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PROBLEM (12.8) A stepped shaft ABC (G = 42 GPa) is subjected to torques as shown in Fig.
P12.8. For TB = 5 kN ⋅ m and TC = 2 kN ⋅ m, what is the strain energy of the shaft?
SOLUTION
TAB = 3 kN ⋅ m
TBC = 2 kN ⋅ m
Segment AB
J AB =
U AB
π
(60) 4 = 127.17 × 10−8 m 4
32
T 2L
(3 × 103 ) 2 (0.6)
= 50.55 J
=
=
2GJ 2(42 ×109 )(127.17 × 10−8 )
Segment BC
J BC =
U BC
π
(40) 4 = 25.12 × 10−8 m 4
32
T 2L
(2 × 103 ) 2 (0.4)
= 75.83 J
=
=
2GJ 2(42 × 109 )(25.12 × 10−8 )
Total strain energy
U = 50.55 + 75.83 = 126.4 J
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