Critical Stress Calculation for Aluminum Column (Euler's Formula)

________________________________________________________________________
PROBLEM (11.30) A rectangular aluminum (E = 70 GPa) tube of uniform thickness t =
20 mm (Fig. P11.30) serves as a 6-m-long column fixed at both ends. Calculate the critical
stress in the column.
SOLUTION
33
min 1(200 100 160 60 )
12
I=×−× 64
13.79 10 mm=×
33
200 100 160 60 10.4 10Am=×−×= × m
min min 36.4 0.5 3
e
rIA mmLL== ==m
3,000 36.4 82.4
e
Lr==
Hence,
229
22
(70 10 ) 101.8
( ) (82.4)
cr e
E
M
Pa
Lr
ππ
σ
×
== =
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