Thresholds for hanger slackening and cable shortening in the Melan equation for suspension bridges

TL;DR

This paper investigates the limits of the Melan equation's applicability in suspension bridges by analyzing hanger slackening and cable shortening, highlighting differences between vibrational modes and their impact on structural assumptions.

Contribution

It introduces thresholds for hanger slackening and cable shortening, clarifying when the Melan equation's assumptions break down in suspension bridge modeling.

Findings

Even vibrational modes do not cause cable shortening.

Thresholds for hanger slackening are identified.

Differences between beam and plate models are analyzed.

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.