Guidelines on the Design of Floor for Vibration Due to Human Actions (Part III)

SEB GUIDELINES SEBGL  –  OTH5

Guidelines on the Design for Floor Vibration Due to Human Actions

Part III: Vibration Effect to Grandstands, Sensitive Equipment and Facilities

STRUCTURAL ENGINEERING BRANCH ARCHITECTURAL SERVICES DEPARTMENT September 2011

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No./Revisi on No. : 1

Page 1 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Issue/Revis ion Date : September 2011

CONTENTS Content Page 1.

Introduction ......................................... ............................................................... ............................................ ............................................. ........................... .... 3

2.

Grandstand Vibration ........................................... .................................................................. ............................................. ............................. ....... 3

3.

Sensitive Equipment and Facilities............................................. .................................................................... ............................ ..... 30

4.

Design References .......................................... ................................................................ ............................................ .................................... .............. 47

Copyright and Disclaimer of Liability This Guideline or any part of it shall not be reproduced, copied or transmitted in any  form or by any means, electronic or mechanical, including photocopying, recording, or  any information storage and retrieval system, without the written permission from  Architectural  Architectural Services Department. Department. Moreover, Moreover, this Guideline is intended for the internal  use of the staff in Architectural Services Department only, and should not be relied on by any third party. No liability is therefore therefore undertaken undertaken to any third party. While every every effort  has been made to ensure the accuracy and completeness of the information contained in this Guideline at the time of publication, no guarantee is given nor responsibility taken by   Architectural Services Department for errors or omissions in it. The information is   provided solely on the basis that readers will be responsible for making their own assessment assessment or interpretation of the information. Readers are advised to verify all relevant  representation, statements and information with their own professional knowledge.  Architectural Services Department accepts no liability for any use of the said information and data or reliance placed placed on it (including the formulae formulae and data). data). Compliance with this Guideline does not itself confer immunity from legal obligations.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No./Revisi on No. : 1

Page 2 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Issue/Revis ion Date : September 2011

CONTENTS Content Page 1.

Introduction ......................................... ............................................................... ............................................ ............................................. ........................... .... 3

2.

Grandstand Vibration ........................................... .................................................................. ............................................. ............................. ....... 3

3.

Sensitive Equipment and Facilities............................................. .................................................................... ............................ ..... 30

4.

Design References .......................................... ................................................................ ............................................ .................................... .............. 47

Copyright and Disclaimer of Liability This Guideline or any part of it shall not be reproduced, copied or transmitted in any  form or by any means, electronic or mechanical, including photocopying, recording, or  any information storage and retrieval system, without the written permission from  Architectural  Architectural Services Department. Department. Moreover, Moreover, this Guideline is intended for the internal  use of the staff in Architectural Services Department only, and should not be relied on by any third party. No liability is therefore therefore undertaken undertaken to any third party. While every every effort  has been made to ensure the accuracy and completeness of the information contained in this Guideline at the time of publication, no guarantee is given nor responsibility taken by   Architectural Services Department for errors or omissions in it. The information is   provided solely on the basis that readers will be responsible for making their own assessment assessment or interpretation of the information. Readers are advised to verify all relevant  representation, statements and information with their own professional knowledge.  Architectural Services Department accepts no liability for any use of the said information and data or reliance placed placed on it (including the formulae formulae and data). data). Compliance with this Guideline does not itself confer immunity from legal obligations.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No./Revisi on No. : 1

Page 2 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Issue/Revis ion Date : September 2011

1.

Introduction

1.1

Part I and Part II of this set of Guidelines (available: http://asdiis/sebiis/2k/resource_centre/ ) focus on human-induced vibration on lightweight floors with large span due to rhythmic activities and walking respectively. Part III of this set of Guidelines Guidelines will focus on the effect of humanhumaninduced vibration on grandstands and sensitive facilities (e.g. hospital ward, radio studio, high precision laboratory) or equipment (e.g. high precision microscope, MRI), especially on delicate and expensive health care and medical equipment whose accuracy are sensitive to vibration.

1.2

This set set of Guidelines will further be divided divided into into two sections. Section 2 will be on grandstands, and Section 3 will be on the sensitive equipment or facilities. Again, as in Part I and Part II of this set of Guidelines, design examples will be included to illustrate the procedures in checking the vibration effects to these structures, facilities and and equipment. However, designers designers should note note that this set of  Guidelines provides basic knowledge on the subject, and designers should therefore carry out their own research to suit suit their own problems. A list of design references references is included at the end of this Guideline.

2.

Grandstand Vibration

2.1

Types of Grandstand

2.1.1 A grandstand is a structure which provides seating seating for spectators at entertainment or sporting events. events. Grandstands typically typically have seats, seats, or benches, arranged arranged in tiered rows with access to the seats from aisles that run perpendicular to the rows of  seating. Grandstands are typically classified into three distinct types: permanent, permanent, demountable and retractable –  retractable – the the latter two are sometimes sometimes termed as “bleacher”. “bleacher”. 2.1.2 Retractable stands ( Photo 1) are typically installed in the indoor arena in indoor recreation centres. centres. They are used during particular events, and and remain retracted at other times. Retractable stands are are most sensitive to front-to-back front-to-back sway loading as this is the direction of retraction. Like retractable retractable stands, stands, demountable stands (Photo 2 and Figure 1) are also lightweight temporary structures whose trussed appearances are reminiscent of scaffolding systems. Unlike retractable stands, demountable stands are typically erected for a single specific event and therefore left in place for a short duration. Usually, demountable stands are proprietary products designed, supplied and installed by specialist contractor employed by the event organizers. organizers. Because of of the limited time for installation, such such type of structure, despite with bracing, remains extremely lightweight and is thus easily excited by occupant activities. Demountable stands therefore tend to be particularly sensitive to side-to-side sway loading. loading. Two serious incidents of collapse collapse of demountable stands occurred in the UK during during 1993 and 1994 1994 (IStructE 2007). The UK Department of  the Environment therefore appointed the Institution of Structural Engineers, who in collaboration with the Steel Construction Institute, published a guide for clients, contractors, engineers engineers and suppliers of demountable demountable structures. structures. This guide has then been updated with latest technological and regulatory changes, and designers for demountable grandstands can now refer its latest version as IStructE (2007), Temporary Demountable Structures: Guidance on Procurement, Design and Use Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No./Revisi on No. : 1

Page 3 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Issue/Revis ion Date : September 2011

rd

(London: IStructE, 3 ed) on the structural aspects for both retractable and demountable stands. An information information paper paper on the analysis analysis and design of  demountable grandstands is being prepared, and when completed, it will be posted onto URL: http://asdiis/sebiis/2k/resource_centre/ .

Photo 1 Retractable Grandstand at Tsuen Wan Sports Ground Ground

Photo 2 Demountable Grandstand in Bellinzona, Bellinzona, Switzerland

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No./Revisi on No. : 1

Page 4 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Issue/Revis ion Date : September 2011

Figure 1 Arrangement of Proprietary Proprietary Demountable Grandstand Grandstand at 2009 East Asian Games Opening Ceremony

2.1.3 In both retractable and demountable stands, IStructE (2007) recommends a simplified approach to include the following notional horizontal load to design the grandstand for the effect induced by different categories of spectator action: Category 1 6% of the vertical imposed load Category 2 7.5% of the vertical imposed load Category 3 10% of the vertical imposed load Category 1 spectator action includes nominal potential for spectator movement, which excludes synchronized and periodic crowd movement at golf tournament, athletic events, events, etc. Category 2 spectator action action includes potential for spectator spectator movement. Again, this category excludes synchronized and periodic crowd Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No./Revisi on No. : 1

Page 5 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Issue/Revis ion Date : September 2011

movement at musical concerts, football matches, etc. Category 3 spectator action includes potential for synchronized and periodic crowd movement. However, for grandstands with the natural vertical frequency less than 8.4Hz or the natural horizontal frequencies less than 4.0Hz, IStructE (2007) recommends a full dynamic analysis of the grandstand instead of using the simplified approach. 2.1.4 The focus of this set of Guidelines is, however, on permanent grandstands ( Photo 3 and Figure 2), as they are usually designed and constructed under the supervision of  our Department, although in theory this set of Guidelines can also be used for the design of vibration for retractable and/or demountable stands. Permanent grandstands are used to house spectators around regularly used sports facilities. Secondary facilities such as toilets, changing rooms, offices, kiosks and meeting rooms are usually situated beneath the seating deck. Structures of this type have been increasingly lightweight and flexible using structural steel, gaining height and utilising multiple cantilever tiers to increase capacities whilst ensuring good lines of  sight.

Photo 3 Permanent Grandstand at Hong Kong Stadium

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 6 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Figure 2 Structural Layout of Grandstand at Hong Kong Stadium

2.1.5 A typical grandstand with multiple cantilever tiers ( Figure 2) consists of a series of  raked beams of reinforced concrete or structural steel construction that support the seating decks. The seating decks which serve as the bleachers spanning between the raked beams are usually precast concrete. Upper tier has several of the foremost rows of seats positioned on a cantilever over the lower tier, and similarly, the lower tier has several of the foremost rows of seats positioned on a cantilever over the concourse. Ellis and Ji (2000) note that although sway and front-to-back vibration in horizontal direction may often be the most important modes for demountable and retractable grandstands, vertical modes are usually the most important ones for permanent grandstand for human-induced dynamic crowd loads. 2.1.6 There have been no internationally recognized design standards for grandstand vibrations and acceptable criteria until recently. In 2006, the Canadian Commission on Building and Fire Codes published a commentary to Canadian National Building Code 2005, (commonly known as “ Commentary D”), which contains assessment method and limits on the peak acceleration for grandstand vibrations. In 2007, ISO published a new edition of    ISO 10137: Bases for Design of Structures  –  Serviceability of Buildings and Walkways against Vibrations , which contains acceptance criteria for the limits for such structures. In 2008, the joint working group formed by IStructE, the UK Department for Communities and Local Government and the UK Department for Culture Media and Sport and chaired by Dr J W Dougill published their report   Dynamic Performance Requirements for  Permanent Grandstands Subject to Crowd Action (2008) giving recommendations for management, design and assessment of grandstands. Recently, Jones et al (2011), after reviewing 162 publications on this subject, summarized the state-of-art on the acceptable criteria for human-induced vibration for grandstands, the loads generated by various actions of occupants on grandstands, the methods for predict

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 7 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

the dynamic behaviour of the grandstands, and the various types of in-situ measurements. 2.1.7 The following discussion on the analysis and design of human-induced vibration on grandstands will therefore mainly be based on the acceptable criteria contained in the internationally recognized design standards, and the literature review by Jones et al (2011). Moreover, the discussion will be supplemented with the latest literature, especially latest work on this subject by Willford (2005). 2.2

Historical Review

2.2.1 The following historical review was provided by Jones et al (2011). In the late 18th century, grandstands were rarely recognized as being a unique type of structure. In 1932, the American Standards Agency investigated and documented sway loads which could arise due to the dynamic actions of occupants. However, there is no explicit provision on the method to model the human dynamic loads. In 1985, the Canadian National Building Code recommended that the structure of grandstands should be designed for forces due to swaying of 0.3kN per metre length of seats parallel to the row and half this value perpendicular to each row. At that time, it was still not known the loads generated by dancing or jumping and whether occupants could act in synchronized manner for a sustained period of time. The Supplement to the National Building Code subsequently suggested that the human dynamic load should be referenced to that due to rhythmic activity. This suggestion was not, however, intended for the design of grandstand. 2.2.2 In 1992, a temporary grandstand, erected to increase the capacity of a stadium from 8,500 to 18,000 in Bastia, Corsica, collapsed killing 17 and injuring over 2,500 people (Ellis and Ji 2000). In the UK, 18 people were injured in 1993 when seating collapsed at a gospel meeting, and about 1,100 spectators were also involved in the collapse of a demountable structure at a pop concert in 1994. Following the collapses, a working group was formed by IStructE to examine the effects of  dynamic loading on temporary grandstands. In 1994, the UK Department of the Environment issued an interim guide  Interim Guidance on Temporary Grandstands (1994), which specifies the frequency limits for checking temporary grandstands used at pop concerts.  BS 6399-Part 1:1996  was later promulgated to incorporate the frequency limits with the alternative that safety may be achieved by ensuring that the structure can withstand the dynamic loads. 2.2.3  BS 6399-Part 1:1996  recognized that dynamic loads are only significant when any crowd movement is synchronized. In practice, this only occurs in conjunction with a strong musical beat such as in pop concerts. The dynamic loading is thus related to the beat frequency of the music and is periodical in both horizontal and vertical directions. If the synchronized movement excites a natural frequency of the affected part of the structure, resonance will occur which can greatly amplify its response. It therefore specifies that in order to avoid resonance effects, the natural vertical frequency shall be greater than 8.4Hz and the natural horizontal frequencies shall be greater than 4.0Hz. However, these recommendations were found to be too onerous for general use. In 1997, Ellis and Ji (1997) published a BRE Digest (commonly known as “ Digest 426 ”) to supplement  BS 6399-Part 1:1996 .  BS 6399-

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 8 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Part 1:1996  was therefore revised in 2002, which suggested designers to follow  Digest 426  instead.

2.2.4 At about the same time, the UK Department of Culture, Media and Sport revised the Guide to Safety at Sports Ground  (commonly known as the “Green Guide”), and the Green Guide specifies a minimum natural vertical frequency recommendations of 6 Hz based upon observations of successful structures. However, many cantilever grandstands with less than the 6Hz limit still perform satisfactory under normal loading (Ellis and Littler 2004). The Green Guide further presents methods for dynamic assessment, which was also later found to be conservative. As a result, IStructE/DTLR/DCMS issued  Dynamic Performance Requirements for Permanent  Grandstands Subject to Crowd Action: Interim Guidance on Assessment and Design (2001) (the “  Interim Guidance”), which specified vertical frequency limits for different categories of use (3.5Hz for new grandstands for normal non-rhythmic loading and 6Hz for those for pop concerts). Failure to meet the minimum natural frequencies required by the interim guidance necessitated full dynamic analysis of  the structure be undertaken but, as with earlier documents, no methodology for this process was provided or explained. 2.2.5 Another limitation of the  Interim Guidance was that it only considers the vertical frequency of the empty grandstand as the single criterion for acceptance, and the behaviour of the crowd was not considered. In 2008, IStructE/DTLR/DCMS replaced the   Interim Guidance by   Dynamic Performance Requirements for  Permanent Grandstands Subject to Crowd Action (IStructE/DTLR/DCMS 2008). In 2007, ISO published a new edition of    ISO 10137: Bases for Design of  Structures  –  Serviceability of Buildings and Walkways against Vibrations , which contains acceptance criteria on the limits for such structures. Across the Atlantics, Commentary D contains assessment method and limits on the peak acceleration for grandstand vibrations. In the following section, the recommendations given in IStructE/DTLR/DCMS (2008) and  ISO 10137:2007 , which represent the latest state of the art, will be presented. 2.3

Acceptability Criteria for Grandstand Vibration

2.3.1 Minimum Frequency of the Structure 2.3.1.1 IStructE/DTLR/DCMS (2008) specify two routes for the design and assessment of  grandstand subject to dynamic crowd loading: Route 1 and Route 2, depending on different types of events and crowd behaviour. Route 1, which is similar to that in the  Interim Guidance, Green Guide,  Digest 426 , or  BS 6399-Part 1:1996 , limits the natural frequency of the grandstand which is empty of people for different scenarios of use ranging from Scenario 1 (a low profile sporting event with a relaxed viewing public) to Scenario 4 (high energy events such as pop/rock  concerts with vigorous participation of the crowd) as shown in Table 1.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 9 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 1 Summary of Minimum Frequency of Empty Grandstand for Route 1

Scenario Exemplar Event

Crowd Behaviour

1

Sporting events with less than maximum attendance

2

Normally relaxed viewing public predominantly seated with spontaneous response to single events Predominantly seated audience with minor excitation Potentially excitable crowd standing and participating during some part of the programme

Classical concert, or well-attended sporting event High profile sporting events and concerts with medium tempo music and revival pop-concerts with cross generation appeal High energy concerts Excited crowd, mostly with periods of high standing and bobbing with intensity music some jumping (Source: IStructE/DTLR/DCMS 2008: 3)

3

4

Minimum Vertical Frequency 3.5Hz

3.5Hz

6Hz

6Hz

2.3.1.2 The acceptable minimum natural frequency in Table 1 is less than the acceptable minimum natural frequency of 9Hz in Part I of this set of Guidelines. This is because crowds are particularly dense and the environment is noisy and chaotic in grandstands, and hence IStructE/DTLR/DCMS (2008) therefore adopt lower acceptable criteria on minimum vertical frequency. 2.3.1.3 Route 2 is only applicable to Scenarios 2, 3 and 4, in which instead of satisfying the minimum vertical frequency, designer can limit the acceleration under the dynamic crowd loading. Such approach is in line with the latest recommendations in ISO 10137:2007  and Commentary D. 2.3.2 Maximum allowable acceleration 2.3.2.1 In Part I of this set of Guidelines, the baseline curve as recommended by  ISO 2631-2: 1989 has been presented, which showed that humans are sensitive enough to detect vibrations as low as 0.5% g. However, although various allowable peak  accelerations have been specified for different types of occupancy based on this baseline curve, there has not been a specific criterion for grandstand until the recent codes and guidelines. As stated in last paragraph, all these latest codes and guidelines (IStructE/DTLR/DCMS 2008,  ISO 10137:2007  and Canadian National   Building Code 2005 now explicitly acknowledge the distinct characteristics of  grandstands, in that crowds are particularly dense and the environment is noisy and chaotic in a manner rarely found elsewhere. The limits (shown in Table 2) imposed by these codes and guidelines are therefore higher than other occupancy. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 10 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 2 Summary of Maximum Allowable Acceleration for Route 2 Codes or Guidelines IStructE/DTLR/DCMS (2008)

Limits on Allowable Acceleration

 ISO 10177: 2007  Canadian National Building Code 2005

3% g rms acceleration for Scenario 2 7.5% g rms acceleration for Scenario 3 20% g rms acceleration for Scenario 4 10% g rms acceleration 18% g peak acceleration

2.3.2.2 Both IStructE/DTLR/DCMS (2008) and   ISO 10177:2007  adopt the root mean square (rms) acceleration as the acceptance criterion; whilst Canadian National  Building Code 2005 specifies a limit on the peak acceleration. Rms acceleration is calculated by averaging the square of the acceleration over an interval of time. The choice of the interval of time is controversial, and this set of Guidelines suggests adopting the recommended interval of 10 seconds as proposed in  ISO 10177:2007  and IStructE/DTLR/DCMS (2008), which is more common for checking against comfort. 2.3.2.3 Another controversial issue is whether the rms acceleration shall be weighted accordingly to the excitation frequency. If the vibration is predominantly at one frequency, then there is no need to weigh the rms acceleration. However, when the vibration contains a range of frequencies, then   BS 6841 gives different weighting values for different excitation frequencies as shown in Table 3. Table 3 Weighting Values for Different Excitation Frequencies

Frequency (Hz) 1.00 1.25 1.60 2.00 2.50 3.15 4.00 5.00 6.30 8.00

Weighting Value 0.5000 0.5590 0.6320 0.7070 0.7910 0.8870 1.0000 1.0000 1.0000 1.0000 (Sourc e: BS 6841 )

However, IStructE/DTLR/DCMS (2008) consider that no weighing values are required to calculate the rms acceleration for the range of frequencies encountered with crowd motion. Rather, IStructE/DTLR/DCMS (2008) suggest the rms accelerations calculated from the first three harmonics of the dominant excitation frequency are to be combined to give the total response “root sum squares” of the rms accelerations as follows:

R T  R 12  R 22  R 32 Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 11 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

where RT is the total response rms acceleration, and R 1, R2 and R3 are respectively st nd rd the rms accelerations due to the 1 , 2 and 3 harmonics of the excitation frequency. 2.3.2.4 Intermittent Vibration Ellis and Littler (2004) note that the above criteria may not be applicable to intermittent vibration, where only there are only isolated incidents of high peak  acceleration for short duration. They therefore propose to limit the vibration dose value (VDV) instead. Details of the expression to calculate the VDV, the limits on the VDV, and the procedures of this approach will be described in Section 3. 2.3.3 Suggested Acceptable Criteria for Grandstands 2.3.3.1 This set of Guidelines recommends that a stringent vertical natural frequency of  the grandstand should be adopted, and the vertical natural frequency of the grandstand empty of people should not be less than 6Hz. Should this stringent limit on vertical natural frequency be exceeded, the maximum peak or rms acceleration under dynamic loading should be checked. Either the rms limits specified in IStructE/DTLR/DCMS (2008) or the peak limit in Canadian National  Building Code 2005 (Table 2) may serve as the reference. When the vibration contains maximum accelerations over a range of frequencies, designer can weigh the rms accelerations at different excitation frequencies given in Table 3, or can calculate the total response by finding the root sum squares of  the rms accelerations at the first three harmonics. 2.3.3.2 In the next section, a method to calculate of the vertical natural frequency of the grandstand empty of people will be introduced, which will then be followed by the assessment of the dynamic loading when assessment of the rms acceleration or peak acceleration is required. 2.4

Method to Assess Dynamic Response of Grandstand

2.4.1 Calculation of the Vertical Natural Frequency There are two methods to calculate the natural frequency of an empty grandstand, namely: approximate methods using hand calculation, and numerical methods using computer software. IStructE/DTLR/DCMS (2008) commented that the approximate method, although is unlikely to be sufficiently accurate, provides a fast way to check the results from numerical methods. Moreover, the approximate methods work well for simple single-span or cantilever structures (which are predominantly the usual structural forms for grandstand). Table 4 gives the formulae for calculating the fundamental natural frequency of an empty grandstand.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 12 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 4 Formulae for Calculating Natural Frequency of Grandstand

Source IStructE/DTLR/DCMS (2008)

Formula A  f   where A lies between 15 and 20, and



 (mm) is the deflection under dead load Willford (2005)

 f   0.56

 EI 

for cantilever structure, which mL4 is the exact solution for a cantilever beam with uniformly mass m.

Example 1 in Section 2.6 illustrates the procedures of these methods.

2.4.2 Calculation of Acceleration due to Dynamic Loading 2.4.2.1 Types of Dynamic Loading Ellis and Littler (2004a) note that the most tedious task in calculating the dynamic response of a grandstand in service is to model the loads produced by crowds. The dynamic load used in calculating the rms or peak acceleration for grandstand depends on the types of activity, which include: jumping loads, bouncing/bobbing/jouncing loads, foot-stamping and hand-clapping loads, and leaping loads. The following paragraphs will briefly describe the characteristics of  these types of dynamic loading. Jumping is the launching one‟s self in the vertical direction, removing the entire body from contact with the ground. There is a period of zero loading, followed by a rapid impact load with a significant peak which is several times the static weight of the jumper (as shown in Figure 4(a)). Jumping occurs typically at a goal at a football match (Ellis and Littler 2004a). Well coordinated jumping crowds (e.g. as a result of music being playing) may cause much higher structural accelerations resulting in more serious repercussions such as panic. However, Ellis and Littler (2004) questioned whether jumping (which is usually found on dance floor) is a suitable model for grandstands. Dougill et al (2006) further note that jumping is usually not a structural problem as compared with bobbing as described below, because for raked grandstands with limitations on space due to fixed seating, occupants find it difficult or uncomfortable to jump even with music being played.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 13 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Figure 4(a) Force-Time Graph for Jumping (Source : Jones et al (2011: 1539))

Bobbing (also known as “bouncing”) and jouncing occur more common than   jumping. Bobbing and jouncing (as shown in Figure 4(b)) are the response of  occupants to aural stimulation, and typically consist of  attempting to „jump‟ whilst the feet remaining in contact with the structure. The difference between bobbing and jouncing is that in jouncing the heels temporarily leave contact with the structure only to impact later, whilst in bobbing there is no such a heel strike. Bobbing differs from jumping in that whereas jumping over 3.5Hz is very hard to achieve, bobbing can reach 6Hz (Yao et al 2004). Hence, grandstands with relatively high fundamental natural frequency of over 5Hz are still susceptible to excitation by the bobbing. Another difference is that as the feet of the occupants are in permanent contact with the structure, they can easily feel the structural motion and then tune their motion to exacerbate it, similar to what happens on a swing (Yao et al 2004).

Figure 4(b) Force-Time Graph for Bobbing (Source : Jones et al (2011: 1539))

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 14 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Stamping is an activity that can be performed when either standing or seated. It is characterized by rapid foot motions and negligible motions of the upper body. Clapping involves forceful large amplitude motions of the upper body, but the overall centre of mass does not shift significantly. As there is restricted motion in the centre of mass during these activities, the resulting loading would generally be less that by more vigorous actions such as bouncing and jumping. However, the ease of crowd coordination and high frequency of repetition may still result in noticeable vibrations. Leaping to the feet is a common response to exciting events that occur frequently during goals in football matches. Loads generated by this action are mostly in the horizontal front-to-back direction. A load of this type is transient, and is dangerous to retractable or demountable structures; but is not a controlling criterion on permanent grandstands. Occasionally, crowds may engage in concentrated cheering efforts that feature abrupt rising, such as the „Mexican Wave‟, when participants rise in turn r ather than all at once. This form of  excitation, whilst visually spectacular, is not a particularly onerous form of  dynamic loading. 2.4.2.2 Load Models The above paragraph has described the characteristics of the various types of  dynamic loading for grandstands, and concluded that bobbing is most relevant loading for grandstands, although jumping can cause higher structural accelerations. In the analysis of the dynamic response of the grandstands, it is necessary to model these two types of loading by a force-time history function. In Part I of this set of Guidelines, the dynamic loads due to rhythmic activities have been represented by a Fourier series of the form: 

F (t )  G (1.0 

 r  sin( 2n  f  t     )) n

 p

n

n 1

where F(t) is the time varying force, G is the load density of the crowd, t  is the th time,  f  p is the frequency of the load, r n is the n Fourier coefficient, and  n is the phase lag. Similarly, both jumping and bobbing can also be modelled by similar Fourier series with different coefficients and phase angles. Coordinated Jumping Table 5(a) summarizes the recommended values given in   ISO 10137:2007  for various types of dynamic loads for modelling the loading due to vertical action for seated audience and coordinated jumping, and  ISO 10137:2007  suggests that the phase angle for jumping can be assumed to be zero, and that for all other activities, o a phase shift of 90 can be assumed for harmonic contributions below the resonance frequency of the grandstand.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 15 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 5(a) Recommended Fourier Coefficients for Jumping Activities

Activity Seated audience

Forcing frequency f  p (Hz) 1.5-3.0

Coordinated  jumping (without seats) Coordinated  jumping (with seats)

1.5-3.5

1.5-3.5

1

Crowd Density

One person per seat 2 1.25m per person

One person per seat

Coefficients r 1 r 2 r 3 0.5 0.25 0.15 1.7

1.0

0.4

1.7

1.0

0.4

(Source: ISO 10137:2007 ) 1

Notes: The weight of each person may be taken as 75kgf (Smith et al 2009). 2 The dynamic action produced by a group of participants also depends on the degree of  coordination of the participants, and hence a coordination factor C(N) can be applied to the forcing function F(t) as follows: F(t) N  = F(t)×C(N), where N is the number of participants. The following table summarizes the different C(N) values for coefficients r 1, r 2 and r 3 for coordinated jumping as suggested in  ISO 10137:2007 . Harmonic coefficients r 1 r 2 r 3

Values of C(N) for different degree of Coordination High Medium Low 0.80 0.67 0.50 0.68 0.50 0.40 0.50 0.40 0.30

  ISO 10137 states that the values of C(N) are only applicable for a group of at least 50 participants, and all values shall be taken as 1 for 5 participants. Intermediate values can be obtained by linear interpolation.   ISO 10137 further states that for seated audience, the coordination factor shall be taken as 1.

Bobbing IStructE/DTLR/DCMS (2008), based on the work of Dougill et al (2006), give the following expression for the dynamic loads: 3 F (t )    mg  G sin( 2 ift     ) i i i 1 where F(t) is the time varying force,   is crowd effectiveness factor which is a measure of whether the crowd is likely to react with discomfort or even panic in extreme cases, mg is the load density of the crowd, t  is the time,  f  is the frequency of the load and IStructE/DTLR/DCMS (2008) recommends that a good th approximation of its value is the frequency of the musical beat, Gi is i harmonic load generated by activity of the crowd, and  i is the phase lag (and IStructE/DTLR/DCMS (2008) recommends to set them as zero).    (the crowd th effectiveness factor) and Gi (i harmonic load generated by activity of the crowd) depend on the different activities, and Table 5(b) gives their recommended values as given in IStructE/DTLR/DCMS (2008).

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 16 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 5(b) Recommended Values of  and Gi Gi Examples of activity i=1 i=2 i=3 Seated audience with occasional 0.12 0.15 0 coordinated rhythmic movement from standing people Active crowd with moderate bobbing 0.188 0.047 0.013

Active crowd mostly standing and 0.375 0.095 0.026 bobbing with some jumping (Source: IStructE/DTLR/DCMS 2008)

   e

e

2( f  1.8)

2( f  1.8)

1 cosh( f   2)

In order to help designer to input the time-history functions for different activities in the computer analysis, these time-history functions have been uploaded onto the following URL: http://asdforum/phorum/read.php?f=24&i=209&t=209 2.4.2.3 Human-Structure Interaction In-situ measurements of grandstands have been carried out by Ellis and Ji (2000). The results from computer models have found to be “heavily overestimated” both in terms of equivalent static loads and acceleration. The previous method of  utilising load coefficients independent of group size, was therefore overconservative, especially when used in conjunction with empty structure models. Ellis and Ji (2000) found that the stationary crowd provides a significant increase in the damping capacity of the system, and that the stationary crowd also provides a spring-mass system to the vibration of the grandstand.   BRE Digest 426  was therefore updated in 2004 to consider the phenomenon of human – structure interaction, which alters the natural frequencies and damping of the occupied structure, as well as to recommend the use of Fourier coefficients for dynamic loading which vary with group size. Subsequent laboratory and full-scale studies (e.g. Yao et al 2004, Reynolds et al 2004, Dougill et al 2006, Sim et al 2006, Reynolds et al 2007, Pavic and Reynolds 2008) confirmed that it is necessary to consider the human-structure interaction especially where there is dense crowd loading and when the mass of the passive crowd is significant compared with the weight of the structure. Sim et al (2006) found that for grandstand structures with natural frequencies below 2Hz, a passive crowd adds significant mass to the system, whilst for those with natural frequencies above 2Hz, it adds significant damping. In order to model the effect of the human-structure interaction, Jones et al ( 2011) summarized that there are the following two approaches: a) b)

reducing the loads and increasing the damping ratios; modelling the behaviour of the crowd by a spring-mass system.

Jones et al (2011), however, commented that the first approach cannot model the changes in the frequency of the grandstand due to the occupants, and therefore

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 17 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

suggested the use of spring-mass models to model the crowd. Figure 5 shows two such models.

Figure 5 Modelling Human-Structure Interaction by Spring-Mass Models

The properties of the spring-mass models depend on whether people are predominantly standing or sitting, and whether the crowd is active or passive. The details of the various models are outside the scope of this set of Guidelines, and designers may refer to Jones et al (2011) for the summary. 2.4.2.4 Simplified Formulae The above paragraphs describe the loading to be included in the accurate prediction of the peak acceleration due to different types of loading on the grandstands. The computation is quite tedious, especially to take in account of the phenomenon of human-structure interaction. In this paragraph, the simplified methods suggested by Willford (2005) and Parkhouse and Ward (2008) to predict the peak acceleration will be described. Willford‟s (2005) Method The following steps are suggested to calculate the peak acceleration for a cantilever grandstand: Step 1: Divide the cantilever member into different nodal points (usually corresponding to the rows of the seating decks) as shown in Figure 6.

Figure 6 Nodal Points in a Cantilever Grandstand Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 18 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Step 2: Lump the mass of the cantilever member mi at nodal point i, and obtain the relative displacement µ i at the nodal point i for the mode shape. The typical values of relative displacements µ i for uniformly loaded member st at the 1 mode are given Table 6. st

Table 6 Displacements at 1 mode for uniformly loaded cantilever beam Total number of  node

Relative nodal displacement for uniformly loaded cantilever member st at 1 mode

n=5 0

0.097

0.34

0.658

1

0

0.064

0.23

0.641

0.725

1

0

0.045

0.166

0.34

0.547

0.771

1

0

0.034

0.125

0.26

0.425

0.61

0.804

0

0.026

0.097

0.205

0.34

0.493

0.658

0

0.021

0.079

n=6

n=7

n=8 1

n=9 0.828

1

n=10 0.166

0.277

0.406

0.547

0.695

0.847

1

Step 3: Calculate the modal mass Mi at each nodal point by multiplying m i by 2 µ i , i.e. M i  m i  μ i2 where mi is the mass of the cantilever member at nodal point i, and µ i is the relative displacement at the nodal point i for the mode shape. Step 4: Calculate the total occupant weight Wi at nodal point i, and calculate the modal force Fi at nodal point i by multiplying W i by the dynamic load factors (DLFs) as follows: Fi  Wi  DLF The DLFs depend on the natural frequency of the grandstand structure, the excitation frequency and the type of activity. As stated above, it is difficult to predict the exact type of activities on the grandstand. There are also limited in-situ measurements for DLFs for different activities. Measurements have, however, been reported by Pernica (1990), Allen (1990) and Ellis and Ji (2002) for jumping - the strongest vertical excitation. They usually employed a conservative testing frequency of  2Hz. Based on the measured results, Willford (2005) suggested that the DLFs for the different excitation frequencies as shown Figure 7(a). In Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 19 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

using Figure 7(a), the excitation frequency (or more exactly the harmonics of the excitation frequency, as it is very difficult if not impossible to jump at over 3.5Hz) should be chosen to be as close as possible to the fundamental natural frequency of t he structure.

Figure 7(a) DLFs for the Harmonics of Jumping Load with a Group of N people

Step 5: Calculate the peak acceleration using the following equation: F 1 a  M 2ξ where F 

n

F μ i

i 1

i

,M 

n

n

M  m μ i

i

i 1

2 i

and  is the damping ratio of 

i 1

the structure. Step 6: To cater for the phenomenon of human-structure interaction, the following additional steps are suggested: Estimate the percentage (r%) of passive crowd. Calculate the human-mass ratio, which is the ratio of the weight of  passive audience to the weight of the structure as follows: n

W r i

i 1 n

m g i

i 1

Modify the modal properties by using the factors from Figures 7(b) and 7(c).

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 20 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Figure 7 (b) Modification Factor for Mass due to Human-Structure Interaction

Figure 7 (c) Modification Factor for Damping due to Human-Structure Interaction

Step 7: Calculate the peak acceleration taking into account of human-structure interaction using the modified M and F by the following equation: F r 1  a M 2ξ Park house and Ward‟s (2008) Method Parkhouse and Ward (2008) give a simplified procedure using design charts to calculate the rms accelerations for different scenarios, once the natural frequency of the empty grandstand and the modal mass ratio are found. Their method adopts the two degree of freedom system (i.e. the crowd is represented by a mass connected by springs and dampers to the structure) as suggested in IStructE/DTLR/DCMS (2008), and hence incorporates the human-structure interaction effect in their design charts. The load models are the same as those given in Table 5(a). Their method has a further advantage that it gives the rms accelerations for the different scenarios as stated in IStructE/DTLR/DCMS (2008).

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 21 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

The procedures of their method for calculating the rms accelerations of a cantilever grandstand are simplified as follows: Step 1:

Divide the cantilever member into different nodal points (usually corresponding to the rows of the seating decks) as shown in Figure 6.

Step 2:

Lump the mass of the cantilever member mi at nodal point i, and obtain the relative displacement µ i at the nodal point i for the mode shape.

Step 3:

Calculate the modal mass Mi at each nodal point by the following equation: M i  m i  μ i2 where mi is the mass of the cantilever member at nodal point i, and µ i is the relative displacement at the nodal point i for the mode shape.

Step 4:

Calculate the modal mass ratio μ by the following equation:

m μ μ m i

2 i

i

Step 5:

Calculate the crowd location factor λ by the following equation: λ  

Step 6:

m μ m μ i

i

i

2 i

Read the rms acceleration from the following charts for different natural frequency f s, µ and scenarios:

Scenario 2

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 22 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Scenario 3

Scenario 4

Step 7:

Multiply the value of the rms acceleration by λ/1.5 to get the predicted rms acceleration.

Example 2 in Section 2.6 illustrates the procedures of these two methods. 2.5

In-Situ Testing

2.5.1 Need for and Purposes of Testing IStructE/DTLR/DCMS (2008) strongly suggest that in-situ testing of grandstands should be carried out due to the “uncertainties in determining dynamic properties solely by calculation and the benefits of obtaining confirmation of the values used in design or assessment”. The aims of testing are as follows: Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 23 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

1. 2. 3. 4.

to check the natural frequency of the grandstand, especially when Route 1 acceptance criterion is adopted; to validate the modal properties adopted in the calculation; to check the actual performance of the grandstand for specified design scenario; and to monitor the performance of the grandstand under crowd loading during actual events.

In the following three circumstances, IStructE/DTLR/DCMS (2008) consider that testing must be carried out: 1. 2. 3.

grandstands for pop-concerts and other similar events, where high energy synchronized rhythmic crowd movement is expected; grandstands where significant complaints have been received concerning motion; and grandstands where there is a change of use to one involving significantly greater dynamic crowd activity.

2.5.2 Types of Tests 2.5.2.1 IStructE/DTLR/DCMS (2008) classify the in-situ measurements into two types: Type 1 and Type 2. Type 1 tests aim at giving the natural frequency, whilst Type 2 tests can give more detailed information, including natural frequencies, mode shapes, damping ratio, etc. Ambient excitation, heel-drop and drop-weight hammer are typical Type 1 tests. Ambient excitation measures the response of the structure that is excited by the ambient vibrations (e.g. wind, traffic). The advantage of ambient excitation is that the test can be performed while the structure is occupied, and it is significantly less expensive than any forced vibration tests. However, the accuracy level of natural frequencies obtained using ambient excitation is less than that due to forced vibration tests. Ambient excitation further cannot identify all the modes (especially the higher harmonics), because of the deficiency of some frequency ranges in the input power spectrum. 2.5.2.2 The more comprehensive Type 2 tests can be performed by the use of shakers. There are two main types of shakers commonly used for such measurements. Rotating eccentric mass shakers are capable of generating relatively large forces, but are typically heavy, limited to harmonic loading, slow and very cumbersome to use on stadia. Electrodynamic shakers typically produce smaller forces, but they facilitate the use of broadband excitation signals for improved efficiency of  testing and accuracy. One point to be noted in using shaker to stimulate the harmonic loading is that the shaker shall be able to generate periodic load with frequency as low as 1Hz. This may prove to be difficult for the rotating eccentric mass shakers. One limitation in using shakers in the testing is that it is difficult to excite the entire grandstand using the shaker(s), and hence if full-scale performance test is required, project officer may require employing participants to generate rhythmic loads to measure the actual performance. Our Department had carried out full-scale performance test in the project of Tin Shui Wai Public Library cum IRC, and project officer may refer to Li et al (2011), Au et al (2011) and Wong et al (2011) for the set-up and the details of the test, and the test results. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 24 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

2.5.2.3 Besides generating the force, it is necessary to measure the acceleration at various points of the grandstand using accelerometers. For accelerometers, they should be capable of measuring low frequencies, say as low as 0.5Hz, as human-induced vibration may be of such magnitude. 2.5.3 Equipment Available in SEB Two types of accelerometer ( Table 7) to measure acceleration have been purchased by SEB, and project officer can ultilise them to carry out testing of structures susceptible to human-induced vibration. Both of them can measure low level acceleration in steady-state or low frequency environment. On site, the accelerometers can be attached to the test floor system with adhesive or with the screws. Table 7 Accelerometers Available in SEB Brand and model name Photo Detailed specification Kistler 8330B3 Sensitivity 1200 mV/g (uni-axial) Noise floor level: 5.7µg Frequency range: 0-2000Hz Acceleration range: ±3g

Dytran 7523A1 (tri-axial)

550mV/g Noise floor level: 3mg Frequency range: 0-1500Hz (x- and y-directions), 0500Hz (z-direction) Acceleration range: ±2g

In Table 7, sensitivity is the output voltage produced by a force measured in g. A high sensitivity means that for a given change in acceleration, there will be a larger change in signal. Since larger signal changes are easier to measure, a higher sensitivity in mV/g means that one can get more accurate readings. For the frequency range, human-induced vibration on floor structure is usually at low frequency, usually less than 2Hz. Motion below 10 Hz produces very little vibration in terms of acceleration, moderate vibration in terms of velocity, and relatively large vibrations in terms of displacement. At such low acceleration, the main difficulty in measuring vibrations is to minimize electronic noise. In order to have adequate voltage signals at the acquisition equipment, the low frequency accelerometers should have greater output sensitivity (usually 500mV/g) than general-purpose accelerometers. The data obtained by the accelerometers need to be processed in order to display the measured acceleration versus time, and SEB had purchased a data processing equipment (DeweSoft Dewe-43), which has eight 24-bit input channels and eight output channels, together with the software to convert the data. 2.6

Design Examples

2.6.1 Example 1 is to calculate the vertical natural frequency of an empty grandstand, and Example 2 is to calculate the acceleration for grandstand under dynamic load. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 25 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

2.6.2 Example 1 - Calculation of Vertical Natural Frequency for an Empty Grandstand This example gives the calculation of the natural frequency of the cantilever grandstand at the lower tier of the Hong Kong Stadium by the methods of Willford (2005) and IStructE/DTLR/DCMS (2008). The structural layout of the cantilever grandstand is at Figure 2, and the member sizes and properties are as follows:

Slab thickness = 185mm Beam size = 1000mm×945mm Typical bay width =10.5m Plan length of cantilever = 7.37m Inclined length L = 8.073m Rise of cantilever = 3.296m Number of rows provided = 6 Number of seats per row = 21 (within a typical bay width 10.5m) Total number of occupant = 6×21 = 126 Weight of unit occupant = 75kg 3 Concrete density = 24 kN/m Finishes plus services = 2 kPa Young‟s modulus of concrete = 23.7kNmm -2 Damping ratio = 0.05 Willford's (2005) Method 4

I of beam = 0.07033m Inclined length L = 8.073m Occupant weight per row = 15.8kN per row Beam SW = 2.3t/inclined length Slab SW = 6.1t/inclined length Other dead load = 0.3t/inclined length Total weight per unit length = 8.6t/inclined length

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 26 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Fundamental natural frequency  f   0.56

 EI  mL4

= 3.79Hz

IStructE/DTLR/DCMS‟s (2008) Method Deflection under dead load  =

wL4 8EI

Fundamental natural frequency  f  

= 27.7mm A



= 2.85 to 3.8Hz (with A from 15 to 20)

2.6.3 Example 2 – Calculation of Peak Acceleration due to Dynamic Load Example 2 follows from Example 1. As the natural frequency for the cantilever grandstand is less than 6Hz, IStructE/DTLR/DCMS (2008) specifies that the acceleration due to the dynamic load is to be checked. The simplified methods of  Willford (2005) and Parkhouse and Ward (2008) will be used. There are 6 rows, and n is therefore chosen as 6.

mi = 11.7t for i = 1 to 6 (since uniform mass along the cantilever structure) The fundamental natural frequency  f  = 3.79Hz, and hence choose the excitation frequency to be 1.9Hz, so that its second harmonic matches with the fundamental natural frequency of the grandstand. Willford's (2005) Method From Figure 7(a), for N=126 and  f = 3.79Hz, DLF = 0.4. st

Nodal Point

1 Mode Shape Displacement µ i

mi (tones)

Modal mass 2 Mi= mi× µ i

1 2 3 4 5 6

1.0 0.725 0.641 0.23 0.063 0

11.7 11.7 11.7 11.7 11.7 11.7

11.7 6.15 4.81 0.62 0.05 0 M = 23.33 t



Occupant Weight Wi (kN) 15.8 15.8 15.8 15.8 15.8 15.8

Modal Force DLF×Wi× µ i 6.32 4.58 4.05 1.45 0.40 0 F = 17.07 kN

Assuming that 50% of the occupants will remain passive, i.e. r = 0.5. Calculate human-mass ratio using: n

W r i

i 1 n



m g

0.5  15.8  6 11.7  6  9.81

 0.06

i

i 1

The effect of human-structure interaction is not apparent, as this grandstand is constructed of reinforced concrete, where the self-weight accounts for a large proportion of the loading. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 27 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Then, obtain the effective mass and the additive damping due to human-structure interaction in Figure 7(b) and (c) respectively. Modified M = 23.33×1.05 = 24.50 t, and modified damping ratio = 0.05+0.005 = 0.055. Calculate the peak acceleration using: F r 1 17.07  0.5 1 a     1.31ms  2 (or 13.35 %g) M 2ξ 24.50 2  0.055 Parkhouse and Ward‟s (2008) Method Nodal Point 1 2 3 4 5 6 

Mode Shape µ i 1.0 0.725 0.641 0.23 0.063 0

mi (tones) 11.7 11.7 11.7 11.7 11.7 11.7

2 Modal mass Mi= m i  μ i 11.7 6.15 4.81 0.62 0.05 0 M = 23.33 t

 m μ = 0.33 Modal mass ratio μ = m  m μ = 1.33 Crowd location factor λ   m μ 2 i

i

i

i

i

i

2 i

For Scenario 2, rms acceleration = 1.7% g from the graph.

Therefore, predicted rms acceleration = 1.7% g ×1.33/1.5 = 1.51 % g.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 28 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

For Scenario 3, rms acceleration = 10.5% g from the graph.

Therefore, predicted rms acceleration = 10.5% g ×1.33/1.5 = 9.31 % g.

For Scenario 4, rms acceleration = 24.8% g from the graph.

Therefore, predicted rms acceleration = 24.8% g ×1.33/1.5 = 22 % g.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 29 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

3.

Sensitive Equipment and Facilities

3.1

Floors that support sensitive equipment (e.g. in surgery rooms, laboratories) and facilities (e.g. hospital wards, studio) need to have an environment where any vibration will not affect the equipment or the occupants of the facilities. This has been becoming more particularly important, as today‟s medical facilities in hospitals or laboratories rely on high-tech imaging equipment including MRI, CT, X-ray equipment that are much more sensitive to floor vibrations than before. Moreover, occupants and patients of such facilities require a “vibration-free” environment to carry out their delicate work or to receive their treatment respectively. For sensitive equipment, the manufacturers or the suppliers will usually provide acceptable vibration criteria for the equipment, or such data will be available in the catalogues or specifications. If several equipment items with different vibration sensitivities are to be supported on the same floor, the floor should be designed to accommodate the most sensitive item.

3.2

However, the exact brand and/or model of the equipment to be installed will only be known at the late stage (usually after the award of the construction contract). Designers have to limit the vibration response of the floors on “generic” criteria as discussed in the following paragraphs, and then check the criteria against those specified by the equipment actually delivered. They are termed “generic” because they were intended to meet the needs of the requirements of most sensitive equipment generally available in the market rather than a particular model.

3.3

Generic Criteria for Design of Flooring System for Sensitive Equipment and Facilities

3.3.1 The acceptable criteria due to vibration for sensitive equipment have been studied extensively (e.g. Ungar and White 1979, Gordon 1991) since the 1970s. The generic criteria are usually expressed in terms of the root mean square (rms) velocity of the flooring system due to vibratory sources over the frequency range of  4Hz to 80Hz (Figure 8). In Part I of this set of Guidelines, the base curve of  ISO 2931-2:1989 has been discussed. Human discomfort is usually limited to resonant frequency in the range of 1-8Hz, and the base and the factored curves for different activities in term of the rms velocity are also included in Figure 8. Unlike human discomfort, velocity (rather than displacement or acceleration) is usually used as the measure of vibration acceptance criterion because it has been found that resonance of equipment usually occurs on a curve of constant velocity at a higher frequency, typically in the frequency range above 8Hz. Brownjohn and Middleton (2008) note that part of the logic behind using velocity as the measure of vibration is that for the short duration of the specific manufacturing operation or measurement, displacements must be of the same order as the feature sizes of the components being manufactured or measured. 3.3.2 Gordon (1991), based on his study on different types of sensitive equipment and the in-situ measurements on the effects of vibration on these different types of sensitive equipment, developed a set of the widely adopted acceptable generic vibration curves (VC) for different types of sensitive equipment for a frequency range from 4Hz to 80Hz. These curves increasing in severity from VC-A to VC-E specify appropriate vibration limits for different types of sensitive equipment. These Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 30 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

criteria specify allowable values of vibration in terms of the rms velocity produced by the external source. It has further been noted that the lowest resonant frequency for sensitive equipment is generally higher than 8 Hz, and that above 8Hz, the allowable values of the vibration limits remain generally constant. Gordon (1991) further noted that although some manufacturers may specify acceptable rms velocity above 80Hz, vibration is “rarely a problem” at such high frequency.

Figure 8 Generic Acceptable Criteria (VC) Curves for Vibration-Sensitive Equipment

3.3.3 The VC curves specify that rms vibrations should not exceed 3µm/s (VC-E), 6µm/s (VC-D), 12.5µm/s (VC-C), 25µm/s (VC-B) or 50µm/s (VC-A) for different Table 8 gives the widely adopted equipment with different sensitivities. interpretation of the generic vibration criteria (e.g. NIH 2008; UK Department of  Health 2008; NSW Department of Environment and Conservation 2006) for different types of sensitivities and activities. These curves and interpretations are applicable to continuous vibrations.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 31 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 8 Acceptable Criteria for Vibration-Sensitive Equipment

Generic Vibration Criteria  ISO 2631  ISO 2631

VC-A VC-B

VC-C

VC-D VC-E

3.4

Functional uses of the flooring system Public and administrative areas Precision laboratories for optical microscopes to 100X, operating theatre, animal research facility, or surgery rooms Precision laboratories for optical microscopes to 400X Precision laboratories for optical microscopes to 1000X, rooms for micro surgery, eye surgery, or neuro surgery Precision laboratories for optical microscopes to 30000X, rooms for MRI Rooms for electron microscopes, mass spectrometers and E-beam systems Rooms for microelectronics equipment such long path, laser-based, small target systems

Acceptable rms velocity 200μm/sec 100μm/sec

50μm/sec 25μm/sec

12.5μm/sec

6.25μm/sec 3.13μm/sec

Intermittent Vibration

3.4.1 Intermittent vibration is the “interrupted periods of continuous or repeated periods of impulsive vibration, or continuous vibration that varies significantly in magnitude” (NSW Department of Environment and Conservation 2006) . Typical situations include impulsive vibration occasional dropping of heavy equipment, occasional loading and unloading, blasting, or passing trains or heavy vehicles, forging machines, impact pile driving, where the vibration is either not of constant amplitude or not continuous. 3.4.2 Both NSW Department of Environment and Conservation (2006) and Ellis (2001) propose to adopt the vibration dose value (VDV) as the acceptance criterion for floors subjected to intermittent vibration. The VDV is calculated from the frequency weighted acceleration a(t) versus time, using the following equation ( BS 6472 Appendix B):

 T   VDV    a(t) 4 dt     0  

1/4

where T is the total period of the day during which vibration may occur. The VDV 1.75 (in m/s ) is related to the fourth power of a(t) and is also related to the duration of  the peak acceleration. Thus, the VDV is related to both the magnitude of the vibrations and how many times they occur. It therefore doubles the effect of  isolated incidents of high peak acceleration during intermittent vibration much more than the duration. For example, doubling the peak acceleration will double the VDV, whilst doubling the duration will only result in an increase of just 19%. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 32 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

3.4.3 Example 4 in Section 3.8 demonstrates how to calculate the VDV due to intermittent vibration will be given. Once the VDV is computed, Table 9 summarizes the limits for the maximum VDV for different occupancy as given by Ellis and Littler (2004), NSW Department of Environment and Conservation (2006) and BS 6472. Table 9 Limits on VDVs for Different Occupancy Uses

Occupancy Uses Critical areas Residences Office Workshops Grandstands

3.5

Low probability of  Adverse comment adverse comment possible 0.1 0.2 0.2-0.4 0.4-0.8 0.4 0.8 0.8 1.6 0.6-1.2 1.2-2.4 (Source : Ellis and Littler 2004)

Adverse comment probable 0.4 0.8-1.6 1.6 3.2 2.4-4.8

Sources of Vibration

3.5.1 Potential vibration sources for typical buildings include: a) b) c) d)

wind-induced; ground motions due to road and rail traffic, or nearby construction activities; machinery; and human-induced (e.g. footfall vibration).

3.5.2 Vibration due to wind-induced or construction activities is random and usually intermittent. Although the calculation for both vibration sources has not yet been well-documented, SEB has published the following two set of guidelines (available: http://asdiis/sebiis/2k/resource_centre/ ) providing crude methods to predict the dynamic response of the structure due to wind and construction activities respectively: a) b)

SEBGL-OTH3 Guidelines on the Design for Wind-Induced Vibration ; and SEBGL-PL13 Guideline on Groundborne Vibration Induced by Piling Operation.

3.5.3 To deal with vibration due to machinery, machinery should be chosen and placed at a location such that it will not affect the sensitive equipment, and building layout at planning stage therefore is critical. Once an inappropriate location is chosen, it will require tedious modification works to minimize the vibration produced by machinery. The coordination among project architect, BS engineer and structural engineer is therefore essential at the early stage of the project. 3.5.4 In the following paragraphs, footfall vibration and traffic-induced vibration will be discussed, and simplified methods will be presented.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 33 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

3.6

Calculation of rms velocity of a flooring system due to footfall vibration

3.6.1 The other common source of dynamic load is the footfall vibration induced by the occupants, where the equipment is housed close to a corridor. Footfall-induced vibrations are relatively random and continuous in nature, and are generally most severe at the middle of structural bays and least severe near columns and/or structural walls. Similarly, walkers in the middle of a structural bay produce more vibration than do walkers closer to columns and/or structural walls. The vibrations due to footfalls also generally increase with increased walker speed. 3.6.2 In Part II of this set of Guidelines, procedures to calculate the peak acceleration of a flooring system due to footfall vibration were described. Instead of calculating the peak acceleration, the following will describe the steps to calculate rms vibration velocity due to footfall vibration. Murray et al (1997) give the following steps in computing the velocity of a flooring system due to footfall vibration. Step 1:

Calculate the fundamental frequency f n of the flooring system. details, designers may refer to Part I of this set of Guidelines.

Step 2:

Calculate the maximum displacement using the following formulae: Fm Δ p f o2 X max  2f n2

For

Fm is the maximum force due to a footfall, which depends on the walking pace speed and the weight of the walker, and f o is the footfall frequency. Both of them can be referenced from Table 10. p (in mm/kN) is the mid-span flexibility of the flooring system, which is the deflection at the middle of the flooring system under the action of a unit load. Table 10 Values of Fm, f o and Uv due to a Footfall Walking Pace Fm (kgf) f o (Hz) * Steps/minute 100 (fast) 1.4 5.0 75 (moderate) 1.25 2.5 50 (slow) 1.1 1.4 (Source : Murray et al 1997) Note:

Step 3:

.

2

Uv (kN Hz ) 110 25 6.8

*

Willford and Young (2006) suggest that fast walking pace likely occurs at corridor and circulation zones and within office bays and residential rooms in a building, whilst moderate walking pace is usually found within laboratories, operating theatres, and the like.

Calculate the ratio of f n /f o. Here, it is necessary to distinguish a “high frequency” flooring system from a “low-frequency” flooring system. Wyatt (1989) defines a “high-frequency” flooring system as one “where the natural frequency of the floor exceeds that of the third harmonic of  the walking pace”. If it is a high frequency floor, then the maximum velocity can be calculated from the formula: V=2f nXmax

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 34 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

However, if f n /f o >> 0.5, it is a low-frequency flooring system, and the maximum velocity should be determined by the following formula: U vΔ p V f n where Uv is a parameter, which can be referenced from Table 10. Step 4:

Convert peak values to the rms velocity, and to compare the calculated rms velocity to the appropriate criteria in Figure 8 or Table 10. The relationship between the rms values and peak values may be taken as about 70% of the peak values (Ungar, 2007).

Example 3 in Section 3.8 illustrates the above procedures.

3.6.3 If the calculated rms velocity exceeds the appropriate criteria, the possible design options that can be employed to limit footfall-induced vibrations are: a)

b)

c)

relocation of sensitive equipment and/or corridor, e.g. locate corridors near columns and/or structural walls, do not locate corridors within sensitive bays; and locate vibration sensitive equipment near columns and/or structural walls, away from the middle of structural bays; increasing the structural stiffness of the flooring system to reduce footfallinduced vibrations. To a good approximation, the floor vibration scales as floor stiffness to the – 3/2 power. Hence, the floor vibration can be reduced by adopting a stiffer floor system. installing vibration isolator, which places the sensitive equipment on a large inertial mass supported by a suspension with low rigid body resonant frequencies. These designs use pneumatic springs, which produced rigid body resonant frequencies in the 1-3 Hz range.

3.6.4 Crowd Effect In Part II of this set of Guidelines, the crowd effect due to the flow of pedestrians have been discussed extensively, and it was noted that the crowd effect depends on the size of the crowd (which in turn depending on the floor area) and the possibility of synchronization between people in the crowd. A conservative magnification factor of   N  for the peak acceleration due to crowd, where  N  is the number of  persons on the floor system at any one time, was noted. Indeed, the derivation of  the magnification factor  N  is based on random vibration theory together with the assumption that pedestrian loads are modelled as random processes. Given the fact that the footfall velocity is also generated by the random process of pedestrians, the magnification factor of   N  is also applicable to calculate the rms velocity due to footfall vibration of a crowd of size  N . 3.7

Traffic-Induced Vibration

3.7.1 Traffic-induced vibration has recently become a hot topic in both design and research in Hong Kong, China and overseas. High speed rails are now being constructed in China, Hong Kong and Europe, leading to the concerns about the annoying vibration for people living and working in neighbouring buildings. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 35 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Studies by Hunaidi (2000) found that traffic vibrations are mainly caused by heavy vehicles such as trains, buses and trucks, and those passenger cars and light trucks “rarely induce vibrations that are perceptible in buildings”. A rule of thumb is that vibration from vehicles of less than 3.5 tonne gross weight is rarely perceptible in buildings. Hence, there should be no adverse effect on sensitive equipment in buildings located within a compound where frequent heavy traffic is unlikely. For other cases, substantial vibration may be induced, especially if the road surface rough includes a harmonic component that coincides with the natural frequencies of  the vehicle and/or those of the sub-soil. Such sources predominantly produce vibration of frequencies in the range from 5Hz to 25Hz, coinciding with the sensitivities of most sensitive equipment. 3.7.2 Traffic-induced vibration is radiated through the ground, and is measured as particle velocity in v (in mm/s). In the US, the particle velocity is expressed as vibration decibels (VdB). The vibration decibels (VdB) can be converted to mm/s by the following formula:

  v    v ref     

L v  20  log 10 

where Lv is the velocity level in decibels, v is velocity, and v ref  is the reference -5 -6 velocity which is usually taken as 2.54×10 mm/s or 1×10 in/sec . 3.7.3 Ground-borne vibration by traffic, although may be perceived, is not annoying to pedestrians, as pedestrians are themselves walking at a certain speed. However, when traffic-induced vibration is perceptible inside buildings, it may affect the accuracy of sensitive equipment, or the occupants of the facilities. Research notes that the vibratory effect of road and rail traffic to buildings is fairly complicated, as it depends on many factors, including: the condition of road (especially any irregularity); the vehicle weight; sub-soil and geological conditions; distance from the road; and type of building. Numerical models (such as modelling by finite elements) have been developed. However, such models are very time consuming with the capacity and speed of the available computers and even with computers that will come in the next 10 years. Yang and Huang (2011) commented that 2D analysis may underestimate the soil damping and ignore wave propagation in the 3D, and that 3D analysis is extremely time-consuming; whilst Madshus et al (1996) commented that numerical models “can at present mainly serve as development tools to widen the understanding and to guide the development of empirical models”. Thus, analytical models are mostly suitable for very simple cases where both the geometry and geological conditions of the site are not too complicated. Empirical or semi-empirical models are usually used in order to predict ground-borne vibration due to train traffic especially in the preliminary phase of the projects when high accuracy in the prediction is not needed. 3.7.4 Semi-empirical simplified procedures in estimating traffic-induced vibration level inside a building have been given by US Federal Transit Administration‟s publication Transit Noise and Vibration Impact Assessment (Hanson et al 2006) and Norwegian Geotechnical Institute (Madshus et al 1996). These procedures are based on extensive in-situ measurements of vibration propagation, and they are expected to provide an approximate estimate for the preliminary design phase. The generation of the vibration is modelled at the “source” through the “medium” and

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 36 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

then reception by the “receiver”. The following flowchart explains the propagation of the vibratory source to the floor of the building from a transit system:

(Source : Modified from Hanson et al 2006) The following paragraphs will describe the procedures of these methods, and design example will be given in Section 3.8. 3.7.5 Method of FTA (Hanson et al 2006) 3.7.5.1 In the method of FTA, the following factors are included: soil conditions, types of  the vehicles, quality of the track or road surface, speed of the vehicles, distance from the trains or traffic lane to building, and building foundation, structure and number of floors. It is further assumed that the effects of these factors can be treated as separable, and hence the resulting vibration on a building can be estimated by adding and/or subtracting the corresponding factors in the vibration of the ground. The vibration at the receiver Lv is therefore modelled by the following equation (Hanson et al 2006): Lv = LF + TM + Cbuilding + SF where

and

LF = vibration produced by source; TMline = transfer mobility which accounts for the effect of geology; Cbuilding = corrections for building coupling loss and amplification due to resonance; and SF = safety factor.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 37 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

3.7.5.2 FTA gives three steps in predicting traffic-induced vibration, namely screening, general assessment, and detailed analysis. Screening method is appropriate during the preliminary assessment. More detailed analysis will only be required if the screening identifies any sensitive receiver within the screening distances. A simplified rule of thumb given by FTA for institutional building is that for frequent rail traffic and with freight train speed of less than 55mph, the screening distance is 120 ft (about 37m); whilst for a trunk road with frequent bus service of  less than 50mph, the screening distance is 50 ft (about 16m). 3.7.5.3 For development within the screening distance, a general assessment is required. The following summarizes the steps in the general assessment: Step 1: Estimate the ground level rms velocity due to traffic. Figure 9 gives an estimate of the ground level rms velocity against distance for different types of heavy traffic. The figure was developed by in-situ measurements of vibration induced by transit systems in the US. The top curve applies to trains that are powered by diesel or electric locomotives. It includes intercity passenger trains and commuter rail trains. The curve for rapid transit rail cars covers both heavy and light-rail vehicles on at-grade and subway track. The lowest curve represents that induced by a typical bus operating on smooth roadway.

Figure 9 Estimate of rms velocity in VdB (Source : Modified from Hanson et al 2006)

Step 2: Once the base curve has been selected, adjustments have to be made due to speed, wheel and rail type and condition, type of track support system, geological conditions, type of building foundation, and number of floors above the basement level. Table 11(a) gives those adjustment factors to the vibration source. Step 3: Table 11(b) gives those adjustment factors to the vibration path. Step 4: Table 11(c) gives those adjustment factors to the vibration receiver. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 38 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Step 5: The resulting predictions are then augmented with a factor of safety to account for the uncertainties in the coupling loss, attenuation through the building structure, etc, and a uniform adjustment of +5 dB is often adopted (Zapfe et al 2009). Table 11(a) Adjustment due to the vibration source Factors

Adjustment Vehicle Speed

Speed of Vehicle

60 mph 50 mph 40 mph 30 mph 20 mph

  e    l   c    i    h   e    V    f   o    t   c   e    f    f    E

Vehicle Parameters Vehicle with stiff primary suspension

Resilient Wheels Worn Wheels or Wheels with Flats Resiliently Supported Tiers Track Conditions Worn or Corrugated Track Special Trackwork Jointed Track or Uneven Road Surfaces Track Treatments Type of Track Structure

   1

   k   c   )   a   l   y   r    T  n    f   o   o   s   n   s    i   r   a   e   r    t    t   c   r   a   o   r   f   a   (    h    C

Note:

1

Reference Graph 50 mph 30 mph +1.6 dB +6.0 dB 0.0 dB +4.4 dB -1.9 dB +2.5 dB -4.4 dB 0.0 dB -8.0 dB -3.5 dB

+8 dB (Include this adjustment when the primary suspension has a vertical resonance frequency greater than 15 Hz) 0 dB +10 dB -10 dB +10 dB +10 dB +5 dB

Relative to at-grade tie and ballast: Elevated structure Open cut Relative to bored subway tunnel in soil: Station Cut and cover Rock-based

-10 dB 0 dB -5 dB -3 dB - 15 dB

Both FTA and Norwegian Geotechnical Institute methods are based on the measurements of railway, and there are no data to account for the pavement condition for motor vehicle. Designers should make judgment on the effect for pavement when considering traffic-induced vibration by motor vehicles.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 39 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Table 11(b) Adjustment due to the vibration path Factors 2 Geological conditions

Adjustment 3 Efficient propagation in soil

Efficient propagation 4 in rock layer

5

Coupling loss due to building foundation

Note:

2

3

4

5

Distance 50 ft 100 ft 150 ft 200 ft

Wood Frame Houses 1-2 Story Masonry 3-4 Story Masonry Large Masonry on Piles Large Masonry on Spread Footings Foundation in Rock 

+10 dB Adjustment +2 dB +4 dB +6 dB +9 dB -5 dB -7 dB -10 dB -10 dB -13 dB 0 dB

Vibration may be “efficient” or “normal” propagated by the underlying geological conditions. Some geological conditions (e.g. shallow bedrock, stiff clayey soil) are found to be associated with efficient propagation. Investigation of ground investigation records is therefore required to identify whether efficient propagation is possible. Further details of ground investigation works that can be carried out to validate the transfer mobility will be given in next paragraph. Soil has been adopted as a basis for the production of the curve in Figure 9, and hence no adjustment is required for normal propagation in soil. For efficient propagation in soil, the vibration attenuation in Figure 9 should be increased by 10dB. For efficient propagation in rock, although the vibration still attenuates with distance as in Figure 9, this attenuation rate is different for rock. Positive adjustment is required to account for lower attenuation of  vibration in rock compared to soil. That is, if the distance from the source is longer, the degree of  “compensation” is more. Coupling loss represents the vibration attenuation when vibration energy is transmitted from ground into the building foundation.

Table 11(c) Adjustment due to the receiver Factors Floor-to-floor attenuation

Amplification due to resonances of floors, walls, and ceilings

Adjustment 1 to 5 floors above grade: 5 to 10 floors above grade: +6 dB

-2 dB/floor -1 dB/floor

3.7.5.4 Detailed analysis FTA recommends that a detailed analysis is required when the general assessment has indicated potential impact and the project has entered the final design and construction stage, or when there is particularly a sensitive development within the screening distances. In the detailed analysis, in-situ measurements will be carried out to obtain the site-specific frequency components of the vibration signal and the transfer mobility. Vibration propagation tests are suggested by FTA to validate the transfer mobility. The theory behind such tests is to create vibration pulses that travel from the source to the receiver using the same path that will be t aken by the vibration induced by the traffic. A heavy weight is dropped onto the ground or at the bottom of a drillhole drilled to the depth of the future underground rail, and the vibration on the ground surface is measured by successive geophones installed at several distances from the impact. Figure 10 shows the schematic design of the set-up, and designer is suggested to refer Hanson et al (2006) for the detailed procedures to compute the transfer mobility from the measured data. The results from the in-situ measurements give an accurate data on the ground transmission properties. The subsequent step then involves analytical models or semi-empirical adjustments in Table 11 to predict the propagation of vibration from the building foundation to the receiver. Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 40 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Figure 10 Set-up to validate transfer mobility (Source : Modified from Hanson et al 2006)

3.7.6 Method of Norwegian Geotechnical Institute (Madshus et al 1996) The method of Norwegian Geotechnical Institute are based on the data collected from measurements at different sites and various building types along the railway lines in Norway and Sweden. At each site, the vibration was measured simultaneously at several points on the ground surface in the propagation region, on building foundations and on floors, and on the railway embankment. The method then noted that the vibration at mid-spans of a building v (in mm/s) is the results of  the factors given in the following equation: v = VTFSFDFRFB where VT = vibration level (in mm/s) on the ground at a distance of 15m from the source from a source at 70km/h; -B FD = a factor for the distance attenuation = (D/15) , and D is the distance from the centre of the source to the receiver and B increases from 0.3 to 0.9 from soft to medium ground condition; FR = a factor for the quality of track, which varies from 0.7 for high quality track to 1.3 for old track; * FB = building amplification factor = 1.3 for timber single storey house and 1.9 for a 2-storey building; -A and FS = effect of speed of vehicle = (S/70) , and S is the speed of the train or vehicle and A varies from 0.9 to 1.1. Note:

*

Madshus et al (1996) note that the data for F B showed great variation, and a typical standard deviation of 1.2 was recorded. Hence, designers should note such limitation when adopting the appropriate value to suit t he individual case.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 41 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

3.8

Design Examples

3.8.1 Example 3 calculates the rms velocity in rc flooring system induced by footfall vibration. Example 4 gives an example to calculate the VDV of a flooring system subjected to intermittent vibration. Examples 5 and 6 calculate the rms velocity induced a flooring system induced to traffic. 3.8.2 Example 3 – Calculation of rms Velocity due to Footfall Vibration The structural plan is shown as follows:

The floor construction consists of a concrete slab on secondary steel I-beams at 1.5m c/c supported on primary girders on steel columns at 4m c/c with height 5m. The weight of the floor is 3.1kPa. Both the secondary I-beams and girders are assumed to be simply supported. The moments of inertia of the each secondary Ibeam 20310223kg/mUB and each primary girder 610229140kg/mUB are 6 4 6 4 28.910 mm and 1,12010 mm respectively. The floor is designed for use of  sugery. The deflections due to the weight supported by each element (secondary I-beams, primary girders and steel columns) are determined as follows: The deflection of the secondary steel I-beam due to the floor weight is Δ j 

5w j L4 j 384E s I j



5  (3.1  1.5)  (4000) 4 384  205000  28.9  10 6

 2.62mm

The deflection of the primary steel girders due to the floor weight i s Δg 

5w g L4g 384E s I g



5  (3.1  4.0)  (12000) 4 384  205000  1120  10 6

 14.58mm

The axial shortening of the columns c is calculated from the axial stress due to the weight sup ported. Assuming an axial stress, σa, of 40MPa, σ L 40  5000  0.98mm Δc  a c  E 205000

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 42 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

The total deflection is 2.62 + 14.58 + 0.98 = 18.18mm, and the fundamental natural frequency  f n  0.18

g

  j   g   c

 0.18

9.81 18.18  10

3

 4.18Hz

After calculating fundamental natural frequency, it is necessary to calculate the maximum displacement due to the footfall using: Fm Δ p f o2 X max  2f n2 To calculate p, apply 1kN at the middle of the flooring system, and Murray et al (1997) gives the following approximate method: First, calculate the deflections due to the secondary and main beams are as follows: Δ j  and

Δg 

L3 j 48E s I j L3g 48E s I g

 

4000 3 48  205000  28.9  10

 2.25  10 -4 mm

6

12000 3 48  205000  1120  10

6

 7.84  10 5 mm

-4 -5 -4 Then, p= j+0.5g=2.25×10 +0.5×7.84×10 = 2.64×10 mm/kN

Fast walking: X max 

Moderate walking: X max 

Slow walking: X max 

.

2

Fm = 1.4kgf, f o=5Hz, Uv=110 kN Hz Fm Δ p f o2 2 n

2f 



1.4  10 2  2.64  10 4  5 2 2  4.18

 2.64  10 6 mm

2

.

Fm = 1.25kg, f o=2.5Hz, Uv=25 kN Hz Fm Δ p f o2 2 n

2f 



1.25  10 2  2.64  10 4  2.5 2 2  4.18

.

2 n

2f 



1.1  10 2  2.64  10 4  1.4 2 2  4.18

2

 5.90  10 7 mm

2

Fm = 1.1kg, f o=1.4Hz, Uv=6.8 kN Hz Fm Δ p f o2

2

2

 1.63  10 7 mm

Here, f n /f o is approximately 1, and hence, the peak and the rms velocities are: V=2f nXmax -6 -6 Fast walking: V= 2×4.18×2.64×10 = 69.3×10 mm/s = 69.3µm/sec Rms velocity = 0.7×69.3 = 48.5µm/sec -7 -6 Moderate walking: V= 2×4.18×5.90×10 = 15.5×10 mm/s = 15.5µm/sec Rms velocity = 0.7×15.5 = 10.9µm/sec -7 -6 Slow walking: V= 2×4.18×1.63×10 = 4.3×10 mm/s = 4.3µm/sec Rms velocity = 0.7×4.3 = 3.0µm/sec The note to Table 10 notes that fast walking pace likely occurs at corridor and circulation zones and within office bays and residential rooms in a building, whilst moderate walking pace is usually found within laboratories, operating theatres, and the like. For surgery purpose, the permitted rms velocity is 100μm/sec, and hence

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 43 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

the flooring system is suitable for surgery purpose, where moderate walking is likely. Designer may note that this flooring system is still suitable for surgery purpose with rms velocity of 48.5µm/sec, even when it is located near a corridor where fast walking is likely. However, in the latter case designer should consider the possibility of crowd movement. Section 3.6.4 suggests that the crowd effect can be modelled by a factor of   N  , and hence if there is a group of 5 people likely to walk  at fast pace on the corridor, the rms velocity will become 48.5µm/sec× 5 =108 µm/sec, exceeding the permitted rms velocity of  100μm/sec. This tallies with our usual practice not to locate surgery rooms near corridor where fast walking is likely! 3.8.3 Example 4 – Intermittent Vibration Consider Example 3 again, and in addition to footfall vibration, there are intermittent vibratory sources, producing the peak accelerations (ranging from 2.9%g to 9.1%g) in the following table: Duration (seconds) 10 20 40 100 120

-2

Peak Acceleration (ms ) 0.59 0.49 0.58 0.91 0.29

Frequency (Hz) 4 5 6.3 8 10

The VDV due to the intermittent vibrations are calculated as follows:

ai (ms )

f (Hz)

Weighting Wi

0.59 0.49 0.58 0.91 0.29

4 5 6.3 8 10

1 1 1 1 0.8

-2

Therefore, VDV  75.791/4 =2.95 m/s

Frequency weighted acceleration -2 a(t) (ms ) 0.59 0.49 0.58 0.91 0.23

Duration T (s)

a(t) ×T

10 20 40 100 120 

1.21 1.15 4.53 68.57 0.33 75.79

4

1.75

. 1.75

For surgery, the calculated VDV exceeds the adverse comments level (0.4 m/s ), and measures have to be taken to reduce the peak acceleration and/or duration of the intermittent vibration. 3.8.4 Example 5 – Calculation of rms Velocity due to External Traffic Consider a two-storey building located adjacent to a road as shown in the following figure. There are rubber-tired vehicles on the road, which can travel at a maximum Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 44 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

speed of 70 km/h. The building rests on pad footings on hard sand and gravel soils. The floor system has a fundamental natural frequency of around 16 Hz.

Method of FTA From Figure 9, with a distance of 12m (40 feet), the rms of ground-surface vibration levels = 65 VdB for rubber-tired vehicle at 30 mph. From Table 11, adjustment factors due to: 1. Speed of vehicle at 70 km/h (44mph) = +3.33 dB 2. Coupling loss to foundation for building on spread footings = -13 dB 3. Floor to floor attenuation at 1/F = -2 dB 4. Amplification due to resonance of floor = +6dB 5. Allowance for uncertainties = +5 dB Therefore, the adjusted maximum rms of ground-surface vibration levels = 65 + 3.33 – 13 – 2 + 6 + 5 = +64.33 VdB Hence, rms velocity v can be obtained from:

  v    v   ref   

L v  20  log 10 

giving v = 0.042 mm/sec Method of Norwegian Geotechnical Institute From Figure 9, with a distance of 12m (40 feet), the rms of ground-surface vibration levels = 65 VdB for rubber-tired vehicle at 30 mph (48km/h). With the adjustment by FTA for speed, the rms of ground-surface vibration levels = 68.33 VdB at 70 km/h. Therefore VT = 0.065 mm/s on the ground at a distance of  15m from the source from a source at 70km/h. Here, the speed of the source has been adjusted to 70km/h, and hence F S=1.0. Take B = 0.7 for medium ground condition and F D= (12/15)

-0.7

= 1.14.

Assume FR=0.7, rms velocities on the building for different values of F B are summarized in the following table:

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 45 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Values of FB 1.9 1.3

v = VTFSFDFRFB (mm/s) 0.099 0.067

3.8.4 Example 6 – Calculation of rms Velocity due to Railway Consider Example 5 again, and instead of a road, there is an on-grade railway adjacent located at a distance of 15m to the two-storey building. The freight train is moving at a speed of 70 km/h. Method of FTA From Figure 9, with a distance of 15m, the rms of ground-surface vibration levels = 84.5 VdB for a freight train at 50 mph. From Table 11, adjustment factors due to: 1. Speed of train at 70 km/h (44mph) = -1.14 dB 2. Jointed track = +5 dB 3. High-resilience fasteners used on the track = -5 dB 4. Coupling to foundation for building on spread footings = -13 dB 5. Floor to floor attenuation at 1/F = -2 dB 6. Amplification due to resonance of floor = +6 dB 7. Allowance for uncertainties = +5 dB Therefore, the adjusted maximum rms of ground-surface vibration levels = 84.5 -1.14 + 5 – 5 – 13 – 2 + 6 + 5 = +79.36 VdB Hence, rms velocity v can be obtained from:

  v    v   ref   

L v  20  log 10 

giving v = 0.236 mm/sec Method of Norwegian Geotechnical Institute From Figure 9, with a distance of 15m, the rms of ground-surface vibration levels = 84.5 VdB for a freight train at 50 mph. With the adjustment by FTA for speed, the rms of ground-surface vibration levels = =84.5-1.14 = 83.36 VdB at 70 km/h (44mph). Therefore VT = 0.374 mm/s on the ground at a distance of 15m from the source from a source at 70km/h. Here, the speed of the source has been adjusted to 70km/h, and hence F S=1.0. Take B = 0.7 for medium ground condition and F D= (15/15)

-0.7

= 1.0.

Assume FR=0.7, rms velocities on the building for different values of F B are summarized in the following table:

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 46 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Values of FB 1.9 1.3

4.

v = VTFSFDFRFB (mm/s) 0.497 0.340

Design References Au, S K, Ni, Y C, Zhang, F L and Lam, H F (2011), “Field Me asurement and Modal Identification of a Coupled Floor Slab System”, Presented at the Twelfth East Asia‐ Pacific Conference on Structural Engineering and Construction, Hong Kong, 26-28 January 2011. Allen, D E (1990), “Building Vibration from Human Activities”, Concrete International, ACI, 12 (6), pp. 66-73. ANSI (1983),   American National Institute Standard ANSI 53.29-1983: Guide for the  Evaluation of Human Exposure to Vibration in Buildings (New York: ANSI). Bennett, R M (1997), “Spectator Live Loads during Football Games”,  Journal of Structural  Engineering, 123(11), pp. 1545-7. BSI (1987),  BS 6841-1987: Guide to Measurement and Evaluation of Human Exposure to Whole-Body Mechanical Vibration and Repeated Shock  (London: BSI). BSI (1992),   BS 6472-1992: Guide to Evaluation of Human Exposure to Vibration in  Buildings (1 Hz to 80 Hz) (London: BSI). Brownjohn, J (2006), “Vibration Control of Ultra-Sensitive Facilities”, Structures and   Buildings, 159(5), pp. 295-306 (available: http://vibration.shef.ac.uk/pdfs/ ; accessed: 30 June 2011). Canadian Commission on B uilding and Fire Codes (2005), “ Commentary D: Deflection and vibration criteria for serviceability and fatigue limit states” , in National Research Council of  Canada (2005), User’s Guide - NBC 2005: Structural Commentaries (Part 4 of Division B) (Ottawa: NRC), pp. D1-D10. Brownjohn, J and Middleton, C T (2008), “Procedures for Vibration Serviceability Assessment of High-Frequency Floors”, Engineering Structures , 30(6), pp. 1548-59. Department of Culture, Media and Sport, UK (1997), Guide to Safety at Sports Ground  (London: Stationery Office) (available: http://www.scribd.com/doc/ ; accessed: 30 June 2011). Department of Health, UK (2008),   Health Technical Memorandum 08-01: Acoustics (London: Department of Health Estates and Facilities Division). Department of Environment and Conservation, NSW (2006),   Assessing Vibration: a Technical Guideline (Sydney: Department of Environment and Conservation) (available: www.environment.nsw.gov.au; accessed: 5 July 2011).

Dougill, J W, Wright, J R, Parkhouse, J G and Harrison, R E (2006), “Human Structure Interaction during Rhythmic Bobbing”, The Structural Engineer , 84(22), pp. 32-39. Ellis, B R and Ji, T (1997),  BRE Digest 426: the Response of Structures to Dynamic Crowd  loads (London: BRE). Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 47 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

Ellis, B R and Ji, T (2000), “The Response of Grandstands to Dynamic Crowd Loads”, Structures and Buildings , 140, November, pp. 355-65 (available: http://personalpages. manchester.ac.uk/staff/tianjian.ji/ ; accessed: 30 June 2011). Ellis, B R and Ji, T (2002), “On the Loads Produced by Crowds Jumping on Floors”, Presented at the 5th European Conference on Structural Dynamics, Munich, Germany, 2-5 September 2002. Ellis, B R and Littler, J D (2004), “Response of Cantilever Grandstands to Crowd Loads Part 1: Serviceability Evaluation”, Structures and Buildings , 157(5B4), pp. 235-41. Ellis, B R and Littler, J D (2004a), “Response of Cantilever Grandstands to Crowd Loads Part 2: Load Estimation”, Structures and Buildings , 157(5B5), pp. 297-307. FGI (2010), Guidelines for Design and Construction of Health Care Facilities (Dallas: FGI). Greenwood, R D, and Cowell, R (1992) , “International Convention Centre, Birmingham: Structures and Railway Vibration Isolation”, Structures and Buildings , 94, August, pp. 25362. Hanson, C E, Towers, D A, and Meister, L D (2006),   Report prepared by Harris Miller    Miller & Hanson Inc. for Federal Transit Administration: Traffic Noise and Vibration   Impact Assessment  (Washington, DC: US Department of Transportation) (available: http://www.fta.dot.gov/ ; accessed: 30 June 2011). Hicks S J and Devine P J (2004),   Design Guide on the Vibration of Floors in Hospitals (Berkshire: SCI). ISO (2007),  ISO 10137-2007: Bases for Design of Structures - Serviceability of Buildings and Walkways against Vibrations (Geneva: ISO). ISO (1989),  ISO 2631-2: 1989 Evaluation of Human Exposure to Whole-Body Vibration -Part 2: Continuous and Shock-Induced Vibrations in Buildings (1 to 80 Hz) (Geneva: ISO). IStructE/DTLR/DCMS (2001),   Dynamic Performance Requirements for Permanent  Grandstands Subject to Crowd Action: Interim Guidance on Assessment and Design (London: IStructE). IStructE (2007), Temporary Demountable Structures: Guidance on Procurement, Design rd and Use (London: IStructE, 3 ed). Jones, C A, Reynolds, P and Pavic , A (2011), “Vibration Serviceability of Stadia Structures Subjected to Dynamic Crowd Loads: a Literature Review ”, Journal of Sound and Vibration , 330(8), pp. 1531-66.

Li, W W, Wong C T, Leung M K and Fung S C (2011), “Floor Vibration due to Human Rhythmic Activities: Tin Shui Wai Public Library cum Indoor Recreation Centre”, Presented at the Twelfth East Asia ‐ Pacific Conference on Structural Engineering and  Construction, Hong Kong, 26-28 January 2011. Madshus, C, Bessason, B and Harvik, L (1996), “Prediction Model for Low Frequency Vibration from High Speed Railways on Soft Ground”,   Journal of Sound and Vibration,

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 48 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011

193(1), pp. 195-203 (available: http://notendur.hi.is/bb/BBgreinar/ ; accessed: 4 September 2011) . Murray, T M, Allen, D E and Ungar, E E (1997), Steel Design Guide Series 11: Floor  Vibrations due to Human Activity (Chicago: American Institute of Steel Construction). National Institutes of Health (NIH) (2008),   Design Requirements Manual for Biomedical   Laboratories and Animal Research Facilities (Maryland: NIH) (available: http://orf.od.nih.gov/ ; accessed: 30 June 2011).

Pavic, A and Reynolds, P (2008), “Experimental Verification of Novel 3DOF Model of  th Grandstand Crowd-Structure Dynamic Interaction”, Presented at the 26  International  Modal Analysis Conference , Orlando, Florida, 4-7 February 2008. Pernica, G (1990), “Dynamic Load Factors for Pedestrian Movements and Rhythmic Exercises”, Canadian Acoustics , 18(2), pp. 3-18. Reynolds, P, Pavic, A and Carr, J (2007), “A Remote Monitoring System for Stadia Dynamics”, Structures and Buildings, 157(6), pp. 385-93. Reynolds, P, Pavic, A and Carr, J (2007), “Experimental Dynamic Analysis of the Kingston Communications Stadium” , The Structural Engineer , 85(8), pp. 33-9. Sim, J, Blakeborough A and Williams M (2006), “Modelling Effects of Passive Crowds on Grandstand Vibration”, Structures and Buildings , 159(SB5), pp. 261-72). Talja, A, Vepsä, A, Kurkela, K and Halonen, M (2008),   Rakennukseen Siirtyvän   Liikennetärinän Arviointi (  Assessment of Traffic-Induced Vibrations in Buildings ) (Kemistintie, Finland: VTT) (available: http://www.vtt.fi/ ; accessed: 1 March 2011). Ungar, E E and White R W (1979), “Footfall -Induced Vibrations of Floors Supporting Sensitive Equipment”, Sound and Vibration , 13(10), pp. 10-3.

Ungar, E E (2007), “Vibration Criteria for Healthcare Facility Floors”, Sound and Vibration , 41(9), pp. 26-7 (available: http://www.sandv.com/downloads/0709unga.pdf ; accessed: 4 September 2011) . Willford, M (2005), “Dynamic Performance of Stands”, in Culley, P and Pascoe, J (eds.) Stadium Engineering (London: Thomas Telford Publications), pp. 47-54. Willford M and Young P (2006),   A Design Guide for Footfall Induced Vibration of  Structures (Surrey: The Concrete Centre).

Wong, C T, Leung, M K and Chow, H M (2011), “Floor Vibration Induced by Human Rhythmic Activities: Design and Post-Construction Validation at Tin Shui Wai Public Library cum Indoor Recreation Centre”, To be Presented at the 14th Asia Pacific Vibration Conference, Hong Kong, 5-8 December 2011 . Wyatt T A (1989), Design Guide on the Vibration of Floors (Ascot, Berkshire: SCI). Yao, S, Wright, J R, Pavic, A and Reynolds, P (2004 ), “Experimental Study of Human Induced Dynamic Forces Due to Jumping on a Perceptibly Moving Structure”,  Journal of  Sound and Vibration , 296(1-2), pp. 150-65.

Structural Engineering Branch, ArchSD Guidelines on Grandstands and Sensitive Equipment Issue No./Revision No. : 1

Page 49 of 49

File code : PartIII.doc CTW/MKL/CHL/HMC/KYL/MMT Issue/Revision Date : September 2011