________________________________________________________________________
PROBLEM (12.10) The steel shaft ABC (G = 80 GPa) of Fig. P12.8 is subjected to torques TB = 0
and TC . Calculate the strain energy of the shaft when the maximum shearing stress is 50 MPa.
SOLUTION
Segment BC
484
(40) 25.12 10
32
BC
Jm
π
−
==×
8
6
max 25.12 10
50 10 628
0.02
J
TN
c
τ
−
×
==× = m⋅
22
98
(628) (0.4) 3.925
2 2(80 10 )(25.12 10 )
BC TL
UJ
GJ −
== =
××
Segment AB
484
(60) 127.17 10
32
AB
Jm
π
−
==×
2
98
(628) (0.6) 1.163
2(80 10 )(127.17 10 )
AB
UJ
−
==
××
=+=
Total strain energy
UJ 3.925 1.163 5.088
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