薄壁箱梁的约束扭转和畸变效应分析

发布时间：2018-04-01 20:26

本文选题：薄壁箱梁　切入点：约束扭转　出处：《兰州交通大学》2015年硕士论文

【摘要】：箱形梁由于抗扭刚度大、施工适应性强等优点而广泛应用于桥梁工程中,高强轻质日益成为箱梁结构发展的主要趋势。对于整体结构而言,箱梁的扭转和畸变是不可忽略的变形,而薄壁箱梁的约束扭转和畸变效应分析也一直是国内外许多学者广泛关注并研究的课题。针对目前混凝土箱梁的约束扭转和畸变效应分析中主要存在的问题,本文以单室斜腹板直线箱梁作为研究对象,主要从以下几个方面分别对箱梁的约束扭转和畸变效应进行深入研究。针对斜腹板薄壁箱梁的约束扭转分析,本文是在箱梁承受荷载作用时假定其截面形状保持不变的前提下进行的。在纯扭转理论的基础上计入由翘曲扭转产生的断面剪切变形。通过选取广义翘曲位移自由度,利用平面应力问题中应力与应变之间的关系以及翘曲正应力在箱梁平面内满足自身平衡等条件,推导出有关约束扭转翘曲正应力的计算表达式及约束扭转微分方程。以扭转角、翘曲位移、翘曲双力矩和扭矩为4个初参数,给出了微分方程的解。针对约束扭转问题中需要用到的箱形截面扭转几何特性,本文通过选取辅助极点,导出了计算扭转中心、主扇性坐标及主扇性惯性矩的简便公式,通过数值算例验证了本文方法的正确性。结合数值算例,详细分析了集中扭矩作用于不同位置时翘曲双力矩沿梁长的变化,揭示了斜腹板倾角、悬臂板宽度及梁高等参数变化对箱形截面扭转几何特性和翘曲应力的影响规律。针对斜腹板薄壁箱梁的畸变效应分析,本文通过选取更具一般性的畸变角?D作为畸变位移,忽略由于畸变变形产生的剪切应变,建立了两部分畸变角分量之间的关系,推导出角点应力比和畸变中心的计算式以及考虑畸变效应时体系的总势能,基于最小势能原理建立了畸变控制微分方程。以畸变角、畸变翘曲位移、畸变翘曲双力矩及畸变矩作为4个初参数,给出了微分方程的初参数解。对简支箱梁模型的畸变翘曲应力计算表明:本文计算值与有关文献中给出的计算值吻合良好,验证了本文方法的正确性。结合数值算例,分析了相关截面参数变化对畸变翘曲应力的影响。对在自由端处受扭转荷载和畸变荷载的悬臂箱梁计算表明,按本文方法求得的翘曲应力值与有限元计算值及其他文献给出的计算值均吻合良好。
[Abstract]:Box girder is widely used in bridge engineering because of its great torsional stiffness and strong construction adaptability. The high strength and light weight is becoming the main trend of box girder structure development.For the whole structure, the torsion and distortion of box girder can not be ignored, and the analysis of constraint torsion and distortion effect of thin-walled box girder has been widely concerned and studied by many scholars at home and abroad.Aiming at the existing problems in the analysis of the restrained torsion and distortion effect of concrete box girder, this paper takes the single chamber oblique web straight box girder as the research object.The restrained torsion and distortion effect of box girder are studied from the following aspects.In view of the constrained torsional analysis of thin-walled box girder with oblique web, the section shape of box girder is assumed to remain unchanged when the box girder is subjected to load.The shear deformation caused by warping torsion is taken into account on the basis of pure torsion theory.By selecting the degree of freedom of the generalized warping displacement, using the relation between stress and strain in plane stress problem and the condition that warpage normal stress satisfies its own balance in the plane of box girder, etc.The expression of constrained torsional warpage stress and the constrained torsional differential equation are derived.The solution of differential equation is given with four initial parameters of torsion angle, warpage displacement, warping double torque and torque.In view of the geometrical characteristics of torsion of box section used in constrained torsion problem, a simple formula for calculating torsional center, principal fan coordinate and principal fan moment of inertia is derived by selecting auxiliary poles.A numerical example is given to verify the correctness of the proposed method.Combined with a numerical example, the variation of warping double torques along the beam length when the concentrated torque acts on different positions is analyzed in detail, and the inclined angle of the inclined web is revealed.The influence of cantilever width and beam height on torsional geometry and warping stress of box section.According to the analysis of the distortion effect of the thin wall box girder with inclined web, this paper selects the more general distortion angle D as the distortion displacement, neglects the shear strain caused by the distortion deformation, and establishes the relationship between the two parts of the distortion angle component.The formulas for calculating the stress ratio of corner point and the center of distortion and the total potential energy of the system considering the distortion effect are derived. Based on the principle of minimum potential energy, the differential equation of distortion control is established.Taking the distortion angle, the distortion warpage displacement, the distortion warping double moment and the distortion moment as the four initial parameters, the initial parameter solution of the differential equation is given.The calculation of the distortion warpage stress of simply supported box girder model shows that the calculated values in this paper are in good agreement with the calculated values given in the relevant literature, which verifies the correctness of the proposed method.Combined with numerical examples, the effect of the variation of cross-section parameters on the distortion warpage stress is analyzed.The calculation of cantilever box girder subjected to torsional and distorted loads at the free end shows that the values of warpage stress obtained by the present method are in good agreement with the calculated values of finite element method and other literatures.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U441;U448.213

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