Buckling of elastic columns with second-mode imperfections

The pin-ended, slender, Euler strut has been used as the archetypal buckling problem for many years (Euler in Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentes, Bousquet, Lausanne, 1744). Even though it is not conventionally imperfection-sensitive (i.e., in which the magnitude of the buckling load is compromised by the presence of imperfections), initial geometric imperfections are still important, and 3D-printing now allows a versatility in geometric prescription and accuracy previously unavailable. This paper focuses attention on Euler struts, primarily from an experimental viewpoint, in which a second mode (full sine wave) initial shape, with varying magnitude, is used to produce specimens, test them, and compare with the elementary theory.