Archive of Applied Mechanics

, Volume 89, Issue 11, pp 2281–2312 | Cite as

Static and dynamic responses of suspended arch bridges due to failure of cables

  • D. S. SophianopoulosEmail author
  • G. T. Michaltsos
  • H. I. Cholevas


A mathematical model is proposed to investigate the behavior of a suspended arch bridge, subjected to sudden failure of cables. The main aim of this study is to analyze the effects produced by potential cables failure scenarios on the deformations and stresses of the bridge. The studied suspended arch bridge has a dense arrangement of cables, but the method described herein may be easily extended to the case of a sparse arrangement of cables. The theoretical formulation is based on a continuum approach, which has been used in the literature to analyze such bridges. Finally, the equations obtained are solved using the Duhamel’s integrals and the Laplace transform. For an exemplary bridge, results are obtained for the cases of failure of one, two and five cables, and important conclusions for structural design purposes are drawn.


Dynamics of bridges Suspended arch bridges Failure of cables Dynamic amplification factor 

List of symbols

Upper case latin


Cross-sectional area


Modulus of elasticity of steel material (deck and arch)


Shear modulus


Heaviside function


Moment of inertia of the arch at the mid-span section


Moment of inertia with respect to y-axis


Moment of inertia with respect to z-axis

\(I_{\omega }\)

Warping resistance of the deck


Rotational mass moment of inertia of the deck


Saint-Venant torsional moment of inertia


Length of the bridge structure


Average geometrical radius of the arch


Modal amplitudes


Modal amplitudes


Shape functions

Lower case latin


Subscript denoting properties of the arch


Half-width of the deck


Subscript denoting properties of the cables


Subscript denoting properties of the deck


Sag of the arch at the middle of the bridge span


Time functions


Mass per unit length


External moment acting on the deck


External applied force with respect to y-axis, acting on the deck


External applied force with respect to z-axis, acting on the deck


Stress per unit length of cables


Stress per unit length of the left line of cables


Stress per unit length of the right line of cables


Forces developing on the cables


Axes designation


Vertical displacement


Length of the cables at position x


\(\varphi _d\)

Rotational deformation of the arch

\(\upsilon \)

Horizontal displacement

\(\Phi \)

Modal amplitudes



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • D. S. Sophianopoulos
    • 1
    Email author
  • G. T. Michaltsos
    • 2
  • H. I. Cholevas
    • 1
  1. 1.Department of Civil EngineeringUniversity of ThessalyVólosGreece
  2. 2.National Technical University of AthensAthensGreece

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