In this paper, a new beam Euler–Bernoulli finite element for the transverse static bending analysis of cracked slender strip tapered footings on an elastic two-parameter soil is presented. Standard Hermitian cubic interpolation functions are selected to derive the closed-form expressions of complete stiffness matrix and the load vector. The efficiency of the proposed finite element is verified on an example with several width tapering variations of a simple cracked footing with the results of governing differential equation. Another novelty of this study is improved bending moment functions with included discontinuity conditions at the crack location. These functions now accurately describe the bending moments in the vicinity of the crack of the finite element.

本文提出了一种新的梁欧拉-伯努利有限元，用于弹性二参数土上开裂细长条形锥形基础的横向静力弯曲分析。选择标准厄米特三次插值函数导出完整刚度矩阵和载荷矢量的闭式表达式。所提出的有限元的效率通过简单裂纹基础的几个宽度锥度变化的示例以及控制微分方程的结果得到验证。这项研究的另一个新颖之处是改进了弯矩函数，其中包括裂纹位置的不连续条件。这些函数现在可以准确地描述有限元裂纹附近的弯矩。