Problem $2/4$:

A uniform beam $($not shown$)$ is simply supported over a span of $6m.$

It carries a trapezoidally distributed load with intensity varying from

$30k\frac{N}{m}$ at the left$-$hand support to $90k\frac{N}{m}$ at the right$-$hand

support. Find the equation of the deflection curve and hence the

deflection at the mid$-$span point. The second moment of area of the cross$-$section of the beam is

$120{10}^{6}m{m}^4$ and Young's modulus $E=206,000\frac{N}{m}{m}^2.($Answer: $41mm$ downward$)$