A simply supported beam made of rolled steel joist (I-section: 450mm ´ 200mm) has a span of 5m and it carries a central concentrated load W. The flanges are strengthened by two 300mm ´ 20mm plates, one riveted to each flange over the entire length of the flanges. The second moment of area of the joist about the principal bending axis is 35,060 cm4. Calculate:
(i) the greatest central load the beam will carry if the bending stress in the 300 mm´2Omm plates is not to exceed 125 MPa.
(ii) the minimum length of the 300 mm plates required to restrict the maximum bending stress in the flanges of the joist to 125 MPa.