Anisotropic Beams by Moment-Differential Method

In solving for the stresses in anisotropic prismatic beams using the theory of elasticity, it is found that there is a definite relationship between the normal stresses and the internal moments. For beams subjected to bending only, the normal stresses can be expressed as sums of internal moments and differentials of moments multiplied with constant coefficients. For members subjected to both bending and axial compression, the solution for normal stresses neglecting secondary effects due to deflections, can be expressed as sums of moments and differentials, and axial loads and differentials of axial loads, multiplied with constant coefficients. The general solution is in the form of an infinite series with the coefficients which can be solved for particular cases. Rather than having to solve a vast number of simultaneous equations, as in previous methods, this method provides direct solutions to anisotropic beam problems.