Question

A simply supported beam of span L and flexural rigidity EI is subjected to a concentrated load of W at mid span. The ratio of maximum deflection to maximum slope anywhere in the beam is

• A. $L/2$
• B. $L/3$
• C. $L/4$
• D. $L/5$

Hint:

Memorizing the standard deflection and slope formulas for simply supported and cantilever beams is essential for solving these types of problems quickly.
- SS Beam, Center Load P: $\delta_{max} = PL^3/(48EI)$, $\theta_{max} = PL^2/(16EI)$.
- SS Beam, UDL w: $\delta_{max} = 5wL^4/(384EI)$, $\theta_{max} = wL^3/(24EI)$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Fixed beam 8m span, 96kN at center, EI=51200 kNm². Find max deflection.

Step 2: Key Formula (Alternate):
δ_max = PL³/(192EI) for fixed beam with central point load.

Step 3: Detailed Explanation:
δ = 96×8³/(192×51200) = 96×512/(192×51200). Cancel 96: 192=2×96. Cancel 512: 51200=100×512. δ = 1/(2×100) = 0.005m = 5mm.

Step 4: Final Answer:
Maximum deflection is 5 mm.