Column buckling coupled with fracture

The analysis of buckling of elastic columns is one of the first problem in structural engineering that was historically solved. Critical loads of perfect columns with various end restrains have been derived . Nevertheless, the perfect column is an idealized model. In reality, inevitable imperfections should be considered. Solutions for later disturbing load, crookedness or load eccentricity have been proposed. Another frequent imperfection to be taken into account is the weakness at an interior location due to a partial crack. In this paper the influence of this type of imperfection on the critical load is analyzed. The weakness can be modeled as an internal hinge strengthened by a rotational spring. The spring constant can be determined on the basis of the energy released due to the crack and Catigliano’s theorem. Exact critical loads for various end conditions, crack locations and cross sections are obtained.