On Timoshenko's correction for shear in vibrating beams

Abstract

The note is a review of studies of the shear coefficient K occurring in Timoshenko's differential equation for flexural vibrations of beams. Expressions of K hitherto proposed for circular and rectangular cross sections are tabulated, together with new expressions hitherto overlooked and unknown, and compared with one another. It is pointed out that the expressions of K=(6+12 sigma +6 sigma 2 )/(7+12 sigma +4 sigma 2 ) for the circle and K=(5+5 sigma )/(6+5 sigma ) for the rectangle, where sigma is Poisson's ratio, which have been found in Timoshenko's (1922) paper, will be the most probable ones at the present stage of theories and experiments.