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Total strain energy stored in a simply supported beam of span ‘L' and flexural rigidity ‘El’ subjected to a concentrated load ‘W at the centre is equal to
  • a)
    W2L3/40EI
  • b)
    W2L3/60EI
  • c)
    W2L3/96EI
  • d)
    W2L2/240EI
Correct answer is option 'D'. Can you explain this answer?
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Total strain energy stored in a simply supported beam of span ‘L...
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Total strain energy stored in a simply supported beam of span ‘L...
Strain Energy in Simply Supported Beam
The total strain energy stored in a simply supported beam of span 'L' and flexural rigidity 'EI' subjected to a concentrated load 'W' at the centre can be calculated using the formula:

W^2L^2/240EI

Explanation:

Understanding the Formula
- The formula for calculating the total strain energy in a simply supported beam under a concentrated load at the centre is derived based on the beam theory and the concept of strain energy.
- The formula takes into account the load 'W', span 'L', and flexural rigidity 'EI' of the beam to determine the amount of strain energy stored in the beam.

Calculation Steps
1. Start with the formula: Total strain energy = W^2L^2/240EI
2. Substitute the values of the load 'W', span 'L', and flexural rigidity 'EI' into the formula.
3. Calculate the total strain energy using the given values.

Final Thoughts
- The correct formula for calculating the total strain energy stored in a simply supported beam under a concentrated load at the centre is W^2L^2/240EI.
- This formula is derived from the basic principles of beam mechanics and is essential for analyzing the behavior of beams under loading conditions.
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