Nonlinear analysis of RC beams using a hybrid shear-flexural fibre beam model

Abstract

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

Shear strengthening of reinforced concrete beams by means of vertical prestressed reinforcement

“…The detailed description and validation of the shear-sensitive fibre beam model for concrete structures can be found elsewhere (Ferreira 2013;Ferreira et al 2014b). Only a brief reference to the fundamentals of the model is presented in this paper focusing on the new formulation for vertical prestressing (unbonded and bonded).…”

“…For concrete in tension a linear response is assumed before cracking and a tension stiffening curve is considered in the cracked stage. A modified version of the exponential tension stiffening curve of (Cervenka 1985) is used, being calibrated so that it produces null stiffening for beyond yielding of steel (Ferreira 2013;Ferreira et al 2014b). The tensile strain when tensile stress is equal to zero is assumed as the yielding strain of steel as proposed by Mohr, Bairán and Mari 2010.…”

“…In this manner the plane section theory is coupled with a shear stress constraint, and the determination of the fibre state is performed using a hybrid stress-strain input information. The strain-stress state of each fibre is determined by means of a inner iterative procedure as explained in (Ferreira et al 2014b). The criteria for dividing the cross section into shear resistant and non shear resistant fibres are explained in ; essentially the fibres that belong to the web of the cross section discounting the cover area are set as shear resistant; also the fibres located in a shear effective width of the flanges are considered as shear resistant.…”

“…A shear-sensitive fibre beam model was recently developed and validated by the authors Ferreira, Bairán, Marí and Faria 2014b). The 1D fibre beam model accounts for axial force-bending-shear force interactions in a computationally efficient manner and allows for the nonlinear, time-dependent and strengthening analysis of shear critical concrete frame structures.…”

“…The shear-sensitive 1D fibre beam model was presented elsewhere (Ferreira 2013, Ferreira et al 2014b. A preliminary study on shear strengthening with bonded vertical prestressing was presented in ) but without comparison with experimental results.…”