Seismic response of stone masonry spires: Analytical modeling

Stone masonry spires are vulnerable to seismic loading. Computational methods are often used to predict the dynamic linear elastic response of masonry towers and spires, but this approach is only applicable until the first masonry joint begins to open, limiting the ability to predict collapse. In this paper, analytical modeling is used to investigate the uplift, rocking and collapse of stone spires. General equations for static equilibrium of the spire under lateral acceleration are first presented, and provide a reasonable lower bound for predicting collapse. The dynamic response is then considered through elastic modal analysis and rigid body rocking. Together, these methods are used to provide uplift curves and single impulse overturning collapse curves for a complete range of possible spire geometries. Results are used to evaluate the historic collapse of two specific stone spires.

► The seismic capacity of stone spires is dependent on both the elastic oscillation and rocking response.
► Elastic dynamics is used to predict loss of inter-stone contact during an earthquake.
► Rigid body rocking is used to quantify the overturning capacity of stone spires.
► Uplift and collapse curves are dimensionless and apply to all spire geometries.
► Results are used to evaluate the collapse of two specific stone spires.