# 1) A reinforced concrete beam has square cross section (h × h). There are 4 stee

1) A reinforced concrete beam has square cross section (h × h). There are 4 steel reinforcing bars (each ofdiameter ds). The reinforcement is symmetrically placed in each corner of the beam section, such that thedistance from the centre of the bar to any edge of the section is e. It should be taken thatρsteel = 7800 kg/m3, ρconcrete = 2450 kg/m3, Econcrete = 35000 MPa and Esteel = 200000 MPa, and that bothmaterials exhibit linear elastic behaviour. The concrete cracks in tension at 10 MPa. The beam can beconsidered as a cantilever beam of length L. Given h=375 (mm) ds=20 (mm) e=35 (mm).a) What is the self weight per unit length of the beam?b) Under self weight only, calculate the length of the beam (L) such that it just cracks under its selfweight.c) Now consider the same beam with the same length but it is now a simply supported beam. Anadditional point load, P, is then applied at midspan. What value of P (in conjunction with self weight)will induce cracking? Draw the stress and strain distributions for both the steel and the concrete onthe critical cross-section just prior to cracking.