{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T08:06:56Z","timestamp":1768637216715,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T00:00:00Z","timestamp":1606176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>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\u2019 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.<\/jats:p>","DOI":"10.3390\/polym12122773","type":"journal-article","created":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T09:06:28Z","timestamp":1606208788000},"page":"2773","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Numerical Study of Using FRP and Steel Rebars in Simply Supported Prestressed Concrete Beams with External FRP Tendons"],"prefix":"10.3390","volume":"12","author":[{"given":"Miao","family":"Pang","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China"}]},{"given":"Zhangxiang","family":"Li","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Roadway Bridge &amp; Structure Engineering, Wuhan University of Technology, Wuhan 430070, China"}]},{"given":"Tiejiong","family":"Lou","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Roadway Bridge &amp; Structure Engineering, Wuhan University of Technology, Wuhan 430070, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/S0958-9465(02)00086-0","article-title":"Reinforcement corrosion in concrete structures, its monitoring and service life prediction\u2014A review","volume":"25","author":"Ahmad","year":"2003","journal-title":"Cem. Concr. Compos."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105698","DOI":"10.1016\/j.jcsr.2019.105698","article-title":"Numerical evaluation of prestressed steel-concrete composite girders with external FRP or steel tendons","volume":"162","author":"Lou","year":"2019","journal-title":"J. Constr. Steel Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109927","DOI":"10.1016\/j.engstruct.2019.109927","article-title":"Moment redistribution versus neutral axis depth in continuous PSC beams with external CFRP tendons","volume":"209","author":"Lou","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_4","first-page":"163","article-title":"Behavior of anchored carbon fiber-reinforced polymer strips used for strengthening concrete structures","volume":"113","author":"Sun","year":"2016","journal-title":"ACI Mater. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"111251","DOI":"10.1016\/j.compstruct.2019.111251","article-title":"Developing an anchored near-surface mounted (NSM ) FRP system for fuller use of FRP material with less epoxy filler","volume":"226","author":"Sun","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.conbuildmat.2019.05.117","article-title":"Innovative warp and woof strap (WWS) method to anchor the FRP sheets in strengthened concrete beams","volume":"218","author":"Mostofinejad","year":"2019","journal-title":"Constr. Build. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1016\/j.compstruct.2018.09.071","article-title":"Effects of transverse constraints on the longitudinal compressive strength of unidirectional CFRP pultruded plates and rods","volume":"207","author":"Wang","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"111948","DOI":"10.1016\/j.compstruct.2020.111948","article-title":"Damage pattern recognition and damage evolution analysis of unidirectional CFRP tendons under tensile loading using acoustic emission technology","volume":"238","author":"Xu","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_9","unstructured":"ACI committee 440 (2006). Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars, ACI 440.1R-06."},{"key":"ref_10","unstructured":"ACI committee 440 (2004). Prestressing Concrete Structures with FRP Tendons, ACI 440.4R-04."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"04014078","DOI":"10.1061\/(ASCE)CC.1943-5614.0000544","article-title":"Bond durability of basalt fiber\u2013reinforced polymer bars embedded in concrete under direct pullout conditions","volume":"19","author":"Abed","year":"2015","journal-title":"ASCE J. Compos. Constr."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.conbuildmat.2015.02.036","article-title":"Bond degradation of basalt fiber-reinforced polymer (BFRP) bars exposed to accelerated aging conditions","volume":"81","author":"Altalmas","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.12989\/acc2014.2.1.001","article-title":"Effects of harsh environmental exposures on the bond capacity between concrete and GFRP reinforcing bars","volume":"2","author":"Abed","year":"2014","journal-title":"Adv. Concr. Constr."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"88","DOI":"10.15554\/pcij.09011998.88.101","article-title":"Behavior of externally draped CFRP tendons in prestressed concrete bridges","volume":"43","author":"Grace","year":"1998","journal-title":"PCI J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1016\/j.cemconcomp.2005.05.003","article-title":"Factors affecting the external prestressing stress in externally strengthened prestressed concrete beams","volume":"27","author":"Ghallab","year":"2005","journal-title":"Cem. Concr. Compos."},{"key":"ref_16","first-page":"1138","article-title":"Analysis of concrete beams prestressed and post-tensioned with externally unbonded carbon fiber reinforced polymer tendons","volume":"31","author":"Ghrib","year":"2005","journal-title":"Can. J. Civ. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.engstruct.2015.06.052","article-title":"Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique","volume":"101","author":"Wang","year":"2015","journal-title":"Eng. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"04017032","DOI":"10.1061\/(ASCE)CC.1943-5614.0000811","article-title":"Experimental Evaluation of Bent FRP Tendons for Strengthening by External Prestressing","volume":"21","author":"Zhu","year":"2017","journal-title":"ASCE J. Compos. Constr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1016\/j.conbuildmat.2012.04.055","article-title":"Numerical analysis of behaviour of concrete beams with external FRP tendons","volume":"35","author":"Lou","year":"2012","journal-title":"Constr. Build. Mater."},{"key":"ref_20","first-page":"521","article-title":"Reinforced concrete T-beams externally prestressed with unbonded carbon fiber-reinforced polymer tendons","volume":"109","author":"Bennitz","year":"2012","journal-title":"ACI Struct. J."},{"key":"ref_21","unstructured":"ACI Committee 318 (2014). Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14), American Concrete Institute."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Abed, F., Oucif, C., Awera, Y., Mhanna, H.H., and Alkhraisha, H. (2020). FE modeling of concrete beams and columns reinforced with FRP composites. Def. Technol.","DOI":"10.1016\/j.dt.2020.02.015"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.istruc.2019.06.019","article-title":"Experimental and finite element investigation of the shear performance of BFRP-RC short beams","volume":"20","author":"Abed","year":"2019","journal-title":"Structures"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Al-Rahmani, A., and Abed, F.H. (2013, January 28\u201330). Numerical investigation of hybrid FRP reinforced beams. Proceedings of the 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), Hammamet, Tunisia.","DOI":"10.1109\/ICMSAO.2013.6552565"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1016\/j.compstruct.2017.09.016","article-title":"Cracking control comparison in the specifications of serviceability in cracking for FRP reinforced concrete beams","volume":"182","author":"Ju","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/j.conbuildmat.2017.08.006","article-title":"Relationship between the shear capacity and the flexural cracking load of FRP reinforced concrete beams","volume":"154","author":"Alam","year":"2017","journal-title":"Constr. Build. Mater."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.engstruct.2016.11.007","article-title":"Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams","volume":"131","author":"Barris","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.compstruct.2015.06.018","article-title":"Prediction of load-deflection behavior of multi-span FRP and steel reinforced concrete beams","volume":"132","author":"Dundar","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.compositesb.2014.10.044","article-title":"Neutral axis depth and moment redistribution in FRP and steel reinforced concrete continuous beams","volume":"70","author":"Lou","year":"2015","journal-title":"Compos. Part B Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1016\/j.compstruct.2013.08.029","article-title":"Experimental response and code modelling of continuous concrete slabs reinforced with BFRP bars","volume":"107","author":"Mahroug","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1016\/j.engstruct.2006.03.020","article-title":"Finite element modeling of concrete beams prestressed with external tendons","volume":"28","author":"Lou","year":"2006","journal-title":"Eng. Struct."},{"key":"ref_32","unstructured":"CEN (2004). Eurocode 2: Design of Concrete Structures\u2014Part 1-1: General Rules and Rules for Buildings. EN 1992-1-1, European Committee for Standardization."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Bernardo, L., Nepomuceno, M., and Pinto, H. (2019). Neutral axis depth versus ductility and plastic rotation capacity on bending in lightweight-aggregate concrete beams. Materials, 12.","DOI":"10.3390\/ma12213479"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"72","DOI":"10.15554\/pcij.11011985.72.91","article-title":"Ultimate stress of unbonded tendons in partially prestressed concrete beams","volume":"30","author":"Du","year":"1985","journal-title":"PCI J."},{"key":"ref_35","unstructured":"JGJ\/T 92-93 (1993). Technical Specification for Concrete Structures Prestressed with Unbonded Tendons, China Planning Press."},{"key":"ref_36","unstructured":"JGJ 92-2016 (2016). Technical Specification for Concrete Structures Prestressed with Unbonded Tendons, China Architecture & Building Press."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/12\/12\/2773\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:36:44Z","timestamp":1760179004000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/12\/12\/2773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,24]]},"references-count":36,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["polym12122773"],"URL":"https:\/\/doi.org\/10.3390\/polym12122773","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,24]]}}}