Mathematical modeling of oval arches. A study of the George V and Neuilly Bridges

In this work we approach the mathematical modeling of oval arches of n centers and we present an analytical study of their geometry given the expressions of the elements that define them and the tangency points as a function of span, sagita and the radius of the circumferences of which they are formed, using Mathematica software to perform interactive graphs and calculations. This allows to mathematically model an existing arch or to design the construction of a new one. We apply the results obtained in the modeling of the Orléans Bridge over the River Loire (1751-1760) whose construction - initiated by Hupeau and completed by Perronet - made of three-centered oval arches and in the Neuilly Bridge over the River Seine, close to Paris, which is formed of eleven-centered oval arches.