Question

A beam is supported at its ends by two supports which are $12m$ apart. Since the load is concentrated at its centre, there is a deflection of $3cm$ at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection $1cm$?

Answer 1

Hence RQ=1cm
$QR=3cm-1cm=2cm=\frac{2}{100}m$
let $OP=x$
$\Rightarrow Q$ is $(x,\frac{2}{100})$ lies on parabola
$x^2=4\left(300\right)(\left(\frac{2}{100}\right)=24$
$\Rightarrow x=\sqrt{24}=2\sqrt{6}m$
$\therefore$ Required distance is $2\sqrt{6}m$.