A rolled steel joist \(400 \mathrm{~mm} \times 200 \mathrm{~mm} \times 20 \mathrm{~mm}\) is freely supported on a span of \(4 \mathrm{~m}\). The flanges are strengthened by two \(250 \mathrm{~mm} \times 20 \mathrm{~mm}\) plates, one riveted to each flange. Calculate

(a) the maximum central load the beam can carry if the stress in the plate is not to exceed \(125 \mathrm{MPa},(b)\) the minimum length of the strengthening plates required to restrict the maximum stress to \(125 \mathrm{MPa}\).