polymers Article Numerical Study of Using FRP and Steel Rebars in Simply Supported Prestressed Concrete Beams with External FRP Tendons Miao Pang 1, Zhangxiang Li 2 and Tiejiong Lou 2,* 1 Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China; [email protected] 2 Hubei Key Laboratory of Roadway Bridge & Structure Engineering, Wuhan University of Technology, Wuhan 430070, China; [email protected] * Correspondence: [email protected] Received: 2 November 2020; Accepted: 18 November 2020; Published: 24 November 2020 Abstract: This study aimed at examining the feasibility of using fiber-reinforced polymer (FRP) rebars instead of steel ones in prestressed concrete beams (PCBs) with external FRP tendons. By applying an experimentally validated program, numerical tests were performed on simply supported PCBs, with investigated variables including rebars’ type and area. Three types of rebars were considered, i.e., carbon, glass FRPs (CFRP, GFRP), and reinforcing steel. The ratio of tensile rebars ranged from 0.22% to 2.16%. The results indicated that the beams with CFRP rebars exhibited better crack mode and higher ultimate load than the beams with GFRP or steel rebars. GFRP rebars led to considerably higher ultimate deflection and tendon stress increment than steel rebars. In addition, several models for calculating the ultimate stress in unbonded tendons were assessed. An analytical model was also proposed to predict the tendon stress at ultimate and flexural strength in externally PCBs with steel and FRP rebars. The model predictions agreed well with the numerical results. Keywords: fiber-reinforced polymer; beams; rebars; flexural strength; structural analysis 1. Introduction Steel corrosion would lead to the deterioration of reinforced or prestressed concrete beams (RCBs or PCBs) [1]. An effective solution to this problem is to replace steel reinforcement with fiber-reinforced polymer (FRP). In addition to their non-corrosive property, FRP composites are high-strength, light-weight, and nonmagnetic. These composite materials are increasingly used for strengthening structural elements [2–8]. Different types of FRP composites are available, such as aramid, basalt, carbon, and glass FRPs (AFRP, BFRP, CFRP, and GFRP). Unlike steel reinforcement with ductile characteristics, FRP composites are linear-elastic materials without yielding [9,10]. In addition, the FRP modulus of elasticity is usually lower than that of steel reinforcement [9,10]. Hence, some concerns on the use of FRP reinforcement instead of steel reinforcement may arise, e.g., ductility and deflection issues due to the lack of yielding and low modulus of elasticity for FRP composites. The bond performance of FRP reinforcement in concrete under environmental exposure is also a concern. It was generally demonstrated that harsh environments have adverse effects on FRP reinforcement’s bond durability [11–13]. External prestressing has been widely used in the retrofit or construction of various concrete structures. Extensive research has been conducted concerning PCBs with external FRP tendons. Grace and Abdel-Sayed [14] carried out tests on four specimens to examine the behavior of PCBs with combined externally unbonded and internally bonded CFRP tendons. Their test results showed that the ductility could be improved by strengthening using draped external CFRP tendons. Polymers 2020, 12, 2773; doi:10.3390/polym12122773 www.mdpi.com/journal/polymers Polymers 2020, 12, x FOR PEER REVIEW 2 of 16 Beeby [15] presented the test results of 16 PCBs with external AFRP tendons. They studied several Polymers 2020, 12, 2773 2 of 16 factors influencing the ultimate stress in external FRP or steel tendons and proposed modifying the BS8110 equation. Abdel Aziz et al. [16] developed an analytical method to predict the load-deflection Ghallabbehavior and of PCBs Beeby with [15] presentedexternal CFRP the test tendons. results ofWang 16 PCBs et al. with [17 external] tested AFRPfour specimens tendons. They, including studied 3 severalPCBs with factors external influencing BFRP thetendons ultimate and stress one incontrol external reinforced FRP or steel concrete tendons beam and (RCBs). proposed Their modifying study theshowed BS8110 that equation. using BFRP Abdel composites Aziz et al. [16 as] developed external tendons an analytical for strengthening method to predict RCBs the load-deflectioncan effectively behaviorimprove ofstructural PCBs with perform externalance. CFRP Zhu tendons. et al. [18 Wang] experimentally et al. [17] tested investigated four specimens, the influence including of bending 3 PCBs withangle external and radius BFRP on tendons external and FRP one tendons control reinforced’ performance concrete. They beam concluded (RCBs). Theirthat FRP study tendons showed’ load that usingcapacitie BFRPs are composites reduced as as the external bending tendons angle increases for strengthening or the bending RCBs canradius effectively decreases. improve Both numerical structural performance.and experimental Zhu investigations et al. [18] experimentally [19,20] showed investigated that behaviors the influence of PCBs of with bending external angle CFRP and radiusand steel on externaltendons FRPare similar. tendons’ performance. They concluded that FRP tendons’ load capacities are reduced as theIn bending PCBs with angle external increases tendons, or the some bending bonded radius rebars decreases. need to be Both provided numerical to avoid and behaving experimental as a investigationstied arch and limit [19,20 the] showed crack width that behaviors and spacing of PCBs [21]. with Previous external studies CFRP demonstrated and steel tendons that areexternally similar. PCBsIn without PCBs with bonded external rebars tendons, exhibit somesignificant bonded crack rebars concentration, need to be which provided can to be avoid effectively behaving relieved as a tiedby providing arch and limitbonded the rebars crack width[19]. In and existing spacing works [21]. on Previous PCBs with studies external demonstrated FRP tendons, that steel externally rebars PCBswere usually without provided. bonded rebars The performance exhibit significant of conventional crack concentration, RCBs with which FRP rebars can be instead effectively of steel relieved ones byhas providing been extensively bonded studied rebars [ 19[22].– In30]. existing However, works the onfindings PCBs withobtained external from FRP the tendons, study of steelRCB rebarss with wereFRP/steel usually rebars provided. may not The be performance valid for PCBs of conventional with external RCBs FRP with tendons FRP rebarsas the insteadlatter is of a steel different ones hasstructural been extensively system from studied the former [22–30 due]. However, to external the prestressing. findings obtained The influence from the of study using of FRP RCBs rebars with FRPinstead/steel of rebarssteel ones may on not the be behavior valid for of PCBsPCBs with external external FRP FRP tendons tendons has as yet the to latter be inv isestigated. a different structuralThis paper system presents from the a numerical former due and to analytical external prestressing.study to evaluate The the influence feasibility of usingof providing FRP rebars FRP insteadrebars instead of steel onesof steel on theones behavior in PCBs of PCBswith withexternal external FRP FRP tendons. tendons A has comprehensive yet to be investigated. numerical evaluationThis paper was conducted presents a on numerical simply supported and analytical PCBs study using to an evaluate experimentally the feasibility validated of providing program, FRPwhere rebars investigated instead ofvariables steel ones includ in PCBsed the with typeexternal and amount FRP tendons.of bonded A rebars. comprehensive An analytical numerical model evaluationwas also proposed was conducted to predict on the simply tendon supported stress at PCBs ultimate using and an flexural experimentally strength validatedin externally program, PCBs wherewith steel investigated and FRP rebar variabless. included the type and amount of bonded rebars. An analytical model was also proposed to predict the tendon stress at ultimate and flexural strength in externally PCBs with2. Numerical steel and Program FRP rebars. and Verification 2.2.1. Numerical Numerical ProgramProgram and Verification A numerical program employing the Euler–Bernoulli beam element was developed [31]. The 2.1. Numerical Program finite element assumes negligible shear deformation, small strains with large displacements, and moderateA numerical rotations. program The p employinglane section the hypothesis Euler–Bernoulli was also beam adopted. element The was element developed has [six31]. degrees The finite of elementfreedomassumes as shown negligible in Figureshear 1, where deformation, u, v, and θ small are the strains axial, with transverse large displacements, displacements and, and moderate rotation, rotations.respectively The, and plane the section subscripts hypothesis 1 and 2 was refer also to adopted. the two end The elementnodes. A has linear six degreesvariation of for freedom u and as a showncubic variation in Figure for1, where v alongu ,thev, andx-axisθ are is assumed. the axial, transverseBy applying displacements, an updated Lagrangian and rotation, approach, respectively, the andgoverning the subscripts equations 1 and were 2 refer developed to the two, where end nodes. the stiffness A linear variationmatrix consists for u and of a cubicthe material variation and for vgeometricalong the stiffx-axisness is assumed.matrices.