Question

Two simply supported beams ‘A’ and ‘B’ of same breadth and depth and same material carries constant central load W at the centre. The span of beam B is double that of beam A. The deflection of beam B compared to beam A will be

1. one-half
2. one-eighth
3. four times
4. eight times

Answer 1

Correct Answer - Option 4 : eight times

Concept:

Deflection of simply supported beam:

Concentrated load P at the centre:

\(δ = \frac{{P{L^3}}}{{48EI}}\)

Therefore, for two shafts of the same material, same cross-sectional area and carries a constant central load W their deflection is directly proportional to the cube of span i.e., 

δ ∝ L³

Calculation:

Given:

L_B = 2L_A

\(\frac{δ_B}{δ_A}=\frac{(L_B)^3}{(L_A)^3}\) = (2)³ = 8

δ_B = 8δ_A 

∴ the deflection of beam B is 8 times as compared to beam A.