Consider the general case of a prismatic beam subjected to bending-moment components My an...

Consider the general case of a prismatic beam subjected to bending-moment components My and Mz , as shown, when the x, y, z axes pass through the centriod of the cross section. If the material is linear elastic, the normal strss in the beam is a linear function of position such that σ = a + by + cz. Using the equilibriumconditions determine the constants a, b, c, and show that the normal stress can be determined from the equation  where the moments and products of inertia are defined in Appendix A.