The effect of longitudinal cracks and interface adhesion on buckling of columns: analytical solution

This paper focuses on development of a new mathematical model and its analytical solution for the buckling analysis of elastic columns with preexisted longitudinal cracks and finite adhesion between the cracked sections. Consequently, the analytical solution for the buckling loads is derived for the first time. The critical buckling loads are calculated for two different types of connections between the cracked sections, namely for slipping only and simultaneous slipping and uplifting between them. The parametric study is performed to analyze the effect of the crack length on the critical buckling loads. It is shown that the critical buckling load can be greatly affected by the crack length and type of the connection between the cracked sections. Finally, the presented results obtained can be used as a benchmark solution.