Equations for shear design and crack width control of deep beams

Abstract

Deep beams in concrete infrastructures work mainly in shear. It is therefore important to assess the shear resistance of such a beam, as well as the evolution of the diagonal shear crack that develops on it, with a view to taking adequate measures to ensure its compliance during its service life. This work is therefore divided into an Ultimate Limit State study and a Serviceability Limit State study of deep beams; and more precisely of simply supported deep beams subjected to point loads. At Ultimate Limit States, the aim is to define relatively simple closed-form design equations against shear failure as in the case of slender beams. These equations are obtained by simplifying the full process established on the Two-Parameter Kinematic Theory which predicts the shear strength of a deep beam based on four components: the critical loading zone (CLZ), the aggregate interlock, the stirrups and the dowel action. The simplifications made to this method are designed to make it non-iterative, and to reduce the number of shear strength components from four to three by neglecting the dowel action contribution. At Serviceability Limit States, the aim is to establish a relationship between the applied shear and the width of the critical diagonal crack, in order to predict it at each loading stage of the beam. The approach developed is based on a rapid crack-based assessment model which enables to evaluate the residual shear capacity of a deep beam through three on-site measurements and two simple closed equations. It incorporates a crack-control effect likely to develop in some deep beams, so as to gain greater accuracy in predicted crack-width values.