大跨径三塔结合梁斜拉桥几何非线性分析研究
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摘要
在建的武汉二七长江大桥采用主跨为616米的三塔结合梁斜拉桥结构形式,是目前世界上跨度最大的三塔结合梁斜拉桥。由于采用三塔斜拉桥的结构体系,结构整体柔性增大,几何非线性问题进一步突出。同时由于采用了结合梁形式,钢和混凝土材料性能差异较大,造成整体结构内力和空间分布变化特性十分复杂,因此开展三塔结合梁斜拉桥结构几何非线性研究是十分必要的。
本文以二七长江大桥为工程背景,首先开展三塔结合梁斜拉桥非线性有限元模型研究,然后基于双主梁非线性空间模型,考虑索的垂度效应、梁柱效应和大位移效应,进行三塔结合梁斜拉桥几何非线性分析,研究各种几何非线性因素对三塔结合梁斜拉桥内力和位移的影响。最后提出斜拉索无应力索长精确算法,并给出了斜拉桥初始成桥索力的计算方法。本文研究对于全面掌握大跨径结合梁斜拉桥的结构内力特性,进一步提高结合梁斜拉桥的计算分析水平,具有重要的理论和实际意义。主要内容和成果如下：
(1)运用大型有限元分析软件ANSYS的APDL语言以及参数化技术,采用空间板壳与梁杆单元相结合,建立了三塔结合梁斜拉桥结构双主梁非线性模型,并通过与单主梁有限元模型对比分析,充分验证了该双主梁模型的有效性和正确性。结果表明基于杆、板(壳)及空间梁单元相结合的双主梁模型可以用于大跨径三塔结合梁斜拉桥非线性分析,具有较好的计算精度,能准确反映结构的内力空间分布及变形特征。
(2)基于双主梁非线性有限元模型,定义了线性、计入斜拉索垂度效应的非线性、计入梁柱效应和大位移效应的非线性以及计入全部非线性因素的综合非线性四种工况,分析三塔结合梁斜拉桥在四种工况下的几何非线性行为,研究各种几何非线性因素对三塔结合梁斜拉桥内力和变形的影响。结果表明各种几何非线性因素都会影响结构的变形和受力状态。斜拉索垂度效应是大跨度斜拉桥结构几何非线性的主要因素,同时计入三种非线性较计入单项非线性因素对于桥梁结构的非线性影响大。各种非线性因素对不同构件受力的影响程度不同,对主梁和塔的位移而言,斜拉索的垂度效应影响大于梁柱效应和大位移效应,对于主梁和塔的内力而言,斜拉索的垂度效应影响小于梁柱效应和大位移效应,而对于斜拉索的索力,几何非线性效应的影响均很小。
(3)提出了一种斜拉索无应力索长精确求解方法,其特点是用索端力的精确计算式代替索端节点力的平均值,建立已知端张力时斜拉索特征参数约束方程,求解无应力索长,同时避免了无应力索长初值的选取问题。并运用该方法计算了二七长江大桥的斜拉索无应力长度,并与解析法、等效模量法对比,结果表明该方法正确有效。
(4)基于非线性有限元方法,利用ANSYS二次开发功能,运用APDL语言开发了大跨三塔斜拉桥调索程序,给出了一种三塔斜拉桥成桥初始索力确定方法。并将该程序应用于二七长江大桥索力分析,结果表明该程序实现了自动完成调索过程,调索速度快精度高。
Wuhan Erqi Yangtze River Bridge is the longest span composite girder cable-stayed bridge with three towers under construction. The main span is 616 m. Due to the cable-stayed bridge system with three towers, the flexibility of bridge is increased, and geometrically nonlinear problem is further highlighted. On the other hand, owing to the combined girder form for long-span composite girder cable-stayed bridge with three towers, material properties of steel and concrete is greatly different, which result in complex internal force change and distribution. Therefore, the geometrically nonlinear analysis is very necessary for composite girder cable-stayed bridge with three towers.
Taking Erqi Yangtze River Bridge as an example, First the spatial nonlinear finite element model is established. Secondly, based on double girder nonlinear finite element model, cable sag, beam-column effect and large displacement effect were considered. The various influences of geometrically nonlinearity are studied on internal force and deflection in four cases. An accurate solution method of unstressed cable length and a cable force adjusting programme were proposed, which are applied in Erqi Yangtze River Bridge. These studies have important theoretical and practical significance to grasp internal force characteristics and further improve the calculation analysis level for longest span composite girder cable-stayed bridge. The main contents and conclusions of the research are listed as follows:
(1) The spatial double girder nonlinear finite element model is established through link elements, shell and spatial beam elements by APDL parameterization technique.compared with single girder model, the spatial double girder nonlinear model was fully verified the effectiveness and correctness. The results show the spatial double girder nonlinear model can be used to the nonlinear analysis of long-span composite girder cable-stayed bridge with three towers, which has good precision.
(2) Based on double girder nonlinear finite element model, the nonlinear analysis was developed under four cases, which including linear case, cable sag case, beam-column effect and large displacement case, all nonlinear case. The various nonlinear factors effect on internal force and deflection are studied. The results show all kinds of geometry nonlinear factors will affect the deformation and stress state of bridge. Cable sag is the most important factors. The geometric nonlinear effect considering all factors is larger than only considering a nonlinear factor. The nonlinear effect is different on internal force and displacement to different component. As far as the displacement of main girders and towers concerned, Cable sag effect is larger than beam-column effect and large displacement effect. For internal force of main girders and towers, cable sag effect is few than beam-column effect and large displacement effect, but for internal force of cables, three nonlinear factors effect is all few.
(3) Determination of unstressed cable length is important to realize the initial configuration of long span cable-stayed bridge. Based on centenary theory, an accurate solution method of unstressed cable length is proposed; the end force of cable is used, characteristic parameter constraint equations is established when the cable tension known, its iterative is given when An accurate solution method of unstressed cable length is applied. The unstressed cable length of a long span cable stayed bridge is calculated, through contrasted with analytic solution and Ernst method, the results show the reliability of the method.
(4) Based on nonlinear finite element methods, A cable force adjusting programme is proposed by means of ANSYS secondary development, the initial cable forces is iteratively calculated and repeatedly adjusted so that calculating cable force match with design cable under dead load. Simultaneously all kinds of geometric nonlinearity are considered. This cable force adjusting programme are applied to analyze the bridge-completing initial cable force of Erqi Yangtze River Bridge, The results show that the cable-force-adjusting programme is convenient and high efficient in analysis of cable-stayed bridges with three towers.
本文以二七长江大桥为工程背景,首先开展三塔结合梁斜拉桥非线性有限元模型研究,然后基于双主梁非线性空间模型,考虑索的垂度效应、梁柱效应和大位移效应,进行三塔结合梁斜拉桥几何非线性分析,研究各种几何非线性因素对三塔结合梁斜拉桥内力和位移的影响。最后提出斜拉索无应力索长精确算法,并给出了斜拉桥初始成桥索力的计算方法。本文研究对于全面掌握大跨径结合梁斜拉桥的结构内力特性,进一步提高结合梁斜拉桥的计算分析水平,具有重要的理论和实际意义。主要内容和成果如下：
(1)运用大型有限元分析软件ANSYS的APDL语言以及参数化技术,采用空间板壳与梁杆单元相结合,建立了三塔结合梁斜拉桥结构双主梁非线性模型,并通过与单主梁有限元模型对比分析,充分验证了该双主梁模型的有效性和正确性。结果表明基于杆、板(壳)及空间梁单元相结合的双主梁模型可以用于大跨径三塔结合梁斜拉桥非线性分析,具有较好的计算精度,能准确反映结构的内力空间分布及变形特征。
(2)基于双主梁非线性有限元模型,定义了线性、计入斜拉索垂度效应的非线性、计入梁柱效应和大位移效应的非线性以及计入全部非线性因素的综合非线性四种工况,分析三塔结合梁斜拉桥在四种工况下的几何非线性行为,研究各种几何非线性因素对三塔结合梁斜拉桥内力和变形的影响。结果表明各种几何非线性因素都会影响结构的变形和受力状态。斜拉索垂度效应是大跨度斜拉桥结构几何非线性的主要因素,同时计入三种非线性较计入单项非线性因素对于桥梁结构的非线性影响大。各种非线性因素对不同构件受力的影响程度不同,对主梁和塔的位移而言,斜拉索的垂度效应影响大于梁柱效应和大位移效应,对于主梁和塔的内力而言,斜拉索的垂度效应影响小于梁柱效应和大位移效应,而对于斜拉索的索力,几何非线性效应的影响均很小。
(3)提出了一种斜拉索无应力索长精确求解方法,其特点是用索端力的精确计算式代替索端节点力的平均值,建立已知端张力时斜拉索特征参数约束方程,求解无应力索长,同时避免了无应力索长初值的选取问题。并运用该方法计算了二七长江大桥的斜拉索无应力长度,并与解析法、等效模量法对比,结果表明该方法正确有效。
(4)基于非线性有限元方法,利用ANSYS二次开发功能,运用APDL语言开发了大跨三塔斜拉桥调索程序,给出了一种三塔斜拉桥成桥初始索力确定方法。并将该程序应用于二七长江大桥索力分析,结果表明该程序实现了自动完成调索过程,调索速度快精度高。
Wuhan Erqi Yangtze River Bridge is the longest span composite girder cable-stayed bridge with three towers under construction. The main span is 616 m. Due to the cable-stayed bridge system with three towers, the flexibility of bridge is increased, and geometrically nonlinear problem is further highlighted. On the other hand, owing to the combined girder form for long-span composite girder cable-stayed bridge with three towers, material properties of steel and concrete is greatly different, which result in complex internal force change and distribution. Therefore, the geometrically nonlinear analysis is very necessary for composite girder cable-stayed bridge with three towers.
Taking Erqi Yangtze River Bridge as an example, First the spatial nonlinear finite element model is established. Secondly, based on double girder nonlinear finite element model, cable sag, beam-column effect and large displacement effect were considered. The various influences of geometrically nonlinearity are studied on internal force and deflection in four cases. An accurate solution method of unstressed cable length and a cable force adjusting programme were proposed, which are applied in Erqi Yangtze River Bridge. These studies have important theoretical and practical significance to grasp internal force characteristics and further improve the calculation analysis level for longest span composite girder cable-stayed bridge. The main contents and conclusions of the research are listed as follows:
(1) The spatial double girder nonlinear finite element model is established through link elements, shell and spatial beam elements by APDL parameterization technique.compared with single girder model, the spatial double girder nonlinear model was fully verified the effectiveness and correctness. The results show the spatial double girder nonlinear model can be used to the nonlinear analysis of long-span composite girder cable-stayed bridge with three towers, which has good precision.
(2) Based on double girder nonlinear finite element model, the nonlinear analysis was developed under four cases, which including linear case, cable sag case, beam-column effect and large displacement case, all nonlinear case. The various nonlinear factors effect on internal force and deflection are studied. The results show all kinds of geometry nonlinear factors will affect the deformation and stress state of bridge. Cable sag is the most important factors. The geometric nonlinear effect considering all factors is larger than only considering a nonlinear factor. The nonlinear effect is different on internal force and displacement to different component. As far as the displacement of main girders and towers concerned, Cable sag effect is larger than beam-column effect and large displacement effect. For internal force of main girders and towers, cable sag effect is few than beam-column effect and large displacement effect, but for internal force of cables, three nonlinear factors effect is all few.
(3) Determination of unstressed cable length is important to realize the initial configuration of long span cable-stayed bridge. Based on centenary theory, an accurate solution method of unstressed cable length is proposed; the end force of cable is used, characteristic parameter constraint equations is established when the cable tension known, its iterative is given when An accurate solution method of unstressed cable length is applied. The unstressed cable length of a long span cable stayed bridge is calculated, through contrasted with analytic solution and Ernst method, the results show the reliability of the method.
(4) Based on nonlinear finite element methods, A cable force adjusting programme is proposed by means of ANSYS secondary development, the initial cable forces is iteratively calculated and repeatedly adjusted so that calculating cable force match with design cable under dead load. Simultaneously all kinds of geometric nonlinearity are considered. This cable force adjusting programme are applied to analyze the bridge-completing initial cable force of Erqi Yangtze River Bridge, The results show that the cable-force-adjusting programme is convenient and high efficient in analysis of cable-stayed bridges with three towers.
引文
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