基于尺寸效应的无腹筋钢筋混凝土梁的剪切强度公式
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摘要
取无腹筋钢筋混凝土梁的临界斜裂缝及其顶端横截面所截隔离体为研究对象,根据极限平衡法,建立平衡方程组。分析临界剪压区主应力与梁斜截面破坏形式的关系,并对临界剪压区进行应力分析,再应用Baant提出的尺度律,得到同时适用于斜拉破坏和剪压破坏的无腹筋钢筋混凝土梁的剪切强度公式,其中,临界剪压区高度是该公式的未知参数。通过对Baant试验数据库进行Levenberg-Marguardt非线性最小二乘曲线拟合,得到临界剪压区高度与各参数的幂指数关系。最后经与Collins试验数据库比较可知,相对于ACI 318-08和GB 50010-2010对应的剪切强度公式,所得的剪切强度公式能更好地与试验数据吻合,且和Baant的剪切强度公式计算结果接近。
Based on the limit equilibrium method,equilibrium equations were established by studying the free body composed of the critical inclined crack and the top cross-section from reinforced concrete beams without web reinforcements.Analyzing the relationships between principal stresses of the critical shear compression zone and damage forms,stress analysis of the critical shear compression zone was done.Then by applying Baant’s size effect law,a shear strength formula of reinforced concrete beams without stirrups for both diagonal tension failure and shear compression failure was obtained,where the critical shear compression zone height was the unknown parameter.And then by Levenberg-Marguardt nonlinear least-square curve fitting on Baant’s test database,exponential relationship between the height of the critical shear compression zone and parameters was gotten.Finally,comparison with Collins’test database shows that the obtained shear strength formula can be demonstrated to agree more favorably with the test database than those from ACI 318-08 and GB 50010-2010,and close with Baant’s shear strength formula.
Based on the limit equilibrium method,equilibrium equations were established by studying the free body composed of the critical inclined crack and the top cross-section from reinforced concrete beams without web reinforcements.Analyzing the relationships between principal stresses of the critical shear compression zone and damage forms,stress analysis of the critical shear compression zone was done.Then by applying Baant’s size effect law,a shear strength formula of reinforced concrete beams without stirrups for both diagonal tension failure and shear compression failure was obtained,where the critical shear compression zone height was the unknown parameter.And then by Levenberg-Marguardt nonlinear least-square curve fitting on Baant’s test database,exponential relationship between the height of the critical shear compression zone and parameters was gotten.Finally,comparison with Collins’test database shows that the obtained shear strength formula can be demonstrated to agree more favorably with the test database than those from ACI 318-08 and GB 50010-2010,and close with Baant’s shear strength formula.
引文
[1]Baant Z P,Yu Q,Gerstle W,Hanson J,Ju J W.Justification of ACI446proposal for updating ACI code provisions for shear design of reinforced concrete beams[J].Structural Journal,2007,104(5):601-610.
[2]管品武,徐泽晶,王博.钢筋混凝土构件抗剪承载力分析方法比较[J].世界地震工程,2002,18(3):95-101.(GUAN Pin-wu,XU Ze-jing,WANG Bo.Shear capacity analysis methods on RC members[J].World Earthquake Engineering,2002,18(3):95-101.(in Chinese))
[3]Gastebled O J,May I M.Fracture mechanics model applied to shear failure of reinforced concrete beams without stirrups[J].Structural Journal,2001,98(2):184-190.
[4]施岚青.钢筋混凝土构件抗剪能力计算的几点建议[J].清华大学学报(自然科学版),1973,16(1):54-83.(SHI Lan-qing.Several suggestions for reinforced concrete members’shear capacity cal-culation[J].Journal of Tsinghua University(Science and Technology),1973,16(1):54-83.(in Chi-nese))
[5]高丹盈,刘建秀,李宗坤.钢筋钢纤维混凝土梁斜截面抗剪强度的理论模式[J].工程力学,1984,11(2):130-137.(GAO Dan-ying,LIU Jian-xiu,LI Zhong-kun.Theoretical model on shear strength of reinforced fiber concrete beams[J].Engineering Mechanics,1984,11(2):130-137.(in Chinese))
[6]陈文钦,牛绍仁,秦文钺.集中荷载下钢筋混凝土约束梁抗剪强度的试验研究[J].重庆建筑工程学院学报,1984(3):57-84.(CHEN Wen-qin,NIU Shao-ren,QIN Wen-yue.Research on shear strength of reiforced concrete restrained bearms under centralized load[J].Journal of Construction En-gineering College,1984(3):57-84.(in Chinses))
[7]卫纪德.连续构件受剪性能研究之一:集中荷载作用下有腹筋约束梁的受剪强度[J].哈尔滨建筑工程学院学报,1985(3):16-31.(WEI Ji-de.Research of shear behavior of continuous members(1)the shear strength of beams with overhangs and web reinforcement under concentrated loads[J].Journal of Harbin University of Civil Engineering and Architecture,1985(3):16-31.(in Chinese))
[8]卫纪德,付有仓,关波,朱聘儒.集中荷载作用下钢筋混凝土伸臂梁、连续梁的抗剪强度[J].哈尔滨建筑工程学院学报,1987(2):43-54.(WEI Ji-de,FU You-cang,GUAN Bo,ZHU Pin-ru.Shear strength of reinforced concrete cantilever beams and continuous beams subject to concentrated loads[J].Journal of Harbin University of Civil Engineering and Architecture,1987(2):43-54.(in Chinese))
[9]支运芳,蒋超,甘民,陈永庆.纵筋率对有腹筋约束梁受剪性能影响的研究[J].重庆建筑大学学报,2003,27(4):64-69.(ZHI Yun-fang,JIANG Chao,GAN Min,CHEN Yong-qing.Study on effect of longitudinal reinforcement ratio on shear behavior of restrained beams with web reinforcement[J].Journal of Chongqing Jianzhu University,2003,27(4):64-69.(in Chinese))
[10]李立仁,蒋传星,支运芳.纵筋率对无腹筋约束梁抗剪性能影响的研究[J].重庆建筑大学学报,2008,30(1):49-53.(LI Li-ren,JIANG Chuan-xing,ZHI Yun-fang.Effect of longitudinal rein-forcement rate on shear behavior of beams without web reinforcement restriction[J].Journal of Chongqing Jianzhu University,2008,30(1):49-53.(in Chinese))
[11]杨卓琦,罗林,王启智.纵筋率对钢筋混凝土梁剪切强度的影响[J].工业建筑,2010,40(9):88-91.(YANG Zhuo-qi,LUO Lin,WANG Qi-zhi.Effect of longitudinal reinforcement ratio on shear strength of reinforced concrete beams[J].Industrial Construction,2010,40(9):88-91.(in Chi-nese))
[12]魏巍巍,贡金鑫,田磊.钢筋混凝土构件受剪承载力对比分析[J].建筑科学与工程学报,2010,27(2):25-37.(WEI Wei-wei,GONG Jin-xin,TIAN Lei.Comparative analysis of shear capacity for reinforced concrete members[J].Journal of Architecture and Civil Engineering,2010,27(2):25-37.(in Chinese))
[13]于磊,车轶,宋玉普.若干规范无腹筋梁受剪承载力公式比较[J].水利水电科技进展,2010,30(4):90-94.(YU Lei,CHE Yi,SONG Yu-pu.Comparison among shear design formulae in differ-ent codes for beams without web reinforcement[J].Advances in Science and Technology of Water Re-sources,2010,3(4):90-94.(in Chinese))
[14]Kani G N J.How safe are our large reinforced concrete beams?[J].ACI Journal,1967,64(3):128-141.
[15]Shioya T,Iguro M,Nojiri Y,Akiyama H,Okada T.Shear strength of large reinforced beams[C]//Li V C,Baant Z P,eds.Fracture Mechanics:Application to Concrete,SP-118.American Concrete Insti-tute,Farmington Hills,Mich,1989:259-279.
[16]Baant Z P,Kazemi M T.Size effect of diagonal shear failure of beams without stirrups[J].ACI Struc-tural Journal,1991,88(3):268-276.
[17]Collins M P,Kuchma D.How safe are our large,slightly reinforced concrete beams,slabs,and foot-ings?[J].ACI Structural Journal,1999,96(4):482-490.
[18]Baant Z P,Kim J K.Size effect in shear failure of longitudinally reinforced concrete beams[J].ACI Journal,1984,64(3):128-141.
[19]Baant Z P,Yu Q.Design against size effect on shear strength of reinforced concrete beams without stirrups—Ⅰ:formulation[J].ACI Structural Journal,2005,131(12):1877-1885.
[20]Baant Z P,Yu Q.Design against size effect on shear strength of reinforced concrete beams without stirrups—Ⅱ:verification and calibration[J].ACI Structural Journal,2005,131(12):1886-1897.
[21]Baant Z P,Chen E P.Scaling of structural failure[J].Applied Mechanics Reviews ASME,1997,50(10):593-627.
[22]ACI Committee318.Building Code Requirements for Structural Concrete(ACI318-08)and Commen-tary[S].American Concrete Institute318,Farmington Hills,Mich,2008:155-159.
[23]中华人民共和国住房和城乡建设部.GB50010-2010混凝土结构设计规范[S].北京:中国建筑工业出版社,2010.(Ministry of Housing and Urban-Rural Development of the People’s Republic of China.GB50010-2010Code for Design of Concrete Structures[S].Beijing:China Architecture&Building Press,2010.(in Chinese))[24]CSA Committee A23.3.CSA A23.3-04Design of Concrete Structures[S].Mississauga:Canadian Standards Association,2004.
[25]EN1992-1-1Euro code2:Design of Concrete Structures—Part1-1:General Rules and Rules for Buildings[S].London:Communities and Local Government Publications,2004.
[26]Kim W,White R N.Initiation of shear cracking in reinforced concrete beams with no web reinforce-ment[J].ACI Structural Journal,1991,88(3):301-308.
[27]Baant Z P.Fracturing truss model:size effect in shear failure of reinforced concrete[J].Journal of Engineering Mechanics,ASCE,1997,123(12):1276-1288.
[28]Kotsovos M D,Pavlovic M N.Ultimate Limit-State Design of Concrete Structures:a New Approach[M].London:Thomas Telford,1998:208.
[29]Zarais P D,Papadakis G C.Diagonal shear failure and size effect in RC beams without web reinforce-ment[J].Journal of Structural Engineering,ASCE,2001,127(7):733-742.
[30]Tureyen A K,Frosch R J.Concrete shear strength another perspective[J].ACI Structural Journal,2003,100(5):609-615.
[31]Choi K K,Park H G,Wight J K.Unified shear strength model for reinforced concrete beams—partⅠ:development[J].ACI Structural Journal,2007,104(2):142-152.
[32]ACI-ASCE Committee326.Shear and diagonal tension[J].ACI Journal Proceedings,1962,59(2):277-334.
[33]Baant Z P,Hsu-Huei Sun.Size effect in diagonal shear failure:influence of aggregate size and stirrups[J].ACI Material Journal,1987,84(4):259-272.
[34]Tureyen A K,Frosch R J.Shear tests of FRP-reinforced concrete beams without stirrups[J].ACI Structural Journal,2002,99(4):427-434.
[35]Reineck K H,Kuchma D A,Kim K S,Marx S.Shear database for reinforced concrete members with-out shear reinforcement[J].ACI Structural Journal,2003,100(2):240-249.
[36]Brown M D,Bayrak O,Jirsa J O.Design for shear based on loading conditions[J].ACI Structural Journal,2006,103(4):541-550.
[37]Collins M P,Bentz E C,Sherwood E G.Where is shear reinforcement required?review of research re-sults and design procedures[J].ACI Structural Journal,2008,105(5):590-600.
[38]Mphonde A G,Frantz G C.Shear tests of high-and low-strength concrete beams without stirrups[J].ACI Journal Proceedings,1984,81(3):350-357.
[39]Elzanaty A H,Nilson A H,Slate F O.Shear capacity of reinforced concrete beams using high-strength concrete[J].ACI Journal Proceedings,1986,83(2):290-296.
[40]Mathey R G,Watstein D.Shear strength of beams without web reinforcement containing deformed bars of different yield strengths[J].ACI Journal Proceedings,1963,60(2):183-208.
[41]贡金鑫,魏巍巍,胡家顺.中美欧混凝土结构设计[M].北京:中国建筑工业出版社,2007.(GONG Jin-xin,WEI Wei-wei,HU Jia-shun.Design of Concrete Structure Based on Chinese,American and European Codes[M].Beijing:China Architecture&Building Press,2007.(in Chinese))
[2]管品武,徐泽晶,王博.钢筋混凝土构件抗剪承载力分析方法比较[J].世界地震工程,2002,18(3):95-101.(GUAN Pin-wu,XU Ze-jing,WANG Bo.Shear capacity analysis methods on RC members[J].World Earthquake Engineering,2002,18(3):95-101.(in Chinese))
[3]Gastebled O J,May I M.Fracture mechanics model applied to shear failure of reinforced concrete beams without stirrups[J].Structural Journal,2001,98(2):184-190.
[4]施岚青.钢筋混凝土构件抗剪能力计算的几点建议[J].清华大学学报(自然科学版),1973,16(1):54-83.(SHI Lan-qing.Several suggestions for reinforced concrete members’shear capacity cal-culation[J].Journal of Tsinghua University(Science and Technology),1973,16(1):54-83.(in Chi-nese))
[5]高丹盈,刘建秀,李宗坤.钢筋钢纤维混凝土梁斜截面抗剪强度的理论模式[J].工程力学,1984,11(2):130-137.(GAO Dan-ying,LIU Jian-xiu,LI Zhong-kun.Theoretical model on shear strength of reinforced fiber concrete beams[J].Engineering Mechanics,1984,11(2):130-137.(in Chinese))
[6]陈文钦,牛绍仁,秦文钺.集中荷载下钢筋混凝土约束梁抗剪强度的试验研究[J].重庆建筑工程学院学报,1984(3):57-84.(CHEN Wen-qin,NIU Shao-ren,QIN Wen-yue.Research on shear strength of reiforced concrete restrained bearms under centralized load[J].Journal of Construction En-gineering College,1984(3):57-84.(in Chinses))
[7]卫纪德.连续构件受剪性能研究之一:集中荷载作用下有腹筋约束梁的受剪强度[J].哈尔滨建筑工程学院学报,1985(3):16-31.(WEI Ji-de.Research of shear behavior of continuous members(1)the shear strength of beams with overhangs and web reinforcement under concentrated loads[J].Journal of Harbin University of Civil Engineering and Architecture,1985(3):16-31.(in Chinese))
[8]卫纪德,付有仓,关波,朱聘儒.集中荷载作用下钢筋混凝土伸臂梁、连续梁的抗剪强度[J].哈尔滨建筑工程学院学报,1987(2):43-54.(WEI Ji-de,FU You-cang,GUAN Bo,ZHU Pin-ru.Shear strength of reinforced concrete cantilever beams and continuous beams subject to concentrated loads[J].Journal of Harbin University of Civil Engineering and Architecture,1987(2):43-54.(in Chinese))
[9]支运芳,蒋超,甘民,陈永庆.纵筋率对有腹筋约束梁受剪性能影响的研究[J].重庆建筑大学学报,2003,27(4):64-69.(ZHI Yun-fang,JIANG Chao,GAN Min,CHEN Yong-qing.Study on effect of longitudinal reinforcement ratio on shear behavior of restrained beams with web reinforcement[J].Journal of Chongqing Jianzhu University,2003,27(4):64-69.(in Chinese))
[10]李立仁,蒋传星,支运芳.纵筋率对无腹筋约束梁抗剪性能影响的研究[J].重庆建筑大学学报,2008,30(1):49-53.(LI Li-ren,JIANG Chuan-xing,ZHI Yun-fang.Effect of longitudinal rein-forcement rate on shear behavior of beams without web reinforcement restriction[J].Journal of Chongqing Jianzhu University,2008,30(1):49-53.(in Chinese))
[11]杨卓琦,罗林,王启智.纵筋率对钢筋混凝土梁剪切强度的影响[J].工业建筑,2010,40(9):88-91.(YANG Zhuo-qi,LUO Lin,WANG Qi-zhi.Effect of longitudinal reinforcement ratio on shear strength of reinforced concrete beams[J].Industrial Construction,2010,40(9):88-91.(in Chi-nese))
[12]魏巍巍,贡金鑫,田磊.钢筋混凝土构件受剪承载力对比分析[J].建筑科学与工程学报,2010,27(2):25-37.(WEI Wei-wei,GONG Jin-xin,TIAN Lei.Comparative analysis of shear capacity for reinforced concrete members[J].Journal of Architecture and Civil Engineering,2010,27(2):25-37.(in Chinese))
[13]于磊,车轶,宋玉普.若干规范无腹筋梁受剪承载力公式比较[J].水利水电科技进展,2010,30(4):90-94.(YU Lei,CHE Yi,SONG Yu-pu.Comparison among shear design formulae in differ-ent codes for beams without web reinforcement[J].Advances in Science and Technology of Water Re-sources,2010,3(4):90-94.(in Chinese))
[14]Kani G N J.How safe are our large reinforced concrete beams?[J].ACI Journal,1967,64(3):128-141.
[15]Shioya T,Iguro M,Nojiri Y,Akiyama H,Okada T.Shear strength of large reinforced beams[C]//Li V C,Baant Z P,eds.Fracture Mechanics:Application to Concrete,SP-118.American Concrete Insti-tute,Farmington Hills,Mich,1989:259-279.
[16]Baant Z P,Kazemi M T.Size effect of diagonal shear failure of beams without stirrups[J].ACI Struc-tural Journal,1991,88(3):268-276.
[17]Collins M P,Kuchma D.How safe are our large,slightly reinforced concrete beams,slabs,and foot-ings?[J].ACI Structural Journal,1999,96(4):482-490.
[18]Baant Z P,Kim J K.Size effect in shear failure of longitudinally reinforced concrete beams[J].ACI Journal,1984,64(3):128-141.
[19]Baant Z P,Yu Q.Design against size effect on shear strength of reinforced concrete beams without stirrups—Ⅰ:formulation[J].ACI Structural Journal,2005,131(12):1877-1885.
[20]Baant Z P,Yu Q.Design against size effect on shear strength of reinforced concrete beams without stirrups—Ⅱ:verification and calibration[J].ACI Structural Journal,2005,131(12):1886-1897.
[21]Baant Z P,Chen E P.Scaling of structural failure[J].Applied Mechanics Reviews ASME,1997,50(10):593-627.
[22]ACI Committee318.Building Code Requirements for Structural Concrete(ACI318-08)and Commen-tary[S].American Concrete Institute318,Farmington Hills,Mich,2008:155-159.
[23]中华人民共和国住房和城乡建设部.GB50010-2010混凝土结构设计规范[S].北京:中国建筑工业出版社,2010.(Ministry of Housing and Urban-Rural Development of the People’s Republic of China.GB50010-2010Code for Design of Concrete Structures[S].Beijing:China Architecture&Building Press,2010.(in Chinese))[24]CSA Committee A23.3.CSA A23.3-04Design of Concrete Structures[S].Mississauga:Canadian Standards Association,2004.
[25]EN1992-1-1Euro code2:Design of Concrete Structures—Part1-1:General Rules and Rules for Buildings[S].London:Communities and Local Government Publications,2004.
[26]Kim W,White R N.Initiation of shear cracking in reinforced concrete beams with no web reinforce-ment[J].ACI Structural Journal,1991,88(3):301-308.
[27]Baant Z P.Fracturing truss model:size effect in shear failure of reinforced concrete[J].Journal of Engineering Mechanics,ASCE,1997,123(12):1276-1288.
[28]Kotsovos M D,Pavlovic M N.Ultimate Limit-State Design of Concrete Structures:a New Approach[M].London:Thomas Telford,1998:208.
[29]Zarais P D,Papadakis G C.Diagonal shear failure and size effect in RC beams without web reinforce-ment[J].Journal of Structural Engineering,ASCE,2001,127(7):733-742.
[30]Tureyen A K,Frosch R J.Concrete shear strength another perspective[J].ACI Structural Journal,2003,100(5):609-615.
[31]Choi K K,Park H G,Wight J K.Unified shear strength model for reinforced concrete beams—partⅠ:development[J].ACI Structural Journal,2007,104(2):142-152.
[32]ACI-ASCE Committee326.Shear and diagonal tension[J].ACI Journal Proceedings,1962,59(2):277-334.
[33]Baant Z P,Hsu-Huei Sun.Size effect in diagonal shear failure:influence of aggregate size and stirrups[J].ACI Material Journal,1987,84(4):259-272.
[34]Tureyen A K,Frosch R J.Shear tests of FRP-reinforced concrete beams without stirrups[J].ACI Structural Journal,2002,99(4):427-434.
[35]Reineck K H,Kuchma D A,Kim K S,Marx S.Shear database for reinforced concrete members with-out shear reinforcement[J].ACI Structural Journal,2003,100(2):240-249.
[36]Brown M D,Bayrak O,Jirsa J O.Design for shear based on loading conditions[J].ACI Structural Journal,2006,103(4):541-550.
[37]Collins M P,Bentz E C,Sherwood E G.Where is shear reinforcement required?review of research re-sults and design procedures[J].ACI Structural Journal,2008,105(5):590-600.
[38]Mphonde A G,Frantz G C.Shear tests of high-and low-strength concrete beams without stirrups[J].ACI Journal Proceedings,1984,81(3):350-357.
[39]Elzanaty A H,Nilson A H,Slate F O.Shear capacity of reinforced concrete beams using high-strength concrete[J].ACI Journal Proceedings,1986,83(2):290-296.
[40]Mathey R G,Watstein D.Shear strength of beams without web reinforcement containing deformed bars of different yield strengths[J].ACI Journal Proceedings,1963,60(2):183-208.
[41]贡金鑫,魏巍巍,胡家顺.中美欧混凝土结构设计[M].北京:中国建筑工业出版社,2007.(GONG Jin-xin,WEI Wei-wei,HU Jia-shun.Design of Concrete Structure Based on Chinese,American and European Codes[M].Beijing:China Architecture&Building Press,2007.(in Chinese))
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