Question

What is the delection at the hinge for the beam shown below ?

• A. 0
• B. $\frac{P{L}^3}{3EI}$
• C. $\frac{P{L}^3}{24EI}$
• D. $\frac{P{L}^3}{48EI}$

Answer 1

The correct option is D $\frac{P{L}^3}{48EI}$

Free body diagram of the given beam is shown below.




$\therefore \frac{P\times (L/2{)}^3}{3EI}-\frac{R\times (L./2{)}^{2}3}{3EI}=\frac{R\times (L/2{)}^3}{3Ei}$

$\Rightarrow \frac{P{L}^3}{24EI}=\frac{R{L}^3}{12EI}$

$\Rightarrow R=\frac{P}{2}$

Deflection at the hinge is given by

${\delta }_c=\frac{R(L/2{)}^3}{3EI}$

$=\frac{P}{2}\times \frac{L^3}{24EI}=\frac{P{L}^3}{48EI}$