Engineering Failure Analysis 44 (2014) 315–337 Contents lists available at ScienceDirect Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal Resisting system and failure modes of masonry domes Paolo Foraboschi Dipartimento Architettura Costruzione Conservazione, Università IUAV di Venezia, Venice, Italy article info abstract Article history: The research synthesized in this paper focused on ultimate strength, structural safety Received 25 October 2013 assessment, and collapse of masonry domes. Activity was directed at analyzing the Received in revised form 1 May 2014 relationships between safety factor and geometry, and carrying out research targeted at Accepted 6 May 2014 reducing the incidence and severity of structural failures in cultural buildings. This paper Available online 23 May 2014 shows that the resisting system of a masonry dome is not the two-dimensional shell, but a one-dimensional mechanism that derives from the splitting of the shell and drum. Keywords: The resisting system, whose geometry depends on the dome shape and brick or stone pat- Brunelleschi’s dome tern, may include the lantern and/or the masonry constructions around the drum. Dome’s failure Force-resisting system Well-known domes taken from architectural cultural heritage are used to exemplify the Palladio’s dome pivotal role of geometry and construction techniques in providing ultimate strength. These Vasari’s dome examples also show the importance of considering the architectural design of the time, in structural analyses. The results found in the paper suggest how to provide masonry domes with adequate safety, using the minimal level of structural intervention; in particular, without altering the way the building reacts to applied loads. Hence, the paper helps understand how to reduce the amount of structural work, which, in turn, guarantees conservation and resto- ration, as well as safeguarding. The conclusions are devoted to analyzing which observations are valid for seismic assessment and how the other observations have to be modified for seismic actions. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction This paper is devoted to masonry domes, with special reference to those of buildings deemed important to the culture— especially history and architecture—of an area, i.e. cultural buildings and architectural heritage. In order to take advantage of architectural heritage, every building must undergo safety assessment, though cultural buildings have survived for centuries. In fact, on one hand masonry degradation due to aging has marginal structural effects, but on the other hand a building may have suffered from structural damage [1–5] (earthquakes [6–13], overloadings [14–18], soil or foundation failure [2,6,7,11,14,19]). Moreover, safety demand is higher than in the past, and longevity does not ensure that safety of the building complies with modern codes [1,3,6–8,10,19,20]. Taking advantage of architectural heritage also requires some cultural buildings to undergo change of occupancy or remodeling, because the modern use of historical buildings is different from the original use. These two needs must satisfy the requirements of safeguarding, renovation, and conservation, which however are in conflict with each other. E-mail address: [email protected] http://dx.doi.org/10.1016/j.engfailanal.2014.05.005 1350-6307/Ó 2014 Elsevier Ltd. All rights reserved. 316 P. Foraboschi / Engineering Failure Analysis 44 (2014) 315–337 Safeguarding, which consists of protecting human lives and cultural heritage, aims at prolonging the life of historical con- structions to the utmost. Thus, when structural safety results to be inadequate, safeguarding calls for a structural interven- tion [11,15,20–23]. Renovation, which consists of modifying the building or part thereof, aims at meeting the present occupants’ needs. Thus, when the original architecture is not compatible with the present use, renovation calls for an architectural intervention [5,16,18]. Conservation, which consists of preserving the cultural aspects of the architectural heritage, aims at retaining authenticity of buildings’ architectural identity. Thus, conservation calls for interventions that do not alter the building or part thereof, i.e. that guarantee integrity. Integrity includes those visual aspects and physical elements that make up the appearance of a building, and that are sig- nificant to its cultural value. In particular, integrity includes the overall shape of the building, its materials, decorative details, interior spaces, and features, as well as the various aspects of its site and environment (character-defining features). Nevertheless, integrity is not limited to only this, but it also includes the structure and craftsmanship; to maintain the original structural behavior of the building and the historical construction technique is mandatory for guaranteeing integrity. Accordingly, integrity requires that, after the intervention, the way the building reacts to applied loads is equal to the way it reacted before the intervention. An intervention that modifies the original structural behavior alters the cultural building, compromising its integrity. After such an intervention, the building loses authenticity. Hence, making use of cultural heritage requires a balance between safeguarding, renovation, and conservation. Balance means that the cultural buildings have to be subjected only to interventions that are necessary to guarantee adequate safety and functionality (minimal intervention). Moreover, balance means that an intervention has not to modify the original struc- tural behavior. A balance is often not reached in Italy, which is regrettable since Italy has a huge number of cultural buildings of any sort, and is home to the greatest number of UNESCO World heritage sites. Despite the fact that only few countries in the world can boast a collection of cultural buildings as great in magnitude as Italy can, the Italian structural codes devoted to assessment of existing buildings [24,25] tend to unbalance the equilibrium in favor of safeguarding, which means that conservation is penalized and renovation is scarcely considered. 1.1. Aims and objectives of the research Highlighted, are the new requirements for existing masonry structures that have been adopted by a number of codes of the new generation [26], in particular in Italy [24,25]. These codes consider only the least common denominator in the structural behavior of masonry constructions, which is the load-carrying capacity due to the masses. In so doing, codes ignore architect’s initial design intentions and disregard specific construction techniques and devices, which lead to a substantial underestima- tion of the safety factor. These requirements are suitable for new masonry buildings, where steel bars and beams reinforce the masonry elements, but are inappropriate for cultural buildings, which are made of unreinforced masonry. Unacceptable cultural and economical penalty could be imposed to architectural heritage should assessment allow only for the load-carrying capacity provided by the masses. Thus, there is an acute need for a new code approach that allows architectural heritage to be assessed differently from new buildings. With reference to masonry domes, on one hand there are a great number of consolidated research findings (too many to be cited individually), but on the other hand they have not been incorporated into practice. Considering this, activity was directed at carrying out research that advances the state-of-the-practice on masonry domes. This paper provides material to identify and assess the actual resisting system of masonry domes, which is different from that recognized by the codes. 2. Review of the structural behavior of the masonry arch In masonry structures, typically, compression stresses are drastically lower than crushing strength [3,8,13–16,20,22, 27–30]. Thus, crushing is not a significant mode of failure for masonry structures, excluding columns made of poor masonry or subjected to moisture and salt crystallization. In masonry structures, tension stresses, including the principal stresses due to shear stresses, reach tension strength in numerous points. Thus, cracking of masonry is a common phenomenon [2,3,7,15,19,20,23,30–32]. Under the higher loads, thus, masonry is cracked and tension stresses are redundant. Therefore, the ultimate load is carried by compression and shear stres- ses only. It follows that failure occurs when a load causes the masonry structure to turn into an unstable mechanism, rather than when a load induces excessive stresses into the masonry. At the ultimate, a masonry structure behaves as an assemblage of rigid blocks, which passes from a stable to an unstable state as the load increases and surpasses the ultimate load. Thus, the load-carrying capacity of a masonry structure fundamen- tally depends on the points that the loads are applied to and on the shape of the mechanism that the structure converts into. Conversely, a masonry structure does not primarily fail due to a lack of material strength; however, compression strength and tension strength influence the load-carrying capacity. Masonry compression strength influences the distance of each rota- tion pin from the edge of the cross-section. In masonry arches and domes, however, this distance is almost always negligible. P. Foraboschi / Engineering Failure Analysis 44 (2014) 315–337 317 Masonry tension strength influences how the structure splits into blocks. For some types of