Resumen de A framework for 3d nonlinear analysis of reinforced concrete frames under general loading
Modern guidelines for design and assessment of reinforced concrete structures under seismic and other extreme loads require nonlinear analysis. The complex structural response can be obtained by means of three-dimensional finite element models, although its application is limited due to their high computational cost. Alternatively, if the structure can be assimilated by line elements, the structure can be simulated by means of frame elements. These formulations have demonstrated to be robust and efficient. The main drawback of most of the beam-column models is that they neglect or consider in an oversimplified way the interaction between axial and transverse internal forces. Consequently, most frame models are not able to trace different failure modes in reinforced concrete elements such as shear or torsional failures. Besides, the simplifications made in those models affect also their ability to reproduce even common failure modes such as flexural or axial failures.
The main goal of this thesis is to develop a robust and efficient numerical tool capable of reproducing different failure modes of reinforced concrete frame elements. It is also desired that the model is able to reproduce complex phenomena such as passive confinement in an objective way. The developed tool is aimed to be used in the design or assessment of full scale structures under general loading conditions. In order to accomplish this objective, the problem is dealt by means of a multilevel framework.
At the constitutive level, a new plastic-damage model for concrete that incorporates a variable dilatancy parameter is developed. It is demonstrated that dilatancy affects the free expansion of concrete, the softening behavior under shear stresses and the response of passively confined elements. The model is based on a well-known plastic-damage model, which is modified by means of a dilatancy parameter that depends on the plastic-damage and stress states.
At the sectional level, a new model that introduces an efficient numerical technique is developed. The new model is based on a total interaction sectional model that reproduces the kinematic behavior of the cross-section by means of a two-component displacement field. One component of the displacements satisfies the traditional hypothesis of Euler-Bernoulli while the complementary field reproduces warping and distortion. This field enables the model to obtain the triaxial stress and strain tensors on each point of the cross-section domain. The complementary displacement field is obtained by considering the inter-fiber three-dimensional equilibrium. The displacement field is expressed by means of a set of b-spline functions predefined on the cross-section domain. Thus, a significant reduction on the degrees of freedom involved on the cross section state determination is obtained compared against a finite element solution. This makes the model suitable of its implementation at the element level.
Further, at the element level a force-based formulation is used. The model strictly satisfies the equilibrium between nodal and sectional forces. On each integration point of the elements, the higher order sectional model described earlier can be used to represent the sectional behavior. The models are implemented into an open-source collaborative finite element software focused on the nonlinear seismic analysis of structures.
The presented models are validated, both separately and jointly, by comparison of numerical results with experimental tests available in the literature. Validation includes a wide range of concrete strengths, reinforcing materials, section geometries and types and arrangements of reinforcements. Several loading conditions are simulated making emphasis on the ability of the model to represent different failure modes such as shear, torsion and coupled modes. Finally yet importantly, the simulation of a real full-scale bridge is done to test the capabilities of the proposed model.
