| | Over the last few years, scholars have revisited the classical issue of
identifying the limit equilibrium states of the symmetrical masonry arches of different
shapes and corresponding theoretical minimum thickness, when subjected to self-weight.
More than century ago, Serbian scholar Milutin Milankovitch in his remarkable work set
the complete and correct theory of thrust line for the equilibrium of the arch of general
shape, and computed the minimum thickness of semicircular arch. Although pointed
arches, beside circular and elliptical, are very common in historic structures,
particularly in Gothic architecture, the lack of information about their structural
behaviour according to thrust line analysis is noticeable.
In this paper, the characteristic elements of analysis, as well as computation, such as
eccentricity, being the measure of pointedness, or the position of the application points
of relevant forces, which diverse the pointed from semicircular arches, have been
noticed. Furthermore, radial stereotomy, which assumes that joints between voussoirs
are concurrent to the centre of the arch, considering both incomplete and overcomplete
arches, is employed. Accordingly, the analytical expressions of the arch ring area and
its centroid are provided, and, after equilibrium i.e. static approach, expression for the
thrust line has been derived. Hence, it represents the basis for the various computational
analyses of the mechanical behaviour of Gothic masonry arches, as well as other types
of circular based arches and vaults containing the pointed crown. |
