大跨度三主桁高速铁路桥梁静力特性分析
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摘要
内力横向分配问题是三主桁高速铁路桥梁静力特性研究的重点之一,优化分析方法是提高大跨度三主桁桥梁的静力分析效率的有效途径。本文从以下几个方面对此进行了研究,并取得了一些成果:
(1)内力横向分配
用框架分析法,推导了两桁式桁架桥的竖向位移差计算公式,建议参考单箱双室、单室箱梁桥分别计算三桁式桁架桥在偏载和满载下的位移差。三主桁桥梁的内力横向分配比两主桁桥梁要复杂得多,其横向刚度的影响因素也多。
有限元分析结果表明,三片式桁拱桥的内力横向分配和位移协调主要靠横向联接系的刚度来保证,而保证横梁刚结对于横向联接系的横向刚度至关重要。桁拱桥也可通过调节吊杆的拉力来使桁间位移进一步协调。
索力对于保证三主桁斜拉桥的桁间位移协调起关键作用。可以通过索力函数法和框架分析法得到桥梁的最优索力,使得各工况作用下桥梁的最大横向扭转角均满足要求。
(2)五跨连续梁模型
对于120m+5×168m+120m的七跨连续梁,虽然其跨度差超过28%,但是计算结果表明这种七跨结构可以采用五跨(120m+3×168m+120m)连续梁模型来分析,这样可减少分析问题的规模。
(3)桥面板分析
对于带纵梁的开口肋桥面板,利用板单元、梁单元以及粗糙梁单元三种模型计算得到的桥面主桁弦杆受力很接近,且桥面板的应力数值和分布也几乎相同,所以可以用子模型方法分析这种桥面板。
而对于带大闭口肋的桥面板,按板单元以及梁单元两种模型分析的结果相差较大,故不宜用子模型分析这种桥面板,需用板单元忠实建模,对于重复部分,可以用子结构有限元法分析。
(4)空间分析模型
从能量角度出发,研究了三主桁桥的弯矩功和轴力功的比率关系,计算结果表明大多数杆件的弯矩功可以忽略,即大多数杆件可以用杆单元而不用梁单元来分析,这样可以大量减少模型的总自由度数,缩短计算时间。
(5)计算结果的整理
研究了铁路桥梁影响线的计算结果快速整理方法,给出了自动生成结果报表的方法,减少了人工劳动,提高了工作效率。
(6)基础分析
用轴对称有限元法求解地基基本解,然后用半解析半数值法分析基础,具有极高的分析效率。由于轴对称有限元法是二维算法,兼有数值方法的优点,且可利用现有的商业有限元软件平台,故非常适合求解层状地基的基本解。
本文的研究成果可以作为南京大胜关长江大桥和郑州黄河公铁两用大桥的设计依据,也可作为类似三主桁桥梁研究的参考。
Research of transverse distribution of internal forces i of great importance in studying characteristics of high-speed railway bridge with three main trusses, and optimization analysis method is an effective way to improve research efficience for long span bridge with three main trusses. Some achievements listed as bellow have obtained in this dissertation:
(1) Transverse distribution of internal forces
With the method of frame analysis, formula for calculating vertical displacement difference on steel truss bridge with two main trusses, have been derived. The vertical displacement difference on steel truss bridge with three main trusses acting by offset load can be calculated by the formula of girder with with double chamberes in its box section, and on the acting of full load, the formula of girder with with one chamber in its box section can be referenced. The transverse distribution of internal forces in bridge with three main trusses is much more complex than that in bridge with two main trusses.
Results obtained from FEM show that transverse distribution of internal forces and transverse displacement coordination in arch bridge with three main trusses lie on the stiffness of cross linking system, so keeping the nodes of floor beam fixed is a guarantee to the stiffness of cross linking system. Truss arch bridge can also get better displacement coordination among three trusses by adjusting the tension of hanger rod.
Cable tension plays a key role in keeping displacement coordination among three trusses in cable-stayed bridge with three main trusses. The best bridge cable tension, which makes maximum rotational angle of section under various loads can meet demand, is analized by cable tension function method and frame analysis method.
(2) Analizing model of five-span continuous beam
To a seven-span continuous beam with length of 120m+5×168m+120m, although the difference between the spans is more than 28 percent, the calculating results show that the seven-span beam can be analized by the modeled of five-span continuous beam (120m+3×168m+120m).
(3) Analysis of the deck
To the deck with opening rib and stringer, inneral forces of the main beam are very close to each other in three analysizing models: plate element model, beam element model, and larger size beam element model. Both the stress value and its distribution of deck occur with same features in the three models. All of those show that the deck with opening rib and stringer can be analysized by submodel.
To the deck with large closed rib, inneral forces of the main beam are very different in two analysizing models: plate element model, plate and beam element model. It inferrs that the deck with large closed rib should analized by plate element model. To structure with many same parts, it can be studied by substructure FEM.
(4) Spatial analysis model
From energy point of view, the ratio of of moment energy and force energy is studied. Studied results show the moment energy in most bars can be negected, that is to say, the majority of bars can be modeled by link element instead of beam element. This model can reduce the total number of degrees of freedom and shorten the calculating time.
(5) Automation of calculation
A fast calculation method for the influence line of railway bridge as well as method for statement generated automatically by computers are given in the dissertation to reducing the workforce and improve work efficiency.
(6) Analysis of foundation
The Semi-analytical and semi-numerical (SASN) method has a high efficiency in analizing foundation. The fundamental solution of soil in SASN method can be easily obtained by axisymmetric FEM. Axisymmetric FEM is a kind of 2D algorithm with many advantages as numerical method does, so it can be used to impove the efficiency of studying the fundamental solution of layered soil by existing commercial FEM software.
The work of this dissertation can be used for the engineering design of Nanjing Dashengguan Yangtze River Bridge and Zhengzhou Yellow River Bridge, but also as reference for the mechanics analysis of bridge with three main trusses.
(1)内力横向分配
用框架分析法,推导了两桁式桁架桥的竖向位移差计算公式,建议参考单箱双室、单室箱梁桥分别计算三桁式桁架桥在偏载和满载下的位移差。三主桁桥梁的内力横向分配比两主桁桥梁要复杂得多,其横向刚度的影响因素也多。
有限元分析结果表明,三片式桁拱桥的内力横向分配和位移协调主要靠横向联接系的刚度来保证,而保证横梁刚结对于横向联接系的横向刚度至关重要。桁拱桥也可通过调节吊杆的拉力来使桁间位移进一步协调。
索力对于保证三主桁斜拉桥的桁间位移协调起关键作用。可以通过索力函数法和框架分析法得到桥梁的最优索力,使得各工况作用下桥梁的最大横向扭转角均满足要求。
(2)五跨连续梁模型
对于120m+5×168m+120m的七跨连续梁,虽然其跨度差超过28%,但是计算结果表明这种七跨结构可以采用五跨(120m+3×168m+120m)连续梁模型来分析,这样可减少分析问题的规模。
(3)桥面板分析
对于带纵梁的开口肋桥面板,利用板单元、梁单元以及粗糙梁单元三种模型计算得到的桥面主桁弦杆受力很接近,且桥面板的应力数值和分布也几乎相同,所以可以用子模型方法分析这种桥面板。
而对于带大闭口肋的桥面板,按板单元以及梁单元两种模型分析的结果相差较大,故不宜用子模型分析这种桥面板,需用板单元忠实建模,对于重复部分,可以用子结构有限元法分析。
(4)空间分析模型
从能量角度出发,研究了三主桁桥的弯矩功和轴力功的比率关系,计算结果表明大多数杆件的弯矩功可以忽略,即大多数杆件可以用杆单元而不用梁单元来分析,这样可以大量减少模型的总自由度数,缩短计算时间。
(5)计算结果的整理
研究了铁路桥梁影响线的计算结果快速整理方法,给出了自动生成结果报表的方法,减少了人工劳动,提高了工作效率。
(6)基础分析
用轴对称有限元法求解地基基本解,然后用半解析半数值法分析基础,具有极高的分析效率。由于轴对称有限元法是二维算法,兼有数值方法的优点,且可利用现有的商业有限元软件平台,故非常适合求解层状地基的基本解。
本文的研究成果可以作为南京大胜关长江大桥和郑州黄河公铁两用大桥的设计依据,也可作为类似三主桁桥梁研究的参考。
Research of transverse distribution of internal forces i of great importance in studying characteristics of high-speed railway bridge with three main trusses, and optimization analysis method is an effective way to improve research efficience for long span bridge with three main trusses. Some achievements listed as bellow have obtained in this dissertation:
(1) Transverse distribution of internal forces
With the method of frame analysis, formula for calculating vertical displacement difference on steel truss bridge with two main trusses, have been derived. The vertical displacement difference on steel truss bridge with three main trusses acting by offset load can be calculated by the formula of girder with with double chamberes in its box section, and on the acting of full load, the formula of girder with with one chamber in its box section can be referenced. The transverse distribution of internal forces in bridge with three main trusses is much more complex than that in bridge with two main trusses.
Results obtained from FEM show that transverse distribution of internal forces and transverse displacement coordination in arch bridge with three main trusses lie on the stiffness of cross linking system, so keeping the nodes of floor beam fixed is a guarantee to the stiffness of cross linking system. Truss arch bridge can also get better displacement coordination among three trusses by adjusting the tension of hanger rod.
Cable tension plays a key role in keeping displacement coordination among three trusses in cable-stayed bridge with three main trusses. The best bridge cable tension, which makes maximum rotational angle of section under various loads can meet demand, is analized by cable tension function method and frame analysis method.
(2) Analizing model of five-span continuous beam
To a seven-span continuous beam with length of 120m+5×168m+120m, although the difference between the spans is more than 28 percent, the calculating results show that the seven-span beam can be analized by the modeled of five-span continuous beam (120m+3×168m+120m).
(3) Analysis of the deck
To the deck with opening rib and stringer, inneral forces of the main beam are very close to each other in three analysizing models: plate element model, beam element model, and larger size beam element model. Both the stress value and its distribution of deck occur with same features in the three models. All of those show that the deck with opening rib and stringer can be analysized by submodel.
To the deck with large closed rib, inneral forces of the main beam are very different in two analysizing models: plate element model, plate and beam element model. It inferrs that the deck with large closed rib should analized by plate element model. To structure with many same parts, it can be studied by substructure FEM.
(4) Spatial analysis model
From energy point of view, the ratio of of moment energy and force energy is studied. Studied results show the moment energy in most bars can be negected, that is to say, the majority of bars can be modeled by link element instead of beam element. This model can reduce the total number of degrees of freedom and shorten the calculating time.
(5) Automation of calculation
A fast calculation method for the influence line of railway bridge as well as method for statement generated automatically by computers are given in the dissertation to reducing the workforce and improve work efficiency.
(6) Analysis of foundation
The Semi-analytical and semi-numerical (SASN) method has a high efficiency in analizing foundation. The fundamental solution of soil in SASN method can be easily obtained by axisymmetric FEM. Axisymmetric FEM is a kind of 2D algorithm with many advantages as numerical method does, so it can be used to impove the efficiency of studying the fundamental solution of layered soil by existing commercial FEM software.
The work of this dissertation can be used for the engineering design of Nanjing Dashengguan Yangtze River Bridge and Zhengzhou Yellow River Bridge, but also as reference for the mechanics analysis of bridge with three main trusses.
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