Design equations from empirical and semi-empirical resisting models: a reliability-based approach

The resisting models used in engineering practice can be based both on physical laws, such as equilib-rium of forces, and on semi-empirical or empirical formulations fitted on experimental results. In order to use both these models for design and verification purposes, they should be based on a spe-cific level of reliability provided by national and international codes. Specifically, empirical or semi-empirical resisting models are calibrated defining empirical coef-ficients to fit a set of experimental data. Then, the only application of partial safety factors to material properties does not allow a proper estimation of the structural reliability. For this reason, the defini-tion of design expressions from empirical or semi-empirical resisting models should be based on a probabilistic procedure able to define a final formulation in agreement with a specific level of reliabil-ity. In the present paper, a methodology based on the Monte Carlo method for the probabilistic cali-bration of empirical and semi-empirical resisting models is proposed. Its application to the probabilis-tic calibration of the semi-empirical model proposed by fib Model Code 2010 for the estimation of laps and anchorages tensile strength in reinforced concrete structures is described. Afterwards, the results are compared to the ones obtained with the direct application of partial safety factors to mate-rials strength within the original formulation and, finally, the differences are commented.