Arch shapes on early bridges

In 1675 Robert Hooke provided the principles of catenary theory but the practice of arch building had long preceded him.  The Etruscans, the Romans, the Persians and the Chinese Dynasties all built masonry arched bridges. Many Roman bridges remain intact in Europe, today, but in Scotland nothing remains.  In Europe, arch building became a lost art for 600 years but re-emerged in the 11th century. The Romanesque semicircular arch then became the fundamental solution for ecclesiastical architecture as well as for bridges; a semi-circle had been the Roman mainstay for arches, and it was this that they copied. Some Romanesque bridges can be seen in Europe, but in this period most were made of wood and some of those in masonry may have had a late Roman origin.  Fountains Abbey Guesthouse bridge  in Yorkshire is a rare example of an English  Norman (Romanesque) arched bridge.   Exeter Bridge (below) was recently uncovered. There are no Norman bridges in Scotland.    

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Romanesque architecture  gave way to Gothic in the 12th and 13th centuries. (The oldest known pointed arch is in ancient Byzantium and dates from the 6th century.)   An ogive or Gothic arch has a geometry which is closer in shape to a catenary/parabola.  Consequently, cathedral arches and rib-vaults could be given slimline voussoirs, and  bridges built in the gothic  shape could be slimmer yet strong. 

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 There is an odd additional stratagem here:  a weight on the tip (crown) of the arch alters the geometry of the thrust line even further,  bringing it more into line with an ogive shape, which confers stability.  This additional stablity was known about in medieval times, but seldom seen on bridges.   However, below is the Puente del Diablo near Barcelona, a 13th century 37 m arch on the River Liogregat . Note the remarkably slim voussoirs. 

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Huge Gothic domes, such as that of Florence Cathedral (1436), were often given large heavy lanterns or bell towers on the top, a manoeuvre which achieves the same end.    

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Not all medieval bridge arches from this period are of ogive shape; there are some semicircular and segmental arches.   Segmental arches have a flattened profile akin to a small segment of a  circle and a  parabola or a catenary can still be drawn within the voussoirs, particularly if they are wide enough.  Interestingly, the flatter the arch,  the more a parabola coincides with circle-segment.  This was clearly known a long time ago,  as in France and  Italy  there are many medieval segmental bridges. In Scotland, there are only a few.   

 The Renaissance brought an end to the building of pointed bridge arches. Rounded arches predominated thereafter.      

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Dec. 2012                                      Site last updated  November 2017