A post$-$tensioned beam concrete beam of rectangular section is $250$ mm wide and $450$ mm deep. The beam is prestressed by two cables of area $510$ mm$2$ each, which are initially prestressed to $1500$ N$/$mm$2.$ The eccentricity of the cables is $90$ mm through the length of the beam, and the span of the beam is $8$ m$.$ Ignoring all losses find the deflection at the center when the beam supports its weight.

What would be the deflection at the center when the beam carries an imposed load of $15$ KN$/$m and there is a $20\%$ loss in prestress? Concrete weights $24$ KN$/$m$3.$ The modulus of elasticity for concrete is $40$ KN$/$mm$2.$