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EXAMPLE 6
Copyright 2011 Pearson Education South Asia Pte Ltd
The two solid steel shafts are coupled together using the
meshed gears. Determine the angle of twist of endA
of shaftAB when the torque 45 Nm is applied. Take G to be 80
GPa.ShaftAB is free to rotate within bearings E and F, whereasshaft
DC is fixed at D. Each shaft has a diameter of 20 mm.
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EXAMPLE 6 (cont)
Copyright 2011 Pearson Education South Asia Pte Ltd
From free body diagram,
Angle of twist at C is
Since the gears at the end
of the shaft are in mesh,
Solutions
( ) ( ) Nm5.22075.0300
N30015.0/45
==
==
xDT
F
( )( )( )( ) ( )[ ]
rad0269.01080001.02
5.15.2294
+=+
==
JG
TLDCC
( ) ( )( ) rad0134.0075.00269.015.0 =B
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EXAMPLE 6 (cont)
Copyright 2011 Pearson Education South Asia Pte Ltd
Since the angle of twist of endA
with respect to endB
of shaftAB
caused by the torque 45 Nm,
The rotation of endA is therefore
Solutions
( )( )
( )( ) ( )[ ]rad0716.0
1080010.02
24594/
+=+
==
JG
LTABAB
BA
(Ans)rad0850.00716.00134.0/ +=+=+= BABA
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EXAMPLE 6 (cont)
Copyright 2011 Pearson Education South Asia Pte Ltd
Since the angle of twist of endA
with respect to endB
of shaftAB
caused by the torque 45 Nm,
The rotation of endA is therefore
Solutions
( )( )
( )( ) ( )[ ]rad0716.0
1080010.02
24594/
+=+
==
JG
LTABAB
BA
(Ans)rad0850.00716.00134.0/ +=+=+= BABA
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
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Further examples (shear stress and angle of
twist)
Copyright 2011 Pearson Education South Asia Pte Ltd
