宽幅叠合梁第二体系分析

发布时间：2018-12-17 11:20

【摘要】：双边箱断面叠合梁斜拉桥是一种典型的大跨度桥梁形式。与钢斜拉桥相比具有其刚度大、抗风稳定性好等特点,而且能够避免正交异性钢桥面板带来的疲劳问题。叠合梁斜拉桥的中跨主梁是宽幅叠合梁。对于宽幅叠合梁的计算,目前多采用空间实体有限元建立节段模型进行分析,建模和计算过程复杂耗时。论文采用理论推导和有限元相结合的方式,研究了宽幅叠合梁第二体系的应力和变形的简化计算方法。具体而言,论文主要做了以下工作:(1)采用三比拟杆法分析了简支梁叠合梁和悬臂叠合梁的应力简化计算问题。首先按照应力相等的原则,将叠合梁比拟为只承受轴力的加劲杆和只承受剪力的系板的组合体系。然后根据加劲杆和系板之间的静力平衡条件和变形协调条件建立微分方程组。接着根据边界条件和荷载条件求解出混凝土板的应力计算公式。最后根据定义得到混凝土翼缘板的有宽度公式。(2)将宽幅叠合梁划分为三个体系进行简化分析。第一体系为边箱梁和混凝土板组成的主梁;第二体系为横梁和混凝土板组成的叠合梁;第三体系为支承在横梁上混凝土桥面板。然后对于第二体系的边界条件进行了简化分析,得到第二体系在荷载作用下的内力计算公式。提出了第二体系简化力学模型中的支点抗弯刚度的简化计算方法。最后按照弯矩零点将第二体系解肢为等效简支梁和等效悬臂梁进行分析。(3)采用能量变分法分析了第二体系的挠度简化计算问题。首先选择三次抛物线作为翼缘板合理的纵向翘曲位移模式,选取剪力滞翘曲位移和挠度两个广义位移计算出结构的总势能,然后按照最小势能原理得出控制微分方程和自然边界条件,接着根据结构的边界条件和荷载条件求出待定系数得到挠度公式,最后把等效悬臂梁长进行了修正并考虑剪切变形对挠度的影响得到改进的挠度计算公式。(4)基于有限元法,采用通用有限元计算软件ANSYS,建立宽幅叠合梁的实体有限元模型。分析了均布荷载和集中荷载作用下第二体系的挠度和应力。最后将简化计算方法和有限元方法的结果进行对比,说明了第二体系应力和挠度简化计算公式的适用性和精度。
[Abstract]:The two-sided box section composite girder cable-stayed bridge is a typical long-span bridge form. Compared with the steel cable-stayed bridge, it has the advantages of high stiffness and good wind stability, and can avoid the fatigue problem caused by orthotropic steel bridge face. The middle span main beam of the composite girder cable-stayed bridge is a wide composite beam. For the calculation of wide-width composite beam, the segmental model is usually established by finite element method, and the modeling and calculation process is complicated and time-consuming. In this paper, the simplified calculation method of stress and deformation of the second system of wide-width composite beam is studied by combining theoretical derivation with finite element method. The main work of this paper is as follows: (1) the simple beam and cantilever superimposed beam are analyzed by using the three-bar analogy method. Firstly, according to the principle of equal stress, the composite beam is compared to a composite system of stiffened bar with only axial force and tie plate with only shear force. Then the differential equations are established according to the static equilibrium conditions and deformation coordination conditions between the stiffener bar and the mooring plate. Then the stress calculation formula of concrete slabs is obtained according to boundary conditions and load conditions. Finally, the width formula of concrete flange slabs is obtained according to the definition. (2) the broad composite beams are divided into three systems for simplified analysis. The first system is composed of side box girder and concrete slab, the second system is a composite beam composed of crossbeam and concrete slab, and the third system is concrete deck slab supported on crossbeam. Then the boundary conditions of the second system are simplified and the formulas for calculating the internal force of the second system under load are obtained. A simplified method for calculating the flexural stiffness of fulcrum in the simplified mechanical model of the second system is presented. Finally, according to the moment zero point, the second system is analyzed as an equivalent simply supported beam and an equivalent cantilever beam. (3) the simplified deflection calculation of the second system is analyzed by using the energy variational method. First, the cubic parabola is chosen as the reasonable longitudinal warping displacement model of the flange plate, and the total potential energy of the structure is calculated by selecting the shear lag warping displacement and the deflection two generalized displacements. Then the governing differential equation and natural boundary conditions are obtained according to the principle of minimum potential energy, and then the deflection formula is obtained according to the boundary conditions and load conditions of the structure. Finally, the equivalent cantilever beam length is modified and the deflection calculation formula is improved considering the effect of shear deformation on deflection. (4) based on the finite element method, the general finite element software ANSYS, is used to calculate the deflection. The solid finite element model of a wide composite beam is established. The deflection and stress of the second system under uniform and concentrated loads are analyzed. Finally, the results of simplified calculation method and finite element method are compared to illustrate the applicability and accuracy of the simplified formula of stress and deflection of the second system.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：U448.27

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