sm11 70

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PROBLEM (11.70) A square fixed-pinned end aluminum alloy 6061-T6 column of width
a supports a compression load P. Determine the permissible length of the bar.
Given: a = 2.2 in., P = 40 kips
SOLUTION
4
22.2 0.6351 .
12 23 23
aIa
Aa I r in
A
= = ====
3
2
40(10 ) 8.26
(2.2)
all Pksi
A
σ == =
Assume 66Lr≥ and use Eq. (11.29)
33
2
51000(10 ) 8.26(10 )
()
all Lr
σ ==
Solving
78.58 66
L
r=>
(O.K.)
Hence
78.57(0.6351) 49.9 .Li== n
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PROBLEM (11.71) A solid round aluminum strut (alloy 6061-T6) of length L and pinned
ends supports an axial load P. Calculate the minimum permissible diameter d of the member.
Given: L = 400 mm, P = 60 kN
SOLUTION
24
464
ddI
AIr
A
ππ
===
4
d
=
Assume 9.5 66
L
r
<≤ and use Eq.(11.28).
3
2
0.6 60(10 )
[140 0.87( )]
44
all dd
σπ =− =
2
2 0.0764
140 (0.87) dd −=
, 140 21.74 0.0764 0dd−=
−
or
2
1.74 (1.74) 4(140)(0.0764) 0.0304
2(140)
dm
±+
==
30.4mm
=
Since
30.4 400
7.6 52.6 66
44 7.6
dL
rmm
r
== = = = <
Assumption is O.K.
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