sm11 15

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PROBLEM (11.15) Two aluminum alloy 2014-T6 bars are used as compression members,
each with an effective length of Le , have the cross sections shown in Fig. P11.15. Calculate:
(a) The wall thickness of the hollow square bar so that the bars have the same cross-sectional
area.
(b) The critical load of each bar.
Given: Le = 8 ft, E = 10.6 x 106 psi (from Table B.4)
SOLUTION
(a) Same area:
22 2
()
4oi o
dd bb
2
i
π
−=−
22 22 2 2 2
()2(21.
44
io oi
bb dd 5)
π
π
=− − =− −
or
1
1.62 . ( ) 0.19 .
2
ioi
bintbb==−=in
(b) Circular bar
44 4 4 4 ( ) (2 1.5 ) 0.537 .
64 64
oi
π
I
dd in
π
=−=−=
22 6
22
(10.6 10 )(0.537) 6.1
(8 12)
cr e
EI
Pk
L
ππ ×
== =
×ips
Square bar
44 4 4 4
11
( ) (2 1.62 ) 0.759 .
12 12
oi
I
bb in=−=−=
22 6
22
(10.6 10 )(0.759) 8.62
(8 12)
cr e
EI
Pk
ip
L
ππ ×
== =
×s
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