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

In the cross section of pipes and radiator elements a certain
temperature gradient is established which leads to the appearance of
thermal stresses.
The following is
an approach to solving this problem.
We shall fix the element rigidly in the axial direction. Then
elastic and thermal strains will equal each other, i.e., AL =A.
Let us find the stresses in the element in this position.
The application of bonds leads to a disruption of the boundary
conditions of a free system. We restore the boundary conditions by
applying to the system a force equal to the reaction arising in the
attachment, but opposite in direction. Let us find the stresses
from this force. They will only be elastic.
Y 3'
Fig. 4.12.
Symmetrical temperature gradient.
It is completely obviously that the sum of the stresses of the
first and second calcolations gives us the real thermal stresses
in the element.
Examples of gradients can be very different. Let us examine
the first case when the temperature gradient is symmetric (Fig. 4.12)
relative to the axis.
In the presence of such a temperature gradient throughout the
cross section in a free, unattached elemen't, thermal stresses arise.
We shall evaluate these stresses.
1450