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

Thus, the bend obtained from equation (5.14) is
the shell as the result of its
thermal loading.
the total bend of
The procedure for determining w y and wp is shown in Fig. 5.111.
Let us examine the stress and strain of the shell as a result
of a given temperature gradient At.
If the temperature gradient is a constant value, i.e., At const,
then from equation (5.14) it is apparent that wIV = 0. Then
w = w 0 + W = w ; w 0 = 0. Furthermore,
Ehý Eh ast .
r 2 D rD
hence
=wq-=raA; w' -w" =w'-W V= O;
W =-raat+W 0;=O;
W = W -- w=raAt.
Thus, uniform heating of a free shell does not cause thermal
stresses in it; shell deformation is equal to unconstricted thermal
deformation.
If
the temperature gradient varies according to linear Iaw,
i.e., Ar B 0 Blx, x it is apparent from equation (5.14) that
w 1 Y=O; W•--w+Wq='w,,; U'-=-0;
W Wq---!raAt--ra (B. + BIx);
•dz.-=ra . 1 ; W"= 7A"' =w•IV=~O;
w = - wy w= raAt =ra (Bo + 8 1 x).
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