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By S. S. Gill

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Damp out away from the edge as cp increases, and we put The boundary conditions are rp = 0, BASIC PRINCIPLES FIG. 6 , , , . , etc. e. the value of A and y for Ma and H are applied separately and the totals are found by superposition. 2. 10] are often used in the stress analysis of pressure vessel problems. A segment is called shallow if the ratio of its height h (see Fig. 8) to base diameter is less than about y. However, the results are often applicable to shells which are not shallow if the loads cause stresses which are restricted to shallow zones.

1) 48 THE STRESS ANALYSIS OF PRESSURE VESSELS FIG. 16 BASIC PRINCIPLES FIG. 17 To these stresses we add the membrane stresses and the final results are shown in Fig. 16. One final point about the junction of two shells of different geometry is most easily explained by considering the junction of a cylinder and part of a sphere as shown in Fig. 17a. This would clearly be an extremely bad design for a pressure vessel, but it illustrates an important point which arises in the analysis of branches in spherical vessels.

14] Morley gives an alternative set of equations. 4]. In Chapter 5 the Donnell equations are used and the corresponding expressions for the stress resultants in terms of w, v, w, are given. 4. 15] may be used. 30) where BASIC PRINCIPLES 37 and Corresponding expressions for w, v and all the stress resultants are given by Hoff. Graphs of al9 (}l9 a2, f}2 are given as functions of r/t for values of n from 1 to 10. There is, however, one important point about the stress resultants at the boundary x = constant which should be noted : Fig.

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