The large-deflection analysis of a tapered beam-column under transverse loadings and restrained axially is presented. The proposed method is based on the Differential Transform Method (DTM) but with improved efficiency. This is achieved by separately analyzing and incorporating the differential transform of the trigonometric functions $sin\theta$ and $cos\theta$ with $\theta \left(\stackrel{-}{s}\right)={\sum }_{k=0}^m{u}_k{\stackrel{-}{s}}^k$ being the solution to the problem making possible to work with series of order m = 20 without incurring into excessive computational effort and calculation time. The transformed equations convert the governing integro-differential equation of the problem into a polynomial equation with the coefficients $u_k$found by recurrence with its solution much easier to determine. The accuracy of the improved DTM depends on the order m of the series becoming the “exact” solution to the differential integral equation as m tends to infinity. The minimum value of m required in the expansion depends on the applied loads on the beam-column, its support conditions and geometry. Two classic beam-columns are analyzed herein using the proposed method: 1) a simple-supported beam-column partially restrained axially subject to a uniformly distributed transverse load; and 2) a tapered cantilever beam-column subject to a concentrated transverse load at the free end. The obtained results are compared with those reported by other researchers with excellent agreement showing the validity and simplicity of the proposed method and its corresponding equations.

提出了在横向荷载作用下轴向约束的锥形梁柱的大挠度分析。所提出的方法基于差分变换方法（DTM），但效率有所提高。这是通过分别分析并合并三角函数的微分变换来实现的$s\mathrm{一世}ñ\theta$ 和 $CØs\theta$ 与 $\theta \left(\stackrel{--}{s}\right)={\sum }_{ķ=0}^{米}{ü}_{ķ}{\stackrel{--}{s}}^{ķ}$是解决问题的方法，使得可以处理m  = 20的序列，而不会造成过多的计算工作量和计算时间。变换后的方程将问题的控制积分微分方程转换为系数为的多项式方程${ü}_{ķ}$通过重复发现其解决方案容易得多。改进的DTM的精度取决于级数m，因为m趋于无穷大，因此成为微分积分方程的“精确”解。m的最小值膨胀所需的力取决于在梁柱上施加的载荷，其支撑条件和几何形状。本文中使用提出的方法对两个经典的梁柱进行了分析：1）简单支撑的梁柱在轴向上受到部分约束而受到均匀分布的横向载荷；2）锥形悬臂梁柱在自由端受到集中的横向载荷。将获得的结果与其他研究人员报告的结果进行了比较，结果非常吻合，表明了该方法及其相应方程的有效性和简便性。