基于精细化数值模拟的悬索桥施工阶段结构力学性能研究
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摘要
近年来对悬索桥的分析计算越来越精细化,甚至细致的分析了索鞍顶推导致的主缆与索鞍的切点变化。但这种精细化分析主要是针对成桥后的结构所进行的。处于施工阶段,特别是吊装加劲梁阶段的结构由于其自身特点而使得分析更加复杂,此时结构的力学性能和抗震性能就更需要细致的分析研究了。本文运用精细化有限元技术分析了施工阶段悬索桥主要部件——主塔、主缆——的结构力学性能,以及施工阶段悬索桥的抗震性能。
本文所指精细化有限元分析主要体现在采用了高精度的单元以模拟结构的主要部件:
首先采用了计算精度与三维实体单元相仿而计算效率高得多的纤维单元模型来模拟主塔。与此同时,为更好地解决复杂受力状态下剪切变形不可忽略问题的弹塑性分析,本文以传统纤维模型理论为基础,提出了一种通过泊松比考虑剪切变形影响的纤维模型,解决了纤维模型模拟长宽比很小构件时位移计算结果与实验结果相差较大的问题。与实验结果对比表明,对于长宽比很小的构件,考虑剪切变形纤维模型的位移结果比纯弯曲纤维模型结果精确15%~25%,所得滞回环更加符合剪切形构件滞回环的形状特征。
由于主缆在成缆后其真实形状是曲线的,故采用了能充分考虑空间各种内力变形耦合效应的空间曲梁单元模拟主缆。在学习前人工作的过程中,发现现有曲梁理论在大位移、大转角情况下的几何方程存在缺陷,也没有能真正考虑空间各种内力的耦合效应。因此,研究曲杆大位移、大转角、大曲率情况下的分析理论不仅具有理论意义,也可用于悬索桥的精细化分析,具有工程实际意义。为弥补现有曲梁理论的缺陷,借助随动曲线坐标描述和张量分析等数学工具,系统地推导了大位移、大转角、大曲率情况下任意空间曲梁的几何方程、空间双向弯、扭耦合的平衡微分方程、非线性虚功方程和本构方程。将直梁单元位移分量插值的思想改进为位移矢量插值用以建立曲梁单元的位移场,分别建立了适用于任意曲线形式的全拉格朗日(TL)和修正拉格朗日(UL)增量格式空间曲梁有限元列式。算例对比结果表明,曲梁单元的精度明显的高于分段直梁单元。一般情况下,仅用直梁单元数量五分之一的曲梁单元就可以达到相同的计算精度。给出了曲梁单元一致质量矩阵的形成方法,并对静力凝聚法进行了改进而提出了广义静力凝聚方法。
由于采用的是自研究的高精度单元,故无法使用现有的商用软件进行分析。因研究工作的需要,需要自主研发一套特色鲜明的具有自主知识产权的分析软件。在上述理论准备基础上,作为第一阶段工作开发了MockCool软件。考虑剪切变形纤维模型分析功能、几何非线性空间曲梁单元分析功能、拆卸单元(约束)内力自动转换加载功能、改进的大质量法处理边界等功能是MockCool独有的特点。通过和MIDAS计算结果以及文献结果(实验结果)的对比,验证了MockCool计算结果的正确性和合理性。
在上述理论准备和软件研发的基础上,针对悬索桥施工阶段的特点,应用自开发的软件进行了大量计算分析,有针对性的研究了施工阶段悬索桥的两大部件——主缆和主塔——的结构力学性能:
大跨度悬索桥成桥后主缆的弯曲刚度确系很小而可以忽略。然而在进行加劲梁吊装时,主缆的弯曲刚度对此时的结构分析有没有影响?有多大影响?至今无人能够回答。为了定量回答悬索桥主缆弯曲刚度的影响大小,在数值分析时考虑了悬索桥主缆的弯曲刚度,针对不同跨度情况的主缆进行了弯曲应力的参数分析,结果表明:在施工吊装加劲梁阶段,大跨度桥梁的主缆弯曲次应力最大达到了主应力的15%;随着主缆截面直径与跨度之比(截跨比)的增大弯曲次应力将迅速增大,当截跨比大于1/400时,弯曲次应力大于主应力的30%。由此可见:对大跨度悬索桥进行成桥后分析,忽略弯曲次应力是合理的;但是处于施工阶段的桥梁,特别是小跨度悬索桥弯曲次应力是不可忽视的;应用自开发的曲梁单元分析结果比通用直梁单元分析结果模型大,分析精度更高,更适合分析小跨度悬索桥模型。
针对主塔,采取与成桥后考虑主缆等构件影响的成桥主塔作对比的手段,分析了施工时未挂主缆的施工主塔的力学性能,进行了弹性和大位移弹塑性分析。定性地研究了悬索桥主塔的失稳和破坏的形态,定量的分析了主塔的安全储备。结果表明,就所论的计算模型而言,虽然二者的弹性失稳问题均属于第二类极值型稳定问题,但是由于边界条件的不同,不仅弹性失稳模态不同,弹塑性极限承载力的差别也很大,施工主塔分析结果将高估主塔成桥后真实工作时的轴向压力承载能力。
同样是采用与成桥结构对比的手段,分析了从空缆到成桥各阶段悬索桥的抗震性能:
由于采用的是与成桥对比的手段,故首先需要对成桥结构进行抗震性能研究。
针对不同的物理量,对几何非线性影响、地面输入地震动方向、人工地震动记录功率谱模型等因素对悬索桥单点激励地震反应时程分析结果的影响进行了逐一的分析。结果表明:进行单点激励分析时几何非线性的影响不大;多维分析的结果和单维分析的结果的差别较大,分析应采用三维地震动分析;Kanai-Tajimi模型生成的地震动激励较其它模型更适合进行大跨悬索桥地震反应时程分析。在此基础上对江阴大桥模型进行了多点激励弹塑性动力增量时程分析。结果表明在遭遇设计设防烈度7度的罕遇地震时,主塔基本处于正常工作状态。就数值分析结果而言,当遭遇9度以上的罕遇地震时,主塔将有可能进入危险状态。说明大桥拥有较大的安全冗余度。
对处于施工阶段(吊装加劲梁)的江阴大桥,进行了随着施工进展的阶段抗震性能研究。结果表明:处于施工阶段的结构的自振周期比成桥状态的自振周期大,而且随着施工的进展同一阶数的振型形状排序会发生变化;时程分析发现,当输入激励不大时(小于400 gal),施工阶段的结构响应小于成桥结构响应。此情况下,设计只要能保证成桥状态的结构安全,则施工阶段结构也是安全的;当输入激励较大时,由于施工阶段极强的几何非线性,引起了主缆加劲梁系统较大的荡漾,使得施工阶段结构的响应远大于成桥状态响应。建议在施工阶段采取一些临时的连接以限制加劲梁荡漾位移以预防不测。
Suspension bridge analysis and computation have become increasingly refined in recent years, with even intensive analysis to examine on the changes of tangent point between the main cable and cable saddle resulted from cable saddle pushing. Such refined analysis, however, is mostly done on structures after completion. Structures under construction, especially in the process of hoisting and mounting stiffened girders, add to the complexity of analysis due to their unique characteristics. In this case, it is all the more necessary to conduct intensive analysis of the mechanical properties and seismic properties of the structures. With the use of refined finite element technology, the dissertation dissects the structural mechanical properties of main tower and main cable as the major components of suspension bridge as well as the seismic properties of suspension bridge at construction stage.
The refined finite element analysis referred to in the dissertation lies largely in the adoption of high-precision elements to simulate the main components of the structure.
First of all, the main power is simulated by fiber element model, which has similar computational precision but higher computational efficiency compared to 3D solid modeling. Furthermore, to better deal with the elastic-plastic analysis of appreciable issues with shear effects under complicated stress state, the dissertation builds on traditional fiber modeling theory and puts forward a fiber model that considers the effects of shearing deformation through Poisson ratio, and thus addresses the problem of significance difference between computational and experimental results of displacement of components with small length-width ratio. Comparison with experimental results finds that for such components, computational results of the fiber model which considers shearing deformation are 15% to 25% more precise than those of pure bending fiber model, and that the hysteresis loops obtained are more consistent with the shear-type components form features.
Given the fact that main cables are curved after cabling is completed, spatial curved beam elements are used to simulate the main cables as the former fully considers the coupling effects of various types of internal forces and deformation. During study of previous works, it is found that the existing curved beam theories have drawbacks with geometrical equations under the circumstances of large displacement and big angles of rotation, and fail to actually take into account the coupling effects of various spatial internal forces. Therefore, studying the analytical theory under the circumstances of large displacement, big angles of rotation, and great curvature of curved bars will be not only of theoretical significance but also of practical engineering significance as it can be applied to the refined analysis of suspended bridges. In order to make up for the drawbacks of existing curved beam theories, with the use of mathematical tools including co-moving curvilinear coordinate representation and tensor analysis, the geometric equations, spatial two-directional bend-rotation coupled equilibrium differential equation, nonlinear virtual work equation and constitutive equation of arbitrary spatial beams under the circumstances of large displacement, big angles of rotation, and great curvature are systematically derived. The idea of straight beam element displacement component interpolation is improved to displacement vector interpolation to establish displacement field that applies to any curve types of Total Lagrangian (TL) and Updated Lagrangian (UL) incremental finite element formulations for spatial curved beams. Comparison of calculation results indicates that the precision with curved beam elements is noticeably higher than that with segmented straight beam elements. Typically, it takes only one fifth as many curved beam elements to achieve the same level of calculation precision as it takes straight beam elements. Method of forming the consistent mass matrix for curved beam elements is given. In addition, static condensation method is improved and the generalized static condensation.
Existing commercial software cannot be applied to conduct analysis due to use of highly precise elements from independent research. The authors’research necessitates a set of purpose-built and proprietary analytical software. Building on the foregoing theoretical preparation, software MockCool is developed as the first phase of work. MockCool is featured with its capabilities of fiber model analysis considering shear deformation, analysis of spatial curved beam elements with large deformation, automatic conversion between and loading of disassembled elements and (restraint) internal forces, and dealing with boundaries with improved large mass method, etc. Comparison of computational results with MIDAS and literature results (experimental results), the accuracy and rationality of MockCool’s computational results are verified.
Based on the foregoing theoretical preparation and software development, using the independently developed software, a great quantity of computation and analysis are done specific to the characteristics of suspension bridge under construction, and the structural mechanical properties of main cable and main tower, the two major components of a suspension bridge under construction.
The bending stiffness of main cable after cabling is completed for long-span suspension bridge is indeed negligible. However, during hoisting of stiffened girders, does the bending stiffness of the main cable have any effect on the structural analysis at this point of time? How much effect? No one has been able to answer these questions as of now. In order to give a quantitative answer as to how much effect there is of the bending stiffness of a suspension bridge’s main cable, numerical analysis takes the bending stiffness into consideration and analyzes bending stress parameters of main cable with different spans. Results are as follows: During hositing of stiffened girders, the secondary bending stress of the main cable of long-span suspension bridge peaks at 15% of the primary stress. The secondary bending stress is going to grow rapidly with the increased ratio of diameter of main cable section to the span (section-to-span ratio). When the section-to-span ratio exceeds 1:400, the secondary bending stress becomes greater than 30% of the primary stress. This shows that it is reasonable to ignore the secondary bending stress after completion of long-span suspension bridge, but the secondary bending stress of bridges under construction, especially that of a short-span suspension bridge, cannot be ignored. Compared to analysis using straight beam element, analysis using the independently developed curved beam element results in larger model and greater precision, and is more suitable for analysis of short-span suspension bridge model.
As for main tower, mechanical properties of main tower under construction with the main cable not yet attached are analyzed by comparing with main tower after completion, where the effects of main cable and other members are considered after completion of the bridge. Elasticity and elastic-plastic analyses are done. The instability and failure modes of main tower of suspension bridge are examined in a qualitative way. Quantitative analysis is done to address the margin of safety for the main tower. Results suggest that for the computational models discussed here, although both the main tower under construction and the main tower after completion have the same type of instability issue, which is elastic instability, they have different boundary conditions. Hence, they have different modes of elastic instability and significantly different elastic-plastic ultimate bearing capacities. Analytical results of the main tower under construction are to overestimate the axial compression load capacity under real working condition after completion of the main tower.
Seismic properties of suspension bridge at different stages from unloaded cable to completed bridge are examined by comparing again with the structure after completion.
Because of the comparison with completed bridge, it is first necessary to study the seismic properties of the completed structure.
Specific to different physical quantities, the paper examines various factors one by one, including geometrical non-linearity, direction of seismic ground motion input, and artificial ground motion recording power spectrum, to see how they affect the analysis results of response time history of bridge to earthquake under single-point excitation. Results indicate the following: (a) during the single-point excitation analysis, geometrical non-linearity does not have much effect; (b) there are significant differences between the results of multi-dimension and single-dimension analysis and the 3D seismic motion analysis should be used; and (c) Relative to other models, Kanai-Taijimi model generates seismic motion excitation that is more suitable for analysis of earthquake response time history of long-span suspension bridge. Based on these findings, multi-point elastic-plastic and incremental dynamic analysis of time history are done with the model of Jianyin Bridge. Results of the analysis suggest that the main tower will basically remain its normal working condition in rare cases of an earthquake at seismic fortification level 7. According to the results of numerical analysis, in the rare cases of an earthquake above level 9, the main tower may become at risk. This means that the Bridge has a considerable margin of safety.
Seismic properties of Jiangyin Bridge under construction (with stiffened girders being hoisted) are examined while the construction is under way. Results of such analysis indicate the following: (a) natural vibration period of the structure under construction is longer than that of the completed bridge, and the vibration mode sequencing of the same order would change as the construction moves on; (b) time-history analysis finds that the response of structure under construction is smaller than that of completed structure when the excitation input is modest (<400 gal). Under such circumstances, as long as the design can guarantee the safety of completed structure, the structure during construction stage would be safe too. When the excitation input is greater, the geometrical non-linearity during construction would cause the main cable’s stiffened girder system sway noticeably, and thus make the response of the structure under construction way greater than that of completed bridge. Some provisional connections are recommended during construction to restrain the swaying displacement of stiffened girders against risks.
本文所指精细化有限元分析主要体现在采用了高精度的单元以模拟结构的主要部件:
首先采用了计算精度与三维实体单元相仿而计算效率高得多的纤维单元模型来模拟主塔。与此同时,为更好地解决复杂受力状态下剪切变形不可忽略问题的弹塑性分析,本文以传统纤维模型理论为基础,提出了一种通过泊松比考虑剪切变形影响的纤维模型,解决了纤维模型模拟长宽比很小构件时位移计算结果与实验结果相差较大的问题。与实验结果对比表明,对于长宽比很小的构件,考虑剪切变形纤维模型的位移结果比纯弯曲纤维模型结果精确15%~25%,所得滞回环更加符合剪切形构件滞回环的形状特征。
由于主缆在成缆后其真实形状是曲线的,故采用了能充分考虑空间各种内力变形耦合效应的空间曲梁单元模拟主缆。在学习前人工作的过程中,发现现有曲梁理论在大位移、大转角情况下的几何方程存在缺陷,也没有能真正考虑空间各种内力的耦合效应。因此,研究曲杆大位移、大转角、大曲率情况下的分析理论不仅具有理论意义,也可用于悬索桥的精细化分析,具有工程实际意义。为弥补现有曲梁理论的缺陷,借助随动曲线坐标描述和张量分析等数学工具,系统地推导了大位移、大转角、大曲率情况下任意空间曲梁的几何方程、空间双向弯、扭耦合的平衡微分方程、非线性虚功方程和本构方程。将直梁单元位移分量插值的思想改进为位移矢量插值用以建立曲梁单元的位移场,分别建立了适用于任意曲线形式的全拉格朗日(TL)和修正拉格朗日(UL)增量格式空间曲梁有限元列式。算例对比结果表明,曲梁单元的精度明显的高于分段直梁单元。一般情况下,仅用直梁单元数量五分之一的曲梁单元就可以达到相同的计算精度。给出了曲梁单元一致质量矩阵的形成方法,并对静力凝聚法进行了改进而提出了广义静力凝聚方法。
由于采用的是自研究的高精度单元,故无法使用现有的商用软件进行分析。因研究工作的需要,需要自主研发一套特色鲜明的具有自主知识产权的分析软件。在上述理论准备基础上,作为第一阶段工作开发了MockCool软件。考虑剪切变形纤维模型分析功能、几何非线性空间曲梁单元分析功能、拆卸单元(约束)内力自动转换加载功能、改进的大质量法处理边界等功能是MockCool独有的特点。通过和MIDAS计算结果以及文献结果(实验结果)的对比,验证了MockCool计算结果的正确性和合理性。
在上述理论准备和软件研发的基础上,针对悬索桥施工阶段的特点,应用自开发的软件进行了大量计算分析,有针对性的研究了施工阶段悬索桥的两大部件——主缆和主塔——的结构力学性能:
大跨度悬索桥成桥后主缆的弯曲刚度确系很小而可以忽略。然而在进行加劲梁吊装时,主缆的弯曲刚度对此时的结构分析有没有影响?有多大影响?至今无人能够回答。为了定量回答悬索桥主缆弯曲刚度的影响大小,在数值分析时考虑了悬索桥主缆的弯曲刚度,针对不同跨度情况的主缆进行了弯曲应力的参数分析,结果表明:在施工吊装加劲梁阶段,大跨度桥梁的主缆弯曲次应力最大达到了主应力的15%;随着主缆截面直径与跨度之比(截跨比)的增大弯曲次应力将迅速增大,当截跨比大于1/400时,弯曲次应力大于主应力的30%。由此可见:对大跨度悬索桥进行成桥后分析,忽略弯曲次应力是合理的;但是处于施工阶段的桥梁,特别是小跨度悬索桥弯曲次应力是不可忽视的;应用自开发的曲梁单元分析结果比通用直梁单元分析结果模型大,分析精度更高,更适合分析小跨度悬索桥模型。
针对主塔,采取与成桥后考虑主缆等构件影响的成桥主塔作对比的手段,分析了施工时未挂主缆的施工主塔的力学性能,进行了弹性和大位移弹塑性分析。定性地研究了悬索桥主塔的失稳和破坏的形态,定量的分析了主塔的安全储备。结果表明,就所论的计算模型而言,虽然二者的弹性失稳问题均属于第二类极值型稳定问题,但是由于边界条件的不同,不仅弹性失稳模态不同,弹塑性极限承载力的差别也很大,施工主塔分析结果将高估主塔成桥后真实工作时的轴向压力承载能力。
同样是采用与成桥结构对比的手段,分析了从空缆到成桥各阶段悬索桥的抗震性能:
由于采用的是与成桥对比的手段,故首先需要对成桥结构进行抗震性能研究。
针对不同的物理量,对几何非线性影响、地面输入地震动方向、人工地震动记录功率谱模型等因素对悬索桥单点激励地震反应时程分析结果的影响进行了逐一的分析。结果表明:进行单点激励分析时几何非线性的影响不大;多维分析的结果和单维分析的结果的差别较大,分析应采用三维地震动分析;Kanai-Tajimi模型生成的地震动激励较其它模型更适合进行大跨悬索桥地震反应时程分析。在此基础上对江阴大桥模型进行了多点激励弹塑性动力增量时程分析。结果表明在遭遇设计设防烈度7度的罕遇地震时,主塔基本处于正常工作状态。就数值分析结果而言,当遭遇9度以上的罕遇地震时,主塔将有可能进入危险状态。说明大桥拥有较大的安全冗余度。
对处于施工阶段(吊装加劲梁)的江阴大桥,进行了随着施工进展的阶段抗震性能研究。结果表明:处于施工阶段的结构的自振周期比成桥状态的自振周期大,而且随着施工的进展同一阶数的振型形状排序会发生变化;时程分析发现,当输入激励不大时(小于400 gal),施工阶段的结构响应小于成桥结构响应。此情况下,设计只要能保证成桥状态的结构安全,则施工阶段结构也是安全的;当输入激励较大时,由于施工阶段极强的几何非线性,引起了主缆加劲梁系统较大的荡漾,使得施工阶段结构的响应远大于成桥状态响应。建议在施工阶段采取一些临时的连接以限制加劲梁荡漾位移以预防不测。
Suspension bridge analysis and computation have become increasingly refined in recent years, with even intensive analysis to examine on the changes of tangent point between the main cable and cable saddle resulted from cable saddle pushing. Such refined analysis, however, is mostly done on structures after completion. Structures under construction, especially in the process of hoisting and mounting stiffened girders, add to the complexity of analysis due to their unique characteristics. In this case, it is all the more necessary to conduct intensive analysis of the mechanical properties and seismic properties of the structures. With the use of refined finite element technology, the dissertation dissects the structural mechanical properties of main tower and main cable as the major components of suspension bridge as well as the seismic properties of suspension bridge at construction stage.
The refined finite element analysis referred to in the dissertation lies largely in the adoption of high-precision elements to simulate the main components of the structure.
First of all, the main power is simulated by fiber element model, which has similar computational precision but higher computational efficiency compared to 3D solid modeling. Furthermore, to better deal with the elastic-plastic analysis of appreciable issues with shear effects under complicated stress state, the dissertation builds on traditional fiber modeling theory and puts forward a fiber model that considers the effects of shearing deformation through Poisson ratio, and thus addresses the problem of significance difference between computational and experimental results of displacement of components with small length-width ratio. Comparison with experimental results finds that for such components, computational results of the fiber model which considers shearing deformation are 15% to 25% more precise than those of pure bending fiber model, and that the hysteresis loops obtained are more consistent with the shear-type components form features.
Given the fact that main cables are curved after cabling is completed, spatial curved beam elements are used to simulate the main cables as the former fully considers the coupling effects of various types of internal forces and deformation. During study of previous works, it is found that the existing curved beam theories have drawbacks with geometrical equations under the circumstances of large displacement and big angles of rotation, and fail to actually take into account the coupling effects of various spatial internal forces. Therefore, studying the analytical theory under the circumstances of large displacement, big angles of rotation, and great curvature of curved bars will be not only of theoretical significance but also of practical engineering significance as it can be applied to the refined analysis of suspended bridges. In order to make up for the drawbacks of existing curved beam theories, with the use of mathematical tools including co-moving curvilinear coordinate representation and tensor analysis, the geometric equations, spatial two-directional bend-rotation coupled equilibrium differential equation, nonlinear virtual work equation and constitutive equation of arbitrary spatial beams under the circumstances of large displacement, big angles of rotation, and great curvature are systematically derived. The idea of straight beam element displacement component interpolation is improved to displacement vector interpolation to establish displacement field that applies to any curve types of Total Lagrangian (TL) and Updated Lagrangian (UL) incremental finite element formulations for spatial curved beams. Comparison of calculation results indicates that the precision with curved beam elements is noticeably higher than that with segmented straight beam elements. Typically, it takes only one fifth as many curved beam elements to achieve the same level of calculation precision as it takes straight beam elements. Method of forming the consistent mass matrix for curved beam elements is given. In addition, static condensation method is improved and the generalized static condensation.
Existing commercial software cannot be applied to conduct analysis due to use of highly precise elements from independent research. The authors’research necessitates a set of purpose-built and proprietary analytical software. Building on the foregoing theoretical preparation, software MockCool is developed as the first phase of work. MockCool is featured with its capabilities of fiber model analysis considering shear deformation, analysis of spatial curved beam elements with large deformation, automatic conversion between and loading of disassembled elements and (restraint) internal forces, and dealing with boundaries with improved large mass method, etc. Comparison of computational results with MIDAS and literature results (experimental results), the accuracy and rationality of MockCool’s computational results are verified.
Based on the foregoing theoretical preparation and software development, using the independently developed software, a great quantity of computation and analysis are done specific to the characteristics of suspension bridge under construction, and the structural mechanical properties of main cable and main tower, the two major components of a suspension bridge under construction.
The bending stiffness of main cable after cabling is completed for long-span suspension bridge is indeed negligible. However, during hoisting of stiffened girders, does the bending stiffness of the main cable have any effect on the structural analysis at this point of time? How much effect? No one has been able to answer these questions as of now. In order to give a quantitative answer as to how much effect there is of the bending stiffness of a suspension bridge’s main cable, numerical analysis takes the bending stiffness into consideration and analyzes bending stress parameters of main cable with different spans. Results are as follows: During hositing of stiffened girders, the secondary bending stress of the main cable of long-span suspension bridge peaks at 15% of the primary stress. The secondary bending stress is going to grow rapidly with the increased ratio of diameter of main cable section to the span (section-to-span ratio). When the section-to-span ratio exceeds 1:400, the secondary bending stress becomes greater than 30% of the primary stress. This shows that it is reasonable to ignore the secondary bending stress after completion of long-span suspension bridge, but the secondary bending stress of bridges under construction, especially that of a short-span suspension bridge, cannot be ignored. Compared to analysis using straight beam element, analysis using the independently developed curved beam element results in larger model and greater precision, and is more suitable for analysis of short-span suspension bridge model.
As for main tower, mechanical properties of main tower under construction with the main cable not yet attached are analyzed by comparing with main tower after completion, where the effects of main cable and other members are considered after completion of the bridge. Elasticity and elastic-plastic analyses are done. The instability and failure modes of main tower of suspension bridge are examined in a qualitative way. Quantitative analysis is done to address the margin of safety for the main tower. Results suggest that for the computational models discussed here, although both the main tower under construction and the main tower after completion have the same type of instability issue, which is elastic instability, they have different boundary conditions. Hence, they have different modes of elastic instability and significantly different elastic-plastic ultimate bearing capacities. Analytical results of the main tower under construction are to overestimate the axial compression load capacity under real working condition after completion of the main tower.
Seismic properties of suspension bridge at different stages from unloaded cable to completed bridge are examined by comparing again with the structure after completion.
Because of the comparison with completed bridge, it is first necessary to study the seismic properties of the completed structure.
Specific to different physical quantities, the paper examines various factors one by one, including geometrical non-linearity, direction of seismic ground motion input, and artificial ground motion recording power spectrum, to see how they affect the analysis results of response time history of bridge to earthquake under single-point excitation. Results indicate the following: (a) during the single-point excitation analysis, geometrical non-linearity does not have much effect; (b) there are significant differences between the results of multi-dimension and single-dimension analysis and the 3D seismic motion analysis should be used; and (c) Relative to other models, Kanai-Taijimi model generates seismic motion excitation that is more suitable for analysis of earthquake response time history of long-span suspension bridge. Based on these findings, multi-point elastic-plastic and incremental dynamic analysis of time history are done with the model of Jianyin Bridge. Results of the analysis suggest that the main tower will basically remain its normal working condition in rare cases of an earthquake at seismic fortification level 7. According to the results of numerical analysis, in the rare cases of an earthquake above level 9, the main tower may become at risk. This means that the Bridge has a considerable margin of safety.
Seismic properties of Jiangyin Bridge under construction (with stiffened girders being hoisted) are examined while the construction is under way. Results of such analysis indicate the following: (a) natural vibration period of the structure under construction is longer than that of the completed bridge, and the vibration mode sequencing of the same order would change as the construction moves on; (b) time-history analysis finds that the response of structure under construction is smaller than that of completed structure when the excitation input is modest (<400 gal). Under such circumstances, as long as the design can guarantee the safety of completed structure, the structure during construction stage would be safe too. When the excitation input is greater, the geometrical non-linearity during construction would cause the main cable’s stiffened girder system sway noticeably, and thus make the response of the structure under construction way greater than that of completed bridge. Some provisional connections are recommended during construction to restrain the swaying displacement of stiffened girders against risks.
引文
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