The title of this chapter is that of a Handbook (Frost 1990) compiled by the Towers and Belfries Committee of the Central Council of Church Bell Ringers. The Handbook concentrates of course on matters related to bells, but it is also an invaluable source of information regarding the structure and maintenance of masonry towers. Naturally enough, it does not discuss the kind of large-scale disaster referred to in Chapter 2 – the overall collapse of towers such as those at Winchester, Gloucester or Worcester, or the hasty insertion of props at Wells. These disasters occurred within the soil-mechanics time scale for consolidation, of up to twenty years (although, as has been noted, some towers have survived for much longer periods before mysteriously collapsing). It seems evident that settlement of foundations leading to tilt may be a cause of potential danger for a tower; many do, in fact, survive the original high-risk period in which settlement occurs, and appear to survive at alarming angles of inclination (the eye is sensitive to very small deviations from the vertical). Perhaps the most famous example is the campanile of Pisa, but there are many others in Italy, particularly in Venice and in the islands of the lagoon.

Masonry is an assemblage of stones – or bricks, or indeed sun-dried mud (adobe) – classified for convenience with certain distinct labels, as Byzantine, Romanesque, Gothic, but recognized by engineers as having a common structural action. This action arises directly from the properties of the material.

It is prudent and convenient to regard a masonry building as a collection of dry stones (or bricks etc.), some squared and well fitted, some left unworked, and placed one on another to form a stable structure. Mortar may have been used to fill interstices, but this mortar will have been weak initially, and may have decayed with time – it cannot be assumed to add strength to the construction. Stability of the whole is assured, in fact, by the compaction under gravity of the various elements; a general state of compressive stress exists, but only feeble tensions can be resisted.

All this must have been well understood by medieval cathedral builders, although they would not have had numerical concepts of stress or of the strength of their material. A modern engineer would perhaps make calculations to relate these quantities. In this connexion reference to nineteenth-century practice in the design of great masonry arches is illuminating. An indirect parameter was used to express the strength of stone – the height to which a prismatic column might (theoretically) be built before crushing at its base due to its own weight.

The wall

The three basic assumptions about the behaviour of masonry – no tensile strength, infinite compressive strength, no slip of the stones – have effectively eliminated material properties from the discussion. The previous chapters have attempted the analysis of arches, domes and vaults from, so to speak, a somewhat distant viewpoint; it is the overall shape of these structures, rather than their detailed construction, which controls structural action. Such geometrical considerations are also paramount for the study of the flying buttress made at the end of this present chapter, but a closer view must be taken of, for example, the wall, if its action (and its pathology) are to be understood.

Some elementary geometry is of course involved even in the idealization of a wall as a flat-sided slab of uniform thickness. It seems obvious, for example, that the wall must not be too thin compared with its height and length, and this intuition can be supported easily by rational argument. A thin wall may be built vertically and remain upright under the action of its own weight, but it must have some reasonable margin of safety against settlement and accidental tilt of its foundations. The centre of gravity of a cross-section of the wall must not move outside the verticals drawn through the limits of its base, and a certain minimum ratio of thickness to height will give the required margin.

A dome is a rounded vault forming a roof over a large interior space (e.g. Hagia Sofia, c. AD 532 with a span of about 31 m; St Peter's Rome, c.1560—90, 42.5 m). The word in Italy (duomo) and Germany (Dom) has come to stand for the whole cathedral, and indeed the etymology is from the Latin domus, house (of God). The French use both dôme and coupole (cf. Italian cupola) for the vault; the English cupola is sometimes reserved for a very small domed roof, as for example on the lantern mounted on the eye of a dome proper, cf. the cross-section of St Paul's Cathedral shown in fig. 8.9.

The ‘rounded vault’ of the dome can take many forms. Perhaps the simplest of these is a shell of revolution, in which every horizontal section is circular; an egg in an egg-cup is a shell of this kind. The inner dome of St Paul's is roughly spherical, and has an open eye, while the main dome carrying the lantern is conical, but both are shells of revolution, as is the surface of the third lead-covered timber outer dome; all have circular horizontal sections.

‘The Stone Skeleton’ was published as an article in the International Journal of Solids and Structures in 1966. That paper explored the mode of action of masonry construction, using the principles of plastic design developed originally for steel frames. The principles were applied to the analysis of the structural system of the Gothic cathedral, and the flying buttress and the quadripartite vault were treated in some detail, together with a brief discussion of domes. The paper attempted, in part, to treat the main elements in masonry construction, but there were very large gaps in the study. Other papers followed, filling in some of the holes, on spires and fan vaults, for example, on a fuller discussion of domes, and on the mechanics of arches. Some of the analytical work was collected and published in book form: Equilibrium of shell structures, Oxford, 1977, and The masonry arch, Ellis Horwood, 1982.

This present book attempts a synthesis of these studies of masonry, and presents a view of structural action which, it is hoped, will be helpful to those who wish to understand how a particular stone building might behave. Numerical calculations are made when they are necessary for the exposition, but there is virtually no mathematics in the present text; the analytical background may be found in relevant papers quoted in the bibliography. In particular, some attention is paid to the pathology of the different structural forms, and this is, of course, relevant to the repair and maintenance of a building.

It is, perhaps, trivial to remark of Greek, Roman, Byzantine, Romanesque and Gothic buildings that some of them still exist. The observation has force, however, when placed in a structural context. A masonry structure — a cathedral from the High Gothic period, for example — may be viewed in many ways: from the liturgical aspect, or the cultural, the historical, or the aesthetic, all of which may give rise to disputes of one sort or another. There remains one viewpoint which seems to engender an unequivocal statement: the large masonry building is clearly a feat of structural engineering. Moreover, the mere survival of ancient buildings implies an extreme stability of their structure.

Minor failures have, of course, occurred, and there have been major catastrophes. The fact remains that two severe earthquakes only slightly damaged Hagia Sofia, and the bombardments of the Second World War often resulted in a medieval cathedral left standing in the ruins of a modern city. At a much less severe level of disturbance, the continual shifts and settlements of foundations experienced over the centuries seem to cause the masonry structure no real distress, although, as will be seen, there may be an initial high-risk period of about a generation after completion of the building. It is the intention of this book to explain this extraordinary stability. A discussion of the actual structural behaviour of masonry is necessarily involved, and some of the history of structural analysis will be touched on, since it may help to deepen understanding.