The incursion of the paradigm of elasticity theory into the mechanical modelling of vaults has its origins in the history of construction as well as in the history of theory. The process of abandoning the thrust line theory and of reinterpreting the vault into an elastic curved bar took place in the 19th century against the background of the rise of wrought iron girder construction. An initial culmination of this development was the introduction of wrought iron into the construction of bridges and halls, starting in the mid-1800s. The transition in practice from cast to wrought iron made it easier to accept elasticity theory in practical design. The lag in experimental research became evident. German development in the 1860s was influenced considerably by the work of Navier, Bresse and others. Thus Bendel and Winkler after him applied the theory of elastic arches to the static analysis of the bridge over the Rhine at Koblenz. This paper analyses the formation of a practical theory of curved bars and its interaction with the practice of design.