Three different grandstand structures are assessed using the simplifi ed method outlined in Figure 2 and they are presented at the end of this paper with the appropriate modal information as worked examples. In each case ‘accurate’
answers, obtained by analysing the structure with all the crowd units represented as shown on the left of Figure 1b, are also provided to give an indication of errors likely to be associated with the simplifi ed method. The examples chosen are typical of structures that fail the Route 1 natural frequency criteria but which pass the more realistic Route 2 vibration response criteria.
2D models have been used for the examples because they demonstrate the method and the issues most clearly; the method and the principles apply equally to 3D models.
Guidance on important factors to be included in analytical models is provided in the Recommendations (Appendix 3). The worked examples presented in this paper have been analysed using the DynamAssist structural dynamics software7. Example 1
The grandstand of Example 1 has two natural frequencies between 4 and 5Hz, but both of these modes combine signifi cant sway of the main
Figure 7 - Sensitivity, Ʉ, of Scenario 3 and 4 accelerations to changes in structural damping
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Conclusions
Recently published recommendations1 have introduced a new analysis method for predicting vibration levels that can be generated by crowds of people in a grandstand, taking account of the effects of human-structure interaction.
This paper has presented a simplifi ed procedure for applying the new method, which only requires a modal analysis of the empty structure and knowledge of the crowd’s location. The procedure has been used to derive design charts, showing the sensitivity of grandstand response to natural frequency and modal mass ratio.
A number of worked examples have been provided to demonstrate the application of the procedure.
Results calculated more accurately have been presented alongside those from the simplifi ed method.
These show that the simplifi ed method gives good agreement with the more precise method.
Previous guidance on grandstand dynamics used only the natural frequency of the structure to judge the acceptance of the structure. The design charts clearly demonstrate that the modal mass ratio also has a very signifi cant effect on the dynamic response. Indeed, grandstands that may have failed the previous check based solely on natural frequency may be found to be acceptable when the modal mass ratio is taken into account.
The design charts can readily be used to consider the effect of changes in natural frequency and modal mass ratio on the likely acceleration levels.
In particular, the effect of modal mass ratio can be used to confi rm the suitability of crowd management decisions. This has been demonstrated in the Worked Examples, where a decision to keep the front two rows of a grandstand’s cantilever unoccupied made the structure suitable for a Scenario 4 event.
The design charts are based on a structural damping ratio of 2%, as specifi ed in the Recommendations.
The effect of different structural damping ratios has been considered.
It has been found that, because the damping of the crowd in a full stadium is generally greater than that of the structure, a grandstand’s response to dynamic crowd action is relatively insensitive to changes in its own damping, except when there is a very low modal mass ratio. This is particularly signifi cant if considering the use of additional damping as a remedial measure; the improvement in performance will be less than anticipated if human-structure interaction is ignored.
Acknowledgements
The authors wish to acknowledge the valuable discussions with Dr John Dougill, Chairman of the Working Group, and support from Prof. Mike Otlet of Atkins.
This paper was originally published in The Structural Engineer, 88 (7) 7 April 2010, pp 27-34.
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Worked examples
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References
Institution of Structural Engineers, Department for Communities and Local Government and Department 1.
for Culture, Media and Sport. Dynamic performance requirements for permanent grandstands subject to crowd action: Recommendations for management, design and assessment. London : IStructE, Dec 2008.
Institution of Structural Engineers, Department for Transport, Local Government and the Regions and 2.
Department for Culture, Media and Sport. Dynamic performance requirements for permanent grandstands subject to crowd action: interim guidance on assessment and design. London : IStructE, 2001.
BS 6399-1: 1997: Loadings for buildings. Part 1: Code of practice for dead and imposed loads. London : BSI, 1996.
3.
Ellis, B.R. and Ji, T. The response of structures to dynamic crowd loads.
4.
BRE Digest 426.Garston: BRE Bookshop, 2004.
‘Commentary D: Defl ection and vibration criteria for serviceability and fatigue limit 5.
states’, in National Research Council of Canada. User’s Guide - NBC 2005: structural commentaries (Part 4 of Division B). Ottawa: NRC, 2005, pp D1-D10.
Dougill, J.W., Wright, J.R., Parkhouse, J.G. and Harrison, R.E. ‘Human structure interaction 6.
during rhythmic bobbing’. The Structural Engineer, 84(22), 21 Nov 2006, pp 32-39.
DynamAssist structural dynamics software – version 3.
7.
www.DynamAssist.com
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Abstract
Bridge H01
Bridge H01 is a 52 m single-span integral highway bridge of steel-concrete composite “open top” box-girder construction. It is situated in the north of the Olympic Park and carries a local distributor road over the River Lea. It was the fi rst box girder bridge to be erected in the Olympic Park and was opened to construction traffi c in October 2009. It is planned to be opened for public use in December 2010 for access to the Stratford City development. The general arrangement is shown in Figure 1.
An open top box girder solution was adopted for Bridge H01 for a number of reasons:
The absence of outstand
•
fl anges give a sleek appearance and reduce opportunity for bird roosting.
Introduction
The Olympic Park bridges in Stratford include 11 highway bridges, 13 pedestrian bridges, 6 underpasses and many other temporary bridges with spans up to 56.5 m. Many of them carry major utilities over waterways or railways. The bridge and associated wingwall designs, including fi nishes, are co-ordinated to fi t seamlessly with the Park's topography and landscape during the Games period and in Legacy. Minor modifi cations to some bridges will be required after the Games for Legacy transformation.
This paper describes the particular technical challenges encountered on two of the bridges, H01 and L01.
In preparation for the 2012 Olympic and Paralympic Games, many bridges were required crossing over waterways, highways and railways. This paper describes the technical challenges on two of the Atkins designed bridges - H01 and L01.
Bridge H01 is a single-span integral highway bridge of composite steel box-girder construction that carries a local distributor road over the River Lea in the north of the Olympic Park. It was the fi rst box girder bridge to be erected in the Olympic Park and was opened to construction traffi c in October 2009.
It is planned to be opened for public use in December 2010 for access to Stratford City. Box girders are torsionally stiff in their completed state but are less so during construction if they are “open top”, as here, and require restraint to the compression fl ange during deck slab construction to prevent lateral buckling. The design of Bridge H01 utilised vertical cross-bracing at regular centres for this purpose, but detailed analysis indicated that this alone was insuffi cient to prevent signifi cant second order twisting effects under torsional loading. The paper discusses how the designers addressed these issues and how updated national box girder design guidance was produced as a result.
Footbridge L01 crosses Ruckholt Road and provides the vital northern link to the Olympic Park for pedestrians to and from the Northern Spectator Transport Mall. Its construction is expected to be completed in June 2011. The single span structure is a unique form of construction whose behaviour is a hybrid between that of a tied arch and Vierendeel girder. The steel bridge deck itself is 42m long and 5.5m wide, while the arch rib is made exceptionally slender by exploiting the overall Vierendeel girder behaviour. The closely spaced solid plate hangers provide both lateral and in-plane stability while creating a striking effect in elevation. The complex geometry required elastic critical buckling analysis to determine the resistance of the arch and non-linear analysis to assess the effects of arch deformation on the rigid hangers and deck. The main learning points from the analysis and design of this unique structure are presented in this paper.