圬工拱桥计算方法研究
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摘要
圬工拱桥是一种历史悠久的桥梁结构型式。它以坚固耐久、外形美观、载重潜力大、维修费用省、取材方便、所需技术工种较少、施工技术简单、建造成本低等特点而著称。但由于圬工拱桥所用材料的特殊性,其自身的发展受到很大的限制。不久前湖南凤凰桥的垮塌给世人敲响了桥梁建设的警钟,同时也广泛引起了广大桥梁建设者对圬工拱桥建设的注意。现行的圬工拱桥的计算方法,绝大多数还是以传统拱轴理论为依托,将拱上建筑视为荷载的形式加载至主拱圈上。这种传统的计算方法未能很好的体现拱上建筑与主拱圈的联合作用,即未能很好的体现拱上建筑与主拱圈作为一个整体承受荷载的效果。有限元方法的问世很好的弥补了这一传统计算方法的缺陷,通过建立理论模型,将主拱圈与拱上建筑构成一个统一的整体承受外部荷载,这不仅能更加科学的分析主拱圈的受力特性。也弥补了传统计算理论无法按照实际施工工况逐步分析结构受力的缺点。使得对于圬工拱桥的受力特性的分析,更加全面、更加接近工程实际。
鉴于本文重点在于研究圬工拱桥计算方法,故首先介绍了圬工拱桥的发展史、传统设计理论的研究概况及目前各种设计理论及设计方法。重点介绍了传统理论中无铰拱的计算方法。通过对传统计算方法的阐述,分析了各种设计理论及方法的不足,结合实际工程中圬工拱桥的坍塌案例进而提出圬工拱桥设计理论研究的实际意义。
由于圬工材料不是均质材料,且将有限元方法应用于圬工拱桥这种特定的桥型并不是较为常见的计算方法,故文中以洛泽河桥为工程实例,分别采用传统悬链线拱轴理论、MIDAS/CIVIL有限元计算程序及桥梁博士计算程序对其进行了静动力及温度效应的分析。并将传统悬链线拱轴理论、MIDAS/CIVIL梁单元、桥梁博士在恒载作用以及温度效应下的分析结果进行了对比,以确定MIDAS/CIVIL梁单元对圬工拱桥计算分析的准确性,得出了悬链线拱轴理论可以对圬工拱桥受力特性进行初步控制,但不能很好反映分步施工情况下,圬工拱桥实际受力情况的结论。随后,以三种不同的单元(梁单元、壳单元、实体单元)对洛泽河桥进行了有限元分析,将三者的分析结果进行了对比。发现对于大跨径圬工拱桥,要精确分析实际受力情况,最适宜的分析方法还是采用实体单元进行仿真分析。
随后,根据前述计算所得出的结论并结合传统悬链线拱轴理论,对不同跨径不同矢跨比的等截面圬工拱桥进行了有限元模拟分析,得出了不同跨径及矢跨比情况下,如何合理选择主拱圈材料及截面的结论。
Masonry arch bridge is sort of bridge with a long history. It is peculiar for its feature that it's beautiful, firm and durable, low-cost in maintenance and repair, convenient in collecting construction materials, simple in construction technique, low cost in construction, and it need less categories of technique workers than the other kind of bridges. However, since the materials used in masonry arch bridge are particular, the application of the bridge is restricted. It's the collapse of Fenghuang bridge in Hunan, which just happened not long ago, that brings about a big bomb in the field of bridge construction and makes lots of bridge constructor focus their attention on the construction of masonry arch bridge. Majority of the present calculating methods are based on the traditional ones, which regarded the structure above the main arch as a sort of load that worked on the main arch. Thus the coactions of the structure above the main arch and the main arch, which means that the structure above the main arch and the main arch should be regarded as an integration to bear load, couldn't be well reflected according to the traditional calculating method. By establishing theoretical models in finite element method whose emerging greatly fill up the blank of the traditional calculating method, which make the main arch and the structures above the main arch integrated to bear external load, the mechanical characteristics of the main arch under the external load can be analyzed more properly and scientifically. The FEM also make up that the traditional calculating method couldn't analyze the bridge step by step according to the construction stage, which make the analyzing course more effective and could be widely applied in the actual projects.
Since this paper focus on discussing calculating method of the arch bridges, the history of masonry arch bridge's development and the general situation of research in the theory of traditional design methods have been expressed in the very beginning. By elaborating the traditional calculating method, both the advantages and the disadvantages of varieties of the present design theories and methods are represented in this text, which mostly introduced the calculating method of the arch with no articulations. Combined with the cases that bridge collapse in the actual projects ,it is proposed that it make sense to research on design theory and calculating method of masonry arch bridges.
As masonry materials are not homogeneous, and the finite element method has not been widely applied in this typical bridge. Therefore, as for instance, traditional catenary arch axis theory (calculating method), midas/civil FEM calculating program and doctorbridge calculating program are used to analyze the Luozehe bridge under static load , dynamic load and temperature effect. On one hand, the analyzing results in different methods had been compared afterwards in order to check if the analyzing method used in the element of beam is accurate. And then it is found out that the calculating result of traditional catenary arch axis theory could play a role of preliminary control of the mechanical characteristics of main arch. But it could not well express the mechanical characteristics of main arch step by step as the construction stage. On the other hand, three different elements-beam, shell, solid are used to establish totally different models to calculate the static and dynamic effect of Luozehe bridge. By comparing the result from three different models, it is confirmed that only the simulation analyzing method used solid element can exactly reveal the mechanical characteristics of main arch of big span masonry arch bridge.
And then according to the conclusions made above, masonry arch bridges with uniform sections, under different span of different ratio of rise to span are simulated in FEM program. And how to choose proper materials and sections under different spans of different ratios of rise to span is quantified.
鉴于本文重点在于研究圬工拱桥计算方法,故首先介绍了圬工拱桥的发展史、传统设计理论的研究概况及目前各种设计理论及设计方法。重点介绍了传统理论中无铰拱的计算方法。通过对传统计算方法的阐述,分析了各种设计理论及方法的不足,结合实际工程中圬工拱桥的坍塌案例进而提出圬工拱桥设计理论研究的实际意义。
由于圬工材料不是均质材料,且将有限元方法应用于圬工拱桥这种特定的桥型并不是较为常见的计算方法,故文中以洛泽河桥为工程实例,分别采用传统悬链线拱轴理论、MIDAS/CIVIL有限元计算程序及桥梁博士计算程序对其进行了静动力及温度效应的分析。并将传统悬链线拱轴理论、MIDAS/CIVIL梁单元、桥梁博士在恒载作用以及温度效应下的分析结果进行了对比,以确定MIDAS/CIVIL梁单元对圬工拱桥计算分析的准确性,得出了悬链线拱轴理论可以对圬工拱桥受力特性进行初步控制,但不能很好反映分步施工情况下,圬工拱桥实际受力情况的结论。随后,以三种不同的单元(梁单元、壳单元、实体单元)对洛泽河桥进行了有限元分析,将三者的分析结果进行了对比。发现对于大跨径圬工拱桥,要精确分析实际受力情况,最适宜的分析方法还是采用实体单元进行仿真分析。
随后,根据前述计算所得出的结论并结合传统悬链线拱轴理论,对不同跨径不同矢跨比的等截面圬工拱桥进行了有限元模拟分析,得出了不同跨径及矢跨比情况下,如何合理选择主拱圈材料及截面的结论。
Masonry arch bridge is sort of bridge with a long history. It is peculiar for its feature that it's beautiful, firm and durable, low-cost in maintenance and repair, convenient in collecting construction materials, simple in construction technique, low cost in construction, and it need less categories of technique workers than the other kind of bridges. However, since the materials used in masonry arch bridge are particular, the application of the bridge is restricted. It's the collapse of Fenghuang bridge in Hunan, which just happened not long ago, that brings about a big bomb in the field of bridge construction and makes lots of bridge constructor focus their attention on the construction of masonry arch bridge. Majority of the present calculating methods are based on the traditional ones, which regarded the structure above the main arch as a sort of load that worked on the main arch. Thus the coactions of the structure above the main arch and the main arch, which means that the structure above the main arch and the main arch should be regarded as an integration to bear load, couldn't be well reflected according to the traditional calculating method. By establishing theoretical models in finite element method whose emerging greatly fill up the blank of the traditional calculating method, which make the main arch and the structures above the main arch integrated to bear external load, the mechanical characteristics of the main arch under the external load can be analyzed more properly and scientifically. The FEM also make up that the traditional calculating method couldn't analyze the bridge step by step according to the construction stage, which make the analyzing course more effective and could be widely applied in the actual projects.
Since this paper focus on discussing calculating method of the arch bridges, the history of masonry arch bridge's development and the general situation of research in the theory of traditional design methods have been expressed in the very beginning. By elaborating the traditional calculating method, both the advantages and the disadvantages of varieties of the present design theories and methods are represented in this text, which mostly introduced the calculating method of the arch with no articulations. Combined with the cases that bridge collapse in the actual projects ,it is proposed that it make sense to research on design theory and calculating method of masonry arch bridges.
As masonry materials are not homogeneous, and the finite element method has not been widely applied in this typical bridge. Therefore, as for instance, traditional catenary arch axis theory (calculating method), midas/civil FEM calculating program and doctorbridge calculating program are used to analyze the Luozehe bridge under static load , dynamic load and temperature effect. On one hand, the analyzing results in different methods had been compared afterwards in order to check if the analyzing method used in the element of beam is accurate. And then it is found out that the calculating result of traditional catenary arch axis theory could play a role of preliminary control of the mechanical characteristics of main arch. But it could not well express the mechanical characteristics of main arch step by step as the construction stage. On the other hand, three different elements-beam, shell, solid are used to establish totally different models to calculate the static and dynamic effect of Luozehe bridge. By comparing the result from three different models, it is confirmed that only the simulation analyzing method used solid element can exactly reveal the mechanical characteristics of main arch of big span masonry arch bridge.
And then according to the conclusions made above, masonry arch bridges with uniform sections, under different span of different ratio of rise to span are simulated in FEM program. And how to choose proper materials and sections under different spans of different ratios of rise to span is quantified.
引文
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[18]王志辉.半圆石拱桥施工过程的承载力分析.2006年9月.第14卷.第3期.76-79.
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