异型拱桥的非线性受力行为研究及动力特性分析
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摘要
基于太原市南中环蝶形拱桥的施工监控项目,利用Fortran语言编写了多个计算分析模块,并在此基础上开展了以该蝶形拱桥为代表的异型拱桥的几何非线性、施工阶段的索力优化、动力冲击系数等方面的研究,主要研究内容如下：
1、推导了空间变截面梁单元积分格式的单元刚度矩阵；编写了结构几何非线性分析的程序模块,程序中考虑了各种特殊问题的处理,如用龙贝格积分求解变截面梁单元的刚度矩阵、通过三次坐标轴旋转进行坐标转换、单元刚度矩阵是否考虑剪切变形、计算任意带刚臂单元的刚度矩阵、释放梁端约束、利用行变换和列变化来处理任意相关关系的主从约束；在非线性分析模块中设置了两级标识符,在索的垂度标识符下设置了主吊杆、斜拉杆和副吊杆的子标识符,在梁柱效应标识符下设置了拱肋单元和主梁单元的子标识符,在大位移效应标识符下设置了横向位移和竖向位移的子标识符。
2、对太原市南中环蝶形拱桥这种异型拱桥的受力行为进行了分析；并在非线性有限元程序的基础上,利用独立模型分析了典型施工阶段的几何非线性特性以及成桥状态时在桥面恒活载的作用下拱肋、主梁和索的几何非线性特性；更加细致地研究了结构各点的横向位移和竖向位移、拱肋和主梁单元的梁柱效应及三种索的垂度效应对各量值的非线性影响；讨论了拱肋外倾角、矢跨比、含钢率、索的疏密度及布置形式等对结构几何非线性特性的影响；针对月牙形拱桥、飞燕式拱桥和拱塔斜拉桥等新型桥型,对比总结了各种异型拱桥的几何非线性特点。
3、利用结构稳定性分析的计算模块,在南中环桥原设计的基础上改变各种设计参数,研究了该桥型稳定性的影响因素及其影响程度。
4、提出了用于施工阶段索力优化的割线迭代法,并与传统的正装迭代法进行了比较；结合实际工程,针对拱梁组合式桥梁提出了确定调索顺序及索的初始张拉力的思路及应遵循的原则和方法,并与实测数据对比验证了该方法的有效性；针对多索面的复杂桥型,在成桥状态下对各种索的敏感度进行了分析,提出了根据敏感度分析确定不同类型索的调索顺序的新思路；
5、利用子空间迭代法编写了结构自振特性分析的计算程序,并将计算结果和实测结果进行了对比；编写了路面不平度的数值模拟和利用耦联系统模型进行车桥耦合动力分析的计算程序,在此基础上研究了行车速度、偏载距离、结构阻尼、路面不平度、行车方向、轴距、车间距、及索的布置方式等对该异型拱桥各构件动力冲击系数的影响,并从拱肋的外倾角、矢跨比等角度分析了各参数对结构动力性能的影响。
Several calculation and analysis modules are compiled in Fortran language and then against the special-shape arch bridge represented by butterfly-shape arch bridge, the geometrical nonlinearity, optimization of cable tension in construction stage and dynamic impact factors are studied based on the construction monitoring project of the butterfly-shape arch bridge in south central region of Taiyuan City. The main research contents include:
1. The stiffness matrix of spatial tapered beam element in integration scheme is deduced; the program module on geometrical nonlinearity analysis of structure is compiled. Alternative managements are given to various special problems in the module, such as adopting romberg integration to count stiffness matrix of tapered beam element, transforming coordinates by three coordinate axis rotation, considering the shearing deformation on element stiffness matrix or not, calculating stiffness matrix of element with any rigid arm, releasing beam-end restraint, solving master-slave constrains with any correlation through row and rank transformation;two-stage identifiers are set in nonlinearity analysis program modules, among which, sub identifiers of main cable,stay cable and side cable are set under identifiers of cable sag, sub identifiers of arch rib elements and main girder elements are set under identifiers of beam-column effect, and sub identifiers of lateral displacement and vertical displacement are set under identifiers of large displacement effect.
2. Taking the butterfly-shape arch bridge in south central region of Taiyuan City as an example, explanation to mechanical behavior of special-shape arch bridge is conducted; on the basis of nonlinear finite element program, geometrical nonlinearity character of structure in typical construction stage as well as that of arch rib, main girder and cable under dead and live load in finished bridge state are described using independent model; further research on nonlinear effects of lateral displacement and vertical displacement of nodes, beam-column effects of arch rib and girder element, and sag effects of three kinds of cables on different contents are provided; influences of angle of depression, rise/span ratio, steel ratio, stand density and arrangement form of cables on geometrical nonlinearity character of structure are discussed; through contrasts of various new bridges such as crescent-shaped arch bridge, flying-swallow-type arch bridge and arch pylon cable-stayed bridge, a summary on geometrical nonlinearity characters of various special-shape arch bridges is made.
3. As with the use of stability analysis program, influencing factors of stability of butterfly-shape arch bridge and the influence degree are studied by the alteration of design parameters on the basis of original design of the bridge.
4. The secant iterative method used for cable tension optimization in construction stage is put forward and put into comparison with traditional forward-analysis iterative method. According to condition monitoring, some basic principles and methods for the determination of the adjusted order and cable initial tension in view of arch-beam composite structured bridge are proposed, and those methods are proved to be effective in comparison with measured data; sensitivity of various cables in finished bridge state are analyzed, on the above basis, a new way for the adjust order of different cables is put forward in view of the complicated multi-cable bridge.
5. As with the adoption of subspace iteration method, the calculation program used to analyze self-vibration characteristic of structure is compiled, and the results are brought into comparison with measured data; the road surface roughness is simulated using the numerical method and vehicle-bridge coupling vibration analysis based on coupling system model are conducted, on the basis of related calculation program, influences of running speed, unbalance loading distance, structural damping, road surface roughness, moving direction, wheelbase, vehicle gap, and arrangement form of cables on dynamic impact coefficients of the special-shape arch bridge are studied, simultaneously, effects of various design parameters such as angle of depression and rise/span ratio on dynamic characteristics of structure are presented.
1、推导了空间变截面梁单元积分格式的单元刚度矩阵；编写了结构几何非线性分析的程序模块,程序中考虑了各种特殊问题的处理,如用龙贝格积分求解变截面梁单元的刚度矩阵、通过三次坐标轴旋转进行坐标转换、单元刚度矩阵是否考虑剪切变形、计算任意带刚臂单元的刚度矩阵、释放梁端约束、利用行变换和列变化来处理任意相关关系的主从约束；在非线性分析模块中设置了两级标识符,在索的垂度标识符下设置了主吊杆、斜拉杆和副吊杆的子标识符,在梁柱效应标识符下设置了拱肋单元和主梁单元的子标识符,在大位移效应标识符下设置了横向位移和竖向位移的子标识符。
2、对太原市南中环蝶形拱桥这种异型拱桥的受力行为进行了分析；并在非线性有限元程序的基础上,利用独立模型分析了典型施工阶段的几何非线性特性以及成桥状态时在桥面恒活载的作用下拱肋、主梁和索的几何非线性特性；更加细致地研究了结构各点的横向位移和竖向位移、拱肋和主梁单元的梁柱效应及三种索的垂度效应对各量值的非线性影响；讨论了拱肋外倾角、矢跨比、含钢率、索的疏密度及布置形式等对结构几何非线性特性的影响；针对月牙形拱桥、飞燕式拱桥和拱塔斜拉桥等新型桥型,对比总结了各种异型拱桥的几何非线性特点。
3、利用结构稳定性分析的计算模块,在南中环桥原设计的基础上改变各种设计参数,研究了该桥型稳定性的影响因素及其影响程度。
4、提出了用于施工阶段索力优化的割线迭代法,并与传统的正装迭代法进行了比较；结合实际工程,针对拱梁组合式桥梁提出了确定调索顺序及索的初始张拉力的思路及应遵循的原则和方法,并与实测数据对比验证了该方法的有效性；针对多索面的复杂桥型,在成桥状态下对各种索的敏感度进行了分析,提出了根据敏感度分析确定不同类型索的调索顺序的新思路；
5、利用子空间迭代法编写了结构自振特性分析的计算程序,并将计算结果和实测结果进行了对比；编写了路面不平度的数值模拟和利用耦联系统模型进行车桥耦合动力分析的计算程序,在此基础上研究了行车速度、偏载距离、结构阻尼、路面不平度、行车方向、轴距、车间距、及索的布置方式等对该异型拱桥各构件动力冲击系数的影响,并从拱肋的外倾角、矢跨比等角度分析了各参数对结构动力性能的影响。
Several calculation and analysis modules are compiled in Fortran language and then against the special-shape arch bridge represented by butterfly-shape arch bridge, the geometrical nonlinearity, optimization of cable tension in construction stage and dynamic impact factors are studied based on the construction monitoring project of the butterfly-shape arch bridge in south central region of Taiyuan City. The main research contents include:
1. The stiffness matrix of spatial tapered beam element in integration scheme is deduced; the program module on geometrical nonlinearity analysis of structure is compiled. Alternative managements are given to various special problems in the module, such as adopting romberg integration to count stiffness matrix of tapered beam element, transforming coordinates by three coordinate axis rotation, considering the shearing deformation on element stiffness matrix or not, calculating stiffness matrix of element with any rigid arm, releasing beam-end restraint, solving master-slave constrains with any correlation through row and rank transformation;two-stage identifiers are set in nonlinearity analysis program modules, among which, sub identifiers of main cable,stay cable and side cable are set under identifiers of cable sag, sub identifiers of arch rib elements and main girder elements are set under identifiers of beam-column effect, and sub identifiers of lateral displacement and vertical displacement are set under identifiers of large displacement effect.
2. Taking the butterfly-shape arch bridge in south central region of Taiyuan City as an example, explanation to mechanical behavior of special-shape arch bridge is conducted; on the basis of nonlinear finite element program, geometrical nonlinearity character of structure in typical construction stage as well as that of arch rib, main girder and cable under dead and live load in finished bridge state are described using independent model; further research on nonlinear effects of lateral displacement and vertical displacement of nodes, beam-column effects of arch rib and girder element, and sag effects of three kinds of cables on different contents are provided; influences of angle of depression, rise/span ratio, steel ratio, stand density and arrangement form of cables on geometrical nonlinearity character of structure are discussed; through contrasts of various new bridges such as crescent-shaped arch bridge, flying-swallow-type arch bridge and arch pylon cable-stayed bridge, a summary on geometrical nonlinearity characters of various special-shape arch bridges is made.
3. As with the use of stability analysis program, influencing factors of stability of butterfly-shape arch bridge and the influence degree are studied by the alteration of design parameters on the basis of original design of the bridge.
4. The secant iterative method used for cable tension optimization in construction stage is put forward and put into comparison with traditional forward-analysis iterative method. According to condition monitoring, some basic principles and methods for the determination of the adjusted order and cable initial tension in view of arch-beam composite structured bridge are proposed, and those methods are proved to be effective in comparison with measured data; sensitivity of various cables in finished bridge state are analyzed, on the above basis, a new way for the adjust order of different cables is put forward in view of the complicated multi-cable bridge.
5. As with the adoption of subspace iteration method, the calculation program used to analyze self-vibration characteristic of structure is compiled, and the results are brought into comparison with measured data; the road surface roughness is simulated using the numerical method and vehicle-bridge coupling vibration analysis based on coupling system model are conducted, on the basis of related calculation program, influences of running speed, unbalance loading distance, structural damping, road surface roughness, moving direction, wheelbase, vehicle gap, and arrangement form of cables on dynamic impact coefficients of the special-shape arch bridge are studied, simultaneously, effects of various design parameters such as angle of depression and rise/span ratio on dynamic characteristics of structure are presented.
引文
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