Question

The deflection of the free end of a cantilever beam subjected to a concentrated load at its mid span is given by:

• A. \( \frac{PL^3}{3EI} \)
• B. \( \frac{PL^3}{8EI} \)
• C. \( \frac{PL^3}{24EI} \)
• D. \( \frac{5PL^3}{48EI} \)

Hint:

Remember, deflection formulas vary based on the load position and beam support conditions; always verify the loading scenario before applying any formula.

Answer 1

The Correct Option is C

The deflection \( \delta \) at the free end of a cantilever beam subjected to a concentrated load \( P \) at its mid-span can be calculated using the beam theory, which yields: \[ \delta = \frac{PL^3}{24EI} \] where \( P \) is the load, \( L \) is the length of the beam, \( E \) is the modulus of elasticity, and \( I \) is the moment of inertia of the beam's cross-section.