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

The wall stress of this sphere is determined from formula (2.32):
pr
The wall stress of the cylinder .= pr/h = c. c" The spheridal
end plate of a cylindrical shell with the radius of the sphere equal
to the radius of the cylinder is
not a reasonable design with respect
to either weight or dimensions. As seen from Fig. 2.26a, if the
thicknesses of the cylinder material and the end plate are identical,
stresses a 1 in them will be different; a = pr/2h = 0.511c
eiL4HJ = 0.87 pr/h [4An = cylinder]; the structure will be
too heavy. A decrease in the thickness of the end plate by a factor
of two (Fig. 2.26b) does not lead to an equally strong construction.
There is a new disadvantage - the weld seam is located at the point
where the cylinder changes into a sphere. A change in the thickness
of the material in the design is also technologically undesirable.
The dimensions are as large as before.
The two designs of end plates, presented in Figs. 2.27a and b,
are also not reasonable since in them bending moments load the
tiansitional parts of the shells.
If we assume that the radius of a spherical end plate is r 2R,
the additional maximum pulling stress from bending ox = ° max a',
point A, which is found on the internal surface of the element
(Fig. 2.27), exceeds oa in the two indicated cases (a and b) b:, a
factor of 30 and by a factor of 6, respectively, i.e.,
0 x max = 30(p c and ax max =
6
c' c3
shape.
Considerably more reasonable is
an end plate of elliptical
Stress analysis of an elliptical end plate
The elliptical shape is taken for an end plate of reactor
housings and of various volumes. We know that for an ellipse with
semiaxes a and b the principal radii of curvature (Fig. 2.28a) will
be expressed by formulas:
135