sm11 29

________________________________________________________________________
PROBLEM (11.29) A fixed-ended long column of rectangular cross section 1 in.by 3 in.
is made of aluminum alloy. Determine the minimum length Lc that the column may have and the
corresponding critical load Pcr.
Given: E = 10 x 106 psi, σp = 18 ksi
SOLUTION
34
min 1(3)(1) 0.25 .
12
I
in==, 2 13 3 .Ai=× = n
3
min 0.25 3 286.68 10 .ri
−
==×n
Equation (11.10):
26
3
10 10
( ) 74.048
18 10
eCpl
LE
r
ππ
σ
×
== =
×
n
or
, 21.376 .
e
Li=42.752 .
0.5
e
CL
Li== n
Thus,
226
22
(10 10 )(0.25) 54
(21.376)
cr e
EI
Pk
L
ππ ×
== =
ips
ps
or
18(3) 54
cr p
PA ki
σ
== =
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