[D 2] Nevertheless, this type's most notable ancient vault is arguably the Treasury of Atreus,[D 3] an imposing tholos tomb in Mycenae, Greece, constructed circa 1250 BCE.
They were erected to facilitate transportation along the route connecting the prominent Mycenaean settlements of Mycenae, Argos, and Tiryns to the port of Palea Epidavros.
[D 4] In more recent times one may observe the employment of this architectural construction principle of an arch in the Etruscan walls of the city of Volterra, which dates from the 3rd or 2nd century BCE.
[3] It is widely accepted that the oldest known vaulted Roman structure is the Cloaca Maxima, a sewer constructed under the rule of Tarquinius Priscus around 600 BCE.
[5] The bridge was constructed by Marcus Aemilius Lepidus in 179 BCE and underwent numerous restorations, the most recent of which was conducted by Pope Gregory XIII in 1575.
One of the most ancient structures in Roman roadways is the Milvian Bridge,[7] constructed over the Tiber by the consul Marcus Aemilius Scaurus in 115 BCE.
Situated approximately three kilometers from Rome, where the Via Flaminia and the Via Cassia converge to traverse the river, the Milvian Bridge served as the obligatory gateway for those arriving from the north.
[16] In France, the Pont du Gard is a Roman aqueduct bridge comprising three levels, with a maximum height of 47.40 meters at its highest point.
It was probably constructed during the first half of the 1st century, serving to maintain the continuity of the Roman aqueduct that transported water from Uzès to Nîmes, a distance of 50 kilometers.
[P2 8] It is almost certain that the Chinese independently invented the arch, either before or after the Greeks, and that they constructed vaulted bridges at an early date, possibly even before the Romans.
[21] Following the decline of the Roman Empire, a period of approximately five centuries, or half of the millennium, was characterized by the dominance of the Middle Ages.
Originally constructed from wood, it was subsequently rebuilt in stone in 1345 by either Taddeo Gaddi or Neri di Fioravante [fr], depending on the source.
[19] In the West, between the 15th and 16th centuries, the architects of the renowned bridges in Florence, Venice, and other Italian cities drew inspiration from the regular forms of the past.
[33] The bridge facilitated passage between the Louvre Palace and the Abbey of Saint-Germain-des-Prés, which was situated adjacent to the monument erected in honor of Henri IV on the downstream point of the Île de la Cité.
The bridge was constructed using advanced architectural techniques and materials, enabling it to withstand centuries of conflict, except for the most recent one.
Common formulas were derived from observation and practice, with thicknesses at specific points, such as the crown, haunches, piers, or abutments, being determined based on the span of the bridge.
[37] Despite the absence of tangible practical outcomes, he elucidated two concepts that would prove instrumental a century later:[P1 1][M 1] In 1777, Jean-Rodolphe Perronet, the inaugural director of the National School of Bridges and Roads[38] and a distinguished builder, established the initial guidelines for calculating the thickness of vaults and piers.
While medieval bridges had previously been sufficient, the narrow, often-repaired structures with cramped roadways were no longer adequate for the demands of growing commercial exchanges.
In Spain, the Toledo Bridge, constructed between 1720 and 1732, is also a monumental work adorned with numerous Baroque sculptures, which contribute to its status as a notable architectural landmark.
[P3 4] The Seventeen-Arch Bridge, constructed during the reign of Emperor Qianlong, connects Nanhu Island to the eastern shore of the lake.
At the beginning of the 19th century, architects and engineers had amassed considerable practical experience in the construction of stone and wooden bridges.
In 1810, Louis-Charles Boistard [fr] demonstrated, following a series of experiments, that the failure of vaults was caused by the rotation of four blocks.
[42] In his lectures at the School of Bridges and Roads (1825), Navier introduced the concept of material elasticity and defined the "central third rule", which establishes a limit within which the pressure center line of the vault must remain.
[40] These results allowed Édouard Mery [fr] to publish in 1840[43] a method for verifying vaults that were used throughout the 19th century and are still occasionally used today.
[44][M 2] "Mery's diagram" is based on the principle that "the intrados and extrados form two limits which the pressure curve must never exceed, and when this happens, equilibrium is impossible".
In 1817, the Frenchman Louis Vicat discovered the principle of hydraulicity in lime, related to the proportion of clay and the firing temperature, and published his work without a patent.
The layout of the railroads could not follow the contours of the land due to the low gradients allowed, less than 10 mm per meter at the beginning, and the large radius curves required for vehicle stability.
[P1 6] In eastern Germany, the Göltzschtal Viaduct, spanning the Göltz River on the Regensburg-Leipzig line, is the largest masonry bridge ever built.
It can be made of rubble, ashlar, or brick, with the visible face generally flat, although some structures have moldings when specific ornamentation [fr] is desired.
The parapet consists of three parts: If the bridge has multiple spans, the adjacent vaults rest on a common support called a pier.