Three‐Dimensional Analytical Model of a Free‐Standing Square Rocking Column

A three‐dimensional analytical two‐degree‐of‐freedom (2DOF) model is developed to describe the bounded rocking response of free‐standing rigid square columns subjected to bidirectional seismic excitation. The formulation extends Housner's classical planar theory by deriving the full three‐dimensional equations of motion for a column constrained to rock only within its original footprint, so that it can be used to model a rocking bridge column. Energy dissipation is introduced exclusively through instantaneous, inelastic impacts occurring during transitions between edges and corners, assuming angular momentum conservation. Three distinct impact mechanisms are identified and incorporated into a numerical integration framework capable of capturing transitions between rest, edge rocking, and corner rocking. The resulting motion exhibits strong coupling between orthogonal rotations and energy transfer between rocking directions during impacts. A comparative statistical study involving 176 near‐fault, pulse‐like ground motions demonstrates that square columns dissipate more energy and are, thus, more stable than their cylindrical counterparts, indicating superior inherent stability and enhanced impact‐induced damping capacity.