{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T21:31:52Z","timestamp":1781127112382,"version":"3.54.1"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T00:00:00Z","timestamp":1550620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51878054"],"award-info":[{"award-number":["51878054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51578072"],"award-info":[{"award-number":["51578072"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51708036"],"award-info":[{"award-number":["51708036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2017JQ5092"],"award-info":[{"award-number":["2017JQ5092"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["300102288401"],"award-info":[{"award-number":["300102288401"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Adding fibers is highly effective to enhance the deflection and ductility of fiber-reinforced polymer (FRP)-reinforced beams. In this study, the stress and strain conditions of FRP-reinforced lightweight aggregate concrete (LWC) beams with and without fibers at ultimate load level were specified. Based on the sectional analyses, alternative equations to predict the balanced reinforcement ratio and flexural capacity for beams failed by balanced failure and concrete crushing were established. A rational equation for estimating the short-term stiffness of FRP\u2013LWC beams at service-load levels was suggested based on Zhu\u2019s model. In addition, the contribution of the steel fibers on the short-term stiffness was quantified incorporating the effects of FRP reinforcement ratio. The proposed short-term stiffness model was validated with measured deflections from an experimental database for fiber-reinforced normal weight concrete (FNWC) beams reinforced with FRP bars. Furthermore, six glass fiber-reinforced polymer (GFRP)-reinforced LWC beams with and without steel fibers were tested under four-point bending. Based on the test results, the proposed models and procedures according to current design codes ACI 440.1R, ISIS-M03, GB 50608, and CSA S806 were linked together by comparing their predictions. The results showed that increasing the reinforcement ratio and adding steel fibers decreased the strain of the FRP bars. The flexural capacity of the LWC beams with and without steel fibers was generally underestimated by the design codes, while the proposed model provided accurate ultimate moment predictions. Moreover, the proposed short-term stiffness model yielded reasonable estimations of deflection for both steel fiber-reinforced lightweight aggregate concrete (SFLWC) and FNWC beams.<\/jats:p>","DOI":"10.3390\/s19040873","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T11:45:39Z","timestamp":1550663139000},"page":"873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Flexural Capacity and Deflection of Fiber-Reinforced Lightweight Aggregate Concrete Beams Reinforced with GFRP Bars"],"prefix":"10.3390","volume":"19","author":[{"given":"Xi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Chang\u2019an University, Xi\u2019an 710061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yijia","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chang\u2019an University, Xi\u2019an 710061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chang\u2019an University, Xi\u2019an 710061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.conbuildmat.2016.04.052","article-title":"Experimental study on the bond durability between steel-FRP composite bars (SFCBs) and sea sand concrete in ocean environment","volume":"115","author":"Dong","year":"2016","journal-title":"Constr. Build. Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.engstruct.2017.01.005","article-title":"Investigation of the behaviour of reinforcement-free concrete deck slabs restrained by FRP rods","volume":"135","author":"Zheng","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.compstruct.2015.05.028","article-title":"Influence of arching action on shear behaviour of laterally restrained concrete slabs reinforced with GFRP bars","volume":"132","author":"Zheng","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Xia, L., and Zheng, Y. (2018). Deep embedment (DE) FRP shear strengthening of concrete bridge slabs under loads close to supports. Appl. Sci., 8.","DOI":"10.3390\/app8050721"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Xu, K., Ren, C., Deng, Q., Jin, Q., and Chen, X. (2018). Real-time monitoring of bond slip between GFRP bar and concrete structure using piezoceramic transducer-enabled active sensing. Sensors, 18.","DOI":"10.3390\/s18082653"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2393","DOI":"10.1016\/j.conbuildmat.2007.09.001","article-title":"Fly ash lightweight aggregates in high performance concrete","volume":"22","author":"Kayali","year":"2008","journal-title":"Constr. Build. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.conbuildmat.2014.05.003","article-title":"Long-term behaviour of concrete produced with recycled lightweight expanded clay aggregate concrete","volume":"65","author":"Bogas","year":"2014","journal-title":"Constr. Build. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, P., Sui, L., Xing, F., Huang, X., Zhou, Y., and Yun, Y. (2018). Effects of aggregate types on the stress-strain behavior of fiber reinforced polymer (FRP)-confined lightweight concrete. Sensors, 18.","DOI":"10.3390\/s18103525"},{"key":"ref_9","unstructured":"ACI 440.1R (2015). Guide for the Design and Construction of Structural Concrete Reinforced with Fiber-Reinforced Polymer Bars, American Concrete Institute."},{"key":"ref_10","unstructured":"CSA S806 (2012). Design and Construction of Building Structures with Fibre-Reinforced Polymers, Canadian Standards Association."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.conbuildmat.2013.02.065","article-title":"Flexural durability of FRP bars embedded in fiber-reinforced-concrete","volume":"44","author":"Wang","year":"2013","journal-title":"Constr. Build. Mater."},{"key":"ref_12","first-page":"667","article-title":"Durability of steel fibre reinforced concrete","volume":"212","author":"Lambrechts","year":"2003","journal-title":"Spec. Publ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/j.compositesb.2012.01.044","article-title":"Effect of steel and synthetic fibers on flexural behavior of high-strength concrete beams reinforced with FRP bars","volume":"43","author":"Yang","year":"2012","journal-title":"Compos. Part. B Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1016\/j.engstruct.2011.02.014","article-title":"Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars","volume":"33","author":"Issa","year":"2011","journal-title":"Eng. Struct."},{"key":"ref_15","first-page":"185","article-title":"Bending and bond behavior of concrete beams reinforced with plastic rebars","volume":"1","author":"Faza","year":"1990","journal-title":"Transport. Res. Rec."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.compositesb.2016.06.013","article-title":"Predicting service deflection of ultra-high-performance fiber reinforced concrete beams reinforced with GFRP bar","volume":"99","author":"Yoo","year":"2016","journal-title":"Compos. Part B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.conbuildmat.2017.12.003","article-title":"Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars","volume":"161","author":"Zhu","year":"2018","journal-title":"Constr. Build. Mater."},{"key":"ref_18","unstructured":"ACI 544.4R (2018). Guide to Design with Fiber-Reinforced Concrete, American Concrete Institute."},{"key":"ref_19","unstructured":"JGJ12-2006 (2006). Technical Specification for Lightweight Aggregate Concrete Structures, China Engineering and Construction Society Press."},{"key":"ref_20","unstructured":"GB 50608 (2010). Technical Code for Infrastructure Application of FRP Composites, China Planning Press."},{"key":"ref_21","first-page":"44","article-title":"Experimental study and theoretical calculation on the flexural stiffness of concrete beams reinforced with FRP bars","volume":"48","author":"Zhu","year":"2015","journal-title":"Chin. Civ. Eng. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2821","DOI":"10.1061\/(ASCE)0733-9445(1992)118:10(2821)","article-title":"Flexural Analysis of Reinforced Concrete Beams Containing Steel Fibers","volume":"118","author":"Oh","year":"1992","journal-title":"J. Struct. Eng."},{"key":"ref_23","first-page":"1077","article-title":"Flexural behavior and serviceability of normal- and high-strength concrete beams reinforced with glass fiber-reinforced polymer bars","volume":"110","author":"Ahmed","year":"2013","journal-title":"ACI Struct. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1061\/(ASCE)1090-0268(2005)9:2(117)","article-title":"Behavior of aramid fiber-reinforced polymer reinforced high strength concrete beams under bending","volume":"9","author":"Rashid","year":"2005","journal-title":"J. Compos. Constr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1016\/j.conbuildmat.2006.05.021","article-title":"Strength and serviceability performance of beams reinforced with GFRP bars in flexure","volume":"21","author":"Saikia","year":"2007","journal-title":"Constr. Build. Mater."},{"key":"ref_26","unstructured":"ISIS-M03 (2007). Reinforcing Concrete Structures with Fibre Reinforced Polymers, Intelligent Sensing for Innovative Structures."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1061\/(ASCE)0733-9445(2005)131:5(752)","article-title":"Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber reinforced polymer bars","volume":"131","author":"Bischoff","year":"2005","journal-title":"J. Struct. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1061\/(ASCE)CC.1943-5614.0000164","article-title":"Equivalent moment of inertia based on integration of curvature","volume":"15","author":"Bischoff","year":"2011","journal-title":"J. Compos. Constr."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1061\/(ASCE)1090-0268(2006)10:3(183)","article-title":"Critical review of deflection formulas for FRP-RC members","volume":"10","author":"Mota","year":"2006","journal-title":"J. Compos. Constr."},{"key":"ref_30","unstructured":"ACI 440.3R (2004). Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures, American Concrete Institute."},{"key":"ref_31","first-page":"53","article-title":"The story behind proposed changes to ACI 440 deflection requirements for FRP-reinforced concrete","volume":"264","author":"Bischoff","year":"2009","journal-title":"Spec. 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