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

W/
dr
(2.48)
"The sign is negative because with an increase in bend the slope
angle decreases.
A plate element removed from the central axis 0 - r a distance
z is in a two-dimensional stressed state. The strains of this
element (Fig. 2.118) are
and the stresses
Or
1L'2
9 E, -+ (2.49)~) 2.,
These stresses determine the supporting capacity of the plate.
Let us find er and e . We shall examine the strain of the
plate element.
Figure 2.118 shows a plate element dr before and after strain.
Thce normal which occupied position AB before plate deflection turns
angle 0 and occupies position A'B' according to the hypothesis of
the invariability of the normal. The normal A 3 .B 1 turns angle
e + dO. Segment CC 1 , located distance z from the middle surface in
a radial direction, achieves elongation
C1C' CC, - +(10-) z-d.
The dimension of element CC1 before strain is dr. Thus, relative
elongation of the plate In a radial direction is
163
Ai" -63