# Design of Plate and Shell Structures

By
President Global Engineering & Technology
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ISBN-10:
0791801993
No. of Pages:
490
Publisher:
ASME Press
Publication date:
2003
In Chapter 8 the basic equations of equilibrium for the membrane forces in shells of revolution due to axisymmetric loads were developed. Referring to Fig. 8-4, itwas shown that the two governing equations of equilibrium are given by Eqs. (8-9) and (8-11) as
$ddϕ(rNϕ)−r1Nθcosϕ+pϕrr1=0$
and
$Nϕr1+Nθr2=pr.$

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.

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