INCIPIENT DEFORMATION MECHANISMS OF A SEMICIRCULAR CANTILEVER BEAM SUBJECTED TO AN OUT-OF-PLANE STEP-LOADING

The incipient dynamic deformation mechanisms for a rigid-plastic semi- circular cantilever beam subjected to an out-of-plane step-loading app lied at its tip depend on the non-dimensional force f and a structural parameter eta, which is the ratio of the fully plastic torque and the Fully plastic bending moment of the cross-section of the beam. When e ta > 1, mechanisms with a single plastic hinge provide complete soluti ons for the incipient dynamic response. For semi-circular beams for wh ich eta lies in the range 0.316 < eta < 1 (solid circular and square c ross-sections, and thin-walled circular tubular sections all fall into this range), as the magnitude of the applied load f is increased, the incipient deformation mechanism changes from a single-hinge one to a double-hinge one and finally to a triple-hinge one. The last of these contains an interior combined torsion-bending (T-M) hinge, an interior pure-torsion hinge and a hinge at the root. While the triple-hinge pr ovides a complete solution, the single-hinge mechanism gives a good ap proximate solution to the problem, provided the load f is sufficiently large. The case when eta < 0.316 while f is very large remains to be fully analysed although some incipient deformation mechanisms for this case are also studied herein.