Static bending analysis of a transversely cracked strip tapered footing on a two-parameter soil using a new beam finite element

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.