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A small element at the critical section of a component is in a bi-axial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion Energy Theory is:
[GATE-1997]
- a)220 MPa
- b)110 MPa
- c)314 MPa
- d)330 MPa
Correct answer is option 'C'. Can you explain this answer?
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A small element at the critical section of a component is in a bi-axia...
According to distortion energy theory if maximum stress (σt) then
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A small element at the critical section of a component is in a bi-axia...
Given:
- Principal stresses: σ1 = 360 MPa, σ2 = 140 MPa
To find:
- Maximum working stress according to Distortion Energy Theory
Assumption:
- The bi-axial stress state is in the elastic range.
Solution:
The Distortion Energy Theory, also known as von Mises Theory, states that failure occurs when the distortion energy per unit volume reaches a critical value. This theory assumes that failure occurs when the distortional strain energy in a material reaches the same value for any state of stress that causes failure.
The formula for the distortion energy theory is given by:
σe = √[((σ1 - σ2)^2 + (σ2 - σ3)^2 + (σ3 - σ1)^2)/2]
Calculations:
In this case, since the stress state is bi-axial, the third principal stress (σ3) is assumed to be zero.
Therefore, the formula for the distortion energy theory simplifies to:
σe = √[(σ1 - σ2)^2 + (σ2 - 0)^2 + (0 - σ1)^2]/√2
= √[2(σ1^2 + σ2^2)]/√2
= √(σ1^2 + σ2^2)
= √(360^2 + 140^2)
= √(129600 + 19600)
= √149200
≈ 386.1 MPa
Answer:
The maximum working stress according to Distortion Energy Theory is approximately 386.1 MPa, which is not listed in the given options. Therefore, none of the given options (a, b, c, d) is correct.
- Principal stresses: σ1 = 360 MPa, σ2 = 140 MPa
To find:
- Maximum working stress according to Distortion Energy Theory
Assumption:
- The bi-axial stress state is in the elastic range.
Solution:
The Distortion Energy Theory, also known as von Mises Theory, states that failure occurs when the distortion energy per unit volume reaches a critical value. This theory assumes that failure occurs when the distortional strain energy in a material reaches the same value for any state of stress that causes failure.
The formula for the distortion energy theory is given by:
σe = √[((σ1 - σ2)^2 + (σ2 - σ3)^2 + (σ3 - σ1)^2)/2]
Calculations:
In this case, since the stress state is bi-axial, the third principal stress (σ3) is assumed to be zero.
Therefore, the formula for the distortion energy theory simplifies to:
σe = √[(σ1 - σ2)^2 + (σ2 - 0)^2 + (0 - σ1)^2]/√2
= √[2(σ1^2 + σ2^2)]/√2
= √(σ1^2 + σ2^2)
= √(360^2 + 140^2)
= √(129600 + 19600)
= √149200
≈ 386.1 MPa
Answer:
The maximum working stress according to Distortion Energy Theory is approximately 386.1 MPa, which is not listed in the given options. Therefore, none of the given options (a, b, c, d) is correct.
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A small element at the critical section of a component is in a bi-axial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion Energy Theory is:[GATE-1997]a)220 MPab)110 MPac)314 MPad)330 MPaCorrect answer is option 'C'. Can you explain this answer?
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A small element at the critical section of a component is in a bi-axial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion Energy Theory is:[GATE-1997]a)220 MPab)110 MPac)314 MPad)330 MPaCorrect 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 small element at the critical section of a component is in a bi-axial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion Energy Theory is:[GATE-1997]a)220 MPab)110 MPac)314 MPad)330 MPaCorrect 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 small element at the critical section of a component is in a bi-axial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion Energy Theory is:[GATE-1997]a)220 MPab)110 MPac)314 MPad)330 MPaCorrect answer is option 'C'. Can you explain this answer?.
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