Abstract The structural stability of a column with rectangular and circular cross-section under axial compression is studied based on various higher-order shear deformation beam theories. This paper has two-fold objectives. One is to introduce a transition parameter to describe the direction of axial load from Engesser’s hypothesis to Haringx’s one, then a unified method is presented to determine the critical load. The other is to introduce new cross-section warping shapes of rectangular and circular columns, then the buckling loads are exactly calculated and compared for various warping shapes. A governing equation for buckling of a column under axial compression is first derived. The buckling loads of a prismatic column with typical ends such as clamped-clamped, pinned-pinned, and clamped-free columns are determined and an explicit expression is obtained in terms of the Euler buckling load. The effects of the warping shape of the cross-section on the buckling loads are analyzed. The Haringx buckling load is greater than the Engesser buckling load that gives a conservative estimate of the critical load. A comparison of these buckling loads with Euler loads is made. The obtained results indicate that Euler buckling loads are both significantly overestimated for short columns or those with weak shear rigidity. The buckling loads are nearly not affected for very slender columns or those with high shear rigidity. The Euler loads are recovered from the present ones for columns in the case of shear locking. The buckling loads are also dependent on the warping shape of the cross-section.

中文翻译：

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翘曲形状对圆柱和矩形柱轴压屈曲的影响

摘要 基于各种高阶剪切变形梁理论，研究了矩形和圆形截面柱在轴压作用下的结构稳定性。本文有两个目标。一种是引入一个过渡参数来描述从Engesser假设到Haringx假设的轴向载荷方向，然后提出一种统一的方法来确定临界载荷。另一种是引入新的矩形和圆柱截面翘曲形状，然后准确计算和比较各种翘曲形状的屈曲载荷。首先推导出柱在轴压下屈曲的控制方程。具有典型端部的棱柱的屈曲载荷，例如夹钳、销钉、确定了无夹柱，并根据欧拉屈曲载荷获得了明确的表达式。分析了截面翘曲形状对屈曲载荷的影响。Haringx 屈曲载荷大于给出临界载荷保守估计的 Engesser 屈曲载荷。将这些屈曲载荷与欧拉载荷进行了比较。获得的结果表明，对于短柱或抗剪刚度较弱的柱，欧拉屈曲载荷均被显着高估。对于非常细长的柱子或具有高剪切刚度的柱子，屈曲载荷几乎不受影响。在剪切锁定的情况下，欧拉载荷从柱的当前载荷中恢复。屈曲载荷还取决于横截面的翘曲形状。