悬链线斜靠式拱肋系侧倾失稳临界荷载
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摘要
基于能量分析方法,推导了主拱肋和稳定拱肋拱轴线为悬链线的斜靠式拱肋系侧倾失稳临界荷载计算公式,并通过与有限元数值计算结果比较,证明了该计算公式的正确性,进一步验证了所提出的拱肋系侧倾失稳时横撑切向和径向力学模型的适用性,并将拱轴线为悬链线和圆弧曲线的斜靠式拱肋系的侧倾失稳临界荷载进行了比对分析,阐明了圆弧曲线代替悬链线斜靠式拱肋系侧倾失稳临界荷载的适用条件。研究结果表明:拱轴线的线型对斜靠式拱肋系的侧倾失稳临界荷载有一定的影响;当稳定拱肋倾角较小时,悬链线拱肋系的侧倾失稳临界荷载与圆弧曲线拱肋系的差异不超过5%;当矢跨比较小时,圆弧曲线拱肋系代替悬链线拱肋系的侧倾失稳临界荷载产生的误差在10%以下,但矢跨比较大时,二者的差异较大,不可等同。
Based on energy analysis method,the calculation formula of lateral buckling critical load of the leaning-type arch ribs with the catenary arch axis is derived.Compared with the results obtained from FEM,the analytical solution formula presented is verified in this paper.The applicability of the lateral and radial mechanical models of transverse brace between the main arch rib and stable arch rib proposed are validated.Furthermore,the lateral buckling critical load under circular arch axis and catenary are compared,while the quantity relationship and the applicable condition that replacing the lateral buckling critical load of catenary arch with the circular arch are analyzed.It is shown that the line-type of arch axis has a certain extent impact on the lateral buckling critical load of the leaning-type arch ribs.When the incline angle of stable ribs is small,the difference of the lateral buckling critical load between the catenary arch rib system and circular arch rib system is less than 5%.The error induced by the lateral buckling critical load of circular arch rib system replacing that of the catenary arch rib system will be less than 10% when the rise-span ratios are small enough.With the increasing of rise-span ratios,the differences will increase and the replacement is not feasible.
Based on energy analysis method,the calculation formula of lateral buckling critical load of the leaning-type arch ribs with the catenary arch axis is derived.Compared with the results obtained from FEM,the analytical solution formula presented is verified in this paper.The applicability of the lateral and radial mechanical models of transverse brace between the main arch rib and stable arch rib proposed are validated.Furthermore,the lateral buckling critical load under circular arch axis and catenary are compared,while the quantity relationship and the applicable condition that replacing the lateral buckling critical load of catenary arch with the circular arch are analyzed.It is shown that the line-type of arch axis has a certain extent impact on the lateral buckling critical load of the leaning-type arch ribs.When the incline angle of stable ribs is small,the difference of the lateral buckling critical load between the catenary arch rib system and circular arch rib system is less than 5%.The error induced by the lateral buckling critical load of circular arch rib system replacing that of the catenary arch rib system will be less than 10% when the rise-span ratios are small enough.With the increasing of rise-span ratios,the differences will increase and the replacement is not feasible.
引文
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[9]项海帆.拱结构的稳定与振动[M].北京:人民交通出版社,1991:75―123.Xiang Haifan.The stability and vibration of archstructure[M].Beijing:China Communications Press,1991:75―123.(in Chinese)
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[12]杨永清.抛物线双肋拱在非保向力作用下的横向稳定性[J].西南交通大学,2003,38(3):310―313.Yang Yongqing.Lateral stability of parabolic double-ribarch under non-directional load[J].Journal of SouthwestJiaotong University,2003,38(3):309―313.(in Chinese)
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[14]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,LüZhitao.Lateral buckling load of tied-archbridges with transverse braces[J].EngineeringMechanics,2004,21(3):21―24,54.(in Chinese)
[2]Richard M,Andreas A.Field testing and simulation ofdynamic properties of a tied arch railway bridge[J].Engineering Structures,2006,28:143―152.
[3]Laurent,N.Vincent de Ville de Goyet,RenéMaquoi.Optimum bracing of the arches of tied-arch bridges[J].Journal of Constructional Steel Research,1991,18:239―249.
[4]Nazmy A S.Stability and load-carrying capacity ofthree-dimensional long-span steel arch bridges[J].Computers and Structures,1997,65(6):857―868.
[5]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 vibrations of bridge structures[M].Beijing:China Railway Publishing House,1996.(inChinese)
[6]陈淮,胡锋,申哲会,杨磊.斜靠式拱桥稳定性分析[J].福州大学学报,2005,33:182―186.Chen Huai,Hu Feng,Shen Zhehui,Yang Lei.Stabilityanalysis of leaning-type arch bridge[J].Journal ofFuzhou University,2005,33:182―186.(in Chinese)
[7]刘爱荣,申富林,邝钜滔,张俊平,禹奇才.斜靠式拱肋系侧倾失稳临界荷载计算方法[J].工程力学,2011,28(12):166―172.Liu Airong,Shen Fulin,Kuang Jutao,Zhang Junping,YuQicai.Calculation method for lateral buckling criticalload of leaning-type arch ribs system[J].EngineeringMechanics,2011,28(12):166―172.(in Chinese)
[8]刘爱荣,申富林,张俊平,禹奇才,汪荷玲.斜靠式拱肋系侧倾失稳临界荷载计算方法[J].土木工程学报,2012,45(4):107―116.Liu Airong,Shen Fulin,Zhang Junping,Yu Qicai,WangHeling.Analytical solution of lateral buckling criticalload for leaning-type arch bridges[J].China CivilEngineering Journal,2012,45(4):107―116.(inChinese)
[9]项海帆.拱结构的稳定与振动[M].北京:人民交通出版社,1991:75―123.Xiang Haifan.The stability and vibration of archstructure[M].Beijing:China Communications Press,1991:75―123.(in Chinese)
[10]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.Qian Lianping,Xiang Haifan.A practical method forlateral buckling analysis of arch bridges[J].Journal ofTongji University,1989,17(2):161―172.(in Chinese)
[11]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―45.Jin Weiliang,Zhao Guofan.Lateral buckling of X-typetwin ribbed arch braced with transverse beams[J].ChinaCivil Engineering Journal,1989,22(2):44―54.(inChinese)
[12]杨永清.抛物线双肋拱在非保向力作用下的横向稳定性[J].西南交通大学,2003,38(3):310―313.Yang Yongqing.Lateral stability of parabolic double-ribarch under non-directional load[J].Journal of SouthwestJiaotong University,2003,38(3):309―313.(in Chinese)
[13]陈彦江.大跨度钢管混凝土拱桥的横向稳定性研究[D].哈尔滨:哈尔滨工业大学,2001.Chen Yanjiang.Lateral stability study of load spanconcrete filled steel tubulear arches bridge[D].Haerbin:Haerbin Institute of Technology,2001.(in Chinese)
[14]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,LüZhitao.Lateral buckling load of tied-archbridges with transverse braces[J].EngineeringMechanics,2004,21(3):21―24,54.(in Chinese)
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