Question

A reinforced concrete beam has square cross section (h × h). There are 9 steel reinforcing bars (each of diameter ds), 3 evenly spaced towards the top, 3 along the neutral axis, and 3 evenly spaced towards the bottom. The vertical distance from the centre of the bar to top (or bottom) edge of the section is called the cover, and is denoted as e. It should be taken that ρsteel = 7850 kg/m3, ρconcrete = 2350 kg/m3, Econcrete = 30000 MPa and Esteel = 195000 MPa, and that both materials exhibit linear elastic behaviour. The concrete cracks in tension at 4.5 MPa. The beam can be considered as a simply supported beam of length L where L is based on the given span to depth ratio of the beam. The beam also experiences an unknown vertical load Pat midspan.

a) What is the self weight per unit length of the beam?

b) 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 on the critical cross-section when this occurs.

h=360mm ds=16mm e=40mm span/depth = 20

Answer 1