平行组拼双拱肋系平面外弹塑性稳定性及计算方法

发布时间：2018-10-12 15:52

【摘要】：平行组拼双拱是一种在桥梁工程领域以及工民建领域都有广泛应用的组拼拱形式,由于横向支撑的刚度往往小于主拱肋刚度,使得平面外稳定性成为平衡其经济性与安全性的一个重要指标。目前对平行双拱平面外弹塑性稳定承载力计算方法的研究非常少见,为其平面外稳定性设计带来了诸多不便。本文以均匀受压无铰圆弧平行组拼双拱为对象,系统研究了其平面外弹塑性稳定性能,提出了其平面外弹塑性稳定承载力实用计算公式,具体研究内容如下:(1)提出了圆管截面均匀受压无铰圆弧拱的平面外弹塑性稳定承载力计算方法。考虑结构几何初始缺陷及材料非线性,采用大挠度弹塑性有限元数值分析的方法,以190根圆弧截面无铰圆弧拱为研究对象,分析了其在均匀受压情况下的平面外弹塑性稳定性能,揭示了设计参数对面外稳定性影响规律。并在拱的正则化长细比坐标下,获得了各种设计参数拱的统一稳定曲线。借助该稳定曲线,得到了圆管截面均匀受压无铰圆弧拱的平面外弹塑性稳定承载力的实用计算公式。(2)推导了拱顶s/2范围内均布横向支撑的平行组拼双拱的平面外弹性失稳临界荷载解析解公式。基于Ritz法,考虑了结构平面外失稳时主拱肋的整体和局部变形能、横撑在径向和切向平面内的弯曲变形能以及外力势能,构造了平行双拱平面外失稳的能量方程,并利用势能驻值原理得到了拱顶s/2范围内均布横向支撑的圆弧平行双拱的平面外弹性失稳临界荷载解析解公式,为后续研究平行双拱的平面外弹塑性稳定承载力计算公式奠定了基础。(3)提出了圆管截面均匀受压无铰圆弧平行组拼双拱的平面外弹塑性稳定承载力计算方法。以不同设计参数的918根圆管截面无铰平行双拱为研究对象,考虑结构几何初始缺陷及材料非线性,采用大挠度弹塑性有限元数值分析方法,分析了几何初始缺陷、矢跨比、长细比、横撑长度、横撑根数以及主拱截面尺寸等设计参数对平行组拼双拱的影响规律,得到了其平面外弹塑性稳定系数。在此基础上,在平行组拼双拱的正则化长细比坐标下,借助于中国钢结构规范GB50017-2003中轴压柱子稳定系数曲线的Perry-Robertson公式,利用Matlab程序对平行组拼双拱的平面外弹塑性稳定系数数据点进行拟合,得到了适用于平行组拼双拱的稳定建议曲线。基于该稳定建议曲线,提出了圆管截面均匀受压无铰圆弧平行双拱的平面外弹塑性稳定承载力的实用计算公式。
[Abstract]:Parallel assembly double arch is a widely used form in the field of bridge engineering and civil engineering, because the stiffness of transverse support is often less than that of main arch rib. So that the off-plane stability becomes an important index to balance its economy and security. At present, the research on the calculation method of the elastoplastic stability of parallel double arch is very rare, which brings a lot of inconvenience to the design of the out-of-plane stability. In this paper, the elastoplastic stability of parallel arches with unhinged circular arcs under uniform compression is studied systematically, and a practical formula for calculating the load-carrying capacity of out-of-plane elastic-plastic stability is put forward. The main contents of this paper are as follows: (1) A method for calculating the elastic-plastic stability capacity of circular arches under uniform compression of pipe sections is presented. Considering the initial defects of structure geometry and material nonlinearity, a large deflection elastic-plastic finite element numerical analysis method was used to study 190 arches with no hinged arc section. The elastoplastic stability in the case of uniform compression is analyzed, and the influence of design parameters on the external stability is revealed. The uniform stability curves of the arch with various design parameters are obtained under the regularized aspect ratio coordinates of the arch. With this stable curve, A practical formula for calculating the external elastoplastic stability capacity of an unhinged circular arched arch with uniform compression of pipe section is obtained. (2) an analytical formula for the out-of-plane elastic instability critical load of a parallel group of two arches with uniform transverse bracing in the range of S / 2 is derived. Based on the Ritz method, the whole and local deformation energy of the main arch rib, the bending deformation energy and the external force potential energy of the transverse brace in radial and tangential plane are considered, and the energy equation of the external instability of the parallel double arch plane is constructed. The analytical formula of out-of-plane elastic instability critical load of circular arc parallel double arch with uniform transverse bracing in the range of S / 2 is obtained by using the standing principle of potential energy. It lays a foundation for the further study on the calculation formula of the lateral elastoplastic stability bearing capacity of parallel double arch. (3) A method for calculating the elastoplastic stability capacity of parallel arch with uniform compression of pipe section under uniform compression without hinged arc is proposed. Taking 918 unhinged parallel double arches with different design parameters as the research object, considering the initial structural defects and material nonlinearity, the finite element method of large deflection elastic-plastic finite element analysis is used to analyze the geometric initial defects and the rise-span ratio. The influence of the design parameters such as slenderness ratio, transverse brace length, root number of transverse brace and cross-section size of main arch on the parallel combination of double arches is obtained, and the elastoplastic stability coefficient is obtained. On this basis, with the aid of the Perry-Robertson formula of the stability coefficient curve of the axial compression column of the Chinese steel structure code GB50017-2003, under the regularized aspect ratio coordinate of the parallel group of double arches, the stability coefficient curve of the column is obtained by means of the Chinese steel structure code. The Matlab program is used to fit the extraplanar elastic-plastic stability coefficient data points of parallel double arches, and the proposed stability curve for parallel double arches is obtained. Based on the proposed stability curve, a practical formula for calculating the external elastoplastic stability bearing capacity of the uniform compression unhinged circular arc parallel double arch of a circular pipe is presented.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U442

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