The Development of Euler Hyperbola in Heavy Bars

Euler [1] discovered the critical buckling force of the bars under an axial load. Euler, however ignored bar's own weight in his calculations. He drew the line diagram of critical strength vs bars slenderness ratio, the so called Euler-Hyperbole. The goal of this paper is to extend Euler-Hyperbole to heavy bars. Furthermore, factors which have effects on critical buckling forces will be analysed. This study may lead to economical gain, since materials are fully utiliesed.