A shaft having length equal to 10 m and diameter equal to (57) mm is simply supported at both ends. The shaft carries four masses (157) kg, (207) kg, (257) kg and (307) kg. These masses are located at a distance of 1.5 m, 2.5 m, 5.5 m and 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m2 and mass density for the shaft material is 7500 kg/m3. Determine critical speed of the shaft in revolutions per minute for the following two cases: Effect of the mass of the shaft is neglected.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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A shaft having length equal to 10 m and diameter equal to (57) mm is simply supported at both ends. The shaft carries four masses (157) kg, (207) kg, (257) kg and (307) kg. These masses are located at a distance of 1.5 m, 2.5 m, 5.5 m and 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m2 and mass density for the shaft material is 7500 kg/m3. Determine critical speed of the shaft in revolutions per minute for the following two cases:

  1. Effect of the mass of the shaft is neglected.
  2. Effect of the mass of the shaft is considered.

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