张拉预应力筋阶段的T型梁应力分析
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摘要
采用装配式的预应力混凝土T型梁桥具有桥梁上、下部同时施工、T型梁预制质量易于保证等优点，该桥型是目前公路桥梁经常使用的型式。预应力筋的张拉顺序与T型梁的张拉效果有着密切关系。不适当的预应力筋张拉顺序会导致T型梁局部应力过大而开裂，因此掌握此阶段的应力十分重要。
本文首先对预应力混凝土结构在国内外发展和研究现状进行了阐述，介绍了材料非线性、边界非线性的基本理论，并确定了本文非线性有限元分析模型中所采用的材料本构关系、强化模型和非线性方程求解方法。介绍了张拉预应力筋阶段T型梁的试验概况。由于在张拉预应力筋过程中T型梁与张拉台座之间的接触长度很难确定，所以计算此阶段的T型梁受力情况比较困难，通常在计算时把T型梁假设为简支得出近似解，本文采用接触单元解决此问题。基于大型有限元软件ANSYS建立了全梁有限元模型，采用三种工况张拉预应力筋，分析T型梁跨中的应力、反拱度和侧向位移与张拉预应力筋顺序的关系。根据桥梁规范计算了T型梁跨中和四分之一跨径处的应力。将根据桥梁规范计算结果、有限元模型计算结果和实测结果进行了比较，分析了产生差异的原因。建立了梁端部局部承压有限元模型，采用三种工况张拉预应力筋，分析了张拉预应力筋过程中的应力分布，讨论了锚垫板下混凝土的应力与张拉预应力筋顺序的关系。
Prefabricated prestressed concrete T-shaped beam bridge was one of the most popularpattern in the highway bridge currently for its many advantages, such as its up and lower partcan be done on the same time and the quality of the T-shaped beam can be easily assured. Therelation between sequence of tensioning tendons with tensioning effect of T-shaped beam isclosed. Improper sequence of tensioning tendons may cause high partial stress and the T-shaped beam may crack, so it is important to check the stress in this situation.
Firstly, the domestic and international development and the research condition ofPrestressed concrete were generalized in this paper. The basic theories on the materialnonlinearity and boundary nonlinearity were analyzed, then the method adopted in the finiteelements method nonlinear analysis which contains the relation of the stress and the strain forthe material, hardening models, and the solution of nonlinear equations were introduced. Thenthe T-shaped beam experiment was introduced. It is difficult to calculate the stress of T-shapedbeam during the procession of tensioning tendons for the contact length between beam withabutment was hard to decide, usually suppose the T-shaped beam was simple-supported thencalculate similarly, try to calculate the stress accurately based on contact element of ANSYSprogram in this paper. Establish one finite element model of whole beam, tension the tendonsby three sequences. The relation between the stress on L/2, reversed, deflection, side bend ofthe T-shaped beam with the sequence of tensioning tendons was analyzed. Meanwhile calculatethe stress of T-shaped beam on the L/2 and L/4 according to the bridge code. The resultaccording to the bridge code、by ANSYS program and experiment are compared, the cause ofdifferentiation was analyzed. One finite element model of end beam was established, tensionthe tendons by three sequences, the stress distribution during the procession of tensioning thetendons was analyzed, the relation between the stress of concrete under the anchorage with thesequence of tensioning tendons was discussed.
本文首先对预应力混凝土结构在国内外发展和研究现状进行了阐述，介绍了材料非线性、边界非线性的基本理论，并确定了本文非线性有限元分析模型中所采用的材料本构关系、强化模型和非线性方程求解方法。介绍了张拉预应力筋阶段T型梁的试验概况。由于在张拉预应力筋过程中T型梁与张拉台座之间的接触长度很难确定，所以计算此阶段的T型梁受力情况比较困难，通常在计算时把T型梁假设为简支得出近似解，本文采用接触单元解决此问题。基于大型有限元软件ANSYS建立了全梁有限元模型，采用三种工况张拉预应力筋，分析T型梁跨中的应力、反拱度和侧向位移与张拉预应力筋顺序的关系。根据桥梁规范计算了T型梁跨中和四分之一跨径处的应力。将根据桥梁规范计算结果、有限元模型计算结果和实测结果进行了比较，分析了产生差异的原因。建立了梁端部局部承压有限元模型，采用三种工况张拉预应力筋，分析了张拉预应力筋过程中的应力分布，讨论了锚垫板下混凝土的应力与张拉预应力筋顺序的关系。
Prefabricated prestressed concrete T-shaped beam bridge was one of the most popularpattern in the highway bridge currently for its many advantages, such as its up and lower partcan be done on the same time and the quality of the T-shaped beam can be easily assured. Therelation between sequence of tensioning tendons with tensioning effect of T-shaped beam isclosed. Improper sequence of tensioning tendons may cause high partial stress and the T-shaped beam may crack, so it is important to check the stress in this situation.
Firstly, the domestic and international development and the research condition ofPrestressed concrete were generalized in this paper. The basic theories on the materialnonlinearity and boundary nonlinearity were analyzed, then the method adopted in the finiteelements method nonlinear analysis which contains the relation of the stress and the strain forthe material, hardening models, and the solution of nonlinear equations were introduced. Thenthe T-shaped beam experiment was introduced. It is difficult to calculate the stress of T-shapedbeam during the procession of tensioning tendons for the contact length between beam withabutment was hard to decide, usually suppose the T-shaped beam was simple-supported thencalculate similarly, try to calculate the stress accurately based on contact element of ANSYSprogram in this paper. Establish one finite element model of whole beam, tension the tendonsby three sequences. The relation between the stress on L/2, reversed, deflection, side bend ofthe T-shaped beam with the sequence of tensioning tendons was analyzed. Meanwhile calculatethe stress of T-shaped beam on the L/2 and L/4 according to the bridge code. The resultaccording to the bridge code、by ANSYS program and experiment are compared, the cause ofdifferentiation was analyzed. One finite element model of end beam was established, tensionthe tendons by three sequences, the stress distribution during the procession of tensioning thetendons was analyzed, the relation between the stress of concrete under the anchorage with thesequence of tensioning tendons was discussed.
引文
[1] 沈蒲生．混凝土结构设计原理．北京：高等教育出版社，2002：236～242
[2] James R Libby. Modern Prestressed Concrete Design Principles and Construction Methods. San Diego: Van Nostrand Reinhold Ltd, 1977, 43～52
[3] 房贞政．无粘结与部分预应力结构．北京：人民交通出版社，1999：1～5
[4] 张树仁，郑绍琏，黄侨，鲍卫刚．钢筋混凝土及预应力混凝土桥梁结构设计原理．北京：人民交通出版社，2005：265～268 311～313．
[5] 贾艳敏，高力．结构设计原理．北京：人民交通出版社，2004：170～185
[6] 林同炎，NED H．BURNS著．预应力混凝土结构设计．路湛沁，黄棠，马誉美译．第三版．北京：中国铁道出版社，1983：20～35
[7] 周志祥，范量，吴海军．预应力混凝土桥梁新技术——探索与实践．北京：人民交通出版社，2004：3～5
[8] 朱新实，刘效尧．预应力技术及材料设备．北京：人民交通出版社，2005：11～12
[9] Hrennikoff. Solution of Problems in Elasticity by the Frame Work Method. Journal of Applied Mechanics Can Geotech J, 1941, 9(1):169～175
[10] McHenry. A Lattice Analogy for the Solution of Plane Stress Problems. Journal of Institution of Civil Engineers, 1943, 9(1):63～80
[11] Cournt. Variation Methods for the solution of Problems of Equilibrium and Vibrations. Bulletin of the American Mathematical Society, 1943, 9(1):63～80
[12] Clough. The Finite Element Method in Plane Stress Analysis. Journal of Eng Mach Div ASCE, 1977, 5(2):43～56
[13] Szabo, Lee. Derivation of Stiffness Matrices for Problems in Plane Elasticity by Galerkin's Method. International Journal of Numerical Methods in Engineering ASCE, 1969, 12(5):103～105
[14] Zienkiewicz, Parekh. Transient Field Problem: Two-Dimensional and Three-Dimensional Analysis by Isoparamtreic Finite Elements. International Journal of Numerical Methods in Engineers, 1970, 9(1): 63～80
[15] Daryl L Logan著．有限元方法基础教程．伍义生，吴永礼译．北京：电子工业出版社．2003：1～5
[16] 王心勇，辛全才，宋娟．钢筋混凝土结构的非线性有限元分析．人民黄河，2006，28(8)：60～61
[17] 杜培荣，祁顺彬．钢筋混凝土结构数值模型的改进．盐城工学院学报(自然科学版)， 2004，17(2)：25～28
[18] 张卫辉．考虑粘结滑移的钢筋混凝土．湖南大学硕士论文，2006：11～16
[19] 江见鲸，陆新征，叶列平．混凝土结构有限元分析．北京：清华大学出版社，2004：86～98
[20] 吕西林，金国芳，吴晓涵．钢筋混凝土结构非线性有限元理论与应用．上海：同济大学出版社，1997：13～17
[21] 陈惠发，A F萨里普著．混凝土和土的本构关系．余天庆，王勋文，刘西拉，韩大建译．北京：中国建筑工业出版社，2004：220～221
[22] Robert L Taylor. On a Finite Element Method for Dynamic Contact IMPact Problems[J]. Int. J. Number Methods Eng., 1993, 18(36):123～140
[23] Huang Zhenyu. An Interval Entropy Penalty Method for Nonlinear Global Optimization[J]. Reliable Computing, 1998, 6(4):15～25
[24] Zavarise G., Wriggers P, Schrefler B A. On Augmented Lagrangian Algorithms for The Mechanical Contact Problems with Friction[J]. Int. J. Number Methods Eng., 1995, 16(38):929～949
[25] D Goldfarb, R Polyak. A Modified Barrier-Augmented Lagrangian Method for Constrained Minimization[J]. Computational Optimization and Applications, 1999, 16(14): 55～74
[26] 王满生，周锡元，胡聿贤．桩土动力分析中接触模型的研究[J]．岩土工程学报，2005， 27(6)：616～620
[27] O C Zienkiewicz，R L Taylor著．有限元方法——固体力学．庄茁，岑松译，北京：清华大学出版社，2006：331～336
[28] 钱俊梅，江晓红，仲小冬，范军．浅谈基于ANSYS软件的接触分析问题．煤矿机械，2006，27(7)：62～64
[29] 张亚欧，谷志飞，宋勇．ANSYS7.0有限元分析实用教程．北京：清华大学出版社，2004：276～277
[30] 张印阁，冯玉平，张宏祥．桥梁结构现场检测技术．哈尔滨：东北林业大学出版社，2003：13～37
[31] Kim, J H, M yang H. Evolutionary programming techniques forced strained optimization problems. IEEE Trans on Evolu.tionary Computation, 1997, 1(2): 129～140
[32] Adeli H, Cheng N T. Augmented Lagarangian genetic algorithm for structural optimization. J Aerosp Engrg ASCE, 1994, 7(1):104～118
[33] Adeli H, Kamal O. Efficient optimization of space trusses. Comp and Struct, 1986, 24(3): 501～511
[34] 刘世忠．基于ANSYS的钢筋混凝土结构非线性有限元分析．北京：工程结构，2002，26(2)：92～95
[35] 陆新征，江见鲸．用ANSYS Solid65单元分析混凝土组合构件复杂应力．建筑结构，2003，(6)：47～51
[36] 龚曙光，谢桂兰等．ANSYS工程应用实例解析．北京：机械工业出版社，2003：73～82
[37] 郝文化．ANSYS在土木工程应用实例．北京：中国水利水电出版社，2005：100～106
[38] 顾杰隽，陈少锋．T梁反拱值的产生及控制．公路，2004，(8)：283～284
[39] 李东梅．后张40 m工形梁侧弯原因分析与防治措施．铁道建筑，2006,(1)：18～19
[40] 吴银利，李强，段树金．预应力混凝土梁侧弯的控制措施．桥梁，2005，(2)：60～61
[41] 中华人民共和国行业标准．公路钢筋混凝土及预应力混凝土桥涵设计规范(JGJ D62-2004)，．北京：人民交通出版社，2004：181～182
[42] Huang T. Stresses in end zones of a post-pensioned prestressed beam [J]. ACI Journal, 1964, 61(5): 589～601
[43] Marshall W T. A theory for end zone stresses in pre-tensioned concrete beams [J]. PCI Journal, 1966, 11(2): 45～51
[44] Wollmann G. P, Breen J E. Discussion of "Stress distribution and cracking behavior at anchorage zones in prestressed concrete members" [J]. ACI Structural Journal, 1998, 95(4): 458～459
[45] Gergely P, Sozen M A. Design of anchorage zone reinforcement in prestressed concrete members [J]. PCI Journal, 1967, 12(2): 63～75
[46] Stone W C, Breen J. E. Behavior of post-tensioned girder anchorage zones [J]. PCI Journal, 1984, 29(1): 64～109
[47] Sarles D, Itani R Y. Effect of end blocks on anchorage zone stresses in prestressed concrete girders [J]. PCI Journal, 1984, Z9(6): 100～114
[48] 郑文忠，张吉柱．密布预应力束锚具下混凝土局部受压承载力计算方法。建筑结构学报，2004，25(4)：60～65
[2] James R Libby. Modern Prestressed Concrete Design Principles and Construction Methods. San Diego: Van Nostrand Reinhold Ltd, 1977, 43～52
[3] 房贞政．无粘结与部分预应力结构．北京：人民交通出版社，1999：1～5
[4] 张树仁，郑绍琏，黄侨，鲍卫刚．钢筋混凝土及预应力混凝土桥梁结构设计原理．北京：人民交通出版社，2005：265～268 311～313．
[5] 贾艳敏，高力．结构设计原理．北京：人民交通出版社，2004：170～185
[6] 林同炎，NED H．BURNS著．预应力混凝土结构设计．路湛沁，黄棠，马誉美译．第三版．北京：中国铁道出版社，1983：20～35
[7] 周志祥，范量，吴海军．预应力混凝土桥梁新技术——探索与实践．北京：人民交通出版社，2004：3～5
[8] 朱新实，刘效尧．预应力技术及材料设备．北京：人民交通出版社，2005：11～12
[9] Hrennikoff. Solution of Problems in Elasticity by the Frame Work Method. Journal of Applied Mechanics Can Geotech J, 1941, 9(1):169～175
[10] McHenry. A Lattice Analogy for the Solution of Plane Stress Problems. Journal of Institution of Civil Engineers, 1943, 9(1):63～80
[11] Cournt. Variation Methods for the solution of Problems of Equilibrium and Vibrations. Bulletin of the American Mathematical Society, 1943, 9(1):63～80
[12] Clough. The Finite Element Method in Plane Stress Analysis. Journal of Eng Mach Div ASCE, 1977, 5(2):43～56
[13] Szabo, Lee. Derivation of Stiffness Matrices for Problems in Plane Elasticity by Galerkin's Method. International Journal of Numerical Methods in Engineering ASCE, 1969, 12(5):103～105
[14] Zienkiewicz, Parekh. Transient Field Problem: Two-Dimensional and Three-Dimensional Analysis by Isoparamtreic Finite Elements. International Journal of Numerical Methods in Engineers, 1970, 9(1): 63～80
[15] Daryl L Logan著．有限元方法基础教程．伍义生，吴永礼译．北京：电子工业出版社．2003：1～5
[16] 王心勇，辛全才，宋娟．钢筋混凝土结构的非线性有限元分析．人民黄河，2006，28(8)：60～61
[17] 杜培荣，祁顺彬．钢筋混凝土结构数值模型的改进．盐城工学院学报(自然科学版)， 2004，17(2)：25～28
[18] 张卫辉．考虑粘结滑移的钢筋混凝土．湖南大学硕士论文，2006：11～16
[19] 江见鲸，陆新征，叶列平．混凝土结构有限元分析．北京：清华大学出版社，2004：86～98
[20] 吕西林，金国芳，吴晓涵．钢筋混凝土结构非线性有限元理论与应用．上海：同济大学出版社，1997：13～17
[21] 陈惠发，A F萨里普著．混凝土和土的本构关系．余天庆，王勋文，刘西拉，韩大建译．北京：中国建筑工业出版社，2004：220～221
[22] Robert L Taylor. On a Finite Element Method for Dynamic Contact IMPact Problems[J]. Int. J. Number Methods Eng., 1993, 18(36):123～140
[23] Huang Zhenyu. An Interval Entropy Penalty Method for Nonlinear Global Optimization[J]. Reliable Computing, 1998, 6(4):15～25
[24] Zavarise G., Wriggers P, Schrefler B A. On Augmented Lagrangian Algorithms for The Mechanical Contact Problems with Friction[J]. Int. J. Number Methods Eng., 1995, 16(38):929～949
[25] D Goldfarb, R Polyak. A Modified Barrier-Augmented Lagrangian Method for Constrained Minimization[J]. Computational Optimization and Applications, 1999, 16(14): 55～74
[26] 王满生，周锡元，胡聿贤．桩土动力分析中接触模型的研究[J]．岩土工程学报，2005， 27(6)：616～620
[27] O C Zienkiewicz，R L Taylor著．有限元方法——固体力学．庄茁，岑松译，北京：清华大学出版社，2006：331～336
[28] 钱俊梅，江晓红，仲小冬，范军．浅谈基于ANSYS软件的接触分析问题．煤矿机械，2006，27(7)：62～64
[29] 张亚欧，谷志飞，宋勇．ANSYS7.0有限元分析实用教程．北京：清华大学出版社，2004：276～277
[30] 张印阁，冯玉平，张宏祥．桥梁结构现场检测技术．哈尔滨：东北林业大学出版社，2003：13～37
[31] Kim, J H, M yang H. Evolutionary programming techniques forced strained optimization problems. IEEE Trans on Evolu.tionary Computation, 1997, 1(2): 129～140
[32] Adeli H, Cheng N T. Augmented Lagarangian genetic algorithm for structural optimization. J Aerosp Engrg ASCE, 1994, 7(1):104～118
[33] Adeli H, Kamal O. Efficient optimization of space trusses. Comp and Struct, 1986, 24(3): 501～511
[34] 刘世忠．基于ANSYS的钢筋混凝土结构非线性有限元分析．北京：工程结构，2002，26(2)：92～95
[35] 陆新征，江见鲸．用ANSYS Solid65单元分析混凝土组合构件复杂应力．建筑结构，2003，(6)：47～51
[36] 龚曙光，谢桂兰等．ANSYS工程应用实例解析．北京：机械工业出版社，2003：73～82
[37] 郝文化．ANSYS在土木工程应用实例．北京：中国水利水电出版社，2005：100～106
[38] 顾杰隽，陈少锋．T梁反拱值的产生及控制．公路，2004，(8)：283～284
[39] 李东梅．后张40 m工形梁侧弯原因分析与防治措施．铁道建筑，2006,(1)：18～19
[40] 吴银利，李强，段树金．预应力混凝土梁侧弯的控制措施．桥梁，2005，(2)：60～61
[41] 中华人民共和国行业标准．公路钢筋混凝土及预应力混凝土桥涵设计规范(JGJ D62-2004)，．北京：人民交通出版社，2004：181～182
[42] Huang T. Stresses in end zones of a post-pensioned prestressed beam [J]. ACI Journal, 1964, 61(5): 589～601
[43] Marshall W T. A theory for end zone stresses in pre-tensioned concrete beams [J]. PCI Journal, 1966, 11(2): 45～51
[44] Wollmann G. P, Breen J E. Discussion of "Stress distribution and cracking behavior at anchorage zones in prestressed concrete members" [J]. ACI Structural Journal, 1998, 95(4): 458～459
[45] Gergely P, Sozen M A. Design of anchorage zone reinforcement in prestressed concrete members [J]. PCI Journal, 1967, 12(2): 63～75
[46] Stone W C, Breen J. E. Behavior of post-tensioned girder anchorage zones [J]. PCI Journal, 1984, 29(1): 64～109
[47] Sarles D, Itani R Y. Effect of end blocks on anchorage zone stresses in prestressed concrete girders [J]. PCI Journal, 1984, Z9(6): 100～114
[48] 郑文忠，张吉柱．密布预应力束锚具下混凝土局部受压承载力计算方法。建筑结构学报，2004，25(4)：60～65