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A simply supported beam of span L carries a UDL of w. N m−1. What is the magnitude of concentrated load to be supplied at the centre of this beam which would produce the same deflection as the UDL?
  • a)
    3/8 wL
  • b)
    wL/ 2
  • c)
    5 / 8 wL
  • d)
    7 / 8 wL
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A simply supported beam of span L carries a UDL of w. N m−1. What is ...
P = 5/8 ∙ w ∙ L
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A simply supported beam of span L carries a UDL of w. N m−1. What is ...
Given:
- Span of the beam = L
- UDL = w N/m
- We need to find the magnitude of concentrated load that would produce the same deflection as the UDL

Formula:
- Deflection due to UDL = 5wL^4 / 384EI
- Deflection due to concentrated load at the centre = FL^3 / 48EI

Where,
- F is the magnitude of concentrated load at the centre
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam

Calculation:
- The deflection due to UDL and concentrated load should be equal, so equating the above two formulas:
5wL^4 / 384EI = FL^3 / 48EI

- Simplifying the equation:
F = (5/8)wL

Therefore, the magnitude of concentrated load to be supplied at the centre of the beam which would produce the same deflection as the UDL is (5/8)wL.

Hence, the correct answer is option C.
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A simply supported beam of span L carries a UDL of w. N m−1. What is the magnitude of concentrated load to be supplied at the centre of this beam which would produce the same deflection as the UDL?a) 3/8 wLb) wL/ 2c) 5 / 8 wLd) 7 / 8 wLCorrect answer is option 'C'. Can you explain this answer?
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