Sectional response - eesd-epfl/OpenSees GitHub Wiki
From lumped rotations at the rotational interfaces, the element calculates smeared deformations along a certain integration length for each section, which is a user input. In such way the flexural behaviour can be expressed in terms of a proper moment/curvature sectional model. The first section has, in addition, to account for the torsional response of the element, which is treated as linearly elastic.
The implementation of the macroelement allows for the use of any sectional model in Opensees, including fibre sections of generic shape making use of complex uniaxial material models at the local scale.
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However, in order to keep the simplicity of the macroelement formulation proposed in Penna et al. (2014), which makes use of an analytically integrated section modelling the rocking response, a specific sectional model was implemented. Such sectional model provides a direct relation between sectional deformations and forces of a rectangular section, without a numerical integration of a fibre response, postulating that the material has zero tensile strength and limited compressive strength.
The coupled response for in-plane and out-of-plane rocking is exact if no compressive damage occurs, resulting in a nonlinear elastic model. The sectional response in absence of compressive damage is obtained by analytical integration of the stresses in the compressed part of the section, possible as long as the material response is linear elastic in compression. A nonlinear correction term is applied to account in simplified manner for the crushing of the material. The material model that is postulated features no softening once the maximum strength is attained, infinite ductility and unloading to the origin.
The response under different angles of rotation of such section model is reported in the figure.
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As a consequence of the formulation of the element and of the applied sectional model, the response of the element when subjected to an out-of-plane constant acceleration profile approximates the rocking rigid-body solution, when P-Δ effects are accounted for.
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