Question

The depression produced at the end of a $50cm$ long cantilever on applying a load is $15mm$. The depression produced at a distance of $30cm$ from the rigid end will be

• A. 3.24 mm
• B. 1.62 mm
• C. 6.48 mm
• D. 12.96 mm

Answer 1

Answer: (C)

6.48 mm

Length of cantilever, $L=50cm=0.5m$
Deflection at the end $w\left(L\right)=15mm$
Find: Deflection $w\left(x\right)$ at 30cm from rigid end.
Depression at a point in a cantilever beam with load at one end is given by,$w\left(x\right)=\frac{P{x}^2(3L-x)}{6EI}$
We have,
$\frac{w\left(x\right)}{w\left(L\right)}=\frac{\frac{P{x}^2(3L-x)}{6EI}}{\frac{P{L}^3}{3EI}}$
$\frac{w\left(0.3m\right)}{w\left(0.5m\right)}=\frac{\frac{P{\left(0.3\right)}^2\left(3\right(0.5)-0.3)}{6EI}}{\frac{P(0.5{)}^3}{3EI}}$

This gives, $w\left(0.3m\right)=6.48mm$