Question

A cantilever beam, 3m long, carries a uniformly distributed load over the entire length. If the slope at the end is $1^{\circ }$, the deflection at the free end is

• A. 49.27 mm
• B. 39.27mm
• C. 30.27mm
• D. 20.27 mm

Answer 1

The correct option is B 39.27mm



${\theta }_B=\frac{w{L}^3}{6E{I}^{\prime }}\frac{w{I}^4}{8EI}$

${\Delta }_B=\frac{w{I}^3}{6EI}=\frac{6I}{8}$

$={\theta }_B\times \frac{6I}{8}=\frac{\pi }{180}\times \frac{6\times 3}{8}$

= 0.0392 m = 39.2 mm