DERIVATION OF IN-PLANE STRESS STATE SOLUTION ON ORTHOTROPIC ELASTIC BEAMS OF RECTANGULAR SECTION UNDER UNIFORMLY DISTRIBUTED LOADS FROM CLASSIC ONES

The purpose of this paper is to describe the derivative process of the theoretical solutions of the equations of orthotropic elastic rectangular beams with uniformly distributed loads. On the process of inducing, it indicates the exact physical meaning in practical expressions, and in addition reveals the cause of the confusion of shear deformation coefficients in Timoshenko's beam theory. In order to comprehend the deformation and in-plane stress state of the beam, the beam theory has been extended, which incorporates Young's modulus Ey , Shear modulus Gxy and Poisson's ratio vxy in turn. Then, we summarize the results as the non-dimensional expressions, indicating the closed-form solution of the equations under the given conditions. Also, some examples are shown under different boundary conditions.