sm7 12

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PROBLEM (7.12) An aluminum, alloy 6061-T6, beam of hollow circular cross section (Fig.
P7.11) has an allowable bending strength all
σ
. Determine:
(a) The largest bending moment M about the z axis that may be applied based on a safety
factor ns with respect to yielding of the aluminum.
(b) The corresponding radius of curvature
ρ
of the beam.
Given: D = 2 in., d = 1.5 in., ns = 1.9
SOLUTION
(from Table B.4)
9
38 10 10
yksi E psi
σ ==×
44
()
64
I
Dd
π
=−
44 3
(2 1.5 ) 248.51(10 ) .
64 in 4
π
−
=− =
(a) 38
1. 20
1.9
y
all s
cin ks
ni
σ
σ ====
33
(1)
; 20(10 ) 248.51(10 )
all Mc M
I
σ
−
==
Solving,
4.97 .
M
kip in=⋅
(b) 3
63
14.97(10)
0.002
(10 10 )(248.51 10 )
M
EI
ρ
−
== =
××
or
500 41.67in ft
ρ
==
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