POST BUCKLING BEHAVIOR OF A CIRCULAR ROD CONSTRAINED WITHIN A CIRCULAR CYLINDER
SORENSON, KENNETH GORDON
Doctor of Philosophy
It has been previously demonstrated that an axially loaded weightless circular rod buckles helically when constrained within a circular cylinder. The effects of pinned and fixed end conditions on the behavior of such a helically buckled rod are investigated. Both end conditions locate the rod end on the cylinder axis. The pinned end condition considers the rod end free to rotate about all three axes, allows axial translation, and prevents radial movement. The fixed end condition allows axial rotation and translation, requires the rod end to be tangent to the cylinder axis, and prevents radial movement. Both end conditions are found to perturb the helix in an exponentially decaying manner for a distance of less than one pitch length. Far from the end, the rod behaves as an undisturbed constant-pitch helix. The distance from the rod end to the point of initial contact with the cylinder wall is calculated. Closed form analytical solutions are obtained for the deflected shapes and internal reactions of the end sections. The maximum internal bending moment for the pinned-end case is 19.5% higher in the end section than in the helical section. The maximum bending moment for the fixed-end case also occurs in the end section and is 1% higher than in the helical section. The solution procedure applies to rods of either finite or infinite length. Experimental results confirm the analytical findings.