Static Analysis of Euler-Bernoulli Beam with Arbitrary Number of Oblique Cracks: a Semi-Analytical Method

Due to the complexity of modeling, few studies have focused on the effects of oblique cracks on Euler-Bernoulli beams, particularly when the beam contains an arbitrary number of unilateral oblique cracks subjected to arbitrary transverse loads. This paper presents a semi-analytical solution for the static analysis of Euler-Bernoulli beams with an arbitrary number of oblique cracks, derived using Dirac delta functions within a generalized expression of beam flexibility. The semi-analytical solution only requires the application of boundary conditions for calculation and has been validated against finite element analysis. The effects of crack number, relative depths, and inclination angles of cracks on the static response of the beam are further explored. The results demonstrate that the proposed method can efficiently and accurately predict the static behavior of obliquely cracked beams, providing a novel and practical tool for engineering applications.