Numerical and analytical evaluation of stirrup-induced confinement on resistance of RC beams using lower bound limit analysis

Abstract

In this paper, a modified three-dimensional element is introduced for limit analysis of RC structures, which considers more aspects of structural behaviour. Using the introduced element, the influence of stirrup confinement on the shear and moment resistance of RC beams is evaluated by lower bound limit analysis. To analyse and solve the relevant optimization problem, the semidefinite programming method, SDP, is employed. The modified Mohr–Coulomb yield criterion is utilized to constrain the concrete stress state. Beams with a constant amount of shear reinforcement per unit length, with different values of stirrup spacing, are studied. It means that they only differed in the effect of confinement induced by stirrup reinforcements. The performance of the proposed element is verified by comparing the results of numerical limit analyses with experimental results. This comparison revealed the efficiency and accuracy of the proposed model and the capability of the introduced element to take the effect of stirrup-induced confinements into account. After modelling and investigating the effect of stirrup confinement in load bearing of RC beams, a simplified equation for the design and practical purposes is proposed. Using this equation, the shear resistance of the beams could be modified for different stirrup space choices. The results obtained from this simplified equation are compared with numerical limit analysis and experimental results. The comparisons indicate the reasonable accuracy of the proposed equation.