Improved beam finite element for the stability analysis of slender transversely cracked beam-columns

This paper presents a new geometrical stiffness matrix for a transversely cracked beam-column with linear distribution of axial compressive force. This matrix can be utilized in a beam finite element model of the structure for analyzing ultimate buckling load, according to the Euler’s elastic flexural buckling theory. Derivation of the matrix is based on a simplified beam computational model of cracked beams, which is ideal for the purposes of inverse identification problems as it incorporates only the major essential parameters. cal examples covering several structures under different boundary conditions are briefly presented in order to demonstrate the potential of the presented matrix. The results obtained using the presented matrix are further compared with values from large 2D finite element models, where a complete detailed description of the crack was achieved using the discrete approach. It is evident that any radical difference in computational effort is not reflected by significant differences in the results between the models. wly presented matrix and the previously presented stiffness matrix for analysis of transverse displacements, present an efficient tool not only for buckling analysis of cracked beam structures but also for a better description of the structure regarding the inverse identification of cracks.