大跨度钢管混凝土拱桥抗震性能及动力稳定研究
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摘要
钢管混凝土拱桥因其良好的力学性能和施工方便等优点在我国得到了广泛的应用。以跨径308的南浦大桥为工程背景,深入细致地研究了大跨度钢管混凝土拱桥的非线性地震响应特性、多维多点地震响应特性以及在地震荷载下的动力稳定性能。在对Lyapunov运动稳定理论研究的基础上,提出了拱结构的运动稳定性实用判别准则。
联合应用虚拟激励法和伽辽金法,得到了弹性圆拱在平稳和非平稳水平随机地震作用下的随机响应的半解析解。通过算例分析并与有限元计算结果相比较,验证了该方法的计算精度和计算效率。
对大跨度钢管混凝土拱桥进行了三维地震激励下的非线性时程分析,研究了几何非线性、材料非线性、阻尼比及桥道系参与等因素对拱桥地震响应的影响。研究结果表明:考虑桥道系后,拱脚附近截面的横向弯矩和轴力有了较大幅度的增加;几何非线性对钢管混凝土的地震响应有一定影响,由于刚度的减弱而使拱肋位移和大部分截面轴力增加,材料非线性使拱脚附近截面处于不利状态。
对南浦大桥进行三维正交地震动多点激励下的平稳随机响应分析。数值仿真了该拱桥在一维P波、一维SH波、一维SV波多点激励下的地震响应以及考虑互谱的三维多点激励地震响应。数值分析结果表明:考虑地震动的空间效应对拱肋内力有很大改变,地震动空间变化对拱肋内力的影响主要来自行波效应。三维地震作用比单维地震作用的拱肋内力有较大增幅。对大跨度钢管混凝土拱桥,必须进行多维多点地震激励的响应分析,否则有可能严重低估结构的地震设计内力。
提出了结构运动稳定性实用判别准则以及该准则的具体实施步骤,研究了拱结构在阶跃荷载、周期荷载以及地震激励下的失稳特征,指出结构整体刚度矩阵出现负的特征值是结构失稳的必要条件,可依此判断结构动力失稳临界荷载的下限值,位移时程曲线发散、性质发生改变或发生跳跃、运动状态混沌,可作为结构动力失稳的依据。
对大跨桁式中承式钢管混凝土拱桥进行了静力和弹塑性动力稳定分析研究。结果表明材料非线性对大跨度拱桥的静力稳定影响是显著的。在大跨度拱桥的弹性动力稳定分析中,B-R准则失效,可采用结构整体刚度矩阵出现负的特征值来判断结构动力失稳临界荷载。横向激励是使拱桥动力失稳的最不利激励方向。初始几何缺陷对拱桥的静力稳定影响很大,而对拱桥的动力稳定影响很小。地震波扰动对拱桥静力稳定系数影响很小。拱桥的弹塑性动力失稳模态为拱肋局部屈曲失稳。
Concrete filled steel-tube (CFST) arch bridge has been widely applied in our country for its good mechanical properties and facilitated in construction et al. Taking 308m span Nanpu Bridge as the object of study, the nonlinear seismic response behavior, the seismic response characteristic under multi-dimensional and multi-support excitation and the dynamical stability properties of long-span CFST arch bridge were investigated in depth. The motion stability practical criterion of arch structure is brought forward on the base of Lyapunov theorem of motion stability.
The semi-analytical solution of elastic circular arch under horizontal random stationary and non-stationary seismic excitation was studied by the method combining the pseudo-excitation algorithm with Galerkin algorithm. A numerical example was given to demonstrate the accuracy and efficiency by comparing the results with finite element method.
The nonlinear time-history analysis of long-span CFST arch bridge under three-dimensional earthquake excitations was performed. The influence of geometrical non-linearity, material non-linearity, damping ratio and bridge deck was studied by seismic response analysis. The results show that the lateral bending moment and axial force around the springing of arch rib increase greatly taking account of bridge deck. Geometrical non-linearity has some effect on seismic response of CFST arch bridge. The displacement of arch rib and the axial force of most section increase because of the reduction of stiffness. Material non-linearity put the sections of springing of arch rib nearby at a disadvantage.
The random seismic response analysis of Nanpu Bridge under multi-support excitations of three-dimensional orthogonal earthquake motion was performed. The seismic response of the arch bridge under one-dimensional P-wave, one-dimensional SH-wave, one-dimensional SV-wave and three-dimensional considering cross-power spectrum of multi-support earthquake excitations were numerically simulated. The results show that the internal forces of arch rib may be greatly changed by considering the spatial variation of seismic motion. The influence of spatial variation of seismic motion on the internal forces of arch rib primarily comes from travel ing-wave. The internal forces of arch rib under three-dimensional earthquake excitations are greater than that under one-dimensional excitation. The random seismic analysis under three-dimensional and multi-support earthquake excitations must be performed for the long-span CFST arch bridge otherwise the seismic design forces of the structure are likely to underestimate seriously.
The practical stability criterion of structure motion and the specific steps were proposed. The instable characteristics of arch structure were investigated under step load, cyclic load and earthquake excitation. It is indicated that negative eigenvalue appearing in structure whole stiffness matrix is requirements for structure instability and the lower limit of critical load of structure dynamical instability is estimated. The displacement time-history curve becoming divergent, a change of qualities, a leap taking place or the motion chaos can be basis for structure dynamical instability.
The static and dynamic plastical stability analysis of long-span half-through trussed CFST arch bridge were studied. The result indicates that the material non-linearity decreases static stability coefficient of long span arch bridge greatly. The Budiansky-Roth criterion is invalidate in the analysis of elastic dynamic stability of long span arch bridge and the critical load of dynamic stability can be estimated by negative eigenvalue appearing in structure whole stiffness matrix. Lateral earthquake excitation is the most disadvantageous direction in dynamic buckling analysis. Initial geometric imperfection makes no difference on dynamic stability of arch bridge but yet affect static stability of arch bridge deeply. The plastic dynamic buckling mode of arch bridge is partial buckling of arch rib and seismic wave disturbance has little influence on static stability coefficient of arch bridge.
联合应用虚拟激励法和伽辽金法,得到了弹性圆拱在平稳和非平稳水平随机地震作用下的随机响应的半解析解。通过算例分析并与有限元计算结果相比较,验证了该方法的计算精度和计算效率。
对大跨度钢管混凝土拱桥进行了三维地震激励下的非线性时程分析,研究了几何非线性、材料非线性、阻尼比及桥道系参与等因素对拱桥地震响应的影响。研究结果表明:考虑桥道系后,拱脚附近截面的横向弯矩和轴力有了较大幅度的增加;几何非线性对钢管混凝土的地震响应有一定影响,由于刚度的减弱而使拱肋位移和大部分截面轴力增加,材料非线性使拱脚附近截面处于不利状态。
对南浦大桥进行三维正交地震动多点激励下的平稳随机响应分析。数值仿真了该拱桥在一维P波、一维SH波、一维SV波多点激励下的地震响应以及考虑互谱的三维多点激励地震响应。数值分析结果表明:考虑地震动的空间效应对拱肋内力有很大改变,地震动空间变化对拱肋内力的影响主要来自行波效应。三维地震作用比单维地震作用的拱肋内力有较大增幅。对大跨度钢管混凝土拱桥,必须进行多维多点地震激励的响应分析,否则有可能严重低估结构的地震设计内力。
提出了结构运动稳定性实用判别准则以及该准则的具体实施步骤,研究了拱结构在阶跃荷载、周期荷载以及地震激励下的失稳特征,指出结构整体刚度矩阵出现负的特征值是结构失稳的必要条件,可依此判断结构动力失稳临界荷载的下限值,位移时程曲线发散、性质发生改变或发生跳跃、运动状态混沌,可作为结构动力失稳的依据。
对大跨桁式中承式钢管混凝土拱桥进行了静力和弹塑性动力稳定分析研究。结果表明材料非线性对大跨度拱桥的静力稳定影响是显著的。在大跨度拱桥的弹性动力稳定分析中,B-R准则失效,可采用结构整体刚度矩阵出现负的特征值来判断结构动力失稳临界荷载。横向激励是使拱桥动力失稳的最不利激励方向。初始几何缺陷对拱桥的静力稳定影响很大,而对拱桥的动力稳定影响很小。地震波扰动对拱桥静力稳定系数影响很小。拱桥的弹塑性动力失稳模态为拱肋局部屈曲失稳。
Concrete filled steel-tube (CFST) arch bridge has been widely applied in our country for its good mechanical properties and facilitated in construction et al. Taking 308m span Nanpu Bridge as the object of study, the nonlinear seismic response behavior, the seismic response characteristic under multi-dimensional and multi-support excitation and the dynamical stability properties of long-span CFST arch bridge were investigated in depth. The motion stability practical criterion of arch structure is brought forward on the base of Lyapunov theorem of motion stability.
The semi-analytical solution of elastic circular arch under horizontal random stationary and non-stationary seismic excitation was studied by the method combining the pseudo-excitation algorithm with Galerkin algorithm. A numerical example was given to demonstrate the accuracy and efficiency by comparing the results with finite element method.
The nonlinear time-history analysis of long-span CFST arch bridge under three-dimensional earthquake excitations was performed. The influence of geometrical non-linearity, material non-linearity, damping ratio and bridge deck was studied by seismic response analysis. The results show that the lateral bending moment and axial force around the springing of arch rib increase greatly taking account of bridge deck. Geometrical non-linearity has some effect on seismic response of CFST arch bridge. The displacement of arch rib and the axial force of most section increase because of the reduction of stiffness. Material non-linearity put the sections of springing of arch rib nearby at a disadvantage.
The random seismic response analysis of Nanpu Bridge under multi-support excitations of three-dimensional orthogonal earthquake motion was performed. The seismic response of the arch bridge under one-dimensional P-wave, one-dimensional SH-wave, one-dimensional SV-wave and three-dimensional considering cross-power spectrum of multi-support earthquake excitations were numerically simulated. The results show that the internal forces of arch rib may be greatly changed by considering the spatial variation of seismic motion. The influence of spatial variation of seismic motion on the internal forces of arch rib primarily comes from travel ing-wave. The internal forces of arch rib under three-dimensional earthquake excitations are greater than that under one-dimensional excitation. The random seismic analysis under three-dimensional and multi-support earthquake excitations must be performed for the long-span CFST arch bridge otherwise the seismic design forces of the structure are likely to underestimate seriously.
The practical stability criterion of structure motion and the specific steps were proposed. The instable characteristics of arch structure were investigated under step load, cyclic load and earthquake excitation. It is indicated that negative eigenvalue appearing in structure whole stiffness matrix is requirements for structure instability and the lower limit of critical load of structure dynamical instability is estimated. The displacement time-history curve becoming divergent, a change of qualities, a leap taking place or the motion chaos can be basis for structure dynamical instability.
The static and dynamic plastical stability analysis of long-span half-through trussed CFST arch bridge were studied. The result indicates that the material non-linearity decreases static stability coefficient of long span arch bridge greatly. The Budiansky-Roth criterion is invalidate in the analysis of elastic dynamic stability of long span arch bridge and the critical load of dynamic stability can be estimated by negative eigenvalue appearing in structure whole stiffness matrix. Lateral earthquake excitation is the most disadvantageous direction in dynamic buckling analysis. Initial geometric imperfection makes no difference on dynamic stability of arch bridge but yet affect static stability of arch bridge deeply. The plastic dynamic buckling mode of arch bridge is partial buckling of arch rib and seismic wave disturbance has little influence on static stability coefficient of arch bridge.
引文
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