顶部弹性嵌固、底部嵌固桩的稳定性分析

Axial Buckling Analysis for Pile Elastically Fixed at Top and Fixed at Bottom

用能量法对顶部自由、底部嵌固桩在顶部集中荷载和桩侧摩阻力作用下的竖向稳定性问题进行了研究．对于部分埋置于Ｗｉｎｋｌｅｒ 地基中的桩，首先建立了桩的受力模型，根据边界条件给出了桩的挠曲函数，导出了系统总势能的表达式；然后根据最小势能原理推导了求解失稳问题的计算公式，用数值方法求得了桩的临界长细比（λｃｒ）的数值解，通过对数值解的分析，最后得到了简便易用的λｃｒ近似计算公式，并给出了算例． 计算表明：地基的抗力对λｃｒ有重要影响，当地基的抗力较大时，桩侧摩阻力对λｃｒ影响甚小．

Study on axial stability of top elastically fixed and bottom fixed pile acted by lateral friction and vertical concentrated load at the top was carried out by using the energy method. The mechanical model for the pile partly embedded in Winkler subsoil was set up, the deflection function of the pile was given according to its boundary conditions, and the expression of the total potential energy of the pile soil system was developed at first. A series of formulas for solving stability problem were developed according to the principle of the least potential energy, and critical slenderness ratio of the pile ( λ cr ) was solved by numerical method. According to the results of data process, a simple approximate formula for calculating λ cr was obtained. A calculating example was taken at last, and the following conclusions were obtained: the resistance of the subsoil has important influence on λ cr , and the lateral friction on the pile has less influence on λ cr when the resistance of the subsoil is large.