Question

Deflection at the free end of a cantilever beam of length 2 m with 5 kN point load at the end is .......

• A. \( \frac{5 \times 2^3}{3EI} \)
• B. \( \frac{5 \times 2^2}{2EI} \)
• C. \( \frac{5 \times 2^3}{6EI} \)
• D. \( \frac{5 \times 2^3}{2EI} \)

Hint:

For cantilever beams with a point load at the free end, remember: \[ \delta = \frac{P L^3}{3EI} \] This is a fundamental formula in structural analysis.

Answer 1

The Correct Option is A

Step 1: Formula for cantilever beam deflection under point load
The standard formula for maximum deflection \( \delta \) at the free end of a cantilever beam subjected to a point load \( P \) at its tip is: \[ \delta = \frac{P L^3}{3EI} \] Where:
- \( P = 5 \, \text{kN} \) (point load)
- \( L = 2 \, \text{m} \) (length of cantilever)
- \( E \) = Modulus of Elasticity
- \( I \) = Moment of Inertia
Step 2: Substituting values into formula: \[ \delta = \frac{5 \times 2^3}{3EI} \] Step 3: Final Answer Hence, the correct expression is: \[ \boxed{\frac{5 \times 2^3}{3EI}} \]