Vibration and buckling analysis of a cracked stepped column using finite element method

Abstract

Components with varying cross-sections are most common in buildings and bridges as well as in machine parts. The stability of such structural members subjected to compressive forces is a topic of considerable scientific and practical interest. Tapered and stepped columns are very much useful in structural engineering because of their reduced weight compared to uniform columns for the same axial load carrying capacity or buckling load. In the current study free vibration and buckling analysis of a cracked two stepped cantilever column is analyzed by finite element method for various compressive loads. Simple beam element with two degrees of freedom is considered for the analysis. Stiffness matrix of the intact beam element is found as per standard procedures. Stiffness matrix for cracked beam element is found from the total flexibility matrix of the cracked beam element by inverse method in line with crack mechanics and published papers by researchers. Eigen value problem is solved for free vibration analysis of the stepped column under different compressive load. Variation of free vibration frequencies for different crack depths and crack locations is studied for successive increase in compressive load. Buckling load of the column is estimated from the vibration analysis.