Title: Thresholds for hanger slackening and cable shortening in the Melan equation for suspension bridges,
Abstract: The Melan equation for suspension bridges is derived by assuming small
displacements of the deck and inextensible hangers. We determine the thresholds
for the validity of the Melan equation when the hangers slacken, thereby
violating the inextensibility assumption. To this end, we preliminarily study
the possible shortening of the cables: it turns out that there is a striking
difference between even and odd vibrating modes since the former never shorten
the cables. These problems are studied both on beams and plates.