Refined engineering beam theory based on the asymptotic expansion approach

A systematic derivation of a refined engineering theory governing the response of elastic beams is presented. The method employed to accomplish this is that of asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the three-dimensional linear elasticity theory. The present beam theory contains more information than the classical Timoshenko theory. A new shear coefficient is defined and compared with existing ones.