Enhanced transverse displacements analysis of transversely cracked beams with a linear variation of width due to axial tensile forces

Abstract

This paper considers the analysis of slender single-sided transversely cracked beams with a linear variation of width where transverse displacements can occur exclusively due to axial tensile forces. The simplified model where the crack is represented through an internal hinge endowed with a rotational spring that takes into account the cracked cross section's residual stiffness has already established itself as a decent alternative to the detailed 2D or 3D finite element, offering a good ratio between the accuracy of its results against the computational efforts required. The first stage of the presented research proved that the solutions of the bending governing differential equations with directly included axial tensile force are not required. However, the need for enhancement of the model's governing parameters clearly emerged. Thus, the definitions of the moment lever arm and rotational spring stiffness were studied and fittingly updated. In the last stage, the modelling of the considered phenomenon by a newly derived one-dimensional beam finite element with closed-forms of the element's stiffness matrix and load vector was executed. At the end of the study, the performance and the quality of the newly obtained solutions were verified through several comparative case studies that complement the derivations. K E Y W O R D Saxial tensile forces, beam finite element, linear variation of width, transverse cracks, transverse displacements