Separated variable approach to the bending stress analysis of the beam under general transverse distributed load

By considering the effect of the constraint at the fixed end, the stress distribution of a straight beam loaded by general transverse distributed loads is analyzed by using the separated variable method. The normal stress and shearing stress distributions along the beam height and axial directions are obtained. The result is compared with the solution of mechanics of materials. It shows that, on the cross section in the vicinity of the fixed end, the distributions of shearing stress obtained from two approaches are much different, but the maximum values are nearly identical, whereas, except for the maximum value, the distributions of normal stresses have little difference. And the solutions of two approaches are accordance with each other in the far field off the fixed end.