The analysis of masonry architecture: a historical approach.(Invited Review Paper)

Abstract: Traditional unreinforced masonry architecture has disappeared from new building activity in the western world. Nevertheless, the architectural heritage of masonry must be preserved, and this involves structural analysis. The classical theory of structures does not apply well to such heterogeneous structures with unknown boundary conditions. Nevertheless, there exists a theory of masonry structures based in simple assumptions about the material: good compressive strength, almost no tensile strength and a constructive care to avoid sliding failure. The theory was born at the end of the 17th Century, developed during the 18th and was applied in the 19th Century. It was abandoned and eventually forgotten at the beginning of the 20th Century. After half a century, in the 1960s, Heyman incorporated the old theory within the frame of modern limit analysis with its implicit treasure of critical observation and experience. The safe theorem permits using equilibrium equations and simple material statements cited. No affirmation about boundary conditions, impossible to know and essentially changing, is made (other than the usual about strength and small displacements). In the first part of the paper, an outline of the old theory is summarised and discussed. In the second part, the main ideas and concepts of limit analysis of masonry structures are discussed.

Keywords: Arches, Architectural heritage, Architectural history, Building materials, Domes, Elastic analysis, Finite element method, Graphical equilibrium analysis, History, Limit analysis, Masonry architecture, Masonry structures, Safety, Stability, Statics, Structural behaviour, Theory of structures, Vaults

Introduction

Masonry was the main building material in the western world until the beginning of the 20th Century. Masonry vaults are no longer built, but we have to preserve our architectural heritage. In many cases, it is a matter of cosmetic maintenance. However, sometimes, the building presents, or seems to present, structural problems. It may happen, also, that the loads have increased and the safety of the structure should be checked for the new use. In these last situations, a structural analysis is needed.

The problem is that masonry structures are essentially different from modern structures of steel, reinforced concrete or laminated wood. The usual structural theory of framed, trussed or shell structures made of reinforced concrete or steel is of no use to study masonry architecture. In Figure 1a, a constructive section of a medieval building is represented. In the first place, no such linear elements as columns and beams are seen. The structural elements are two- or three-dimensional, but not linear, as in frame or truss theories, or thin as in the usual shell theory.

Let us consider now the material. Though from the outside, regular ashlar masonry would be seen, the internal structure is, in fact, much more irregular and complex. The wall, for example, consists of two skins of ashlar masonry and a nucleus made of rubble with some kind of mortar. The masonry material is, in itself, a structure. How to apply, then, the usual material assumptions: continuity, isotropy, definite elastic or non-elastic properties? Figure 1b shows a few of the usual masonry types. If we try to define, for example, an elastic modulus: Where? At the outer skin, in the inside skin, at the nucleus? Besides, it is a fact that masonry buildings present cracks, and these cracks run often through the whole thickness of walls and vaults. They may have been closed at the surface (by some plasterwork), but the crack remain inside, hidden and unknown. Finally, speaking of boundary conditions, it is well known that the foundations of most masonry buildings are superficial and present noticeable settlements: they are far from the rigid foundations of the structural textbooks. They are unknown, and essentially unknowable, as slight changes of the soil conditions, the sudden action of loads (e.g., storms or earthquakes) could alter the response to the loads.

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