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

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. . . S_..<br />

I i.<br />

stresses. Maximum i generalized stresses in the 1ýquat<strong>of</strong>ia2, c~ross<br />

! I<br />

section are<br />

q•OI5L I 2<br />

Substituting a -6 *5a4 ) we obtain at point A stress ai = .2<br />

<strong>The</strong> stress a~ is equal to~ a 0 where oq;on'ithe en'd plate 'is equal to<br />

zero.<br />

I<br />

I<br />

Thus, in the central part <strong>of</strong> ti~e end plate the gener'alized<br />

stresses are almost equivalent to stresses in a cylindrical shelL<br />

Consequently, an elliptical end plate can be' made <strong>of</strong> Ailmost equal<br />

strength with a cylindrical shell by varying the dimensio'hs a <strong>and</strong><br />

b <strong>of</strong> the ellipse.<br />

f bending<br />

<strong>The</strong> disadvantage <strong>of</strong> an elliptioal end plate is thevariablb<br />

value <strong>of</strong> the radius <strong>of</strong> curAture with respect to angle ai. lometimes<br />

the end plate is formed similarly to an elliptical une but with the<br />

radii <strong>of</strong> two circumferences (Fig. '2.29).<br />

<strong>The</strong> v.dximum stress at point A as a resulth<strong>of</strong> the appearance <strong>of</strong><br />

iroment M~ will be [~<br />

0 431 max (r/6.60prý c, <strong>and</strong>-'if<br />

p = 0.251, as is frequen.tly' the case, then 0 na~ 1i. 25ar i.e.,<br />

very nearly the maximum stress <strong>of</strong> a cylindrical shell.<br />

139

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