斜靠式拱桥侧倾失稳临界荷载解析解
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摘要
以新型空间拱桥——斜靠式拱桥为研究对象,提出斜靠式拱桥发生侧倾失稳时主拱肋与稳定拱肋间横撑切向和径向受力模型,基于Ritz法,构造桥梁各主要构件的变形能、外力势能以及吊杆非保向力势,首次推导出斜靠式拱桥侧倾失稳临界荷载的解析解,并通过与有限元计算结果比较,验证该解析解计算公式的正确性。进一步分析稳定拱肋、吊杆非保向力、以及主拱肋与稳定拱肋间横撑对斜靠式拱桥侧倾失稳临界荷载的影响。研究结果表明:①增设稳定拱肋可使桥梁侧倾失稳临界荷载提高1.6～1.8倍左右,同时随着稳定拱肋倾角的增加,临界荷载呈增大趋势;②受吊杆非保向力以及桥面系的影响,桥梁侧倾失稳临界荷载可提高约3.5倍左右;③横撑的径向抗弯刚度对斜靠式拱桥侧向失稳临界荷载影响较大。
A new leaning-type arch bridge was studied.Both lateral and radial mechanical models of the transverse brace between the main arch rib and the stable arch rib were proposed,when lateral buckling occurs.Based on Ritz method,numerical model of the main members of leaning-type arch bridge for calculation of the deformation energy,external loading potential energy and non-directional load potential energy of the hangers were constructed,and an analytical solution of the lateral buckling critical load was derived.Comparing results with those obtained from FEM calculations,it was verified that the analytical solution presented in this paper is sufficiently accurate.The study indicate that: 1)the lateral buckling critical load can be increased about 1.6~1.8 times by setting the stable arch ribs,and the critical load would increase with the increase of the inclination angle of the stable arch rib;2) the critical load can be increased by 3.5 times due to the influence of the non-directional load of the hangers and bridge deck;3) the radial bending stiffness of transverse braces has great impact on the critical load.
A new leaning-type arch bridge was studied.Both lateral and radial mechanical models of the transverse brace between the main arch rib and the stable arch rib were proposed,when lateral buckling occurs.Based on Ritz method,numerical model of the main members of leaning-type arch bridge for calculation of the deformation energy,external loading potential energy and non-directional load potential energy of the hangers were constructed,and an analytical solution of the lateral buckling critical load was derived.Comparing results with those obtained from FEM calculations,it was verified that the analytical solution presented in this paper is sufficiently accurate.The study indicate that: 1)the lateral buckling critical load can be increased about 1.6~1.8 times by setting the stable arch ribs,and the critical load would increase with the increase of the inclination angle of the stable arch rib;2) the critical load can be increased by 3.5 times due to the influence of the non-directional load of the hangers and bridge deck;3) the radial bending stiffness of transverse braces has great impact on the critical load.
引文
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[11]刘钊,吕志涛.有横撑系杆拱桥的侧向稳定承载力[J].工程力学,2004,21(3):21-24,54(Liu Zhao,Lu Zhitao.Lateral buckling load of tied-arch bridges with transversebraces[J].Engineering Mechanics,2004,21(3):21-24,54(in Chinese))
[12]向中富.中承式拱桥横向屈曲临界荷载实用计算[J].重庆交通学院学报,1995,14(1):27-31(Xiang Zhongfu.Practical calculation of the lateral stability of the midhight-deck arch bridge[J].Journal of Chongqing JiaotongInstitute,1995,14(1):27-31(in Chinese))
[13]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996(Li Guohao.Stability and vibration of bridgestructures[M].Beijing:China Railway Publishing House,1996(in Chinese))
[2]刘爱荣,禹奇才,宋瑞,等.地震作用下斜靠式拱桥的动力稳定性[J].深圳大学学报:理工版,2010,27(3):286-290(Liu Airong,Yu Qicai,Song Rui,et al.Dynamicstability of leaning-type arch bridge under earthquake[J].Journal of Shenzhen University:Science and EngineeringEdition,2010,27(3):286-290(in Chinese))
[3]刘爱荣,禹奇才,张俊平,等.斜拱肋倾角变化对斜靠式拱桥地震响应的影响[J].暨南大学学报:自然科学与医学版,2010,31(3):268-272(Liu Airong,Yu Qicai,Zhang Junping,et al.Influence of variation of incline angleof inclined arch rib on the seismic response of leaning-typearch bridge[J].Journal of Jinan University:NaturalScience and Medicine Edition,2010,31(3):268-272(inChinese))
[4]Nazmy A S.Stability and load-carrying capacity of three-dimensional long-span steel arch bridges[J].Computersand Structures,1997,65(6):857-868
[5]陈淮,孙应桃.斜靠式拱桥拱肋倾角变化对稳定性能的影响[J].铁道科学与工程学报,2009,6(1):21-24(Chen Huai,Sun Yingtao.Variational sloping angle ofarch rib influenced on the stability of double X-shaped archbridge[J].Journal of Railway Science and Engineering,2009,6(1):21-24(in Chinese))
[6]陈淮,胡锋,申哲会,等.斜靠式拱桥稳定性分析[J].福州大学学报:自然科学版,2005,33(增1):182-186(Chen Huai,Hu Feng,Shen Zhehui,et al.Stabilityanalysis of double X-shape arch bridge[J].Journal ofFuzhou University:Natural Science Edition,2005,33(S1):182-186(in Chinese))
[7]Lim N H,Kang Y J.Out of plane stability of circulararches[J].International Journal of Mechanical Sciences,2004,46(8):1115-1137
[8]钱莲萍,项海帆.空间拱桥结构侧倾稳定性的实用计算[J].同济大学学报,1989,17(2):161-172(QianLianping,Xiang Haifan.A practical method for lateralbuckling analysis of arch bridges[J].Journal of TongjiUniversity,1989,17(2):161-172(in Chinese))
[9]金伟良,顾淑兴,赵国藩.无横撑肋拱桥横向稳定性的研究[J].中国公路学报,1989,2(3):42-48(JinWeiliang,Gu Shuxing,Zhao Guofan.The lateral stabilityof tied arch bridge without bracing beams[J].ChinaJournal of Highway and Transport,1989,2(3):42-48(inChinese))
[10]金伟良,赵国藩.X型双肋拱系的侧倾屈曲[J].土木工程学报,1989,22(2):44-54(Jin Weiliang,Zhao Guofan.Lateral buckling of X-type twin ribbed arch braced withtransverse beams[J].China Civil Engineering Journal,1989,22(2):44-54(in Chinese))
[11]刘钊,吕志涛.有横撑系杆拱桥的侧向稳定承载力[J].工程力学,2004,21(3):21-24,54(Liu Zhao,Lu Zhitao.Lateral buckling load of tied-arch bridges with transversebraces[J].Engineering Mechanics,2004,21(3):21-24,54(in Chinese))
[12]向中富.中承式拱桥横向屈曲临界荷载实用计算[J].重庆交通学院学报,1995,14(1):27-31(Xiang Zhongfu.Practical calculation of the lateral stability of the midhight-deck arch bridge[J].Journal of Chongqing JiaotongInstitute,1995,14(1):27-31(in Chinese))
[13]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996(Li Guohao.Stability and vibration of bridgestructures[M].Beijing:China Railway Publishing House,1996(in Chinese))
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