failure modes at the end of the test the experimental ones. Load (kN) Load (kN) Load (kN) Advances in Civil Engineering 15 (B1) (B2) (B3) (B4) (B5) (B6) (B7) (B8) (a) (b) (c) Figure 20: (a) Crack patterns and the failure modes at the end of test for all models, (b) crack patterns for B1 from experimental test [11], and (c) cracks patterns for B2 from experimental test [11]. (ii) A closer look at the ﬁndings of the load capacity models with the same percentage reinforcement for all models found that the ultimate load was at ratio). the model B8, where the ultimate load increased (iii) /e increase in the load capacity did not exceed by 14.8% when transferred between the B2 and 14.47% when transferring from B5 to B6 model; in B8 models in spite of the corrosion of the main spite of the B5 model has almost half percentage reinforcement at the tension zone which was reinforcement ratio with respect to B6 model (these 20% in B8 compared to that in B2. Furthermore, models have the same BFRP layer’s number). the diﬀerence in the percentage reinforcement /erefore, it is concluded that the midspan wrap- ratio did not exceed 0.25 between the B8 and B1 ping technique was more eﬀective as compared to models; but the B8 model achieved the increase the bottom technique of wrapping as regards to the in load capacity of 80% compared to the B1 presented models. On the other hand, BFRP model. On the contrary, under the strengthened composites made the yield load becomes larger so beams with only three layers of BFRP, the yield that the stiﬀness of the composite model becomes and ultimate loading was increased by about higher. In addition, there was an enhancing in 39% and 28%, respectively (between B1 and B3 elastic deformation in presence of BFRP sheets. 16 Advances in Civil Engineering dynamic loading on the composite system, the orientation of (iv) Under the same percentage reinforcement ratio, an increasing number of BFRP layers (approached to ﬁbers and other arrangements of wrapping by BFRP, and the degree of composite interaction, besides thermal eﬀects eight layers) decreased deﬂection ductility index by about 46%, which took place between B2 and B6 (environmental and ﬁre conditions) with existence of BFRP models. /e peak decreasing in the deﬂection duc- composites on RC beams. Moreover, the current strategy of tility index was recorded between B1 and B6 models simulating interaction and bonding of RC beams with BFRP and was approximately 78%. However, based on composites can be used as a starting point for strengthening prestigious studies that presented in the literature and rehabilitating the other composite systems by this kind survey of this research, it was determined that the of ﬁber, such as the RC columns and slab. deﬂection ductility decreased in the RC beams with diﬀerent strategies of strengthening them by FRP Data Availability family. Hence, the current study gives us a better /e data used to support the ﬁndings of this study are in- vision about the real structural response of such cluded within the article. members. (v) Presence of BFRP makes the slope of the load strain Conflicts of Interest more than the control models do which indicate that the equivalent composite modulus of elasticity /e authors declare that they have no conﬂicts of interest. is more than the modulus of elasticity of concrete. (vi) Generally, there were no remarkable diﬀerences in References the crack patterns of all proposed models. Two modes of failure were experienced of all suggested [1] B. Umberto and D. Nicholas, “/ermal and ﬁre characteristics of FBR composites for architectural applications,” Polymers, models. /ese models ﬁrstly exhibited a ﬂexural vol. 7, no. 11, pp. 2276–2289, 2011. tension failure, while at the ultimate load, the ﬁnal [2] V. Dhand, G. Mittal, K. Y. Rhee, S.-J. Park, and D. Hui, “A failure mode was a ﬂexural compression. 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