Vibration and buckling analysis of cracked beam-columns

Abstract

An important task for engineers is to determine the effect of the damage like transverse cracks on the stability characteristic of structures. The presence of cracks causes changes in the physical properties of a structure and its dynamic response characteristics. The monitoring of the changes in the response parameters of a structure has been widely used for the assessment of structural integrity, performance and safety. The buckling load is one of the important parameter for stability of a structural member. The present work is aimed at finding the buckling load of a cracked beam-column with a single edge crack.Finite element method is adopted for the dynamic analysis of the beam -column. Additional flexibility coefficients of the cracked beam element are computed using 6-point Gauss quadrature and theories of fracture mechanics.Flexibility coefficients of an intact element are added to the additional flexibility matrix to get the total flexibility matrix of the element. Over all flexibility matrix of the cracked element is then obtained from the total flexibility matrix. Stiffness matrix of the cracked element is derived from the overall flexibility matrix of the element for the analysis of an Euler beam-column of mild steel with cantilever end conditions. The first four natural frequencies and the corresponding mode shapes of vibration are obtained by dynamic analysis solving the eigen value problem using a FORTRAN code. The computed results are compared with previous studies and the present formulation is established. Buckling load is then obtained solving another eigen value problem of stiffness matrix and stress matrix of the beam-column. Variation of buckling load with respect to relative crack depth, position of the cracked section and different length of span are studied. It is found that the presence crack weakens the member by decreasing the frequencies of vibration as well as buckling load. How ever this effect is more pronounced when the crack is near to the fixed end than free end. For small cracks with relatively lesser RCD value the decrease of buckling strength is less but for bigger cracks with higher RCD value the buckling strength decreases rapidly.