ABSTRACT
Rigorous analysis of reinforced concrete members loaded into the inelastic range requires the knowledge of the relationship between moment and curvature. This knowledge is necessary for better evaluation of the deflections and possible redistribution of bending moments after cracking in statically indeterminate reinforced concrete members. In this research work, a considerably simplified theory for the analysis of moment-curvature relationship and hence deflection of reinforced concrete beams in the cracking stage is presented. The theory assumes concrete to have a non-zero tensile capacity. The non-linear behaviour of concrete in compression was accounted for by assuming a parabolic stress-strain relationship. For the purpose of this work, the stress-strain diagram of concrete in tension was approximated by a bilinear curve. These assumptions led to a third degree equation to determine the position of the neutral axis according to the equilibrium of internal forces. Having the position the position of the position of the neutral axis, it was possible to find the moments and the curvatures for an assumed value of strain in the tensile reinforcement. By increasing the value of the strain and repeating the above procedure, we obtain the moment-curvature diagrams. Good agreement was found between the results of this the and the experimental results of previous investigators. To further confirm the validity the theory, six full sized reinforced concrete beams grouped into two sets were tested. The first set of beams have cross sectional dimensions 300mm by 100mm and the second set has dimensions 100mm by 300mm. Each of the beams has total span 4.0m. All the beams were reinforced with deformed bars of varying diameters. Stirrups were provided throughout the length of each beam. It was found that results of the experiments were in good agreement with the theory.