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ABSTRACT
Human-Structure Interaction in Cantilever Grandstands
There is a risk that excessive vibration in long span cantilever grandstands can betriggered by the spectators synchronising their jumps to the music played. If thejumping frequeny excites a resonance of the grandstand, large force could begenerated. This thesis studies human-structure interaction in cantilever grandstands,with emphasis on modelling the passive and jumping crowds, and analysing theresponse of a single degree-of-freedom (SDOF) structural system.Preliminary work on analysing a cantilever occupied by seated humans shows that itis acceptable to use a SDOF structural system for analysis which meant emphasis oflater work could be placed on understanding the interaction between a passive crowd
and the structure.Human dynamic models from published biomechanics studies are used to develop apassive crowd model. A transfer function, fitted to the crowd apparent mass, is usedto define the crowd model. It is found that the passive crowd can be approximatedwell by using a single 2DOF system. The combined passive crowd-structure system is modelled as a feedback system and a parametric study is conducted. It is found that
the passive crowd adds significant mass and damping to the structure and these effects vary with the natural frequency of the structure.
Records of forces of people jumping to a beat are used to develop a probabilistic model of crowd jumping loads. Key parameters are introduced to characterise the timing and shape of the jumping impulses. An analytical function is used to approximate the impulse shape. All parameters are characterised with probability distribution functions.
Using the fitted probability distribution functions, the Monte Carlo method is used to simulate individual jumping load-time histories and to obtain the structural responsesdue to group jumping loads. The variations of the structural response with the natural frequency of the empty structure and the size of the active crowd are presented in charts. As expected, the worst response is found on structures with natural frequencies coinciding with the first three harmonics of the crowd jumping loads. For structures occupied by passive crowds, a significant reduction in the structural response is found at resonance excited by the second and third harmonics, due to high levels of damping provided by the passive crowds. On variation of the structural response with the crowd size, it is found that the structural response becomes asymptotic for groups larger than 16 people.
Experimental individual jumping and bobbing tests are conducted at six distinct beat frequencies to look at the variations of the impulse shape and degree of synchronisation with the beat frequency. The bobbing action is found to have a higher inherent variability between individuals compared to jumping. Jumping tests involving two people facing each other are also conducted. The results show that there is a better synchronisation when two people are jumping together compared to when jumping alone.
1. Introduction
1.1. The Problem
Problematic levels of vibration are being reported in several stadiums around the world, especially during pop concerts and football matches, due to excitations by rhythmic crowd motions such as clapping, foot stamping, bobbing or jumping. A few examples are given here. Firstly, the Maracana football stadium in Brazil (Batista and Magluta 1993), with a capacity of 150,000 people, is a reinforced concrete structure with a cantilever stand 21 m long. The natural frequencies of the cantilever stand when empty were 4.6, 6.6 and 17.0 Hz. It was reported that high levels of acceleration and large displacements could be felt during football games. Cracks were found in the cantilever beams, most probably due to large displacements and hence over-stressing of the structure. Another example, the Feyenoord Stadium in the Netherlands (van Staalduinen and Courage 1994), with a capacity of 61,000 people, had also experienced strong
vibrations during pop concerts. The grandstand had natural frequencies of 2.3, 4.6 and 5.8 Hz. Strong vibrations were reported on the upper tier during pop concerts. To reduce the vibration level, the displacement of the stand was monitored during pop concerts and the audio system was turned down when there was excessive vibration.
The Morumbi Stadium in Brazil (Almeida and Rodrigues 1998), with a capacity of 80,000, had a few modes ranging from 2.2 to 4.0 Hz. Complaints were received 1.Introduction 1-2 from the crowds on the vibration of the structure. Tuned mass dampers were fitted
to the stadium to reduce the vibration level (GERB Vibration Control Systems 2005). In the UK, excessive movements have been reported on several modern footballstadiums during pop concerts or football matches, including Manchester United’s Old Trafford Stadium (Rogers 2000), Arsenal’s Highbury Stadium (Rogers 2000), Liverpool’s Anfield Stadium (Rogers and Thompson, 2000) and The Millennium Stadium in Cardiff (Otlet 2004). To rectify the problem in the Old Trafford Stadium, the local authority restricted the use of the problematic tier to football match usage while for the Highbury Stadium, tuned mass damp ers were fitted.
Steel columns were fitted to the Anfield Stadium to raise its natural frequency while a series of temporary supports were installed at The Millennium Stadium prior to a pop concert. All the stadiums mentioned above have large cantilever spans with natural frequencies that fall within the frequency range of human-induced loadings. In addition, they are often subjected to rhythmic human-induced loadings, especially in pop concerts in which the crowds synchronise their movements with the music
played. The high flexibility of the cantilever tiers and the rhythmic crowd motion produce resonant or near-resonant dynamic behaviour which may lead to excessive vibration. This may cause human discomfort, crowd panic or at the extreme, a possible collapse of the structure.
1.2. Current approach to the problem
To tackle this problem, existing codes and guidelines, including National Building Code of Canada (1990), BS 6399 (British Standards Institution 1996) and Guide toSafety at Sports Grounds (Department of National Heritage and Scottish Office1997) specify that a dynamic analysis should be performed for stadiums withnatural frequencies below certain threshold values. However, none of these codesand guidelines provides the tools that would allow a designer to analyse theperformance expected of these structures.
1.3. Human-structure interaction
Generally, the crowds on a cantilever grandstand can be classified into active andpassive crowds. An active crowd moves rhythmically by jumping, bobbing orswaying, usually following a musical beat or crowd chanting. A passive crowdremains stationary by either sitting or standing on the structure. A dynamic analysisof the cantilever grandstand involves the study of how each of these two crowdsinteracts with the structure. The active crowd is known to exert external dynamicloads on the structure by their rhythmic motions. For the passive crowd, modal tests
on several stadiums have shown that it behaves as a dynamic system added to themain structural system.The dynamic analysis of a cantilever grandstand consists of four main tasks:
(a) Modelling the passive crowd.
(b) Defining the dynamic load induced by the active crowd.
1.Introduction 1-4
© Analysing the passive crowd-structure system subjected to the dynamicload.
(d) Assessing the resultant vibration level prediction for serviceability
criteria.Current knowledge and practice are deficient in all four main areas mentionedabove. Therefore, no sensible analysis has yet been conducted on a cantilevergrandstand to estimate its dynamic response when subjected to a crowd rhythmicmotion.
1.4. Aims of this thesis
This thesis addresses the first three areas that are identified as deficient above. Forthe passive crowd, the aim is to develop a simple dynamic model to represent thecrowd as a system added to the main structural system. A frequency responseanalysis is then conducted on the joint crowd-structure system to investigate howthe dynamic properties of the occupied structure are different from when thestructure is empty. For the active crowd, the action of jumping, which is the mostsevere form of crowd-induced loading, is the subject of research in this thesis. In
addition, an initial investigation on the action of bobbing is conducted. Once thepassive and active crowds are defined, a dynamic analysis is conducted to calculatethe response of a structure occupied by both active and passive crowds. Theoutcome of this thesis gives an indication on the vibration levels to be expected oncantilever grandstands when occupied by various ratios of active to passive crowds.
1.Introduction 1-5
1.5. Thesis outlineThe outline of this thesis is as follows. Firstly, a literature review is presented inChapter 2 to discuss the nature of the vibration problem on cantilever grandstandsand to review current progress in tackling the problem. The remainder of the thesisis divided into three parts: Parts I and II deal with modelling the passive and activecrowds respectively. Part III deals with simulating the crowd jumping loads and
calculating the resultant responses on a passive crowd-structure system.
Part I: Chapter 3 looks at the dynamics of a cantilever beam occupied by passivehumans and subjected to dynamic loads. Chapter 4 investigates the effect of apassive crowd on the dynamic characteristics of a single degree-of-freedom (SDOF)structural system. The results are presented in charts which enable engineers toestimate the amount of reduction in natural frequency and structural response for anoccupied structure.
Part II: Chapter 5 deals with statistical modelling of individual jumping loads
which are obtained from experimental tests.Part III: Chapter 6 deals with simulating the crowd jumping loads and calculatingthe resultant responses on a passive crowd-SDOF system. The results are presented
in charts to allow engineers to estimate the structural responses due to various ratiosof active to passive crowds. Chapter 7 reports on some experimental tests involvingtwo subjects jumping together and a single subject bobbing.Lastly, in Chapter 8, conclusions are drawn from Parts I, II and III. Chapter 2
2. Literature review
In this chapter, the first two sections (2.1 and 2.2) serve to provide some
background while the rest of this chapter reviews two main areas which are thefocus of this thesis: modelling the passive and active crowds.
Firstly, in section 2.1, the problematic mode of vibration encountered on cantilevergrandstands is identified. Then the findings from several onsite measurements ofstadiums are reviewed in order to give a better understanding on the nature of theproblem. This is followed by a review on the recommendations provided by existingcodes and guidelines (section 2.2). The deficiencies in these codes and guidelinesare identified. The rest of this chapter reviews current research work on modelling
the passive (section 2.3) and active (section 2.4) crowds. For the active crowd,emphasis is placed on modelling the jumping load but a very brief review onbobbing load (section 2.5) is included. In the last section, some concluding remarksare presented, mainly to identify areas that require further research.
2.1. Vibration problem on grandstands
2.1.1. Vertical mode of vibration
In order to determine the dynamic performance of a grandstand when subjected tohuman-induced loads, the designer needs to identify the low-frequency modes of theproposed structure. Often, it is possible for a number of global and local modes tobe excited and these modes can be classified into three directions: vertical, front-to2.Literature review 2-2
back and side-to-side (Reid et al. 1997). For a grandstand with multiple tiers, thecantilever sections in the tiers above the ground level (shown by the circled sectionin Fig. 2.1) are most vulnerable to vibration in the vertical direction, especially forlong span tiers. This thesis is concerned with this local vertical mode of vibration.
2.1.2. Onsite monitoring
Several onsite measurements have been conducted on stadiums during pop concertsand sports events. There are two main emphases in these works, one is to monitorthe response of the grandstands when subjected to crowd rhythmic motions and theother is to investigate the dynamic properties of the grandstands when occupied bypassive crowds.
Littler (1998, 1999) measured the performance of stadiums in the UK during popconcerts. Altogether, the responses of five large cantilever grandstands with naturalfrequencies between 4.64 Hz and 7.3 Hz when empty were measured. Thespectators in all four concerts were quite diverse. In one concert, all the spectatorsconsisted of 16 to 25 years olds among which two-thirds were male. At the start ofeach song, a large proportion of the spectators jumped to the music for 20 to 30
seconds. Another concert by an artist who has been popular for 30 years had a wideage range. Most of the spectators were standing and clapping and there was nowidespread jumping. In all concerts, the motions were perceptible and severalpeople remarked about the movements but none complained. The peakaccelerations recorded were between 0.48 and 1.62 m/s2. The frequency responsespectra showed that there were significant responses due to excitations by the firstthree harmonics of the crowd-induced loads.
2. Literature review 2-3
On the other hand, several modal tests and experimental studies showed thatstructures have different dynamic characteristics when empty compared to whenoccupied by passive spectators. Modal test conducted on the Twickenham Stadium(Ellis and Ji 1997), which had a natural frequency of 7.32 Hz when empty, foundthat there were two modes at 5.41 Hz and 7.91 Hz when occupied. Other modaltests on three cantilever grandstands (Littler 1998, 1999) showed that the naturalfrequencies of the empty grandstands ranged from 4 to 6 Hz and a reduction of
between 0.3 Hz and 0.5 Hz was observed on all grandstands when occupied byspectators. For the Bradford Stadium which had modes between 3.28 Hz to 5.75 Hz,modal tests conducted during 20 football matches and 9 rugby matches (Reynolds etal. 2004) showed that there was a reduction inthe natural frequencies when thestand was occupied by seated or standing spectators. A slightly greater reduction
was observed when the spectators were standing than when seated, illustrating theeffect of crowd configuration. An increase in the damping ratio was also reported.Experimental tests conducted on a SDOF platform occupied by a standing person(Harrison and Wright 2004) showed that there was a reduction in the naturalfrequency and an increase in the damping. However, a vibration test on an18.68 Hz beam (Ellis and Ji 1997) showed that there was an increase in the natural
frequency when a person was seated or standing on the beam while no change wasrecorded when the person was jumping or walking on the beam.
2.1.3. Modelling of stadiums
Several works on the computer modelling of grandstands with emphasis on the
dynamic behaviour have been conducted. In particular, a comparative study on the
use of 2D and 3D FE models (Mandal and Ji 2004) found that a 2D model was
2. Literature review 2-4
sufficient to examine the behaviour of a grandstand in the vertical direction.
However, the presence of non-structural elements might have a significant influenceon the modal properties and it is difficult to model them accurately. Discrepanciesbetween the calculated and measured modal properties were found for a grandstandin a football stadium (Reynolds and Pavic 2002) due to additional stiffness providedby the joints between the main structural members. Another example is the City ofManchester Stadium (Reynolds et al. 2005) in which the perimeter concrete
blockwork wall was found to have a significant influence on the natural frequenciesof the structure.
2.2. UK codes and guidelines
Three codes and guidelines are relevant for engineers designing a stadium in the UKand they are reviewed below.In BS 6399: Part 1 (British Standards Institution 1996), it is stated that for an empty
structure with a vertical frequency less than 8.4 Hz and a horizontal frequency lessthan 4 Hz, a dynamic analysis is required to assess its ability to withstand thedynamic loadings in the vertical and two orthogonal horizontal directions. Thevertical threshold frequency is obtained by considering up to the third harmonic ofuency limit of 2.8 Hz. Guidance on
individual jumping load is given in Annex A.The ‘Green Guide’ (Department of National Heritage and Scottish Office 1997)adopts the same strategy of recommending a dynamic analysis for a grandstand but
2. Literature review 2-5
with natural frequencies of less than 6 Hz vertically and 3 Hz horizontally when thestructure is occupied by spectators.
In 2001, an interim guidance was published (IStructE/ODPM/DCMS WorkingGroup 2001) due to growing concern on the dynamic performance of moderngrandstands when used for pop concerts. The interim guidance recommendsdifferent natural frequency thresholds for permanent grandstands based on thedegree of synchronisation of the crowd activities on the grandstands. Forgrandstands used solely for viewing events with no external stimulus to coordinatethe crowd movement, a natural frequency threshold of 3 Hz is recommended. Forgrandstands used for pop concerts with the crowds coordinating their movements tothe music played, a natural frequency threshold of 6 Hz is recommended. An
advisory note was published subsequently (IStructE/ODPM/DCMS Working Group2003) to address issues related to the determination of the structure’s naturalfrequencies. It highlights the need to consider the effect of the non-structuralelements. The working group is currently preparing a final guide on designingstadiums subjected to different crowd activities.
2. Literature review 2-62.3. Passive crowd modelling
This section reviews the work on passive crowd modelling in the areas of civilengineering and biomechanics.
2.3.1. Civil engineering
In civil engineering, passive human occupants were known to contribute a
significant amount of damping to floor systems. It was commented that humanoccupants provided excellent damping, with the floor damping increasing by 300 %due to the presence of four people on a steel joist-concrete slab floor (Lenzen 1966).Free vibration tests on nailed wood-joist floors with human occupants seated andlying on the floor found that the occupant’s physique influenced the damping
capacity provided to the floor (Polensek 1975). Heel impact and shaker impact testsconducted on a composite concrete slab and an open web steel joist floor found thatthe heel impact test gave higher damping than the shaker impact test due to dampingprovided by the person (Rainer and Pernica 1981). In the same study, it was alsonoted that damping increased with the modal amplitude at the location of the person.
Early efforts to model a single standing occupant using a lumped parameter modelcan be found in the dynamic analysis of floor response by Foschi and Gupta (1987)and Folz and Foschi (1991). The former used a SDOF system while the latter usedboth 2DOF and 11DOF systems. Later developments included the use of anundamped continous model (Ji 1995) and a SDOF system (Zheng and Brownjohn2001) to represent a standing person.2. Literature review 2-7In modelling cantilever grandstands, the need is to model a group of people ratherthan single individuals. It is possible to represent each individual in the group using
a lumped parameter model but the resultant crowd model will have too manydegrees of freedom. Ellis and Ji (1997) proposed using an undamped SDOF systemto represent the passive crowd on a grandstand. However, it is more desirable toinclude damping in the model considering the high damping capacity of the humanbody. Sachse et al. (2002) conducted experimental tests involving a 15000 kg beamoccupied by 5 seated occupants. A SDOF system was used to model the occupants
and its modal properties were obtained by curve-fitting the measured FRFs. InSachse’s tests, the total mass of the human occupants was only 5% of the mass ofthe structure. Hence the influence of the human occupants on the measured FRFsmight be very small and it might be affected by noise in the measurements.The ISO 5982 (International Organization of Standardisation 1981) uses 2DOFlumped parameter models to represent a seated and standing human but according toFairley and Griffin (1984) these models were derived from studies of heavy people.ke into account the slight variation between each jump.