Nonlinear behavior of rocking beam-columns with confined ends

A study was made on the behavior of beam-columns prior and leading to rocking as a stage in developing models for discrete progressive collapse of structures and for deliberate weakening of structures as a retrofit technique. Following a sequence of cracking, yielding, crushing and rocking, beam-columns continue to sustain loads and have limited deformations if properly confined at their ends. Comparing with the conventional beam-columns, the boundary conditions of rocking beam-column vary continuously from fixed state to cracking, yielding, and ultimate crushing before overturning. Furthermore, the rocking beam-column has two different elastic stress distributions through the length of the element: linear and nonlinear. The nonlinear stress distribution develops near contact boundaries when there is insufficient tension resisting capacity. In this study, the nonlinear stress distribution contributing to the lateral and vertical displacement is derived from mechanical models. Before overturning, after end cracking, the rocking beam-column behaves nonlinearly in both lateral and vertical directions. Analytical results of force-displacements for rocking beam-columns with rotation constraints at their boundaries are derived and compared with FEM results. The paper will present the modeling and several applications.