Keywords: masonry dome, cultural heritage, numerical modelling, static assessment, dynamic assessment, non-linear analysis.

This chapter approaches the problem of safety evaluation of an emblematic monument: the Brunelleschi's dome of Santa Maria del Fiore in Florence (Italy) which was declared part of the UNESCO World-Wide Heritage in late 1982 together with the city centre. The dome dates back to the fourteenth century. The problem is a topical engineering concern as in modern societies the preservation of the cultural heritage is an important issue both for their economic and social value. In addition to their historical interest, cultural heritage significantly contributes to the economy in a context where tourism becomes one of the major industries. Therefore preserving historical constructions is not only a cultural or scientific requirement but also an economic and developmental demand.

With this aim, in this chapter, the safety and vulnerability of Brunelleschi's dome is considered by the careful use of numerical analyses as an example of practical engineering problems in the field of historical construction. After a short description of both the main geometric characteristics and the relevant constructive aspects designed by Brunelleschi, the present cracking pattern on the dome is sketched. After that the latest results obtained concerning the identification of the static and dynamic behaviour of the dome is reported, paying specific attention to the causes and the development of the cracks. Using the finite element (FE) technique three-dimensional non-linear analyses have been performed and a new improved numerical model (that has been realised taking into account the results of a three-dimensional numerical survey of the whole dome) is described. The non-linear behaviour of masonry material has been considered through proper constitutive assumptions. The basic concepts of the assessment methodology considered in the present study is the achievement of an adequate knowledge of the structural static behaviour (and materials for that matter) that are essential for seismic evaluation purposes.

The final aim of the present study is to offer a contribution to the issue of modelling and analysis of monumental masonry buildings, stressing the role of structural engineering in the conservation of historical structures. Thus in this chapter the careful use of numerical analyses to face practical engineering problems in the field of historic constructions is presented through discussing the safety and vulnerability of Brunelleschi's dome.

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