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本文通过微元体的变形和受力分析，导出了弯曲井眼中受压管柱的屈曲方程──一个合参数。的四阶非线性常微分方程。ε是一个综合考虑轴压（Ｆ０）、管柱截面抗弯刚度（ＥＪ）、井眼轴线轨迹曲车半径（Ｒ）以及共眼有效半径（ｒ）的无因次参数。本文利用线性化方法及小参数摄动法求得了屈曲方程的一次分叉点ε１及二次分叉点ε２。当ε＞ε１时，管柱处于稳定状态，对应于屈曲方程的零解；当ε２＜ε≤ε１时，管柱处于正弦屈曲状态，对应于屈曲方程的周期解；当ε≤ε２时，管柱处于螺旋屈曲状态，对应于屈曲方程的螺线解。本文给出的弯曲井眼中受压管柱的两个临界屈曲载荷（与两个分叉声、对应），发生螺旋屈曲时的螺距等理论结果与他人发表的实验结果吻合较好。
In this paper, the buckling equation of the bent tubular column in bent hole is deduced by the deformation and force analysis of the micro-body. The Fourth Order Nonlinear Ordinary Differential Equations. ε is a dimensionless parameter that takes into account the axial compression (F0), the section stiffness (EJ) of the column, the radius (R) of the trajectory of the borehole trajectory and the effective radius of the common eye (r). In this paper, the first-order bifurcation point ε1 and the second-order bifurcation point ε2 of the buckling equation are obtained by using the linearization method and the small parameter perturbation method. When ε> ε1, the column is in steady state, corresponding to the zero solution of buckling equation. When ε2 <ε≤ε1, the string is in sinusoidal buckling state, which corresponds to the periodic solution of buckling equation. When ε≤ε2, The column is in a helical buckling state, corresponding to the helical solution of the buckling equation. The theoretical results of two critical buckling loads (corresponding to two bifurcations) and helical pitch when helical buckling are given in this paper are in good agreement with those published by others.