A simply supported beam A carries a point load at its mid-span. An identical beam B carries the same total load uniformly distributed over the entire span. The ratio of the maximum deflections of beams A and B is:
Try it first: pick an option, then read the explanation.
Correct answer: D. 8/5
Asked in SSC JE 25/01/2018 (Evening); also SSC JE 2013
Detailed Explanation
Write both central deflections in terms of the same total load W (for the UDL, w = W/L).
\[ \delta_A = \frac{WL^3}{48EI},\qquad \delta_B = \frac{5wL^4}{384EI} = \frac{5WL^3}{384EI} \]
\[ \frac{\delta_A}{\delta_B} = \frac{384}{5\times48} = \frac{8}{5} \]
Why “8/5” Is Correct
The ratio is 8/5: concentrating the same load at mid-span deflects the beam 1.6 times as much as spreading it out.
Why the Other Options Are Wrong
- A. 2/3: 2/3 does not follow from the two formulas.
- B. 3/2: 3/2 is close but not exact.
- C. 5/8: 5/8 is the inverse ratio δB/δA.
Key Point
Same total load W: δ(central point)/δ(UDL) = 8/5.
Key Concepts for Students
- Bending moment ratio for the same case: (WL/4)/(WL/8) = 2.
- Equal central deflection needs W = (5/8)wL.
- Always check whether 'same load' means same total load.
Practice more: this is question 25 in Slope and Deflection MCQs – Part 2. Try the whole set and check every answer instantly.