defined in Table 5, and was obtained by applying a 0.2=percent strain off- 
set as illustrated by the dotted lines in Figure 1. The abscissa is a 
ratio of the TMB empirical theoretical elastic buckling pressure P, to the 
same equilibrium yield pressure. The points display over a wide range of 
elastic stability, defined as the ratio of P, to a the proximity of the 
test results to an idealized plot of a perfectly plastic (plateau) stress- 
Strain curve indicated by the solid line in Figure 6. 
The value of the comparison is to indicate that for accurately 
machined spherical shells with similar stress-strain curves, the results 
define an empirical curve (dotted line in Figure 6) which departs from the 
elastic portion of the ideal curve at some arbitrary elastic stability 
ratio and rejoins the plateau of the ideal curve at some higher arbitrary 
elastic stability ratio. 
The purpose of obtaining such an empirical plot is to establish 
for any thin spherical shell design a practical design curve from which a 
single design formula can be selected. By knowing the design values of 
Shell radius, material compressive stress as determined from test coupons, 
and required collapse pressure, an approximate elastic stability ratio can 
be calculated. If the ratio were to fall on the elastic portion of the 
ideal curve, the shell would be designed using the TMB empirical elastic 
equation; if on the plateau of the ideal curve, the shell would be designed 
using the simple equilibrium yield pressure formula Wee and if the ratio 
were to fall on the empirical portion of the curve, then the shell could be 
designed by method of trial and error, using the reduced value of Pryp/P,, 
found on the ordinate of the empirical curve. 
By using any other selected empirical pressure formula, an 
empirical curve similar to that in Figure 6 could be derived to gain the 
same practical end. A Similar curve is currently being developed as a 
part of the Model Basin hemispherical head program for high-strength steel 
models.“ The models of Reference 7, however, are of a larger scale 
(approximately 3 to 5 1/2 ft in diameter) and are not machined but are 
fabricated by welding, resulting in a similar, yet individual curve to the 
one presented in this report. Each of the fabricated models of Reference 7 
is constructed of pressed segmented sections, resulting in bending due to 
misalignment and sizeable residual stresses due to welding, undoubtedly 
