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A component is subjected to a flexural stress which fluctuates between 310N/mm2 and -160N/mm2 . If endurance strength is half of the ultimate strength, the minimum ultimate strength according to Gerber relation is (Factor of safety = 2)
- a)963.4
- b)822.1
- c)701.5
- d)679.9
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A component is subjected to a flexural stress which fluctuates betwee...
Given,
σmax = 310 MPa
σmin = -160 MPa
Se = 0.5 sut
N = 2
By Gerber relation
Sut = 963.35 MPa
Most Upvoted Answer
A component is subjected to a flexural stress which fluctuates betwee...
To solve this problem, we can use the Gerber relation, which relates the alternating stress (σ_a) to the ultimate strength (σ_u) of a material. The Gerber relation is given by:
(σ_a / σ_u)^2 + (σ_m / σ_e)^2 = 1
where:
σ_a = alternating stress
σ_u = ultimate strength
σ_m = mean stress
σ_e = endurance strength
We are given that the alternating stress fluctuates between 310 N/mm^2 and -160 N/mm^2. To find the minimum ultimate strength, we need to find the maximum alternating stress.
Let's calculate the maximum alternating stress:
Maximum alternating stress (σ_a) = (310 N/mm^2 - (-160 N/mm^2)) / 2
= 470 N/mm^2
We are also given that the endurance strength (σ_e) is half of the ultimate strength (σ_u). Therefore:
σ_e = σ_u / 2
Substituting these values into the Gerber relation:
(470 N/mm^2 / σ_u)^2 + (0 / (σ_u / 2))^2 = 1
Simplifying the equation:
(470 N/mm^2 / σ_u)^2 = 1
Taking the square root of both sides:
470 N/mm^2 / σ_u = 1
σ_u = 470 N/mm^2
Since the factor of safety is given as 2, we can find the minimum ultimate strength by dividing the calculated value by the factor of safety:
Minimum ultimate strength = 470 N/mm^2 / 2
= 235 N/mm^2
Therefore, the minimum ultimate strength according to the Gerber relation is 235 N/mm^2.
(σ_a / σ_u)^2 + (σ_m / σ_e)^2 = 1
where:
σ_a = alternating stress
σ_u = ultimate strength
σ_m = mean stress
σ_e = endurance strength
We are given that the alternating stress fluctuates between 310 N/mm^2 and -160 N/mm^2. To find the minimum ultimate strength, we need to find the maximum alternating stress.
Let's calculate the maximum alternating stress:
Maximum alternating stress (σ_a) = (310 N/mm^2 - (-160 N/mm^2)) / 2
= 470 N/mm^2
We are also given that the endurance strength (σ_e) is half of the ultimate strength (σ_u). Therefore:
σ_e = σ_u / 2
Substituting these values into the Gerber relation:
(470 N/mm^2 / σ_u)^2 + (0 / (σ_u / 2))^2 = 1
Simplifying the equation:
(470 N/mm^2 / σ_u)^2 = 1
Taking the square root of both sides:
470 N/mm^2 / σ_u = 1
σ_u = 470 N/mm^2
Since the factor of safety is given as 2, we can find the minimum ultimate strength by dividing the calculated value by the factor of safety:
Minimum ultimate strength = 470 N/mm^2 / 2
= 235 N/mm^2
Therefore, the minimum ultimate strength according to the Gerber relation is 235 N/mm^2.
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A component is subjected to a flexural stress which fluctuates between 310N/mm2 and -160N/mm2 . If endurance strength is half of the ultimate strength, the minimum ultimate strength according to Gerber relation is (Factor of safety = 2)a) 963.4b) 822.1c) 701.5d) 679.9Correct answer is option 'A'. Can you explain this answer?
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A component is subjected to a flexural stress which fluctuates between 310N/mm2 and -160N/mm2 . If endurance strength is half of the ultimate strength, the minimum ultimate strength according to Gerber relation is (Factor of safety = 2)a) 963.4b) 822.1c) 701.5d) 679.9Correct answer is option 'A'. 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 component is subjected to a flexural stress which fluctuates between 310N/mm2 and -160N/mm2 . If endurance strength is half of the ultimate strength, the minimum ultimate strength according to Gerber relation is (Factor of safety = 2)a) 963.4b) 822.1c) 701.5d) 679.9Correct answer is option 'A'. 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 component is subjected to a flexural stress which fluctuates between 310N/mm2 and -160N/mm2 . If endurance strength is half of the ultimate strength, the minimum ultimate strength according to Gerber relation is (Factor of safety = 2)a) 963.4b) 822.1c) 701.5d) 679.9Correct answer is option 'A'. Can you explain this answer?.
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