Open Access Research

Steady-state solutions for a suspension bridge with intermediate supports

Claudio Giorgi* and Elena Vuk

Author Affiliations

DICATAM, Università degli Studi di Brescia, Via Valotti 9, Brescia, 25133, Italy

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Boundary Value Problems 2013, 2013:204  doi:10.1186/1687-2770-2013-204

Published: 9 September 2013

Abstract

This work is focused on a system of boundary value problems whose solutions represent the equilibria of a bridge suspended by continuously distributed cables and supported by M intermediate piers. The road bed is modeled as the junction of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/204/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/204/mathml/M1">View MathML</a> extensible elastic beams which are clamped to each other and pinned at their ends to each pier. The suspending cables are modeled as one-sided springs with stiffness k. Stationary solutions of these doubly nonlinear problems are explicitly and analytically derived for arbitrary k and a general axial load p applied at the ends of the bridge. In particular, we scrutinize the occurrence of buckled solutions in connection with the length of each sub-span of the bridge.

MSC: 35G30, 74G05, 74G60, 74K10.

Keywords:
extensible elastic beam; suspension bridge; boundary value problems for nonlinear higher-order PDE; bifurcation and buckling