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

Full deflection of shell wp = w0 + w . Stresses in the shell
are determined by the elastic component of the bend
S= w -P- ra t=Wo+ W%-- rcAt.
Since w. = raAt, the function w 0 will be the elastic bend. The
usual form of bend and stress diagram is shown in Fig. 5.24d.
Example 5.3. Find the circular stresses of a cylindrical
anode by the integral method. The conditions for the problem are
the same as in example 5.1. Calculation is presented in Table 5.11.
Let us find the bend of the shell w 0 from formula (5.33). The
initial function w 0 is a straight line with a bend at the attachment
spot %0 = raAt 0 = 0.455 mm. This quantity is found in the "factor"
column.
We obtain the bend w 0 1 in the first approximation in line 10
and in the second approximation in line 19. This Loend determines
stresses a in the shell (line 21):
E
j-W
r
Full bend of the shell we find in line 22: w = w 0 + w = w 0 FrAt.
Bends w are shown in
Fig. 5.22 by the dashes.
Stress in a shell in the presence of
temperature gradient through the thickness
Let us assume that temperature gradient At through the thickness
of the shell changes according to linear law (Fig. 5.25) and is
identical on its entire length. At points located at a consicerable
distance from the ends of the shell there is no bend. The shell
element is in the same stressed state as a plate with nonuniform
heating.
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