Toward a New Engineering Theory of Bending: Fundamentals

The classical engineering theory of bending due to Bernoulli and Euler serves as a cornerstone for structural analysis and design. Limitations of this theory, however, become apparent in flexural wave propagation studies; it predicts infinite phase velocity as the wavelength becomes shorter. This theoretical deficiency is corrected by Timoshenko theory which accounts for transverse shear deformation. A thorough study of exact elasticity solutions reveals that there are two additional effects that are the same order as transverse shear in bending behavior. A new theory accounting for them is presented, along with several applications. The new equations are no more complicated than those of Timoshenko-ty pe theory, yet they yield solutions which are exact or indistinguishable from exact in the examples studied.