An analytical method to determine the post-cracking flexural stress in pretensioned concrete beams

•Stresses in cracked pretensioned concrete beams are often unknown.•A novel use of section analysis is presented to calculate stresses in cracked concrete.•Laboratory experimentation results shows very good agreement with proposed method.•The method can be used up to ultimate flexural capacity of pretensioned beams. This work presents a novel application of section analysis methods to calculate post-cracking flexural stresses in pretensioned concrete beams, with primary application to railroad crossties (sleepers). The proposed methodology is particularly useful to estimate concrete stresses generated when constitutive relationships between strain and stresses of concrete are complex. To validate the method, bending strength of beams are predicted and the results are compared with laboratory testing data. The proposed procedure is independent of the need for strain computations, and the bending strength calculations are based on the compressive strength of concrete as opposed to a hypothetical crushing strain value (commonly assumed to be 0.003). Experimental results demonstrate very good agreement with the proposed model, with a level of accuracy that exceeds the traditional approach using Whitney’s block. While being structurally conservative by slightly overestimating stresses, the method yielded prediction errors of 9% or less for the investigated beams.