The equilibrium and elastic stability of a thin twisted strip
1—Many problems of elasticity have been solved, correct to the first order of displacements, but comparatively few when second order terms are considered. The first order, or “St. Venant”, solution of the problem of the torsion of a prism with rectangular cross-section is well known. In a particular case, namely, a flat rectangular bar or thin strip, it can be observed by experiment that it is possible to produce a twist, without overstrain, which is much larger than that allowed for by the ordinary first order theory. It is to be expected, therefore, that the usual linear relation between the couple and the twist will no longer be true in this case. In the first part of this paper, 3, 4, a formula for the couple is found which includes a second order term depending on the cube of the twist. It is found that this second order term arises solely from the extension or contraction of linear elements, which, in the unstrained state, were parallel to the length of the strip. This formula was tested in some experiments which are described in 17. A greement between theory and experiment was fairly good, but, at a well-defined value of the twist, the strip became unstable and the formula no longer applied. This is clearly shown in figs. 3, 4. A theoretical investigation was then made into the Elastic Stability of a thin twisted strip and this work is contained in 5-14.