Abstract
•Hellinger-Reissner variational formulation leads to a modified theory of pretwisted bars.•The modified theory satisfies stress free boundary conditions on the side surface of pretwisted bars.•In the modified theory pre-twisted bars have bending stiffness that decreases with increasing magnitude of pretwist.•The modified theory leads to substantially lower buckling loads.•According to the modified theory, buckling load monotonically decreases with pretwist increasing past a threshold value that depends on the bar’s cross section and on the boundary conditions.
Some seventy years ago the so-called “helical fiber model” was proposed to address existing discrepancies between experimental observations and theoretical predictions for pretwisted bars. The discrepancies concerned effects the pretwist had on bending and torsional behavior of such bars, but the same model was later used to show that the previously used theory is also likely to provide unconservative (thus unsafe) estimates of their buckling loads. In spite of the theoretical and practical significance of that finding the “helical fiber model” was deemed too approximate, intuitive and, ultimately, it seems to have been abandoned. As far as buckling is concerned, all publications of the last several decades appear to be based on the original theory that was earlier shown to possibly significantly overestimate the buckling load for pretwisted bars. Thus, in this work the problem of pretwisted bars’ buckling is revisited. As most formulations of the problem, the proposed approach is approximate but, as much as possible, it is justified using established principles of mechanics. In particular, two-field Hellinger-Reissner mixed method is used to define axial and bending stiffness of pretwisted bars, with special attention paid to the definition of the stress field. Although the developments presented in this work follow a different path, the main features of the final model are similar to those of the “helical fiber model” introduced much earlier. However, the proposed formulation affords some additional flexibility in the way it may be used. Numerical examples are presented to illustrate effects of the discussed developments.