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Matrix method for stability and second-order analysis of Timoshenko beam-column structures with semi-rigid connections

机译：半刚性连接的Timoshenko梁柱结构的稳定性和二阶分析的矩阵方法

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摘要

The first- and second-order stiffness and load matrices of a beam-column of symmetric cross section with semi-rigid connections including the effects of end axial loads (tension or compression) and shear deformations along the member are derived in a classical manner. Both matrices can be used in the stability, first- and the second-order elastic analyses of framed structures made of Timoshenko beam-columns with rigid, semi-rigid and simple connections of symmetric cross sections. The "modified" stability approach based on Haringx's model described by Timoshenko and Gere [1] is utilized in all matrices. The model proposed which is an extension of that presented by Aristizabal-Ochoa [2] captures the models of beams and beam-columns based on the theories of Bernoulli-Euler, Timoshenko, and bending and shear. The closed-form second-order stiffness matrix and load vector derived and presented in this paper find great applications in the stability and second-order analyses of structures made of beam-columns with relatively low shear stiffness such as orthotropic composite polymers (FRP) and multilayer elasto-meric bearings commonly used in seismic isolation of buildings. The effects of torsional warping along the members are not included. Analytical studies indicate that the buckling load and the stiffness of framed structures are reduced by the shear deformations along the members. In addition, the phenomenon of buckling under axial tension forces in members with relatively low shear stiffness is captured by the proposed equations. Tension buckling must not be ignored in the stability analysis of beam-columns with shear stiffness CAS of the same order of magnitude as EI/h2. The validity of both matrices is verified against available solutions of stability analysis and nonlinear geometric elastic behavior of framed structures with semi-rigid connections using a single segment for each beam and column member without introducing additional degrees of freedom. Four examples are included that demonstrate the simplicity, effectiveness and accuracy of the proposed method and corresponding matrices.
机译：以经典方式得出具有半刚性连接的对称截面的梁柱的一阶和二阶刚度和载荷矩阵，其中包括端部轴向载荷（拉伸或压缩）和剪切变形的影响。两种矩阵均可用于由Timoshenko梁柱制成的框架的稳定性，一阶和二阶弹性分析，这些框架具有对称截面的刚性，半刚性和简单连接。在Timoshenko和Gere [1]中描述的基于Haringx模型的“改进”稳定性方法可用于所有矩阵。提出的模型是Aristizabal-Ochoa [2]提出的模型的扩展，它基于Bernoulli-Euler，Timoshenko和弯曲与剪切的理论，捕获了梁和梁柱的模型。本文得出并提出的封闭形式的二阶刚度矩阵和载荷矢量在具有较低剪切刚度的梁柱结构（如正交各向异性复合聚合物（FRP）和弹性梁）的结构的稳定性和二阶分析中具有很大的应用价值。多层弹性轴承，通常用于建筑物的隔震。不包括沿成员的扭转翘曲的影响。分析研究表明，框架构件的剪切变形会降低框架结构的屈曲载荷和刚度。另外，所提出的方程式还捕获了抗剪刚度相对较低的构件在轴向拉力作用下的屈曲现象。在抗剪刚度CAS与EI / h2相同数量级的梁柱的稳定性分析中，不能忽略拉伸屈曲。相对于可用的稳定性分析和具有半刚性连接的框架结构的非线性几何弹性行为的可用解决方案，验证了这两个矩阵的有效性，对于每个梁和柱构件，使用单个段，而没有引入额外的自由度。包括四个示例，它们演示了所提出方法和相应矩阵的简单性，有效性和准确性。

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