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

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For greater accuracy in determining Oa2 the values or a r2
should also be substituted instead of arl in all terms df equation
(3.92). However, while only slightly affecting the result, this
somewhat increases the computational work and Is expedient only in
exceptional cases when Cr 2 differs considerably from arl'
Total stresses are determined from the cited equations. IJf
we must calculate the stresses only from forces of inertia (the disk
is cold or uniformly heated,, then all terms containing t and E
disappear. In determining thermal stresses we should assume w = 0.
Stresses in
disks of constant thickness:
Disks of constant thickness are ubed in some designs ih spite i
of the loss in weight as compared with disks of conical and hyperbolic
shapes with identical safety factors.
The differential stress equations for disks of constant thickness
can be solved completely for the given disk parameters (dimensions,
material, temperature radial distribution, and boundary conditi.ns).
It is simplest to analyze the effect of individual factors on stress
using an example of such disks.
Figures 3.56 and 3.57 present graphs showing the distribution of
radial and circular stresses along the radius of a disk ,of constant
thickness: a) rotating, uniformly heated without a loop load (Fig.
3.56); b) nonrotating, but nonunifQrmly heated (Fig. 3.57).,
j -
An analysis of the curves (see Fig. 3.56) leads tl the following
conclusions:
- circular btresses uq ave always greater than radial stresses
a r;
in a disk having an opening of "zero" radius (puncture),
stresses a9 double while stresses ar reduce to zero. In this case,
a 3K is twice as long as it is for a disk without an opening.
Hence the conclusion concerning the more rational shape , of a disk
without an opening.
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