It is not certain whether catenary theory was known or understood by the early master masons, but it appears that the concept was known of in China. In Europe, early-medieval writing was in Latin and largely the preserve of clerics who seldom had an interest in engineering, so on the whole there is very poor documentation on the practical detail of construction. However, in 15th century Italy, Brunelleschi appeared to have used catenary concepts in his building of the Cathedral of Santa Maria Fiore, and Renaissance architects certainly applied principles of geometrical equilibrium. There were some prescriptions or rules of thumb and occasionally some complex formulae, empirically recommending maximum ratio size for semicircular arches. Palladio (Venice c.1560) and Serlio (Bologna c.1540) both recorded the average arch thickness and span of the Roman antiquities. The most prolific author and architect was Leon Battista Alberti (Genoa c.1450): his De Re Aedificatoria was the first printed book on architecture. On the matter of bridges he recommended that pier width should be one quarter of span and that voussoir width should be one fiftheenth of span. He also recognised that segmental arches were important, and for these he proposed a voussoir crown thickness of one fifth of the intrados radius. In the light of modern engineering design, informed by plastic theory and limit analysis, these ancient empirical solutions may seem simplistic, yet Roman arches are still standing today and Medieval cathedrals remain safe despite their complexity of vaults and flying buttresses.
In medieval times the masons were builders, masters of work, architects and engineers, rolled into one. Master-masons were the consultants of the period: prosperous middle class professionals in charge of other craftsmen with support from qualified journeyman masons (day-wage or journée) and apprentices. The Master Mason was the architect and master of works. Well-known names were in great demand, even internationally. Their journeymen colleagues were divided into quarrymen who extracted the stone, sawyers who cut the fairly undressed blocks, bankers who worked on site dressing the stone and sizing it, carvers who applied art and design and fixers who raised the blocks and put them in place. Sandsone and granite blocks were extracted from the quarry in dimensions which matched the natural bedded layers. Bonfires were applied to expand the rock. Crowbars and wedges were used. The finer ashlar blocks were then cut with saws sprinkled with a mixture of iron filings and sand. These were 'sounded' or lightly struck with a hammer; if a stone rang like a bell it was good; if a dull thud, it was rejected. Rubble blocks were roughly dressed by hammer and often squared. Ashlar was usually reserved for the voussoirs and rubble for the spandrels and abutments, though this was not always the case. Mortar was made from quicklime or slaked lime and sand which took some time to set as it slowly turned back into calcium carbonate. The speed at which it would ‘go off’ or set was determined by the amount of impurity; a faster set was needed in the cold Scottish climate, particularly for pointing. However, for pointing ashlar, lime putty ( very pure hydrated lime) was mixed with whitening( chalk) , linseed oil and sometimes horsehair.
Independent designer architects did not appear until around 1700. In England, Christopher Wren (1670s) may be thought of as the first independent architect. He had never worked on a building site and tended to keep his hands clean. The title of Master Mason changed to Master of Works.
In 1716 Henri Gautier, a french doctor, mathematician and architect wrote the first book on the construction of bridges. His Traité de Ponts addressed all aspects of design, choice of site, construction and contemporary regulations. He reported on the great 17th Century Italian masters and using examples both wooden and masonry, provided operational instructions for the size and shape of piers, cutwaters, arches, spandrels and parapets. His primary planning points were as follows-
- Choose the spot on the river where it is shallowest, where the bottom is firm and even.
- Avoid turbulent water and rapids.
- Avoid sand and gravel because these materials are easily carried away by the violence of big water which alter the bed of the river and damages the foundations of the piers often causing ruin of bridges
- The run of water should be straight without elbows or bends because these deviations risk destruction by the force of current isolating the piers. Alternatively detritus ( ordures), carried by the river, will gather at the piers obstructing the mouth of the arches.
- Even numbers of piers so that there is an arch in the middle, where normally you find the most flow, and it also makes the bridge more balanced and nicer to look at
- Base it in the season of the year when the river is lowest, like Autumn.
- If it is on rock or solid ground you don’t have to dig too much but if its on sand or pebbles it is better to remove these until you find a solid base, or if that is too difficult, dig out as much as you can and use piles for the rest.
- Piers must not occupy less than one sixth of the width of the river, nor more than one quarter of the width of an arch
- They should be of good blocks of stone linked by crampons of iron, by which this means of enchainment they will function as one large stone
- Normally one should build advances or sallies ( cutwaters ) at right angles around the piers to better split the water and resist the damage of trees and other things the river carries when it is in spate.
- The arches must be made of strong, long stones, well jointed, the strongest ones being right in the centre because these carry the pressure from one to another, entirely to the piers.
An interesting perspective is that in 1716 Gautier devotes as many pages to wooden bridges as he does to masonry.
Many of these principles were later endorsed by Charles Hutton, in his very mathematical treatise, The Principles of Stone Bridges, published in 1772.
Even a simple semi-circular voussoir arch cannot be built without faux-works or centering, because the structure will not stand up until the keystone is in place at the top. Temporary centering structures were made of wood and the carpenters often erected, dismantled and re-erected the same centering on different rings of the arch, across the barrel, until each keystone was installed (left). More frequently, an entire arch was constructed on wood. Hutton notes that timber centering was a significant part of the cost and that the same profile could only be used if all the arches were the same size. Hence variable sized arches were rare and expensive.
Medieval builders sometimes avoided the need for centering by using a weight and tie system as shown left.
It was always known that abutments had to be constructed in solid anchored masonry; frequently ashlar was used and sometimes short wooden piles were driven into the foundation layer in advance of the masonry.
The construction of multi-arch segmental bridges posed a particular problem. Here, each arch provides the lateral resistance buttressing for its immediate neighbour, but the obvious implication is that false-work centering is required for the entire structure, all at the same time, to avoid complete collapse. Once completed, however, the advantage of low flat segmental arches lies in reduced height for a given span, so that fewer piers are needed, implying less risk of being washed away by floodwaters. There is also more flexibility and room for diversity with a slimmer more elegant profile and a clear advantage of less steep gradients on the approach. The disadvantage lies in that very interdependence; if flood waters engulf these flatter arches they may well all collapse at the same time.
Multispan bridges had always presented the extra challenge of constructing piers in mid-stream. Gautier discusses this in broad principles. Ruddock provides a modern detailed analysis. When possible a rock foundation was chosen and a site without tidal range was preferred. A small tidal range might permit the Roman approach of constructing a wooden cofferdam on the river bed (Old Scots: bulwark. Old French: bâtardeau) In this case, a gin and ram was employed to drive piles into the mud, adjacent to each other, until a full semi-wartertight circle was completed, perhaps 50ft. in diameter; then the central pool was emptied by chains of men with ladders and scoops. A wider tidal range usually required starlings: these were artificial islands. The construction was similar to a cofferdam, but piles were driven into the river bed and a chamber was constructed; rubble was then poured in to the chamber on each receding tide. The stone piers were built on top of the starling. This arrangement was more commonly seen below English bridges and was clearly recorded at Berwick. The French called this an encaissement and filled it with a crude concrete mix. A more common approach, seen more often in Scotland, and also useful for a significant tidal height, was to sink a large wooden frame or brander made up of longditudinal planks. This frame would would be filled directly with rubble and sunk on the required spot. In this way a different form of starling was created which had no vertical piles. The French called it a 'crêche’, the English, a ‘ grating’. Hutton ’s late 18th century glossary describes a Caisson, not as a cofferdam, as would be expected, but as a wooden boat on which the pier was constructed in ashlar, only to be be sunk when it reached low-tide level height. This appears to be a later version of a grating.
Finally, Gautier described one further approach: that of diverting the whole river while foundations were being built. He tells us that Trajan employed this approach on his famous bridge over the Danube in 105AD. This may have been less of a last resort than one might think; Hughes (1839) describes a variation suitable for a meandering river on a lowland basin: the bridge would be built on dry land in advance of a permanent diversion of the river, as shown below. There are no known examples in Scotland but this may be because of the absence of records.
Multispan bridges need piers with triangular cutwaters facing the current, to provide the best protection against scouring (undermining of the foundations by the current). In the 15th century Alberti pointed out that these were just as important on the downstream side. In earlier times ‘framing and setting’ of short piles overlaid with masonry formed a defence which was installed in advance of the pier. This divided the current and was more disposable and renewable. The single most important element of maintenance was the constant attention to the risk of scouring.
On top of the piers, the centering for all the arches would then be built, and this would be followed by the voussoir arches in solid dressed masonry. If ribs were used these were almost always in ashlar. Puddled clay might be used as a waterproofing over the top (extrados) of the arch. Sometimes a second order of voussoirs was built, often called a countercourse. The spandrels were last to be constructed, with infill rubble to provide a plane for the cobbled surface. Parapets were an optional extra, sometimes deliberately omitted: for example, the old packhorse bridges required that nothing should impede the large panniers on each side of the horse.
It is now known that most bridge arches experienced some outward shift (spreading) of the abutments, probably when the centering was removed. This minor settlement caused cracks in the arch in three places, usually at the crown and at both haunches. An arch structure is no less stable because of these hinges but any deterioration leading to a fourth hinge would be unsustainable. This three-hinged state is so common that it can be considered a natural state.
Jean Randolph Perronnet was the most eminent late 19th century bridge builder, and the architect of the huge segmental Paris Pont de Neuilly in 1783. He and his contemporaries were very critical of medieval engineering but their criticism was misplaced and lacked perspective. Many medieval structures have remained upright for 400 years and many more were destroyed in the 19th century, not because they were at risk, but only because they were too narrow for increasing traffic. These old bridges frequently spanned wide, deep, fast flowing rivers with frequent flooding. Their longevity was largely a function of repair to the foundations: constant attention to starlings or branders, to avoid scouring and regular inspection of abutments which are always at risk of displacement. However, some design features were pivotal to this success. Segmental arches with their lower profile, have to be built with a very high standard of masonry, if they are to survive the years; however, semicircular and Gothic arches create less dependence between arches so that the whole structure can survive the collapse of a single arch; also they have more height, ensuring that the river banks will burst before water levels reach the crown, an event which is frequently fatal. Many old bridges have flood arches on dry land which also helps. These design features have been incorporated repeatedly, over 2000 years. That, itself, is a recommendation.
Today these old masonry arch bridges are often expected to carry modern traffic. Many are from the 17th and 18th centuries, and indeed eight of the pre-1600 bridges still remain on the Scottish road network . In all cases, the implied live loads are far beyond the expectations of the original builders. Since the 18th century, engineers have attempted to answer questions about the safety of existing bridges and about their carrying capacity. Hooke developed catenary theory in the late 17th century. Danyzy’s elegant experiments in 1732 identified a hinging failure leading to collapse. Castigliano introduced non-linear elastic stress analysis in the later 19th century, and Pippard's elastic method in the 1930's was further developed into the MEXE system, which has been in general use since the 1940s; it is thought to overestimate the carrying capacity of short spans but underestimate it for longer arches. Heyman, in the 1970s introduced plastic (as opposed to elastic) limit analysis systems which are deployed extensively in computer programs. All of these systems are to some degree underpinned by line of thrust theory and computations around expected end-point 'hinge' failures of the old arches. This is not the only approach; recently the important strengthening role played by the infill has led to the development of some new modelling strategies. Today, 3D nonlinear finite element analysis (FEA) has become a routine computer assisted, graphic approach to stresses and displacements.