Calibration of the reliability-oriented new design model for reinforced concrete beams strengthened under 30 % of ULS load

Abstract External reinforcement of reinforced concrete (RC) beams using additional rebar is a widely used technique for strengthening and repairing them, either during the technical upgrading of areas or due to the physical wear of the considering members. This study modifies the existing design equation for unstrengthened rectangular cross-section RC beams specified in current standards. The modified equation is developed and calibrated using the structural reliability analysis approach. In our case, this approach generates a model for evaluating the reliability of RC beams strengthened under 30 % of ULS load (most commonly, that a self-weight of members – typical conditions during reconstruction) using Monte Carlo simulation (MCS) across various design parameter combinations. It incorporates random parameters such as material strength, external loads, geometry of sections, and the load level during the process of strengthening. The implementation was carried out using the PTC Mathcad Prime. The suggested model was validated against theoretical and experimental data from earlier authors’ studies on RC beams strengthened in the tension zone. Reliability parameters, including the reliability index ( β ) and the failure probability P ( β ), were calculated for a series of samples. An analysis was conducted to evaluate the influence of the selected input variables on these reliability metrics. The relationship between input variables, the reliability index, and the failure probability of the strengthened beams was thoroughly examined by applying the developed algorithm in the PTC Mathcad Prime environment.