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The strain energy in a member is proportional to
  • a)
    total strain multiplied by the volume of themember
  • b)
    product of stress and the correspondingstrain
  • c)
    product of strain and Young’s modulus ofthe material
  • d)
    the maximum strain multiplied by the lengthof the member
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The strain energy in a member is proportional toa)total strain multipl...
Explanation:

The strain energy in a member is the energy stored within the member due to the deformation caused by the applied loads. The strain energy can be calculated by integrating the product of stress and the corresponding strain over the volume of the member. Therefore, the correct option is 'B'.

Details:

Product of Stress and Strain:

Stress is defined as force per unit area and strain is defined as the change in length per unit length. When a load is applied to a member, it causes deformation in the member. The deformation can be measured by the change in length or change in shape of the member. The stress and strain are related by the material properties of the member, such as Young's modulus, Poisson's ratio, etc. The product of stress and strain gives the energy stored in the member due to the deformation caused by the applied load.

Integration over Volume:

The stress and strain are not constant throughout the volume of the member. Therefore, to calculate the total strain energy, we need to integrate the product of stress and strain over the volume of the member. This integration gives the total strain energy stored in the member.

Proportional to:

The proportionality constant between the strain energy and the product of stress and strain depends on the material properties of the member. Therefore, the strain energy is proportional to the product of stress and strain.

Conclusion:

The strain energy in a member is proportional to the product of stress and the corresponding strain. This is because the strain energy is stored in the member due to the deformation caused by the applied load, and the deformation is related to the stress and strain by the material properties of the member.
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Community Answer
The strain energy in a member is proportional toa)total strain multipl...
Both A and B option are correct
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The strain energy in a member is proportional toa)total strain multiplied by the volume of thememberb)product of stress and the correspondingstrainc)product of strain and Young’s modulus ofthe materiald)the maximum strain multiplied by the lengthof the memberCorrect answer is option 'B'. Can you explain this answer?
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