Question

A beam with overhang supports two concentrated loads P and Q as shown in the figure. The ratio of Q/P, so that deflection at D will be zero is_____

• A. 4

Answer 1

The correct option is A 4

By super –position method:

${\delta }_1=\theta \times \frac{L}{2}$

${\delta }_1=\frac{Q.L^2}{16EI}\times \frac{L}{2}$

${\delta }_1=\frac{Q{L}^3}{32EI}$

A moment of $\frac{PL}{2}$ at C is also acting

${\delta }_2=\frac{P{\left(\frac{L}{2}\right)}^3}{3EI}+\frac{\left(\frac{PL}{2}\right).L}{3EI}\times \frac{L}{2}$

$=\frac{P{L}^3}{24EI}+\frac{P{L}^3}{12EI}=\frac{P{L}^3}{8EI}$

For deflection at D to be zero

${\delta }_1={\delta }_2$

$\frac{Q{L}^3}{32EI}=\frac{P{L}^3}{8EI}$

$\frac{Q}{P}=\frac{32}{8}=4$