基于拉压杆模型的预应力深梁抗剪承载力
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摘要
为了给中国桥梁工程中的深梁抗剪设计提供理论依据,针对深梁应变分布不符合平截面假定,在结构设计中属于力流紊乱区的问题,借助拉压杆模型理论对预应力作用下的混凝土深梁极限抗剪承载力展开试验与数值研究。首先利用通用有限元分析软件ANSYS并结合Tcl/tk语言联合开发插件程序,以图形用户界面的方式实现深梁拉压杆模型的自动构形。然后,借助生成的拉压杆模型,按改进的破坏准则推导考虑预应力效应的深梁极限抗剪承载力公式,并通过12组数值试验确定主拉应力沿深梁拉压杆模型压杆分布的不均匀系数表达式。最后,通过有黏结与无黏结预应力混凝土深梁试验对推导的预应力深梁极限抗剪承载力公式的有效性进行验证。研究结果表明:对于有黏结预应力混凝土深梁试验,试验结果与Tan教授预测结果的比值均大于与本文计算结果的比值,前者平均值为1.27,后者为1.10;对于无黏结预应力混凝土深梁试验,试验结果与Tan教授预测结果之比的平均值为1.13,与本文计算结果之比的平均值为1.10;相对于已有预测值,计算结果与试验结果更加吻合,并且偏于安全,说明该公式可以较可靠地预测深梁的实际承载力,具有一定的理论价值和实用意义。
Deep beams are generally classified as a discontinuity region(D-region),where the conventional plane bending theory does not apply.To provide a theoretical foundation for deep beams design in bridge structures,both experiments and numerical simulations were conducted to investigate the shear-carrying capacity of prestressed concrete deep beams by means of the strutand-tie model theory.First,apractical program was developed to automatically generate the strut-and-tie model of prestressed deep beams using a combination of the finite element analysis software ANSYS and Tcl/tk language.Second,the shear strength formula of prestressed deepbeams was derived with the aid of the strut-and-tie model according to a modified failure criterion.At the same time,expressions for two key coefficients in the formula were derived using 12 sets of numerical simulations.Finally,two tests were conducted to verify the effectiveness of the formula for predicting the shear strength of prestressed deep beams.In the first test,the average ratio of the test results to results obtained by Professor Tan was 1.27,which was larger than the ratio of the test results to the author's prediction results(i.e.,1.10).In the second test,the former ratio was 1.13,while the latter ratio was 1.10.A comparison of the results indicate that the predicted values in this study shows better agreement with the experimental values than existing solutions,and these prediction values stand on the conservative side.It indicates that the shear strength formula derived in this study can predict the actual bearing capacity of deep beams,which has some theoretical value and practical significance.
Deep beams are generally classified as a discontinuity region(D-region),where the conventional plane bending theory does not apply.To provide a theoretical foundation for deep beams design in bridge structures,both experiments and numerical simulations were conducted to investigate the shear-carrying capacity of prestressed concrete deep beams by means of the strutand-tie model theory.First,apractical program was developed to automatically generate the strut-and-tie model of prestressed deep beams using a combination of the finite element analysis software ANSYS and Tcl/tk language.Second,the shear strength formula of prestressed deepbeams was derived with the aid of the strut-and-tie model according to a modified failure criterion.At the same time,expressions for two key coefficients in the formula were derived using 12 sets of numerical simulations.Finally,two tests were conducted to verify the effectiveness of the formula for predicting the shear strength of prestressed deep beams.In the first test,the average ratio of the test results to results obtained by Professor Tan was 1.27,which was larger than the ratio of the test results to the author's prediction results(i.e.,1.10).In the second test,the former ratio was 1.13,while the latter ratio was 1.10.A comparison of the results indicate that the predicted values in this study shows better agreement with the experimental values than existing solutions,and these prediction values stand on the conservative side.It indicates that the shear strength formula derived in this study can predict the actual bearing capacity of deep beams,which has some theoretical value and practical significance.
引文
[1]LIM E,HWANG S J.Modeling of the Strut-and-tie Parameters of Deep Beams for Shear Strength Prediction[J].Engineering Structures,2016,108:104-112.
[2]汪梦甫,徐亚飞,陈红波.PE-ECC短梁抗剪性能研究[J].湖南大学学报:自然科学版,2015,42(11):10-16.WANG Meng-fu,XU Ya-fei,CHEN Hong-bo.Research on Shear Behavior of PE-ECC Short Beam[J].Journal of Hunan University:Natural Sciences,2015,42(11):10-16.
[3]BRINSON L C.One-dimensional Constitutive Behavior of Shape Memory Alloys:Thermomechanical Derivation with Non-constant Material Functions and Redefined Martensite Internal Variable[J].Journal of Intelligent Material Systems and Structures,1993,4(2):229-242.
[4]邓明科,卢化松,杨开屏,等.型钢高延性混凝土短梁抗剪性能试验研究[J].建筑结构学报,2015,36(10):73-80.DEGN Ming-ke,LU Hua-song,YANG Kai-ping,et al.Experimental Study on Shear Behavior of Steel Reinforced High Ductile Concrete Short Beams[J].Journal of Building Structures,2015,36(10):73-80.
[5]黄华,杨琪,郑益斌,等.加筋高性能砂浆加固RC梁抗剪性能及承载力计算[J].长安大学学报:自然科学版,2015,35(1):76-83.HUANG Hua,YANG Qi,ZHENG Yi-bin,et al.Shear Behavior and Bearing Capacity Calculation of RC Beams Strengthened with High Performance Ferrocement Laminate[J].Journal of Chang’an University:Natural Science Edition,2015,35(1):76-83.
[6]CHEN Q,LEVY C.Active Vibration Control of Elastic Beam by Means of Shape Memory Alloy Layers[J].Journal of Smart Materials and Structures,1996,5(4):400-406.
[7]YANG K H,ASHOUR A F.Strut-and-tie Model Based on Crack Band Theory for Deep Beams[J].Journal of Structural Engineering,2011,137(10):1030-1038.
[8]黄华,刘伯权,贺拴海,等.高强钢绞线网加固RC梁抗剪剥离承载力计算[J].中国公路学报,2013,26(2):102-109.HUANG Hua,LIU Bo-quan,HE Shuan-hai,et al.Calculation of Shear Debonding Capacity of RC Beams Strengthened with High Strength Steel Wire Mesh[J].China Journal of Highway and Transport,2013,26(2):102-109.
[9]黄侨,张连振,马桂军.基于塑性理论的钢筋砼简支深梁的抗剪强度研究(一)[J].工程力学,2005,22(4):167-170.HUANG Qiao,ZHANG Lian-zhen,MA Gui-jun.Shear Strength Analysis of Simply Supported Reinforced Concrete Deep Beams Based on Plastic Theory:PartΙ[J].Engineering Mechanics,2005,22(4):167-170.
[10]黄侨,张连振,马桂军.基于塑性理论的钢筋砼简支深梁的抗剪强度研究(二)[J].工程力学,2005,22(6):155-158.HUANG Qiao,ZHANG Lian-zhen,MA Gui-jun.Shear Strength Analysis of Simply Supported Reinforced Concrete Deep Beams Based on Plastic Theory:PartⅡ[J].Engineering Mechanics,2005,22(6):155-158.
[11]RITTER W.Die Bauweise Hennebique(Construction Techniques of Hennebique)[J].Schweizerische Bauzeitung,1899,33(7):59-61.
[12]深梁专题组.钢筋砼深梁的试验研究[J].建筑结构学报,1987,8(4):23-35.Research Group on Deep Beam.Experimental Investigation of Reinforced Concrete Deep Beam[J].Journal of Building Structures,1987,8(4):23-35.
[13]YUN Y M.Computer Graphics for Nonlinear Strut Tie Model Approach[J].Journal of Computing in Civil Engineering,2000,14(2):127-133.
[14]CIANCIO D,ROBINSON S.Use of the Strut-and-tie Model in the Analysis of Reinforced Cement-stabilized Rammed Earth Lintels[J].Journal of Materials in Civil Engineering,2011,23(5):587-596.
[15]COOK W D,MITCHELL D.Studies of Disturbed Regions Near Discontinuities in Reinforced Concrete Members[J].ACI Structural Journal,1988,85(2):206-216.
[16]MARTI P.Basic Tools of Reinforced Concrete Beam Design[J].ACI Structural Journal,1985,82(1):46-56.
[17]刘钊.桥梁概念设计与分析理论[M].北京:人民交通出版社,2010.LIU Zhao.Conceptual Design and Analytical Theory of Bridges[M].Beijing:China Communications Press,2010.
[18]LIANG Q Q,XIE Y M,STEVEN G P.Generating Optimal Strut-and-tie Models in Prestressed Concrete Beams by Performance—Based Optimization[J].ACI Structural Journal,2001,98(2):226-232.
[19]TAN K H,TONG K,TANG C Y.Direct Strut and Tie Model for Prestressed Deep Beams[J].Journal of Structural Engineering,2001,127(9):1076-1084.
[20]COLLINS M P,MITCHELL D.Prestressed Concrete Structures[M].Upper Saddle River:Prentice Hall,1991.
[21]COOK R D,YOUNG W C.Advanced Mechanics of Materials[M].New York:Macmillan Publishing Company,1985.
[22]TAN K H,TONG K.Shear Behaviour and Analysis of Partially Prestressed I-girders[J].The Structural Engineer,1999,77(23/24):28-34.
[23]TAN K H,LU H Y,TENG S.Size Effect in Large Prestressed Concrete Deep Beams[J].ACI Structural Journal,1999,96(6):937-946.
[2]汪梦甫,徐亚飞,陈红波.PE-ECC短梁抗剪性能研究[J].湖南大学学报:自然科学版,2015,42(11):10-16.WANG Meng-fu,XU Ya-fei,CHEN Hong-bo.Research on Shear Behavior of PE-ECC Short Beam[J].Journal of Hunan University:Natural Sciences,2015,42(11):10-16.
[3]BRINSON L C.One-dimensional Constitutive Behavior of Shape Memory Alloys:Thermomechanical Derivation with Non-constant Material Functions and Redefined Martensite Internal Variable[J].Journal of Intelligent Material Systems and Structures,1993,4(2):229-242.
[4]邓明科,卢化松,杨开屏,等.型钢高延性混凝土短梁抗剪性能试验研究[J].建筑结构学报,2015,36(10):73-80.DEGN Ming-ke,LU Hua-song,YANG Kai-ping,et al.Experimental Study on Shear Behavior of Steel Reinforced High Ductile Concrete Short Beams[J].Journal of Building Structures,2015,36(10):73-80.
[5]黄华,杨琪,郑益斌,等.加筋高性能砂浆加固RC梁抗剪性能及承载力计算[J].长安大学学报:自然科学版,2015,35(1):76-83.HUANG Hua,YANG Qi,ZHENG Yi-bin,et al.Shear Behavior and Bearing Capacity Calculation of RC Beams Strengthened with High Performance Ferrocement Laminate[J].Journal of Chang’an University:Natural Science Edition,2015,35(1):76-83.
[6]CHEN Q,LEVY C.Active Vibration Control of Elastic Beam by Means of Shape Memory Alloy Layers[J].Journal of Smart Materials and Structures,1996,5(4):400-406.
[7]YANG K H,ASHOUR A F.Strut-and-tie Model Based on Crack Band Theory for Deep Beams[J].Journal of Structural Engineering,2011,137(10):1030-1038.
[8]黄华,刘伯权,贺拴海,等.高强钢绞线网加固RC梁抗剪剥离承载力计算[J].中国公路学报,2013,26(2):102-109.HUANG Hua,LIU Bo-quan,HE Shuan-hai,et al.Calculation of Shear Debonding Capacity of RC Beams Strengthened with High Strength Steel Wire Mesh[J].China Journal of Highway and Transport,2013,26(2):102-109.
[9]黄侨,张连振,马桂军.基于塑性理论的钢筋砼简支深梁的抗剪强度研究(一)[J].工程力学,2005,22(4):167-170.HUANG Qiao,ZHANG Lian-zhen,MA Gui-jun.Shear Strength Analysis of Simply Supported Reinforced Concrete Deep Beams Based on Plastic Theory:PartΙ[J].Engineering Mechanics,2005,22(4):167-170.
[10]黄侨,张连振,马桂军.基于塑性理论的钢筋砼简支深梁的抗剪强度研究(二)[J].工程力学,2005,22(6):155-158.HUANG Qiao,ZHANG Lian-zhen,MA Gui-jun.Shear Strength Analysis of Simply Supported Reinforced Concrete Deep Beams Based on Plastic Theory:PartⅡ[J].Engineering Mechanics,2005,22(6):155-158.
[11]RITTER W.Die Bauweise Hennebique(Construction Techniques of Hennebique)[J].Schweizerische Bauzeitung,1899,33(7):59-61.
[12]深梁专题组.钢筋砼深梁的试验研究[J].建筑结构学报,1987,8(4):23-35.Research Group on Deep Beam.Experimental Investigation of Reinforced Concrete Deep Beam[J].Journal of Building Structures,1987,8(4):23-35.
[13]YUN Y M.Computer Graphics for Nonlinear Strut Tie Model Approach[J].Journal of Computing in Civil Engineering,2000,14(2):127-133.
[14]CIANCIO D,ROBINSON S.Use of the Strut-and-tie Model in the Analysis of Reinforced Cement-stabilized Rammed Earth Lintels[J].Journal of Materials in Civil Engineering,2011,23(5):587-596.
[15]COOK W D,MITCHELL D.Studies of Disturbed Regions Near Discontinuities in Reinforced Concrete Members[J].ACI Structural Journal,1988,85(2):206-216.
[16]MARTI P.Basic Tools of Reinforced Concrete Beam Design[J].ACI Structural Journal,1985,82(1):46-56.
[17]刘钊.桥梁概念设计与分析理论[M].北京:人民交通出版社,2010.LIU Zhao.Conceptual Design and Analytical Theory of Bridges[M].Beijing:China Communications Press,2010.
[18]LIANG Q Q,XIE Y M,STEVEN G P.Generating Optimal Strut-and-tie Models in Prestressed Concrete Beams by Performance—Based Optimization[J].ACI Structural Journal,2001,98(2):226-232.
[19]TAN K H,TONG K,TANG C Y.Direct Strut and Tie Model for Prestressed Deep Beams[J].Journal of Structural Engineering,2001,127(9):1076-1084.
[20]COLLINS M P,MITCHELL D.Prestressed Concrete Structures[M].Upper Saddle River:Prentice Hall,1991.
[21]COOK R D,YOUNG W C.Advanced Mechanics of Materials[M].New York:Macmillan Publishing Company,1985.
[22]TAN K H,TONG K.Shear Behaviour and Analysis of Partially Prestressed I-girders[J].The Structural Engineer,1999,77(23/24):28-34.
[23]TAN K H,LU H Y,TENG S.Size Effect in Large Prestressed Concrete Deep Beams[J].ACI Structural Journal,1999,96(6):937-946.