Question

A cantilever beam of span 2 m carries a concentrated load of 48 kN at the free end. If the flexural rigidity of beam EI = 20,000 kNm$^2$, the slope at the free end is

• A. $3.2 \times 10^{-3}$ radians
• B. $4.8 \times 10^{-3}$ radians
• C. $48 \times 10^{-3}$ radians
• D. $64 \times 10^{-3}$ radians

Hint:

Memorize the standard formulas for cantilever beam slope and deflection:
- Load at Free End (P):
- Max Slope = $PL^2 / (2EI)$
- Max Deflection = $PL^3 / (3EI)$
- UDL over entire span (w):
- Max Slope = $wL^3 / (6EI)$
- Max Deflection = $wL^4 / (8EI)$

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Simply supported beam span S=2L, UDL=w. Find mid-span deflection formula.

Step 2: Key Formula (Alternate):
Standard formula: δ_max = 5wS⁴/(384EI). Substitute S=2L and simplify.

Step 3: Detailed Explanation:
δ = 5w(2L)⁴/(384EI) = 5w×16L⁴/(384EI) = 80wL⁴/(384EI). Divide by 16: 5wL⁴/(24EI).

Step 4: Final Answer:
Deflection is 5wL⁴/(24EI).