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Purpose: A nonlinear finite element (FE) beam-column model for the analysis of reinforced concrete (RC) frames with due account of shear is presented in this paper. The model is an expansion of the traditional flexural fibre beam formulations to cases where multiaxial behaviour exists, being an alternative to plane and solid FE models for the nonlinear analysis of entire frame structures. The paper aims to discuss these issues.\ud Design/methodology/approach: Shear is taken into account at different levels of the numerical model: at the material level RC is simulated through a smeared cracked approach with rotating cracks; at the fibre level, an iterative procedure guarantees equilibrium between concrete and transversal reinforcement, allowing to compute the biaxial stress-strain state of each fibre; at the section level, a uniform shear stress pattern is assumed in order to estimate the internal shear stress-strain distribution; and at the element level, the Timoshenko beam theory takes into account an average rotation due to shear.\ud Findings: The proposed model is validated through experimental tests available in the literature, as well as through an experimental campaign carried out by the authors. The results on the response of RC elements critical to shear include displacements, strains and crack patterns and show the capabilities of the model to efficiently deal with shear effects in beam elements.\ud Originality/value: A formulation for the nonlinear shear-bending interaction based on the fixed stress approach is implemented in a fibre beam model. Shear effects are accurately accounted during all the nonlinear path of the structure in a computationally efficient manner.Peer ReviewedPostprint (published version

Strengthening RC elements critical to shear with prestressed transversal reinforcement can be an efficient method to increase the shear resistance of structures, allowing the development of the full flexural capacity. However, research on the performance of this technique is very scant, and methods for designing the optimum amount of prestressed transversal reinforcement and assessing the retrofitted structure have not been produced yet. Nonlinear FE models are an important tool regarding predicting the efficiency of these interventions. In this paper a shear-sensitive fibre beam formulation is extended in order to account for the effects of unbonded vertical external prestressed reinforcement in the structural response of RC beams. The model is validated with experimental tests available in literature, succeeding in capturing the gain of shear strength brought by different strengthening solutions. A parametric study is performed to find the optimal quantity of transversal reinforcement that ensures flexural failure mechanism in a beam with insufficient internal shear reinforcement. The relative simplicity of the numerical model makes it suitable for engineering practice.

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