Structural study of masonry buttresses: the stepped form

The stability of masonry buttresses under horizontal forces is of paramount importance for the safety of vaulted structures, and yet has been the subject of limited studies. In particular, buttresses of non-rectangular geometries such as trapezoidal and stepped buttresses, which are typical of Gothic architecture, have not been sufficiently investigated. This study follows on from a companion paper devoted to masonry with trapezoidal buttresses. Based on similar modelling approaches and assumptions, the present paper aims to predict the failure of stepped buttresses. The analytical solution, obtained by treating masonry as a continuum with no tension resistance and accounting for the formation of a fracture prior to collapse, is compared with the predictions of the discrete element method. The numerical approach considers masonry as an assemblage of rigid blocks with no-tension frictional joints and is based on time-stepping integration of the equations of motion of the individual blocks. The relative efficiency of different buttress shapes for a given total volume is also compared, and an example buttress is used as a benchmark to demonstrate the pratical applicability of the proposed models.