Inelastic force-based plastic hinge frame element type- infrmFBPH

This is the plastic-hinge counterpart to the infrmFB element, featuring a similar distributed inelasticity forced-based formulation, but concentrating such inelasticity within a fixed length of the element, as proposed by Scott and Fenves [2006].

The advantages of such formulation are not only a reduced analysis time (since fibre integration is carried out for the two member end sections only), but also a full control/calibration of the plastic hinge length (or spread of inelasticity), which allows the overcoming of localisation issues, as discussed e.g. in Calabrese et al. [2010].

The number of section fibres used in equilibrium computations carried out at the element's end sections needs to be defined. The ideal number of section fibres, sufficient to guarantee an adequate reproduction of the stress-strain distribution across the element's cross-section, varies with the shape and material characteristics of the latter, depending also on the degree of inelasticity to which the element will be forced to. As a crude rule of thumb, users may consider that single-material sections will usually be adequately represented by 100 fibres, whilst more complicated sections, subjected to high levels of inelasticity, will normally call for the employment of 200 fibres or more. However, and clearly, only a sensitivity study carried out by the user on a case-by-case basis can unequivocally establish the optimum number of section fibres.

In addition, the plastic hinge length needs also to be defined, with the user being referred to the literature [e.g. Scott and Fenves 2006, Papadrakakis 2008, Calabrese et al. 2010] for guidance.

In this element's dialog box it is also possible to define an element-specific damping, as opposed to the global damping described in here. To do so, users need simply to press the Damping button and then select the type of damping that better suits the element in question (users should refer to the Damping menu for a discussion on the different types of damping available and hints on which might the better options). Users are reminded also that damping defined at element level takes precedence over global damping, that is, the "globally-computed" damping matrix coefficients that are associated to the degrees-of-freedom of a given element will be replaced by coefficients that will have been calculated through the multiplication of the mass matrix of the element by a mass-proportional parameter, or through the multiplication of the element stiffness matrix by a stiffness-proportional parameter, or through the calculation of an element damping Rayleigh matrix.

Similarly to infrmFB, changes in reinforcement details can be achieved with the use of a single infrmFBPH element per member, when multiple sections have been defined. It is noted that these sections may differ only in the reinforcement (i.e. section type, dimensions and materials have to be the same).

Note: If Rayleigh damping is defined at element level, using varied coefficients from one element to the other, or with respect to those employed in the global damping settings, then non-classical Rayleigh damping is being modelled, classing Rayleigh damping requires uniform damping definition.

Local Axes and Output Notation