A series of reinforced concrete beams spaced at 5 m centres and spanning 7.5 m support a 175 mm thick reinforced concrete slab as shown in Figure 3. The imposed floor loading is 3 kN/m^{2} and the load induced by the weight of concrete is 24 kN/m^{3}, Design the beam using both elastic and limit state method.
p_{cb} = 10 N/mm^{2}, pst = 140 N/mm^{2}, m = 15
f_{y} = 250 N/mm^{2}, fcu = 30 N/mm^{2}