Abstract
We investigate the effects of steady aerodynamic loads on stability and natural frequencies of long-span suspension bridges through a simplified analytical model. The single (central) span suspension bridge model is considered, and the linearized integro-differential equations describing the flexural-torsional deformations of the bridge deck-girder are adopted as starting point. Thus, taking into account the second-order effects induced by a constant transverse wind in the bridge equations of motion, we derive a generalized eigenvalue problem in which all configurations intermediate between those of pure lateral-torsional buckling, pure torsional divergence, and pure free vibrations can be investigated. We show that the natural frequencies of a suspended deck-girder depend upon the mean (quasi-static) wind loading. As a consequence, the input parameters to the aeroelastic stability analysis result affected by that dependence, suggesting the possibility of modifying the dynamic stability analysis in order to take into account the mentioned influence. Based on this fact, possible implications for the flutter analysis of long-span suspension bridges are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Due to the assumption of axial inextensibility of the hangers, the additional vertical deflections in the cables, v R (z) and v L (z), are equal to the vertical deflections of the deck-girder in correspondence of the same vertical lines (Fig. 45.2). These additional deflections are related to the kinematic descriptors v(z) and ϑ(z) by the following equations: v R (z) = v(z) – b ϑ(z), v L (z) = v(z) + b ϑ(z), being b the half distance between the vertical planes containing the cables (Fig. 45.2).
- 2.
(·)″ = d2(·)/dz 2.
- 3.
I ϑG = μ g (I P /A), where I P is the polar area moment of inertia and A is the area of the deck-girder cross-section.
- 4.
With the assumption of small oscillations, the horizontal forces in the main cables may be regarded as constant along the z-axis.
- 5.
Both frequencies ω v and ω ϑ are nondimensionalized with respect to ω v1.
- 6.
If \( {\overline{p}}_x=0 \), then the flexural and torsional oscillations of the bridge are uncoupled [see Eq. (45.13)].
References
Larsen A (ed) (1992) Aerodynamics of large bridges. Balkema, Rotterdam
Simiu E, Scanlan RH (1996) Wind effects on structures: fundamentals and applications to design, 3rd edn. Wiley, New York
Dyrbye C, Hansen SO (1997) Wind loads on structures. Wiley, Chichester
Larsen A, Esdahl S (eds) (1998) Bridge aerodynamics. Balkema, Rotterdam
Jurado JA, Hernández S, Nieto F, Mosquera A (2011) Bridge aeroelasticity. Sensitivity analysis and optimal design. WIT Press, Southampton
Cai CS, Montens S (2000) Wind effects on long-span bridges. In: Chen WF, Duan L (eds) Bridge engineering handbook. CRC, Boca Raton
Bleich HH (1935) Die Berechnung verankerter Hängebrücken. Julius Springer, Vienna
Como M (2002) Stabilità aerodinamica dei ponti di grande luce. In: Giangreco E (ed) Ingegneria delle strutture. UTET, Torino
Holms JD (2007) Wind loading of structures, 2nd edn. Taylor & Francis, New York
Bathe KJ (1982) Finite element procedures in engineering analysis. Prentice-Hall, Inc., Englewood Cliff
Scanlan RH, Tomko JJ (1971) Airfoil and bridge deck flutter derivatives. J Eng Mech Div Proc ASCE 97(6):1717–1737
Namini A, Albrecht P, Bosh H (1992) Finite element-based flutter analysis of cable-suspended bridges. J Struct Eng ASCE 118(6):1509–1529
Abdel-Ghaffar AM (1982) Suspension bridge vibration: continuum formulation. J Eng Mech ASCE 108:1215–1232
Abdel-Ghaffar AM, Rubin LI (1983) Nonlinear free vibrations of suspension bridges: theory. J Eng Mech ASCE 109:313–345
Lacarbonara W (2013) Nonlinear structural mechanics: theory, dynamical phenomena and modeling. Springer, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Piana, G., Manuello, A., Malvano, R., Carpinteri, A. (2014). Natural Frequencies of Long-Span Suspension Bridges Subjected to Aerodynamic Loads. In: Catbas, F. (eds) Dynamics of Civil Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04546-7_45
Download citation
DOI: https://doi.org/10.1007/978-3-319-04546-7_45
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04545-0
Online ISBN: 978-3-319-04546-7
eBook Packages: EngineeringEngineering (R0)