Mechanical Engineering Principles

TWISTING OF SHAFTS 125

of twist of this shaft, due to this torque,

over a length of 1 m, given that the rigid-

ity modulus,G=40 GPa.

[76.8 mm, 1.49°]

4. A shaft to the blades of a helicopter trans-
   mits 1000 hp at 200 rev/min. Neglecting
   transmission losses, determine the mini-
   mum external and internal diameters of
   the hollow circular section aluminium
   alloy shaft, when the maximum permis-
   sible shear stress in the shaft is limited
   to 30 MPa. It may be assumed that the
   external diameter of this shaft is twice its
   internal diameter. What will be the result-
   ing angle of twist of this shaft over a
   length of 2 m, given that the modulus of
   rigidity,G= 26 .9 GPa.?
   [186 mm, 93 mm, 1.374°]


5. A solid circular section shaft of diameter
   dis subjected to a torque of 1000 N m. If
   the maximum permissible shear stress in
   this shaft is limited to 30 MPa, determine
   the minimum value ofd. [55.4 mm]


6. If the shaft in Problem 5 were to be
   replaced by a hollow shaft of external
   diameterd 2 and internal diameter 0.5d 2 ,
   determine the minimum value ford 2 ,the
   design condition being the same for both
   shafts. What percentage saving in weight
   will result by replacing the solid shaft by
   the hollow one.
   [56.6 mm, 28.3 mm, 21.7%]

Exercise 51 Short answer questions on
the twisting of shafts

1. State three practical examples where the
   torsion of shafts appears


2. State the relationship between shear stress
   τand torqueTfor a shaft.


3. State the relationship between torqueT
   and angle of twistθfor a shaft.


4. State whether a solid shaft or a hollow
   shaft is structurally more efficient.

Exercise 52 Multi-choice questions on the

twisting of shafts (Answers on

page 284)

1. The maximum shear stress for a solid
   shaft occurs:

(a) at the outer surface

(b) at the centre

(c) in between the outer surface and the

centre

2. For a given shaft, if the values of torque
   T, lengthLand radiusrare kept con-
   stant, but rigidityGis increased, the value
   of shear stressτ:

(a) increases

(b) stays the same

(c) decreases

3. If for a certain shaft, its length is doubled,
   the angle of twist:

(a) doubles

(b) halves

(c) remains the same

4. If a solid shaft is replaced by a hollow
   shaft of the same external diameter, its
   angle of twist:

(a) decreases

(b) stays the same

(c) increases

5. If a shaft is fixed at its two ends and
   subjected to an intermediate torqueTat
   mid-length, the maximum resulting torque
   is equal to:

(a)T (b)

T

2

(c) zero

6. If a hollow shaft is subjected to a torque
   T, the shear stress on the inside surface is:

(a) a minimum

(b) a maximum

(c) zero