Response Spectrum Method Based Research On The Footbridge Vibrations Response Due To Pedestrian Walking

While the issue of footbridge vibration is becoming increasingly prominent,pedestrian induced footbridge vibration analysis gradually rises as an importantelement in the design of modern footbridges. However, as the main expression form ofpedestrian loading, pedestrian walking force model need to be determined first as aprecondition to vibration analysis. Meanwhile, the interaction between pedestrian andbridge complicates the analysis process, causing the typical load-response relation instructural dynamics no longer suitable for footbridge vibration calculation. Therefore,the critical point for pedestrian induced footbridge vibration analysis is to explore theeffect of interaction explicitly. On the other hand, the ultimate goal for the research onpedestrian induced vibration is to develop a simple and practical vibration analysismethod, facilitating engineers to use.Centering on the above issue, the dissertation is organized in6chapters. In thefirst chapter, a comprehensive literature review is presented, solely focusing on thelarge social influence after pedestrian induced vibration events, as well as on theadvancing of state on pedestrian walking force, the interaction between pedestrian andbridge, and the method for pedestrian induced footbridge vibration calculation.Chapter2specially investigates the model of pedestrian walking force, as well aspedestrian walking gait parameters which affect the model. Built in chapter3and4isa theoretical framework on the interaction between pedestrian and bridge. Alsoestablished here is a mathematical expression for the interaction. Chapter5is devotedto the research into theory and methodology for pedestrian induced footbridgevibration calculation. On this basis, a response spectrum (RS) is developed forapplication. Provided as an example, chapter6employs the RS methodology tocalculate the response of No.47bridge under pedestrian action, the reliability ofwhich is validated by comparing the results with in-site test. Following work withdistinctive feature from others has been done in the thesis:1) On the basis of extensive literature review, a full stochastic pedestrian walkingforce model is proposed in time domain, which is capable of considering the doublevariability of pedestrian walking gait parameter simultaneously, namely inter-andintra-subject variability.2) The distribution of pedestrian walking gait parameters involved in the walkingforce model is systematically addressed. Particularly, by utilizing peak detection algorithm to extract instantaneous pacing frequency (IPF) from acceleration signals, itshows that IPFs generally are normally distributed, with a standard deviationfollowing uniform distribution, independently of the mean pacing frequency.3) Proceeding from the perspective of human body dynamics, Lagrange methodsof first and second kind are employed respectively to develop a passive walkingnonlinear model, which includes two sub-models for single and double support phase.The model, capable of simulating the basic features of human walking process, takesfully into account that the center of pressure (CoP) makes progress forward duringstance phase. Furthermore, a solution method to the differential algebraic equations(DAEs) involved in the model is presented and the determination of stable gaitparameter is discussed in detail. In addition, via dynamic mechanical analysis to themodel, a walking load expression is derived.4) Aiming at the development of balance controller for pedestrian walking, alinear inverted pendulum (LIP) model is introduced to elicit the governing equationfor foot placement, which is founded on the theory of instantaneous capture point(ICP) and then is applied to the said walking model above for controlling.5) By applying the foot placement strategy and inspired from the mechanicaldriving technique for aerodynamic force identification, the property of walking forceunder vibration environment is explored extensively and the method of evaluating theeffect of interaction between pedestrian and bridge is proposed as well. By doing so,an analytical model dealing with the interaction effect is fitted out, which indicatesthat the additional damping effect, as a result of interaction, decrease with increasingbridge vibration amplitude, suggesting that the larger the vibration is, the smaller thedamping added into the system, and therefore exposing bridges more prone to theexcessive vibration.6) To quantify the overall effect of interaction between pedestrian and bridge, aforced vibration experiment was carried out in laboratory. By comparison with testresults, the analytical model is further approved to accurately calculate the interactioneffect exerted by a pedestrian.7) Based on the theory of forced vibration, footbridge vibration response tocrowd flow is elaborated in time domain. By combined use of numerical simulation tofootbridge response and the distribution theory of generalized extreme value (GEV), areference response spectrum (RRS) is constructed. Through extensive parameteranalysis, a series of modification factor to RRS is obtained, expanding the RRS into ageneralized response spectrum (GRS). Also covered in this dissertation is the detailed modification approach for considering the interaction effect between pedestrian andbridge, enabling the results from forced vibration theory to better reflect the realsituation of footbridge response.8) A versatile program has been integrated for footbridge vibration analysis.Using the program, the response of No.43bridge to pedestrian crossing is calculated.Then results are compared between measured and predicted vibration response,including the response estimate obtained according to worldwide design code, whichfurther validates the practicability and reliability of the program.