Question

A beam is supported at its ends by 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

The beam takes the shape of a parabola, whose equation is of the form $x^2=4ay...\left(i\right)$

Since the point $B(6,\frac{3}{100})$ lie on it, we have

$(4\times a\times \frac{3}{100})=36$
$\Rightarrow a=\frac{36\times 12}{12}$
$\Rightarrow a=300m.$

Let $RQ$ be the deflection. Then,

$RQ=\frac{1}{100}m$ and $Q$ is $Q(a,\frac{2}{100})$

$\therefore x^2=4\times 300\times \frac{2}{100}\iff x=2\sqrt{6}m$ is the required distance.