考虑滑移效应的组合梁的理论分析与试验研究
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摘要
组合梁由于其良好的整体性能和经济效益，在目前的建筑及桥梁结构领域得到了广泛的应用。界面滑移效应使其挠度增大，而在工程设计中，组合梁的挠度验算是主要矛盾，由此带来的设计问题因而也成为了关注的热点。当前组合梁挠度计算方法还有待改进，对于连接程度和挠度之间的直接影响关系没有精确的分析，影响组合梁挠度的具有明确物理意义的关键参数亦未有定论，而找出这个关键参数对组合梁考虑滑移效应下变形规律的深入研究有很大的益处。
本论文从组合梁基本原理入手，演绎了力学基本微分方程的建立、求解全过程，得出在三种荷载情况下微分方程的解析解；进而经由曲率方程直接二次积分给出了在三种荷载下的组合梁理论位移计算公式，和国内少数文献相比更为严格、简练，有现实意义；在此基础上采用数值分析和数据拟合的方法，选定合适的自变量，提出了考虑界面滑移的组合梁截面刚度修正系数的表达式，该表达式顺应设计者习惯、简单明了、物理意义明确并能满足设计精度的要求，同时还探讨了影响组合梁挠度的主要参数；针对部分抗剪连接组合梁，提出了挠度增大系数的表达式，形式直观、计算简便，基本满足工程设计精度要求，同时它还给出了某一根组合梁按不同连接程度来设计时其挠度的变化全过程规律，视野很宽，对设计者有启示效果；最后以观察试件的受力和变形全过程、理解构件的破坏机理及验证基本理论假设和所提公式为目的，本文还进行了不同形式的钢—混凝土组合梁的试验研究，测试内容包括应变、滑移、挠度及特征荷载等，试验结果与本文理论分析结果基本吻合，同时累积的一些试验资料也为进一步的理论建设打下了基础。
Because of good behaviors and economic performance, the steel-concrete composite beams are widely used in architecture and bridge structure field. On account of the slips in the interface, the deflection of the beams increases notably. At the same time, the check of deflection is an important factor which need to be considered in composite beams design. So, the accurate calculation of the composite beams' deflection become a little bit hot problem. At present, the calculation method predicting the deflection of simply supported steel-concrete composite beams still need to improve; there isn't accurate analysis of relationship between the connection degree and the deflection; the key parameter reflecting the structural mechanism of the deflection doesn't have a hard conclusion.
Based on the basic principle, this paper deduced the whole proeesseses that the mechanics basic differential equation build up and solve, found out analytical solution of the equation under three kinds of load; though two direct integral calculuses of the curvature differential equation, this paper deduced theories formulas of the displacement to composite beams, which is more strict and refinement compared with a handful of local literature and has realistic meaning; then made selection suitable independent variable factor, deduced the formula expressing the reduced stiffness ratio considering slip effect by numerical analysis and fitting data, which is of simple form, and can reflect the structural mechanism for composite steel-concrete girders with partial shear connection, show the adequate accuracy, moreover the key parametric analys of deflection is performed; aim at the beams with partial shear connection, the formula expressing the increased deflection which is simplified and fulfil accuracy requirements is put forward, furthermore it shows the regulation of deflection variety with variety of connection degree and the effect of the apocalypse for design; finally, to observe the whole beating capacity and deflection processeses of pieces, comprehend destructive mechanism, and validate the correctness of the theories and formulas in this paper, the experimental analysis under static concentrate lateral loads were presented, which agree beter with the results of investigations from in the paper, include strain、slip、deflection and characteristic loads etc, moreover these experiment information have a well guideline to further theoretical analysis too.
本论文从组合梁基本原理入手，演绎了力学基本微分方程的建立、求解全过程，得出在三种荷载情况下微分方程的解析解；进而经由曲率方程直接二次积分给出了在三种荷载下的组合梁理论位移计算公式，和国内少数文献相比更为严格、简练，有现实意义；在此基础上采用数值分析和数据拟合的方法，选定合适的自变量，提出了考虑界面滑移的组合梁截面刚度修正系数的表达式，该表达式顺应设计者习惯、简单明了、物理意义明确并能满足设计精度的要求，同时还探讨了影响组合梁挠度的主要参数；针对部分抗剪连接组合梁，提出了挠度增大系数的表达式，形式直观、计算简便，基本满足工程设计精度要求，同时它还给出了某一根组合梁按不同连接程度来设计时其挠度的变化全过程规律，视野很宽，对设计者有启示效果；最后以观察试件的受力和变形全过程、理解构件的破坏机理及验证基本理论假设和所提公式为目的，本文还进行了不同形式的钢—混凝土组合梁的试验研究，测试内容包括应变、滑移、挠度及特征荷载等，试验结果与本文理论分析结果基本吻合，同时累积的一些试验资料也为进一步的理论建设打下了基础。
Because of good behaviors and economic performance, the steel-concrete composite beams are widely used in architecture and bridge structure field. On account of the slips in the interface, the deflection of the beams increases notably. At the same time, the check of deflection is an important factor which need to be considered in composite beams design. So, the accurate calculation of the composite beams' deflection become a little bit hot problem. At present, the calculation method predicting the deflection of simply supported steel-concrete composite beams still need to improve; there isn't accurate analysis of relationship between the connection degree and the deflection; the key parameter reflecting the structural mechanism of the deflection doesn't have a hard conclusion.
Based on the basic principle, this paper deduced the whole proeesseses that the mechanics basic differential equation build up and solve, found out analytical solution of the equation under three kinds of load; though two direct integral calculuses of the curvature differential equation, this paper deduced theories formulas of the displacement to composite beams, which is more strict and refinement compared with a handful of local literature and has realistic meaning; then made selection suitable independent variable factor, deduced the formula expressing the reduced stiffness ratio considering slip effect by numerical analysis and fitting data, which is of simple form, and can reflect the structural mechanism for composite steel-concrete girders with partial shear connection, show the adequate accuracy, moreover the key parametric analys of deflection is performed; aim at the beams with partial shear connection, the formula expressing the increased deflection which is simplified and fulfil accuracy requirements is put forward, furthermore it shows the regulation of deflection variety with variety of connection degree and the effect of the apocalypse for design; finally, to observe the whole beating capacity and deflection processeses of pieces, comprehend destructive mechanism, and validate the correctness of the theories and formulas in this paper, the experimental analysis under static concentrate lateral loads were presented, which agree beter with the results of investigations from in the paper, include strain、slip、deflection and characteristic loads etc, moreover these experiment information have a well guideline to further theoretical analysis too.
引文
[1] 朱聘儒．钢-混凝土组合梁设计原理[M]．北京：中国建筑工业出版社，1989
[2] 聂建国．钢-混凝土组合梁结构--试验、理论与应用[M]．北京：科学出版社，2005
[3] 朱聘儒，国明超，朱起，等．钢-砼组合梁协同工作的分析及试验[J]．建筑结构学报，1987，8(5)：42-51
[4] 夏骏，钢-混凝土组合梁挠度计算简化方法和负弯矩区的畸变屈曲分析[D]：[硕士学位论文]．浙江：浙江大学建筑工程学院，2006，5-6
[5] Shunichi Nakamura. Construction considerations for composite steel and concrete floor systems[J]. Journal of. Structural Engineering, 2002, 128(9): 1099-1110
[6] 聂建国，余志武．钢-混凝土组合梁在我国的研究及应用[J]．土木工程学报，1990，32(2)：3-6
[7]肖辉，李爱群，陈丽华，等．钢与混凝土组合梁的发展研究和应用[J]．特种结构，2005，22(1)：41
[8] Andrews E S, Elementary principles of reinforced concrete construction[M]. Scott, Greenwood and Sons, 1912
[9] Newmark N M, Siess C P, Viest I M. Test and analysis of composite beams with incomplete interaction[J]. Experimental Stress Analysis, 1951, 9(6): 896-901
[10] Yam L C P, Chapman J C. Inelastic Behaviour of Continuous Composite Beams of Steel and Concrete[J]. Proc. Instn Cir. Engrs, Part2, 1972, 53(12): 487-501
[11] 刘肖冰．部分剪力连接钢-混凝土简支组合梁的滑移效应分析[D]：[硕士学位论文]．哈尔滨工业大学，2005，4
[12] 蒋丽忠，余志武，李佳．均布荷载作用下钢-混凝土组合梁滑移及变形的理论计算[J]．工程力学，2003，20(2)：134-135
[13] 余志武，蒋丽忠，李佳．集中荷载作用下钢-混凝土组合梁界面滑移及变形[J]．土木工程学报，2003，36(8)：3-4
[14] 余志武，周凌宇，蒋丽忠．钢-混凝土连续组合梁滑移与挠度耦合分析[J]．工程力学，2004，21(2)：78-81
[15] 孙文彬．部分剪力连接钢-砼组合梁的滑移及曲率分析[J]．力学与实践，2001，23：44-47
[16] 孙文彬．部分剪力连接钢-混凝土简支组合粱变形计算[J]．辽宁工程技术大学学报，2003，(1)：72-73
[17] 聂建国，沈聚敏，袁彦声．钢-混凝土简支组合梁变形计算的一般公式[J]．工程力 学，1994，11(1)：21-27
[18] 聂建国．考虑滑移效应的钢-混凝土组合梁变形计算的折减刚度法[J]．土木工程学报，1995，5：11-13
[19] GB50017-2003，中华人民共和国国家标准：钢结构设计规范[S]．北京：中国计划出版社，2003
[20] Johnson R P, May I M. Partial-Interaction Design of Composite Steel and Concrete Structure[J]. The Structure Engineering, 1975, 53(8): 305-311
[21] Crisinel M. Partial-interaction analysis of composite beams with profiled sheeting and non welded shear connectiors[J]. J. Constructional Steel res. (15): 65-98.
[22] American Institute of Steel Construction. Load and Resistance Factor Design Specification for Structural Steel Buildings AISC[S]. Chicago, 1999
[23] Eurocode4. Design of Composite Steel and Concrete Structures[S]. London, British Standards Institution, 1994: 106-108
[24] JGJ99-98，中华人民共和国国家标准：高层民用建筑钢结构技术规程[S]．北京：中国建筑工业出版社，1998
[25] 王景全，吕志涛，刘钊．部分剪力连接钢-混凝土组合梁变形计算的组合系数法[J]．东南大学学报(自然科学版)，2005，35(1)：7-9
[26] [S].1960
[27] 朱聘儒．钢-混凝土组合梁设计原理(第二版)[M]．北京：中国建筑工业出版社，2006
[28] Chapman J C , Balakrishnan S. Experiments on composite beams[J]. The structural Engineer, 1964, 42(11)
[29] Colin Davies. tests on half-scale steel-concrete composite beams with welded stud connectors[J]. The structural engineer, 1969, 47(1)
[30] GB／T2975-1998，中华人民共和国国家标准：钢及钢产品力学性能试验取样位置及试样制备[S]．北京：中国标准出版社，1999
[31] GB／T228-2002，中华人民共和国国家标准：金属材料室温拉伸试验方法[S]．北京：中国标准出版社，2002
[32] 许兰兰，寇立亚．钢-混凝土组合梁混凝土翼板有效宽度对梁挠度的影响[J]．建筑技术开发，2005，32(12)：56—57，91
[33] 周凌宇，余志武，蒋丽忠．组合梁滑移和剪切变形双重效应的有限元分析[J]．中国铁道科学，2004，25(3)：61—64
[34] 彭桂林，陈瑞生．简支组合梁弹性变形及极限抗弯承载力计算[J]．结构工程师，2004，(1)：21
[35] 毛学明，赵人达，万臻．钢-混凝土组合梁界面纵向剪力重分布[J]．西南交通大学学报，2006，41(2)：175—178
[2] 聂建国．钢-混凝土组合梁结构--试验、理论与应用[M]．北京：科学出版社，2005
[3] 朱聘儒，国明超，朱起，等．钢-砼组合梁协同工作的分析及试验[J]．建筑结构学报，1987，8(5)：42-51
[4] 夏骏，钢-混凝土组合梁挠度计算简化方法和负弯矩区的畸变屈曲分析[D]：[硕士学位论文]．浙江：浙江大学建筑工程学院，2006，5-6
[5] Shunichi Nakamura. Construction considerations for composite steel and concrete floor systems[J]. Journal of. Structural Engineering, 2002, 128(9): 1099-1110
[6] 聂建国，余志武．钢-混凝土组合梁在我国的研究及应用[J]．土木工程学报，1990，32(2)：3-6
[7]肖辉，李爱群，陈丽华，等．钢与混凝土组合梁的发展研究和应用[J]．特种结构，2005，22(1)：41
[8] Andrews E S, Elementary principles of reinforced concrete construction[M]. Scott, Greenwood and Sons, 1912
[9] Newmark N M, Siess C P, Viest I M. Test and analysis of composite beams with incomplete interaction[J]. Experimental Stress Analysis, 1951, 9(6): 896-901
[10] Yam L C P, Chapman J C. Inelastic Behaviour of Continuous Composite Beams of Steel and Concrete[J]. Proc. Instn Cir. Engrs, Part2, 1972, 53(12): 487-501
[11] 刘肖冰．部分剪力连接钢-混凝土简支组合梁的滑移效应分析[D]：[硕士学位论文]．哈尔滨工业大学，2005，4
[12] 蒋丽忠，余志武，李佳．均布荷载作用下钢-混凝土组合梁滑移及变形的理论计算[J]．工程力学，2003，20(2)：134-135
[13] 余志武，蒋丽忠，李佳．集中荷载作用下钢-混凝土组合梁界面滑移及变形[J]．土木工程学报，2003，36(8)：3-4
[14] 余志武，周凌宇，蒋丽忠．钢-混凝土连续组合梁滑移与挠度耦合分析[J]．工程力学，2004，21(2)：78-81
[15] 孙文彬．部分剪力连接钢-砼组合梁的滑移及曲率分析[J]．力学与实践，2001，23：44-47
[16] 孙文彬．部分剪力连接钢-混凝土简支组合粱变形计算[J]．辽宁工程技术大学学报，2003，(1)：72-73
[17] 聂建国，沈聚敏，袁彦声．钢-混凝土简支组合梁变形计算的一般公式[J]．工程力 学，1994，11(1)：21-27
[18] 聂建国．考虑滑移效应的钢-混凝土组合梁变形计算的折减刚度法[J]．土木工程学报，1995，5：11-13
[19] GB50017-2003，中华人民共和国国家标准：钢结构设计规范[S]．北京：中国计划出版社，2003
[20] Johnson R P, May I M. Partial-Interaction Design of Composite Steel and Concrete Structure[J]. The Structure Engineering, 1975, 53(8): 305-311
[21] Crisinel M. Partial-interaction analysis of composite beams with profiled sheeting and non welded shear connectiors[J]. J. Constructional Steel res. (15): 65-98.
[22] American Institute of Steel Construction. Load and Resistance Factor Design Specification for Structural Steel Buildings AISC[S]. Chicago, 1999
[23] Eurocode4. Design of Composite Steel and Concrete Structures[S]. London, British Standards Institution, 1994: 106-108
[24] JGJ99-98，中华人民共和国国家标准：高层民用建筑钢结构技术规程[S]．北京：中国建筑工业出版社，1998
[25] 王景全，吕志涛，刘钊．部分剪力连接钢-混凝土组合梁变形计算的组合系数法[J]．东南大学学报(自然科学版)，2005，35(1)：7-9
[26] [S].1960
[27] 朱聘儒．钢-混凝土组合梁设计原理(第二版)[M]．北京：中国建筑工业出版社，2006
[28] Chapman J C , Balakrishnan S. Experiments on composite beams[J]. The structural Engineer, 1964, 42(11)
[29] Colin Davies. tests on half-scale steel-concrete composite beams with welded stud connectors[J]. The structural engineer, 1969, 47(1)
[30] GB／T2975-1998，中华人民共和国国家标准：钢及钢产品力学性能试验取样位置及试样制备[S]．北京：中国标准出版社，1999
[31] GB／T228-2002，中华人民共和国国家标准：金属材料室温拉伸试验方法[S]．北京：中国标准出版社，2002
[32] 许兰兰，寇立亚．钢-混凝土组合梁混凝土翼板有效宽度对梁挠度的影响[J]．建筑技术开发，2005，32(12)：56—57，91
[33] 周凌宇，余志武，蒋丽忠．组合梁滑移和剪切变形双重效应的有限元分析[J]．中国铁道科学，2004，25(3)：61—64
[34] 彭桂林，陈瑞生．简支组合梁弹性变形及极限抗弯承载力计算[J]．结构工程师，2004，(1)：21
[35] 毛学明，赵人达，万臻．钢-混凝土组合梁界面纵向剪力重分布[J]．西南交通大学学报，2006，41(2)：175—178