钢—混凝土组合箱梁及其框架结构的静动力性能分析
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摘要
钢-混凝土组合箱梁在桥梁工程和高层建筑中已经得到了广泛的应用,目前国内外关于钢-混凝土组合箱梁的静动力性能研究存在的问题有：考虑剪力滞效应的钢-混凝土组合箱梁解析方法及梁段有限元法研究主要集中于工字形组合梁、关于组合箱梁畸变屈曲临界弯矩的计算方法过于复杂、考虑剪力滞效应的动力响应计算方法尚未见报道、弯矩-曲率恢复力模型大都基于构件、弹塑性地震响应时程分析大多基于层模型等,理论研究严重滞后于工程实践,开展考虑剪力滞效应的钢-混凝土组合箱梁的静动力性能试验研究和理论分析,可推广钢-混凝土组合箱梁在桥梁工程和超高层建筑中的应用。本文针对目前研究现状开展的主要研究工作如下：
(1)在考虑混凝土板和钢梁底板因剪力滞效应引起的纵向翘曲、钢梁剪切变形及钢梁与混凝土板间界面滑移的基础上,应用能量变分原理导出钢-混凝土简支组合箱梁受横向荷载作用下的剪力滞控制微分方程和边界条件,获得横向荷载作用下的箱梁应力、挠度和滑移解析解。根据虚功原理,提出同时考虑滑移效应、剪力滞及剪切变形效应的组合梁单元及等效节点力向量,编制组合梁梁段有限元程序。应用本文解析解分别对集中荷载和均布荷载作用下的组合箱梁应力、挠度和滑移进行计算,并同现有试验结果进行比较,验证本文解析解及梁段有限元法的正确性。利用本文计算方法对混凝土顶板及钢梁底板剪力滞系数进行参数分析,并在大量计算数据基础上提出较为准确的混凝土顶板及钢梁底板剪力滞系数经验计算公式。
(2)考虑钢-混凝土组合箱梁负弯矩区钢梁侧向弯曲屈曲及侧向弯扭屈曲两种重要屈曲模式,在建立钢梁腹板对钢梁底板的转动约束刚度及侧向约束刚度的计算方法的基础上,结合薄壁杆件的屈曲理论提出钢-混凝土组合箱梁负弯矩区的侧向弯曲屈曲弯矩及侧向弯扭屈曲弯矩计算方法。通过实例分析现有计算方法存在的理论缺陷,验证本文计算方法的实用性和适用性。
(3)综合考虑组合箱梁剪力滞、滑移、剪切变形和转动惯量等多重因素的影响,推导组合箱梁的控制微分方程及自然边界条件,获得儿种常用边界条件的组合箱梁固有频率方程,提出一种能对工程中常用组合箱梁自振特性进行分析的方法,通过算例验证该方法的有效性；利用中心差分法对振动微分方程进行求解,获得组合梁在任意荷载作用下的动力响应,通过算例将差分数值计算结果与ANSYS有限元计算结果进行比较,证明该方法的正确性。
(4)进行4根不同剪力连结度及腹板高厚比钢-混凝土简支组合箱梁低周反复荷载试验研究,对钢-混凝土组合箱梁的破坏形态、滞回规律、骨架曲线、延性、耗能能力、刚度退化规律等抗震性能进行深入的分析,重点考察剪力连结度及腹板高厚比对钢-混凝土组合箱梁抗震性能的影响；考虑剪力连接度和界面滑移的影响,提出组合箱梁正向、负向截面弯矩-曲率弹性刚度及截面屈服弯矩计算方法,建立简单适用的组合箱梁截面弯矩-曲率骨架曲线的三折线模型,在试验数据与理论分析的基础上,获得了组合箱梁正向及负向刚度退化规律表达式,并进一步提出简单明了的钢-混凝土组合箱梁截面弯矩-曲率顶点指向型滞回模型。
(5)将本文提出的弯矩-曲率恢复力模型程序化,建立适合钢-混凝土组合箱梁的弹塑性地震分析的多段变刚度杆单元刚度矩阵和适用于组合结构数值计算的弯矩-曲率滞回模型转化关系,结合本文提出的多段变刚度杆单元刚度矩阵及弯矩-曲率滞回模型转化关系编制组合结构弹塑性地震响应时程分析计算程序。利用本文计算程序对不同设计参数的钢-混凝土全组合框架结构进行弹塑性地震动力响应计算,提出组合框架合理的抗震设计建议。
Steel-concrete composite box-beams have been widely used in bridge engineering and high rise buildings. At present, there were many open questions on the dynamic and static performance considering the shear lag effect of steel-concrete composite box girder, such as the experimental study and theoretical analysis on the dynamic and static performance considering the shear lag effect of steel-concrete composite box girder concentrated on I-type steel-concrete composite girder, the computing method about distortional buckling critical bending moment of the steel-concrete composite box girder was too complex, dynamic response analysis methods considering the shear lag effect of steel-concrete composite box girder had not been reported, bending moment-curvature restoring force calculation models were mostly based on component, and the elastoplastic seismic response time history analysis program of composite structures were mostly based on layer model, and so on. The theoretical research laged behind the engineering practice seriously. By developing the experimental study and theoretical analysis on the dynamic and static performance considering the shear lag effect of composite box-girders, the composite box-girders can be used popularization and application in bridge engineering and super high rise building. The main research works completed in this paper are as follows:
(1) Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams, shear deformation of steel beams and interface slip between steel beams and concrete slabs, the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading was derived using energy-variational method. According to the virtual work principle, the unit stiffness matrix and equivalent nodal force vector of the composite beam were established in consideration of the slip effect, shear lag effect and shear deformation. The closed-form solutions and beam finite element method calculate results of stress, deflection and slip of box beams under lateral loading were obtained, and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the validity of the closed-form solution. The parameter analysis of shear lag coefficient of concrete roof and steel baseplate had been proceeded using calculation method of this paper. The relatively accurate shear lag coefficient of concrete roof and steel baseplate was put forward.
(2) Lateral bending buckling and lateral flexural-torsional buckling are both important buckling modes for steel-concrete composite beams in the negative moment region, and only the lateral bending buckling is considered in the existing computing method, so there is some limitations. Based on the rotational restraint stiffness and lateral restraint stiffness calculation formulas provided by the steel beam web plate to the lower cloud point flange and the thin-walled bar buckling theory, the calculation formulas of the lateral bending and lateral flexural-torsional buckling moment of the steel-concrete composite beams in the negative moment are derived. The example analysis shows that the existing computing methods all have some theory shortcomings, and the computing method of this paper is more reasonable. At the same time, the calculation results of this paper is more concise than the calculation formulas of the same type, easy to be applied, so it is suitable for engineering application.
(3) Based on Hamilton principle, the governing differential equations and the corresponding boundary conditions of steel-concrete composite box girder with consideration for the shear lag effect meeting self equilibrated stress, shear deformation, slip, as well as rotational inertia were induced. Therefore, natural frequency equations were obtained for the boundary types, such as simple support, cantilever, continuous girder and fixed support at two ends. The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified, which also shows that the correctness of longitudinal warping displacement functions is reasonable. The proposed approach provided theoretical basis for further research of free vibration characteristics of steel-concrete composite box-girder. The vibration differential equations were solved using central difference method, and the dynamic response of steel-concrete composite box girder under arbitrary loading was obtained. The finite element computed results was compared with the difference computed results and the validity of the difference method was verified.
(4) Four specimens of steel-concrete composite box-girders with different shear connection degree and height-width ratio of web plate under cyclic points concentrated loads were experimentally studied. The failure mode, load-deflection hysteretic curves, ductility, energy-dissipating capacity, rigidity degeneration etc were deeply studied. The shear connection degree and height-width ratio are considered as the experimenters parameters of the seismic performance. The influence of shear connection degree on bending rigidity of steel-concrete composite box-girders was considered by power function interpolation method. The positive and reverse elastic stiffness of bending moment-curvature considering the interface slip was put forward, and also the section yield moment. The trilinear skeleton model of bending moment-curvature was proposed, and the computing method of the model is very simple, which is convenient to be used in engineering. Best on the test data and theoretical analysis, The positive and reverse stiffness degradation rule was obtained, the trilinear bending moment-curvature restoring force calculation model was further proposed, and the computing method of the model is also very simple, which is convenient to hand computation.
(5) The trilinear bending moment-curvature restoring force calculation model proposed in the text was programmed, the variable stiffness rod element stiffness matrix suiting elastoplastic seismic analysis on steel-concrete composite box-girders was proposed. The conversion diagram suit on numerical calculation of composite structures was programmed. Based on the conversion diagram and the variable stiffness rod element stiffness matrix, the elastoplastic seismic response time history analysis program of composite structures was programmed using Wilson-θ incremental numerical calculation method. Some steel-concrete composite frame structure specimens with different design parameter were calculated using the elastoplastic seismic response time history analysis program. The reasonable anti-seismicdesign suggestions were proposed.
(1)在考虑混凝土板和钢梁底板因剪力滞效应引起的纵向翘曲、钢梁剪切变形及钢梁与混凝土板间界面滑移的基础上,应用能量变分原理导出钢-混凝土简支组合箱梁受横向荷载作用下的剪力滞控制微分方程和边界条件,获得横向荷载作用下的箱梁应力、挠度和滑移解析解。根据虚功原理,提出同时考虑滑移效应、剪力滞及剪切变形效应的组合梁单元及等效节点力向量,编制组合梁梁段有限元程序。应用本文解析解分别对集中荷载和均布荷载作用下的组合箱梁应力、挠度和滑移进行计算,并同现有试验结果进行比较,验证本文解析解及梁段有限元法的正确性。利用本文计算方法对混凝土顶板及钢梁底板剪力滞系数进行参数分析,并在大量计算数据基础上提出较为准确的混凝土顶板及钢梁底板剪力滞系数经验计算公式。
(2)考虑钢-混凝土组合箱梁负弯矩区钢梁侧向弯曲屈曲及侧向弯扭屈曲两种重要屈曲模式,在建立钢梁腹板对钢梁底板的转动约束刚度及侧向约束刚度的计算方法的基础上,结合薄壁杆件的屈曲理论提出钢-混凝土组合箱梁负弯矩区的侧向弯曲屈曲弯矩及侧向弯扭屈曲弯矩计算方法。通过实例分析现有计算方法存在的理论缺陷,验证本文计算方法的实用性和适用性。
(3)综合考虑组合箱梁剪力滞、滑移、剪切变形和转动惯量等多重因素的影响,推导组合箱梁的控制微分方程及自然边界条件,获得儿种常用边界条件的组合箱梁固有频率方程,提出一种能对工程中常用组合箱梁自振特性进行分析的方法,通过算例验证该方法的有效性；利用中心差分法对振动微分方程进行求解,获得组合梁在任意荷载作用下的动力响应,通过算例将差分数值计算结果与ANSYS有限元计算结果进行比较,证明该方法的正确性。
(4)进行4根不同剪力连结度及腹板高厚比钢-混凝土简支组合箱梁低周反复荷载试验研究,对钢-混凝土组合箱梁的破坏形态、滞回规律、骨架曲线、延性、耗能能力、刚度退化规律等抗震性能进行深入的分析,重点考察剪力连结度及腹板高厚比对钢-混凝土组合箱梁抗震性能的影响；考虑剪力连接度和界面滑移的影响,提出组合箱梁正向、负向截面弯矩-曲率弹性刚度及截面屈服弯矩计算方法,建立简单适用的组合箱梁截面弯矩-曲率骨架曲线的三折线模型,在试验数据与理论分析的基础上,获得了组合箱梁正向及负向刚度退化规律表达式,并进一步提出简单明了的钢-混凝土组合箱梁截面弯矩-曲率顶点指向型滞回模型。
(5)将本文提出的弯矩-曲率恢复力模型程序化,建立适合钢-混凝土组合箱梁的弹塑性地震分析的多段变刚度杆单元刚度矩阵和适用于组合结构数值计算的弯矩-曲率滞回模型转化关系,结合本文提出的多段变刚度杆单元刚度矩阵及弯矩-曲率滞回模型转化关系编制组合结构弹塑性地震响应时程分析计算程序。利用本文计算程序对不同设计参数的钢-混凝土全组合框架结构进行弹塑性地震动力响应计算,提出组合框架合理的抗震设计建议。
Steel-concrete composite box-beams have been widely used in bridge engineering and high rise buildings. At present, there were many open questions on the dynamic and static performance considering the shear lag effect of steel-concrete composite box girder, such as the experimental study and theoretical analysis on the dynamic and static performance considering the shear lag effect of steel-concrete composite box girder concentrated on I-type steel-concrete composite girder, the computing method about distortional buckling critical bending moment of the steel-concrete composite box girder was too complex, dynamic response analysis methods considering the shear lag effect of steel-concrete composite box girder had not been reported, bending moment-curvature restoring force calculation models were mostly based on component, and the elastoplastic seismic response time history analysis program of composite structures were mostly based on layer model, and so on. The theoretical research laged behind the engineering practice seriously. By developing the experimental study and theoretical analysis on the dynamic and static performance considering the shear lag effect of composite box-girders, the composite box-girders can be used popularization and application in bridge engineering and super high rise building. The main research works completed in this paper are as follows:
(1) Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams, shear deformation of steel beams and interface slip between steel beams and concrete slabs, the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading was derived using energy-variational method. According to the virtual work principle, the unit stiffness matrix and equivalent nodal force vector of the composite beam were established in consideration of the slip effect, shear lag effect and shear deformation. The closed-form solutions and beam finite element method calculate results of stress, deflection and slip of box beams under lateral loading were obtained, and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the validity of the closed-form solution. The parameter analysis of shear lag coefficient of concrete roof and steel baseplate had been proceeded using calculation method of this paper. The relatively accurate shear lag coefficient of concrete roof and steel baseplate was put forward.
(2) Lateral bending buckling and lateral flexural-torsional buckling are both important buckling modes for steel-concrete composite beams in the negative moment region, and only the lateral bending buckling is considered in the existing computing method, so there is some limitations. Based on the rotational restraint stiffness and lateral restraint stiffness calculation formulas provided by the steel beam web plate to the lower cloud point flange and the thin-walled bar buckling theory, the calculation formulas of the lateral bending and lateral flexural-torsional buckling moment of the steel-concrete composite beams in the negative moment are derived. The example analysis shows that the existing computing methods all have some theory shortcomings, and the computing method of this paper is more reasonable. At the same time, the calculation results of this paper is more concise than the calculation formulas of the same type, easy to be applied, so it is suitable for engineering application.
(3) Based on Hamilton principle, the governing differential equations and the corresponding boundary conditions of steel-concrete composite box girder with consideration for the shear lag effect meeting self equilibrated stress, shear deformation, slip, as well as rotational inertia were induced. Therefore, natural frequency equations were obtained for the boundary types, such as simple support, cantilever, continuous girder and fixed support at two ends. The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified, which also shows that the correctness of longitudinal warping displacement functions is reasonable. The proposed approach provided theoretical basis for further research of free vibration characteristics of steel-concrete composite box-girder. The vibration differential equations were solved using central difference method, and the dynamic response of steel-concrete composite box girder under arbitrary loading was obtained. The finite element computed results was compared with the difference computed results and the validity of the difference method was verified.
(4) Four specimens of steel-concrete composite box-girders with different shear connection degree and height-width ratio of web plate under cyclic points concentrated loads were experimentally studied. The failure mode, load-deflection hysteretic curves, ductility, energy-dissipating capacity, rigidity degeneration etc were deeply studied. The shear connection degree and height-width ratio are considered as the experimenters parameters of the seismic performance. The influence of shear connection degree on bending rigidity of steel-concrete composite box-girders was considered by power function interpolation method. The positive and reverse elastic stiffness of bending moment-curvature considering the interface slip was put forward, and also the section yield moment. The trilinear skeleton model of bending moment-curvature was proposed, and the computing method of the model is very simple, which is convenient to be used in engineering. Best on the test data and theoretical analysis, The positive and reverse stiffness degradation rule was obtained, the trilinear bending moment-curvature restoring force calculation model was further proposed, and the computing method of the model is also very simple, which is convenient to hand computation.
(5) The trilinear bending moment-curvature restoring force calculation model proposed in the text was programmed, the variable stiffness rod element stiffness matrix suiting elastoplastic seismic analysis on steel-concrete composite box-girders was proposed. The conversion diagram suit on numerical calculation of composite structures was programmed. Based on the conversion diagram and the variable stiffness rod element stiffness matrix, the elastoplastic seismic response time history analysis program of composite structures was programmed using Wilson-θ incremental numerical calculation method. Some steel-concrete composite frame structure specimens with different design parameter were calculated using the elastoplastic seismic response time history analysis program. The reasonable anti-seismicdesign suggestions were proposed.
引文
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