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Volumetric strain (ev) is given by ____
Here, σx = stress in x-direction, σy = stress in y-direction, σz = stress in z-direction, μ = Poisson ratio and E = Modulus of Elasticity.
- a)(σ1+σ2+σ3)×(1−2μ)/E
- b)(σ1+σ2+σ3)×(2−μ)/E
- c)(σ1+σ2+σ3)/E×(1−2μ)
- d)(σ1+σ2+σ3)/E×(2-μ)
Correct answer is option 'A'. Can you explain this answer?
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Volumetric strain (ev) is given by ____Here, σx = stress in x-directi...
Volumetric strain (ev) = ex + ey + ez
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Here ex, ey, and ez are the strain in the x, y, and z directions, respectively.
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Volumetric strain (ev) is given by ____Here, σx = stress in x-directi...
Volumetric strain (εv) is a measure of the change in volume of a material under stress. It is given by the formula:
εv = -σx/E - σy/E - σz/E + 2μ(σx + σy + σz)/E
where σx, σy, and σz are the stresses in the x, y, and z directions respectively, E is the modulus of elasticity, and μ is the Poisson ratio.
To derive this formula, we start with the definition of strain, which is the ratio of change in length to the original length. In three dimensions, this can be expressed as:
εx = ΔLx/L0
εy = ΔLy/L0
εz = ΔLz/L0
where ΔLx, ΔLy, and ΔLz are the changes in length in the x, y, and z directions respectively, and L0 is the original length.
Next, we relate the changes in length to the stresses using Hooke's Law, which states that the strain is proportional to the stress:
εx = σx/E
εy = σy/E
εz = σz/E
where E is the modulus of elasticity.
To account for the change in volume, we sum up the changes in length in all three directions:
εv = εx + εy + εz
Substituting the expressions for εx, εy, and εz, we get:
εv = σx/E + σy/E + σz/E
However, this formula only accounts for the change in volume due to the normal stresses. To also consider the effect of shear stresses, we multiply the sum of the normal stresses by a factor of 2μ, where μ is the Poisson ratio:
εv = σx/E + σy/E + σz/E + 2μ(σx + σy + σz)/E
Simplifying this expression, we get:
εv = (σx + σy + σz)/E - 2μ(σx + σy + σz)/E
Factoring out (σx + σy + σz)/E, we get:
εv = (σx + σy + σz)/E(1 - 2μ)
Therefore, the correct formula for volumetric strain (εv) is option A: (σx σy σz)(1 - 2μ)/E.
εv = -σx/E - σy/E - σz/E + 2μ(σx + σy + σz)/E
where σx, σy, and σz are the stresses in the x, y, and z directions respectively, E is the modulus of elasticity, and μ is the Poisson ratio.
To derive this formula, we start with the definition of strain, which is the ratio of change in length to the original length. In three dimensions, this can be expressed as:
εx = ΔLx/L0
εy = ΔLy/L0
εz = ΔLz/L0
where ΔLx, ΔLy, and ΔLz are the changes in length in the x, y, and z directions respectively, and L0 is the original length.
Next, we relate the changes in length to the stresses using Hooke's Law, which states that the strain is proportional to the stress:
εx = σx/E
εy = σy/E
εz = σz/E
where E is the modulus of elasticity.
To account for the change in volume, we sum up the changes in length in all three directions:
εv = εx + εy + εz
Substituting the expressions for εx, εy, and εz, we get:
εv = σx/E + σy/E + σz/E
However, this formula only accounts for the change in volume due to the normal stresses. To also consider the effect of shear stresses, we multiply the sum of the normal stresses by a factor of 2μ, where μ is the Poisson ratio:
εv = σx/E + σy/E + σz/E + 2μ(σx + σy + σz)/E
Simplifying this expression, we get:
εv = (σx + σy + σz)/E - 2μ(σx + σy + σz)/E
Factoring out (σx + σy + σz)/E, we get:
εv = (σx + σy + σz)/E(1 - 2μ)
Therefore, the correct formula for volumetric strain (εv) is option A: (σx σy σz)(1 - 2μ)/E.
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Volumetric strain (ev) is given by ____Here, σx = stress in x-direction, σy = stress in y-direction, σz = stress in z-direction, μ = Poisson ratio and E = Modulus of Elasticity.a)(σ1+σ2+σ3)×(1−2μ)/Eb)(σ1+σ2+σ3)×(2−μ)/Ec)(σ1+σ2+σ3)/E×(1−2μ)d)(σ1+σ2+σ3)/E×(2-μ)Correct answer is option 'A'. Can you explain this answer?
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Volumetric strain (ev) is given by ____Here, σx = stress in x-direction, σy = stress in y-direction, σz = stress in z-direction, μ = Poisson ratio and E = Modulus of Elasticity.a)(σ1+σ2+σ3)×(1−2μ)/Eb)(σ1+σ2+σ3)×(2−μ)/Ec)(σ1+σ2+σ3)/E×(1−2μ)d)(σ1+σ2+σ3)/E×(2-μ)Correct answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Volumetric strain (ev) is given by ____Here, σx = stress in x-direction, σy = stress in y-direction, σz = stress in z-direction, μ = Poisson ratio and E = Modulus of Elasticity.a)(σ1+σ2+σ3)×(1−2μ)/Eb)(σ1+σ2+σ3)×(2−μ)/Ec)(σ1+σ2+σ3)/E×(1−2μ)d)(σ1+σ2+σ3)/E×(2-μ)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Volumetric strain (ev) is given by ____Here, σx = stress in x-direction, σy = stress in y-direction, σz = stress in z-direction, μ = Poisson ratio and E = Modulus of Elasticity.a)(σ1+σ2+σ3)×(1−2μ)/Eb)(σ1+σ2+σ3)×(2−μ)/Ec)(σ1+σ2+σ3)/E×(1−2μ)d)(σ1+σ2+σ3)/E×(2-μ)Correct answer is option 'A'. Can you explain this answer?.
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