sm11 53

________________________________________________________________________
PROBLEM (11.53) An aluminum hollow box column of length L is fixed at its base and
free at its top as shown in Fig. P11.53. If an eccentric load P acts at the middle of side AB (that
is, e = 50 mm) of the free end, calculate the largest stress σmax in the column.
Given: L = 2 m, E = 70 GPa, P = 150 kN, e = 50 mm
SOLUTION
24
e
LLm
=
=
200 100 160 60A
=
×−×
=× 32
10.4 10 mm
33
1(200 100 160 60 )
12
I=×−×
=× 64
13.79 10 mm
36.4rI A mm==
mm
ec50
=
=
Thus,
22
50 50 1.89 54.95
(36.4) 2e
L
ec
rr
×
== =
Use Eq.(13.20b) with :
e
LL=
33
max 39
3
×
53.1
150 10 150 10
1 1.89sec 54.95
10.4 10 70 10 (10.4 10 )
σ
−−
⎡⎤
⎛⎞
××
⎢⎥
=+
⎜⎟
⎜⎟
××
⎢⎥
⎝⎠
⎣⎦
M
Pa
=
A
P
10 mm 0
L
200 mm
D
C 20 mm
P
B
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