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A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be
[2006]
- a)1071 cycles
- b)15000 cycles
- c)281914 cycles
- d)928643 cycles
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cylindrical shaft is subjected to an alternating stress of 100 MPa. ...
By concept of straight line,
At y = 2
⇒ x = 5.4501
log10N = 5.4501, N = 281914
At y = 2
⇒ x = 5.4501
log10N = 5.4501, N = 281914
Most Upvoted Answer
A cylindrical shaft is subjected to an alternating stress of 100 MPa. ...
Given:
- Alternating stress = 100 MPa
- Fatigue strength for 1000 cycles = 490 MPa
- Corrected endurance strength = 70 MPa
To find:
- Estimated shaft life
Solution:
The estimated shaft life can be calculated using the Goodman equation, which relates the alternating stress and the endurance strength.
The Goodman equation is given by:
1/Sa + 1/Se = 1/Su
where:
- Sa is the alternating stress
- Se is the corrected endurance strength
- Su is the ultimate tensile strength
Step 1:
Let's calculate the ultimate tensile strength (Su) using the given data:
Sa = 100 MPa
Se = 70 MPa
1/Sa + 1/Se = 1/Su
Substituting the values:
1/100 + 1/70 = 1/Su
Solving this equation:
0.01 + 0.0142857 = 1/Su
0.0242857 = 1/Su
Su = 1/0.0242857
Su = 41.2 MPa
Step 2:
Now that we have the ultimate tensile strength (Su), we can use the Goodman equation to calculate the estimated shaft life.
1/Sa + 1/Se = 1/Su
Substituting the values:
1/100 + 1/70 = 1/41.2
Simplifying the equation:
0.01 + 0.0142857 = 0.0242718
0.0242857 = 0.0242718
Since the values on both sides of the equation are approximately equal, we can consider the shaft life to be equal to the given number of cycles for the corrected endurance strength.
Therefore, the estimated shaft life is 281,914 cycles (option C).
- Alternating stress = 100 MPa
- Fatigue strength for 1000 cycles = 490 MPa
- Corrected endurance strength = 70 MPa
To find:
- Estimated shaft life
Solution:
The estimated shaft life can be calculated using the Goodman equation, which relates the alternating stress and the endurance strength.
The Goodman equation is given by:
1/Sa + 1/Se = 1/Su
where:
- Sa is the alternating stress
- Se is the corrected endurance strength
- Su is the ultimate tensile strength
Step 1:
Let's calculate the ultimate tensile strength (Su) using the given data:
Sa = 100 MPa
Se = 70 MPa
1/Sa + 1/Se = 1/Su
Substituting the values:
1/100 + 1/70 = 1/Su
Solving this equation:
0.01 + 0.0142857 = 1/Su
0.0242857 = 1/Su
Su = 1/0.0242857
Su = 41.2 MPa
Step 2:
Now that we have the ultimate tensile strength (Su), we can use the Goodman equation to calculate the estimated shaft life.
1/Sa + 1/Se = 1/Su
Substituting the values:
1/100 + 1/70 = 1/41.2
Simplifying the equation:
0.01 + 0.0142857 = 0.0242718
0.0242857 = 0.0242718
Since the values on both sides of the equation are approximately equal, we can consider the shaft life to be equal to the given number of cycles for the corrected endurance strength.
Therefore, the estimated shaft life is 281,914 cycles (option C).
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A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. Can you explain this answer?
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A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. 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 A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. 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 A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. Can you explain this answer?.
A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. 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 A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. 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 A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. Can you explain this answer?.
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A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be[2006]a)1071 cyclesb)15000 cyclesc)281914 cyclesd)928643 cyclesCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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