MAKRIS, NICOS1; ALEXAKIS, HARIS2

1) Professor of Structural Engineering and Applied Mechanics, Department of Civil Engineering, University of Patras, GR-26500 Greece. E-mail: nmakris@upatras.gr

2) Postdoctoral researcher, Department of Civil Engineering, University of Patras, GR-26500 Greece. E-mail: alexakis@upatras.gr

More than a century ago Milankovitch presented a remarkable formulation for the thrust-line of arches that do not sustain tension, and by taking radial cuts he published for the first time the correct and complete solution for the theoretical minimum thickness, t, of a semicircular arch with radius, R. This paper shows that Milankovitch’s solution, t/R=0.1075, is not unique and that it depends on the stereotomy exercised. The adoption of vertical cuts yields a neighbouring thrust-line and a different, slightly higher value for the minimum thickness (t/R=0.1095). This result has been obtained with a geometric and a variational formulation. The paper discusses in depth the effect of the stereotomy on the profile of the thrust-line; while, the variational formulation advanced in this work emerges as a powerful analysis tool since is liberated from the concept of the thrust-line and is employed to compute the minimum thickness of elliptical arches.

Keywords: Stone arches, limit equilibrium analysis, line of resistance, catenary curve, variational formulation