A compound girder is built up from a standard I$-$beam with $250$ mm$\backslash$times $30$ mm steel plate welded onto the flange as shown. The girder simply supported over $10$ m$.($a$)$ What is the maximum uniformly distributed load $($in addition to self$-$weight$)$ that can be applied to the beam if the stresses in bending and shear are not to exceed the values given below?$($b$)$ What is the minimum weld thickness required to join the plates to the beam without overstress?Design Data:Mass steel: $7800$ kg$/$m$3.$Allowable shear stress: $75$ MPa.Allowable bending stress: $110$ MPa.Allowable shear stress in weld throat: $55$ MPa.All dimensions are in mm$.$