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Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress condition in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio μ = 0.3 are given. The principal strains in the plane of the sheet are
[ME 2019,Set-2]
  • a)
    (0.5, -0.15)    
  • b)
    (0.5, 0.0)
  • c)
    (0.35, -0.15)    
  • d)
    (0.5, -0.5)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider a linear elastic rectangular thin sheet of metal, subjected t...
Given
E = 200 MPa
σx = 100 MPa
σy = 0
Principal strain in x-direction
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Most Upvoted Answer
Consider a linear elastic rectangular thin sheet of metal, subjected t...
's modulus of the metal is 200 GPa and its Poisson's ratio is 0.3. The thickness of the sheet is 1 mm.

To determine the strain in the sheet, we can use Hooke's Law for plane stress:

σ = Eε

Where:
σ is the stress (100 MPa)
E is the Young's modulus (200 GPa)
ε is the strain

Rearranging the equation, we can solve for strain:

ε = σ / E

ε = (100 MPa) / (200 GPa)
ε = 0.0005

So, the strain in the sheet is 0.0005.

To determine the change in length of the sheet, we can use the formula for strain:

ε = ΔL / L

Where:
ΔL is the change in length
L is the original length

Rearranging the equation, we can solve for the change in length:

ΔL = ε * L

ΔL = (0.0005) * (L)

Since we don't have the original length of the sheet, we cannot calculate the change in length with the given information.

However, if we assume the original length of the sheet is 1 meter, then the change in length would be:

ΔL = (0.0005) * (1 meter)
ΔL = 0.0005 meters

So, if the original length of the sheet is 1 meter, it would experience a change in length of 0.0005 meters due to the tensile stress.
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Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress condition in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio μ = 0.3 are given. The principal strains in the plane of the sheet are[ME 2019,Set-2]a)(0.5, -0.15) b)(0.5, 0.0)c)(0.35, -0.15) d)(0.5, -0.5)Correct answer is option 'A'. Can you explain this answer?
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