Keywords: segmental systems, bridge systems, flexibility-based element, macro-element, numerical modelling, principle of virtual forces, quasi-static analysis.

Precast segmental concrete bridge construction is currently getting increasing attention both in the United States and around the world mainly due to the advantages that it offers over the more traditional cast-in-place techniques. These advantages include: (i) higher construction quality, since the segments are constructed in a shop under well-controlled quality conditions, and (ii) rapid construction, since as soon as the segments have been carried to the site, only assembly and preparation of the connections is required. Despite the apparent advantages of the segmental bridge construction method, concerns have arisen regarding the performance of such structural systems in regions of moderate to high seismicity. These concerns primarily refer to: (i) the effects of significant joint opening and/or sliding between adjacent segments during earthquake events on the global stability of the structural system and (ii) the reliability of existing analysis tools in predicting the dynamic response of segmental bridge systems under tri-axial earthquake shaking, which is necessary in the context of performance-based design.

Recognizing the need for efficient yet simple analysis tools, a 2-node flexibility-based element capable of capturing key characteristics of the seismic response of rocking columns or segments, such as joint opening and uplift, is formulated in this study. Section force versus deformation relationships are derived in an incremental form by assuming linear variation of the normal strain over the section, whereas the incremental form of the element force versus displacement relations is derived using the principle of virtual forces for two different benchmark elements free of rigid body modes. Considering that the proposed element incorporates only force interpolation shape functions, the element nodal resisting forces under given nodal displacements cannot be computed explicitly. A procedure is established based on a rigorous mathematical approach that makes use of compatibility and equilibrium conditions along the element, and provides the element nodal forces at prescribed nodal displacements as the solution of a system of nonlinear algebraic equations.

Numerical integration along the element length is conducted using Gauss-Lobatto quadrature, whereas integration over the section is conducted by discretizing the section into fibers/cells and adopting the midpoint integration rule.

After implementing the proposed element in a co-rotational framework to account for large displacements, the element is used to model the response of a rocking column under quasi-static monotonic lateral loading. According to the results obtained, the element appears to be able to capture the rocking and uplift response of the system.

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