Archive of Applied Mechanics

, Volume 89, Issue 11, pp 2281–2312

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

• D. S. Sophianopoulos
• G. T. Michaltsos
• H. I. Cholevas
Original

## Abstract

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.

## Keywords

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

## Upper case latin

A

Cross-sectional area

E

Modulus of elasticity of steel material (deck and arch)

G

Shear modulus

H(x)

Heaviside function

$$I_c$$

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

$$I_y$$

Moment of inertia with respect to y-axis

$$I_z$$

Moment of inertia with respect to z-axis

$$I_{\omega }$$

Warping resistance of the deck

$$J_{px}$$

Rotational mass moment of inertia of the deck

$$I_D$$

Saint-Venant torsional moment of inertia

L

Length of the bridge structure

R

Average geometrical radius of the arch

R(t)

Modal amplitudes

T(t)

Modal amplitudes

UWZ

Shape functions

## Lower case latin

a

Subscript denoting properties of the arch

b

Half-width of the deck

c

Subscript denoting properties of the cables

d

Subscript denoting properties of the deck

$$f_0$$

Sag of the arch at the middle of the bridge span

$$f_z(t)$$

Time functions

m

Mass per unit length

$$m_x$$

External moment acting on the deck

$$p_y$$

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

$$p_z$$

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

$$q_c$$

Stress per unit length of cables

$$q_1$$

Stress per unit length of the left line of cables

$$q_2$$

Stress per unit length of the right line of cables

$$q_z(x)$$

Forces developing on the cables

xyz

Axes designation

w

Vertical displacement

z(x)

Length of the cables at position x

## Greek

$$\varphi _d$$

Rotational deformation of the arch

$$\upsilon$$

Horizontal displacement

$$\Phi$$

Modal amplitudes

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## 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