Keywords: masonry, vault, cantilever stairs, roman stairs, tension stresses, equilibrium paths, reinforcement.

The study of masonry buildings is a complex field because any element of the fabric has an own behaviour, deeply influenced, for example, by the shape of the structure, different building materials or any discontinuity, which usually represents a constraint altering the specific response of the single element and acting a series of chain reactions. This study belongs to a larger research project [1,2,3] using both a theoretical approach and some laboratory tests for the optimal theoretical solution of masonry buildings.

This paper provides details of an analysis of the distribution of the stress field and the equilibrium path that is developed for a particular type of masonry stairway such as the "half-barrel" or "cantilever" or "roman" stairways. This typology is largely found in Italian ancient masonry buildings and for their complexity [4] these structures, or similar, are usually studied in a three-dimensions with the support of complex software.

Nevertheless professional practice demands clear and sharp models for structural analysis and calculation, and simplified approaches often help the interpretation of the structural behaviour and suggest procedures for the decision and design in the emergency or in the common refurbishment of a masonry fabric. So in this paper a simplified approach is proposed verifying the equilibrium mechanism of the vaulted stairways by means of a classic "beam model". Starting with the condition that the masonry is not resistant to positive stress and that a no-tension (NT) model [5] can be assumed for the material, a preliminary study to establish knowledge concerning the resistant mechanism is established. Then the stress fields which are equilibrated and compatible with the resistant abilities of the masonry material, such as self weight and live loads, are searched for a solution. In the final part of the paper a suggestion for planning the optimal application of the reinforcement is made on the basis of the analysis.

1

A. Baratta, I. Corbi, "On the Analysis of Regular Masonry Walls", In: Proceedings of the 7th International Masonry Conference, paper 41, 1-8, Westminster, UK, 30/10-1/11/2006.

2

A. Baratta, I. Corbi, O. Corbi, "Stress analysis of masonry structures: arches, walls and vaults", In D'Ayala, Fodde, (Editors), "Structural analysis of historical construction", Balkema Book, CRC Press, Taylor & Francis Group, London, 321-329, 2008.

3

A. Baratta, I. Corbi, O. Corbi, D. Rinaldis, "Experimental survey response of masonry models", In D'Ayala, Fodde, (Editors), "Structural analysis of historical construction", Balkema Book, CRC Press, Taylor & Francis Group, London, 799-807, 2008.

4

J. Heyman, "The mechanics of masonry stairs", Transactions on the Built Environment, 15, 1995.

5

A. Baratta, O. Corbi, "On Variational Approaches in NRT Continua", Intern. Journal of Solids and Structures, 42, 5307-5321, 2005.

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