Power spread plasticity model for inelastic analysis of reinforced concrete structures

In nonlinear analysis of structures the structural elements exhibiting yielding in its sections are usually modeled using concentrated plastic hinges at the end of the elements or fiber models accounting for yielding along the member. In the last four decades however, alternative models were developed based on spread plasticity formulations which consider an extended inelastic zone in proximity of the critical sections, therefore affecting the stiffness (or the flexibility) matrix of the member. Two flexibility formulations were generally considered to account approximately for the variation of curvature in the plasticized zones, one linear and the other uniform. The linear spread plasticity model assumes that the curvature in the plasticized zone is distributed linearly at the ends of the element while the uniform curvature model considers a constant distribution of plasticity. In this study, a power spread plasticity model is proposed which is able to model more complex or various plasticity distribution patterns, including concentrated plasticity (plastic hinge). The derivation is the same as for the previous spread flexibility formulations, where the flexibility coefficients represent the relation between the end moments and the correspondent plane rotations. Considering both flexural and shear flexibilities, the model is developed and implemented in a nonlinear structural analysis platform, IDARC2D. Several nonlinear analyses are carried out on a previously tested full scale bridge pier and a 10-story structure to show the influence of the power values on the cyclic and dynamic structural response. The results of the analyses show that the high order spread plasticity models produce smaller displacement and higher acceleration responses in the structural system. At the end of the paper, an alternative definition for the selection of the power value (variable power) is suggested and the corresponding results are also investigated.