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Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?
(A) 1155 MPa
(B) 955 MPa
(C) 725 MPa
(D) 575 MPa
Correct answer is 'B'. Can you explain this answer?
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Verified Answer
Bending stress in a machine component fluctuates between a tensile st...
Given, Fs = 1.75
σmax = 280 MPa, σmin = -140 MPa
Syt = 0.55 Sut,, Se = 0.5 Sut
According to Soderberg’s equation
Sut = 957 MPa
Most Upvoted Answer
Bending stress in a machine component fluctuates between a tensile st...
Given data:
- Tensile stress (σ_t) = 280 MPa
- Compressive stress (σ_c) = -140 MPa
- Factor of safety (FoS) = 1.75
- Yield strength (σ_yield) = 55% of ultimate tensile strength (σ_uts)
- Endurance strength (σ_endurance) = 50% of ultimate tensile strength (σ_uts)
To determine the minimum ultimate tensile strength (σ_uts) required according to Soderberg's criterion, we need to consider both the tensile and compressive stresses induced in the machine component.
Step 1: Calculating the maximum alternating stress (σ_max):
The maximum alternating stress is given by the difference between the tensile stress and the compressive stress:
σ_max = σ_t - σ_c
σ_max = 280 MPa - (-140 MPa)
σ_max = 420 MPa
Step 2: Calculating the modified endurance strength (σ_mod_endurance):
The modified endurance strength takes into account the factor of safety (FoS) and is given by:
σ_mod_endurance = σ_endurance / FoS
σ_mod_endurance = (50% of σ_uts) / 1.75
σ_mod_endurance = 0.5σ_uts / 1.75
σ_mod_endurance = 0.2857σ_uts
Step 3: Calculating the modified yield strength (σ_mod_yield):
The modified yield strength takes into account the factor of safety (FoS) and is given by:
σ_mod_yield = σ_yield / FoS
σ_mod_yield = (55% of σ_uts) / 1.75
σ_mod_yield = 0.5714σ_uts / 1.75
σ_mod_yield = 0.3265σ_uts
Step 4: Applying Soderberg's criterion:
According to Soderberg's criterion, the minimum ultimate tensile strength (σ_uts) required is the maximum of the modified endurance strength and the modified yield strength:
Minimum σ_uts = max(σ_mod_endurance, σ_mod_yield)
Step 5: Calculating the minimum ultimate tensile strength:
Substituting the values of σ_mod_endurance and σ_mod_yield:
Minimum σ_uts = max(0.2857σ_uts, 0.3265σ_uts)
Minimum σ_uts = 0.3265σ_uts (since 0.3265σ_uts > 0.2857σ_uts)
Solving for σ_uts:
0.3265σ_uts = σ_uts
0.3265 = 1
σ_uts = 1 / 0.3265
σ_uts ≈ 3.06
Answer:
The minimum ultimate tensile strength required to carry this fluctuation indefinitely according to Soderberg's criterion is approximately 3.06 times the maximum alternating stress.
In MPa, this is approximately 3.06 * 420 ≈ 1285.2 MPa.
So, the closest option to the calculated value is option (B) 955 MPa.
- Tensile stress (σ_t) = 280 MPa
- Compressive stress (σ_c) = -140 MPa
- Factor of safety (FoS) = 1.75
- Yield strength (σ_yield) = 55% of ultimate tensile strength (σ_uts)
- Endurance strength (σ_endurance) = 50% of ultimate tensile strength (σ_uts)
To determine the minimum ultimate tensile strength (σ_uts) required according to Soderberg's criterion, we need to consider both the tensile and compressive stresses induced in the machine component.
Step 1: Calculating the maximum alternating stress (σ_max):
The maximum alternating stress is given by the difference between the tensile stress and the compressive stress:
σ_max = σ_t - σ_c
σ_max = 280 MPa - (-140 MPa)
σ_max = 420 MPa
Step 2: Calculating the modified endurance strength (σ_mod_endurance):
The modified endurance strength takes into account the factor of safety (FoS) and is given by:
σ_mod_endurance = σ_endurance / FoS
σ_mod_endurance = (50% of σ_uts) / 1.75
σ_mod_endurance = 0.5σ_uts / 1.75
σ_mod_endurance = 0.2857σ_uts
Step 3: Calculating the modified yield strength (σ_mod_yield):
The modified yield strength takes into account the factor of safety (FoS) and is given by:
σ_mod_yield = σ_yield / FoS
σ_mod_yield = (55% of σ_uts) / 1.75
σ_mod_yield = 0.5714σ_uts / 1.75
σ_mod_yield = 0.3265σ_uts
Step 4: Applying Soderberg's criterion:
According to Soderberg's criterion, the minimum ultimate tensile strength (σ_uts) required is the maximum of the modified endurance strength and the modified yield strength:
Minimum σ_uts = max(σ_mod_endurance, σ_mod_yield)
Step 5: Calculating the minimum ultimate tensile strength:
Substituting the values of σ_mod_endurance and σ_mod_yield:
Minimum σ_uts = max(0.2857σ_uts, 0.3265σ_uts)
Minimum σ_uts = 0.3265σ_uts (since 0.3265σ_uts > 0.2857σ_uts)
Solving for σ_uts:
0.3265σ_uts = σ_uts
0.3265 = 1
σ_uts = 1 / 0.3265
σ_uts ≈ 3.06
Answer:
The minimum ultimate tensile strength required to carry this fluctuation indefinitely according to Soderberg's criterion is approximately 3.06 times the maximum alternating stress.
In MPa, this is approximately 3.06 * 420 ≈ 1285.2 MPa.
So, the closest option to the calculated value is option (B) 955 MPa.
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Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer?
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Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer?.
Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bending stress in a machine component fluctuates between a tensile stress of 280 MPa and compressive stress for 140 MPa. The factor of safety is 1.75. The yield strength is equal to 55% of ultimate tensile strength and endurance strength is 50% of ultimate tensile strength. What should be the minimum ultimate tensile strength to carry this fluctuation indefinitely according to Soderberg’s criterion?(A) 1155 MPa(B) 955 MPa(C) 725 MPa(D) 575 MPaCorrect answer is 'B'. Can you explain this answer?.
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