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I am trying to understand if ancient Romans understood and used the catenary test when building bridges. I cannot find anything online

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    $\begingroup$ Could they build catenary structures? Clearly yes. What, precisely, do you mean by 'catenary test' here? $\endgroup$
    – Jon Custer
    Commented Mar 15, 2023 at 13:54
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    $\begingroup$ The Romans filled their spandrels, so a catenary would not be an optimal load-bearing shape! Even if the word is latin, it is a neologism often attributed to Thomas Jefferson. $\endgroup$ Commented Mar 15, 2023 at 16:33
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    $\begingroup$ I mean that an arch passed the catenary test (and hence an arch can hold its own weight) if a chain can hang entirely inside the profile of that arch $\endgroup$ Commented Mar 16, 2023 at 14:16
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    $\begingroup$ I concur with the comment by Cosmas Zachos. The catenary shape is valid only for the case where the weight per unit of length (length parallel to the curve) is uniform. When the spandrels are filled the sides of the arch are subject to a larger load than the center. For an arch with a span to height ratio of 2:1, with filled spandrels: in that case a semi-circular profile is certainly superior, and quite close to optimal. Example of roman ingenuity: in the construction of the Pantheon dome: for the upper dome levels pumice was used as aggregate in the concrete; they were working the density $\endgroup$
    – Cleonis
    Commented Jan 1 at 13:25

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Not in any explicit way. The observation that compression forces in an arch invert tension forces in a cable, which led to the "catenary test" for arch shapes, was only made by Hooke c. 1670. According to Earliest Known Uses, the name linea catenaria for the hanging chain curve first appears in Huygens's 1690 letter to Leibniz, who then popularized it in a 1691 Acta Eruditorum paper.

Nonetheless, Huerta in Oval Domes suggests that there was rudimentary practical understanding, gained by trial and error, of what the "catenary test" will later spell out :

"In the first two millennia the builders experimented with several types of arches and vaults and there is no direct line of progress towards the voussoir arch with radial joints, which is our conceptual model... The first vaults were quite small, with spans of only about one or two meters, just enough to cover the tomb. This size favoured experimentation: the vault, if not of an adequate form, will distort and the observation of the movements gave the builders a “feeling” for the more adequate forms...

To an architect or engineer with some experience in masonry structures it will be evident that the vault at the bottom right side is the safest, adopting an oval form which will amply contain the trajectory of compressions (the line of thrust or inverted catenary) within the arch. Choisy [1904] was the first to point this fact as the origin of the oval arches. [...] If all the voussoirs of the arch are the same size the line of thrust will have very nearly the form of an inverted catenary. But, it is not necessary that the arch have the form of catenary: it suffices that the catenary can be contained within the masonry."

So even to the extent that line of thrust considerations were understood they were not necessarily reflected by the shape of arches directly. In particular, Romans disfavored oval shapes close to the catenary, preferring circular arches and domes for aesthetic reasons:

"It appears that the Romans did not built oval domes: the central symmetry was considered a requisite and even in the experimentation of the domes in Hadrian’s Villa all the forms present a centralized character. Some exceptions may be found in the apses of thermae, and it is usually presumed that the octagon of the church of St. Gereon in Cologne rests on the oval foundations of a previous Roman building. Choisy discovered that in the bridge of Narni, the central span of the inclined road was adapted by using an arch formed from two quarter-circles of different radii. Perhaps more examples can be found, but it appears that the Romans used the oval form for arches and domes only in exceptional cases."

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  • $\begingroup$ Thank you very much @Conifold $\endgroup$ Commented Mar 17, 2023 at 6:55

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