Buckling of slender prismatic columns with multiple edge cracks using energy approach

In this paper, the elastic stability of slender columns weakened by multiple edge cracks subjected to concentrated loads applied at the ends is presented. The analysis is carried out by using the minimum potential energy technique. The cracked section is modeled by a massless rotational spring which causes discontinuity in the rotations due to bending moments. In the present work, columns with various end conditions such as pinned ends, fixed ends, fixed-pinned ends and fixed-free ends are studied. The analysis depends on the assumed deflection function, which satisfies exactly the end conditions. The buckling loads for each case of end conditions for a column with arbitrary number of cracks along the column length are given in simple and practical equations which also gave accurate results. A comparison between the results of the present analysis and that of some previous studies shows the accuracy and the simplicity of the developed method to find the critical load in such cases.