A Numerical Approach for the Design of RC Beams Subjected to Axial and Transverse Loads

Abstract

Abstract The present contribution deals with a numerical approach for the design of RC beams subjected to axial and transverse loads. It is based on the finite-element implementation of the kinematic approach of the yield design (or limit analysis) theory combined with a “mixed modelling” where the concrete material is regarded as a classical two-dimensional continuum while the longitudinal reinforcements are modelled as one-dimensional elements working in tension-compression only. For the beams reinforced in shear, stirrups are incorporated in the analysis through a homogenization procedure. An optimization problem is formulated, then solved using conic quadratic optimization method. As a result, an upper bound estimate to the yield strength domain of RC beams may be drawn in the plane of axial and transverse loads. For illustrative purpose, calculations are conducted on typical RC beams with different longitudinal and transverse reinforcement degrees. Furthermore, it is shown that such numerical predictions prove to be in good agreement with the results derived from other numerical simulations of the same problem using a finite element-based limit analysis commercial software. In order to assess their practical validity, these predictions are also compared to some available experimental results published in the literature.