Abstract
Two recent theories on torsional oscillation of general doubly-symmetric non-circular cross-section beams incorporate a second order effect, that of in-plane shear deformation involving a change in cross-sectional shape, and are found to give excellent agreement with exact results for an elliptical section rod. For “technical” torsional oscillation theories of I-section beams this in-plane shear has previously been considered within the flanges only; in the present work the greater effect of shear distortion of the web is included, having previously been considered only in static analysis. The theory predicts three modes of wave propagation, one of which is essentially torsional in character; a second mode may be identified with predominatly flange bending according to the second branch of Timoshenko beam theory whilst a new mode involves individual flange torsion with asymmetric web deformation, and has the lowest phase velocity except at the longest wavelength. An alternative symmetric web deformation is also considered.
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