Question

An overhanging beam of uniform EI is loaded as shown below. The deflection at the free end is

• A. $\frac{W{I}^3}{81EI}$
• B. $\frac{W{I}^3}{8EI}$
• C. $\frac{W{I}^3}{27EI}$
• D. $\frac{2W{I}^3}{27EI}$

Answer 1

The correct option is B $\frac{W{I}^3}{8EI}$






Deflection due to cantilever action of load in span BC.

${\Delta }_1\frac{W(L/2{)}^3}{3EI}=\frac{W{L}^3}{24EI}$

${\theta }_B=\frac{\left(WL/2\right)L}{3EI}=\frac{W{L}^2}{6EI}$

$Now{\Delta }_2={\theta }_B.\frac{L}{2}=\frac{W{L}^3}{12EI}$

$\therefore \Delta ={\Delta }_1+{\Delta }_2=\frac{W{L}^3}{8EI}$