计及液压缸作用的起重机伸缩臂欧拉临界力的精确解析解

起重机伸缩臂由多节可轴向相对滑动的变截面箱形臂组成，吊臂自身只承受弯矩，轴向压力则由吊臂内部的支撑液压缸承受，因此，其力学模型不能等同于变截面的阶梯柱。本文给出了考虑液压缸支撑作用的起重机多节伸缩臂在起升平面外的欧拉临界力的精确解析解，并与忽略液压缸支撑作用的计算模型所得欧拉临界力进行比较。分析结果表明，考虑液压缸支撑作用时起重机多节伸缩臂的欧拉临界力大于不考虑液压缸支撑作用的变截面阶梯柱力学模型的欧拉临界力。因此，我国起重机设计规范中所用变截面阶梯柱力学模型计算伸缩臂之稳定性是偏安全的。

Precise analytic solution of crane telescopic boom Euler critical force

Crane telescopic boom consists of multiple variable section box type booms that can axially move. The boom itself can only bear bend torque while axial compression force is carried by support cylinder inside the boom. Therefore, its mechanics model is different from that considering variable section stepped cylinder. This paper covers precise analytic solution of crane telescopic boom Euler critical force considering support cylinder influence. Analysis shows that the value considering the support cylinder is bigger than that obtained neglecting the support cylinder, indicating that calculating crane telescopic boom stability based on variable section stepped cylinder model specified in China＇s Crane Design Specification is relatively safer.