Three-Parameter Kinematic Theory for Shear Strength and Displacement Capacity of Deep Beams

Deep reinforced concrete beams are often used as transfer girders in high rise buildings to support heavy loads from discontinuous columns or shear walls. They are typically designed with strut-and-tie models which are based on a clear visualization of the flow of forces in the member. Strut-and-tie models usually provide conservative shear strength predictions but do not provide accurate assessments of deformation patterns close to failure. Information on ultimate deformations can be critical in, for example, designing members for support settlements or evaluation of structural robustness.
To address these issues, this presentation will discuss an alternative approach based on a kinematic model which describes the deformation patterns of deep beams. Within each shear span this model uses just three parameters: the average tensile strain in the top longitudinal reinforcement, the average tensile strain in the bottom reinforcement, and the vertical deformation of the critical loading zone. The equations of the kinematic model are combined with equilibrium equations and constitutive relationships for the load-bearing mechanisms across a critical shear crack. These equations can be solved with a relatively small number of hand calculations. The three-parameter kinematic theory (3PKT) will be compared to strut-and-tie models with the help of a large test database. Design examples will be used to demonstrate the advantages of the 3PKT.