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

The angle of shift is the variation in the angle BAC and is
equal to the sum of the obtained angle:
V1-i 2
• Ou Oa p
x + y- R 2 1g0
To this quantity there must be added one more term, caused by
bend w. Let us examine Fig. 5.53b. Due to the fact that the
segments dx = AB and dy + AC are rotated, respective]y, by angles
aw/ax and Ow/ay, the angle between them does riot remain a right angle.
It changes exactly by the quantity of the unknown term.
ifx
Fig. 5.54. Finding the components
of deformation.
d
YL-i
As we know, the cosine of the angle between the two straight
lines cos q = 112 + m 1 m 2 + n 1 n 2 , where Zl1, z2, ml, m2, nl, n 2 are the
direction cosines of the lines forming angle p.
In our case
?=900 -- VS;
I-=1; m=O; ni==OCw/Od;
2--O;
m 2 -=1; n-- Ow/Oy.
aw ,aw
Consequently, cos (900 -yg) Yg-ox O "
Thus, in the middle surface the angle of shift is
Ov , O( v9)
"V x72T R 2 1 tgO
OY
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