基于静动力特性的多塔长跨斜拉桥结构体系刚度研究
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摘要
摘要：多塔斜拉桥在二十世纪中期就已经出现,但是发展一直较缓慢,制约其发展的一个关键因素就是整体刚度偏弱,为此国内外学者开展了一定的研究。当多塔斜拉桥进入大跨径时,其刚度问题更加突出,本文在前人研究成果的基础上,结合交通运输部科技项目“多塔长大斜拉桥关键技术研究”(项目号：2013315494011),主要针对多塔长跨斜拉桥的刚度相关问题进行系统性的研究。本文的主要工作包括以下几个方面：
(1)提出了多塔斜拉桥整体刚度指标,定义了多塔斜拉桥竖向刚度代表值,并对其限值进行了讨论,为本文的后续研究提供了判别标准。在广泛收集资料的基础上,对已建及拟建多塔斜拉桥的结构参数进行了统计并结合理论分析提出了多塔斜拉桥的合理塔跨比区间。
(2)提出了多塔斜拉桥结构变形计算的隔离结构法,基于Matlab语言编制了相应程序,提高了刚度参数优化时主梁活载变形计算的效率。基于多塔斜拉桥不同于常规斜拉桥(双塔或单塔斜拉桥)的受力特点,推导了考虑塔梁刚度的拉索支承刚度系数的计算公式并进行了验证。推导公式时,认为中间塔两侧主梁不能与有辅助墩的边跨主梁一样视为刚性梁,而是具有一定的柔度,只对桥塔提供一定程度的约束,同时考虑了桥塔自身抵抗变形的能力,最后讨论了桥塔刚度、主梁刚度、拉索刚度以及拉索倾角等因素对拉索支承刚度的影响,得出的结论可以用于指导概念设计。
(3)以琼州海峡大桥方案之一的主跨828m的五塔斜拉桥为工程算例,研究了多塔长跨斜拉桥刚度问题的解决方法。通过参数敏感性分析,对原方案的刚度参数进行了优化,给出了塔梁刚度取值的合理匹配区间,确定了拉索刚度以及塔跨比的合理取值范围。对采用各种加劲索的方案进行了比较分析,给出了基于静力特性优化后的琼州海峡大桥方案并进行了力学特性检算。
(4)提出了多塔斜拉桥塔梁刚度比的概念,基于拉索支承刚度系数计算式给出了相应的数学表达式。与索的刚度相比,塔的刚度与梁的刚度对多塔斜拉桥整体刚度的影响较大,设计自由度也较大,从刚度的角度出发,可通过塔梁刚度比将多塔斜拉桥划分为柔性塔体系与刚性塔体系。
(5)提出了一种新型的多塔斜拉桥结构体系一改进的莫兰迪结构体系(AMSS)。解决了柔性塔体系的多塔(四塔及以上)长跨斜拉桥的刚度问题。该体系是在斜拉桥索塔顺桥向两侧间隔一定距离设置塔梁竖向支座,从而同时实现塔梁之间的竖向约束和转动约束,在力学行为上接近塔梁固结,而构造上表现为塔梁分离。通过对其力学性能分析,发现其具有塔梁固结体系提高整体刚度的功能,同时避免塔梁固结处产生较大的弯矩。双支承间距的增大可以提高整体刚度也同时带来了托架根部弯矩增大的问题,通过有限元分析对双支承间距合理取值进行了研究。通过实桥试验数据分析了新型结构体系的合理性及解决柔性塔多塔长跨斜拉桥体系刚度问题的有效性。
(6)基于动力特性及地震反应分析对琼州海峡大桥方案做了进一步优化。多塔斜拉桥刚度的增大,提高了结构的静力抗变形能力,但是对动力特性的影响不能一概而论。本文分析了提高桥塔刚度和改变塔梁支承体系等措施对琼州海峡大桥方案动力特性的影响,并基于静动力特性总结了多塔斜拉桥刚度合理取值的方法。
(7)探讨了采用反分析对多塔斜拉桥结构刚度参数进行优化的方法。在刚度参数敏感性分析的基础上,给定一个挠度期望值,反演分析刚度参数,使得参数优化计算更具针对性,避免需要反复调整初始参数的大量有限元试探性分析。参数优化分析时,采用Ansys软件参数化建模技术建立了琼州海峡大桥方案的有限元模型,采用Matlab语言编制了相应的参数优化模型,并通过DOS内部命令,实现两种软件之间的对口连接,使其能够相互调用,降低了编程工作量,提到了工作效率。
ABSTRACT:Cable stayed bridge with multi-tower has already been built in the middle of last century, but it developed slowly. One of the key factors restricting the development of multi-tower cable stayed bridge is its weakness on rigidity, so many researches are focused on enhancing the integral rigidity of multi-tower cable stayed bridge. Then, the integral rigidity problem of long-span cable-stayed bridge with multi-tower is more prominent. On the basis of predecessors' research results, this paper mainly studies on the integral rigidity of long-span cable-stayed bridge with multi-tower systematically, which is funded by science and technology project of Ministry of Transport "The key technology research of large-span multi-tower cable stayed bridge"(project number:2013315494011). In this paper, the main work includes the following several aspects:
(1) An integral rigidity index of multi-tower cable stayed bridge is proposed. A representative value of vertical rigidity is suggested, and the limiting value is discussed as well. It provides a reference standard for the study. On the basis of collecting data widely, statistical analysis on structure parameter of multi-tower cable stayed bridge is conducted, and a optimized range of tower-span ratio is proposed.
(2) The isolation structure method is presented in the structural deformation calculation of multi-tower cable-stayed bridges.Based on Matlab software, corresponding program are compiled, and calculation efficiency of deformation of girder under live load is improved when the rigidity parameters need optimizing. According to the difference of loading features between multi-tower cable-stayed bridges and general ones (twin-tower or single-tower cable-stayed bridges), the formulas of cable supporting rigidity coefficient which include tower-beam rigidity are formed and verified. When the formula is derived, the flexibility of girder between middle towers cannot be ignored as the girder in side span. Middle towers are under little constraints transferred by girders. Combining with its resistance to deformation of tower, a parametric study is carried out to analyze the cable support rigidity. Parameters that potentially affect the cable support rigidity are taken into consideration, including tower rigidity, girder rigidity, cable rigidity and angle. Then the conclusion can be used to guide the conceptual design.
(3) Based on the design scheme of Qiongzhou Strait Bridge, main span is828m of which is cable-stayed bridge with five-tower, the rigidity problem of large span multi-tower cable stayed bridge is researched. By parameters sensitivity analysis, the rigidity parameters are optimized and an appropriate value range of tower and girder rigidity is presented, as well as cable rigidity and tower-span ratio. After comparative analysis of several stiffening cable design, the static performance optimized design scheme of Qiongzhou Strait Bridge is proposed and mechanical properties checked.
(4) The tower-beam rigidity ratio of multi-tower cable-stayed bridge are presented and its mathematical expressions are given. Compared with the rigidity of the cable, rigidity of the tower and rigidity of beam have more obvious influence impact on the on integral rigidity, and their design degrees of freedom are bigger. According to tower-beam rigidity ratio, multi-tower cable-stayed bridges are divided into flexible-tower system and rigid-tower system.
(5) A new mechanical structure system of named advanced Morandi structure system (AMSS) is presented, which could solve the problem that integral rigidity of long-span multi-tower flexible-tower system cable-stayed bridge with four or more towers can't be improved by setting stiffening cables. In the AMSS, the vertical bearing is located on a bracket which has a distance from the tower in longitudinal direction in order to meet the requirements of both vertical and rotational constraints between tower and beam. The mechanical behavior of AMSS is approximate to the fixed tower-beam structure system and its performance is that tower and beam are separated. Based on the analysis of its mechanical properties, it can be found that the AMSS has the equivalent function as the fixed tower-beam structure system in improving integral rigidity, and it has the advantage in avoiding large bending moment of the fixed zone between tower and beam. As the bending moment of the end of bracket become larger with the increase of the space between double supporting, the reasonable value of the space between double supporting is studied by the FEM analysis. The rationality of the AMSS and the effectiveness of improving integral rigidity of long-span multi-tower flexible-tower system cable-stayed bridge are verified by the experimental data.
(6) Based on dynamic and seismic analysis, the design scheme of Qiongzhou Strait Bridge is further optimized. The rigidity increasing leads to the improving of the structure deformation resistance, but the influence of which to the dynamic characteristics is complex and could not be simply perorated. This paper analyzed the influence of increasing tower rigidity and changing tower beam supporting system to dynamic characteristics of Qiongzhou Strait Bridge design scheme, and the method of obtaining a reasonable rigidity value of multi-tower cable stayed bridge is summarized based on static and dynamic characteristics.
(7) The optimizing methods of rigidity of multi-tower cable-stayed bridge by inverse analysis was discussed in this paper. Based on the parameter sensitivity of rigidity, the optimal computation is more targeted by backward deducing the rigidity parameters with a given expected deflection, which in order to avoid repeatedly adjust initial parameters in tentative analysis of finite element analysis. During the parameter optimizing, the FEA model of Qiongzhou Strait Bridge was built in Ansys, and the optimizing model was in Matlab. Through the DOS command, the both programs are successfully connected to transfer from each other, which reduces the workload and enhances the work efficiency
(1)提出了多塔斜拉桥整体刚度指标,定义了多塔斜拉桥竖向刚度代表值,并对其限值进行了讨论,为本文的后续研究提供了判别标准。在广泛收集资料的基础上,对已建及拟建多塔斜拉桥的结构参数进行了统计并结合理论分析提出了多塔斜拉桥的合理塔跨比区间。
(2)提出了多塔斜拉桥结构变形计算的隔离结构法,基于Matlab语言编制了相应程序,提高了刚度参数优化时主梁活载变形计算的效率。基于多塔斜拉桥不同于常规斜拉桥(双塔或单塔斜拉桥)的受力特点,推导了考虑塔梁刚度的拉索支承刚度系数的计算公式并进行了验证。推导公式时,认为中间塔两侧主梁不能与有辅助墩的边跨主梁一样视为刚性梁,而是具有一定的柔度,只对桥塔提供一定程度的约束,同时考虑了桥塔自身抵抗变形的能力,最后讨论了桥塔刚度、主梁刚度、拉索刚度以及拉索倾角等因素对拉索支承刚度的影响,得出的结论可以用于指导概念设计。
(3)以琼州海峡大桥方案之一的主跨828m的五塔斜拉桥为工程算例,研究了多塔长跨斜拉桥刚度问题的解决方法。通过参数敏感性分析,对原方案的刚度参数进行了优化,给出了塔梁刚度取值的合理匹配区间,确定了拉索刚度以及塔跨比的合理取值范围。对采用各种加劲索的方案进行了比较分析,给出了基于静力特性优化后的琼州海峡大桥方案并进行了力学特性检算。
(4)提出了多塔斜拉桥塔梁刚度比的概念,基于拉索支承刚度系数计算式给出了相应的数学表达式。与索的刚度相比,塔的刚度与梁的刚度对多塔斜拉桥整体刚度的影响较大,设计自由度也较大,从刚度的角度出发,可通过塔梁刚度比将多塔斜拉桥划分为柔性塔体系与刚性塔体系。
(5)提出了一种新型的多塔斜拉桥结构体系一改进的莫兰迪结构体系(AMSS)。解决了柔性塔体系的多塔(四塔及以上)长跨斜拉桥的刚度问题。该体系是在斜拉桥索塔顺桥向两侧间隔一定距离设置塔梁竖向支座,从而同时实现塔梁之间的竖向约束和转动约束,在力学行为上接近塔梁固结,而构造上表现为塔梁分离。通过对其力学性能分析,发现其具有塔梁固结体系提高整体刚度的功能,同时避免塔梁固结处产生较大的弯矩。双支承间距的增大可以提高整体刚度也同时带来了托架根部弯矩增大的问题,通过有限元分析对双支承间距合理取值进行了研究。通过实桥试验数据分析了新型结构体系的合理性及解决柔性塔多塔长跨斜拉桥体系刚度问题的有效性。
(6)基于动力特性及地震反应分析对琼州海峡大桥方案做了进一步优化。多塔斜拉桥刚度的增大,提高了结构的静力抗变形能力,但是对动力特性的影响不能一概而论。本文分析了提高桥塔刚度和改变塔梁支承体系等措施对琼州海峡大桥方案动力特性的影响,并基于静动力特性总结了多塔斜拉桥刚度合理取值的方法。
(7)探讨了采用反分析对多塔斜拉桥结构刚度参数进行优化的方法。在刚度参数敏感性分析的基础上,给定一个挠度期望值,反演分析刚度参数,使得参数优化计算更具针对性,避免需要反复调整初始参数的大量有限元试探性分析。参数优化分析时,采用Ansys软件参数化建模技术建立了琼州海峡大桥方案的有限元模型,采用Matlab语言编制了相应的参数优化模型,并通过DOS内部命令,实现两种软件之间的对口连接,使其能够相互调用,降低了编程工作量,提到了工作效率。
ABSTRACT:Cable stayed bridge with multi-tower has already been built in the middle of last century, but it developed slowly. One of the key factors restricting the development of multi-tower cable stayed bridge is its weakness on rigidity, so many researches are focused on enhancing the integral rigidity of multi-tower cable stayed bridge. Then, the integral rigidity problem of long-span cable-stayed bridge with multi-tower is more prominent. On the basis of predecessors' research results, this paper mainly studies on the integral rigidity of long-span cable-stayed bridge with multi-tower systematically, which is funded by science and technology project of Ministry of Transport "The key technology research of large-span multi-tower cable stayed bridge"(project number:2013315494011). In this paper, the main work includes the following several aspects:
(1) An integral rigidity index of multi-tower cable stayed bridge is proposed. A representative value of vertical rigidity is suggested, and the limiting value is discussed as well. It provides a reference standard for the study. On the basis of collecting data widely, statistical analysis on structure parameter of multi-tower cable stayed bridge is conducted, and a optimized range of tower-span ratio is proposed.
(2) The isolation structure method is presented in the structural deformation calculation of multi-tower cable-stayed bridges.Based on Matlab software, corresponding program are compiled, and calculation efficiency of deformation of girder under live load is improved when the rigidity parameters need optimizing. According to the difference of loading features between multi-tower cable-stayed bridges and general ones (twin-tower or single-tower cable-stayed bridges), the formulas of cable supporting rigidity coefficient which include tower-beam rigidity are formed and verified. When the formula is derived, the flexibility of girder between middle towers cannot be ignored as the girder in side span. Middle towers are under little constraints transferred by girders. Combining with its resistance to deformation of tower, a parametric study is carried out to analyze the cable support rigidity. Parameters that potentially affect the cable support rigidity are taken into consideration, including tower rigidity, girder rigidity, cable rigidity and angle. Then the conclusion can be used to guide the conceptual design.
(3) Based on the design scheme of Qiongzhou Strait Bridge, main span is828m of which is cable-stayed bridge with five-tower, the rigidity problem of large span multi-tower cable stayed bridge is researched. By parameters sensitivity analysis, the rigidity parameters are optimized and an appropriate value range of tower and girder rigidity is presented, as well as cable rigidity and tower-span ratio. After comparative analysis of several stiffening cable design, the static performance optimized design scheme of Qiongzhou Strait Bridge is proposed and mechanical properties checked.
(4) The tower-beam rigidity ratio of multi-tower cable-stayed bridge are presented and its mathematical expressions are given. Compared with the rigidity of the cable, rigidity of the tower and rigidity of beam have more obvious influence impact on the on integral rigidity, and their design degrees of freedom are bigger. According to tower-beam rigidity ratio, multi-tower cable-stayed bridges are divided into flexible-tower system and rigid-tower system.
(5) A new mechanical structure system of named advanced Morandi structure system (AMSS) is presented, which could solve the problem that integral rigidity of long-span multi-tower flexible-tower system cable-stayed bridge with four or more towers can't be improved by setting stiffening cables. In the AMSS, the vertical bearing is located on a bracket which has a distance from the tower in longitudinal direction in order to meet the requirements of both vertical and rotational constraints between tower and beam. The mechanical behavior of AMSS is approximate to the fixed tower-beam structure system and its performance is that tower and beam are separated. Based on the analysis of its mechanical properties, it can be found that the AMSS has the equivalent function as the fixed tower-beam structure system in improving integral rigidity, and it has the advantage in avoiding large bending moment of the fixed zone between tower and beam. As the bending moment of the end of bracket become larger with the increase of the space between double supporting, the reasonable value of the space between double supporting is studied by the FEM analysis. The rationality of the AMSS and the effectiveness of improving integral rigidity of long-span multi-tower flexible-tower system cable-stayed bridge are verified by the experimental data.
(6) Based on dynamic and seismic analysis, the design scheme of Qiongzhou Strait Bridge is further optimized. The rigidity increasing leads to the improving of the structure deformation resistance, but the influence of which to the dynamic characteristics is complex and could not be simply perorated. This paper analyzed the influence of increasing tower rigidity and changing tower beam supporting system to dynamic characteristics of Qiongzhou Strait Bridge design scheme, and the method of obtaining a reasonable rigidity value of multi-tower cable stayed bridge is summarized based on static and dynamic characteristics.
(7) The optimizing methods of rigidity of multi-tower cable-stayed bridge by inverse analysis was discussed in this paper. Based on the parameter sensitivity of rigidity, the optimal computation is more targeted by backward deducing the rigidity parameters with a given expected deflection, which in order to avoid repeatedly adjust initial parameters in tentative analysis of finite element analysis. During the parameter optimizing, the FEA model of Qiongzhou Strait Bridge was built in Ansys, and the optimizing model was in Matlab. Through the DOS command, the both programs are successfully connected to transfer from each other, which reduces the workload and enhances the work efficiency
引文
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