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该文由简到繁,分析了等截面到变截面,同时考虑剪切变形和弯曲变形的Timoshenko悬臂柱的弯矩放大系数。通过求解等截面悬臂柱集中力下的基本微分方程,得到弯矩放大系数的表达式。并在此基础上,研究了悬臂柱的轴力、截面的弯曲刚度和剪切刚度均沿高度线性变化的情况。通过研究获得了弯矩放大系数及其沿高度的变化规律,并拟合成与等截面柱具有相似形式的表达式。与ANSYS有限元结果的对比表明,模拟Timoshenko悬臂柱弯矩放大系数的拟合公式均具有良好的精度。
The article from simple to complex, analysis of the cross-section to the variable cross-section, taking into account the shear deformation and bending deformation of Timoshenko cantilever column moment amplification factor. By solving the basic differential equation under the concentrated force of cantilever column with equal cross section, the expression of moment amplification factor is obtained. On this basis, the axial force of the cantilever column, the bending stiffness of the section and the shear stiffness both linearly change along the height. Through the research, the variation law of moment amplification factor and its height along the height is obtained, and the expression with the similar form of the equivalent cross section column is fitted. The comparison with the ANSYS finite element results shows that the fitting formulas of Timoshenko cantilever column moment magnification coefficients have good accuracy.