Stress Diffusion Problems

THE case now to be considered is shown diagrammatically in FIG. 12, which also gives the additional notation required. The problem is to determine how a bending moment, applied at one end to the longer‐ons only, is diffused into the whole section, being finally distributed according to the usual beam theory of bending. The differential equation to be satisfied by the displacement w is equation B(2), and if we take the origin at the centre we may take s=Rψ, h=r, x=R sin ψ and y=R cos ψ. Equation B(2) then becomes: