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For the state of stress of pure shear τ, the strain energy stored per unit volume in the elastic, homogeneous isotropic material having elastic constants E and v will be
- a)τ2(1 + v )/E
- b)τ2(1 + v )/2E
- c)2τ2(1 + v )/E
- d)τ2(2 + v )/2E
Correct answer is option 'A'. Can you explain this answer?
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For the state of stress of pure shear τ, the strain energy stored ...
Pure shear refers to a type of stress where the applied forces act parallel to each other but in opposite directions, causing the material to deform in a shearing manner. In this state of stress, the normal stresses (σx and σy) are zero, while the shear stress (τxy) is non-zero.
The state of stress for pure shear can be represented by the following stress tensor:
σ = [0 τxy]
[τxy 0 ]
In this stress tensor, the normal stresses in the x and y directions are zero, while the shear stress in the xy direction (τxy) is non-zero.
The stress components in this state of stress can be calculated using the equations:
σx = σy = 0
τxy = τyx = τ
where τ is the magnitude of the shear stress.
It is important to note that pure shear is an idealized state of stress and is not commonly encountered in real-world situations. However, it is often used in theoretical and experimental studies to better understand the behavior of materials under shear loading.
The state of stress for pure shear can be represented by the following stress tensor:
σ = [0 τxy]
[τxy 0 ]
In this stress tensor, the normal stresses in the x and y directions are zero, while the shear stress in the xy direction (τxy) is non-zero.
The stress components in this state of stress can be calculated using the equations:
σx = σy = 0
τxy = τyx = τ
where τ is the magnitude of the shear stress.
It is important to note that pure shear is an idealized state of stress and is not commonly encountered in real-world situations. However, it is often used in theoretical and experimental studies to better understand the behavior of materials under shear loading.
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For the state of stress of pure shear τ, the strain energy stored per unit volume in the elastic, homogeneous isotropic material having elastic constants E and v will bea)τ2(1 + v )/Eb)τ2(1 + v )/2Ec)2τ2(1 + v )/Ed)τ2(2 + v )/2ECorrect answer is option 'A'. Can you explain this answer?
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