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

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The quaotity Scx consists of three terms. The first term is
conditioned by dis'lacement u. The left end of ,the element dx
PI
d X
(Fig. 5.51a) obtains displacement u, and, the right end - u + -x.
dx
Displacement w is considered, for the present, equal to zero. The
length increment rf the element will be (Ou/Ox)dx and •the corresponding
elongation per unit length Wu/ax.
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The second term is conditioned by displabbment w (Fig..5.51b).
If before deformation the length was dx, after deformation it will
be dx + (wdx/R 1 ). The length increment is wdx/R 1 and the correspondingi
elongation will be w/RI.
Finally, the third term is
conditioned by tlhe turn of the element
dx in the plane of the arc of the meridian (Fig. 5.51,c) in the
absence of displacemernt u. Segment AB' is larger than segnient AB
by she quantity (,dx/cos e) - dx. Corresponding elongation is
(1 - cos 0)/cos 0 - 02/2. Since angle 0 = Ow/ox, elongati6n is
I /0t'•.2
it
This quantity is a quadratic functioh of bend. With snall bends
can be disregarded.'
St •C'#I a+ d--
Fig. 5.52. Finding t1he ' Rzt;0
circular deformation of A"
an element.
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Summing the obtained expressions, we find
OU W_.. 0 27 .
OX-
,± 2Z -(ax (5-77)
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