Experiment on the torsion buckling of a rod

In this thesis we study, both experimentally and analytically, the torsion buckling of a rod with circular cross section. In the analysis we start with the general equilibrium equations for a straight rod formulated by Love. These equilibrium equations are simplified to two equations in terms of the lateral deflections by considering the situation when the rod is only slightly different from the straight configuration. The key to this derivation is to formulate the correct form of curvatures in terms of the lateral deflections relative to a body-fixed coordinate system. The resulted critical torque is found to be identical to the classical critical torque formulated by Ziegler by ignoring the pre-buckled twisting angle. In the experiment, we design a loading mechanism which allows us to apply the compressive force and torque at the same time. Commercially available aluminum rod with diameter 4.4 mm and length 2.73 m is tested in the experiment. Both ends of the rod are clamped while one end is allowed to slide axially freely. In the experiment we apply a specified compressive force first and then increase the end torque gradually. The axial displacement and the twist angle as functions of end torque are recorded. The critical torque is recognized as the torque at which the rod undergoes a sudden jump in the axial direction. Measured critical loads are compared with the analytical predictions. In the case when the compressive force is close to the Euler buckling load, the discrepancy between the measured critical torque and the theory is in the range of 10%. On the other hand, when the rod buckles solely due to torsion, the discrepancy between experiment and theory can be as high as 20%. The possible causes of the discrepancy are discussed in detail.