FRP筋混凝土梁正截面受弯承载力模型分析
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摘要
结合国内外328组FRP筋混凝土梁受弯试验数据,系统分析了我国规范(GB 50608-2010)、美国规范(ACI 440.1R-15)、加拿大规范(ISIS manual 2007)和意大利规范(CNR-DT 203/2006)的承载力计算模型,对比了各国规范计算结果的准确性和离散程度.通过对受压破坏试件参数ρ_f/ρ_(fb)和c_b/x_(exp)进行回归分析,建立了等效矩形受压区高度x的经验公式,改进了受压破坏FRP筋梁承载力计算公式,并给出了使计算结果具有95%保证率的强度修正系数.结果表明:在ρ_f<ρ_(fb)和ρ_(fb)≤ρ_f<1.5ρ_(fb)两种情况下,各国规范计算值与试验值吻合良好;当1.5ρ_(fb)≤ρ_f时,各国规范计算值均偏保守.与以上规范计算公式相比,该文建议公式的计算值与试验值更为接近.
Collected and analyzed are 328 testing results of flexural capacity of FRP-reinforced concrete beams. The results were employed to assess the accuracy and dispersion degree of the current design formulas in GB 50608, ACI 440.1 R, ISIS manual and CNR-DT 203. Regression analysis of ρ_f/ρ_(fb) and c_b/x_(exp) for specimens controlled by compression failure was carried out and the formula of depth of equivalent rectangular stress block x was obtained. The equation of flexural capacity of FRP-reinforced concrete beams controlled by compression failure was revised and the strength correction coefficient with 95% guarantee rate was proposed. The results showed that when ρ_f<1.5ρ_(fb), the calculation results agreed well with the test results; and when 1.5ρ_(fb)≤ρ_f, however, the average predictions by specifications were all higher than test values by more than 20%. Compared with the standards, the proposed formulas yield estimations closer than the test results.
Collected and analyzed are 328 testing results of flexural capacity of FRP-reinforced concrete beams. The results were employed to assess the accuracy and dispersion degree of the current design formulas in GB 50608, ACI 440.1 R, ISIS manual and CNR-DT 203. Regression analysis of ρ_f/ρ_(fb) and c_b/x_(exp) for specimens controlled by compression failure was carried out and the formula of depth of equivalent rectangular stress block x was obtained. The equation of flexural capacity of FRP-reinforced concrete beams controlled by compression failure was revised and the strength correction coefficient with 95% guarantee rate was proposed. The results showed that when ρ_f<1.5ρ_(fb), the calculation results agreed well with the test results; and when 1.5ρ_(fb)≤ρ_f, however, the average predictions by specifications were all higher than test values by more than 20%. Compared with the standards, the proposed formulas yield estimations closer than the test results.
引文
[1] ACI.Guide for the design and construction of concrete reinforced with FRP bars:ACI 440.1R-15[S]. Farmington Hills:American Concrete Institute, 2015.
[2] ISIS Canada Research Network, Reinforced Concrete Structures with Fibre-Reinforced Polymers[S]. ISIS Manual No. 3, University of Manitoba, Winnipeg, MB, Canada, 2007.
[3] ACTRC.Guide for the design and construction of concrete structures reinforced with fiber-reinforced polymer bars:CNR-DT 203/2006[S]. Rome:Advisory Committee on Technical Recommendations for Construction, 2006.
[4] 中华人民共和国住房和城乡建筑部.纤维增强复合材料建设工程应用技术规范:GB 50608-2010[S].北京: 中国计划出版社,2011.Ministry of Housing and Urban-Rural Construction of the People′s Republic of China. Technical code for infrastructure application of FRP composites:GB 50608-2010[S]. Beijing: China Planning Press, 2011.
[5] KARA I F, ASHOUR A. F. Flexural performance of FRP reinforced concrete beams[J]. Composite Structures, 2012, 94(5), 1616-1625.
[6] RAFI M M, NADJAI A, ALI F, et al. Aspects of behavior of CFRP reinforced concrete beams in bending[J]. Construction & Building Materials, 2008, 22(3):277-285.
[7] JAKUBOVSKIS R, KAKLAUSKAS G, GRIBNIAK V, et al. Serviceability analysis of concrete beams with different arrangements of GFRP bars in the tensile zone[J]. Journal of Composites for Construction, 2014, 18(5):1-10.
[8] MARANAN G B, MANALO A C, BENMOKRANE B, Evaluation of the flexural strength and serviceability of geopolymer concrete beams reinforced with glass-fibre-reinforced polymer (GFRP) bars [J]. Engineering Structures, 2015, 101:529-541.
[9] GOLDSTON M, REMENNIKOV A, SHEIKH M N. Experimental investigation of the behavior of concrete beams reinforced with GFRP bars under static and impact loading [J]. Engineering Structures, 2016, 113:220-232.
[10] EL-NEMR A, AHMED E A, BENMOKRANE B. Flexural behavior and serviceability of normal- and high-strength concrete beams reinforced with glass fiber-reinforced polymer bars[J]. ACI Structural Journal, 2013, 110(6):1077-1087.
[11] EL-NEMR A, AHMED E A, BARRIS C, et al. Bond-dependent coefficient of glass- and carbon-FRP bars in normal- and high-strength concretes[J]. Construction & Building Materials, 2016, 113:77-89.
[12] KASSEM C, FARGHALY A S, BENMOKRANE B. Evaluation of flexural behavior and serviceability performance of concrete beams reinforced with FRP bars [J]. Journal of Composites for Construction, 2011, 15(5):682-695.
[13] ADAM M A, SAID M, MAHMOUD A A, et al. Analytical and experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars [J]. Construction & Building Materials, 2015, 84(2):354-366.
[14] ELGABBAS F, VINCENT P, AHMED E A, et al. Experimental testing of basalt-fiber-reinforced polymer bars in concrete beams[J]. Composites Engineering(Part B), 2016, 91:205-218.
[15] MIàS C, TORRES L, TURON A, et al. Experimental study of immediate and time-dependent deflections of GFRP reinforced concrete beams[J]. Composite Structures, 2013, 96(4):279-285.
[16] BARRIS C, TORRES L, TURON A, et al. An experimental study of the flexural behavior of GFRP RC beams and comparison with prediction models[J]. Composite Structures, 2009, 91(3):286-295.
[17] YANG J M, MIN K H, SHIN H O, et al. Effect of steel and synthetic fibers on flexural behavior of high-strength concrete beams reinforced with FRP bars[J]. Composites Engineering(Part B), 2012, 43(3):1077-1086.
[18] 曾德光. FRP筋混凝土梁的受弯性能试验研究和理论分析[D]. 南京:东南大学, 2005.ZENG Deguang. Experimental study and theoretical analysis on flexural behavior of concrete beam reinforced with FRP tendons [D]. Nanjing:Southeast University, 2005.
[19] WANG H, BELARBI A. Flexural behavior of fiber-reinforced-concrete beams reinforced with FRP rebars [J]. ACI Special Publication, 2005, 166:1797-1800.
[20] REFAI A E, ABED F, AL-RAHMANI A. Structural performance and serviceability of concrete beams reinforced with hybrid (GFRP and steel) bars [J]. Construction & Building Materials, 2015, 96:518-529.
[21] ISSA M S, METWALLY I M, ELZEINY S M. Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars [J]. Engineering Structures, 2011, 33(5):1754-1763.
[22] 徐新生.FRP筋力学性能及其混凝土梁受弯性能研究[D].天津:天津大学, 2007.XU Xinsheng. Research on mechanical property of FRP bars and flexural property of concrete beams with FRP bars [D]. Tianjin:Tianjin University, 2007.
[23] AIELLO M A, OMBRES L. Load-deflection analysis of FRP reinforced concrete flexural members[J]. Journal of Composites for Construction, 2000, 4(4):164-171.
[24] YOO D Y, BANTHIA N, YOON Y S. Flexural behavior of ultra-high-performance fiber-reinforced concrete beams reinforced with GFRP and steel rebars [J]. Engineering Structures, 2016, 111:246-262.
[25] WANG H, BELARBI A. Flexural durability of FRP bars embedded in fiber-reinforced-concrete[J]. Construction & Building Materials, 2012, 44(4):541-550.
[26] LAU D, PAM H J. Experimental study of hybrid FRP reinforced concrete beams[J]. Engineering Structures, 2011, 32(12):3857-3865.
[27] THéRIAULT M, BENMOKRANE B. Effects of FRP reinforcement ratio and concrete strength on flexural behavior of concrete beams[J]. Journal of Composites for Construction, 1998, 2(1):7-16.
[28] OH H, MOON D Y, ZI G. Flexural characteristics of concrete beams reinforced with a new type of GFRP bar [J]. Polymers & Polymer Composites, 2009, 17(4):253-264.
[29] ALSAYED S H, AL-SALLOUM Y A, ALMUSALLAM T H. Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures[J]. Composites Part B Engineering, 2000, 31(6-7):555-567.
[30] RASHID M A, MANSUR M A, PARAMASIVAM P. Behavior of aramid fiber-reinforced polymer reinforced high strength concrete beams under bending[J]. Journal of Composites for Construction, 2005, 9(9):117-127.
[31] MOUSAVI S R, ESFAHANI M R. Effective moment of inertia prediction of FRP-reinforced concrete beams based on experimental results[J]. Journal of Composites for Construction, 2012, 16(5):490-498.
[32] DURANAVIC, N., PILAKOUTAS, K., WALDRON, P. Test on concrete beams reinforced with glass fibre reinforced plastic bars[J]//Non-metallic(FRP) rain forcement for concrete structure:1997, 2:479-486.
[33] ASHOUR A F. Flexural and shear capacities of concrete beams reinforced with GFRP bars[J]. Construction & Building Materials, 2006, 20(10):1005-1015.
[34] SAIKIA B, KUMAR P, THOMAS J, et al. Strength and serviceability performance of beams reinforced with GFRP bars in flexure[J]. Construction & Building Materials, 2007, 21(8):1709-1719.
[35] FAZA, S. S. Bending and bond behavior and design of concrete beams reinforced with fiber reinforced plastic rebars[D]. West Virginia: West Virginia University,1991.
[36] 田盼盼, 沙吾列提·拜开依, 潘梅,等. BFRP筋混凝土梁受弯性能的试验研究[J]. 新疆大学学报(自然科学版), 2015(1): 94-99.TIAN Panpan, SAWULET Bekey, PAN Mei, et al. Experimental study on the flexural behavior of BFRP bar reinforced concrete beams[J]. Journal of Xinjiang University (Natural Science Edition), 2015(1):94-99.
[37] 袁竞峰. 新型FRP筋混凝土梁受弯性能研究[D]. 南京:东南大学, 2006.YUAN Jingfeng. Analysis on flexural behavior of concrete beam reinforced with FRP bars [D]. Nanjing: Southeast University, 2006.
[38] 刘华杰. 纤维塑料筋混凝土受弯构件试验研究与理论分析[D].上海:同济大学, 2003.LIU Huajie. Experimental and theory analytical studies on concrete flexural members reinforced with FRP rebars[D]. Shanghai:Tongji University, 2003.
[39] TOUTANJI H, DENG Y. Deflection and crack-width prediction of concrete beams reinforced with glass FRP rods[J]. Construction & Building Materials, 2003, 17(1):69-74.
[40] BENMOKRANE B, CHAALLAL O, MASMOUDI R. Flexural response of concrete beams reinforced with FRP reinforcing bars[J]. ACI Structural Journal, 1996, 93(1):46-55.
[41] 郑永峰. FRP筋混凝土梁受力性能的试验研究及有限元分析[D]. 济南:济南大学, 2008.ZHENG Yongfeng. Experimental research and finite element analysis of concrete beams reinforced with FRP bars[D]. Jinan:University of Jinan, 2008.
[42] 李海霞. FRP配筋混凝土梁试验研究及理论分析[D]. 武汉:华中科技大学, 2007.LI Haixia. Theroy analytical and experimental studies on concrete beam reinforced with FRP bars[D]. Wuhan:Huazhong University of Science and Technology,2007.
[43] 唐协. 玻璃纤维(GFRP)筋混凝土构件正截面承载力设计方法研究[D]. 成都:西南交通大学, 2007.TANG Xie. Study on flexural capacity design method of GFRP reinforced concrete members[D]. Chengdu:Southwest Jiaotong University, 2007.
[44] 薛伟辰, 康清梁. 纤维塑料筋混凝土梁受力性能的试验研究[J]. 工业建筑, 1999, 29(12):8-10.XUE Weichen, KANG Qingliang. Experimental study on behaviors of concrete beams reinforced with fiber reinforced plastics bars[J]. Industrial Construction, 1999, 29(12):8-10.
[45] 祁皑, 翁春光. FRP筋混凝土梁延性性能试验研究[J]. 工程抗震与加固改造, 2007, 29(5):63-67.QI Ai, WENG Chunguang. Experimental study on ductility behavior of concrete beams reinforced with FRP rebars[J]. Earthquake Resistant Engineering and Retrofitting, 2007, 29(5):63-67.
[46] 高丹盈, B.Brahim.玻璃纤维聚合物筋混凝土梁正截面承载力的计算方法[J]. 水利学报, 2001, 32(9):73-80.GAO Danying, B. Benmokrane. Calculation method of flexural capacity of GFRP-reinforced concrete beam[J]. Journal of Hydraulic Engineering, 2001, 32(9):73-80.
[47] Comite Euro-International du Beton. Bulletin D’information No.213/214 CEB-FIP Model Code 1990 (Concrete Structures)[S].Lausanne: CEB, 1993.
[48] XUE W, PENG F, ZHENG Q. Design Equations for flexural capacity of concrete beams reinforced with glass fiber-reinforced polymer bars [J]. Journal of Composites for Construction, 2016, 20(3):04015069.
[2] ISIS Canada Research Network, Reinforced Concrete Structures with Fibre-Reinforced Polymers[S]. ISIS Manual No. 3, University of Manitoba, Winnipeg, MB, Canada, 2007.
[3] ACTRC.Guide for the design and construction of concrete structures reinforced with fiber-reinforced polymer bars:CNR-DT 203/2006[S]. Rome:Advisory Committee on Technical Recommendations for Construction, 2006.
[4] 中华人民共和国住房和城乡建筑部.纤维增强复合材料建设工程应用技术规范:GB 50608-2010[S].北京: 中国计划出版社,2011.Ministry of Housing and Urban-Rural Construction of the People′s Republic of China. Technical code for infrastructure application of FRP composites:GB 50608-2010[S]. Beijing: China Planning Press, 2011.
[5] KARA I F, ASHOUR A. F. Flexural performance of FRP reinforced concrete beams[J]. Composite Structures, 2012, 94(5), 1616-1625.
[6] RAFI M M, NADJAI A, ALI F, et al. Aspects of behavior of CFRP reinforced concrete beams in bending[J]. Construction & Building Materials, 2008, 22(3):277-285.
[7] JAKUBOVSKIS R, KAKLAUSKAS G, GRIBNIAK V, et al. Serviceability analysis of concrete beams with different arrangements of GFRP bars in the tensile zone[J]. Journal of Composites for Construction, 2014, 18(5):1-10.
[8] MARANAN G B, MANALO A C, BENMOKRANE B, Evaluation of the flexural strength and serviceability of geopolymer concrete beams reinforced with glass-fibre-reinforced polymer (GFRP) bars [J]. Engineering Structures, 2015, 101:529-541.
[9] GOLDSTON M, REMENNIKOV A, SHEIKH M N. Experimental investigation of the behavior of concrete beams reinforced with GFRP bars under static and impact loading [J]. Engineering Structures, 2016, 113:220-232.
[10] EL-NEMR A, AHMED E A, BENMOKRANE B. Flexural behavior and serviceability of normal- and high-strength concrete beams reinforced with glass fiber-reinforced polymer bars[J]. ACI Structural Journal, 2013, 110(6):1077-1087.
[11] EL-NEMR A, AHMED E A, BARRIS C, et al. Bond-dependent coefficient of glass- and carbon-FRP bars in normal- and high-strength concretes[J]. Construction & Building Materials, 2016, 113:77-89.
[12] KASSEM C, FARGHALY A S, BENMOKRANE B. Evaluation of flexural behavior and serviceability performance of concrete beams reinforced with FRP bars [J]. Journal of Composites for Construction, 2011, 15(5):682-695.
[13] ADAM M A, SAID M, MAHMOUD A A, et al. Analytical and experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars [J]. Construction & Building Materials, 2015, 84(2):354-366.
[14] ELGABBAS F, VINCENT P, AHMED E A, et al. Experimental testing of basalt-fiber-reinforced polymer bars in concrete beams[J]. Composites Engineering(Part B), 2016, 91:205-218.
[15] MIàS C, TORRES L, TURON A, et al. Experimental study of immediate and time-dependent deflections of GFRP reinforced concrete beams[J]. Composite Structures, 2013, 96(4):279-285.
[16] BARRIS C, TORRES L, TURON A, et al. An experimental study of the flexural behavior of GFRP RC beams and comparison with prediction models[J]. Composite Structures, 2009, 91(3):286-295.
[17] YANG J M, MIN K H, SHIN H O, et al. Effect of steel and synthetic fibers on flexural behavior of high-strength concrete beams reinforced with FRP bars[J]. Composites Engineering(Part B), 2012, 43(3):1077-1086.
[18] 曾德光. FRP筋混凝土梁的受弯性能试验研究和理论分析[D]. 南京:东南大学, 2005.ZENG Deguang. Experimental study and theoretical analysis on flexural behavior of concrete beam reinforced with FRP tendons [D]. Nanjing:Southeast University, 2005.
[19] WANG H, BELARBI A. Flexural behavior of fiber-reinforced-concrete beams reinforced with FRP rebars [J]. ACI Special Publication, 2005, 166:1797-1800.
[20] REFAI A E, ABED F, AL-RAHMANI A. Structural performance and serviceability of concrete beams reinforced with hybrid (GFRP and steel) bars [J]. Construction & Building Materials, 2015, 96:518-529.
[21] ISSA M S, METWALLY I M, ELZEINY S M. Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars [J]. Engineering Structures, 2011, 33(5):1754-1763.
[22] 徐新生.FRP筋力学性能及其混凝土梁受弯性能研究[D].天津:天津大学, 2007.XU Xinsheng. Research on mechanical property of FRP bars and flexural property of concrete beams with FRP bars [D]. Tianjin:Tianjin University, 2007.
[23] AIELLO M A, OMBRES L. Load-deflection analysis of FRP reinforced concrete flexural members[J]. Journal of Composites for Construction, 2000, 4(4):164-171.
[24] YOO D Y, BANTHIA N, YOON Y S. Flexural behavior of ultra-high-performance fiber-reinforced concrete beams reinforced with GFRP and steel rebars [J]. Engineering Structures, 2016, 111:246-262.
[25] WANG H, BELARBI A. Flexural durability of FRP bars embedded in fiber-reinforced-concrete[J]. Construction & Building Materials, 2012, 44(4):541-550.
[26] LAU D, PAM H J. Experimental study of hybrid FRP reinforced concrete beams[J]. Engineering Structures, 2011, 32(12):3857-3865.
[27] THéRIAULT M, BENMOKRANE B. Effects of FRP reinforcement ratio and concrete strength on flexural behavior of concrete beams[J]. Journal of Composites for Construction, 1998, 2(1):7-16.
[28] OH H, MOON D Y, ZI G. Flexural characteristics of concrete beams reinforced with a new type of GFRP bar [J]. Polymers & Polymer Composites, 2009, 17(4):253-264.
[29] ALSAYED S H, AL-SALLOUM Y A, ALMUSALLAM T H. Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures[J]. Composites Part B Engineering, 2000, 31(6-7):555-567.
[30] RASHID M A, MANSUR M A, PARAMASIVAM P. Behavior of aramid fiber-reinforced polymer reinforced high strength concrete beams under bending[J]. Journal of Composites for Construction, 2005, 9(9):117-127.
[31] MOUSAVI S R, ESFAHANI M R. Effective moment of inertia prediction of FRP-reinforced concrete beams based on experimental results[J]. Journal of Composites for Construction, 2012, 16(5):490-498.
[32] DURANAVIC, N., PILAKOUTAS, K., WALDRON, P. Test on concrete beams reinforced with glass fibre reinforced plastic bars[J]//Non-metallic(FRP) rain forcement for concrete structure:1997, 2:479-486.
[33] ASHOUR A F. Flexural and shear capacities of concrete beams reinforced with GFRP bars[J]. Construction & Building Materials, 2006, 20(10):1005-1015.
[34] SAIKIA B, KUMAR P, THOMAS J, et al. Strength and serviceability performance of beams reinforced with GFRP bars in flexure[J]. Construction & Building Materials, 2007, 21(8):1709-1719.
[35] FAZA, S. S. Bending and bond behavior and design of concrete beams reinforced with fiber reinforced plastic rebars[D]. West Virginia: West Virginia University,1991.
[36] 田盼盼, 沙吾列提·拜开依, 潘梅,等. BFRP筋混凝土梁受弯性能的试验研究[J]. 新疆大学学报(自然科学版), 2015(1): 94-99.TIAN Panpan, SAWULET Bekey, PAN Mei, et al. Experimental study on the flexural behavior of BFRP bar reinforced concrete beams[J]. Journal of Xinjiang University (Natural Science Edition), 2015(1):94-99.
[37] 袁竞峰. 新型FRP筋混凝土梁受弯性能研究[D]. 南京:东南大学, 2006.YUAN Jingfeng. Analysis on flexural behavior of concrete beam reinforced with FRP bars [D]. Nanjing: Southeast University, 2006.
[38] 刘华杰. 纤维塑料筋混凝土受弯构件试验研究与理论分析[D].上海:同济大学, 2003.LIU Huajie. Experimental and theory analytical studies on concrete flexural members reinforced with FRP rebars[D]. Shanghai:Tongji University, 2003.
[39] TOUTANJI H, DENG Y. Deflection and crack-width prediction of concrete beams reinforced with glass FRP rods[J]. Construction & Building Materials, 2003, 17(1):69-74.
[40] BENMOKRANE B, CHAALLAL O, MASMOUDI R. Flexural response of concrete beams reinforced with FRP reinforcing bars[J]. ACI Structural Journal, 1996, 93(1):46-55.
[41] 郑永峰. FRP筋混凝土梁受力性能的试验研究及有限元分析[D]. 济南:济南大学, 2008.ZHENG Yongfeng. Experimental research and finite element analysis of concrete beams reinforced with FRP bars[D]. Jinan:University of Jinan, 2008.
[42] 李海霞. FRP配筋混凝土梁试验研究及理论分析[D]. 武汉:华中科技大学, 2007.LI Haixia. Theroy analytical and experimental studies on concrete beam reinforced with FRP bars[D]. Wuhan:Huazhong University of Science and Technology,2007.
[43] 唐协. 玻璃纤维(GFRP)筋混凝土构件正截面承载力设计方法研究[D]. 成都:西南交通大学, 2007.TANG Xie. Study on flexural capacity design method of GFRP reinforced concrete members[D]. Chengdu:Southwest Jiaotong University, 2007.
[44] 薛伟辰, 康清梁. 纤维塑料筋混凝土梁受力性能的试验研究[J]. 工业建筑, 1999, 29(12):8-10.XUE Weichen, KANG Qingliang. Experimental study on behaviors of concrete beams reinforced with fiber reinforced plastics bars[J]. Industrial Construction, 1999, 29(12):8-10.
[45] 祁皑, 翁春光. FRP筋混凝土梁延性性能试验研究[J]. 工程抗震与加固改造, 2007, 29(5):63-67.QI Ai, WENG Chunguang. Experimental study on ductility behavior of concrete beams reinforced with FRP rebars[J]. Earthquake Resistant Engineering and Retrofitting, 2007, 29(5):63-67.
[46] 高丹盈, B.Brahim.玻璃纤维聚合物筋混凝土梁正截面承载力的计算方法[J]. 水利学报, 2001, 32(9):73-80.GAO Danying, B. Benmokrane. Calculation method of flexural capacity of GFRP-reinforced concrete beam[J]. Journal of Hydraulic Engineering, 2001, 32(9):73-80.
[47] Comite Euro-International du Beton. Bulletin D’information No.213/214 CEB-FIP Model Code 1990 (Concrete Structures)[S].Lausanne: CEB, 1993.
[48] XUE W, PENG F, ZHENG Q. Design Equations for flexural capacity of concrete beams reinforced with glass fiber-reinforced polymer bars [J]. Journal of Composites for Construction, 2016, 20(3):04015069.