Buckling of heavy bars (Q1275770)

Summary: The calculation of the critical buckling load for a short bar under compression usually neglects the bar weight. This method is no longer acceptable for long heavy bars, where the bar weight must be taken into consideration. In this paper, the critical buckling forces are derived from ten end conditions for heavy bars which are surrounded by air and loaded by compression. We give an analytical solution to the differential equation of the problem, which requires a numerical evaluation. Limited computer capacity permits calculations of critical buckling forces only up to a certain length, thus we treat this analytical solution asymptotically for very long heavy bars. With the help of this asymptotic solution, we are able to calculate the critical buckling forces for long heavy bars.