1、Steel Design Guide SeriesFloor VibrationsDue to Human ActivityFloor VibrationsDue to Human ActivityThomas M. Murray, PhD, P.E.Montague-Betts Professor of Structural Steel DesignThe Charles E. Via, Jr. Department of Civil EngineeringVirginia Polytechnic Institute and State UniversityBlacksburg, Virgi
2、nia, USADavid E. Allen, PhDSenior Research OfficerInstitute for Research in ConstructionNational Research Council CanadaOttawa, Ontario, CanadaEric E. Ungar, ScD, P.E.Chief Engineering ScientistAcentech IncorporatedCambridge, Massachusetts, USAAMERICAN INSTITUTE OF STEEL CONSTRUCTIONCANADIAN INSTITU
3、TE OF STEEL CONSTRUCTIONSteel Design Guide Series 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.Copyright 1997byAmerican Institute of Steel Construction, Inc.All r
4、ights reserved. This book or any part thereofmust not be reproduced in any form without thewritten permission of the publisher.The information presented in this publication has been prepared in accordance with rec-ognized engineering principles and is for general information only. While it is believ
5、edto be accurate, this information should not be used or relied upon for any specific appli-cation without competent professional examination and verification of its accuracy,suitablility, and applicability by a licensed professional engineer, designer, or architect.The publication of the material c
6、ontained herein is not intended as a representationor warranty on the part of the American Institute of Steel Construction or of any otherperson named herein, that this information is suitable for any general or particular useor of freedom from infringement of any patent or patents. Anyone making us
7、e of thisinformation assumes all liability arising from such use.Caution must be exercised when relying upon other specifications and codes developedby other bodies and incorporated by reference herein since such material may be mod-ified or amended from time to time subsequent to the printing of th
8、is edition. TheInstitute bears no responsibility for such material other than to refer to it and incorporateit by reference at the time of the initial publication of this edition.Printed in the United States of AmericaRevision: October 2003The co-sponsorship of this publication by the Canadian Insti
9、tuteof Steel Construction is gratefully acknowledged. 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.TABLE OF CONTENTS1. Introduction . 11.1 Objectives of the Desig
10、n G uide. 11.2 Road Map 11.3 Background. 11.4 Basic Vibration Terminology . 11.5 Floor Vibration Principles . 32. Acceptance Criteria For Human Comfort 72.1 Human Response to Floor Motion. 72.2 Recommended Criteria for Structural Design . . . . 72.2.1 Walking Excitation 72.2.2 Rhythmic Excitation .
11、93. Natural Frequency of Steel FramedFloor Systems 113.1 Fundamental Relationships . 113.2 Composite Action. 123.3 Distributed W e ight 123.4 Deflection Due to Flexure: Continuity. 123.5 Deflection Due to Shear in Beams and Trusses 143.6 Special Consideration for Open Web Joistsand Joist Girders. 14
12、4. Design For Walking Excitation. 174.1 Recommended Criterion . 174.2 Estimation of Required Parameters . 174.3 Application of Criterion 194.4 Example Calculations 204.4.1 Footbridge Examples 204.4.2 Typical Interior Bay of an OfficeBuilding Examples 234.4.3 Mezzanines Examples. 325. Design For Rhyt
13、hmic Excitation . 375.1 Recommended Criterion 375.2 Estimation of Required Parameters . 375.3 Application of the Criterion . 395.4 Example Calculations 406. Design For Sensitive Equipment . 456.1 Recommended Criterion 456.2 Estimation of Peak Vibration of Floor dueto Walking 476.3 Application of Cri
14、terion 496.4 Additional Considerations 506.5 Example Calculations 517. Evaluation of Vibration Problems andRemedial Measures. 557.1 Evaluation. 557.2 Remedial M e a sures 557.3 Remedial Techniques in Development. 597.4 Protection of Sensitive Equipment 60References 63Notation 65Appendix: Historical
15、Development of AcceptanceCriteria. 67 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.Chapter 1INTRODUCTION1.1 Objectives of the Design GuideThe primary objective of
16、 this Design Guide is to provide basicprinciples and simple analytical tools to evaluate steel framedfloor systems and footbridges for vibration serviceability dueto human activities. Both human comfort and the need tocontrol movement for sensitive equipment are considered.The secondary objective is
17、 to provide guidance on developingremedial measures for problem floors.1.2 Road MapThis Design Guide is organized for the reader to move frombasic principles of floor vibration and the associated termi-nology in Chapter 1, to serviceability criteria for evaluationand design in Chapter 2, to estimati
18、on of natural floor fre-quency (the most important floor vibration property) in Chap-ter 3, to applications of the criteria in Chapters 4,5 and 6, andfinally to possible remedial measures in Chapter 7. Chapter 4covers walking-induced vibration, a topic of widespread im-portance in structural design
19、practice. Chapter 5 concernsvibrations due to rhythmic activities such as aerobics andChapter 6 provides guidance on the design of floor systemswhich support sensitive equipment, topics requiring in-creased specialization. Because many floor vibrations prob-lems occur in practice, Chapter 7 provides
20、 guidance on theirevaluation and the choice of remedial measures. The Appen-dix contains a short historical development of the variousfloor vibration criteria used in North America.1.3 BackgroundFor floor serviceability, stiffness and resonance are dominantconsiderations in the design of steel floor
21、 structures andfootbridges. The first known stiffness criterion appearednearly 170 years ago. Tredgold (1828) wrote that girders overlong spans should be “made deep to avoid the inconvenienceof not being able to move on the floor without shakingeverything in the room“. Traditionally, soldiers “break
22、 step“when marching across bridges to avoid large, potentiallydangerous, resonant vibration.A traditional stiffness criterion for steel floors limits thelive load deflection of beams or girders supporting “plasteredceilings“ to span/360. This limitation, along with restrictingmember span-to-depth ra
23、tions to 24 or less, have been widelyapplied to steel framed floor systems in an attempt to controlvibrations, but with limited success.Resonance has been ignored in the design of floors andfootbridges until recently. Approximately 30 years ago, prob-lems arose with vibrations induced by walking on
24、steel-joistsupported floors that satisfied traditional stiffness criteria.Since that time much has been learned about the loadingfunction due to walking and the potential for resonance.More recently, rhythmic activities, such as aerobics andhigh-impact dancing, have caused serious floor vibrationpro
25、blems due to resonance.A number of analytical procedures have been developedwhich allow a structural designer to assess the floor structurefor occupant comfort for a specific activity and for suitabilityfor sensitive equipment. Generally, these analytical toolsrequire the calculation of the first na
26、tural frequency of thefloor system and the maximum amplitude of acceleration,velocity or displacement for a reference excitation. An esti-mate of damping in the floor is also required in some in-stances. A human comfort scale or sensitive equipment crite-rion is then used to determine whether the fl
27、oor system meetsserviceability requirements. Some of the analytical tools in-corporate limits on acceleration into a single design formulawhose parameters are estimated by the designer.1.4 Basic Vibration TerminologyThe purpose of this section is to introduce the reader toterminology and basic conce
28、pts used in this Design Guide.Dynamic Loadings. Dynamic loadings can be classified asharmonic, periodic, transient, and impulsive as shown inFigure 1.1. Harmonic or sinusoidal loads are usually associ-ated with rotating machinery. Periodic loads are caused byrhythmic human activities such as dancing
29、 and aerobics andby impactive machinery. Transient loads occur from themovement of people and include walking and running. Singlejumps and heel-drop impacts are examples of impulsiveloads.Period and Frequency. Period is the time, usually in sec-onds, between successive peak excursions in repeatingev
30、ents. Period is associated with harmonic (or sinusoidal) andrepetitive time functions as shown in Figure 1.1. Frequencyis the reciprocal of period and is usually expressed in Hertz(cycles per second, Hz).Steady State and Transient Motion. If a structural systemis subjected to a continuous harmonic d
31、riving force (seeFigure l.la), the resulting motion will have a constant fre-quency and constant maximum amplitude and is referred toas steady state motion. If a real structural system is subjectedto a single impulse, damping in the system will cause the1 2003 by American Institute of Steel Construc
32、tion, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.motion to subside, as illustrated in Figure 1.2. This is one typeof transient motion.Natural Frequency and Free Vibration. Natural frequencyis the frequency at w
33、hich a body or structure will vibrate whendisplaced and then quickly released. This state of vibration isreferred to as free vibration. All structures have a largenumber of natural frequencies; the lowest or “fundamental“natural frequency is of most concern.Damping and Critical Damping. Damping refe
34、rs to theloss of mechanical energy in a vibrating system. Damping isusually expressed as the percent of critical damping or as theratio of actual damping (assumed to be viscous) to criticaldamping. Critical damping is the smallest amount of viscousdamping for which a free vibrating system that is di
35、splacedfrom equilibrium and released comes to rest without oscilla-tion. “Viscous“ damping is associated with a retarding forcethat is proportional to velocity. For damping that is smallerthan critical, the system oscillates freely as shown in Fig-ure 1.2.Until recently, damping in floor systems was
36、 generallydetermined from the decay of vibration following an impact(usually a heel-drop), using vibration signals from whichvibration beyond 1.5 to 2 times the fundamental frequencyhas been removed by filtering. This technique resulted indamping ratios of 4 to 12 percent for typical office building
37、s.It has been found that this measurement overestimates thedamping because it measures not only energy dissipation (thetrue damping) but also the transmission of vibrational energyto other structural components (usually referred to as geomet-ric dispersion). To determine modal damping all modes ofvi
38、bration except one must be filtered from the record ofvibration decay. Alternatively, the modal damping ratio canbe determined from the Fourier spectrum of the response toimpact. These techniques result in damping ratios of 3 to 5percent for typical office buildings.Resonance. If a frequency compone
39、nt of an exciting force isequal to a natural frequency of the structure, resonance willoccur. At resonance, the amplitude of the motion tends tobecome large to very large, as shown in Figure 1.3.Step Frequency. Step frequency is the frequency of applica-tion of a foot or feet to the floor, e.g. in w
40、alking, dancing oraerobics.Harmonic. A harmonic multiple is an integer multiple offrequency of application of a repetitive force, e.g. multiple ofstep frequency for human activities, or multiple of rotationalfrequency of reciprocating machinery. (Note: Harmonics canalso refer to natural frequencies,
41、 e.g. of strings or pipes.)Mode Shape. When a floor structure vibrates freely in aparticular mode, it moves up and down with a certain con-figuration or mode shape. Each natural frequency has a modeshape associated with it. Figure 1.4 shows typical modeshapes for a simple beam and for a slab/beam/gi
42、rder floorsystem.Modal Analysis. Modal analysis refers to a computational,analytical or experimental method for determining the naturalfrequencies and mode shapes of a structure, as well as theresponses of individual modes to a given excitation. (Theresponses of the modes can then be superimposed to
43、 obtain atotal system response.)Fig. 1.1 Types of dynamic loading. Fig. 1.2 Decaying vibration with viscous damping.2 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher
44、.Spectrum. A spectrum shows the variation of relative am-plitude with frequency of the vibration components that con-tribute to the load or motion. Figure 1.5 is an example of afrequency spectrum.Fourier Transformation. The mathematical procedure totransform a time record into a complex frequency sp
45、ectrum(Fourier spectrum) without loss of information is called aFourier Transformation.Acceleration Ratio. The acceleration of a system divided bythe acceleration of gravity is referred to as the accelerationratio. Usually the peak acceleration of the system is used.Floor Panel. A rectangular plan p
46、ortion of a floor encom-passed by the span and an effective width is defined as a floorpanel.Bay. A rectangular plan portion of a floor defined by fourcolumn locations.1.5 Floor Vibration PrinciplesAlthough human annoyance criteria for vibration have beenknown for many years, it has only recently be
47、come practicalto apply such criteria to the design of floor structures. Thereason for this is that the problem is complexthe loading iscomplex and the response complicated, involving a largenumber of modes of vibration. Experience and research haveshown, however, that the problem can be simplified s
48、uffi-ciently to provide practical design criteria.Most floor vibration problems involve repeated forcescaused by machinery or by human activities such as dancing,aerobics or walking, although walking is a little more com-plicated than the others because the forces change locationwith each step. In s
49、ome cases, the applied force is sinusoidalor nearly so. In general, a repeated force can be representedby a combination of sinusoidal forces whose frequencies, f,are multiples or harmonics of the basic frequency of the forcerepetition, e.g. step frequency, for human activities. Thetime-dependent repeated force can be represented by theFourier series(1.1)whereP = persons weightFig. 1.3 Response to sinusoidal force.Fig. 1.4 Typical beam and floor system mode shapes.3 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not
