Abstract
This paper studies the mathematical model that describes the deformation of a nonprismatic beam by its own weight. The nonprismatic beam is considered to be with circular or rectangular cross-section. We fix the density and hold an angle $\alpha$ at one end but free at the other end. The shape of the beam depends on the angle $\alpha$, the density and the length to that of flexural rigidity. We analyze the bifurcation phenomena for the vertical case, $\alpha = \pi$. Several numerical results are presented.
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