Uncertainty propagation in the serviceability assessment of footbridges

Abstract This paper discusses the serviceability assessment of footbridges considering the uncertainties in definition of their structural and loading parameters. Application of the Taylor Series Expansion method to the closed-form expression of the dynamic response based on the Equivalent Spectral Model allows to obtain analytical solutions for the quantification of uncertainty propagation and to identify the parameters whose uncertainties may cause significant scatter of the results. The proposed analytical solutions are verified by Monte Carlo simulations, in the two classic scenarios of resonance and non-resonance conditions between step frequency and the bridge natural frequency. The approach provides the possibility of going beyond conventional verifications of footbridge vibration level, based on nominal values of load and structural properties. In this framework, serviceability assessment is proposed from a probabilistic point of view, associating a probability of occurrence to each comfort level.

[1]  Babak Moaveni,et al.  Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge , 2011 .

[2]  Stuart Clifford Kerr.  Human induced loading on staircases , 1998 .

[3]  L. G. Jaeger,et al.  Dynamics of structures , 1990 .

[4]  Federica Tubino,et al.  Serviceability assessment of footbridges in unrestricted pedestrian traffic conditions , 2016 .

[5]  Hugo Bachmann,et al.  Vibrations in structures , 1987 .

[6]  Mike Schlaich,et al.  Guidelines for the design of footbridges , 2005 .

[7]  Eleni Chatzi,et al.  Polynomial chaos expansion models for the monitoring of structures under operational variability , 2016 .

[8]  Federica Tubino.  Probabilistic assessment of the dynamic interaction between multiple pedestrians and vertical vibrations of footbridges , 2018 .

[9]  Amin Heidarpour,et al.  A framework for quantification of human-structure interaction in vertical direction , 2018, Journal of Sound and Vibration.

[10]  Álvaro Cunha,et al.  Structural health monitoring of a stress-ribbon footbridge , 2013 .

[11]  S. Alampalli,et al.  EFFECTS OF TESTING, ANALYSIS, DAMAGE, AND ENVIRONMENT ON MODAL PARAMETERS , 2000 .

[12]  Giovanni Solari,et al.  Wind-excited response of structures with uncertain parameters , 1997 .

[13]  D. E. Allen,et al.  Dynamic loading and response of footbridges , 1988 .

[14]  Hoon Sohn,et al.  Effects of environmental and operational variability on structural health monitoring , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Christiane Butz,et al.  Advanced load models for synchronous pedestrian excitation and optimised design guidelines for steel footbridges , 2008 .

[16]  S. C. Kerr,et al.  Human induced loading on flexible staircases , 2001 .

[17]  Y. Tamura,et al.  Evaluation of amplitude-dependent damping and natural frequency of buildings during strong winds , 1996 .

[18]  Guido De Roeck,et al.  Numerical and experimental evaluation of the dynamic performance of a footbridge with tuned mass dampers , 2016 .

[19]  Stana Živanović,et al.  Benchmark Footbridge for Vibration Serviceability Assessment under the Vertical Component of Pedestrian Load , 2012 .

[20]  Human induced Vibrations of Steel Structures Design of Footbridges Background Document , .

[21]  Ahsan Kareem,et al.  Damping in structures: its evaluation and treatment of uncertainty , 1996 .

[22]  V. Askegaard,et al.  Long term observation of RC-bridge using changes in natural frequency , 1988 .

[23]  Aleksandar Pavic,et al.  Experimental identification and analytical modelling of human walking forces: Literature review , 2009 .

[24]  Luisa Pagnini,et al.  Reliability analysis of wind-excited structures , 2010 .

[25]  Paul Reynolds,et al.  Probability-based prediction of multi-mode vibration response to walking excitation , 2007 .

[26]  A. Sofi,et al.  Dynamics of structures with uncertain-but-bounded parameters via pseudo-static sensitivity analysis , 2018, Mechanical Systems and Signal Processing.

[27]  Federica Tubino,et al.  Equivalent spectral model and maximum dynamic response for the serviceability analysis of footbridges , 2012 .

[28]  Guido De Roeck,et al.  Robust design of a TMD for the vibration serviceability of a footbridge , 2016 .

[29]  Aleksandar Pavic,et al.  Experimental methods for estimating modal mass in footbridges using human-induced dynamic excitation , 2007 .

[30]  Geert Lombaert,et al.  Characterisation of walking loads by 3D inertial motion tracking , 2014 .

[31]  Luisa-Carlotta Pagnini,et al.  Model reliability and propagation of frequency and damping uncertainties in the dynamic along-wind response of structures , 1996 .

[32]  Tianjian Ji,et al.  FREQUENCY AND VELOCITY OF PEOPLE WALKING , 2005 .

[33]  Shiqiao Gao,et al.  A novel crowd random loads model for pedestrians walking on footbridge , 2016 .

[34]  Geert Lombaert,et al.  Vibration serviceability of footbridges: Evaluation of the current codes of practice , 2014 .

[35]  Alessandro Corbetta,et al.  Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges , 2016 .

[36]  John T. DeWolf,et al.  Effect of Temperature on Modal Variability of a Curved Concrete Bridge under Ambient Loads , 2007 .

[37]  J. H. Rainer.  Vibrations in structures induced by man and machine , 1988 .

[38]  A. Kareem.  Wind effects on structures: a probabilistic viewpoint , 1987 .

[39]  Bart Peeters,et al.  One year monitoring of the Z24-bridge : Environmental influences versus damage events , 2000 .

[40]  Federica Tubino,et al.  Simplified procedures for vibration serviceability analysis of footbridges subjected to realistic walking loads , 2009 .

[41]  W. Gerrard.  Effect of Temperature , 1976 .

[42]  Joe Keogh,et al.  Reliability Analysis of Footbridge Serviceability Considering Crowd Loading , 2012 .

[43]  Stana Zivanovic,et al.  Probabilistic Assessment of Human Response to Footbridge Vibration , 2009 .

[44]  Annett Wechsler,et al.  Optimization And Anti Optimization Of Structures Under Uncertainty , 2016 .

[45]  Stana Živanović,et al.  Modeling Spatially Unrestricted Pedestrian Traffic on Footbridges , 2010 .

[46]  J W Smith,et al.  DESIGN CRITERIA AND ANALYSIS FOR DYNAMIC LOADING OF FOOTBRIDGES , 1977 .

[47]  Michel van Tooren,et al.  Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles , 2011 .

[48]  Tianjian Ji,et al.  Frequency and velocity of walking people , 2005 .

[49]  Hid N. Grouni,et al.  Methods of structural safety , 1986 .

[50]  Paul J. Barr,et al.  Effects of Temperature on Bridge Dynamic Properties , 2015 .

[51]  Francesco Ricciardelli,et al.  Experimental validation and calibration of pedestrian loading models for footbridges , 2007 .

[52]  Xu Han,et al.  A new measurement for structural uncertainty propagation based on pseudo-probability distribution , 2018, Applied Mathematical Modelling.

[53]  Amr S. Elnashai,et al.  Uncertainties in life-cycle analysis and design of structures and infrastructures , 2011 .

[54]  Hoon Sohn,et al.  Environmental variability of modal properties , 1999 .

[55]  Bruce R. Ellingwood.  DESIGN AND CONSTRUCTION ERROR EFFECTS ON STRUCTURAL RELIABILITY , 1987 .

[56]  Colin Christopher Caprani,et al.  Formulation of human-structure interaction system models for vertical vibration , 2016 .

[57]  Paul Reynolds,et al.  Modal testing and FE model tuning of a lively footbridge structure , 2006 .

[58]  Christos T. Georgakis,et al.  Change in mass and damping on vertically vibrating footbridges due to pedestrians , 2013 .

[59]  Federica Tubino,et al.  Generalized Equivalent Spectral Model for Serviceability Analysis of Footbridges , 2016 .

[60]  Federica Tubino,et al.  Human-Induced Vibrations on Two Lively Footbridges in Milan , 2016 .

[61]  Luisa Pagnini,et al.  The role of parameter uncertainties in the damage prediction of the alongwind-induced fatigue , 2012 .