Optimum Design
165
(d)
Constraint 2 Bending frequency
29.449
_< 1
Torsional buckling [3.21]
0.6E
~CR-- (2~RI)1"5
Now ~ = ~r and ~ is to be greater than 10,000 psi
0.6E
3 < 10,000 psi
0.6
3 1 E
-- 2~’~ V~ 10,000 (R/t) k~ -
(3.51)
(e)
Constraint 3 Torsional buckling
36.7423 × 10 -6 E
--<1
Bending buckling [3.21]
0.4E
CrcR- 2R
t
0.2E
~rCB -- R
t
The left side is 10,000 psi
0.2E
-- < 10,000 psi
R/t
(3.52)
Constraint 4 Bending bucking
0.2E
<1
lO,O00R/t -
(3.53)
There remains three regional constraints, noting R, t, L any of which
are zero will make Eq. (3.49) zero weight.