11 Bending of Shells of Revolution Due to Axisymmetric Loads

In many applications such as at a junction of a spherical to cylindrical shell subjected to axisymmetric loads, bending moments and shear forces are developed at the junction in order to maintain equilibrium and compatibility between the two shells. The effect of these additional moments and shears, Fig. 11-1, on a shell of revolution is the subject of this chapter. The axisymmetric moments and shears at the two circumferential edges of the infinitesimal element are shown in Fig. 11-1. Circumferential bending moments, which are constant in the θ-direction for any given angle ϕ, are applied at the meridional edges of the element. The shearing forces at the meridional edges must be zero in order for the deflections, which must be symmetric in the θ-direction because the loads are axisymmetric, to be constant in the θ-direction for any given angle ϕ.