Axially equilibrated displacement-based fibre beam element for bidirectional response modelling

Cavalieri, Francesco [European Centre for Training and Research in Earthquake Engineering (EUCENTRE), Italy] Calò, Mattia [Department of Civil Engineering and Architecture, University of Pavia, Italy] Saraiva Esteves Pacheco De Almeida, João [UCL] Pinho, Rui [Department of Civil Engineering and Architecture, University of Pavia,Italy]

Although distributed plasticity beam elements include formulations that verify a strict equilibrium of the axial forces along the element length, known as force-based (FB) approaches, the classical conventional displacement-based (DB) elements show advantages in simulating the response of some structural members. However, the latter do not verify strong equilibrium of the axial forces, but only the weak or integral form of equilibrium. To fix this issue, several authors recently proposed enhanced strain formulations that respect a strict equilibrium along the axial direction, obtained through iterations on the cross-sectional average strain in each section. Unfortunately, most research efforts on innovative beam formulations have been directed towards planar (2D) elements, instead of spatial (or 3D) formulations. This work thus presents the implementation of a 3D axially equilibrated DB (DB/ae) beam element in the finite element software OpenSees, as an enhancement of the classical displacement-based (DB/c) formulation. In order to present advantages and drawbacks of the proposed 3D DB/ae beam element, its numerical responses are compared with those obtained from the DB/c and FB elements, first with reference to an application example featuring bidirectional loading, and then taking the experimental data from one series of quasi-static bidirectional cyclic tests, related to two reinforced concrete (RC) thin walls, as benchmark.