薄壁曲线箱梁考虑剪滞效应的弯扭分析

发布时间：2018-02-12 09:45

本文关键词： 薄壁箱梁曲线箱梁剪滞效应弯扭分析　出处：《兰州交通大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着我国现代化事业的日益加快，为了适应复杂的地形地势，曲线梁桥得到了广泛应用。薄壁箱梁由于其独有的特点，在曲线梁桥中被采纳。但箱形梁中的剪力滞现象，使曲线箱梁的弯扭分析变得复杂化。所以早期研究曲线箱梁时，往往不考虑剪力滞效应。后来不少学者开始探讨曲线箱梁考虑剪滞效应的分析，但忽略了剪滞翘曲应力的自平衡性质及二次剪流对约束扭转的影响，使曲线箱梁的弯扭特性不能得到比较客观的反映。本文基于能量变分法，考虑由剪滞翘曲位移产生的剪滞翘曲线应变能和由新的翘曲广义位移产生的翘曲应变能等，建立曲线箱梁的控制微分方程及边界条件，采用迦辽金数值解法进行求解。推导薄壁箱梁几何特性中的扭转中心及主扇性坐标的实用公式，使曲线箱梁的弯扭分析过程相对简化。数值算例验证时，，先利用数学软件MATLAB算出理论值，然后与用ANSYS软件得到的有限元值、试验测出的实测值进行对比，来证明本文方法的合理性。比较剪滞翘曲位移函数由三次抛物线变为二次时，以及曲率半径、宽跨比等参数变化时，对曲线箱梁的影响。研究表明：（1）建立的曲线箱梁控制微分方程，如果忽略剪力滞的影响，且用扭角的一阶导数代替新的翘曲广义位移，会变成符拉索夫方程。导出的扭转中心及主扇性坐标的计算公式对之后计算过程的简化起到了重要作用。用本文方法对水平曲线箱梁有机模型进行求解，得到的计算值与有限元值、实测值基本符合，验证了文中所提出的理论及导出的公式的正确性。（2）当剪滞翘曲位移函数由三次抛物线变为二次时，只有曲线箱梁内力中的剪滞力矩变动较大，而每点的正应力、翘曲双力矩和弯矩都基本不变。（3）由于弯扭耦合作用，曲线箱梁跨中截面内外侧分布的应力并不对称，且应力绝对值随着曲率半径的增大而减小。内力、挠度和扭转角的绝对值也都随着曲率半径的增大而减小。宽跨比对剪力滞系数的影响比起曲率半径略大。在均布荷载作用下，位于跨中截面的剪滞位移和翘曲位移为零。应力和内力的绝对值随着宽跨比的变化规律与随着曲率半径变化的规律一致。
[Abstract]:With the rapid development of modernization in China, curved girder bridges are widely used in order to adapt to the complicated terrain. Thin wall box girder is adopted in curved girder bridges because of its unique characteristics. The bending and torsional analysis of curved box girder becomes more complicated. Therefore, the shear lag effect is often not considered in the early study of curved box girder. Later, many scholars began to discuss the analysis of shear lag effect in curved box girder. However, the self-equilibrium property of shear lag warping stress and the effect of secondary shear flow on restrained torsion are neglected, which makes the bending and torsional characteristics of curved box girder unable to be reflected objectively. Based on the energy variational method, the governing differential equations and boundary conditions of curved box girder are established by taking into account the strain energy of the shear lag curve generated by the shear lag displacement and the warping strain energy generated by the new warping generalized displacement. The practical formulas of torsion center and principal fan coordinate in the geometric characteristics of thin-walled box girder are derived, which simplifies the bending and torsional analysis process of curved box girder. The theoretical values are calculated by using the mathematical software MATLAB, and then compared with the finite element values obtained by ANSYS software, and the experimental measured values are compared to prove the rationality of the method in this paper. When the shear lag displacement function changes from the cubic parabola to the quadratic, the results are as follows: (1) when the shear lag displacement function is changed from a cubic parabola to a quadratic one, The influence of curvature radius and ratio of width to span on curved box girder is studied. 1) the governing differential equation of curved box girder is established. If the influence of shear lag is ignored, the new warping generalized displacement is replaced by the first derivative of torsion angle. The derived formulas of torsion center and principal fan coordinates play an important role in the simplification of the calculation process. The organic model of horizontal curved box girder is solved by the method in this paper. The calculated value is basically in agreement with the finite element value and the measured value, which verifies the correctness of the theory proposed in this paper and the derived formula. 2) when the displacement function of shear lag warpage is changed from cubic parabola to quadratic, only the shear lag moment of curved box girder varies greatly, but the normal stress, warping double moment and bending moment of each point are basically unchanged. 3) because of the coupling of bending and torsion, the stress distribution inside and outside the middle section of curved box girder is not symmetrical, and the absolute value of stress decreases with the increase of curvature radius. The absolute values of deflection and torsion angle also decrease with the increase of radius of curvature. The influence of the ratio of width to span on shear lag coefficient is slightly greater than that of radius of curvature. The shear lag displacement and warping displacement in the middle section of the span are zero. The absolute values of stress and internal force vary with the ratio of width to span and are consistent with the variation of curvature radius.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441

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