sm12 97

________________________________________________________________________
PROBLEM (*12.97) Collar W, illustrated in Fig. P12.97, is dropped h = 1.2 m onto the end B of
the circular bar of diameter d = 25 mm. Calculate the weight of the collar so that the largest stress in the
bar does not exceed 200 MPa.
Given: E = 200 GPa, L = 5 m.
*SOLUTION
26
(0.025) 490.6 10
4
A2 m
π
−
==×. We have st WL
AE
δ =. Thus,
2
max
max 22
[1 1 , [ 1] 1
s
ts
A
Wh
AW
σ
σ
t
h
δ
δ
=++ −=+
or
22
max max
222
11
AA hAE
WW W
σσ
−+=+
L
Solving
2
max
max
2( )
A
W
hE
L
σ
σ
=
+
62 6
96
(200 10 ) (490.6 10 )
1.2(200 10 )
2[ 200 10 ]
5
−
××
=×+× 203.6 N
=
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