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

Explanation

Let the be at the lowest point and the axis vertical. Let the coordinate axes be chosen as shown in figure.
The equation of the parabola takes the form `x^(2)=4ay`. Since it passes through (6,3/100), we have
`6^(2)=4axx(3)/(100)`
`i.e.,a=300`
Let AB be the deflection of the beam which is `(1)/(100)` m. The coordinates of are `(x,2//100)`. Therefore, `x^(2)=4xx300xx(2)/(100)=24`
or `x=2sqrt(6)m`