Curved Beam Problems

Abstract

If we cut the circular annulus of Figure 8.1 along two radial lines, θ = α, β, we generate a curved beam. The analysis of such beams follows that of Chapter 8, except for a few important differences — notably that (i) the ends of the beam constitute two new boundaries on which boundary conditions (usually weak boundary conditions) are to be applied and (ii) it is no longer necessary to enforce continuity of displacements (see §9.3.1), since a suitable principal value of θ can be defined which is both continuous and single-valued.

We first consider the case in which the curved surfaces of the beam are traction-free and only the ends are loaded. As in §5.2.1, we only need to impose boundary conditions on one end — the Airy stress function formulation will ensure that the tractions on the other end have the correct force resultants to guarantee global equilibrium.