Question

The preliminary design of a large shaft connecting a motor to a generator calls for the use of a hollow shaft with inner and outer diameters of 100 mm and 150 mm, respectively. Knowing that the allowable shearing stress is 85 MPa, determine the maximum torque which may be transmitted a) By the hollow shaft as designed (5) b) By a solid shaft of the same weight and length (8) c) By a hollow shaft of the same weight and length, but having outer diameter 200 mm (8) d) Which shaft has maximum torque transmitting capability? WHY?

Answer 1

Given Data: Di - 100 mm => 0,50 mm Do = 150 mm = 2 = 75 mm. Tallow 85 Mpa Now, a) Hollow Shaft as designed: 0,4) 17 (754 - 50 --504) 4 6. Ja = 1 / 82 3.98x107 mim = 3.98 x 105 mA " Tmax = T62 Tx0.075 >> 857103 J 3.98 x 105 45-10 •. T= 446 km, 온 b) Solid Shaft of equal weight Alar = A) → 71 (0-0752 -0.052) = 710 = 03 = 0.056m. Trz 3 Tmax = Txo.056 85x10 = J I - (0-058) Ta 23.44 KN-m.

C) Hollow and shaft of Some weight diameter (do) is 200 mm length (given)? and Ala = ACC) 77 (0.0752 -0.052] = 1 (0:12_C5") 2 I 0.083, *J = (014-0-0834) = 8.25-10 m m. & Tmax Tca J → 85 103 Txo-1 70.125 8.25 x105 ..T 2 70.125 KM-m.

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