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

Example 5.1.
Find the stress and the coefficient of safety
for a cylindrical anode whose dimensions are shown in Fig. 5.22
if the following is given: material is Khl8N9T steel; E = 1.45.10'
daN/mm2; a = (21.2-22.2)10-6 I/C. The left end of the anode is
rigidly attached.
is
distributed linearly.
The temperature along the length of the anode
1. Law of temperature variation along the anode is
At = B0 + B 1 X.
From the condition when x = 0 At = 430'C; when x = 1 At = 58000
we obtain B 0 = 430; B 1 = 4.3.
2. Let us evaluate the length of a shell:
.• - 3 1 rh= 3 J 50.0,-5=1 .1..t,
i.e., the shell is long; Z = 35.
3. We find the reaction Q and MO. If the shell did not have
an attachment, its deformation would be equal to the deformation
of a free shell, i.e., 6 = rcAt; at the attachment point
6= raAt 0 = 50'21.2*10- 6 "130 = 0.455 mm.
Since the shell is
attached, we deform its end by quantity
60= -0.455 and find what force QO and moment M 0 should be applied
for this. We solve the system of equations (5.19) with boundary
conditions:
! ~~~x = O; zt, (o) =- , '(o) =
V (0) (3Mo +QJ) =- to, W'(o)=---L (31MIO 4-Qo)=O
w -2.sD
2:"-OD
hence
Qo
M 0 • 2,.N = 2.0.9-:572.••N6,3.0,455 = 10,02 daN mm/nmm;
-'1-31)-,, -=- 1.0, 2573.166,3-0.455 =.-5, 14 daN/inn.
539