sm12 26

________________________________________________________________________
PROBLEM (*12.26) Figure P12.26 depicts a workpiece clamped to a milling machine table by a
bolt of diameter d tightened to a tension of T. The link AB has a rectangular cross section of width b
and depth h. Calculate:
(a) The strain energy in bolt due to axial load.
(b) The strain energy in link caused by bending.
Given: b = ½ in., h = 5/16 in., d = 1/4 in., T = 120 lb, E = 29 x 106 psi
Assumptions: Bolt and link are made of steel. The effect of the hole in bending of the link is disregarded.
*SOLUTION
(a) Axial strain energy in bolt.
22
22
bPL TL
UAE AE ==
23
26
(120) (1.1875) 610 .
2[ (0.250) (29 10 )]
4
in lb
π
−
==×
×
⋅
(b) Bending strain energy in link.
33
12 (0.5)(0.3125) 12 1.2716 10 .
34
I
bh in
−
== =×
2
02
L
b
M
dx
UEI =∫
12
22
00
1{[ (80 ) (40 ') '}
2
x
dx x dx
EI
=+
∫∫
2144
EI
=
Substituting the data,
63
2144
(29 10 )(1.2716 10 )
b
U− =××
x
A
B
x’
80 lb 40 lb
2 in.
120 lb
1 in.
=×
3
58.1 10 .in lb
−⋅
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