Question

A simply supported beam of span 2L and flexural rigidity EI is subjected to a uniformly distributed load of w/m throughout the span. The deflection at mid span is

• A. $\frac{5 wL^4}{384 EI}$
• B. $\frac{5 wL^4}{48 EI}$
• C. $\frac{5 wL^4}{24 EI}$
• D. $\frac{1 wL^4}{48 EI}$

Hint:

Be very careful when a problem uses non-standard notation for span length (like 2L instead of L).
Always start with the standard formula you have memorized and then carefully substitute the specific variables given in the problem.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Simply supported beam, central point load. Ratio δ_max/θ_max = ?

Step 2: Key Formulas (Alternate):
δ_max = WL³/(48EI). θ_max (at supports) = WL²/(16EI). Divide them.

Step 3: Detailed Explanation:
δ/θ = [WL³/(48EI)]/[WL²/(16EI)] = (L/48)×(16/1) = 16L/48 = L/3.

Step 4: Final Answer:
Ratio is L/3.