## Abstract

Tresca limit pressures for long cylindrical shells and complete spherical shells subjected to arbitrary pressure, and several approximations to the exact limit pressures for limited pressure ranges, are derived. The results are compared with those in Section III-Subsection NB and in Section VIII-Division 2 of the ASME B&PV Code. It is found that in Section VIII-Division 2 the formulas agree with the derived limit pressures and their approximations, but that in Section III-Subsection NB the formula for spherical shells is different from the derived approximation to the limit pressure. The length effect on the limit pressure is investigated for cylindrical shells with simply supported ends. A geometric parameter that expresses the length effect is determined. A formula and its limit of validity are derived for an assessment of the length effect on the limit pressures.

1.
ASME Boiler & Pressure Vessel Code, 1998, American Society of Mechanical Engineers, New York, NY.
2.
Turner
,
L. B.
,
1910
, “
The Stresses in a Thick Hollow Cylinder Subjected to Internal Pressure
,”
Trans. Cambridge Philos. Soc.
,
21
,
14
, pp.
377
396
.
3.
Budynas, R. G., 1977, Advanced Strength and Applied Analysis, McGraw-Hill Publishing Co., New York, NY.
4.
Reismann, H., and Pawlik, P. S., 1980, Elasticity—Theory and Applications, John Wiley and Sons, New York, NY.
5.
Hodge, P. G., 1963, Limit Analysis of Rotationally Symmetric Shells, Prentice-Hall, Inc., Englewood Cliffs, NJ.
6.
ABAQUS, 1999, Hibbit, Karlsson, and Sorensen, Inc., Pawtucket, RI, by Educational License to Lehigh University.