________________________________________________________________________
PROBLEM (*11.55) An aluminum alloy 2014-T6 hollow box column of square cross section and
length L is fixed at its base and free at its top as shown in Fig. P11.55. The column supports a
compressive load P that acts with an eccentricity of e. Determine:
(a) The horizontal deflection of the top of the column.
(b) The maximum stress in the column.
Given: a = 5 in., b = 4.2 in., e = 2.3 in., L = 6 ft, P = 40 kips, E = 10.6 x 106 psi,
σy = 60 ksi (from Table B.4)
*SOLUTION
We have
222 2
5 4.2 7.36 .Aa b in=−=− = 2
44 4 4
11
( ) (5 4.2 ) 26.153 .
12 12 4
I
ab in=−==
26.153 1.885 .
7.36
I
ri
n
A
== =
2.5 . 2 2(6 12) 144 .
2e
a
ci nLL in== = = × =
Hence
22
(2.3)(2.5) 1.618
(1.885)
ec
r==
, 40 5.435
7.86
Pksi
A==
22 6
22
(10.6 10 )(26.153) 131.9
(144)
cr e
EI
Pk
L
ππ
×
== = ips
40 0.303
131.9
cr
P
P==
(a) Apply Eq. (11.18):
max [sec( ) 1]
2cr
P
ve P
π
=−
(2.3)[sec( 0.303 1)] 2.32 .
2in
π
=− =
(b) Use Eq.(11.20a)
max 2
[1 sec( )]
2cr
Pec P
Ar P
π
σ
=+
(5.435)[1 (1.618)sec( 0.303)]
2
π
=+ 18.99 ksi
=
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