Navier&#x2019;s 1823 <i>Memoire</i>: Analyses of Displacements, Stiffness, and Vibration of Suspension Bridges

Abstract

Navier’s 1823 Memoire (C. L. Navier. 1823. Rapport à Monsieur Becquey, Conseiller d’État, Directeur Général des Ponts et Chaussées et des Mines; et mémoire sur les ponts suspendus. Paris: L’Imprimerie Royale) is the seminal analytical study on displacements, stiffness, and vibration of suspension bridges. Navier derived a linearized formula for the vertical displacement at midspan of an unstiffened cable caused by a small change in cable length or span length. He predicted the vertical displacement caused by a concentrated midspan load on a cable with a dominant, uniformly distributed load on its horizontal projection. He thus quantified the geometric stiffness of a cable with a large axial force. Navier also examined the effects of different bearings on displacements of multispan suspension cables subject to unequal vertical loads on adjacent spans. To assess the accuracy of Navier’s quantitative results and to provide insights on structural behavior, geometrically nonlinear models were defined and solved. Navier’s analyses of the vibration of cables and the later contributions of Edward Routh, Hans Reissner, and David Steinman were assessed by geometrically nonlinear OpenSees models of unstiffened and deck-stiffened suspension cables. The influence of Navier’s work on the designs of Charles Ellet and John Roebling was revealed.