Simplified nonlinear analysis to compute neutral axis depth in prestressed concrete rectangular beams

Recent research in concrete analysis and design has revealed that the shear capacity contributed by concrete correlates well with the neutral axis depth. While nonlinear analysis calculation of the neutral axis depth is trivial for reinforced concrete beams, it is iterative for prestressed concrete beams and does not lend itself to straightforward hand calculations. In this study, a program is developed to simulate the response of prestressed concrete rectangular sections subjected to monotonic bending taking into account cracking, yielding and ultimate states. This program is used to benchmark a simplified analytical procedure devised to perform the same task by hand. Accordingly, critical observations made to a large pool of experimental and analytical results reveal that the moment-curvature and moment-extreme fiber strain can be accurately modeled as trilinear relationships. The four key points that define the trilinear functions (initial, cracking, yielding and ultimate) may be computed analytically from simple equations derived based on consistent assumptions with the true behavior. Once the simplified analysis is performed, the computation of the neutral axis depth becomes a simple hand calculation. A parametric study was performed to further simplify the analytical procedure by computing the four key points that define the trilinear functions through linear relationships that were derived based on regression analysis of a large number of beam solutions. The neutral axis depth was calculated using the analytical and the simplified procedures for three beams with different ratios of prestressing steel and concrete strength. The results compared well with the iterative numerical procedure.