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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

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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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. 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'. ii) By applying the appropriate yield criteria, evaluate the factor of safety for the shaft and comment on the value obtained. iv) Produce a neat sketch of the yield criteria failure envelopes for the shaft at point X', indicating all significant detail. v) Given that the shaft outer surface has a 'machined' finish and the shaft operates at a temperature of 85°C and a reliability of 95% is required, determine the factor of safety for the shaft according to the Soderberg theory, commenting on its value. vi) During another loading operation, the shaft is subjected to excessive bending loading conditions that cause the major principal stress to increase to 175 MN/m?. Determine the life expectancy of the shaft. vii) Calculate the total strain energy stored in the shaft during the initial loading. i)
Transcribed Image Text: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. 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'. ii) By applying the appropriate yield criteria, evaluate the factor of safety for the shaft and comment on the value obtained. iv) Produce a neat sketch of the yield criteria failure envelopes for the shaft at point X', indicating all significant detail. v) Given that the shaft outer surface has a 'machined' finish and the shaft operates at a temperature of 85°C and a reliability of 95% is required, determine the factor of safety for the shaft according to the Soderberg theory, commenting on its value. vi) During another loading operation, the shaft is subjected to excessive bending loading conditions that cause the major principal stress to increase to 175 MN/m?. Determine the life expectancy of the shaft. vii) Calculate the total strain energy stored in the shaft during the initial loading. i)
D=100 mm 1.75 kN/m 110 kN 110 kN 2.5 m t=15 mm Shaft Cross-Section Dimensions
Transcribed Image Text:D=100 mm 1.75 kN/m 110 kN 110 kN 2.5 m t=15 mm Shaft Cross-Section Dimensions
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