Flexibility-based finite element models for the nonlinear static and dynamic analysis of concrete frame structures

This study presents a new flexibility-based beam element formulation that is, both, theoretically sound and computationally robust. The proposed formulation assumes that plane sections remain plane, and is presently limited to small deformations. The formulation derives from a two-field mixed method and points directly to the consistent implementation of the element state determination.; The element state determination consists of a nonlinear Newton-Raphson iteration scheme in which the element deformations are kept constant while the element forces are adjusted. During the iterations equilibrium along the element is always satisfied in a strict sense and convergence is reached when the material constitutive relations are satisfied within the specified tolerance.; The new formulation is applied to two beam elements. The first is a beam element that is subdivided into longitudinal steel and concrete fibers with perfect bond. The second is a beam element with an incremental moment-curvature relation that is derived from the application of endochronic theory. The first element naturally includes the interaction between axial force and biaxial bending moments. Such interaction is neglected in the second nonlinear beam that is limited to linear elastic axial behavior.; The proposed formulation is general and can be applied to any nonlinear section force-deformation relation, but the examples in this study are limited to reinforced concrete structures. The proposed method proved to be computationally stable and robust, while being able to describe the complex hysteretic behavior of reinforced concrete members, such as strain hardening, "pinching" and softening under cyclic nodal loads.; A new scheme for the application of element loads in flexibility-based beam finite elements is also presented. The procedure is a natural extension of the element state determination algorithm and is based on the use of the exact internal force distribution under the applied element loads.; Correlation studies between the experimental response of several reinforced concrete elements and the analytical results show the ability of the proposed models to describe the hysteretic behavior of reinforced concrete members. Several parametric studies under static and dynamic loads with the proposed models demonstrate the effectiveness and computational stability of the new formulation.