Asymptotic Derivation of Shear Beam Theory from Timoshenko Theory

摘要

A systematic reduction of Timoshenko beam theory to shear beam theory is presented and compared to a parallel reduction to Euler–Bernoulli theory. The agreement between Timoshenko and shear theories is seen to improve as the ratio of Young's modulus to shear modulus increases, as the mode number increases, and as the beam becomes fatter, which are the opposite trends for agreement between Timoshenko and Euler–Bernoulli theories.