Dynamic Performance Requirements for Permanent Grandstands Subject to Crowd Action
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, N A G R O M A L G : S I C m o r f y p o c d e s n e c i L
The T he Ins Insti titu tuti tion on of Str Struc uctu turra l Engi ngineer neers s
The T he Ins Insti titu tuti tion on of Str Struc uctu turra l Engi ngineer neers s The T he Depa rtm tment ent for C ommu ommuni niti ties es a nd Loc Loc a l G overn overnment ment The T he Depa rtm tment ent for C ul ultu turre Media Me dia and a nd Spo Sporrt
Dec emb ember er 20 2008
Dyn yna amic pe per rfor orm manc e requirements for permanent grands ndsttands subj ubje ec t to c row owd d ac ac tion Rec o mm mmend enda a tio ns for mana manage gement ment,, design and assessment
Publi Pub lis she hed d b y the Ins Insti tituti tutio o n of o f Str Struc uc tur tura a l Eng Enginee ineerrs
The T he Ins Insti titu tuti tion on of Str Struc uctu turra l Engi ngineer neers s The T he Depa rtm tment ent for C ommu ommuni niti ties es a nd Loc Loc a l G overn overnment ment The T he Depa rtm tment ent for C ul ultu turre Media Me dia and a nd Spo Sporrt
Dec emb ember er 20 2008
Dyn yna amic pe per rfor orm manc e requirements for permanent grands ndsttands subj ubje ec t to c row owd d ac ac tion Rec o mm mmend enda a tio ns for mana manage gement ment,, design and assessment
Publi Pub lis she hed d b y the Ins Insti tituti tutio o n of o f Str Struc uc tur tura a l Eng Enginee ineerrs
The T he Ins Insti titu tuti tion on of Str Struc uctu turra l Engi ngineers neers The T he Depa rtm tment ent for C ommu ommuni niti ties es a nd Loc Loc a l G overn overnment ment The T he Depa rtm tment ent for C ul ultu turre Media Me dia and a nd Spo Sporrt
Dec emb embe e r 2008
Dyn yna amic pe per rfor orm manc e requirements for permanent grands ndsttands subj ubje ec t to c row owd d ac ac tion Rec o mm mmend enda a tio ns for mana manage gement ment,, design and assessment
Publi Pub lis she hed d b y the Ins Insti tituti tutio o n of o f Str Struc uc tur tura a l Eng Enginee ineerrs
Membership of the J oint Working Group Dr J W Dougill – Chairman Professor A Blakeborough – Oxford University Mr P Cooper – KW Ltd to July 2007, then INTEC Dr S M Doran – IStructE, Secretary Dr B Ellis – BRE to 2006 now Consultant Mr P F Everall – DCLG (to 2005) Dr T Ji – UMIST/ The University of Manchester Mr J Levison – Football Licensing Authority, d. 12th Dec. 2007 Dr J Maguire – Lloyd’s Register. (received papers from 2002) Mr S Morley – Bianchi Morley Mr M Otlet – W S Atkins Professor G A R Parke – Surrey University (to 2002) Mr J. G. Parkhouse – Parkhouse Consultants Professor A Pavic – The University of Sheffield Mr L Railton – Health and Safety Executive (to 2003) Mr W Reid – Consultant, URS Mr R Shipman, DCLG, (from 2005) Mr P Westbury – Buro Happold. (received papers from 2002) Mr M Willford – Ove Arup Professor J Wright –The University of Manchester/J2W Consulting Ltd
Corresponding Members Mr D Allen, National Research Council of Canada Dr M Kasperski, Bochum University Dr P Reynolds, The University of Sheffield Mr P Wright, Health and Safety Executive, from 2003
Contributors The Joint Working Group wishes to acknowledge the contribution of the following individuals who, though not attending as members of the Group, made presentations on different aspects relating to grandstand design, operation and behaviour. Mr D Allen, National Research Council of Canada Mr J Cutlack, J. Bobrowski and Partners Dr J Dickie, Crowdsafe Ltd Mr C Gleeson, Chelsea Football Club Professor M J Griffin, Institute of Sound and Vibration, Southampton University Dr M Kasperski, Bochum University, Germany Dr J Littler, BRE Dr A J Soane, Bingham Cotterell Published by the Institution of Structural Engineers International HQ, 11 Upper Belgrave Street, London SW1X 8BH, UK ISBN: 978-1-906335-12-0 © 2008: The Institution of Structural Engineers
The Institution of Structural Engineers, DCLG, DCMS and the members who served on the Joint Working Group which produced this report have endeavoured to ensure the accuracy of its contents. However, the guidance and recommendations given in the report should always be reviewed by those using it in the light of the facts of their particular case and specialist advice obtained as necessary. No liability for negligence or otherwise in relation to this report and its contents is accepted by the Institution, the members of the Joint Working Group their servants or agents. Any person using this report should pay particular attention to the provisions of this Condition. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without prior permission of the Institution of Structural Engineers, who may be contacted at 11 Upper Belgrave Street, London SW1X 8BH.
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Dynamic performance requirements for permanent grandstands subject to crowd action
Contents Foreword
v
1
Scope of the Recommendations
1
2
Design event scenarios
2
Listed Engineers
4
3.1 3.2 3.3 3.4 3.5
4 4 4 4 5
3
4
Natural frequencies and other dynamic properties
6
4.1 4.2
6
4.3 4.4
5
6
7
8
9
10
Requirement for spec ialist eng ineering expertise Tec hnical support Discretion on relevance of the Rec ommend ations to spe cific structures J udg ment on relevance of the Rec ommend ations to specific structures Monitoring Background Struc tural mod elling to determine mod al prop erties of the empty grandstand Values for initial design ‘Relevant’ natural frequenc y
6 7 7
Testing
8
5.1 5.2 5.3
8 8 8
Need for testing Aims of testing C ircumstanc es req uiring testing
Management responsibilities
10
6.1 6.2 6.3 6.4 6.5 6.6 6.7
10 10 10 11 12 12 13
Overall responsibility Design of new stands C hange of use and assessment for spec ific events Operationa l strategies to reduce dynamic respo nse and c rowd alarm Handover of new and structurally modified grandstands Operations Ma nual Operation
Route 1: Compliance with natural frequency requirements
15
7.1 7.2 7.3
15 15 15
Vertical excitation Side-to-side horizontal excitation Nod ding modes due to front-to-ba ck excitation
Route 2: Design for managed events
17
8.1 8.2 8.3 8.4 8.5 8.6
17 17 18 18 18 18
Outline Idea lised de scription of c rowd activity Servic ea bility: Toleranc e of motion Servic ea bility: Displac ement limits Ultimate load capa c ity Fatigue
Analysis of dynamic performance
19
9.1 9.2 9.3 9.4
19 19 19 19
Impulse loa ds Horizontal loads due to pe riodic excitation Analysis for vertic al periodic excitation Human struc ture interaction
Use of the Recommendations
Dynamic performance requirements for permanent grandstands subject to crowd action
21
iii
Appendix 1 Background to human structure interac tion
22
A1.1 A1.2
22 22 22 23 23 23
A1.3
A1.4 A1.5
A1.6
Introd uc tion Basic principles A1.2.1 Mod elling human structure interaction A1.2.2 Active and pa ssive be haviour Ap plica tion of the theory A1.3.1 Direc t app lication of the theory A1.3.2 Approximate analysis using an assumed mode shape for the c rowd ’s motion Bod y Unit prop erties and loadings Analysis and results A1.5.1 Mod al analysis A1.5.2 Root mean squa re (RMS) accelerations and ac celeration limits A1.5.3 Analysis with a dominant mod e. A1.5.4 Multi-mode analysis Referenc es
24 24 24 24 24 25 25 26
Appendix 2 Body unit properties and recommended loading
27
A2.1 A2.2 A2.3 A2.4 A2.5
27 27 28 29 30 30 30 31 32
A2.6 A2.7
Bod y unit and structure C rowd bo dy elements Rep resentation of periodic load ing Internal ‘d rivers’- G i – produc ing dynamic crowd loa ding The c rowd effec tiveness fac tor ‘t’ A2.5.1 Sc enario 4 A2.5.2 Sc enarios 2 and 3 Mo nitoring and ba ck analysis Referenc es
Appendix 3 Calculation of modal properties
33
A3.1 A3.2 A3.3
Introd uc tion Mo da l analysis and natural frequenc ies Basic errors: two prime suspects A3.3.1 Distinc tion between force and mass A3.3.2 Stiffness A.3.4 Methods for c alculation of natural frequenc ies A3.4.1 G eneral comment A3.4.2 Approximate analysis A3.4.3 C omp uter based analysis A3.5 C onsequences of mistaken idealisations A3.6 C omment A3.7 Further information
33 33 35 35 35 36 36 36 36 36 37 38
Appendix 4 Dynamic testing of grandstands and seating decks
39
A4.1 A4.2 A4.3 A4.4 A4.5
39 39 40 41 43 43 43 43 44 45 45 47 47
A4.6 A4.7 A4.8
Introd uc tion What should be tested and what results are needed? Analysis and testing Princ iples of dynamic testing Exc itation sources and testing tec hniques A.4.5.1 Ambient vibration survey (AVS) A.4.5.2 Heel-drop testing A.4.5.3 Mea sured impact testing A4.5.4 Shaker testing of different types and comp lexity A.4.5.5 Future developments Spec ifica tion and proc urement Reporting Further Information
Appendix 5 Bibliography
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Dynamic performance requirements for permanent grandstands subject to crowd action
FOREWORD The Joint Working Group met first in January 2000. Its Interim Guidance was published in November 2002 in response to concerns over crowd action on structures generally and on the relevance of available recommendations to dense crowd loading on permanent grandstands. The Interim Guidance used the vertical natural frequency, for the mode of vibration that could be excited and felt by people on the seating deck, as the currency to determine different categories of permissible use. No attempt was made to recommend a method of estimating performance by calculation as it was considered that existing procedures, though widely used, could not be relied on. The Interim Guidance was designed to be safe and straightforward to apply. It provided a significant relaxation of the ‘trigger value’ frequency limits of BS6399 (1996) and the 1997 Green Guide. However, because of the simplification of using natural frequency as the single factor determining a category of use, it was a broad brush treatment. What was needed was a method of design and operation that was based on an estimate of performance that was reasonable when compared with the effects observed with active crowds in real structures. This was the task of the Joint Working Group from 2002 onwards. In addressing the technical issues relating to the analysis of the structure, the Joint Working Group has been closely involved with a number of UK research projects (almost all supported by the Engineering and Physical Sciences Research Council, EPSRC) that have been undertaken since 2000 and which have contributed to an improved understanding of the physical problem of how human beings interact with moderately flexible structures. This work has provided the basis for the technical content in the new Recommendations. However, this could not be seen as an end in itself. A key issue in design is how to deal with uncertainty. With grandstands, there can be no absolute certainty on the way any random group of people will behave. Accordingly, the technical provisions have been set in a framework of procurement, management and operation aimed at minimising risk by managing uncertainty. The Recommendations propose that specially ‘Listed Engineers’, having particular experience and capability, be used in the design and assessment of grandstands for dynamic crowd loading. Design should be based on the concept of managed events described by standard Design Event Scenarios that form part of the specification for a stand. Within these scenarios, the Management of the facility takes responsibility for speci fic agreed measures to mitigate the effects of motion. Hand-over procedures are outlined with the aim of ensuring that the design calculations relate to the as-built structure. The aim of each of these recommendations is to reduce uncertainty where it is possible to do so. The Recommendations are written for everyone who has responsibility for grandstands. This includes the owners, operators, managers, architects, insurers and engineering designers as well as Local Authority staff dealing with building control and safety issues. The Recommendations are accompanied by Appendices directed particularly at the engineering analyst and designer. The Recommendations relating to specification, management and operation should be considered to be of equal importance to providing comfort and safety as the technical guidance addressed principally to the engineering designer.
Dr John W Dougill December 2007
Dynamic performance requirements for permanent grandstands subject to crowd action
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Dynamic performance requirements for permanent grandstands subject to crowd action
1 Scope of the Recommendations The Recommendations given here are for use in the design or assessment of permanent grandstands and relate solely to dynamic action due to crowd activity. Reference should be made to other guidance and relevant Standards for other load cases and design requirements.
The Recommendations also include guidance relating to Management’s role in design and in implementing operational requirements for stands being used for events at which dynamic crowd loading can be expected. This guidance is concerned only with those aspects of crowd management that directly influence the structural response of a grandstand and so supplement, but do not replace legal and Standards’ based requirements for safe operation. The operational arrangements adopted should be taken into account by those undertaking an overall risk assessment at the scheme design stage or for a specific event. The Recommendations apply to grandstands with seating decks constructed in structural steel, reinforced or prestressed concrete and combinations of these forms of construction. No recommendations are made for the use of subsidiary systems to provide additional damping or active control. The Recommendations are considered relevant to grandstands with seating decks having a supported span greater than 6m or cantilever spans of more than 2.5m. However, it is recognised that, even within the declared scope of these Recommendations, there may be particular grandstands for which the layout, form of construction or limited use might render it unnecessary to undertake a full check on dynamic performance. The manner in which this can be dealt with is treated in Section 3 on Listed Engineers. The Recommendations revise and extend the recommendations given in t he November 2001 report ‘Dynamic performance requirements for permanent grandstands subject to crowd action: interim guidance on assessment and design’ , published by the Institution of Structural Engineers and adopted by DCLG and DCMS. This Interim Guidance used the vertical natural frequency of the empty grandstand as the sole criterion for assessing the acceptability of grandstands for use with crowds likely to generate dynamic loading. This convenient, but coarse grained, approach is retained as an option in the present guidance which now provides an alternative approach that depends on engineering estimates of the likely performance of a grandstand for events at which the event organiser is responsible for specific agreed measures relating to crowd management. This alternative approach provides further options for the designer and management as well as addressing a need to account for influences on behaviour additional to natural frequency. As a consequence of this approach, there are two Routes available for design and assessment of grandstand structures subject to dynamic crowd loading, •
•
Route 1: Based on limiting values of natural frequency for the grandstand empty of people. Route 2: Based on estimates of performance of grandstands calculated for specified managed events.
A grandstand may be considered to meet the Recommendations for dynamic crowd loading if the requirements of either one or other of these routes are met together with the separate conditions for horizontal strength and stability. (See Sections 7.2, 7.3 and Table 2).
Dynamic performance requirements for permanent grandstands subject to crowd action
1
2 Design Event Scenarios The Design Event Scenario forms the basis for a design specification for dynamic performance of a grandstand under crowd loading. Table 1 gives standard Design Event Scenarios for use in communicating design objectives in terms of anticipated performance. The Table shows a range of different events together with the expected activity of the crowd and an indication of crowd control measures to be provided by the management of the grandstand. The four performance based scenarios (numbered 1 to 4) correspond to increasing crowd involvement and activity together with increased loading. Scenarios 1 and 2, appropriate for viewing sporting events and classical concerts, would normally be satisfied by Route 1 requirements. Scenario 3 refers to lively concerts and high profile sporting events whilst Scenario 4 is for high energy events such as pop/rock concerts. The Scenarios are provided in order to assist event specific assessment and to provide a yardstick for authorities concerned with safety certification. It will be evident that the Design Event Scenario is the statement of what should be covered in design and what needs to be managed. The Scenario comprises a reference to the category of event in Table 1 with a statement of any additional specific crowd control measures that have been agreed as being required. ( See Section 6.4 on Operational Strategies). It should be noted that the descriptions of exemplar events are indicative rather than prescriptive. For example, an event may be described as a pop-concert for publicity purposes but the crowd’s reaction may be only moderate and so more consistent with a concert with medium tempo music as envisaged for Scenario 3. Accordingly, in using records of past events to assist an assessment for a future event, care should be taken to do this on the basis of observed performance and not solely on a record that a ‘pop-concert’ had been run satisfactorily in the past. (See Section 6.7 on Operation, re. record keeping). The Scenarios are based on experience of events in the United Ki ngdom. In assessing any specific event, judgment will be needed to decide the appropriate category particularly between Scenarios 3 and 4 and, on occasion, whether the crowd at a particular sporting event is likely to be more than usually active with coordinated rhythmic activity. This has become common at football matches in mainland Europe where groups of fans have rehearsed bobbing, treading or stamping in time to a beat provided by their leader. The improved coordination accompanying behaviour of this sort can lead to motion that is more severe than that anticipated for Scenario 4. This could lead to possible discomfort for seated or standing fans not participating in the activity. Such situations need to be recognised and appropriate operational measures adopted by Management. (See Section 6.4 on Operational strategies).
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Dynamic performance requirements for permanent grandstands subject to crowd action
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Dynamic performance requirements for permanent grandstands subject to crowd action
3
3 Listed Engineers
3.1 Requirement for specialist engineering expertise Grandstands, and particularly the combination of a crowd of people and a grandstand, provide technical and managerial problems that can be addressed satisfactorily only by engineers with appropriate specialist expertise in addition to all round competence underpinned by professional qualifications. Whichever Route is chosen for design or assessment, it is important that these functions, and the provision of advice on safe operation, are undertaken by an engineer having relevant expertise in the structural design and safe operation of grandstands. At the request of Government, the Institution of Structural Engineers is putting in place a scheme to provide a list of engineers with specific experience in the design, assessment and safe operation of grandstands for dynamic crowd loading. In these Recommendations, such engineers will be referred to as Listed Engineers. It is proposed that any Design Team dealing with new grandstands or significant alteration to existing grandstands should include a Listed Engineer with particular responsibility for overseeing those aspects of design concerned with dynamic crowd behaviour. Similarly, a Listed Engineer should be employed in assessing existing stadia and in overseeing the hand-over procedures of new and altered grandstands.
3.2 Tec hnical support Listed Engineers will be expected to have sufficient personal specialised knowledge and expertise relating to the design and safe operation of grandstands to advise management on all aspects connected with dynamic crowd loading. However, it would be expected that Listed Engineers themselves may need to employ specialist support in respect of physical testing and the conduct of dynamic structural analysis undertaken under their direction or on their instruction.
3.3 Discretion on relevance of the Recommendations to specific structures Grandstands vary in type, size and manner of use. Depending on the circumstances, detailed consideration of crowd action may not be appropriate for a particular grandstand and, based on their experience and technical background, Listed Engineers will be expected to use their discretion in deciding the relevance of the Recommendations to such cases. The Listed Engineer’s report to the grandstand’s Management should make clear whether discretion has been exercised and the reason for doing so. It will be appreciated that the management of a grandstand has responsibility for the safety of the facility and so needs to understand and take responsibility for accepting the Listed Engineer’s recommendations. The Listed Engineer’s report should also be made available to the Local Authority concerned with Building Control and Safety Certification.
3.4 J udgment on relevance of the Recommendations to specific structures Listed Engineers will be expected to have the necessary background to use their own judgment in interpreting and applying the Recommendations to particular grandstands. The main areas for exercising judgment will normally be in advising the client when choosing the appropriate Design Event Scenario, in detailed consideration of the approximations involved in structural modelling and in assessing the need for structural testing.
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Dynamic performance requirements for permanent grandstands subject to crowd action
In making these judgments, the Listed Engineer should bear in mind that, in respect of dynamic behaviour, the aim should be to remove the need to consider structural behaviour from the wider risk assessment necessary for an event as a whole. If followed, the Route 1 approach provides for this based on measured natural frequencies and the frequency limits in Figure 1. (See Section 6.6 ). The Route 2 approach provides more flexibility in decision making but depends on estimates of performance using calculations based on recommended values for crowd loading that are considered typical for different types of events. Sufficiently accurate values of natural frequency are required for both approaches whilst a Route 2 analysis needs a more complete knowledge of dynamic behaviour including a full set of relevant modal properties. Because of the importance of accurate knowledge of dynamic properties, either in characterising the admissible use of a grandstand using Route 1, or, as the basis of design or assessment by Route 2, it will normally be considered necessary for the values of dynamic properties to be established, or checked, using physical testing. ( See Section 5 on Testing). There will be circumstances where testing is not necessary, so placing a particular responsibility on the Listed Engineer to exercise personal judgment on the need for physical testing to check or establish values of dynamic properties. Such a judgment should not be influenced by considerations of cost, convenience or time pressure but, solely, on a decision that, in the particular circumstances being considered, the wider information available from testing would not materially affect decisions on either design or assessment. As in the use of discretion on the relevance of Recommendations to a particular grandstand, the Listed Engineer’s report to the grandstand’s management should make clear whether personal judgment has been exercised on any particular Recommendation, including the need for testing, and the reason for doing so. The Listed Engineer’s report should also be made available to the Local Authority concerned with Building Control and Safety Certification.
3.5 Monitoring The Listed Engineer should be involved with and advise on any programme to monitor the behaviour of a stand whilst in use under crowd loading. Monitoring could include visual recording of crowd behaviour, acceleration and load measurements, stewards’ reports etc.
Dynamic performance requirements for permanent grandstands subject to crowd action
5
4 Natural Frequencies and other dynamic properties
4.1 Background Partly as a result of testing undertaken since the adoption of the Interim Guidance, the concern on possible differences between calculated values of natural f requency and values determined by competent testing has been reinforced rather than allayed. Differences of up to 30% between measured and calculated natural frequencies have been recorded. Also, it is rare that even approximate agreement between calculated values and those from testing is obtained without some reappraisal of the structural model used in the calculation. The largest differences in values usually follow from misguided initial qualitative assessments of likely structural behaviour that then determine the form and extent of the structural model used in the calculation. However, even with carefully considered structural models and with the most diligent attention to detail, differences of up to 15% between calculated and physically determined values ar e common. These differences can be expected. The structural model will normally be based on assumed material properties and idealisations of the connectivity between structural elements comprising the grandstand structure together with assumptions on how much of the structure needs to be modelled. In addition, there will be uncertainties in the contribution of mass and stiffness from the nonstructural elements. In contrast to this, the as-built structure responds to excitation, either in a test environment or due to crowd loading, according to how it is actually constructed and maintained. The possible discrepancy between values of dynamic properties used in calculation and those found by testing may be sufficient to affect an assessment of performance based on the Route 2 method or a determination of the appropriate category of use by the Route 1 method. The uncertainty attached to using values obtained by calculation alone can be minimised by physical testing of the structure while empty of people; either as part of the hand-over procedures for new or modified structures or as part of a subsequent assessment.
4.2 Structural modelling to determine modal properties of the empty grandstand Although any form of linear elastic dynamic analysis with linear damping may be used, modal analysis using a finite element representation of the grandstand structure is likely to be the preferred method except for all but the simplest structures. Appendix 5 provides details of the theory underlying the method and notes on modelling grandstand structures for calculation of natural frequencies are given in Appendix 3. These notes indicate aspects where particular care needs to be taken in developing the finite element model so that all factors influencing the dynamic characteristics of the grandstand are adequately represented. The structure should be analysed to determine the natural frequencies, mode shapes and related modal masses in the absence of people, but including the mass of all fixtures and fittings that are involved in motion of the structure. The modes that indicate significant motion of the seating deck, and are capable of being excited by people on the deck, need to be identified, together with their natural frequencies. The lowest of these natural frequencies is taken to be the natural frequency for vertical excitation of the empty grandstand to be used in the Route 1 design or assessment. ( See Section 4.4 on Relevant Natural Frequency). A Route 2 estimate of performance should be based on all the modes that are considered to be capable of providing significant motion of the seating deck.
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Dynamic performance requirements for permanent grandstands subject to crowd action
4.3 Values for initial design Engineers undertaking the design of new structures should be aware of the potential difference between natural frequencies calculated using even the best practice and the values that will obtain in the completed structure. In design, it will be prudent to allow for a minimum plus or minus 0.5 Hz variation between calculated values of natural frequency and those that will influence performance in the actual structure. Variations of this magnitude are not unusual in comparing calculated and measured values of natural frequency and can have significant effect on estimates of performance.
4.4 ‘Relevant’ natural frequency Design or assessment using the Route 1 approach is determined by a single value of natural frequency. It is important to note that this is the relevant natural frequency that corresponds to the mode of vibration with the lowest natural frequency at which people can excite the seating deck and feel its motion. It should be noted that the relevant natural frequency may not be the lowest natural frequency that is determined by testing or analysis. Testing might show that a low frequency mode exists but this needs to be assessed to determine whether a crowd on the seating deck can excite the mode significantly. As an example, consider a roof that vibrates with large amplitude vibrations at low frequency when excited by wind action. If the roof and the seating deck are connected so that there is a ‘vibration path’ between them, the effect of the ‘roof mode’ might be found in tests on the seating deck even though the amplitude of the deck displacement is small compared to that of the roof. In such cases, decisions on whether a particular mode is, or is not, ‘relevant’ are better based if the values of natural frequency from testing are supplemented by additional data on other modal properties. Also, inclusion of ambient testing (See Appendix 4) in a test programme would provide information that could help to identify modes driven primarily by sources separate from a crowd on the seating deck. Testing may also reveal the occurrence of so called global modes of vibration in which the whole grandstand, concourses, seating deck and roof may be involved in frontto-back, sway or torsional motion. Again the ‘relevant’ natural frequency is the lowest frequency corresponding to those modes by which people can excite the seating deck through vertical movement and feel its motion. In some global mode cases, such as with front–to-back ‘nodding’ modes of upper cantilevers due to flexibility in the main supporting structure, it may not be possible to decide, from the results of testing alone, which is the appropriate relevant natural frequency on which to base an assessment or indeed whether it is possible that several modes might be simultaneously excited by crowd action. In such cases, it will be necessary to use the Route 2 approach and supplement the assessment with calculations of performance using more than one mode of vibration.
Dynamic performance requirements for permanent grandstands subject to crowd action
7
5 Testing
5.1 Need for testing In deciding on the need for testing, both the Listed Engineer and the Client should be aware of the uncertainties in determining dynamic properties solely by calculation and the benefits of obtaining confirmation of the values used in design or assessment through physical testing of the as-built structure. The Listed Engineer should be fully involved in advising on the choice of a competent Test Agency with appropriate expertise for testing grandstands and should advise on the test programme to be adopted. A revised version of the guidance on testing, first published by the Institution of Structural Engineers in 2002 as the Advisory Note, Dynamic testing of grandstands and seating decks, is provided in Appendix 4.
5.2 Aims of testing Testing may be undertaken with one or more of the following aims in mind. •
•
•
•
To check calculated values of natural frequency used to determine the acceptability of a grandstand according to the Route 1 method. The programme of testing can also be designed to reveal whether the most critical mode of vibration has been identified in the analysis and whether the influence of global modes of vibration needs to be investigated. (See Section 4.4 on Relevant Natural Frequency ). To check values of modal properties against those derived using the analytical model and so determine whether calculations of performance using the Route 2 approach can be considered relevant to the as-built structure. If the discrepancies between calculation and testing are significant, the results from testing can be used to inform revisions of the structural model and estimates of dynamic performance. To demonstrate to the Client that the assumptions used in calculating natural frequencies or calculating performance are consistent with the grandstand meeting the acceptance criteria for the specified Design Event Scenario. To monitor the performance of the grandstand under crowd loading during concerts and other high energy events.
5.3 Circumstances requiring testing In the absence of records of earlier testing to determine natural frequencies, and unless the Listed Engineer recommends that testing is not necessary, the following structures should be tested. •
•
•
Grandstands with seating decks that are to be used with pop-concerts and oth er events, such as some political, sporting or religious events, where high energy synchronised rhythmic crowd movement can be expected (Scenario 3 and 4). Grandstands where significant complaints have been received concerning motion experienced in the stand. Grandstands where there is to be a change of use to one involving significantly greater dynamic crowd activity.
8
Dynamic performance requirements for permanent grandstands subject to crowd action
The tests are to be undertaken on the grandstand empty of people but fully fitted out with seating and services as would be in place during operation. In planning testing, it will be convenient for the Client, and also good practice, to include a programme of testing in the acceptance procedures for new and substantially modified grandstands before handover to the Owners or Managers. The requirements for testing should be linked to the specification of the stand and the Design Event Scenario used in design. ( See Section 6.5 on Handover procedures for new and structurally modified structures).
Dynamic performance requirements for permanent grandstands subject to crowd action
9
6 Management responsibilities
6.1 Overall responsibility The safety of people using viewing facilities such as grandstands is the responsibility of the Owners and Managers of the facility.
6.2 Design of new stands With a new grandstand, it is the Client/Management’s responsibility to make sure, from the outset, that the Design Team includes a Listed Engineer who will have particular responsibility for advising on dynamic performance. Management’s responsibility then continues through subsequent discussions with the Design Team in which the use of the structure, and how it will be operated, is discussed and agreed. Whilst working as a member of the Design Team, the Listed Engineer also reports directly to the M anagement on matters affecting dynamic performance, including any implications that might arise from changes proposed following ‘value engineering’ to meet budget constraints. In principle, all grandstands could be required to be designed to provide both safety and comfort for all possible uses including those likely to produce the most severe dynamic crowd loading that can be envisaged. In many cases, depending on the use of the stands, such designs would not be practical or economic. They would have very high initial cost and would provide levels of performance that might never be needed in the life of the structure. The approach recommended here is for Management to be fully involved in developing operational strategies to be used with the selected Design Event Scenarios that become the agreed basis for design for dynamic crowd loading. Besides the physical characteristics of the grandstand, overall dimensions and capacity, each Scenario should include the descriptions of the crowd and levels of activity to be used by the Design Team in estimating performance together with any crowd control measures that are required to be implemented by Management. It is important that the Management understands its role in setting this agenda for design and the subsequent continuing responsibility to make sure that the control measures anticipated at the design stage are made effective during operation of the stand.
6.3 Change of use and assessment for specific events Management has the responsibility to engage a Listed Engineer and any necessary support, to form an Assessment Team when changes of use of a grandstand are considered that could involve the potential for increased dynamic crowd loading. Here the team is led by the Listed Engineer who reports directly to Management. Management should accept that the Listed Engineer is engaged to provide an objective assessment and not necessarily to approve any proposed arrangement. The Listed Engineer will assess schemes that are proposed and, where this may be helpful, propose additional measures to mitigate dynamic crowd action and its effects. However, there could be situations where the Listed Engineer’s advice is that a grandstand should not be used for certain types of events. It is important that Management should bear in mind the Design Event Scenario already used in design or established in a prior assessment and seek the Listed Engineer’s advice, before proceeding to schedule an event and book a particular Gr oup or Performer. It will be evident that assessment for specific events should not be overshadowed by contractual arrangements in which a Music Group or Performer has already been engaged
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Dynamic performance requirements for permanent grandstands subject to crowd action
to appear. In such circumstances, the Listed Engineer should make sure that the terms of engagement preclude any liability to meet the costs of a cancellation that might be considered a consequence of the Listed Engineer ’s advice.
6.4 Operational strategies to reduce dynamic response and crowd alarm The following are examples of management strategies that can be used to reduce the effects of dynamic crowd loading. •
Netting off. Part of a stand, usually the front rows of a cantilever where dynamic loading has the most severe consequences, can be made inaccessible to spectators by ‘netting off’ the relevant rows.
•
No standing areas. Areas can be designated where spectators are required to remain seated. This would avoid the occurrence of most severe forms of dynamic crowd loading emanating from that area. This strategy requires practical stewarding issues to be addressed because dynamic response could build up quickly were a group of spectators suddenly to become active. For Lively Concerts or Pop-concerts (Design Event Scenarios 3 and 4 in Table 1), the area of designated seating should have specific ticketing arrangements and the seated people should have an adequate view of the stage so that any inclination to rise for a better view is eliminated. The sight lines for designated areas should be assessed on the basis that people in the remainder of the stand may be standing, bobbing or jumping. People in designated seating areas should be advised that they are likely to feel motion of the stand.
•
Temporary supports. If demonstrated by appropriate calculations or past performance, temporary supports (or props) can be used to modify the dynamic behaviour of the grandstand for specific events. Ideally, the potential use of temporary supports should be considered at the scheme design stage when it will be easier to arrange for the supports to be associated with an adequate load path.
•
Curtailment of music. Arrangements can be made to cut the visual and/or audio stimulus to crowd behaviour if the structural response approaches an unacceptable level. This strategy provides an ultimate safeguard but there are difficulties in implementation. Instrumentation is needed to monitor acceleration of the seating deck. The build up of response can be very rapid so that there is a need for a fixed response level for curtailment rather than rely on ad hoc decision making. However, automatic curtailment could be triggered by a single event or sharp transients that have little relevance to the overall reaction of the crowd. One approach used in practice employs a traffic light system on stage with green indicating safe operation, amber showing caution and red indicating danger which should be followed by cut-off.
•
Advice to ticket holders. Experience has shown that it is beneficial to advise the audience that,
a)
during a concert, they may become aware of movement of the stand,
b)
some structural movement due to crowd action is expected and considered in the design, and
c)
the stand is designed and operated to be safe and not fail structurally even under extreme movement.
Experience suggests that advance information of this kind provides reassurance, minimises the likelihood of complaints and reduces a tendency to panic.
Dynamic performance requirements for permanent grandstands subject to crowd action
11
6.5 Handover of new and structurally modified grandstands Where testing is included in the specified handover procedures for a new or significantly structurally modified grandstand, Management, representing the Client, should require the Listed Engineer, in association with the Practice responsible for the design, to: •
•
•
•
•
Measure dynamic properties to determine the relevant vertical natural frequencies and their associated mode shapes and damping values for all relevant areas of seating in the completed structure. These areas of seating are likely to include long back spans and cantilevers on long props to the rear of large seating decks as well as front cantilevers. Review the test results and corresponding values calculated using the analytical model. If necessary, refine the analytical model and compare test and recalculated results. If not already fully allowed for in the calculation of the dynamic properties, consider the effects of the actual values of material properties in the as-built structure, actual connection stiffnesses, foundation stiffness and other boundary conditions used in the analysis (such as the interface with the roof). Report on the results of testing and calculation of dynamic properties. For seating decks designed using the Route 1 method, advise Management on the permissible range of use as given in Figure 1. Alternatively, reassess the design in the light of the test results using the Route 2 method and advise Management on the appropriate Design Event Scenario and associated management requirements. For seating decks designed using the Route 2 approach, confirm that the measured dynamic properties are consistent with the performance calculated to meet, or improve on, the specified Design Event Scenario. Alternatively reassess the calculated performance in the light of the measured properties and advise Management accordingly.
The test results and results of calculations should be fully documented and included in an interpretive report to be included in the grandstand Operations Manual together with detailed structural drawings of the grandstand. Management should review the report and recommendations provided with the Listed Engineer/Design Team and agree any changes necessary to achieve acceptable performance. These should be documented and included in the Operations Manual. It should be noted that it is the responsibility of Management, acting for the Client, to make sure that consequences of the measured dynamic performance and any changes in the Design Event Scenario and associated management requirements are communicated to the Local Authority safety advisory group and all operational personnel including those planning events, police and other emergency services, safety managers, ground staff and stewards as necessary.
6.6 Operations Manual Management should not accept a new or structurally modified stand without being provided with the Operations Manual that has been prepared for the stand by the principal contractor with assistance from the designers where required. The following should be included in the Operations Manual: •
A summary of the dynamic response characteristics including lowest relevant vertical frequencies, associated mode shapes and damping for each significant area of seating in the structure incorporating the stand.
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Dynamic performance requirements for permanent grandstands subject to crowd action
•
•
A description of the Design Event Scenarios considered and the anticipated response of the structure to these together with any crowd management measures required to be implemented by Management. A record of the Engineering Practice and Listed Engineer responsible for the static analysis of the structure and of the dynamic analysis of the structure and the Test Agency responsible for the measurement of dynamic performance. The record should include similar records for any separate sub-analyses of the dynamic performance of elements within the structure carried out by others such as for precast concrete seating units.
The Operations Manual should be up-dated following changes in operational procedures and/or structural modifications.
6.7 Operation The assessment of the dynamic performance of a grandstand should be seen as part of the broader risk assessment dealing with the event, the venue and the crowd and the implications for safe management. In relation to the structure itself, it is accepted that, with appropriate management and controls, many existing stands can be operated safely even though the relevant natural frequency does not satisfy the Route 1 requirements. However, if a stand is to be used in these circumstances, it is important that control measures adopted are based on the following principles. •
•
•
An existing agreed and recorded Design Event Scenario which should include details of any measures adopted to reduce dynamic response. (See Section 6.4). Sufficient knowledge of the relevant dynamic properties of the structure and the behaviour of the stand under earlier, and possibly less severe, conditions of crowd loading. Use of a Listed Engineer for detailed assessment and direction on measures needed to implement Route 2 Recommendations.
In addition, Management should be aware that both design and assessment for dynamic crowd loading involves uncertainties, particularly in the make up of a crowd at any particular event and the level of excitation that the crowd provides to the structure. Because of this, the crowd management requirements included in the Design Event Scenario should be seen as good guidance based on the best knowledge available but subject to review following each event. It is within the responsibilities of Management to build a knowledge base concerning the performance of its grandstands so that management controls can be revised if this is necessary to maintain adequate safety levels. Fine tuning of crowd control measures can be expected following the first use of a stand for different types of events. The knowledge base should typically contain: •
A detailed description of each event.
•
CCTV records of crowd activity preferably synchronised with an audio record.
•
Audio tapes from concerts; particularly pop-concerts and high energy events.
Dynamic performance requirements for permanent grandstands subject to crowd action
13
•
•
Stewards’ reports noting any signs of structural motion and extremes of crowd behaviour including signs of panic. – a standard report form is available and can be downloaded from www.istructe.org/technical/db/277.asp Records of complaints, relating to perception of structural motion, from members of the public attending events. (See Section 8.3 on individuals’ tolerance of motion).
These operational records should be available for reference by the Listed Engineer when employed to advise on modifications to existing procedures or structural modifications.
f 0 >
6 Suitable for all types of events Scenarios 1, 2, 3 and 4
Management to monitor use of incidental music and maintain records of audience feedback including complaints
For seating areas with f 0 < 3, resonance could occur with the first harmonic of the crowd loading with consequent large structural movements
Management is advised to monitor the crowd’s reactions at all events
2
f 0 >
3.5 Minimum for new construction Suitable for viewing sport and other events with predominantly seated audiences. Scenarios 1 and 2
Only Scenario 1
3
Existing stands with 3 < f 0 < 3.5 may be deemed satisfactory for sports viewing (i.e. Scenario 1) on the basis of past experience and use for less lively sections of the crowd
4
5
Relevant vertical natural frequency of seating deck,
6
7
f 0 Hz
Figure 1 Route 1 requirements for different c ategories of use
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Dynamic performance requirements for permanent grandstands subject to crowd action
7 Route 1: Compliance with natural frequency requirements
7.1 Vertical excitation Grandstand seating decks should meet the requirements of relevant natural frequency for different categories of use as shown i n Figure 1.
7.2 Side-to-side horizontal excitation In contrast to temporary or demountable grandstands, there has been little cause for concern over the behaviour of existing permanent grandstands subject to horizontal excitation due to crowds with individuals swaying from side to side or indulging in a Mexican wave. No problems associated with crowd comfort should be experienced for grandstands with natural frequencies for horizontal excitation greater than 1.5 Hz. However, the connection of the seating deck to the principal members and also the primary structure should be designed to resist the horizontal loads due to side-to-side motion of a crowd. Accordingly, it is recommended that the stand should be designed to withstand the additional horizontal loads in Table 2 as part of the design for static loading.
7.3 Nodding modes due to front-to-back excitation Because of the rake of a cantilever seating deck, there will be a horizontal component of displacement as well as a vertical component due to crowd action. This is accentuated if the structure supporting the cantilever is itself flexible. The result is a nodding mode encompassing both the cantilever and its support. This behaviour is distinct f rom side to side motion due to sway of crowd and is primarily a result of vertical excitation wi th the response being magnified due to lack of stiffness in the structure supporting the seating deck. (See Appendix 1, Section A1.5.2 on acceleration limit s). As in the treatment of side-side horizontal excitation, it is recommended that the stand should be designed to withstand the additional horizontal loads in Table 2 as part of the design for static loading. The occurrence of nodding modes and their significance should also be investigated as part of a Route 2 analysis.
Dynamic performance requirements for permanent grandstands subject to crowd action
15
Table 2 Design for horizontal strength and stability To be used with both Route 1 and Route 2 method s of design and assessment In add ition to the operational wind loading, grand stands should be c ap ab le o f withstanding the following lateral loa ding due to crowd action. The loads should be inc orporated in the static de sign for ultimate load of the structure in co mbination with other design loads.
Type of use
Additional static horizontal load as a percentage of the specified static live loading on the seating deck
All grandstands except those used for pop -conc erts or similar lively ac tivity Grand stands to be used for pop-concerts or other lively events
Side to side
Front to back
±5%
±5%
±7½%
±7½%
Notes i)
The loa ds are specified as a percentage of the spe cified live loa ding on the sea ting dec k. Note only loa ding on the seating dec k need s to be considered.
ii)
The horizontal load should be a pp lied in the plane of the sea ting de ck in the way the p eop le a re situated a c cording to the ava ilab le sea ting.
iii) The horizontal load s due to c rowd action are add itional to loadings from other causes and so should be ap plied in c ombination with operational wind loa ds. iv) The pa rtial load fac tors to be used in eac h loa d c ase should be those spe cified for live loa ds in the a pp rop riate C od e of Prac tice for the structural material involved. A pa rtial fac tor of 1.5 should b e used with the given horizontal loa ds in loa d c ombinations with fac tored values of dead a nd imposed loa ds.
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Dynamic performance requirements for permanent grandstands subject to crowd action
8 Route 2: Design for managed events
8.1 Outline The Route 1 design method is intended to provide a simple check for safety and serviceability. The approach is based solely on the physical characteristics of the grandstand and so does not require analysis of the performance of the grandstand under dynamic crowd loading or consideration of particular measures of crowd control that might be adopted by Management. The Route 2 method requires the grandstand to be analysed to estimate its performance under dynamic loadings specified for different classes of activity and size of crowd on the seating deck as described in the relevant Design Event Scenario incorporating the management controls. The recommended method of analysis requires consideration to be given to human structure interaction due to the grandstand acting in combination with the crowd treated as load generating structural elements. (See Appendix 1 giving the background to human structure interaction). The performance of the seating deck is described by the displacements, accelerations and stress resultants calculated using the specified crowd loading. The grandstand’s performance should be assessed on the basis of the given requirements for serviceability and ultimate load capacity. For all except the most flexible structures, integrity checks for ultimate load capacity are likely to be relevant only to connections between structural elements. Also, displacements can be expected to be within acceptable limits provided acceleration li mits related to tolerance of motion are not exceeded.
8.2 Idealised description of crowd activity People attending an event do not sit or stand without moving. All individuals in a crowd are likely to move, and if music is played, the movements tend to become synchronised to the beat. The movements may be an involuntary reaction to the external stimulus and the behaviour of neighbouring people in the crowd. Even at this level, there will be some dynamic response that will be felt by individuals if the grandstand is unduly flexible. However, with events such as pop-concerts, there is an expectation of excitement. The crowd expects to be involved; participation is deliberate and individual motion may become extreme with foot-stamping, bobbing (sometimes termed bouncing) and possibly some jumping on the stand, all in time to a beat. For the purpose of design, sections of a crowd are idealised as being either predominantly, •
Standing with dynamic properties given in Appendix A2 and generating loading due to body motion over a wide frequency range including foot stamping, bobbing and a proportion of jumping (i.e. active), or
•
Seated with the dynamic properties given in Appendix A2 and regarded as inactive (i.e. passive).
If areas of designated seating are used to reduce the overall level of excitation, these must be agreed with Management and controls exercised as outlined in Section 6.4.
Dynamic performance requirements for permanent grandstands subject to crowd action
17
8.3 Serviceability: Tolerance of motion For the purpose of design, the maximum root mean square (RMS) acceleration of the seating deck is used as a measure of what is felt by people in the stand. Maximum RMS acceleration limits are given in Table 1 for the different Design Event Scenarios and are to be used with the loadings recommended in Appendix 2 for Route 2 calculations of performance related to design or assessment. The design acceleration limit for Scenario 4 is regarded as the maximum that can be tolerated without the prospect of panic by individuals in a crowd. For Scenarios 2 and 3, the level of comfort to be provided is essentially a matter for the grandstand Management. The recommended crowd loading is weighted according to the expected occurrence of song frequencies over a number of events and the acceleration limits reflect the situation that seated people will be more sensitive to motion than people who are standing or moving in time to a rhythmic stimulus. The tolerance of motion varies between individuals and will not be the same for different style events. Design according to a given Event Scenario will not necessarily guarantee that all individuals will react with the same degree of satisfaction to the level of comfort provided or that there will be a total absence of complaints. More stringent requirements may be appropriate for some sections of a grandstand or seating deck such as catering areas and hospitality suites where expectations for comfort and operational convenience will be at a premium.
8.4 Serviceability: Displacement limits The maximum dynamic component of displacement due to crowd loading should not exceed 7mm RMS.
8.5 Ultimate load capacity No dynamic loading check is required of ultimate load capacity for grandstands designed and managed for Scenarios 1 or 2 since the ultimate load capacity required by current UK standards for dead and imposed loading for human occupancy, combined with the additional horizontal imposed loads specified in Table 2, will always be sufficient. The same is true for grandstands designed and managed for Scenario 3 or 4 other than those where motion of the deck is significantly affected by a global mode involving the supporting structure for which a separate check may be advisable.
8.6 Fatigue For stadia with frequent use for Scenario 3 and 4 events, the possibility of fatigue damage may need to be considered. The precise use of a stand over time can seldom be anticipated but an initial approximate indication of the potential for fatigue can be based on 20 minutes exposure per concert to Scenario 3 loading. This estimate should be revised as the pattern of use develops over time or in response to observed behaviour.
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Dynamic performanc e requirements for permanent grandstands subjec t to crowd action
9 Analysis of dynamic performance
9.1 Impulse loads No recommendations are made for single sharp increases in load due to sudden movements of members of a crowd as might occur when a goal is scored at a football match. Such events may cause motion that can be felt by members of a crowd but are normally of short duration and so of little significance for crowd comfort. Of much more importance is periodic loading induced by crowd activity coordinated to coincide approximately with a given frequency, possibly promoted by an external stimulus such as a musical beat. In this context, the loading may be more or less severe depending on the freedom of movement of people within the crowd and whether they are seated, standing, bobbing or jumping.
9.2 Horizontal loads due to periodic excitation Until more complete information becomes available, horizontal loads due to crowd action should be treated in the same way as in the Route 1 method so that Grandstands should be designed to resist the equivalent static loads given in Table 2. (See also Sections 7.2 and 7.3). It is hoped that, in time, sufficient information will become available for horizontal actions to be dealt with using a human structure interaction based dynamic analysis as is recommended for vertical loading.
9.3 Analysis for vertical periodic excitation Linear elastic dynamic analysis with linear damping should be used. In practice, except for the simplest structures and crowd configurations, this will involve using modal analysis and a finite element representation of the structural system. Additionally, the effects of human structure interaction need to be included in the analytical process whatever method is adopted. (See Appendices 1 and 2). Except where more precise information is available from testing the as-built structure, damping should be taken to be 2% critical for each mode of vibration considered.
9.4 Human structure interaction Recent research has shown that people involved in any of the three activities of sitting, bobbing or jumping interact with moderately flexible structures such as grandstand seating decks so that the contact forces actually experienced at resonance are significantly different from those measured in tests on stiff or rigid force plates. The existence of these effects does not depend on the motion of the structure being extravagantly large but only on the relative stiffness and damping properties of the crowd and the supporting structure. If the effects due to human structure interaction are ignored in calculations, the response of the structure will be incorrectly represented in the analysis. For most practically designed grandstands, accelerations calculated ignoring human structure interaction will be significantly higher than those calculated taking into account the interaction effects. The recommended analytical method for treating human structure interaction is given in the Appendices. This approach has been developed, using the most recent research and experimental data available, with the aim of reproducing the patterns of behaviour observed in actual structures subject to dynamic crowd loading. The method cannot deal with all the variations in human behaviour and physical characteristics that affect the way in which individual people and crowds interact with a structure. Because of this, the results of analysis should be regarded as indicative of actual behaviour rather than a
Dynamic performance requirements for permanent grandstands subject to crowd action
19
precise prediction of performance for a particular event. More positively, the recommended methods provide a consistent approach to design and assessment that takes account of the major factors that determine the dynamic behaviour of a stand. The Appendices also provide the necessary input concerning loads appropriate to the different Design Event Scenarios together with notes on testing, calculation of natural frequencies and analysis.
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Dynamic performance requirements for permanent grandstands subject to crowd action
10 Use of the Recommendations The Recommendations are addressed to both Management and the Design Team. The Recommendations provide a guide to operational management and a tool for the analysis, design and assessment of grandstand seating decks for dynamic crowd loading. The Recommendations have been prepared on the basis that these are related functions with Management’s role in operating a grandstand having importance similar to that of the Design Team that provides the details for the stand’s construction. The Recommendations represent the most considered view now available for the treatment of dynamic crowd loading on seating decks of permanent grandstands. This is now an area for continuing research and it is likely that the detailed recommendations for analysis will be refined over time. It would be helpful if users of the Recommendations, and researchers, who have relevant material to contribute, would provide the Institution of Structural Engineers with comment so that the Recommendations can, from time to time, be refreshed in the light of experience and new knowledge.
Dynamic performance requirements for permanent grandstands subject to crowd action
21
Appendix 1 Background to human structure interaction
A1.1 Introduction Explicit treatment of human structure interaction has not been previously considered in design guidance for active crowd loading. In the past, it has been assumed that the load induced by an individual, or a crowd, is an externally applied load unaffected by the motion of the structure. This assumption led to loads obtained in tests using people bobbing or jumping on relatively stiff structural elements being presented in recommendations as being appropriate for all situations. For grandstands with dense crowd loading and natural frequencies typically less than 7Hz, this approach gives insufficient consideration to the nature of the loading – due to an individual or a crowd – or to the effects of the mechanical interaction between individuals and the structure. These aspects have been recently addressed (Dougill et al., 2006) using a simple structural model for the active crowd that interacts with the structure during motion. Laboratory based studies have demonstrated the significance of this interaction for a range of support natural frequencies, loading and excitation relevant to grandstands (Yao et al., 2004 and 2006). Also, use of the theoretical model (Pavic and Reynolds, 2008), and independently derived loading data (Parkhouse and Ewins, 2006), has allowed the performance of actual grandstands to be calculated and compared satisfactorily with observed data from stands in service (Pavic and Reynolds, 2008). Both the laboratory tests and full-scale studies have shown that, for practically designed grandstands and dense crowd loading, it is necessary to take account of crowd-structure interaction if the structural response near resonance is not to be significantly overestimated.
A1.2 Basic principles A1.2.1 Modelling human structure interac tion In calculating the relevant dynamic properties of the empty seating deck, a linear elastic representation of the structure will have already been developed, for example using a finite element model. In order to represent the effects of crowd loading, this basic structural model is supplemented by additional elements representing groups of people. These crowd elements, or body units, are spring-mass-damper systems, as shown in Figure A.1.1, each energised by an actuator represented by the forces P(t ) that cause dilation of the crowd or body unit by means of a pair of equal internal forces applied in opposite directions. The properties of the crowd units depend on whether people are predominantly standing or sitting whilst the forces P(t ) relate to the type and intensity of activity in the crowd. In the context of analysis, the body units, with their associated forcing functions, replace the forces that have commonly been prescribed in design guidance to represent crowd loading. Use of the body units provides a model of real-life crowd loading in which motion of the combined structure/crowd system is caused solely by forces generated within the system itself. The motion of each crowd body unit is determined by the relative displacement of the body mass with respect to the point at which the unit is in contact with the structure. As a result, each crowd body unit introduces an additional unknown degree of freedom into the structural system associated with the mass of the crowd body unit. The forces, P(t ), are taken to be periodic. For practical periodic crowd loading, the function can be represented by the first three harmonic components. It follows that the combined structure/crowd system can be analysed using conventional methods of linear dynamic analysis to determine the separate responses due to each load harmonic. The separate responses can then be combined to obtain the total response to crowd loading.
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Dynamic performance requirements for permanent grandstands subject to crowd action
Body unit with mass, spring stiffness and damping
Internal force pair driving the system
Crowd body node with associated nodal displacement
P( t )
Basic structure node with associated nodal displacement
Contact force with the structure
Figure A1.1 Typical bod y unit for incorporation into the basic struc tural model of the supporting structure empty of people Dougill, Wright, Parkhouse and Harrison (2006) provide the governing equations for a system comprising a single degree of freedom structure energised by a single body unit. Formal solutions are given for harmonic loading – P(t ) being either a sine or cosine function of time – together with examples of the resulting behaviour of the combined system. In practice this would correspond to the situation when the unoccupied structure has a single dominant mode and so can be taken as a single degree of freedom system for the purpose of dynamic analysis. If the crowd is relatively homogeneous, it can be defined by a single crowd body unit resulting in a combined two degree of freedom (2DOF) system, as described in A1.5.1.
A1.2.2
Ac tive and pa ssive be haviour
Interaction between a moving structure and a crowd occurs for both active people, who cause the structure to move by their own efforts through the driving forces P(t ), and passive people, who do nothing themselves to cause motion of the structure and for whom P(t )=0. Besides the difference in loading, the dynamic properties of the body units also differ between those representing active and passive people. The recommended standard Design Event Scenarios ( given in Table 1) are based on limiting conditions for various types of events in which everyone is considered to be active so that there is no passive contribution. If designated seating areas are specified in the design or as an agreed operational strategy prior to assessment (as described in Section 6.4 No standing areas) the relevant part of the structural model would need to be combined with the appropriate passive elements in addition to using active elements for those parts of the crowd considered to cause the structure to move.
A1.3 Application of the theory A1.3.1 Direc t applic ation of the theo ry In principle, the most straightforward and accurate way to use the human structure interaction theory is to add crowd body units to the finite element model of the empty structure and to analyse the combined system. No assumptions need be made, beyond those involved in determining the loading and body unit properties and ensuring that the internal damping of the empty structure is suitably modelled, so that the results obtained are analytically correct for the chosen distribution of body units.
Dynamic performance requirements for permanent grandstands subject to crowd action
23
Use of the direct approach would allow a comprehensive analysis of the effect of a particular crowd on a structure. For example, body units, with different properties and loadings, could be used to represent different groups of people on the seating deck, or decks, with different levels of activity including passive behaviour. This amount of local detail is normally unnecessary in design but enough body units need to be used so that the motion of the crowd is adequately represented.
A1.3.2 Approximate analysis using an assumed mode shape for the crowd’s motion An approximate solution can be obtained using an assumed ‘mode shape’ for the displacement of the crowd (and its associated body units) for each mode of the empty structure that is being considered for the seating deck or decks. The modal masses, stiffnesses and internal drivers, P(t ), can then be found using these assumed mode shapes. The structural response then follows through the usual processes of modal analysis using a two degree of freedom model for each relevant mode of the empty structure. The most convenient approach is to assume that the body units adopt mode shapes that are identical to those of the empty structure in their vicinity. This assumption appears to be borne out by observations on cantilever decks and can be shown to be exact for simple structures with constant section properties, fully occupied by a uniform crowd with each part of the crowd having the same properties. This has led to successful correlation between calculated and observed motion for plate-like cantilever grandstands (Pavic and Reynolds, 2008).
A1.4 Body Unit properties and loadings Recommendations for the body unit properties and loadings appropriate to the different Design Event Scenarios are given in Appendix 2.
A1.5 Analysis and results A1.5.1 Modal analysis The most usual form of analysis will be using modal decomposition. In essence this allows the separate contributions of each mode to the overall response to be analysed separately and then combined using the principle of superposition. The process involves identifying the modes of the unoccupied structure that contribute to the motion of the deck, together with their associated mode shapes, and then calculating the relevant modal properties for a two degree of freedom (2DOF) crowd-structure system that can be derived for each mode using the mode shape of the unoccupied structure and the distribution of mass and dynamic loading within the crowd-structure system. (See Appendix 3). For a structure, fully occupied with an active uniform crowd, this leads to a pair of equations corresponding to each mode that describes the motion of the structure itself. These can then be solved to obtain the body unit’s and structure’s response as they relate to that particular mode. A formal solution of these equations for periodic loading is available (Dougill et al., 2006) that can be used to benchmark numerical methods used in analysis
A1.5.2
Roo t mean square (RMS) ac c elerations and ac c eleration limits
Both BS 6841(1987) and ISO2631-1-(1997) use Root Mean Square (RMS) acceleration as the indicator for assessing tolerance of motion. For any function x(t ) the RMS value over the interval of time T is given by,
>
1
t + T
#
RMS ^ x, t, T h = T
24
t
2
H
x dt
1/ 2
(A.1.1)
Dynamic performance requirements for permanent grandstands subject to crowd action
When monitoring actual movements, the underlying periodic mot ion due to crowd activity is accompanied by irregular events. The RMS value therefore varies with time and depends somewhat on the choice of the interval T . A value of 10 seconds is frequently used leading to ‘10 second rolling RMS’ values over the period of observation. Calculations used in design based on periodic motion using the harmonic loading described in Appendix 2 lead to accelerations that are smooth functions of time. T is taken to be the excitation period for the harmonic considered leading to RMS values that are independent of time. For a single harmonic with frequency f and amplitude a, such that x = a cos(2π ft ), the RMS value of the acceleration x is then a/√2. The BS and ISO Standards additionally weight measured RMS acceleration according to excitation frequency. This has not been considered appropriate for the values calculated for the range of frequencies encountered with crowd motion. Accordingly, the acceleration limits in Table 1 of the Recommendations use RMS accelerations calculated for periodic motion and without frequency weighting. For most situations it will be sufficient to consider only the vertical component of acceleration in meeting the limits for acceleration given in Table 1. However, with ‘front-to back’ nodding modes (See Section 7.3) there is the prospect that the horizontal component of acceleration will be significant even with only vertical excitation. The check for acceptable motion should then be based on the limits in Table 1 and the vector sum of the calculated vertical and horizontal RMS accelerations.
A1.5.3
Analysis with a dominant mode.
In general the analysis should cover all modes that are considered to be capable of providing significant motion of the seating deck. (See Section 4.2) . However, in some situations there will be a dominant mode so that the response of the crowd/structure system can be determined from a single pair of equations corresponding to the dominant mode. In general, three loading harmonics will be considered corresponding to excitation at the activity frequency, f , and the resulting higher harmonics with frequencies 2 f and 3 f . The acceptance criteria in the Recommendations are expressed in terms of the maximum permitted Root Mean Square, RMS, accelerations of the structure (see Section 2, Table 1) so that the combined effect from the three harmonics must be determined. This can be done for any given activity frequency from, R
T
=
R
2 1
+
R
2 2
+
2 3
R
(A1.2)
where R1, R2 and R3 are the RMS values for the response (acceleration or displacement as required) due to the 1 st , 2 nd and third harmonics of the activity frequency and RT is the RMS value of the total response at that frequency. In doing the analysis, it should be recognised that the maximum response will not necessarily occur at the natural frequency of the unoccupied structure or even at a natural frequency of the combined crowd/structure system due to frequency dependence of the specified body loading. Accordingly, the analysis will need to include a frequency scan, with results being obtained over a range of closely spaced frequencies, in order to identify the maximum response.
A1.5.4
Multi-mode analysis
In general, more than one mode will need to be considered. Again a frequency scan should be used to determine the RMS responses for a range of frequencies for each loading harmonic and each mode. The results from the separate modes can be combined in a 2 similar manner to that indicated in equation A1.1 with R 1 , for instance, being the sum
Dynamic performance requirements for permanent grandstands subject to crowd action
25
of squares of the RMS contributions to the first harmonic response from all the modes considered.
A1.6 References Yao, S., Wright, J.R., Pavic, A. and Reynolds, P. ‘Experimental study of human-induced dynamic forces due to bouncing on a perceptibly moving structure’, Canadian J. Civil Engineering, 31(6), 2004, pp1109-1118. Yao, S., Wright, J. R., Pavic, A. and Reynolds, P. ‘Experimental study of human-induced dynamic forces due to jumping on a perceptibly moving structure’, J. Sound & Vibration, 296, 2006, pp150-165. Parkhouse, J.G. and Ewins, D.J. ‘Crowd induced rhythmic loading’, Proc. ICE, Structures and Buildings, 159(SB5), Oct 2006, pp247-259. Dougill, J.W., Wright, J.R., Parkhouse, J.G. and Harrison, R.E. ‘Human structure interaction during rhythmic bobbing’, The Structural Engineer , 84(22), 21 Nov 2006, pp32–39. Pavic, A. and Reynolds, P. ‘Experimental verification of novel 3DOF model of grandstand crowd-structure dynamic interaction’. 26 th International modal analysis conference: IMAC-XXVI, Orlando, Florida, 4-7 Feb 2008 , paper 257.
26
Dynamic performance requirements for permanent grandstands subject to crowd action
Appendix 2 Body unit properties and recommended loading
A2.1 Body unit and structure Figure A2.1 shows a typical body unit in place on the supporting structure. The forces produced within the body unit which induce motion are shown as P(t ). The resulting contact force on the support is F (t ). The structure is not shown in detail. If the structure were rigid, the contact force would equate to the force corresponding to conventionally determined Dynamic Load Factors as used in analysis ignoring the effects of human structure interaction. In this Appendix, recommendations are given on values of the body unit properties and internal forces for direct use in design or assessment using this human structure interaction model.
A2.2 Crowd body elements For bobbing that is comfortable and easily maintained, Parkhouse and Ewins’ (2006) results led to the conclusion that the body properties could be taken as independent of group size. (Dougill et al., 2006). For the purpose of analysis, only two types of crowd body element are proposed. These comprise the mass/spring damper system shown in Figure A2.1 with the properties given in Table A2.1
Body unit with mass, spring stiffness and damping
Crowd body node with associated nodal displacement
Internal force pair driving the system
P( t )
Contact force with the supporting structure
F (t )
Common node with body unit and structure with associated nodal displacement
Figure A2.1 G eneral arrangement of body unit and supporting structure
Dynamic performance requirements for permanent grandstands subject to crowd action
27
Table A2.1. Recommended properties of crowd body elements Crowd
Event scenario
Natural frequency Hz
Damping percent critical
Designated a nd c ontrolled ‘no-standing’ areas
See Recommendations Section 6.4
5
40
Predominantly seated
Sc enario 2
5
40
Ac tive and mostly standing
Event Scenarios 3 and 4
2.3
25
The body spring stiffness, k , is found from the body mass, m, and the natural frequency, n, as given in Table A2.1, from, k = 4r n m 2
2
(A2.1)
The linking member with the basic structure marked in Figure A2.1 as containing the common node with the structure can be regarded as rigid but with no mass. The concentrated mass, m, in the element should be calculated from the number of people in the area of seating deck that affects the node of the structural model to which the element is attached, using an average person mass of 80kg.
A2.3 Representation of periodic loading The internal periodic force pair P(t ) in figure A2.1 is described as the sum of by three harmonic components as follows,
(A2.2)
where
t
is the crowd effectiveness factor that reflects design criteria driven primarily by serviceability with commonly occurring events for Scenarios 2 and 3, or mitigation of the potential for panic under extreme motion considered in Scenario 4.
m
is the mass of the crowd associated with the particular body element considered. This is to be taken as 80 kg times the number of people.
g
is acceleration due to gravity 9.81 m/s2.
Gi
is the ith ‘generated load factor’ GLF defining the load generated by activity of the crowd.
f
is the fundamental frequency of the crowd activity in Hz. This corresponds to the musical beat (or frequency of an alternative prompt) in beats per second.
t
is the time in seconds.
ii
is the phase difference of the i th harmonic. These phase differences can be set to zero in calculations if only RMS values of force, displacement or acceleration are required.
28
Dynamic performance requirements for permanent grandstands subject to crowd action
The Generated Load Factors, GLFs, replace the Dynamic Load Factors used in analyses that ignore the effects of human structure interaction. The differences in response are small when the crowd is sparse (that is for low crowd mass to structure mass ratios) and for structures with natural frequencies that are high compared with those of the crowd body elements. In other situations, human structure interaction need s to be considered. The principal assumption in developing the GLFs from available data is that the internal forces P( f,t ) used by groups of people to move on a flexible platform will be the same as would be involved when undertaking the same activity on a rigid base. However, crowds engage in different types of activity and most research has been concerned with jumping that can be related more to aerobics and vigorous dancing than to crowd behaviour in stadia where people react to music, over a wide frequency range, with handclapping, stamping, bobbing and occasional jumping. Accordingly, for the purpose of design, the loading for Scenarios 3 and 4 is idealised and taken to be equivalent to a multiple of loading due to bobbing by groups of 50 people or more modified by an effectiveness factor. The factor takes some account of activity that might occur over a wider frequency range than is covered by the testing and, for the commonly encountered events of Scenarios 2 and 3, also provides a weighting based on the frequency of occurrence of songs with different tempi. The basic loads, Gi, (i = 1,2,3) before modification by an effectiveness factor, t, are based on results for bobbing from extensive recent testing by Parkhouse and Ewins (2006) that also provide data to enable the body unit properties to be determined (Dougill et al., 2006).
A2.4 Internal ‘drivers’- G i – producing dynamic crowd loading The recommended values for the Generated Load Factors are given in Table A2.2. These are derived from the synthesised results for a group of 50 people bobbing on a rigid platform. The values can be taken as constant for larger groups of people. For smaller groups, there is a significant increase in Gi with group size, together with increasing variations from the mean. In modelling a crowd, it is recommended that the crowd is not subdivided into groups of less than 50 people. Table A2.2 Recommended values of the Generated Load Factors, G i, for use in calculations of performance for design or assessment. Scenario
1
2
3
4
Harmonic number i = 1
-------
0.12
0.188
0.375
i =2
i =3
Typical activity represented
Effectiveness factor Not required.
-------
Not required . Route 1 only, but with disc retion available by Listed Engineer (Rec ommend ations Table 1)
Eqn. A2.3
Zero
Predominantly sea ted with oc casional c oordinated rhythmic movement from standing people
Eqn. A2.3
0.047
0.013
All crowd c onsidered ac tive. Mod erate b obb ing a t three quarters Parkhouse and Ewins’ 50 person level
0.095
The whole crowd a ctive. Loa ding taken to b e twice that 0.026 for the commonly occurring events of Scenario 3
-------
0.015
Dynamic performance requirements for permanent grandstands subject to crowd action
Eqn. A2.2
29
A2.5 The crowd effectiveness factor ‘t’. A2.5.1 Sc enario 4 Scenario 4 is concerned with high energy events. The principal concern is safety against the prospect of crowd disturbance, or panic, as a consequence of the motion of the grandstand. Experience suggests that the probability of such a situation occurring is small. However, the consequences of panic in a crowd confined in a grandstand with fitted seats could be dramatic and possibly life threatening. For such an extreme situation it is appropriate to consider an unrestricted frequency range of possible excitation but with some allowance for reduced effectiveness of the loading at low and high excitation frequencies. This is provided by an effectiveness factor shown in Figure A.2.2 and given by the equation,
t ( f) = sech ^ f - 2 h
(A2.3)
where f is the fundamental frequency of the crowd’s activity in Hz and the factor is used in equation A2.2 with the recommended values of Gi in Table A2.2 and the crowd body unit properties of Table A2.1.
1.2
1.0
0.8 t( f )
0.6
0.4
0.2
0 0
1
2
3
4
5
6
Activity frequency, f , Hz
Figure A2.2 Effec tiveness fac tor t(f ) for use with Sc enario 4 in c onsideration of safety A2.5.2. Sc ena rios 2 and 3 Scenarios 2 and 3 are relevant to less energetic events than those of Scenario 4 so that the occurrence of panic due to crowd motion can be discounted. It follows that criteria for structural performance can be set in terms of what is needed to meet a crowd’s expectations of comfort over a period of time and for many events. This element of repeated exposure to crowd action and a cumulative experience of comfort relative to motion of the structure is in direct contrast to conditions for the single extreme event in which safety is the prime consideration. In order to take account of the continuing exposure to a variety of songs of different beat frequencies, the effectiveness factor
30
Dynamic performance requirements for permanent grandstands subject to crowd action
for comfort is weighted, using data from Littler (2003), according to the probability of occurrence of songs in the overall pop repertoire. The probability distribution is approximately Normal with mean 1.8 and standard deviation 0.5, so leading to the effectiveness e
(A2.4)
The resulting effectiveness factor is shown in Figure A2.3. This covers the beat frequency range of commonly occurring songs with a maximum near to that for the most frequently occurring songs, Littler, (2003).
1.2
1.0
0.8 t( f )
0.6
0.4
0.2
0 0
1
2
3
4
5
6
Activity frequency, f , Hz
Figure A2.3 Effec tiveness fac tor t(f ) for use with Sc enarios 2 and 3 in consideration of comfort A2.6 Monitoring and back analysis Event monitoring and subsequent back analysis of performance is most likely to be undertaken under conditions similar to Scenario 3. However, in examining a specific event, a view should be taken of the proportion of the crowd that is actively involved with the remainder being considered as passive. For most events, the loading from active people will correspond to that for bobbing. Appropriate values for the internal drivers Gi are given in Table A2.3. These should be used with the crowd body properties for active and passive crowd body elements in Table A2.1 and the single event effectiveness factor of equation A2.3. An example of monitoring and back analysis is provided by Pavic and Reynolds (2008).
Dynamic performance requirements for permanent grandstands subject to crowd action
31
Table A2.3 Suggested values of the Generated Load Factors, Gi, for use in back analysis of specific events. Harmonic Number Crowd
Ac tive
i =1
i = 2
i = 3
0.25
0.063
0.018
Passive
All zero
Typical ac tivity in identified sections of the crowd
Effec tiveness Factor
A ctive c rowd, ma inly bobbing.
Eqn. A 2.3
Inactive, standing or seated
A2.7. References Dougill, J.W., Wright, J.R., Parkhouse, J.G. and Harrison, R.E. ‘Human structure interaction during rhythmic bobbing’, The Structural Engineer , 84(22), 22 Nov 2006, pp32–39. Littler, J.D. ‘Frequencies of synchronised human loading from jumping and stamping’, The Structural Engineer, 81(22), 18 Nov 2003, pp27–35. Parkhouse, J.G. and Ewins, D.J. ‘Crowd induced rhythmic loading’, Proc. ICE, Structures and Buildings, 159(SB5), Oct. 2006, pp247-259. Pavic, A and Reynolds, P. ‘Experimental verification of novel 3DOF model of grandstand crowd-structure dynamic interaction’, 26 th international modal analysis conference: IMAC-XXVI, Orlando, Florida, 4-7 Feb 2008 , paper 257.
32
Dynamic performance requirements for permanent grandstands subject to crowd action
Appendix 3: Calculation of modal properties
A3.1 Introduction The Recommendations provide alternative routes to design or assessment of a grandstand. Route 1 uses natural frequency as an index of quality for a stand and requires knowledge of the natural frequencies of the stand and identification of the lowest value corresponding to a mode that can be excited by and felt by people on the seating deck. The approach is simple but rendered useless if natural frequencies are not determined to sufficient accuracy. As outlined in the Recommendations, (S ection 4), calculation of natural frequencies may appear to be a straightforward task but, in reality, is complicated by uncertainties in setting up the analytical model with almost inevitable differences between assumptions made for purposes of calculation and the actual behaviour of the as-built structure. The Route 2 approach provides more flexibility for the designer by using calculation to obtain an estimate of performance of a grandstand under prescribed loading appropriate to a given idealised Design Event Scenario. A full dynamic model of the structure is needed for such calculations and the opportunities for error and miss-match between the analytical model and real structural behaviour are certainly not less than in calculations of natural frequencies for Route 1. Clearly, if the calculated dynamic properties are seriously in error, the resulting estimate of performance will have little relation to the behaviour of the as-built structure. To deal with this potentially difficult situation, engineers need to be aware of the assumptions or simplifications made in analysis and how these affect the result of dynamic analysis. They should also recognise that even the most careful attention to detail in analysis cannot guarantee that the analytical model will match the behaviour of the physical as-built structure. As a general rule, it is advisable to check properties obtained by calculation by physical testing so that the analytical model can be refined and made more relevant to the actual structure. This Appendix deals with calculation of modal properties and aims to point out some of the more common sources of error. In doing this, it extends and replaces the A dvisory note on calculation of natural frequencies of grandstand seating decks published in The Structural Engineer, Vol. 81, No.22, November 2003. The need to check calculations by testing grandstands is dealt with in Section 5 of the Recommendations whilst Appendix A4 provides advice on specification, procurement and reporting.
A3.2 Modal analysis and natural frequencies When a linear elastic structure vibrates under arbitrary loading, it does so in a way that its deflection shape at every moment in time can be presented as a linear combination of deformed shapes called mode shapes (Clough and Penzien, 1993). Therefore, for a system with N degrees of freedom, the vector of N unknown displacement functions xi(t ) can be expressed as: N
" x ] t g , =
/ q ] t g " z , r
r
r = 1
(A3.1)
where {zr } is the rth mode shape and qr (t ) is the rth time-dependent scaling factor.
Dynamic performance requirements for permanent grandstands subject to crowd action
33
In other words, when calculating the unknown response, xi(t ), equation A3.1 can be written as: N
x i ] t g =
/ z q ] t g ir
r
r = 1
(A3.2)
where zir is the mode shape amplitude of the r th mode at the point and in the direction of the displacement xi. The mode shapes { zr } are properties which depend only on the mass and stiffness of the structure and do not depend on the dynamic loading, so they do not change with time. The scaling factors qr (t ), also known as generalised or modal coordinates, are functions of time and depend on the dynamic loading. The generalised coordinates qr (t ) are solutions of the following modal equations of motion:
m r q r ] t g + c r q r ] t g + k r q r ] t g = Fr ] t g p
o
r = 1, N
(A3.3)
where mr , is modal mass for the r th mode, cr is modal damping, k r is modal stiffness and F r(t ) is modal force given by: i = N
F ] t g = r
/ z f ] t g ir
i
i=1
(A3.4)
and where f i (t ) is the time-varying physical force acting at the point and in the direction of the displacement xi. For many practical systems in which mass is modelled using only translationally moving lumped masses, mi the modal mass mr can be calculated as: N
mr
= /m z i
2 ir
i=1
(A3.5)
Equation (A3.3) will be recognised as a group of r independent equations. Each describes a single degree of freedom system having its own distinct displacement mode. In these terms, each equation requires its own modal properties: mr , cr and k r associated with the rth mode. An equation can be set up for each of N modes of vibration. Therefore, there will be N natural frequencies ωr: ~r
=
1 2r
k r m r
(A3.6)
Natural frequencies and the corresponding mode shapes are properties of the structure. All flexible structures have natural frequencies. Equation (A3.6) shows that the natural frequency ωr that relates to a particular mode of vibration depends on terms contributing to the modal stiffness k r of the structure and terms contributing to the modal mass mr of the material that moves during vibration in a particular mode. From Equations (A3.3) and (A3.4), it follows that if the external harmonic force f i (t ) has a frequency identical or close to the natural frequency ωs there will be a strong resonant response qs(t ) of mode s. Equation (A3.1) then suggests that this would cause the physical response to be dominated by mode s. Equation (A3.4) also suggests that a mode of vibration will be excited by an external force only if this acts at a point where the amplitude of the mode shape is non-zero.
34
Dynamic performance requirements for permanent grandstands subject to crowd action
A3.3 Basic errors: two prime suspects A3.3.1 Distinc tion betwee n force and mass Equations (A3.5) and (A3.6) make clear that natural frequency involves mass and not force. Accordingly, the input to a dynamic analysis for natural frequency should include all the mass that would be involved in free vibration. This will include the mass of the basic structure plus the mass of all the attachments including seating, partition walls or barriers, hospitality boxes and equipment supported by the seating deck. Note that, in a static analysis to determine forces or bending moments used in strength calculations, the weight of some of the above elements would be treated as forces acting on the primary structure rather than as masses that affect dynamic behaviour. It follows that it is not generally possible to use the analytical model used in a static analysis by merely adding the dynamic loading. The model will need to be reassessed to include lumped masses associated with self weight of both the structure and its appendages. Almost invariably, forces used in static analysis that derive from weight will correspond to mass to be considered in a dynamic analysis. It is easy to overlook the contribution of mass due to a non-structural element or, in the as-built structure, additions made during fit-out. If there are significant differences between calculated results for natural frequency and those obtained from testing, it is suggested that one of the first tasks in checking should be a ‘mass audit’ to see if all the mass that moves is included in the analytical model.
A3.3.2
Stiffness
The stiffness of so-called non-structural elements is often ignored in a static analysis for forces and bending moments. Errors result if this is done in a dynamic analysis for natural frequency. In particular: •
•
•
The stiffness of a seating deck may be underestimated if the stiffness of wing walls, vomitories, partitions and glazing attached to the deck are ignored. The stiffness of a seating deck may be overestimated if a rigid or fixed boundary condition is assumed at the interface with the remainder of the structure. The stiffness of a cantilever deck is very much dependent on the boundary conditions of the cantilever. Therefore, it depends on the stiffness of the connection with the structure supporting the cantilever and by the displacements/rotations in the supporting structure itself at the location of the connection. Clearly, if the access or main supporting structure for a cantilever grandstand is itself flexible, the motion of the cantilever could be determined as much by the motion of the support structure as by the flexibility of the cantilever. Here the need is to check that the analytical model is sufficiently extensive to include the influence of the supporting structure. It will be recognised also that whole-body movement of the support structure can occur due to foundation movement or flexible tie-backs and may not be solely determined by the elements of the main structure.
It will be noted also that the mode shapes obtained from testing can be particularly informative in guiding revisions of an incomplete analytical model.
Dynamic performance requirements for permanent grandstands subject to crowd action
35
A.3.4 Methods for calculation of natural frequencies A3.4.1 G eneral c omment All methods for calculating natural frequencies fit into one of two groups: the approximate method suitable for hand calculations (Blevins, 1995), and numerical methods, suitable for computer applications (NAFEMS, 1992). The two methods are complementary and should be used in parallel as a cross-check whenever possible. Rules of thumb provide a useful check rather than a reliable tool for analysis. Even for simple structures, such rules are unlikely to be sufficiently accurate for assessment or design but can provide a useful check for gross errors in natural frequencies obtained by numerical, typically finite element, analysis or other more involved approximate methods.
A3.4.2 Ap proximate analysis These methods typically yield the natural frequency of t he fundamental mode of vibration and are based on treating this mode as a single degree of freedom system having an assumed, rather than calculated, mode shape. Usually the mode shape is assumed to be identical to the static deflection profile due to self weight applied in the direction of the required mode (vertical or horizontal). The approximation can work quite well for simple single-span or cantilever structures. More complicated structures require a full numerical analysis because of difficulties in estimating the relevant mode shape. Typically, the lowest natural frequency in vibration cycles per second (i.e. in Hz) can be approximated by a non-dimensional constant A divided by the square root of the deflection under dead loading, D, i.e.
f = 1
A D
(A3.7)
For simple beam or cantilever structures, the ‘rule of thumb’ is that A usually lies between 15 and 20 when D is expressed in millimetres. More complex structures may have an A value outside this range.
A3.4.3 C omputer based analysis This is typically done using standard commercial computer software based on finite element analysis. Natural frequencies are found as a result of the so called modal analysis or eigenvalue extraction resulting in mode shapes and the corresponding natural frequencies. For stands comprising nominally identical frames, a 2D ‘ plane frame’ or a 3D ‘slice frame’, finite element analysis can be performed taking into account contributory mass and stiffness corresponding to the frame. If the frames making t he stand are not nominally identical (e.g. they change width or height, or have generally different mass and stiffness properties) a full 3D multi-frame analysis is recommended. Uncertain modelling parameters (e.g. boundary conditions, composite action, material properties, and effects of cracking) should be studied parametrically to explore the uncertainty in the calculated values of dynamic properties. If wide variations occur in the calculated values, the analytical model may need to be revised.
A3.5 Consequences of mistaken idealisations It is clear that the engineer should be aware of the effects of the various assumptions made in calculating natural frequencies and, in analysis, should attempt to represent as closely as possible the geometry of the entire structure and the effect of the non-structural elements.
36
Dynamic performance requirements for permanent grandstands subject to crowd action
In general, assumptions should be made so that the calculated natural frequency will be on the low side, so providing a conservative estimate for assessment purposes. Mistaken idealisations may have the effects shown in Table A3.1 on calculated values of natural frequency. Table A3.1: Idealisation and its effects on the calculated natural frequency Idealisation
Calculated natural frequency
Neglect of significa nt mass including neglec t of mass Too high of non-struc tural elements C onnec tions taken as rigid when flexible
Too high
Only part of the structure considered with the remainder taken as motionless and effectively rigid
Usually too high: with prospect of missing a signific ant mode
Stiffening effects of the ‘not considered part’ of the structure more important than the effects of its mass
Too low
Wrong/ inap propriate mode shape used in approximate method
Too high
Neglec t of foundation flexibility
Too high
Use of too coarse a finite element grid/mesh
Potentially too high
C oncrete assumed to be uncrac ked
Too high
Neg lec t of stiffness arising from interac tion b etween rakers and seating deck
Too low
Assume perfect supports and connections and neglec t of physical slack due to tolerance
Too high
Neglect of stiffness of non-structural elements
Too low
A3.6 Comment It should be recognised that dynamic analysis to obtain modal properties of a real structure, or to estimate its performance under dynamic loading, is a more challenging task than checking for strength under essentially static loading. In calculations for strength, assumptions can be made on structural behaviour concerning connections, ductility and load redistribution that can be made real in design through appropriate detailing. Also, high accuracy is not essential provided the assumptions made are conservative and the resulting structure has a reserve of strength over that called for in the specification. This is not the situation with dynamic analysis. The structure behaves linearly and as it is constructed. There are no opportunities for alternative load paths and the simplifications of behaviour based on ductility, that provide safe routes to simpler design when considering strength under static loading, are not available. Experienced engineers recognise these difficulties and how they are compounded by the task of creating an analytical model that will predict adequately the performance of a ‘still to be constructed’ grandstand. The analytical process itself is almost routine. However, the modelling is often likely to be less than precise and open to surprise for all but the simplest structures. In these circumstances, engineers should normally welcome the opportunity for an independent check of the modal properties by testing and the additional insight this can provide. ( See Appendix 4).
Dynamic performance requirements for permanent grandstands subject to crowd action
37
A3.7 Further information NAFEMS. A finite element dynamics primer. Glasgow: National Agency for Finite Element Methods & Standards, 1992. Clough, R.W. and Penzien, J. Dynamics of Structures. 2nd ed. New York: McGraw-Hill, 1993. Blevins, R.D. Formulas for natural frequency and mode shape , Malabar, FL: Robert E Kreiger Publishing Company, 1995.
38
Dynamic performance requirements for permanent grandstands subject to crowd action
Appendix 4 Dynamic testing of grandstands and seating decks
A4.1 Introduction The Recommendations refer to the need to determine or check values of natural frequencies and other modal properties by testing grandstands as fitted out for use, but empty of people. (See Sections 4 and 5 dealing with dynamic properties and testing ). The Recommendations put particular reliance on Listed Engineers to advise on the form of testing required. (See Listed Engineers, Section 3.4). This Appendix provides additional guidance to the Listed Engineer and also to Management, who may require testing as part of the hand-over procedures for new structures, and for Local Authority Engineers with responsibilities for Building Control and Safety Certification. The Appendix extends and replaces the Advisory Note, Dynamic testing of grandstands and seating decks published by the Institution of Structural Engineers in 2002. No guidance is given on monitoring grandstands in service. References to monitoring are given in the Bibliography, (Appendix 5).
A4.2 What should be tested and what results are needed? The form and extent of testing needed will depend on choice of method – Route 1 or Route 2 – used in design or assessment. The Route 1 method needs only the value of the relevant natural frequency for vertical excitation by crowd action to be determined. (See Section 4.4) . Here testing must be concerned with identifying and determining the lowest natural frequency at which people can excite the seating deck and feel its motion. For simple structures with easily identified modes of vibration relatively simple test methods can be used. If Route 2 (based on performance calculations and satisfying a response based criterion) is used, all the frequencies that are judged to contribute significantly to the dynamic response need to be measured so that the dynamic model of the grandstand can be made as accurate as possible. This requires greater coverage from the test programme with initial calculations from the theoretical model being used to indicate which modes are important and therefore which frequencies need to be confirmed experimentally. Broadly, two types of test are available, corresponding to different levels of information obtained from the tests. •
•
Type 1 Tests provide basic information concerning the minimum relevant natural frequency. Type 2 Tests provide more detailed information than Type 1 tests that, in principle, could provide a full modal description comprising natural frequencies, mode shapes, modal damping ratios and modal masses for all the modes that are considered to be important in the dynamic performance calculations. Tests of this type may be required to check the values of modal properties used in a Route 2 analysis of performance or when the results of Type 1 testing cannot be reconciled with calculated values.
The Listed Engineer will need to specify the type of testing required and which modes of vibration need to be investigated. In addition, it will normally be useful if the testing provides additional information on mode shapes to assist in assessing the significance of any differences between test and calculated results in a Route 2 approach and also the degree to which any mode is likely to be excited by crowd movement.
Dynamic performance requirements for permanent grandstands subject to crowd action
39
The Listed Engineer should also consider where additional information may be needed. This could occur if the Management M anagement had set particular performance specifications for parts of the structure or if information were needed in the context of a possible upgrading of the structure or for introducing damping systems to reduce the effects of vibration. Type 1 testing will normally be sufficient to meet the requirements of the Route 1 approach to satisfying the Recommendations and so enable the Listed Engineer to recommend a category of use. Moreover, if Type Type 1 testing is conducted in such a way that mode shapes are determined in addition to values of natural frequency, comparisons can be made with the calculated mode shapes as a check that natural frequencies obtained by test and calculation are being compared on a like-for-like basis. Type 2 testing will normally be required if a performance based analysis using the Route 2 approach is undertaken. Such testing will allow the designer to assess the accuracy of the natural frequencies and also the mode shapes in the theoretical model. Testing will also allow the experimentally determined modal damping values to be used directly in the performance calculations since damping cannot be determined theoretically theoretically.. Type 2 testing requires more time on site, more specialist equipment and more information processing than Type 1 testing. As a consequence, use of Type 2 testing is likely to cost more than a basic Type 1 test programme. In deciding the form of testing to be used, the additional cost of Type 2 testing needs to be considered in relation to the increased detail and quality of information that can be obtained and the consequent increased surety in achievement of safety and better informed management procedures. To summarise, a Route 1 approach will most often use a Type 1 test with the aim of determining the lowest relevant natural frequency whereas a Route 2 approach will require a Type 2 test and aim to determine the natural frequencies, likely to be significant in a dynamic response calculation, together with their associated modal properties. It should be noted though that, for some structures, it may not always be possible to identify the ‘relevant’ natural frequency using only Type 1 testing.
A4.3 Ana nalysis lysis and testing testing Whether following a Route 1 or 2 approach, the Listed Engineer will be concerned that the values of the relevant natural frequencies have been determined with sufficient accuracy for an appropriate Design Event Scenario to be selected on the basis of natural frequency alone or for a performance based analysis to be relevant to behaviour of the as-built structure. In doing this, and bearing in mind mi nd the idealisations made in even a sophisticated analysis, it should be realised that t hat exact correspondence between measured and calculated values is extremely unlikely. However, However, if the difference in results is substantial, the Listed Engineer could be expected to review the results to check inter alia that: •
•
•
the mode shapes corresponding to the relevant natural frequencies are the same for the calculated results as those found from physical testing, the mass and stiffnes stiffnesss of the structure, and all the non-structural elements associated with the grandstand or seating deck, has been properly represented in the dynamic analysis, and, the support conditions, including the continuity and fixity of the elements of the structure, are appropriately represented in the dynamic analysis.
Such a review could indicate whether the test programme had missed the mode of vibration corresponding to the minimum natural frequency in a Route 1 approach or a relevant mode in a Route 2 approach. The review could show whether the analysis should be refined to
40
Dynamic performance requirements for permanent grandstands subject to crowd action
include some mass or stiffness that had been ignored i gnored in an earlier calculation or extended to examine the significance of assumptions made in modelling the structure. Depending on the circumstances, the Listed Engineer might decide that further Type Type 1 testing is necessary or that more detailed testing is required and so review the testing specification to provide for some form of Type Type 2 testing. It is recommended that an analysis to give an estimate of natural frequencies and mode shapes should be undertaken before testing is commissioned or undertaken. With the Route 2 approach, preliminary dynamic response calculations should be performed to indicate which modes are likely to be significant and the sensitivity to errors on the frequencies could be explored. In doing this, it will be important t o check that the available drawings properly represent the existing structure with any differences being noted for future reference. Only by having the results of an analysis available can additional tests be requested to find a missing mode within wi thin a single programme of testing, so avoiding the Test Agency having to make a second visit to site. Information I nformation on the likely mode shape is also helpful in informing the choice of test points to be used in the test programme. As noted in the Recommendations, (See Section 4.4 on ‘relevant’ natural frequency and Section 5.2 on Aims of Testing) it is important to recognise the existence, for some stadia, of so called ‘global modes’ of vibration. These are typically low frequency modes involving motion of the entire grandstand structure in sideways sway, twist or front to back movement causing ‘nodding’ of the seating decks. Care needs to be taken to identify i dentify global modes in the test process, particularly since some excitation methods (e.g. heel-drop) are unlikely to provide the energy required to excite such modes.
A4.4 Princ inciple iples s of dynamic dynamic testing A variety of excitation methods may be used in dynamic tests on grandstands. These include the use of ambient excitation due to wind or other disturbance, impact testing by heel-drop or calibrated hammer or the use of shakers to provide excitation at a given frequency. Whichever method of testing is used, it is vitally important that the level of excitation available is sufficient to excite all the modes of interest. Also, the instrumentation must be appropriate to record the response of the grandstand with sufficient accuracy to enable meaningful results to be derived. Different testing procedures may be adopted depending on the type of excitation being used, the availability of instrumentation and the amount of detail required in the results. For instance, testing may be undertaken with accelerometers at a number of fixed locations with the excitation sources being moved, from test point to test point, in order to excite different modes and explore the sensitivity of the structure to vibration. Alternatively, Alternatively, the excitation source can be used in one place and the measuring points changed from test to test. A combination of these two approaches may also be appropriate. Also, if mode shapes are to be determined, testing should be performed across a range of test points that are sufficiently closely spaced that mode shapes are uniquely defined, even when there are neighbouring modes with similar shape. In contrast to ambient vibration surveys, heel-drop tests and some forms of measured impact testing, shakers provide a consistent and reproducible source of excitation. This means that, besides providing good quality results for Type 1 testing, shakers can be used for Type 2 testing with the scope, or range of results, being dependent on the experience of the operators and the particular techniques and instrumentation employed. As with all forms of excitation, it is important that the shaker provides sufficient energy to excite the structure at the frequencies of interest. An overview of the different techniques is given in Table A4.1. A more detailed assessment of the different excitation options is given in the following section.
Dynamic performance requirements for permanent grandstands subject to crowd action
41
s s s a i s m y l l a a n d a o o 2 M N e t u n o o t R i c o t n u t F n y a c e v n s e e n l o e r u q p s n e e o r o R N i t F a m r o i o f n t i e r l l a a g b n n i a o i l i e t p i r d m t d a o A D N . e t n m e n i o o c c i i s t f f u e t a o p t i u s a c i s e h l x b s e y a e f i g r d i , r s o s e e e n D M Y e
o N
. h r t y t i c o s . e t n w e s r g n n r i u o i o n i h f d i o i d t d t o s n a e e e s t a e t n g e c e t m n i n i e o d c i a i r c n e t v t r o i x g r b e e p m e . e p f o g c g p r u r i e e t r s e r d n - i o e t k f e a t d s l t t l a h i t u n t s i a f p f r a u t o i h l d s t e u q s l e d r f e u u v s n e d t n r h d e e m u t d r a l e i e t b a r f e c m g w u i n a s o u i e l s n e r i e a y y i q e l s m u r m o t i u d s n b e g l i r a h t u s a s r d e s m o t s e n e e o f n u c e r n P o e Q t M i m a f
e l b a i l e r t o N
n a p h t o r r d l e t t e s e e e B h Y
o N
l e a . s r s r t u a r t n o f o c e c n t u r m s i o t s e e t n e i e g a d i c l c i v i p n f a f r o d r r n u i m P i s s a
s k s s c e e Y Y e d d g s s e . n s t e t e l y n l i l i s d t e i t o . n e i i b s s u s e l e a o 1 s l u s t c e a e e s i p e e m t e , . a t a o i c r s s o n e d l i n a i r p S d . i f m e u e c b p f x v t o n s i t y t y o c u i s o d e t r V n T i i e r v t m r e o i o r D l d n m u q e l r r s o a p b r e t o . p d o l - A a o o e a r p u l s s f r r a c N e l s c f t e m u t e m e o e . a e d t t l h q r r e o a d u i e t o i q e s b u t n r h r l u c t u a n o t a c n c t o r e l b r i o t n b a p n e a t a r a c h c a d g u t h n t , , n e t h h t t u t u p o r s s s s a s t e i s e a p t c i i i a t r r d e s e u t t e o e e e i n S m C w t s w s s m f Y Y b h t i n T E N Y w a r g t n f n . o y l l e o e l . . g e a b d i g m d d i n u n m e e e i s r r r s r r e t q r d i o s u n o u u . e e n s s f s p e e n e t a a i n p h c t t n r a e e e c o o o r e c i o e F m N N d M M o d t m a t n h s h y t g i f d e i p n t d e r e g e w o e n u o o n r i r q r y l a i t o w e d f - d m e t b a i n s i l t e k i s e s i b p l h e e s m s a r p c e c m o r r a h e a o y e u x A H D o h S v p t t E q s i c n i h t s d n c i r n o e e o a i t T t t . c s t a 2 1 g e n d . a r r n u e e e 4 a o i p q y d A h 1 1 1 r i y 1 o l n m c T e t u l e e e e o h p r t b s s p c t p p p c s c y y y y a t a T e T e T e i n m T T T e T
42
e w m o h m , a r t n n i g o e r t o r e a p f u f i t i d d s r n e l a a h t u d f i c o o t t r h e a e s p u m n e a r e h t f o i v n e g o t a a r n i r o o i t p f a o r e p d m r p i o a v o f n e r i p d b n e t l h a i g c a i t y e m c d t n a e e r h g o t s A m d t s o s e e h T t d e r i a v l o u r m c p e i t r h 5 . t a 4 y p A c e n n h t o e i g t t c A a e t h t S s e t s . T d e l o v u s h t e t i r e c f e o m p y t s t s o i l e r a t f p u o a q e h d i n c t i o w a h s e c s u p y e c s t i h t d e o o h t t t d e t n d i n a a u t g r d l o t e a p n i t i i m n s e i i m n i e t l a r , s e p m e v i d i e e v w b o r o d l p H u . . e l s o g n b d w t o i a s e T h e s t t e t e e e f o h h N T m t o
Dynamic performance requirements for permanent grandstands subject to crowd action
A4.5 Excitation sources and testing techniques A.4.5.1 Ambient vibration survey (AVS) This method relies on ambient excitation – typically wind or passing traffic – to excite the structure. The response is measured and spectra are calculated to yield vibration property estimates, either by visual inspection of the spectra or by some form of curve fitting. The method can yield useful results for natural frequencies and mode shapes, if the ambient excitation is able to excite the modes of interest adequately, but results for modal damping can be unreliable. Care is needed in interpreting the results of an ambient vibration survey so that the relevant modes are correctly identified. (See Recommendations, Section 4.4 Relevant Natural Frequency). For example, it would be misguided to focus on ‘roof modes’, which engage only slightly with the seating deck, rather than those modes that engage the seating deck strongly and so could be excited significantly by crowd loading. Also, care must be taken to avoid misinterpreting peaks in the AVS response spectra that are not primarily due to resonant response but correspond to dominant frequencies in the ambient excitation spectrum such as might occur due to vortex shedding or the influence of machinery in the vicinity. This is because the method is based upon the excitation spectrum being flat, or at least smooth, across the frequency range of interest. Also, as the AVS approach depends on the ability of the ambient excitation to vibrate the empty stand, its application may be limited when measuring vertical modes of seating decks that are protected from the wind. Bearing these reservations in mind, AVS should be regarded as a Type 1 test. The test can be used in isolation but, because of the potential difficulties of interpretation, it is normally better used in combination with other techniques. However, because of the difficulties of providing horizontal excitation with significant energy input, it is useful to recognise that an ambient vibration survey may be the only practicable method of detecting the presence of global horizontal modes of grandstand vibration.
A.4.5.2 Heel-drop testing This method is suitable for Type 1 testing of moderate size, simple structural arrangements. Heel-drops should be performed across a grid of test points making sure that all relevant modes of vibration are excited. The natural frequencies of excited modes of vibration will usually show as peaks in the spectra in the response to the heel-drop. The signal received from a heel-drop test usually contains significant noise which overlays the primary effect of the impact. This leads to a poor signal-to-noise ratio and spikes in the spectra that may obscure the peaks corresponding to the modes of vibration. As a consequence, there are difficulties in identifying peaks relating to different modes if these occur at frequencies that do not differ very much in value. It is possible to use one or more heel-drop tests to establish mode shapes by measuring the response across a series of test points. However, if results from several heel-drops are combined, the results may be too crude to enable useful comparison to be made with results from analysis because of variations in excitation between heel-drops. It is unlikely that heel-drop testing by an individual will excite ‘global’ modes involving significant motion of the whole of a large stand.
A.4.5.3 Measured impac t testing Simultaneous measurement of an impact force pulse and the corresponding structural response would enable the full set of modal properties to be determined. The technique is commonly used in laboratory testing and testing of smaller structures, but does not appear to have been used on grandstands where the energy required to excite the structure i s much greater. It is possible that, for large structures, an instrumented sledge-hammer or a drop
Dynamic performance requirements for permanent grandstands subject to crowd action
43
weight and force plate could be used. However, as for a heel-drop, sledge-hammers may not be sufficiently large to excite the structure sufficiently and drop weight devices may be difficult to install on a grandstand and could damage the seating deck. Bearing these difficulties in mind, it is considered that measured impact testing should be considered as a Type 1 test being, in effect, an upgraded heel-drop test in which the excitation is both measured and more repeatable.
A4.5.4
Shaker testing of different types and complexity
There is a wide variety of equipment and techniques available using shakers for dynamic testing. As might be expected, these have been developed furthest in the context of mechanical and aerospace engineering. The latest techniques are now becoming more widely used for site testing structures of significant size so that, from a structural engineering viewpoint, it can be anticipated that the near future wil l bring greater choice in the type of testing that can be employed and the quality of results that can be obtained. In the past, most dynamic testing of grandstands using shaker excitation has used rotating mass shakers. Typically, a constant speed of rotation is used to develop sinusoidal excitation at a particular frequency. The tests are normally repeated for a range of increasing speeds, so providing excitation at a range of discrete frequencies, a procedure referred to as stepped sine excitation. The rotating mass shakers that have been used for grandstands are sufficiently large (i.e. the rotating mass produces sufficient force) to excite a cantilever deck for all the modes of interest. The amplitude of the excitation force is easily calculated knowing the rotating mass, its eccentricity and the speed of rotation. Together with measurements of acceleration from locations on the structure, this enables natural frequencies, mode shapes, modal mass and damping values to be estimated for well-separated modes where single degree of curve fitting is appropriate. This capability goes significantly beyond what is needed for Type 1 testing. As yet, it has not been the practice to instrument the rotating mass shaker so as to record directly the excitation force/time history required for correct estimation of modal properties when there are closely spaced modes of vibration that often occur in cantilevered seating decks. However, some Test Agencies have developed procedures to derive the phase difference between the excitation and response and so improve the identification of modes corresponding to closely-spaced natural frequencies. This allows the full range of modal properties to be determined and, in these terms, tests using a non-instrumented rotating mass shaker meet all the requirements for Type 2 testing. However, the processing of the results involves curve fitting to establish the modal parameters. The accuracy of the results of curve fitting depends on the quantity and quality of information available to define the relationships being described. Accordingly, there will be circumstances when the results of Type 2 tests undertaken with a rotating mass shaker, without additional instrumentation, can be less accurate than if the force/time history had been obtained by direct measurement and the results used when processing the data to determine modal properties. Testing with fully instrumented shakers providing a direct measurement of the force/time history has been standard practice for some time in mechanical and aerospace engineering and is now being used for large–scale civil structural engineering applications. This has led to the use of electrical or hydraulic shakers that provide excitation using an inertial mass oscillating in the direction of excitation. These tend to be smaller than rotating mass shakers but, being portable, can be moved around a structure to provide excitation at different locations. Simultaneous measurement of the shaker excitation force and the corresponding response is used when estimating the Frequency Response Function (FRF) between the
44
Dynamic performance requirements for permanent grandstands subject to crowd action
response and excitation on a test structure. In this case, both modulus and phase information for the FRF is determined directly and used in a curve fitting approach that yields the natural frequency, mode shape, modal damping ratio and modal mass for all the modes of interest. The availability of a complete FRF makes this method the most reliable of all those available, particularly where modes are closely spaced in frequency. Stepped-sine and slow-sweep sine as well as broadband random excitation can be used, depending on the time available for testing, the shaker employed (typically inertial, with acceleration of the mass measured so as to derive the force) and the facilities for information processing. Always providing that the shaker generates sufficient force to excite all the modes of interest, instrumented shakers provide high quality information for both Type 1 and Type 2 testing. Because of the substantial size of a grandstand seating deck, not all commercial shakers will be suitable for testing grandstands. More particularly, the shaker has to be of sufficient size that the oscillatory or rotating mass develops the force necessary to excite all relevant modes of the structure. In practice, this difficulty is avoided by using more than one shaker to achieve the necessary excitation. Besides increasing and distributing the energy input, simultaneous use of shakers at more than one location helps to improve the identification of modes with closely spaced natural frequencies and to minimise the possibility of missing a mode of vibration as could occur with a shaker used in a single location.
A.4.5.5 Future developments It will be evident that there are techniques available in other disciplines that, if properly implemented, can enhance the general capability for dynamic testing of grandstand structures. Almost certainly, greater choice of testing techniques for use on grandstands will become available to the Listed Engineer responsible for procuring testing and using the results. In making this choice, the Listed Engineer will need to consult the proposed Test Agency to ascertain its range of expertise and preferr ed way of working. In a climate of change and new developments, an established track record of on-site dynamic testing of structures of significant size will be a useful recommendation.
A4.6 Specification and procurement The role of the Listed Engineer in preparing the specification, procuring testing and reporting to management is illustrated in Figure A4.1. Note that the need for Type 2 testing may emerge from the procedures indicated if additional information is considered necessary in order to reach a satisfactory conclusion. Prior to commissioning a Test Agency to undertake work, the Listed Engineer should decide whether the Route 1 or 2 approach is to be followed, the extent and types of information required from testing and take a preliminary view of the techniques to be employed. At this stage, it will often be useful to discuss the programme and methods with a possible Test Agency and agree a specification for the work required. The Test Agency should have the necessary experience and capability to undertake the chosen type of testing and deal with the logistical difficulties of on-site testing of major structures. It should also be noted that, although Type 1 tests are simpler than Type 2, there is the same need for experienced personnel to undertake the testing and reporting. For instance, the equipment required for heel-drop tests or ambient vibration monitoring is quite widely available but can be used by inexpert operators so giving results of little value. It is also useful if the Test Agency is able to process and analyse results, at least partially, on site so allowing some flexibility in the programme and avoiding the need for repeat testing on another occasion.
Dynamic performance requirements for permanent grandstands subject to crowd action
45
Start
In the particular circumstances of the structure under consideration, is testing required to confirm the assumptions made in design or assessment?
No
( See Section 3.4 ) Yes
No
Calculate relevant natural frequencies.
Has dynamic testing been previously undertaken on the stand in its present form and is the report of the testing available?
Yes
Compare test and calculated values.
Does the comparison give confidence that the figures are sufficiently accurate to support a recommendation confirming the assumptions made in design or assessment?
No
Yes
Prepare report for management
Decide information required from testing or additional testing.
(See Appendix 4 ) Section 4.7
End
Agree method and extent of testing with Test Agency.
Write requirement specification and recommend experienced Test Agency to Management.
Testing undertaken by Test Agency. The Listed Engineer should be available to review results and revise programme if necessary during testing.
Review test results and compare with calculated values. Refine the analytical model if necessary and compare test and recalculated results.
Figure A4.1 The role of the Listed Engineer
46
Dynamic performance requirements for permanent grandstands subject to crowd action
The specification should be written as a ‘performance’ document, based on the agreed types of testing and the properties required from the tests, with the details of the test programme being left to the Test Agency to decide. However, the specification should include: •
A description of the properties required from testing.
•
Confirmation of the agreed type of testing and the form of presentation of results.
•
•
•
•
A requirement for the work to be undertaken to a recognised quality standard such as BS ISO Standard 14964:2000, ‘ Mechanical vibration and shock – Vibration of stationary structures – Specific requirements for quality management in measurement and evaluation of vibration ’. The time agreed for the delivery of the results and report on the testing. Requirements for reporting, bearing in mind that the Engineer’s report to Management should include ‘an account of the procedures used and the detailed results’. A requirement for a method statement to meet the requirements of Health and Safety, and also CDM Regulations where these are applicable.
The Listed Engineer should be available while testing is in progress in order to review results as they are obtained and, if necessary and possible to arrange, modify the instructions to the Test Agency
A4.7 Reporting The Listed Engineer is required to make a report to Management. This should include: •
•
An explanation of the use of personal judgement in requiring additional testing in situations where test records are already available or of a decision not to test (as outlined in Section 3.4). A note on the choice of Test Agency including the Agency’s track record of on-site testing of structures.
•
The agreed specification for the test programme.
•
The Test Agency’s report of the testing including all results.
•
•
An interpretive appraisal of the results including comparisons with values used in design and the significance of any differences in estimates of performance. Recommendations on any further action required.
A4.8. Further Information More information on methods of testing may be obtained from the following sources: Dynamic Test Agency. Primer on best practice in dynamic testing . London: Chameleon Press, 1993. Maia, N.M. and Silva, J.M.M. eds. Theoretical and experimental modal analysis. Baldock: Research Studies Press, 1997. Ewins, D.J. Modal testing: theory, practice and application . 2nd ed. Baldock: Research Studies Press, 2000.
Dynamic performance requirements for permanent grandstands subject to crowd action
47
Appendix 5 Bibliography The Bibliography is a limited selection from published material. Papers are referenced under the following categories. A
Analytical methods
B
Behaviour of grandstands in service
D
Loading, dynamic load factors, crowd behaviour and tolerance of motion
G
Overviews and general interest
H
Human structure interaction
T
Testing and monitoring of grandstands
M
Management, risk assessment and liability
S
Codes, Standards and Guidance.
Referred to in other Appendices
∗
The entries are given in date order by year. References to papers of particular interest or relevance are annotated with a comment in italics. G/D
Bachmann, H. and Ammann, W. Vibration in structures: induced by man and machines. Zurich: IABSE, 1987. Widely used source of information that has stimulated research and practice
S
BS 6841:1987: Guide to measurement and evaluation of human exposure to whole-body mechanical vibration and repeated shock . London: BSI, 1987
G/D
Allen, D.E. ‘Vibrations from human activities’, Concrete International: Design and Construction, 12(6), June 1990, pp66-73. Wide coverage of Canadian Practice as recommended in successive revisions of Commentaries to the NBC Building Code
A*
NAFEMS. A finite element dynamics primer. Glasgow: National Agency for Finite Element Methods & Standards, 1992.
A*
Clough, R.W. and Penzien, J. Dynamics of structures. 2nd ed. New York: McGrawHill, 1993.
A/T*
Dynamic Test Agency. Primer on best practice in dynamic testing. London: Chameleon Press, 1993.
B
Batista, K.C. and Magluta, C. ‘Spectator-induced vibration of Maracana football stadium’, Proceedings of the 2 nd European conference on structural dynamics: EURODYN ‘93, Trondheim, 21-23 June 1993, vol 2. Rotterdam: Balkema, 1993, pp985-992.
B
Kasperski, M. and Niemann, H.J. ‘Man induced vibration of a stand structure’, Proceedings of the 2 nd European conference on structural dynamics: EURODYN ‘93, Trondheim, 21-23 June 1993, vol 2. Rotterdam: Balkema, 1993, pp977-983. Full coverage of design issues set in the context of determining remedial measures for a grandstand that vibrated excessively under crowd loading. Recommends acceleration limits for design and proposes a 7Hz minimum natural frequency limit for grandstands without additional damping
48
Dynamic performance requirements for permanent grandstands subject to crowd action
B
Van Staalduinen, P. and Courage, W. ‘Dynamic loading of Feyenoord Stadium during pop concerts’, Places of assembly and long-span structures, IABSE Symposium, Birmingham, 1994, IABSE Reports, vol 71, 1994, pp283-288.
A*
Blevins, R.D. Formulas for natural frequency and mode shape . Malabar, FL: Robert E Kreiger Publishing Company , 1995.
D
Ji, T. and Ellis, B.R. ‘Floor vibration induced by dance-type loads: theory’, The Structural Engineer, 72(3), 1 Feb 1994, pp37-44. Highly influential paper in deriving DLFs for individual jumping in terms of contact ratio for a repeated half sine load pulse
D
Ellis, B.R. and Ji, T. ‘Floor vibration induced by dance-type loads: verification’, The Structural Engineer, 72(3), 1 Dec 1994, pp45-50. Includes experimental confirmation of the half sine load pulse assumption for jumping on a very stiff support
D
Kasperski, M. ‘Actual problems with stand structures due to spectator induced vibrations’, Proceedings of the 3rd European conference on structural Dynamics: EURODYN ‘96, Florence, 5-8 June 1996 , vol 1. Rotterdam: Balkema, 1996, pp455-461. Overview including DLFs for different activities including hand clapping and stamping, review of tolerance of motion including potential for panic and example of use of tuned mass dampers
S
BS 6399-1: 1997: Loadings for buildings. Part 1: Code of practice for dead and imposed loads. London: BSI, 1996. First inclusion in UK Code of requirements concerning dynamic loading due to people in buildings. Ji and Ellis (1996) contact ratios identified with specific activities and so DLFs. Also set out natural frequency trigger values as alternatives to assessing performance by calculation
A/T*
Maia, N.M. and Silva, J.M.M eds. Theoretical and experimental modal analysis . Baldock: Research Studies Press , 1997.
H
Ellis B.R. and Ji, T. ‘Human–structure interaction in vertical vibrations’, Proc. ICE, Structures and Buildings, 122(1), Feb 1997, pp1-9. Recognition of role of passive people in moderating motion
S/M
Scottish Office and Department of National Heritage. Guide to safety at sports grounds . 4th ed. London: The Stationery Office, 1997 [the Green Guide]. Mainly concerned with spectator management but includes a brief section on dynamics with different frequency limits for structures at sports grounds to those given in BS 6399 (1996)
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ISO 2631-1: 1997: Mechanical vibration and shock: evaluation of human exposure to whole-body vibration. Part 1: General requirements . Geneva: ISO, 1997.
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Reid, W.M., Dickie, J.F., and Wright, J. ‘Stadium structures: are they excited?’ The Structural Engineer, 75(22), 18 Nov 1997, pp383-388. Useful overview of factors influencing structural design of cantilever grandstands and roofs. Emphasises difficulty of designing practical grandstands to BS6399(1996) frequency limits
M
Chapman, J.C. ‘Collapse of the Ramsgate Walkway’, The Structural Engineer , 76(1), 6 Jan 1998, pp1–10. Although not concerned with stadia, presents important messages to operators of facilities used by the public on their responsibilities in procuring services and overseeing the work of specialists
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Wei, L. and Griffin, M.J. ‘Mathematical models for the apparent mass of the seated human body exposed to vertical vibration’, J. Sound & Vibration, 212(5), 1998, pp855-874. Major study of passive action leading to body unit properties for seated people
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Littler, J.D. ‘The dynamic response of a three tiered cantilever grandstand’, Proceedings of the 4th European conference on structural dynamics: EURODYN ‘99, Prague, 7-10 June 1999 , vol 1. Rotterdam: Balkema, 1999, pp623-628.
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Standing Committee on Structural Safety. Structural Safety 1997-99: review and recommendations. 12 th report of SCOSS . London: SETO, 1999, Section 3.2: ‘Safety of sports stadia structures’, pp28-29. Authorative independent expression of concern on procurement, inspections and maintenance of stadia structures. Also suggests independent checks on structural designs
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Health and Safety Executive. The event safety guide: a guide to health, safety, and welfare at music and similar events . 2nd ed. Sudbury: HSE Books, 1999. Key document providing more information than the ‘Green Guide’ for non- sporting events
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Littler, J.D. Permanent cantilever grandstands: dynamic response. BRE Information Paper IP 5/00. Garston: BRE, 2000.
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Ellis, B.R., Ji, T. and Littler, J.D. ‘The response of grandstands to dynamic crowd loads’, Proc. ICE, Structures and Buildings , 140(4), Nov 2000, pp355-365. Notes human structure interaction due to presence of a passive crowd and corresponding effects on natural frequency of the combined system
A/T*
Ewins, D.J. Modal testing: theory, practice and application . 2nd ed. Baldock: Research Studies Press , 2000.
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Kasperski, M. ‘Safety assessment of stadia in regard to human induced vibrations’, Safer solutions in sport and leisure: responsibilities for crowd management at major events, Manchester, 5 April 2001 [unpublished Institution of Civil Engineers seminar]. Besides loading, and target reliability over life-time use, discusses tolerance of motion and potential for panic due to excessive motion of a stand
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Willford, M. ‘Stadium Dynamics’, Safer solutions in sport and leisure: responsibilities for crowd management at major events, Manchester, 5 April 2001 [unpublished Institution of Civil Engineers seminar]. Overview including statistical appreciation using Monte Carlo modelling and assumed distributions of input variables to achieve probabilistic acceleration predictions for different frequency stands. Concludes deterministic design leads to an overestimate of risk of exceeding any given acceleration limit due to neglect of song frequency input and other factors
Standing Committee on Structural Safety. Structural Safety 2000-01: 13 th report of SCOSS . London: IStructE, 2001, chapter 3: Dynamic response of structures, pp23-26.
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On cantilever decks at sports grounds, expresses concern on the “consequences of a structural collapse or disturbing movement causing panic amongst an occupying crowd…”. Concludes that specifically targeted research needed to resolve uncertainties in design for dynamic crowd loading
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Ginty, D., Derwent, J.M. and Ji, T. ‘The frequency ranges of dance type loads’, The Structural Engineer, 79(6), 20 Mar 2001, pp27–31.
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Dynamic performance requirements for permanent grandstands subject to crowd action
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Institution of Structural Engineers, Department for Transport, Local Government and the Regions and Department for Culture, Media and Sport. Dynamic performance requirements for permanent grandstands subject to crowd action: interim guidance on assessment and design . London: IStructE, 2001. Uses natural frequency for vertical excitation of the stand to set limits on categories of use. Testing required to check calculated natural frequencies. Knowledge base considered inadequate to enable recommendations to be formulated for calculating grandstand performance under crowd loading. Recommendations accepted by UK Government re Building Control and Safety Certification
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Ellis, B.R. and Ji, T. Loads generated by jumping crowds: experimental assessment. BRE Information Paper IP 4/02 . London: CRC, 2002. Only study of large group (up to 64 people) loading and reduction in DLFs for jumping with increasing group size
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Sachse, R., Pavic, A. and Reynolds, P. ‘The influence of a group of humans on modal properties of a structure’, Proceedings of the 5 th European conference on structural dynamics: EURODYN ‘02, Munich, 2-5 September 2002 . Rotterdam: Balkema, 2002, pp1241-1246. Wide ranging study providing body unit models for passive human structure interaction effects
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Littler, J.D. ‘Frequencies of synchronised human loading from jumping and stamping’, The Structural Engineer, 81(22), 18 Nov 2003, pp27–35. Reviews song frequencies experienced at concerts and challenges received wisdom on li mits to possible excitation ranges with tests involving jumping and stamping
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Matsumoto, Y. and Griffin, M.J. ‘Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration’, J. Sound & Vibration, 260(3), pp431-451. Passive action and body unit properties for erect people
S/G
ISO/CD/10137: 2004: Bases for the design of structures: serviceability of buildings and pedestrian walkways against vibration [Committee Draft]. Includes proposals for stadia with loading corresponding to an extreme event involving everyone jumping. Proposes separate acceleration limits for the onset of panic and an upper limit for comfort. It is doubtful that practical cantilever grandstands would meet these requirements
A/D/S
Ellis, B.R. and Ji, T. The response of structures to dynamic crowd loads. BRE Digest 426. Garston: BRE Bookshop, 2004. Provides methods for calculating dynamic response in accordance with BS 6399-1 (1996). Useful guidance for low crowd densities and vigorous activity on relatively stiff structures, (dancing and aerobics). Not applicable to dense crowd loading on flexible grandstands
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Ellis, B.R. and Littler, J. D. ‘The response of cantilever grandstands to crowd loads. Part 1: Serviceability evaluation.’ Proc. ICE, Structures and Buildings, 157(SB4), Aug 2004, pp235–241. Explores the use of the vibration dose value (VDV) approach to assessing tolerance of motion for people in grandstands
A/D
Ellis, B.R. and Littler, J.D. ‘The response of cantilever grandstands to crowd loads. Part 2: Load estimation’, Proc. ICE, Structures and Buildings, 157(SB5), Oct 2004, pp297-307. Back analysis of two cantilever grandstands tiers to determine effective DLFs for crowd loading at concerts with modest excitation levels. Conventional analysis with allowance for crowd size (Ellis & Ji 2002) led to a value of 16% effective damping which was attributed to crowd action. Results applied to other grandstands. High damping clearly the result of human structure interaction
Dynamic performance requirements for permanent grandstands subject to crowd action
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Yao, S., Wright, J. R., Pavic, A. and Reynolds, P. ‘Experimental study of humaninduced dynamic forces due to bouncing on a perceptibly moving structure’, Canadian J. Civil Engineering, 31(6), Dec 2004, pp1109-1118. Unambiguous demonstration of effects of human structure interaction due to an active (i.e. moving) person on a flexible support for a range of natural frequencies and mass ratios typical of practical cantilever grandstands. Significant reductions in contact force at resonance (dropout) observed leading to lower accelerations than would be predicted from conventional theory ignoring active human structure interaction
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Reynolds, P., Pavic, A. and Ibrahim, Z. ‘A remote monitoring system for stadium dynamics’, Proc. ICE, Structures and Buildings, 157(SB6), Dec 2004, pp385-393. Report of long-term monitoring of moderately flexible grandstand mainly used for viewing soccer
A/H
Sachse, R., Pavic, A., and Reynolds, P. ‘Parametric study of modal properties of damped two-degree-of-freedom crowd-structure dynamic systems’, J. Sound & Vibration, 274(3-5), 2004, pp461-480.
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Reynolds, P., Pavic, A. and Willford, M. ‘Prediction and measurement of stadia dynamic properties’, 23rd International modal analysis conference: IMAC XXIII ), Orlando, Florida, 31 Jan-3 Feb 2005 . Account of dynamic testing to obtain modal properties of a curved multi-tier cantilever grandstand with comparison of results from pre test analysis using single frame and 3-D analysis and post testing results from 3-D Finite Element modelling. The post testing analysis satisfactorily reproduced the family of closely spaced modes but with discrepancies in values of natural frequency considered due to the treatment of non-structural elements and omission of the roof in the FE model
G/H
Willford, M. ‘Dynamic performance of stands’, in Culley, P. and Pascoe, J. eds. Stadium Engineering. London: Thomas Telford, 2005, pp47-54. Broad coverage of design of stadia for dynamic loading with particular consideration given to human structure interaction due to passive /inactive people in an otherwise active crowd. Active participation treated using conventional DLFs
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‘Commentary D: deflection and vibration criteria for serviceability and fatigue limit states’, in National Research Council of Canada. User’s guide - NBC 2005: structural commentaries (Part 4 of Division B) . Ottawa: NRC, 2005, ppD1D10. Widely used Code based on performance design principle. 2005 revision includes recommendations for stadia based on serviceability criteria related to Canadian practice and “commonly encountered events”. Does not address concerns on possibility of an extreme event and consequences for safety related to panic due to excessive motion. Not recommended for major stadia with open-ended use
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Reynolds, P. and Pavic, A. ‘The dynamic performance of sports stadia under crowd dynamic loading at concert events’, Proceedings of the 6 th European conference on structural dynamics: EURODYN ‘05, Paris, 4-7 September 2005 . Rotterdam: Millpress, 2005, pp473-478.
T/H
Reynolds, P. and Pavic, A. ‘Vibration of a large cantilever grandstand during an international football match’, ASCE J. Performance of Constructed Facilities , 20(3), Aug 2006, pp202-212. Presents modal properties obtained by testing the empty stand and compares these with properties obtained whilst monitoring the stand during the match. Significant differences were recorded showing the crowd interacted structurally with the basic structure
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Dynamic performance requirements for permanent grandstands subject to crowd action
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Mohanty, P. and Reynolds, P. ‘Modelling of dynamic crowd-structure interactions in a grandstand during a football match’. 24th International modal analysis
H
Yao, S., Wright, J.R., Pavic, A. and Reynolds, P. ‘Experimental study of humaninduced dynamic forces due to jumping on a perceptibly moving structure’, J. Sound & Vibration, 296, 2006, pp150-165. Demonstration that active human structure interaction does not depend on uninterrupted contact with the support with results for jumping similar to those in the 2004 paper by the same authors
D/H
Sim, J., Blakeborough, A. and Williams, M. ‘Modelling effects of passive crowds on grandstand vibration’, Proc. ICE, Structures and Buildings , 159(SB5), Oct 2006, pp261-272.
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Parkhouse, J.G. and Ewins, D.J. ‘Crowd-induced rhythmic loading’, Proc. ICE, Structures and Buildings, 159(SB5), Oct 2006, pp247-259. Results of 1000 tests involving individual bobbing and jumping on force plates at excitation levels comparable to pop-concert participation and leading to synthesis of Dynamic Load Factors for groups of different size
H*
Dougill, J.W., Wright, J.R., Parkhouse, J.G. and Harrison, R.E. ‘Human structure interaction during rhythmic bobbing’. The Structural Engineer , 84(22), 21 Nov 2006, pp32–39. Theoretical development of an active human structure interaction model with properties derived from independent experiments and validation through comparison with results from individual bobbing/bouncing on a flexible platform. Includes discussion of relevance to grandstands
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Alexander, N.A. ‘Theoretical treatment of crowd-structure interaction dynamics’, Proc. ICE, Structures and Buildings , 159(SB6), Dec 2006, pp329-338. Theoretical treatment of similar model to Dougill et al (2006 )
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The Construction (Design and Management) Regulations . Norwich: The Stationery Office, 2007 (SI 2007/320). Important implications for a client requiring construction works
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Reynolds, P., Pavic, A. and Carr, J. ‘Experimental dynamic analysis of the Kingston Communications Stadium’, The Structural Engineer, 85(8), 17 Apr 2007, pp33–39. Includes comparison of calculated and measured dynamic properties
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Institution of Structural Engineers. Temporary demountable structures: guidance on procurement, design and use . 3rd ed. London: IStructE, 2007. Comprehensive guidance on demountable structures. Guidance on horizontal motion is adopted in the present Recommendations (Table 2) but without allowance for geometrical imperfections
T/B/H* Pavic, A. and Reynolds, P. ‘Experimental verification of novel 3DOF model of grandstand crowd-structure dynamic interaction’, 26 th International modal analysis conference: IMAC-XXVI, Orlando, Florida, 4-7 Feb 2008 , paper 257. Includes details of testing a stadium before and during a pop-concert with moderate crowd excitation. Calculations of performance using finite element analysis and the human structure interaction model recommended in Appendices 1 and 2 show acceptable agreement with the measured values of RMS acceleration
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