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 little 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 (below) in Yorkshire is a rare example of an English Norman (Romanesque) arched bridge. Mostly one has to look for moat bridges. Town Bridge (Chantry Bridge) in Bradford on Avon may be an exception. There are no known Romanesque bridges in Scotland.
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. 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.
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.
The early 15th century Renaissance saw a return to semicircular, Tudor, elliptical and segmental arches. This change arrived a little later in Scotland. Long before Robert Hooke’s time, segmental arches had been used for bridges. This shape has a flattened profile akin to a small segment of a circle. Again, a parabola or a catenary can be drawn within the voussoirs, particularly if they are wide enough, but the angle of force lines in such a flattened arch always implies the need for substantial abutments.
In terms of structural equilibrium there may be less difference than might be expected, between a segmental and a semicircular arch. See previous section.