A timber beam is 15 cm deep by 10 cm wide, and carries a central load of 30 kN at the center of a 3 m span; the beam is simply-supported at each end. The timber is reinforced with flat steel plates 10 cm wide by 1.25 cm thick bolted to the upper and lower surfaces of the beam. Taking E for steel as 200 GN/m2 and E for timber as 1 GN/m2, estimate
(i) the maximum direct stress in the steel strips;
(ii) the average shearing stress in the timber;
(iii) the shearing load transmitted by the bolts;
(iv) the bending and shearing deflections at the center of the beam.