Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams

Abstract

A conceptual model for the prediction of the shear-flexural strength of slender reinforced concrete beams with and without transverse reinforcement is presented. The model incorporates the shear transferred by the un-cracked concrete chord, along the crack's length, by the stirrups, if they are, and, in that case by the longitudinal reinforcement. After the development of the first branch of the critical shear crack, failure is considered to occur when the stresses at any point of the concrete compression chord reach the assumed biaxial stress failure envelope. A physical explanation is provided for the evolution of the shear transfer mechanisms, and the contribution of each one at ultimate limit state is formulated accordingly. Simple equations are derived for shear strength verification and for designing transverse reinforcement. The method is validated by comparing its predictions with the results of 1131 shear tests, obtaining very good results in terms of mean value and coefficient of variation. Because of its accuracy, simplicity and theoretical consistency, the proposed method is considered to be very useful for the practical design and assessment of concrete structures subjected to combined shear and bending.Peer ReviewedPostprint (published version

Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams subjected to point or distributed loads

“…The performance of the proposed model and the codes formulation in front of other databases may be seen elsewhere [1]. A simplified version of the proposed model has been also developed to predict the shear strength of concrete beams longitudinally reinforced with FRP bars.…”

“…Currently, large databases compiling shear experiments have been developed by Reineck et al [12,13] in the context of an ACIDAfStb joint group, resulting in a powerful tool for evaluating the adequacy of different formulations to reproduce the role of the design variables. In this paper, the rational shear resistance formulation of Mari et al [1] is briefly presented and evaluated against the latest databases [12,13]. One significant characteristic of the proposed formulation is that most important shear transfer actions are separately considered.…”

“…Moreover, it will be possible to obtain the normal stresses at the critical section at the point of the compressive chord where failure occurs, the shear stress also at the critical point, the principal stresses and to verify that the principal stresses satisfy Kupfer's failure envelope. See reference [1] for further detail of the needed equations.…”

“…Equation (12) has been used to evaluate it. For more information about this equation, or the exact development of any of the contributing components, refer to [1].…”

“…On the other hand, design approaches in most current codes of practice are empirically or semi-empirically based and show large scatter with respect to experimental evidence; thus, large safety factors are needed to assure their safe applicability. Recently, it has been suggested in Mari et al [1] that the fact that most of empirical formulations explicitly or implicitly assume prevailing of one of the above mentioned actions, implies that such type of formulation can only partially explain the phenomenon, being this a plausible explanation of the big dispersion.…”