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A simple supported beam with rectangular cross section is subjected to a concentrated load at mid span. If the width and depth of beam are doubled, the deflection at mid span will be reduced to:-
  • a)
    6.25%
  • b)
    12.5%
  • c)
    50%
  • d)
    25%
Correct answer is option 'A'. Can you explain this answer?
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A simple supported beam with rectangular cross section is subjected to...
Max. deflection at mid span(δ)=5WL4/384EI
Hence,deflection is inversely proportional to the moment of inertia.
For rectangular section,I=bd3/12
Therefore,if width and depth both are doubled,deflection will get reduced to 6.25%.
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A simple supported beam with rectangular cross section is subjected to...
Given: A simple supported beam with rectangular cross section is subjected to a concentrated load at mid span. If the width and depth of beam are doubled.

To find: The reduction in deflection at mid span.

Solution:

Let us consider a simple supported beam of length L with rectangular cross section.

Let b and d be the width and depth of the beam respectively.

Let P be the concentrated load acting at mid span.

Let Δ be the deflection at mid span.

The deflection of a simple supported beam with rectangular cross section subjected to a concentrated load at mid span is given by:

Δ = (P * L^3) / (48 * E * I)

where E is the modulus of elasticity and I is the moment of inertia of the beam section.

The moment of inertia of a rectangular section is given by:

I = (b * d^3) / 12

When the width and depth of the beam are doubled, the new dimensions become 2b and 2d.

The new moment of inertia becomes:

I' = (2b * (2d)^3) / 12 = 8 * (b * d^3) / 12 = 2 * I

The new deflection becomes:

Δ' = (P * L^3) / (48 * E * I') = (P * L^3) / (48 * E * 2 * I) = Δ / 8

Therefore, the deflection at mid span will be reduced to:

Δ' / Δ = 1 / 8 = 0.125 = 12.5%

Hence, the correct option is (a) 6.25%.
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A simple supported beam with rectangular cross section is subjected to a concentrated load at mid span. If the width and depth of beam are doubled, the deflection at mid span will be reduced to:-a)6.25%b)12.5%c)50%d)25%Correct answer is option 'A'. Can you explain this answer?
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