Thrust line analysis and the minimum thickness of pointed masonry arches

Abstract

Over the last few years, scholars have revisited the classical issue of identifying the limit equilibrium states of masonry arches. While the Couplet’s problem was rigorously solved by Serbian scholar Milutin Milankovitch more than a century ago, the minimum thickness of elliptical arches has been recently computed. However, albeit pointed masonry arches are very common in historic structures, particularly in Gothic architecture, their structural behaviour according to thrust line theory is not researched in sufficient detail. Therefore, the aim of this paper is to further develop the geometric formulation, i.e. macroscopic equilibrium analysis of a finite portion of an arch, used for semicircular and semielliptical arches, in order to compute the minimum thickness of pointed arches. Employing radial stereotomy, which concerns generic sections concurrent to the arch’s centre, the present paper derives a closed-form expression of the thrust line of pointed arches under self-weight. The paper concludes that, when the limit equilibrium state is attained, there are four admissible collapse modes with the precise order of the occurrence regarding eccentricity. Considering both incomplete and overcomplete arches, numerical calculations are conducted, resulting in the minimum thickness values of more than hundred arches having various eccentricity. In addition, the limit eccentricity corresponding to the arch having maximum use of its thickness is indicated and particularly treated. Finally, the correlation between eccentricity, embrace angle, and minimum thickness is graphically presented, enabling the clear distinction between the collapse modes.