Torsion of Pretwisted Beams Due to Axial Loading

Abstract

The equations for static torsional deformation of a pretwisted beam under axial loading are obtained from the principle of virtual work. Theory appropriate for a curvilinear coordinate system is used, and warp is included in the analysis from the outset. The present formulation yields the expected result that a pretwisted beam of noncircular cross section will untwist under tensile loading. A slender-beam approximation of the present theory is offered, and the resulting torsion-extension coupling terms are similar but not identical to those in common use in analyses of rotating blades. Numerical results indicate that the effect is not negligible when the ratio of shear modulus to extension modulus is small.