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

It is known that, in this case, the integral (5.9) expresses
the edge effect, i.e., the effect of radial distributed forces and
moments acting on the edges of the shell. Since the applied forces
droduce local bend, rapidly diminishing to zero as the distance from
the end increases, we conclude that the second term in the right side
of equation (5.10) must be zero. Therefore, C3 - C4 = 0,
w=e-PX (Cisin Px+ C 2 cos x). (5.17)
Constants C1 and C 2 are determined from the boundary cmnditicns:
when x = 0 Mx = 0 = Dwt; Qx = Q0 = Dw". If we differentiate
equation (5.17) three times, we obtain
W1 = Pe-,-x [C, (COs;,x-Sill e)-C CO i"xj
i"= 2eP[-C 1 cosIpx + c 2 Sifn Pl
" "-- 2.. 3 e- [C 1 (cos ,x + sin px) + C 2 (cos •x-- sill 3X)].
We
substitute into these equations the following boundary conditions:
cl=_ ---o ; C2=-.• P(o+ý o)
2V2D
2PSD
Finally,
W=e--P" [•m0 (COS ýx - sin ýX) + QO COS PX].
20• (5.18)
Maximum bend on the loaded end is
W(0)-
(Mo0+Qo).
2.3D (5.1,9)
The slope angle of the tangent to the elastic line rin the
loaded end of the shell is found by differentiating exprassion
(5.13):
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