A post$-$tensioned beam of rectangular cross$-$section, $200$ mm wide and $400$ mm deep, is $10$ m long and carries an applied load of $8$ kN$/$m$,$ uniformly distributed on the beam. The effective prestressing force in the cable is $500$ kN$.$ The cable is parabolic with zero eccentricity at the supports and a maximum eccentricity of $140$ mm at the centre of span.

$($a$)$ Calculate the principal stresses at the support.

$($b$)$ What will be the magnitude of the principal stresses at the supports in the absence of prestress?