1Buckling Mode Jump at Very Close Load Values in Unattached Flat-End Columns: Theory and Experiment

Abstract. Buckling of compressed flat-end columns loaded by unattached flat platens is shown, theoretically and experimentally, to occur first at the critical load and associated mode shape of a built-in column, followed extremely closely by a second critical load and different mode shape characterized by column end-tilt. The theoretical critical load for secondary or end tilt buckling is shown to be only 0.13 % greater than the critical load for primary buckling, in which the ends are in full contact with the compression platens. The experimental value is consistent with this theoretical one. Interestingly, under displacement control, the first buckling instability is characterized by a smoothly-increasing applied load, whereas the closely-following second instability causes an abrupt and large load drop (and hence exhibits incremental negative stiffness). The end tilt buckling gives rise to large hysteresis that can be useful in structural damping but that is non-conservative and potentially catastrophic in the context of design of structural support columns. 1