Which statements are true A)A plane state of stress always results in a plane state of strain. B)A uni axial state of stress results in a 3 D state of strain. C)A state of plane strain always results in plane stress conditions. D)A thin sheet of metal stretched in its own plane results in plane strain conditions. Can you please explain which are true.?

Question

Answer

D

Answer

True Statements:

A) A plane state of stress always results in a plane state of strain:
In mechanics, stress and strain are related. Stress refers to the internal forces or pressure acting on a material, while strain represents the deformation or change in shape that occurs in response to stress. When a material is subjected to a plane state of stress, it means that the stress is acting in a single plane. In such cases, the resulting strain will also occur in the same plane, leading to a plane state of strain. Therefore, statement A is true.

B) A uniaxial state of stress results in a 3D state of strain:
Uniaxial stress refers to a condition where stress acts in only one direction. However, the resulting strain will not necessarily be limited to only one dimension. When a material experiences uniaxial stress, it causes deformation in all three dimensions, resulting in a three-dimensional state of strain. Therefore, statement B is false.

C) A state of plane strain always results in plane stress conditions:
Plane strain refers to a condition where deformation occurs in a plane while the material remains relatively constant in the orthogonal direction. When a material is subjected to plane strain, it means that the strain is limited to the plane, and there is no change in the thickness of the material. However, this does not imply that the stress will also be limited to the plane. The stress distribution can be three-dimensional, and it may vary within the material. Therefore, statement C is false.

D) A thin sheet of metal stretched in its own plane results in plane strain conditions:
When a thin sheet of metal is stretched in its own plane, it experiences a deformation that is primarily limited to the plane of the sheet. The thickness of the sheet does not change significantly during this process. This deformation pattern corresponds to the definition of plane strain, where strain occurs in a plane while the material remains constant in the orthogonal direction. Therefore, statement D is true.

In Summary:
- A plane state of stress always results in a plane state of strain (True).
- A uniaxial state of stress results in a 3D state of strain (False).
- A state of plane strain does not always result in plane stress conditions (False).
- A thin sheet of metal stretched in its own plane results in plane strain conditions (True).

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