numerical formulation on crack closing effect in buckling analysis of edge-cracked columns

in this paper, buckling of simply supported column with an edge crack is investigated numerically and analytically. four different scenarios of damage severities are applied to a column, open crack assumption and the effect of closing crack in stability of the column which depends on position and size of cracks, are numerically compared. crack surfaces contact is modeled with gap element using sap2000. for analytical solution, transfer matrix method, combined with fundamental solutions of the intact columns is used to obtain the capacity of slender prismatic columns. the stiffness of the cracked section is modeled by a massless rotational spring and governing equations are obtained explicitly for simply supported column from second-order determinant. as expected results show that the effect of a closing crack in presence of compressive load may lead to an increment in buckling load depending on crack depth and position. for the first time, a dimensionless formulation based on numerical results is presented in this study. proposed formula predicts increment effect of closing crack in buckling results of a notched column.