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

I
These formulas enable us to plot the elliptical surface. Given
the angle a of the vector's radius (this angle agrees with angle 0),
we find the radii of curvature R and R 2 , after which-we plot the
ellipse. For example,
CL =0, ., 21b; (L= 2,R '=b ; R2 =a.
direction.
We find stresses a6 acting on the element in a meridional
Let us project the forces acting on the shell element
onto the x-axis. We obtain (Fig. 2.28a) Ff sin a27r = p~ar 2 , where
r = R2 sin a, or
No pr PR 2
sin 2/z•.( a•
h 2 sinc&'i 2h,2k
2.37}•
,(a)
(b)
Fig. 2.28. Determining stresses in an elliptical end
plate.
Substituting (2.37) into the basic equation (2.30),
the str,:-ss a@ acting in
a peripheral direction:
we find
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