中文摘要：

根据竖向悬臂杆的边界条件、弯曲及剪切屈曲侧移曲线，选取了含有三角函数的表达式来近似表示竖向悬臂杆的弯曲分量和剪切分量，然后利用能量法推导了在轴向均布荷载作用下弯剪型悬臂杆的屈曲临界荷载简化计算公式．通过与有限元计算结果对比，验证了简化算法的可靠性．最后，将本文提出的竖向均布荷载作用下临界荷载计算公式与Timoshenko提出的顶点集中荷载下临界荷载经典理论公式进行对比，发现本文提出的临界荷载计算公式多了一个无量纲的系数，通过参数分析，研究了该系数对公式计算精度的影响．

英文摘要：

According to the boundary conditions, bending and shear buckling displacement curves of vertical cantilever bar, the trigonometric function expressions are selected to approximately express the bending component and shear component of the verti- cal cantilever rod. Then the energy method is used to deduce the buckling critical load calculation formula of the shear bending cantilever bar under vertical uniform loads, and the reliability of the simplified algorithm is verified by compare with the results of finite element calculation. Finally, the result comparison between the recommended formulas under vertical uniformly distributed load in this paper and the Timoshenko equation under top-concentrated load are conducted, and one dimensionless coefficient are recognized. Then the accuracy of the formula is verified through the parameter analysis.