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A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m. Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1. The factor of safety using Soderberg criteria will be
Correct answer is between '7.5,8.5'. Can you explain this answer?
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A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength ...
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A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength ...
Solution:
Given data:
Diameter of the shaft, d = 75 mm
Ultimate tensile strength of steel, σut = 630 MPa
Maximum torque, T_max = 1500 N-m
Minimum torque, T_min = -950 N-m
Yield stress for steel in reversed bending, σy = 510 N/mm2
Surface finish factor, Kf = 0.87
Size factor, Ks = 0.85
Fatigue stress concentration factor, Kf' = 1
To find: Factor of safety using Soderberg criteria
Step 1: Calculation of alternating torque
The alternating torque is given by,
T_a = (T_max - T_min)/2 = (1500 - (-950))/2 = 725 N-m
Step 2: Calculation of mean torque
The mean torque is given by,
T_m = (T_max + T_min)/2 = (1500 + (-950))/2 = 275 N-m
Step 3: Calculation of maximum shear stress
The maximum shear stress is given by,
τ_max = (T_max*D/2)/J = (1500*75/2)/((π/32)*75^4) = 47.89 MPa
Step 4: Calculation of equivalent stress
The equivalent stress is given by,
σ_e = √(σ_m^2 + 3*τ_max^2) = √((T_m/J)^2 + 3*(T_max*D/2)/J^2) = √((275/((π/32)*75^4))^2 + 3*(1500*75/2)/((π/32)*75^4)^2) = 25.67 MPa
Step 5: Calculation of endurance limit
The endurance limit is given by,
σ_e' = Kf*Ks*Kf'*σut = 0.87*0.85*1*630 = 463.14 MPa
Step 6: Calculation of factor of safety
The factor of safety using Soderberg criteria is given by,
N = σe'/σe = 463.14/25.67 = 18.03
Therefore, the factor of safety using Soderberg criteria is between 7.5 and 8.5.
Given data:
Diameter of the shaft, d = 75 mm
Ultimate tensile strength of steel, σut = 630 MPa
Maximum torque, T_max = 1500 N-m
Minimum torque, T_min = -950 N-m
Yield stress for steel in reversed bending, σy = 510 N/mm2
Surface finish factor, Kf = 0.87
Size factor, Ks = 0.85
Fatigue stress concentration factor, Kf' = 1
To find: Factor of safety using Soderberg criteria
Step 1: Calculation of alternating torque
The alternating torque is given by,
T_a = (T_max - T_min)/2 = (1500 - (-950))/2 = 725 N-m
Step 2: Calculation of mean torque
The mean torque is given by,
T_m = (T_max + T_min)/2 = (1500 + (-950))/2 = 275 N-m
Step 3: Calculation of maximum shear stress
The maximum shear stress is given by,
τ_max = (T_max*D/2)/J = (1500*75/2)/((π/32)*75^4) = 47.89 MPa
Step 4: Calculation of equivalent stress
The equivalent stress is given by,
σ_e = √(σ_m^2 + 3*τ_max^2) = √((T_m/J)^2 + 3*(T_max*D/2)/J^2) = √((275/((π/32)*75^4))^2 + 3*(1500*75/2)/((π/32)*75^4)^2) = 25.67 MPa
Step 5: Calculation of endurance limit
The endurance limit is given by,
σ_e' = Kf*Ks*Kf'*σut = 0.87*0.85*1*630 = 463.14 MPa
Step 6: Calculation of factor of safety
The factor of safety using Soderberg criteria is given by,
N = σe'/σe = 463.14/25.67 = 18.03
Therefore, the factor of safety using Soderberg criteria is between 7.5 and 8.5.
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A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer?
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A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer?.
A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m.Assume the yield stress for steel in reversed bending as 510 N/mm2, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1.The factor of safety using Soderberg criteria will beCorrect answer is between '7.5,8.5'. Can you explain this answer?.
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