Buckling of Slender Prismatic Columns with a Single Edge Crack under Concentric Vertical Loads


Abstract: The investigation of the stability behavior of slender columns with cracks is an important problem and finds applications in structural, mechanical and aerospace engineering. This study investigates the buckling of slender prismatic columns with a single nonpropagating edge crack subjected to concentrated vertical loads. The transfer matrix method and fundamental solutions of intact columns (columns without any cracks) are combined for determining the buckling loads of cracked columns. The cracked section is modeled by a massless rotational spring whose flexibility depends on the local flexibility induced by the crack. Eigenvalue equations are obtained explicitly for columns with various end conditions, from second order determinants. Numerical examples show that the effects of a crack on the buckling load of a column depend on the depth and the location of the crack. As expected, buckling load decreases conspicuously as the crack depth increases. For a constant crack depth, a crack located in the section of the maximum bending moment causes the largest decrease in the buckling load. On the other hand, if the crack is located just in the inflexion point at the corresponding intact column, it has no effect on the buckling load. The study showed that the transfer matrix method is a simple and efficient method with which to analyze cracked columns.

Keywords: Buckling, Stability, Slender prismatic columns, Crack

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