WALKING INDUCED FLOOR VIBRATION DESIGN AND CONTROL A dissertation submitted by HUU ANH TUAN NGUYEN for the award of Doctor of Philosophy Faculty of Engineering and Industrial Sciences Swinburne University of Technology 2013 Abstract Disturbing walking-induced vibrations have been observed more frequently in recent times on long span lightweight floor systems as evidenced by the development of a number of new design guidelines for floor vibration assessment Constraining vibration levels to meet human comfort criteria is a vital serviceability requirement in the design of floors The aim of the present research is to minimise the adverse vibrations from footfalls in new floors by providing better estimation of expected response and in existing floors by the use of a new configuration of tuned mass damper (TMD) Current floor vibration guidelines are reviewed and modifications are proposed to enhance the accuracy of floor response prediction A significant finding is the development of an empirical expression for a unique factor that incorporates all effects of the floor properties, pacing rate, resonant harmonic and non-resonant harmonic forcing components on the floor response The peak response due to a moving multiharmonic force can now be easily computed as the multiplication of the proposed factor by the steady state response due to a stationary single-harmonic force Also discussed are finite element (FE) and semi-FE approaches for predicting the worst-case response of floors One major achievement of the present research is the application of an innovative multi TMD system as an effective solution for floor vibration control A closed form solution for natural frequencies and steady state response of systems with multi TMDs is developed to facilitate preliminary design A custom made distributed multiple viscoelastic TMD system has been developed and successfully installed on a real office floor where disturbing walking-induced vibrations were observed Extensive FE investigations and various field tests performed on the real floor reveal that the response i level of the damper-retrofitted floor is suppressed by at least 40% to an acceptable limit for human comfort Another contribution of the present research is the characterisation of human walking force based on the experimental footfall data obtained from an Australian biomechanics research program The descriptive statistics of basic gait parameters are determined and the intra- and inter-subject variability in gait parameters is examined from this footfall database Moreover, design values are proposed for the dynamic load coefficients corresponding to the first ten harmonics of walking Finally, a probabilistic vibration analysis of a floor with and without dampers is conducted with a large number of simulation cases considering the likely variations in loading within each walk and between different walks and the possible changes in the dynamic properties of the floor and dampers This sensitivity analysis automatically covers the effect of damper off-tuning and further validates the effectiveness and reliability of the TMD method when demonstrating that the 90% and 95% fractile response levels of the floor can be reduced by about 43% using the dampers ii Acknowledgments It has been my great honour and real privilege to carry out this research under the supervision of Prof Emad Gad, Prof John Wilson and Prof Nicholas Haritos I am very grateful for their patient guidance, enthusiastic encouragement and constant support throughout my research journey I have benefited a lot from their valuable advice on the planning and development of this research work, research methodology, as well as academic writing and editing in English Besides academic aspects, I admire their generosity, professional and friendly attitude My grateful thanks are also extended to Assoc Prof Noel Lythgo who kindly granted me access to his experimental data on human gait measures and provided me with a brief tutorial on the Vicon Nexus software Moreover, I find myself fortunate to have worked alongside Mr Ibrahim Saidi and I thankfully acknowledge all his dedicated assistance with my experimental work I would like to offer my thanks to Ms Caroline Dean and Mr Sean Kinder for designing a detail of the damper as part of their undergraduate research project; to many friends and colleagues whose names are not mentioned here for their encouragement during my course of study I am really grateful to Swinburne University of Technology for providing me with tuition fee waivers and the Vietnamese Ministry of Education and Training for awarding me a stipend scholarship These supports opened an opportunity for me to be an international student for the first time Most of all, I would like to express my deepest gratitude to all members of my family, especially my beloved parents and wife, for their unconditional support, understanding, abiding love and encouragement This thesis is dedicated to my family, to whom I am greatly indebted iii Candidate’s Declaration I hereby declare that this dissertation represents my own work and effort, except where otherwise acknowledged in the text I certify that this submission, to the best of my knowledge, contains no material previously published or written by another person except where due reference is made in the text I confirm that neither the submission nor the original work contained therein has been previously submitted to this university or any other institution for the award of a degree or other qualification Candidate's signature: _ Huu Anh Tuan Nguyen iv Table of Contents Abstract i Acknowledgments iii Candidate’s Declaration iv List of Figures .xi List of Tables xxi Chapter Introduction 1.1 Background and Motivation 1.2 Research Aim and Objectives 1.3 Research Methodology 1.4 Thesis Layout Chapter 2.1 Literature Review Introduction to Floor Dynamics 2.1.1 Human-induced loading 2.1.2 Floor dynamic properties and response 11 2.1.3 Factors affecting human comfort 17 2.2 Acceptance Criteria 21 2.2.1 Peak acceleration 23 2.2.2 RMS acceleration 23 2.2.3 Vibration dose value 25 2.2.4 RMS velocity 26 2.3 Predicting Dynamic Properties and Walking Response of Floors using Current Guidelines 27 v 2.3.1 AISC/CISC DG11 27 2.3.2 SCI P354 30 2.3.3 CCIP-016 36 2.3.4 EUR DG (HIVOSS) 38 2.4 Finite Element Modelling, Compared with Manual Methods and Physical Experiments 42 2.4.1 Introduction to floor vibration analysis using finite element 42 2.4.2 Analysis of composite floors 43 2.4.3 Analysis of concrete floors 50 2.5 Dynamic Testing of Floor Systems 51 2.5.1 Introduction 51 2.5.2 Unreferenced and instrumented heel drop tests 53 2.5.3 Extraction of natural frequency and damping 56 2.5.4 Measurement of mode shape and modal mass 62 2.5.5 Measurement of walking response 65 2.6 Rectification of Floor Vibrations 68 2.6.1 Structural and architectural modification 68 2.6.2 Specialist damping material 74 2.6.3 Tuned mass damper 78 2.6.4 Active control 89 2.6.5 Semi-active control 93 2.7 An Innovative Viscoelastic Tuned Mass Damper 98 2.7.1 Description of a new damper configuration 98 2.7.2 SDOF model for the sandwich beam TMD 100 2.8 Summary and Conclusions 103 Chapter Improving a Prediction Method for Walking Induced Floor Vibration 107 3.1 Introduction 107 3.2 Determination of Steady State Factor 109 vi 3.2.1 Methodology 109 3.2.2 Moving-walk forcing functions 110 3.2.3 Numerical integration method 112 3.2.4 Results 114 3.2.5 Discussion 116 3.3 Closed Form Expression for Steady State Factor 118 3.3.1 Response to stationary harmonic force 118 3.3.2 Development of empirical expressions for response to moving force 119 3.3.3 Literature proposals 123 3.3.4 Comparison and discussion 125 3.4 Prediction of Floor Response 128 3.4.1 Proposal for a simplified design formula 128 3.4.2 Discussion on required parameters 128 3.5 A Typical Generic Footbridge Worked Example 130 3.6 A Real Composite Floor 131 3.6.1 Description of case study floor 131 3.6.2 Preliminary FE analysis 133 3.6.3 Floor testing 135 3.6.4 Updated FE modal analysis and FE time history analysis 138 3.6.5 Prediction of floor response using the proposed method 140 3.6.6 Discussion 141 3.7 Summary and Conclusions 141 Chapter Comparison of Methods for Walking Induced Floor Vibration 144 4.1 Introduction 144 4.2 Analysis of Floor Vibrations using Finite Elements 145 4.2.1 Resonant frequency and response in worst case 145 4.2.2 Effects of forcing functions based on different guidelines on floor response obtained from time history analysis 153 4.2.3 Calculation examples 157 vii 4.3 Simplified method and Semi-FE method 166 4.3.1 Description of simplified methods 166 4.3.2 Description of Semi-FE method 167 4.3.3 Results and discussion 170 4.4 Summary and Conclusions 175 Chapter Control of Walking Induced Floor Vibration 177 5.1 Introduction 177 5.2 Analysis of System with Multi and Distributed TMDs 178 5.2.1 Development of closed form solutions for natural frequencies and steady state response 178 5.2.2 Application 183 5.2.3 Validation against numerical results 184 5.3 Optimum Parameters for TMD 187 5.3.1 Commonly used formulae for optimum TMD 188 5.3.2 Proposal for new optimum parameters for TMD 190 5.3.3 Comparison and discussion 193 5.4 A Composite Floor Case Study 194 5.4.1 Description of the floor and remedial methods 194 5.4.2 Suppression of floor vibration by means of stiffening 196 5.4.3 Preliminary design of a damper system 201 5.4.4 Numerical study of performance of floor with distributed multiple identical dampers 203 5.4.5 Numerical study of various damper tuning strategies 210 5.4.6 Final design, manufacture and installation of dampers 217 5.4.7 Experimental study of dampers performance 222 5.4.8 Comment on rectifying the composite floor 227 5.5 A Modified Design for Sandwich-Beam Damper 228 5.6.1 Description of a prototype damper with sliding mass 228 5.6.2 Determination of damper's dynamic properties 230 viii 5.6 Summary and Conclusions 233 Chapter Characterisation of Human Walking Force 236 6.1 Introduction 236 6.2 Basic Gait Parameters 237 6.2.1 Description of walking test and participants 237 6.2.2 Determination of gait parameters 238 6.2.3 Intra-subject variability 240 6.2.4 Relationship between different gait parameters 243 6.2.5 Effects of footwear 246 6.3 Walking Force Function 249 6.3.1 Analysis procedure 249 6.3.2 Statistical analysis for design value of dynamic coefficient 253 6.3.3 Simplified design value 260 6.3.4 Comparison with current design guides 262 6.4 Summary and Conclusions 265 Chapter Probabilistic Evaluation of Floor Vibration and TMD Performance 267 7.1 Introduction 267 7.2 Analysis Model 268 7.2.1 Simplified analysis model and equation of motion 268 7.2.2 Numerical integration for MDOF systems 269 7.3 Input Parameters for Random Vibration Analysis 270 7.3.1 Modal properties of the floor 270 7.3.2 Walking force function 271 7.3.3 Modal properties 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Advances in Structural Engineering, 15(3), 547-562 Nguyen, T H., Gad, E F., Wilson, J L., and Haritos, N (2012) "Improving a current method for predicting walking-induced floor vibration." Steel and Composite Structures, 13(2), 139-155 Nguyen, T., Gad, E., Wilson, J., and Haritos, N (fully accepted 2013) "Mitigating footfall induced vibration in long span floors." Australian Journal of Structural Engineering (In press) Refereed Conference Papers Nguyen, T., Gad, E., Wilson, J., and Haritos, N (2010) "Design of multiple viscoelastic tuned mass dampers for floor vibration applications." Incorporating Sustainable Practice in Mechanics and Structures of Materials: proceedings of the 21st Australasian Conference on the Mechanics of Structures and Materials (ACMSM21), Melbourne, Victoria, Australia, 07-10 December 2010 / Sam Fragomeni, Srikanth Venkatesan, Nelson T K Lam and Sujeeva Setunge (eds.), 321-326 Nguyen, T., Gad, E., Wilson, J., Lythgo, N., and Haritos, N (2011) "Evaluation of footfall induced vibration in building floor." Proceedings of the Australian Earthquake Engineering Society 2011 Conference (AEES 2011), Barossa Valley, South Australia, 18-20 November 2011 Nguyen, T H., Gad, E F., Wilson, J L., and Haritos, N (2012) "A New Damper System for Walking Induced Floor Vibration Control." Proceedings of the 10th International Conference on Advances in Steel Concrete Composite and Hybrid Structures, Singapore, 02-04 July 2012 / J Y Richard Liew and Siew Chin Lee (eds.), 1089-1096 Papers in Preparation Nguyen, T., Gad, E., Wilson, J., and Haritos, N (2013) "Analysis of footfall induced floor vibration using Finite elements." (In preparation) 315 Nguyen, T., Gad, E., Wilson, J., Lythgo, N., and Haritos, N (2013) "Characterisation of human walking force." (In preparation) Nguyen, T., Haritos, N, Gad, E., and Wilson, J (2013) "EMA and other dynamic testing of a 2-span prestressed concrete floor." (In preparation) Nguyen, T., Gad, E., Wilson, J., and Haritos, N (2014) “Effect of fit-out and construction type on dynamic properties of floor systems under human excitations.” (In preparation) Nguyen, T., Gad, E., Wilson, J., and Haritos, N (2014) "Probabilistic evaluation of performance of a new TMD system for floor vibration control." (In preparation) 316 [...]... findings on floor vibration analysis using FE modelling and an introduction to dynamic testing of floors Subsequently, a number of methods to mitigate human induced floor vibrations are reported Chapter 3 highlights some limitations of a currently widely used method for predicting floor response to walking, and proposes improvement to this method Design charts and empirical formulae for walking response... of floor dynamics including human induced loading, floor response and human perception are firstly discussed This is followed by an overview of current floor vibration guidelines, which focuses on acceptance criteria and the methods to predict the floor dynamic properties and walking response A considerable amount of literature on finite element techniques for vibration analysis of composite floors and. .. components, namely vibration source, transmission path and receiver (ISO 10137 2007) In the context of humaninduced floor vibrations, examples of vibration source are people walking or running on a floor which is considered as the transmission path, whilst the floor tenants are the receivers whose comfort is affected by the floor vibrations Some basic aspects of human loadings, floor response and human perception... suspended ceiling and ductwork attached below the slab Floor vibration due to human activities is becoming a significant concern to designers and developers of long-span lightweight floor systems Disturbing floor vibrations caused by normal walking have been observed more frequently in recent times as evidenced by the development of new design guidelines (Murray et al 2003, Willford and Young 2006, Feldmann... remedial methods, stiffening technique and TMD, for a real office floor subject to annoying vibrations due to footfall excitations 4 - Develop comprehensive FE models for vibration analysis of the original floor without dampers, the stiffened floor and the floor with dampers Different stiffening scenarios and various tuning policies for the dampers are investigated - Design and build an innovative multiple... background, aim, objectives and methodology is given in Chapter 1 Chapter 2 presents a comprehensive literature review on the design and control of human -induced floor vibrations The chapter firstly covers basic aspects of floor dynamics, various acceptance criteria and different methods introduced by current guidelines for predicting the dynamic properties and response of floor systems These are followed... the bare floor and damper-fitted floor will be computed from which the effectiveness of the dampers can be evaluated Finally, the key findings and contributions of the present work are summarised in Chapter 8 Some proposals for future development of the research are also made 7 Chapter 2 Literature Review This chapter presents a literature review on the design and control of human -induced floor vibrations... The inter- and intra-subject diversity in gait parameters is examined, and the statistics of basic gait parameters such as walking speed, step frequency and step length are found for different walking conditions Furthermore, characteristic design values are proposed for the dynamic load factors that constitute mathematical models for walking excitations Comparison with current floor vibration design guides... examines a simple probability based analysis procedure to assess walking induced vibrations of floors with and without dampers The analysis takes into account the variability in waking force within each walk and between different walks, and the likely change in the dynamic characteristics of both the floor and dampers Some aspects of randomness in gait parameters found in Chapter 6 will be utilised... been investigations on the differences between walking force applied on floors and that applied on slender staircases (Bishop et al 1995, Kerr and Bishop 2001) Whilst office floors and footbridges are usually affected by walking excitation, floor systems of gymnasium and sport halls, concert halls and theatres can be subjected to vibrations due to rhythmic activities Figure 2-2(a) shows a simplified