A hollow steel drive shaft working in a high speed machine is shown in the figure and has an outer diameter of 100 mm and a wall thickness of 15 mm. During a particular loading situation, the shaft is subjected to a uniformly distributed load of magnitude 1.75 kN/m and an axial tensile load of magnitude 110 kN as shown. Also, during service, the shaft rotates at a speed of 500 rev/min and transmits a power of 300 kW. The shaft steel is ductile and has a yield strength in tension of 200 MN/m', an ultimate tensile strength of 475 MN/m² and a Modulus of Rigidity of 81 GN/m. Also, the shaft was designed to have a minimum factor of safety of 2. i) Calculate the component stresses set-up in the shaft material at point X' (bottom surface of the shaft at midspan as indicated in the figure) due to the loading conditions. ii) Determine the magnitude and nature of the principal stresses, and the maximum shear stress analytically and graphically, and the angle of the planes on which the major principal stresses act at point X'. iii) By applying the appropriate yield criteria, evaluate the factor of safety for the shaft and

A hollow steel drive shaft working in a high speed machine is shown in the figure and has an outer diameter of 100 mm and a wall thickness of 15 mm. During a particular loading situation, the shaft is subjected to a uniformly distributed load of magnitude 1.75 kN/m and an axial tensile load of magnitude 110 kN as shown. Also, during service, the shaft rotates at a speed of 500 rev/min and transmits a power of 300 kW. The shaft steel is ductile and has a yield strength in tension of 200 MN/m', an ultimate tensile strength of 475 MN/m² and a Modulus of Rigidity of 81 GN/m. Also, the shaft was designed to have a minimum factor of safety of 2. i) Calculate the component stresses set-up in the shaft material at point X' (bottom surface of the shaft at midspan as indicated in the figure) due to the loading conditions. ii) Determine the magnitude and nature of the principal stresses, and the maximum shear stress analytically and graphically, and the angle of the planes on which the major principal stresses act at point X'. iii) By applying the appropriate yield criteria, evaluate the factor of safety for the shaft and

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.3.10P: Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.

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