Design and Stress Analysis of Extraterrestrial ... - The Black Vault

x or r (distance al- g the generatrices of the shell from the
summit of thE -one to the examined section).
Figure 5.27 shows the positive internal loads applied to an
element cut out of a conical shell. Let us find the membrane stresses
a, and a and strains of the shell.
If fae assume, for exariple, that the internal pressure on the
shell is constant and acts on the entire internal surface of an
uncut snell (Fig. 5.28), the axial force in an arbitrary section
is determined by radius r:
-N., = p;Tr2 sinl2 0, •.n .(5.38)
where 0 is
the angle cf the generatrix of the shell with the x-ax).:
perimeter:
Axial force N x causes normal stresses constant along the
nrh sin 20
where h is
the thickness of the shell and generally variable.
Particularly, when Nx is determined from formula (5.38),
pr t •r-• tg 0."
Let us find circular stresses a., We shall examine the eqLilibrium
of the shell element (Fig. 5.29) separated into spherAcal co
conical section.
Projecting the external and internal forces onto t!e normal
to the surface of the shell, we obtain plidpdr -OahdrdcI,
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