考虑畸变时两室薄壁箱梁的约束扭转分析
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摘要
针对目前箱梁桥某些横截面常因较大的畸变作用而产生明显变形,进而严重影响了桥梁的正常使用性能的情况,通过将符拉索夫广义坐标法与哈密顿对偶求解体系结合起来,并采用两端边值问题的精细积分法,求得考虑畸变时两室薄壁箱梁约束扭转问题中截面的翘曲正应力、畸变角及扭转角的高精度数值解,给出了截面的变形图,并通过实例进行了验证。在算例中,该悬臂梁自由端不考虑畸变时的扭转角为0.001 7 rad,与考虑畸变时的扭转角0.036 6 rad相比明显偏小,这就表明在实际工程中考虑畸变是非常必要的。该方法计算简单、适用性强,为结构设计人员提供一种新的分析结构的理论,可方便用于考虑畸变时两室薄壁箱梁约束扭转的计算。
Aiming at the situation that the obvious deformation of box girder because of some crosssection distortion seriously affects the normal performance of a bridge,combining the Vlasov generalized coordinate method and the Hamilton duality solution system,and using the precise integration method for two-point boundary value problems,a high precision numerical solution of the warping normal stress of the cross section was obtained. The distortion angle and twist angle in the restrained torsion of dual-chamber thin-walled box beam considering distortion and the deformation figure of cross section are given,and they were verified by an example. The torsion angle of the cantilever at the free end is 0. 001 7 rad not considering distortion in the case. It is significantly smaller than the torsion angle of 0. 036 6 rad considering distortion. This suggests that distortion should be taken into account in engineering. This method is simple in calculation and has good applicability,which provides a new structure analysis theory for designers,and it can be conveniently used for the calculation of restrained torsion of dual-chamber thin-walled box beams considering distortion.
Aiming at the situation that the obvious deformation of box girder because of some crosssection distortion seriously affects the normal performance of a bridge,combining the Vlasov generalized coordinate method and the Hamilton duality solution system,and using the precise integration method for two-point boundary value problems,a high precision numerical solution of the warping normal stress of the cross section was obtained. The distortion angle and twist angle in the restrained torsion of dual-chamber thin-walled box beam considering distortion and the deformation figure of cross section are given,and they were verified by an example. The torsion angle of the cantilever at the free end is 0. 001 7 rad not considering distortion in the case. It is significantly smaller than the torsion angle of 0. 036 6 rad considering distortion. This suggests that distortion should be taken into account in engineering. This method is simple in calculation and has good applicability,which provides a new structure analysis theory for designers,and it can be conveniently used for the calculation of restrained torsion of dual-chamber thin-walled box beams considering distortion.
引文
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[12]胡启平,董宝锋,吕铭.基于哈密顿理论的薄壁杆件稳定性分析[J].四川建筑科学研究,2011,37(4):26-29.
[13]胡启平,涂佳黄,梁经群.组合断面薄壁杆件弯扭耦合分析[J].工程力学,2010,27(7):52-55.
[14]胡启平,郭晓,刘昱辰.考虑畸变时薄壁箱梁受扭分析的精细积分法[J].江西科学,2012,30(3):335-337.
[15]钟万勰.矩阵黎卡提方程的精细积分法[J].计算结构力学及其应用,1994(5):113-118.
[2]RENDEK S,BALAZ I.Distortion of thin-walled beams[J].Thin-Walled Structures,2004,42:255-277.
[3]杨绿峰,任晓军,陈建芳,等.有限元法研究闭口薄壁杆件约束扭转[J].广西大学学报:自然科学版,2008,33(1):1-4.
[4]王增荣,李之榕,李仰训.箱梁扭转畸变的分析[J].铁道学报,1985,7(4):87-98.
[5]钟新谷,马平,曾庆元.多室箱形梁非线性有限元分析[J].土木工程学报,1999,32(6):32-39.
[6]刘志翁.薄壁箱梁畸变效应研究[D].兰州:兰州交通大学土木工程学院,2011.
[7]丛欣建.箱梁的扭转畸变分析[D].哈尔滨:东北林业大学土木工程学院,2005.
[8]陆洪民.薄壁箱梁畸变效应研究[D].重庆:重庆交通大学土木工程学院,2013.
[9]徐勋,强士中.薄壁箱梁畸变分析理论的研究[J].工程力学,2013,30(11):192-201.
[10]钟万勰,徐新生.Hamilton体系与弹性力学saint-Venant问题[J].应用数学和力学,1996,17(9):781-789.
[11]胡启平,李张苗,候瑞珀.铁摩辛柯梁梁弯曲问题的对偶求解体系[J].河北建筑科技学院学报,2006,23(3):1-2.
[12]胡启平,董宝锋,吕铭.基于哈密顿理论的薄壁杆件稳定性分析[J].四川建筑科学研究,2011,37(4):26-29.
[13]胡启平,涂佳黄,梁经群.组合断面薄壁杆件弯扭耦合分析[J].工程力学,2010,27(7):52-55.
[14]胡启平,郭晓,刘昱辰.考虑畸变时薄壁箱梁受扭分析的精细积分法[J].江西科学,2012,30(3):335-337.
[15]钟万勰.矩阵黎卡提方程的精细积分法[J].计算结构力学及其应用,1994(5):113-118.