Predicting the non-linear shear behaviour of deep beams based on a two-parameter kinematic model

Deep beams are often used as transfer girders in high rise buildings to support heavy loads from discontinuous columns or shear walls. Several buildings with such transfer girders were affected by the February 2011 earthquake in Christchurch, New Zealand, which produced very large vertical accelerations and overloaded the transfer girders. One of the buildings had to be stabilized urgently in the hours after the earthquake while others sustained significant damage. The structures which remained standing were those capable of redistributing the forces from the damaged transfer girders to less damaged structural members. The extent of such force redistribution, and therefore the ability of the structure to survive extreme events, depends in part on the displacement capacity and post-peak behaviour of the transfer girders. For this reason, the evaluation of structures with deep transfer girders under extreme loading requires accurate models for predicting the complete non-linear response of the girders.
As deep beams usually fail in a brittle manner due to shear, predicting their non-linear behaviour represents a challenging problem even when sophisticated non-linear finite element models are used. This paper will discuss a simpler alternative approach based on a kinematic model for deep beams. The kinematic model describes the deformation patterns of the beam with the help of two degrees of freedom: the average strain along the flexural reinforcement from support to support, and the transverse displacement in the critical zones in the vicinity of the applied loads (critical loading zones). The model assumes that much of the deformations concentrate along a critical diagonal crack which widens and slips as the deflections of the member increase. The equations of the kinematic model are combined with equilibrium equations and constitutive relationships for the load-resisting mechanisms across the critical crack. These mechanisms include diagonal compression in the critical loading zones, aggregate interlock, tension in the stirrups crossing the crack, and dowel action of the longitudinal reinforcement. The complete set of equations is solved iteratively in order to compute the pre- and post- peak response of deep beams. This approach is validated with the help of tests of deep beams. The model will be used to draw conclusions on the effect of the properties of deep beams on their non-linear behaviour.