________________________________________________________________________
PROBLEM (12.9) Rework Prob. 12. 8 for the case in which the segment AB of the shaft is hollow,
the inside diameter is 30 mm, and TB = 1 kNB
⋅
m and TC = 4 kN
⋅
m.
SOLUTION
34
AB BC
T kNm T kNm=⋅ =⋅
0.4 m
A
C
B
30 m
m
60 mm
0.6 m
TC=4 kN
⋅
m
TB=1 kN
⋅
m
40 mm
Segment AB
44 84
(60 30 ) 119.22 10
32
AB
Jm
π
−
=−=×
232
98
(3 10 ) (0.6) 53.92
2 2(42 10 )(119.22 10 )
AB TL
UJ
GJ −
×
== =
××
Segment BC
484
(40) 25.12 10
32
BC
Jm
π
−
==×
32
98
(4 10 ) (0.4) 303.31
2(42 10 )(25.12 10 )
BC
UJ
−
×
==
××
=+ =
Total strain energy
UJ 53.92 303.31 357.2
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