A supported beam with a uniform section spanning over $8$ m is post$-$tensioned by two cables, both

of which have an eccentricity of $120$ mm below the centroid of the section at mid$-$span. The first

cable is parabolic and is anchored at an eccentricity of $120$ mm above the centroid at each end, the

second cable is straight and parallel to the line joining the supports. The cross$-$sectional area of

each cable is $120$ mm$2$ and they carry an initial stress of $1800$ N$/$mm$2.$ The concrete has a cross

section of $3$ x $104$ mm$2$ and a radius of gyration of $150$ mm$.$ The beam supports two concentrated

loads of $30$ kN each at the third point of the span. Ec $=38$ kN$/$mm$2$ and Dc $=24$ kN$/$m$3.$ Calculate

using Lin$$s simplified method

$($a$)$ The instantaneous deflection at the centre of the span: and

$($b$)$ the deflection at the centre of the span after $2$ years, assuming a $20$ per cent loss in

prestress with a creep coefficient,$$ of $2\mathrm{.}0.$