Buckling Loads of Variable Stiffness Columns Loaded by Top Load and Linearly and Parabolically Distributed Loading

This work presents approximate, numerical and exact series solutions for the buckling of variable cross-section columns. The loading on the columns includes tip load, distributed load along the column, and several combinations of these. Solutions are presented for nine combinations of boundary conditions at the two ends of the column. The analysis includes constant cross-section columns with constant distributed load and linearly varying distributed loads. Variable cross-section cases include columns with linear variations of the stiffness, bi-linear variations variation of the stiffness, parabolic variations and bi-parabolic variations variation of the stiffness for columns with rectangular cross-section. The results are compared by the three methods. Many new benchmark results are given for all these cases.