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

i.e.,
the plate bends along a spherical surface whose curvature
is defined by the quantity 1/rx = r = 1/r. The stress
ax cay =a= 6f/h 2
4Z
- A tc
b ~tb *At x ~ 3 8 a
) (a)
Fig. 4.17.
Determining the temperature gradient.
Let us examine the deformation-of a plate during thermal loading.
If
we read the temperature from the middle surface of the plate,
assuming that on one side it is heated and on the other cooled,
it is natural to concluae that the thermal deformations of expansion
and contraction will be proportional to the distance from the middle
surface.
Consequently, we arrive at the same deformation law as in
the pure bend of a plate by bending moments.
If heat is supplied to and drawn from-a plate which is uniformly
heated to temper, .ure to, as was shown in Fig. 4.17a, it can be
established that in
the steady thermal mode the temperature variation
along the thickness will be linerr, while the temperature of the
plate's neutral surface will remain constant, i.e.,
be equal to
Such a temperature variation in
a section causes analogous
thermal deformation. These daformations in an unattached plate will
be proportional to the distance from the middle surface; thus, the
law of variation for thermal deformation is
completely identical
to the law-of deformation with a pure bend by bending moments.
Figure 4.17a shows the temperatures of a plate element during such
heating.
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