Closed-form expressions for predicting moment redistribution in reinforced concrete beams with application to conventional concrete and ultrahigh performance fiber reinforced concrete

The redistribution of moment within a statically indeterminate reinforced concrete beam at the ultimate limit state occurs through variations in the flexural rigidities and through the formation of hinges. The phenomena of moment redistribution (MR) is used to increase the efficiency of reinforced concrete design by allowing moments to be transferred away from critical cross sections thereby resulting in lower design moments. To allow for this effect in design, two main approaches are adopted. The first is to perform an elastic analysis and then to adjust the resulting distribution of moment using a codified MR factor. The second is to apply a plastic analysis allowing for the formation of hinges, and to calculate the rotational requirements at the hinges from first principles. This paper uses fundamental plastic analyses to derive closed-form expressions for the hinge rotational requirements for full MR (that required to achieve the theoretical maximum applied load within the beam based on the moment capacity of sections within the beam). These closed-form solutions are then used to quantify the maximum load on a beam when the rotational capacities at a hinge are less than the rotational requirements for full MR (partial MR). Closed-form solutions are then used to derive MR factors which do not require semimechanical calibration.