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A beam is supported at its ends by suppo...

A beam is supported at its ends by supports which are `12` metres apart. Since tha 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 deflection `1` cm ?

Text Solution

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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`
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