a case study of using metal scaffold system for demountable grandstand: the opening ceremony of hong...
DESCRIPTION
A grandstand is a structure which provides seating for spectators at entertainment or sporting events. Grandstands are typically classified into three distinct types: permanent, demountable and retractable. Structural Engineering Branch (SEB) of the Hong Kong SAR Government has promulgated a set of guidelines in September 2011 - 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 – providing guidance the effect of human induced vibration on permanent grandstands. This paper will focus on the analysis, design and construction of demountable grandstands by sharing the experience on the demountable grandstands erected for the Opening Ceremony of Hong Kong 2009 East Asian Games held on 5 December 2009.Keywords: demountable grandstand, temporary grandstand, East Asian Games 2009, Hong Kong, structural steelTRANSCRIPT
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Information Paper
A Case Study of Using Metal Scaffold System for
Demountable Grandstand:
The Opening Ceremony of Hong Kong 2009 East Asian Games
STRUCTURAL ENGINEERING BRANCH
ARCHITECTURAL SERVICES DEPARTMENT
December 2011
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Table of Contents
1. Introduction ................................................................................................... 1
2. Structural Behaviour and Components ......................................................... 4
3. Design Loading ............................................................................................. 23
4. Dynamic Effects ............................................................................................28
5. Foundation .................................................................................................... 30
6. Construction Supervision .............................................................................. 30
7. Case Study .................................................................................................... 31
8. References ..................................................................................................... 52
Annex A Sample Checking Certificate
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1 Introduction
1.1 A grandstand is a structure which provides seating for spectators at entertainment
or sporting events. Grandstands are typically classified into three distinct types:
permanent, demountable and retractable. Structural Engineering Branch (SEB) has
promulgated a set of guidelines in September 2011 - 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 (available:
http://asdiis/sebiis/2k/resource_centre/) – providing guidance the effect of human
induced vibration on permanent grandstands. This paper will focus on the analysis,
design and construction of demountable grandstands by sharing the experience on
the demountable grandstands erected for the Opening Ceremony of Hong Kong
2009 East Asian Games held on 5 December 2009.
1.2 Demountable stands (Photo 1(a)) are lightweight temporary structures whose
trussed appearances are reminiscent of scaffolding systems. These stands are
typically erected for a single specific event (e.g. parade, sports, and show) and
therefore left in place for a short duration to house the large number of spectators.
However, in some events (e.g. in the Opening Ceremony of Hong Kong 2009 East
Asian Games), such demountable grandstands may have occupancies of up to
thousands of people. Demountable grandstands were widely used in the Sydney
2000 and Beijing 2008 Olympics Games, and in the recent Auckland 2011 Ruby
World Cup to increase the seating capacity of the competition venues. Photo 1(b)
shows a large-scale example of demountable grandstands used in the softball centre
of the Sydney 2000 Olympics Games, where 7,000 additional seats were provided
by such demountable grandstands, and Photo 1(c) shows the scaffold system of
another large-scale example of demountable grandstands used in Eden Park
Stadium of the Auckland 2011 Ruby World Cup, where 10,000 additional seats
were provided by such demountable grandstands.
Photo 1(a) Typical Demountable Grandstand (Bellinzona, Switzerland)
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Photo 1(b) Demountable Grandstand in Softball Centre at
the Sydney 2000 Olympics Games
(Source: www.austseat.com.au/)
Photo 1(c) Scaffold System of the Demountable Grandstand
in Eden Park Stadium at the Auckland 2011 Ruby World Club
(Source: www.zimbio.com/pictures/-sUagbFggBA/)
PH 1.3 Unlike permanent structures, demountable grandstands are usually designed to be
repeatedly assembled and disassembled with the use of lightweight components
such as slender steel tubes. The supporting structure and the member connections
for such grandstands are also designed to make the assembly easily, rapidly and
usually with the use of various types of proprietary scaffold system. Usually,
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demountable stands are proprietary products designed, supplied in modular units
and installed by specialist contractor employed by the event organizers. Moreover,
to ease installation, the supporting scaffold structures consist of slender tubular
members with short spans between supports, rather than having larger steel sections
with longer spans in permanent grandstands. Ellis and Ji (2000) further note that
because of the short spans and slender tubular scaffolds, sway and front-to-back
vibration in horizontal direction are often the most important modes for
demountable grandstands for human-induced dynamic crowd loads, while vertical
modes are usually not a significant problem.
1.4 Because of the limited time for installation and the incentive to save cost, the
structure of such demountable grandstand will just be able to achieve the minimum
factor of safety. A number of accidents involving the collapse of such demountable
grandstands have occurred overseas resulting in a number of casualties. Typical
causes of these collapses are: overloading, lack of bracing, failure in support,
problems with connections, and synchronized movements of audience (de Brito and
Pimentel 2009). Two serious incidents of collapse of demountable stands occurred
in the UK during 1993 and 1994. 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 and suppliers of demountable structures. This guide has then been
updated with latest technological and regulatory changes, and its latest version is
published as Temporary Demountable Structures: Guidance on Procurement,
Design and Use (IStructE 2007).
1.5 The performance of demountable grandstand is the subject of this paper. First,
structural forms and structural components of common types of grandstand are
presented and discussed. Next, the design loading (including the dynamic loads)
for the analysis and design of such structures will be detailed. Finally, the analysis,
design, erection, and inspection process for the demountable grandstands erected
for the Opening Ceremony of Hong Kong 2009 East Asian Games grandstands is
presented and discussed.
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2. Structural Behaviour and Components
2.1 Demountable grandstands can be assembled in a variety of shapes and sizes
depending on the client requirement, nature of the event, weather, type of spectator
and terrain. These structures (Photo 2(a) and Photo 2(b)) typically have seats or
benches arranged in tiered rows with access to the seats from aisles that run
perpendicular to the rows of seating (Figure 1). These structures will usually be
dismantled once the event is completed. Most common demountable grandstands
are one that has a scaffold structure with bracing to provide lateral stability to
which a modular floor and seating system is fixed at the top.
Photo 2(a) Demountable Grandstand (Front Elevation)
(Source: www.layher.com)
Photo 2(b) Demountable Grandstand in Australia (Rear Elevation)
(Source: http://www.austseat.com.au/)
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Figure 1 Typical Demountable Grandstand (Plan)
(Source: Crick and Grondin 2008)
2.2 The structural behaviour of these structures is complex due to the presence of
countless components connected by clamps or simply inserted into each other. The
structural system is such that spans are reduced due to a significant number of
vertical supports, and flexural stiffness in a vertical direction would benefit from
that. On the other hand, along the line of seats (or sometimes called “sway”)
direction, stiffness is mainly due to bracing, whereas perpendicular to the line of
seats (or sometimes called “front to back”) direction, apart from bracing, there is
also the presence of frames to support the seats then contributing to stiffen the
structure in this direction. It is thus expected that the flexibility of the structure in
each direction varies significantly, with implications on its static as well as dynamic
behaviour.
2.3 Components of Grandstand
2.3.1 Demountable grandstands are structures generally made of steel and consist of
members, connectors, and planks erected on site. The structural system is a modular
three-dimensional frame, in which height and length of the structure are adjusted
during design to accommodate a specified number of users. Such 3-D frame
consists of proprietary scaffolds (instead of conventional structural steel sections as
the supporting structure for demountable grandstands due to the relatively faster
speed of assemble and lower material and erection costs of scaffold. Structurally,
these scaffolds serves as “support scaffold” (instead of as “access scaffold”), and
are required to carry heavy imposed load similar to falsework used in concreting.
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However, those scaffolds used in falsework for concreting are sometimes
manufactured as planar moment-resisting frames (or called the “door-type” scaffold
Figure 2(a)). For the proprietary scaffold used in demountable grandstands
(Figure 2(b)), the joints are usually assumed to be pinned-connection, and its
stability must rely on the brace members. Figure 2(c) shows the structural
components of a typical scaffold used for demountable grandstands. Most
proprietary demountable grandstands have similar components in their structures,
and the various common types of connector and bracing members in the scaffold
will be discussed in the following paragraphs.
Figure 2(a) Frame or Door-Type Figure 2(b) Proprietary Scaffold
Scaffold Demountable Grandstand
Figure 2(c) Structural Components of Typical Scaffold
(Source: Rasmussen and Chandrangsu 2009)
2.3.2 Tubes
To ease erection, all proprietary scaffolds are supplied as a modular system with
tubes and connectors. Structural steel tubes are used to make up of the three
elements of a modular unit: standard (the vertical element), ledger (the horizontal
element), and brace (the diagonal element). The standards are connected to create a
lift via connection tubes in sleeve joints (Photo 3), and are connected to the ledgers
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via connectors (Figure 4). Figure 3 shows an example on the size of the
connection tubes, sizes and dimensions of the pins for connecting the connection
tube and standards as extracted from a supplier’s catalogue. Table 1 shows typical
sizes of these three elements in a modular unit (Crick and Grondin 2008). Crick
and Grondin (2008) note that the steel tubes are generally of Canadian Standard
Grade 40.21 300W with minimum yield strength of 44ksi (300MPa). However,
this paper has reservation on the applicability of such general statement, especially
to those tubes used in Hong Kong. Hence, project officer should check the country
of origin of the proprietary scaffold and refer to the catalogues for scaffold to
determine the yield strength of the steel tubes.
Photo 3 Connection tube between upper and lower standards
Figure 3 Connection Tube between Upper and Lower Standards
(Source: http://www.scaffoldgold.com)
Connection Tube
Pin Hole
Details of
Connection Tube
Pin Hole
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Table 1 Typical Sizes of Tubes of a Modular Unit for Scaffold
Elements Length Diameter (mm) Thickness (mm)
Standard 0.5m, 1.0m, 1.5m, 2m or
3m 49 3.2
Ledger US: 2.13m or 3.05m
Europe 2.25m or 1.35m 49 3.2
Brace Length to suit standard
and ledger 45 2.3
2.3.3 Connector
There are several systems of connector that can connect the tubes together. In this
paragraph, three common systems, namely couplers, wedge-based connectors and
spigot (Figure 4), will be described.
Right-angle Swivel
(a) Coupler/Clamp (b) Wedge-based connector
(c) Spigot
Figure 4 Common systems of connector
(Source: De Brito and Pimentel 2009, and Labour Department 2001)
2.3.1.1 Coupler/Clamp
Standards are connected to ledgers via right angle couplers (Photo 4(a)), and
braces are connected to the scaffold via swivel couplers (Photo 4(b)) to form tube
and couple (or tube and clamp) scaffold.
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Photo 4(a) Right-Angle Couplers/Clamps Photo 4(b) Swivel Couplers/Clamps
(Source: www.tubeandclampscaffold.info) (Source: www.aptsuspensions.co.uk)
Tube and clamp scaffold is commonly used in construction. The ledgers and thus
walking-decks can be placed at any height along the standard, and standards can
be spaced at any distance apart up to the maximum distance allowed by
engineering constraints. Tube and clamp scaffold is also the simplest and
versatile system; but is among the most labour-intensive of all scaffolding
applications, and is therefore generally used only when high capacity, unlimited
adaptability and versatility are required.
2.3.1.2 Wedge-based connector
Kwikform (or KwikStage) scaffold (Photo 5(a)) and allround scaffold are using
wedge-based connector. A distinct feature for such connection system is that the
wedge pin can provide some moment carrying capacity, and hence, unlike the
other systems, braces are sometimes not provided for such scaffold system in light
loading (e.g. access scaffold). Further discussion on the effectiveness of such
connection in carrying moment will be given in Section 2.5. Kwikform scaffold
has metal loops attached to the standard at fixed intervals. The ledger has a
hooked head that fits into the loop and a wedge pin to tighten the connection
(Photo 5(b)). A hammer blow is used to drive the wedge pin between the ledger
head and the loop creating a secure connection. The wedge fixing of the ledgers
gives a simple and fast means of erecting access scaffolding without loose parts,
its rigid 4-way fixing giving a positive location without movement, and wedge
fitting on the standard giving guaranteed vertical alignment. To install braces,
steel tubes (Photo 5(c), 5(d) and 5(e)) with pivoted wedge devices at each end
fitting onto the standards.
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(a) (b)
(c) (d) (e)
Photo 5 Kwikform System (Source: www.scaffoldingcn.com and www.rmdkwikform.com)
Allround scaffold (Photo 6(a)) has a rosette (i.e. circular plate with slots) attached
at fixed intervals along the length of the standard. The ledger has a ledger head at
each end that has a horizontal slot that mate with a wedge pin drops down into the
slot on the rosette. The rosettes have 8 slots that allow up to eight members at one
connection. To make a connection, the wedge head is slid over the perforated
rosette. A harmer blow is then used to force the wedge pin into the slot securing
the ledger to standard. Typical connection procedure of the system is shown in
Photo 6(b).
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Photo 6(a) Allround System
(Source: www.layher.com)
Photo 6(b) Connection Procedure of the Allround Scaffold
(Source: www.layher.com)
2.3.1.3 Spigot
Cuplock (or cuplok) scaffold (Photo 7(a)) uses spigot to connect ledger and
standard together. Spigot is a cuplike element fixed to the standard at set intervals
along its length. It allows four members to be connected at one place.
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Photo 7(a) Cuplock Scaffold
(Source: www.scaffoldgold.com and www.indiamart.com)
To make a connection, the ledger end is placed into the bottom cup and the top
cup is screwed down on to the top of the ledger end locking it into place. A
hammer blow is used on the top cup to tighten the connection. Thus the top and
bottom of the ledger head is secured against the standard. Typical connection
procedure of the system is shown in Photo 7(b). Holes are intentionally left in
the upper and lower standards so that pins can be inserted so that the standard is
of the correct plumb and to transmit tensile force along the standard.
Photo 7(b) Connection Procedure of Cuplock Scaffold
(Source: www.scaffoldingasia.com)
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Photo 7(c) Special Braces for Cuplock Scaffold
(Source: www.scaffoldgold.com and http://scaffoldsales.com)
A distinct feature for such connection system (like wedge-based connector) is that
it can provide some moment carrying capacity, and hence braces are sometimes
not provided for such scaffold system (especially as access scaffold). Again,
further discussion on the effectiveness of such connection will be given in Section
2.5. To install braces, steel tubes (Photo 7(c)) with couplers at each end for
fitting onto the standards.
2.3.1.4 For demountable temporary grandstands, modular system scaffold such as the
cuplock, Kwikform and allround scaffolds are used most frequently. Scaffold in
the form of tube and clamp scaffold are considered too slow in construction and
labour intensive.
2.4 Bracing
2.4.1 One of the main reasons for the collapse of demountable grandstands is an
insufficient number of bracing members provided (Bolton 1992; Ji and Ellis 1997).
Demountable grandstands must therefore be provided with sufficient bracing
members to resist horizontal loads and wind loads. It is essential that diagonal
bracing be installed at all times. Free-standing individual support towers, and the
start and end bays must have diagonal bracing installed. Moreover, the bracing
elements also have effects on the permissible loadings on the standards. The
following figure shows 5 arrangements of bracing element in a scaffold system,
namely (0) every bay, (A) every 2nd
bay, (B) every 3rd
bay, (C) every 4th
bay, and
(D) every 5th
bay, in the descending order in their permissible loadings:
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(Source: www.layher.com)
2.4.2 Theoretical study
Extensive study of the effect of the bracing on such lightweight scaffold system has
been carried out by Ji and Ellis (1997). The governing principles in providing
bracing are:
1) the load shall take the shortest path to the supports (the “direct force path
principle”); and
2) the internal forces shall be uniformly distributed (the “uniform force
distribution principle”).
Based on these two principles, they listed out the following five criteria for
arranging bracings in an efficient way in order to achieve a larger lateral stiffness:
(a) Bracing members in different storeys should be provided from the top to the
support of the structure.
(b) Bracing members in different storeys should be directly linked where possible.
(c) Bracing members should be linked in a straight line where possible.
(d) Bracing members at the top adjacent bays should be directly linked where
possible.
(e) If extra bracing members are required, they should be used following the
above four criteria.
2.4.3 Table 2 shows six examples of typical bracing arrangement with descriptions on
which criteria as listed above can be fulfilled. Those systems fulfilling all the above
criteria would perform a higher static stiffness when subjected to horizontal loading.
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Table 2 Typical Bracing Arrangement for Scaffold
Type Bracing Arrangement Descriptions
1
- Satisfy criteria (a)
- Traditional bracing form
- Load transfer from top through all
members
2
- Satisfy criteria (a) and (b)
- Shorter load path than type 1, higher
static stiffness
3
- Satisfy criteria (a), (b) and (c)
- More straightforward force path
- Higher stiffness than type 1 & 2
4
- Satisfy criteria (a), (b), (c) and (d)
- Highest stiffness amongst the first 4
types
5
- More bracing members used, but not
fully follows the criteria
- Lower stiffness than type 4
6
- Satisfy all 5 criteria
- More uniform inner force distribution
- The highest stiffness among all the
above types
(Source: Ji and Ellis 1997)
2.4.3 Among the six types of bracing arrangement, Type 6, which consists of a pair of
straight cross-bracing from the top to bottom, is the most effective bracing system.
Type 6 in Table 2 only shows the ideal arrangement for a scaffold of two storeys
height. Figure 5(a) shows how to modify Type 6 arrangement for scaffold with
more than two storeys. Such bracing system can satisfy the first three criteria, and
has small number of bracing members. Ji (2003) carried out tests on three models
(frames A, B and C) of bracing system (Figure 5(b)(i)), which were made up of
aluminium members same cross-section of 25 mm by 3 mm with an overall
dimension of 1.025 m×1.025m. The frames were fixed at their supports and a
hydraulic jack was used to apply a horizontal force at the top right-hand joint of the
frame. At a load of 1.07kN, the horizontal displacement were respectively 3.0mm
for frame A, 0.73mm for frame B and 2.2mm for frame C (Figure 5(b)(ii)). They
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therefore verified that Type 6 arrangement, which satisfies all five criteria, is the
stiffest.
Figure 5(a) Type 6 Bracing for Multi-Storey Scaffold
Figure 5(b)(i) Models of Bracing Systems
(frames A, B and C being placed from the left to right)
(Source: Ji 2003)
Figure 5(b)(ii) Deflection Curves of Frames A, B and C
(Source: Ji 2003)
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2.4.4 Similar remarks have been made earlier in Grant (1975). Grant (1975) notes that
Type 6 bracing arrangement can result in the vertical loads in the standards to resist
the couple created by the horizontal loads to vary proportionately with their
distance from the centre line (Figure 5(c)), whilst Type 1 or 2 bracing arrangement
will create large vertical forces in the two legs adjacent to the standards in the
bracing bay (Figure 5(d)). Grant (1975) further notes that Type 6 bracing
arrangement can effectively redistribute a concentrated vertical load onto the other
standards (Figure 5(e)).
Figure 5(c) Induced vertical loads on standards using Type 6 bracing
(Source: Grant 1975)
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Figure 5(d) Induced vertical loads on standards using Type 2 bracing
(Source: Grant 1975)
Figure 5(e) Redistribution of concentrated vertical load using Type 6 bracing
(Source: Grant 1975)
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2.4.5 Type 6 bracing arrangement, however, has the following disadvantages:
a) there is no the bracing to the scaffold until its installation is completed, and
hence cannot provide the required stability during erection and dismantle works;
b) the erection of such bracing is much more difficult than the other types, as it is
difficult to align the bracing straight, especially with in the jungle of scaffolds
underneath the seating deck, and Bolton (1997) also raised concerns on the
potential instability of the scaffold system during dismantle when such bracing
has been removed;
c) under the effect of lateral force, the bracing will induce a large tensile force
onto the edge scaffold, which may not be of adequate strength, and anchor or
kentledge may be required at the foundation level to counteract the tensile force;
and
d) such bracing may be required to tie to the scaffold at intermittent levels (Figure
5) by swivel couplers, producing a moment on the thin tubes of the scaffold.
Grant (1975) further comments that in the case that it is not possible to tie the
bracing member to a standard at a node, a ledger is preferred to a standard for
such coupling, as the former is not already heavily loaded;
Hence, in reality, such bracing system will not be adopted by most specialist
contractors, although theoretically such bracing system provides the highest
stiffness. Instead, the common arrangement of bracing system adopted is Type I
(Photo 1(c) and Photo 8).
Photo 8 Typical Bracing System
(Source: http://www.austseat.com.au)
2.4.6 However, even though Type 1 bracing system is usually adopted as bracing system
in such modular scaffold, this paper still recommends that global Type 6 cross-
bracing should be provided around the scaffold system in addition to Type 1 so as
to increase the overall stiffness of the scaffold, especially when the demountable
grandstand is tall. The number of Type 1 bracing may also be reduced. A
suggested arrangement is shown in Figure 6. With such global bracing, there is the
potential for eight braces to interest at one connection, exceeding the maximum of
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4 braces even for allround scaffold system. Hence, it is necessary to attach the
braces to the standard or ledger using swivel couplers.
Figure 6 Preferred Bracing Arrangement at End Bays
2.5 Moment Carrying Capacity of Joint
2.5.1 It is generally assumed in the analysis and design that the joints in these scaffolds
are modelled to be pinned connection (i.e. with no moment carrying capacity). In
reality, they have some degree of fixity, especially the cuplike element in cuplock
scaffold and wedge-based connector in Figure 7(a). The cuplock connections
behave as semi-rigid joints, and show looseness with small rotational stiffness at
the beginning of loading. Once the joints lock into place under applied load, the
joints become stiffer (Godley and Beale 1997). Wedge-type joints are generally
more flexible and closer to pinned connections. They also often display substantial
looseness at small rotations (Godley and Beale 2001). As to spigot joints in the
cuplock system, the spigot can create out-of-straightness of the standards, and the
possibility of the joint to open up due to the gap between the standard and the
spigot can produce complexity in modelling (Enright et al 2000). Figure 7(b)
shows typical moment–rotation curves for cuplock and wedge-type joints. It
should further be noted that the relationship for all types of joint is not generally the
same for positive and negative rotations (Godley and Beale 2001), and that the
curves do not show linear relationship.
2.5.2 Although there is moment carrying capacity of the connections (and indeed, the
catalogues of many proprietary scaffold systems also provide their recommended
moment carrying capacity), project officer should note that the uncertainty and
limitations of such connections in carrying moment as discussed in the above
paragraph. This paper still maintains that in the design of demountable grandstand,
the joints should be modelled as pinned connection, and bracing members are
required to provide lateral stability for the scaffold. The moment carrying capacity
of the connections only serves as additional safety margin, especially during the
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erection and dismantle processes, where the bracing members have not yet been
installed or has been dismantled.
(i) Wedge-based connector (ii) Cuplock connector
Figure 7(a) Moment carrying capacity in wedge-based and cuplock connector
(Source: Godley and Beale 1997, 2001)
Figure 7(b) Typical moment against rotation graph of joint
in proprietary scaffold
(Source: Chandrangsu and Rasmussen 2006)
2.6 Elastic Critical Load Factor λcr
2.6.1 Eurocode 3 defines the elastic critical load factor λcr as the value of the load factor
by which the loads are to be multiplied to check of buildings for “sway mode”
failures. λcr is therefore an important parameter to classify the scaffold frame into
non-sway, sway or ultra-sway sensitive frame. For both sway and ultra-sway
sensitive frames, the load-carrying capacity of the steel tubes in the scaffold system
decreases with the height of the scaffold, as the effective length of tubes increases
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due to the P-- effects. The Code of Practice for the Structural Use of Steel 2005
(the “HK Steel Code”) issued by Buildings Department (as modified by SEI
08/2009: Design Code for Structural Steel) classifies frame using λcr as follows:
a) when λcr 10, the frame is non-sway and the P-- effects can be ignored;
b) when 5≤ λcr<10, the frame is sway and the P--δ effects can be included by
checking the members by either the moment amplification or effective length
methods; and
c) when λcr<5, the frame is ultra-sensitive sway frame, and second order
analysis should be used in the analysis and design to include the P-- effects.
2.6.2 Clause 6.3.2.2 of the HK Steel Code provides two methods to calculate λcr, namely,
the deflection method or the eigenvalue analysis. If eigenvalue analysis is used to
calculate λcr, project officer should first study the form of the buckling mode of the
frame to see if it is a sway buckling mode (Figure 8(a)) or a local column buckling
mode (Figure 8(b)). King (2005) commented that when using eigenvalue analysis
in finding the first sway-mode, “it is important to study the form of each buckling
mode to see if it is a frame mode or a local column mode. In frames where sway
stability is ensured by discrete bays of bracing (often referred to as “braced
frames”), it is common to find that the eigenvalues of the column buckling modes
are lower than the eigenvalue of the first sway mode of the frame. Local column
modes may also appear in unbraced frames at columns hinged at both ends or at
columns that are much more slender than the average slenderness of columns in the
same storey.” Similarly, Rathbone (2002) noted that “where the columns are axial
load predicated, many of the lower buckling modes will be [local] column buckling
modes. It is the [sway] buckling mode of the whole structure that is important” to
include second-order effects.
2.6.3 Therefore, both the deflection method and eigenvalue analysis are applicable to
calculate λcr for the frame with sway buckling mode; but if it is a local column
buckling mode, then the lowest eigenvalue found by the eigenvalue analysis does
not represent the first sway buckling mode λcr. Instead, the eigenvalue analysis
finds the eigenvalue for the column buckling mode. In such case, project officer
should take care in using the eigenvalue analysis and not just use the lowest
eigenvalue which may be local column buckling mode (Figure 8(b)) and it is not
the original intent to use it to define sway sensitivity. Should eigenvalue analysis
be adopted, project officer should therefore scan the output to see which eigenvalue
is the first sway buckling mode. Alternatively, in such case the deflection method
can be used to calculate λcr for the first sway buckling mode.
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Figure 8(a) Sway Buckling Mode Figure 8(b) Local Column Buckling Mode
3 Design Loading
3.1 Demountable grandstand should be designed to form a robust and stable three-
dimensional structural arrangement, which will support the design loadings for the
required period with an adequate margin of safety. The loading appropriate for the
design of demountable grandstand comprises dead, imposed, wind and notional
horizontal loads and may require consideration of dynamic loads from crowd.
3.2 Dead Load
Dead load shall include the self-weight of all fixed elements that form part of the
demountable structure.
3.3 Imposed Load
The minimum imposed load on demountable grandstands is controversial. BS
6399: Part 1 (BSI 1996) originally recommended it to be 5.0kPa, which is the same
as that specified in the Code of Practice for Dead and Imposed Loads 2011 (the
“HK Loading Code”) issued by Buildings Department. However, BS 6399: Part 1
has removed the specified minimum imposed load for grandstands in its
amendment in 2002. At the same time, for assembly areas with fixed seating, both
BS 6399: Part 1 and the HK Loading Code specify a minimum imposed load of
4.0kPa. Hence, project officer is advised to exercise judgment on choosing the
minimum imposed load to be adopted in individual case.
3.4 Wind Load
3.4.1 Design Wind Pressure
The design wind pressure acting on such temporary structures to be adopted in the
analysis and design is a controversial issue. The Code of Practice on Wind Effects
in Hong Kong 2004 (the “HK Wind Code”) issued by Buildings Department are
applicable for permanent building structures. It gives the extreme 3-second gust
wind velocity (and hence the wind pressure) for a return period of 50 years.
However, for demountable grandstand, it is generally intended to be used for a
short duration, and will then dismantled. The HK Wind Code states that the basic
wind pressure may be modified by a factor of 0.7 for temporary building with
design life less than one year. However, Buildings Department, when reviewing
the design wind pressure for hoarding in 1999, recognised that the factor of 0.7 is
conservative, as the original intent was that a temporary structure may last for more
than one year though its design life is one year. Buildings Department therefore
issued APP-21 (Demolition Works - Measures for Public Safety) and APP-23 (Hoardings, Covered Walkways and Gantries (including Temporary Access for
Construction Traffic) - Building (Planning) Regulations Part IX) allowed the
design wind pressure to be modified by a factor of 0.37 in hoarding design, as it
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was noted that such hoarding would usually last for not more than three years, with
a probability of exceedance of 63.6%.
Moreover, another factor to be considered in choosing the design wind pressure is
the seasonal effect. The design 3-second gust at gradient height of 500m in the HK
Wind Code is specified to be 78.7m/s (i.e. a design wind pressure of 3.72kPa), and
the highest recorded 3-second gust in Hong Kong was 65.0m/s (i.e. a design wind
pressure of 2.54kPa) in 1999 due to Typhoon York at Waglan Island at a height of
90m above the mean sea level. BS 6399: Part 2 (BSI 1997) allows partial factors to
be used by taking account of seasonal variations in wind speeds and if necessary by
altering a probability factor to accept a greater than usual degree of risk that the
design wind speed may be exceeded.
During summer, it is unlikely that when typhoon signal no. 8 or above is hoisted, en
event will not be cancelled or all the workers will still be required to work on the
grandstand. A common situation is that when a typhoon signal no. 3 is hoisted,
workers are still required to carry out erection or dismantle work and an event will
still be held with the seats occupied. For a typhoon signal no. 3 is hoisted, the
maximum hourly mean wind speed is only 62km/h, which corresponds to a 3-
second gust of 23.94m/s. During autumn or winter, easterly monsoon wind prevails
in Hong Kong. The highest recorded monsoon 3-second gust at Hong Kong
Observatory was only 29.9m/s (i.e. a design wind pressure of 0.54kPa), which
occurred in 1934 at 61m above the mean sea level, and this recorded value is
already the maximum 3-second gust measured in autumn or winter in Hong Kong
over the past 70 years. As a compromise, this paper therefore considers that a
design 3-second gust wind velocity of 23.94m/s (i.e. a design wind pressure of
0.41kPa) to be adopted for the design at a height of 0m-10m for temporary
grandstand that is likely to experience typhoon during its service life, which
provides a conservative estimate of the wind pressure when the grandstand is
occupied or when the grandstand is being erected or dismantled. Project officer
should exercise judgment in deciding the appropriate design wind pressure to suit
the particular case.
3.4.2 Force Coefficient
The HK Wind Code gives the force coefficient with different solidity ratios for open
frame structures. The choice of solidity ratio for such open multiple frame
structures is again controversial, especially whether the upstream frame can shield
the frames behind (Figure 9). As any upstream obstruction to a permanent
structure may be demolished during the design life of the permanent structure, the
HK Wind Code states that no allowance shall be made for the general or specific
shielding of other structures or natural features. BS 6399: Part 2 (BSI 1997) also
states that an estimate of the total wind load can be obtained by summing up the
loads on each individual frame; but admits that such summation may be very
conservative, especially when the frames are dense and shielded as for demountable
grandstands of this paper. Choi (1984) noted that the amount of shielding depends
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on the solidity ratio of the upstream frame and the spacing between frames, and
recommended to reduce the wind force on the downstream frames by a shielding
factor. BRE Special Digest SD5 (Blackmore 2004) also recommends similar
procedures to calculate the shielding factor to be included in calculating the total
wind load for open frame structures. Figure 10 gives the total force coefficient Cf
as a function of the solidity ratio of the upstream frame, the spacing S, the width
of the structure in the direction of the frame, and the number of frames.
Figure 9 Shielding Effect in Open Frame Structures
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Cf
(a) B/S = 2
Cf
(b) B/S = 5
Cf
(c) B/S = 10
Figure 10 Shielding Effect on Force Coefficient Cf for Open Frame Structures
3.4.3 Dickie (1983) mentioned two aspects to be considered in the design of demountable
grandstands to wind loads: possibility of structural damage at high wind speeds
when the grandstand is empty, and increase in load actions at low wind speeds with
spectators present on the structure. �IStructE (2007) recommends three load cases
to be included in the analysis and design:
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1) a high load factor of 1.4 for the wind loading when the grandstand is empty
combined with a load factor of 1.0 for dead load to check foundations;
2) equal load factors of 1.2 for wind, dead, live, and nominal horizontal loads to
check foundations; and
3) equal load factors of 1.0 for all four aforementioned loads to check
deflections.
3.5 Dynamic Load
3.5.1 For the design of any structure subject to dynamic loads the avoidance of resonance
effects is important. Demountable grandstands are relatively flexible structures
which will respond dynamically to spectator movements. In an investigation of the
dynamic response of 40 empty demountable grandstands carried out by Littler
(1996), only one grandstand was reported to have a vertical natural frequency
below 9 Hz. On the other hand, the natural frequencies of the grandstands in the
sway direction were much lower, in a range from 1.8 to 6.0 Hz, the majority being
between 3.0 and 5.0 Hz. With regard to the front-to-back direction, in most cases
the natural frequencies were higher than those in the sway direction, ranging from
2.1 to over 10 Hz.
3.5.2 Littler (1996) also carried out tests in some grandstands in use. In one of the tested
grandstands, a reduction from 2.7 to 1.7 Hz was observed in the sway direction due
to the presence of a passive audience. Horizontal natural frequencies above 4 Hz
for empty temporary grandstands were therefore cited as a recommendation to
avoid the range of maximum dancing frequencies. This would probably include an
allowance to take into account the effect of human-structure interaction for
structures in use. Horizontal natural frequencies above 4 Hz for the empty structure
were also mentioned in BS 6399: Part 1 (BSI 1996) as a design strategy to avoid
significant resonance effects.
3.5.3 The significance of the natural frequencies to the design is related to the possibility
of potential resonance of the structure due to excitation produced by the spectators,
e.g. in pop concerts or sports events. In the cases in which the fundamental natural
frequencies of the structure are such that potential resonance can occur and there is
a potential for synchronized and periodic movements, a full dynamic analysis is
recommended instead of applying nominal horizontal loads. For grandstands which
may be subject to synchronised and periodic crowd movements, the easiest
approach would be to estimate the vertical and horizontal natural frequencies and to
ensure avoidance of significant resonance effects. Ji and Ellis (1997) recommend a
vertical frequency greater than 8.4 Hz and the horizontal frequencies greater than
4.0 Hz for an empty structure to avoid resonance effects. If it is not possible to
avoid the resonance effect in this way, design of the grandstand will require a
detailed analysis to assess the effects of dynamic loads arising from the anticipated
resonance effects. Where resonance is unlikely, the use of a nominal horizontal
load approach as per the recommendations of IStructE (2007) can be used. This
approach will be discussed in the Section 4.
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4 Notional Horizontal Load Approach
4.1 IStructE (2007) introduces the concept of using notional horizontal loads to account
for, spectator action, and geometrical imperfections of frames (e.g. the lack of
alignment of vertical members). The notional horizontal loads are taken as a
percentage of the imposed vertical load. The notional horizontal loads should be
applied in combination with the wind loads. IStructE (2007) recommends a
simplified approach to include the following notional horizontal load (Table 3) to
design the grandstand for the effect induced by different categories of spectator
action.
Table 3 Notional Horizontal Load for
Different Categories of Spectator Action
Category Spectator activity
Notional
horizontal
load
1
Nominal potential for spectator movement, which
excludes synchronized and periodic crowd
movement. Examples include: lectures/exhibitions,
display/shows, athletic events, golf tournaments and
agricultural shows.
6%
2
Potential for spectator movement more vigorous
than Category 1. Category 2 excludes synchronized
and periodic crowd movement in major musical
concerts, and rugby or football matches.
7.5%
3
Stands with a potential for synchronized and
periodic crowd movement and having vertical and
horizontal fundamental frequencies which avoid
resonance effects. An example is at pop concerts
where strong musical beats are expected.
10%
Notes: For notional horizontal loads, the partial factor should be 1.5 for the load
combination case with factored values of vertical dead and imposed loads.
(Source: IStructE 2007)
4.2 Besides the recommendations in IStructE (2007), the HK Loading Code has
recently introduced a requirement on horizontal imposed loads acting on the
grandstands due to crowd movement. Clause 3.8.2 of the HK Loading Code states
that grandstands, stadiums, assembly platforms, reviewing stands and similar, shall
be designed to withstand minimum horizontal imposed loads due to crowd
movement as follows:
(a) for platforms with seats, the following separate load cases (not applied
simultaneously), applied at floor level at each row of seats:
(i) 0.35 kN/m of seating along the line of seats; or
(ii) 0.15 kN/m of seating perpendicular to the line of the seats.
(b) for platforms without seats, 0.25 kPa of plan area applied in any direction.
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4.3 Usually, there will be about 4 rows of seats per 3m width of the structure, and the
notional horizontal loads can therefore be expressed as an equivalent percentage
of the imposed load as follows:
(i) along the line of seats = 4×0.35/3 = 0.47 kPa = 9.3% of the imposed load (5
kPa);
(ii) perpendicular to the line of seats = 4×0.15/3 = 0.2 kPa = 4.0% of the
imposed load (5 kPa).
Therefore, the HK Loading Code has specified a smaller notional horizontal load
(i.e. 4%) perpendicular to the line of seats than that specified in IStructE (2007) (i.e.
6%) for nominal potential of spectator movement, but a larger notional horizontal
load (9.3%) along the line of seats. It should be further noted that for grandstands
without seats, the notional horizontal load is 0.25kPa in any direction, which is
smaller than that along the line of seats for grandstands with seats. However,
where there are no seats, the audiences are expected to erect a larger horizontal
force on the grandstand due to the larger possibility of crowd movement. Moreover,
in the HK Loading Code, the notional horizontal load is set without due
consideration of the different responses of the audiences for difference types of
events, e.g. lectures, football matches or pop concerts. Therefore, project officer is
advised to refer to IStructE (2007), which is more reasonable, and exercise
judgment in choosing the notional horizontal load to suit the particular case,
especially the probability of synchronized crowd movement.
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5. Foundation
5.1 Demountable structures are generally lightweight and loaded for relatively short
periods. Hence, the bearing pressures and settlement of the ground are not usually
a problem, unless the structure will be in use for a long period, in which case a full
engineering assessment of the ground should be made. The use of permanent
foundations (e.g. pad footings) will be unlikely. Temporary pad steel bases will
have to provide the reactions to the applied loadings.
5.2 In addition to the dead and imposed load, there may be uplift forces and lateral
loads on the foundation due to its lightweight. It is therefore necessary to check the
methods of transferring such loads to the ground, usually using ground anchors by
anchor bolts at the support points (Photo 9). Occasionally, ground anchors cannot
be used because of the nature of the ground. For example, it may not be permissible
to puncture asphalt or concrete finishes. The structure should then be designed to
accept kentledge of sufficient weight to resist the factored uplift forces.
Photo 9 Use of Ground Anchor at the Support of the Standard
6. Construction Supervision
6.1 Usually, demountable stands are proprietary products designed, supplied and
installed by specialist contractor employed by the event organizers. The event
organizers may seek technical assistance from our Department to provide technical
advice on the design which has been prepared and submitted by the Registered
Structural Engineer employed by the specialist contractor. However, project officer
should note that since these structures are often quickly erected immediately before
an event, there may only be a short period of time available for the Registered
Structural Engineer employed by the specialist contractor to check the design prior
to submission and to inspect the workmanship prior to use.
6.2 Another critical stage for a demountable grandstand is during construction and
dismantle works, where bracing members have not yet been provided or are being
removed respectively. In such stage, stability is only provided by the moment
carrying capacity of the connections. Project officer should ensure that sufficient
bracing members are still provided to ensure their stability.
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7. Case Study – East Asian Games 2009
7.1 Background
7.1.1 Held once every four years, the East Asian Games is one of the major events in the
Asian international sports arena. In 2009, Hong Kong hosted the 5th
East Asian
Games (EAG). It was the first time for Hong Kong to host such a large-scale
multi-sport international event, and was an important milestone in holding
international sports event for Hong Kong. An opening ceremony was held on 5
December 2009 at the open space outside the Hong Kong Cultural Centre Piazza
facing the Victoria Harbour. In order to achieve the environmental-friendly and
economical objectives of the event, four temporary demountable grandstands of
different sizes were constructed to provide over 1,500 seats for the guests and
audiences for the opening ceremony. Photo 10 shows the front and side elevations
of the largest grandstand. The structural system including the design and analysis of
the largest demountable grandstand will be discussed in the following paragraphs.
Photo 10 Largest Demountable Grandstand at EAG Opening Ceremony
7.1.2 As such demountable grandstands were proprietary products, the procurement
arrangement was that all demountable grandstands were design-and-build items
designed, erected and dismantled by a specialist contractor employed by the
organizer. The specialist contractor was required to engage a Registered Structural
Engineer (RSE) to prepare the drawings and structural calculation for the
grandstands. The RSE was also required to provide site supervision and to check
that the member sizes, spacing, arrangement of bracings, support details of the
structure had been constructed in accordance with the design drawings and made
necessary arrangement to solve the site problems, e.g. discrepancies between the
site conditions and the design drawings. Upon the completion of the erection of the
grandstands, the RSE was required to certify their safety by issuing a checking
certificate. Our Department was requested to provide technical support to the
organizer on the structural stability of the design, erection and dismantle works.
The specialist contractor was given about one-week time to erect the grandstands,
though the design had been submitted to our Department for comment.
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7.2 Structural Layout and Member Capacities
7.2.1 The largest grandstand was of size 28×31m on plan with maximum height of about
10m above the ground level. It provided 1,572 seats for the audiences of the
opening ceremony. The grandstand was assembled by use of portable tiered system
for the seating and proprietary Layher scaffold for the supporting structure. The
Layher scaffold was an allround scaffold system. The standards and ledgers of the
scaffold were circular hollow section of size 49×3.2mm and the bracings of the
scaffold were circular hollow section of size 45×2.3mm. The catalogue of the
supplier contains the safe working load (Table 4 and Figure 11) on them, which
depending the bracing arrangement, their lengths and their bay width.
Table 4 Safe Working Load for Layher Scaffold (Model: Layher Variant II)
Member
Type Member Size
Safe Working
Load (kN) Remark
Standard 49×3.2mm 37.2
(Compression)*
The member capacity provided in
the supplier’s catalogue is the safe
working load for compression.
Member capacity based on the
condition that:
- length of standard = 2m
- one diagonal brace per 3 bays of
standard (i.e. B diagonal brace)
Ledger 49×3.2mm 15.1
(= 22.7/1.5)
The loading provided in the
supplier’s catalogue is the ultimate
capacity. The safe working loads
are obtained by dividing the
ultimate capacity by 1.5.
Safe working loads of ledger and
bracing are lower than that of the
standard as they are controlled by
the connection joint capacity with
the standard
Bracing 45×2.3mm 5.6
(= 8.4/1.5)
Notes: * Tensile capacity of standard is controlled by the connection capacity of
the pins ( = 3/8” approx.) between the upper and lower standards and
the connection tube (see Figure 3).
It should be noted that the safe working load is controlled by the connection joint
capacity between the members and the computer program is difficult to model the
connection joint capacity. Therefore, the safe working load in supplier’s catalogue
instead of that obtained from the computer program will be used in the design.
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(a) For Standard
(b) For Ledger and Bracing
Figure 11 Members Capacity for Model Layher Variant II (Source: http://www.layher.com.au)
7.2.2 The standards were spaced at about 1.5m along the line of seats and about 3m
perpendicular to the line of the seats. The ledgers were spaced at about 2m in the
vertical direction. Type I bracings (as defined in Table 2 of section 2.4) were
added to provide the lateral stability of the structure. Figure 12 shows the
structural arrangement of the members of the demountable grandstand.
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Figure 12 Typical Section of the Largest Demountable Grandstand at
2009 East Asian Games Opening Ceremony
7.2.2 The standards of the demountable grandstand were either rested on the surface of
the existing structure or ground through pad steel bases in order to provide the
reactions to the applied loads. Photo 11 shows the typical details of the bases of
the standard on the supporting ground.
Photo 11 Typical Base of the Standard
7.3 Structural Analysis and Design by the Specialist Contractor
7.3.1 The RSE employed software SPACE GASS (version 10.50b) in the analysis of the
forces in the scaffold, where the connections between ledger and standard and the
connections between bracing and standard were assumed to pin joints, and due to
symmetry, two 2-D models for respectively along and perpendicular to the line of
seats directions were adopted.
Bracing members to
provide lateral stability Ledger
Standard
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7.3.2 In the design submission, the dead load was assumed to be 1 kPa. For the imposed
load, there would altogether 1,572 seats in the largest grandstand of plan size
28m×31m, and the average weight of an audience was 75kgf. Hence, the actual
imposed load on this grandstand would be 1.35kPa. The RSE had therefore taken
the design imposed load as 4 kPa in accordance with the BS 6399: Part 1 (BSI
1997) and Building (Construction) Regulations Table 1 for the usage of assembly
area with fixed seating. Two separate notional horizontal loads (NHL1 and NHL2)
had been considered in the analysis. NHL1 was taken as 1 kPa in accordance with
Table 2.2 of the HK Steel Code, while NHL2 was taken as 6% of the imposed load
in accordance with the recommendations in IStructE (2007).
7.3.3 Wind loads was taken to be the equivalent wind pressure at tropical cyclone
warning signal no.3 and was calculated as 0.41 kPa. However, the wind loads were
assumed to be not to control the design and ignored in the analysis, as the RSE
noted that the notional horizontal force (NHL) due to the dynamic loads would
exceed the wind loads. In addition, the RSE had imposed a restriction that the
occupancy shall be vacant and structures shall be fenced off or dismantled when
typhoon signal of No. 3 or above is hoisted. Therefore, the design case of wind
loads acting together with the notional horizontal force was not required.
Altogether three loading cases have been considered, including DL+LL,
DL+LL+NHL1 and DL+LL+NHL2 for each of the two 2-D models along and
perpendicular to the line of seats.
7.3.4 The design had been carried out by checking the working load against the safe
working load of each member type as provided in the catalogue of the Layher
system (Table 4). The member forces of the steel members were obtained by using
the first order analysis method in the HK Steel Code. The summary of the
maximum member force against the load bearing capacity for each member type is
shown in Table 5. The location of the critical member of standard (i.e. the member
with the highest utilization ratio) is shown in Figure 13.
Notional
horizontal load,
NHL1 = 1 kPa
Notional
horizontal load,
NHL2 = 6% LL
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Table 5 Summary of Maximum Member Forces
Member Type Maximum Axial
Force (kN)
Safe Working
Load (kN)
Utilization
Ratio
Standard 33.44 37.20 0.90
Ledger 7.87 15.10 0.52
Bracing 5.52 5.60 0.99
Double Bracing 7.08 11.20 0.63
Figure 13 Critical Members in the 2-D Model
(showing the tallest frame along the line of seats direction)
7.3.5 With the adopted model, the maximum utilization factor was 0.986 at one of the
bracing members. No dynamic analysis was carried out, and notational horizontal
force approach was adopted to cater for the dynamic effect. To cater for the
uncertainty and to guard against any lateral movement, altogether 6 pairs of Type 6
global bracing members (as defined in Table 2 of section 2.4) (Figure 14) were
added at the request of our Department to increase the stiffness of the grandstands
to lateral loads.
Standard
(Maximum axial
force = 33.44 kN,
section utilization
= 0.90)
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(a) Perpendicular to the Line of Seats Direction
(b) Along the Line of Seats Direction
Figure 14 Added Global Bracing Members
7.4 Construction Supervision
7.4.1 Due to the tight schedule for erection, some of the connections were not completed
according to the approved drawings, and some bracing members were missing or
were not connected to the nodes between the standard and the ledger (Photo 12(a)
and (b)), and the global bracing members were not provided (Photo 12(c)).
Fortunately, such discrepancies were detected during inspection, and additional
labour and materials were deployed to rectify the deficiencies. The rectification and
final inspection were completed in time such that the checking certificate (at Annex
A) to be issued prior to the opening ceremony. Photo 12(d) shows the grandstand
with all works substantially completed.
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Photo 12(a) Misalignment of the Bracing Member with the Nodes
Photo 12(b) Misalignment of the Bracing Member with the Nodes
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Photo 12(c) Grandstand with global bracing members not yet installed and with
many defects to be rectified (taken on 2.12.2009)
Photo 12(d) Grandstand Substantially Completed (taken on 4.12.2009)
7.5 Lessons Learnt
7.5.1 The opening ceremony was successfully held on 5 December 2009 evening, and the
grandstands served their function to provide temporary seating for over 1,500
audiences. The scaffold system could carry the design imposed load, and no
significant vibration was noted by the audiences. Despite these facts, this paper
would summarise the experience in providing technical support to their design,
erection and construction supervision in the following paragraphs.
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7.5.2 Analysis
7.5.2.1 In the submission from of the specialist contractor, the connections between
ledger and standard and the connections between bracing and standard were
assumed to be pinned joints for simplicity. The elastic critical load factor λcr had
not been checked, and the analysis and design was carried out using 1st order
analysis with no due consideration of the 2nd order (P-) effect. Moreover, 2-D
models were used, and hence the out-of-plane buckling mode was not included in
the analysis. Yet, with our subsequent re-calculations (which are discussed in the
following) the design by the RSE is generally in order.
7.5.2.2 Instead of the 2-D model used by the RSE, we have carried out a 3-D analysis of
the same temporary grandstand by using the same design loading. When
compared with the analysis results of the 3-D model with the 2-D model, it is
found that the location of the critical member of standard (i.e. the standard with
the highest utilization ratio) will be shifted to another member due to the
redistribution of loadings between the members in the 3-D model. However, the
value of the maximum compression force obtained from the 3-D model is
33.68kN which is almost the same as that obtained (33.44kN) from 2-D model
under the same loading case of DL+LL+NHL2 (where LL = 4kPa and NHL2 =
6% LL). This shows that the adoption of 2-D model to obtain the design forces is
generally satisfactory for this temporary grandstand. However, project officer
should note that there may be difference in the analysis results between the 2-D
and 3-D models. The location of the critical member of standard in the 3-D model
is shown in Figure 15.
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Figure 15 Critical Members in the 3-D Model
7.5.2.3 We have also carried out an alternative structural analysis of the same temporary
grandstand with a 3-D computer model by using the minimum imposed load of
5.0kPa as stated in the HK Loading Code (though the actual imposed load on this
grandstand being 1.35kPa) to see if there are the difference between the results
from two different analysis and design methods. Moreover, the member forces
are also checked against the safe working loads as stated in the supplier’s
catalogue. The major differences in the analysis and design method between the
RSE’s submission and our subsequent calculations in the following sections are
shown in Table 6.
Standard
(Axial force = 33.68 kN)
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Table 6 Model and parameters adopted in alternative analysis and design
Model and
Parameters
Design Submission from
Specialist Contractor
Alternative Analysis in
this Paper
Computer Model 2-D 3-D
Design Method
Working load against safe
working load in supplier’s
catalogue
Working load against safe
working load in supplier’s
catalogue
Design Imposed
Load 4 kPa 5 kPa
Design Notional
Horizontal Load
6% of the design imposed
load (from IStructE 2007)
9.3% of the design imposed
load along the line of seats;
and
6.0% of the design imposed
load perpendicular to the
line of seats
(from Section 4.3)
Design Wind Load
0.41 kPa
(the equivalent wind load
at tropical cyclone warning
signal no. 3)
0.41 kPa (from Section 3.4)
7.5.2.4 A 3-D computer model of the grandstand is shown in Figure 16. Sections of the
computer model are shown in Figure 17. Structural analysis has then been
carried out to evaluate the structural adequacy of the scaffold system with the use
of computer software SAP2000.
Figure 16 3-D Model of the Demountable Grandstand
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(a) Perpendicular to the Line of Seats Direction
(b) Along the Line of Seats Direction
Figure 17 Typical Sections of the Demountable Grandstand
7.5.2.5 Section 2.6 states that scaffold system for the demountable grandstands has either
column bucking mode or sway buckling mode depending on the bracing and the
axial load on the standard, and that the lowest eigenvalue found by the eigenvalue
analysis may not represent the first sway buckling mode λcr. In the present case,
the maximum deflection of the grandstand is found to be 8.26mm, and the /H
ratio is 1/1370, and it shows that the scaffold system has sufficient bracing
members to become braced frame. Hence, the dominant buckling mode in the
eigenvalue analysis is the local column buckling mode rather than sway buckling
mode.
7.5.2.6 Both the deflection method and eigenvalue analysis were used to calculate the
elastic critical load factor, λcr, of the structure under each load combination. The
eigenvalue computed using the deflection method is 167, which is much greater
than 10 while the eigenvalue analysis gives smallest eigenvalue of 1.997. From
the deflected shape (shown in Figure 18), the mode of buckling with eigenvalue
of 1.997 is a local column buckling mode. Hence, the eigenvalue of 1.997
obtained from the eigenvalue analysis is due to the large axial load on the
members rather than the deflection due to the horizontal load, and the elastic
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critical load factor, λcr, of the structure should be 167. The assumption in the
original submitted design that 2nd order analysis is not required is therefore
justified.
Figure 18 Deflected shape of the scaffold system with eigenvalue of 1.997
7.5.3 Structural Design
7.5.3.1 In the 3-D model design, the dead load was assumed to be 1kPa, and the imposed
load had been taken as 5kPa in accordance with the HK Loading Code for
grandstand, though the actual imposed load on this grandstand was only 1.35kPa.
Moreover, the following notional horizontal loads as stated in Section 7.5.2.3 had
been adopted at floor level at each row of seats:
(i) 9.3% of the design imposed load along the line of seats; or
(ii) 6.0% of the design imposed load perpendicular to the line of the seats.
The design wind pressure was taken as 0.41kPa. In addition, the force coefficient
taking into account the shielding effect should be taken as 0.8 for a solidity ratio
of 0.04 for 16 nos. of frames along the line of seats and 0.7 for a solidity ratio of
0.06 for 11 nos. of frames perpendicular to the line of seats.
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7.5.3.2 This paragraph intends to compare the difference in the results from the original
design with those adopted values in the above paragraphs. The structure has been
checked and designed by 1st order analysis with the loadings given in Section
7.5.2.3. Altogether 12 nos. of load combination have been considered. The
section utilization ratios of the members of the structure under each load
combination are shown in Table 8. Load cases 3 and 4 are the two most critical
load combinations resulting in the maximum section utilization ratios of 1.26 for
the standards, 0.41 for the ledgers and 1.24 for the bracings. The utilization ratios
are obtained from comparing the member forces obtained from the computer
program SAP2000 with the safe working load in supplier’s catalogue. As stated in
Section 7.2.1, the safe working load in supplier’s catalogue has been used for
comparison instead of that obtained from the computer program. The critical
members (i.e. members with highest utilization ratios) are shown in Figure 19.
7.5.3.3 From the analysis results, it can be observed that the maximum section utilization
ratio of standard and bracing had increased significantly from 0.90 to 1.26 (40%
increase) and from 0.63 to 1.24 (97% increase) respectively with the adoption of
the loadings given in Section 7.5.2. Under the critical load combination of DL +
LL + NHL(±Y) for the standard and bracing, the changes in member forces of the
critical standard and bracing member are shown in Table 7 for easy reference.
Table 7 Comparison of member force obtained from alternative analysis
Model and Parameters Member
Member Force (kN) Section
Utilization DL + LL NHL(Y) DL + LL
+ NHL(Y)
Design Imposed Load:
4 kPa
Design Notional
Horizontal Load:
6% of the design imposed
load (from IStructE 2007)
Standard 24.45 9.17 33.62 0.90
Bracing
(Double) 0.07 7.04 7.11 0.63
Design Imposed Load:
5 kPa
Design Notional
Horizontal Load:
9.3% of the design
imposed load (from HK
Loading Code)
Standard 28.99 17.74 46.73 1.26
Bracing
(Double) 0.07 13.76 13.83 1.24
7.5.3.4 When compared with the member forces between the two different design
loadings in Table 7, the member force of the standard due to DL + LL has only
increased by 18.6% (from 24.45kN to 28.99kN) but the member force due to
notional horizontal loads in the direction along the line of seats has increased
substantially by 93.4% (from 9.17kN to 17.74kN). For the bracing, the member
force due to DL + LL remains unchanged but the member force due to notional
horizontal loads in the direction along the line of seats has increased substantially
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by 95.5% (from 7.04kN to 13.76kN). Therefore, the maximum section utilization
ratios of the standard and bracing have increased significantly from 0.90 to 1.26
(40% increase) and from 0.63 to 1.24 (97% increase) respectively mainly because
of the increase in the adoption of the larger notional horizontal load in the
direction along the line of seats as required by the new HK Loading Code.
7.5.3.5 However, it should be noted that the results are quite conservative because:
a) the imposed load has been taken as 5.0kPa although the actual imposed
load was 1.35kPa; and
b) the wind load has been taken as 0.41kPa, which is the highest wind speed
during the hoisting of typhoon signal no. 3, although the opening
ceremony took place in December 2009 and the RSE had specified that the
grandstand should not be occupied during typhoon signal no. 3 or above
was hoisted.
c) the design notional horizontal load along the line of seats is taken as 9.3%
of the design imposed load instead of 6% as recommended by IStructE
(2007).
Among these factors, it can be noted that the increase in the design notional
horizontal load will increase significantly the member force at the bracing. As
stated in Section 4.3, the notional horizontal load in the Hong Kong Loading
Code is larger than the nominal potential of spectator movement stated in IStructE
(2007) (which is more reasonable in the present opening ceremony), and hence
the inadequacy of the original design to cater for such large notional horizontal
force is expected.
Table 8 Maximum Section Utilization Ratio
Load
Case
Load Combination Section Utilization Ratio
Standard Ledger Bracing
1 DL + LL + NHL (+X) 0.83 0.31 0.56
2 DL + LL + NHL (-X) 0.85 0.27 0.43
3 DL + LL + NHL (+Y) 1.26 0.41 1.23
4 DL + LL + NHL (-Y) 1.28 0.41 1.24
5 DL + LL + WL(+X) + NHL(+X) 0.54 0.22 0.39
6 DL + LL + WL(-X) + NHL(-X) 0.56 0.20 0.36
7 DL + LL + WL(+Y) + NHL(+Y) 0.86 0.40 0.98
8 DL + LL + WL(-Y) + NHL(-Y) 0.86 0.40 0.99
9 DL + WL(+X) 0.12 0.05 0.08
10 DL + WL(-X) 0.13 0.04 0.11
11 DL + WL(+Y) 0.17 0.15 0.27
12 DL + WL(-Y) 0.15 0.15 0.27
where DL= Dead Load, LL = Imposed Load, WL = Wind Load,
NHL = Notional Horizontal Load
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(a) Standard
(b) Ledger
Ledger
(Section utilization = 0.41)
Standard
(Section Utilization = 1.26)
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(c) Bracing
Figure 19 Critical Members
7.5.4 Dynamic Effect
7.5.4.1 Section 3.5.3 notes that where resonance is unlikely, the use of a nominal
horizontal load approach can be used to include the dynamic effect due to crowd.
A modal analysis should therefore be carried out to find out the fundamental
frequency of the empty structure in order to eliminate the possibility of
resonance due to such synchronized movement, which is one of the most
common failure reasons of such demountable grandstand. The mode shapes of
the structure at fundamental frequency along and perpendicular the line of seats
directions are shown in Figure 20. The fundamental frequency of structure is
found to be 10Hz which is much higher than the recommended minimum
horizontal frequency of 4.0Hz as recommended by Ji and Ellis (1997) as
discussed in Section 4.4. The fundamental frequency of the structure is therefore
considered satisfactory and no further rigorous dynamic analysis is required.
Hence, a check of the fundamental frequency in both sway direction is
required to ensure that such demountable grandstands will not be
susceptible to the resonance due to the dynamic load by spectators’
movement.
Bracing
(Section utilization = 1.24)
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7.5.4.2 The added Type 6 global bracing elements have also been included in the
dynamic analysis to investigate their effects, and the results are shown in Table
9. It can be seen that the Type 6 global bracing elements have substantially
improved the stiffness of the scaffold systems, confirming the conclusion from Ji
and Ellis (2001).
(a) Fundamental mode in perpendicular to the line of seats direction
(Frequency = 15 Hz)
(b) Fundamental mode in along the line of seats direction (Frequency = 10 Hz)
Figure 20 Fundamental Mode Shapes of the Grandstands
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Table 9 Comparison of Fundamental Frequency With and Without
Type 6 Global Bracing Members
Direction Mode Shape Frequency
Perpendicular
to the line of
seats
15 Hz
20 Hz
Along the
line of seats
10 Hz
12 Hz
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7.5.5 Construction
7.5.5.1 It has been checked that all the standards are under compression in the working
load condition with the minimum compression force of 0.66kN under all load
combinations (Figure 21), and hence no ground anchors or kentledge are required
to tie the standard onto the ground. Project officer should note that when there
are any tensile force found in the standards from the structural analysis, it is
necessary to check on site to ensure that all pins are installed to connect
upper with lower standards and that the tensile force due to wind or lateral
loads can be transmitted throughout the allround scaffold by using the pins.
Figure 21 Member with the Minimum Compression Force
7.5.5.2 The RSE should be required to check the erection at the earliest moment,
and should station himself or his supervisory staff on site when the erection
of scaffold commences, such that any deviation from the approved drawings
should be rectified immediately. Sufficient labour should be deployed by the
specialist contractor to carry out the rectification works, and the programme
of works, though tight, should allow the inspection by the RSE.
Standard
Minimum compression = 0.66kN
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8 References
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Annex A
Sample Checking Certificate
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