中文摘要：

为了得到平面内弹性支撑阶梯柱刚度与稳定性问题的精确解，对箱形阶梯柱平面内受力模型进行了合理等效。基于纵横弯曲理论，建立了弹性支撑条件下变截面阶梯柱挠曲微分平衡方程，结合边界条件，得到了任意阶变截面阶梯柱端部挠度及结构失稳特征方程的精确递推表达式，从而给出工程中起重机常用节数箱形伸缩臂平面内失稳特征方程的显式表达。将所得的计算结果与ANSYS软件细分单元后的计算结果进行比较分析，验证了推导公式的正确性，从而为工程设计提供了简单、快捷、精确的变截面阶梯柱变形与屈曲临界力确定方法。

英文摘要：

In order to get the precise solution for the stiffness and stability problems of the stepped column that is elastically restrained in a plane, a reasonable equivalence of the in-plane force model for the box stepped column was given. Based on the vertical and horizontal bending theory, this paper establishes the deflection differential equations of the variable cross-section stepped columns elastically restrained. Combining the proper boundary conditions, the precise recurrence expression of the flexibility and structural buckling characteristic equations of the arbitrary sectioned stepped column on the top are represented, and as a result the explicit expression of the commonly used box telescopic boom in practice was given. The stability analysis results obtained in this paper were compared with ANSYS. The comparison shows that the results obtained through ANSYS and the buckling characteristic equations are consistent with each other, which also verifies the correctness of this method. This method offers a simple, convenient and precise way to determine the deflection and buckling critical force of the variable cross-section stepped column.