Optimum Design
173
Stress in a sphere
PR
-- < 15,000 psi
2t -
Regional constraint
Variables
R>0
t>0
P>0
In the cost let
U1 = 2nR2t
U2 = 3nR
t
Volume
1 > 3(57,750 in
3)
-
4nR 3
3(57,750)
Stress
PR
<1
2t(15,000)
(3.94)
(3.95)
(3.96)
(3.97)
(3.98)
PR
UI’ - 2(15,000t)
(2nR2,~6’(3nR) 62
go= \ 61 ,] \t62,]
(3.99)
(3.100)
[-/
PR
\~7
g2 is
)
(3.101)