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8/6/2019 Butterfly 4 Spacial
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JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS
BUTTERFLY STRUCTURE FOR SPATIAL ENCLOSURES
T.C. TRAN 1, J.Y. RICHARD LIEW 2
1Department of Civil Engineering, National University of Singapore, #02-18, BLK E1A, 1 Engineering Drive 2, Singapore,
117576. Email: [email protected]
Department of Civil Engineering, National University of Singapore, #05-13, BLK E1A, 1 Engineering Drive 2, Singapore,117576. Email: [email protected]
Editors Note: Manuscript submitted 26 October 2005; revision received 8 April 2006; accepted for publication 4September 2006. This paper is open for written discussion, which should be submitted to the IASS Secretariat no later thanAugust 2007.
SUMMARY
A novel tensioned membrane structure of striking form named as the butterfly-shape structural system has beenproposed. Basic design concept and versatility of the system to create various structural forms are explained.
Erection procedure of the structure for fast-track construction is presented. An innovative deployable cable-strut structure is proposed for rapid construction of large span arches. Parametric studies are carried out toinvestigate the structural efficiency of two-wing buttefly structure to obtain the optimum span-depth ratio,number of module, and inclination angle of the arch. Finally, assembly process and cost implication of thebutterfly structure are discussed. Advantages of such structures are explored and their potential uses for spaceenclosure are identified.
Keywords: arch; butterfly structure; cable-strut; deployable structure; membrane structures; spatial structure;structural efficiency
1. INTRODUCTION
Arches are the primary generators of saddle forms
of tensioned membrane structures. Parallel crossed
arches are typically used with repeated spacing as
illustrated in figure 1. This form of structures has
been developed by several manufacturers to be used
as temporary shelters [1,2,3]. Membrane is
spreaded along and stretched in between crossed
arches, thus having vault-like shape which is
formed by almost singly-curved surface. Therefore,
high prestress needs to be introduced in membrane
(e.g. using hydraulic jack [11]) to provide necessary
surface stiffness for resisting loads. Furthermore,end bracings are required to provide lateral stability
for the crossed arches (figure 1).
Peter [10] has introduced the use of very light
inclined arch in his Xanadome where the arch is
kept inclined by fans of cables connected to anchor
points at either side of it. In this paper, another idea
of using inclined arch, which is restrained by
membrane and tensioned cables, is presented.
Various forms of a butterfly-shape membrane
structure are proposed as an alternative to
conventional shelters using parallel crossed arches.
The inclined arches are arranged as the boundary ofmembrane which provides space enclosure. Due to
the inclined arches, the curvature of the membrane
increases and thus is more effective in resisting
loads. In addition, more attractive shapes are
created rather than regular forms as in parallel
crossed-arch structures.
Apart from that, the self-weight of inclined arches
helps to tension the membrane during erection.
Hence, membrane can be pre-tensioned by using
cables instead of using hydraulic jack. The
deployability of butterfly structure to open andtension the membrane with the use of inclined
arches and cables helps to reduce erection time and
cost. The use of deployable cable-strut structures
[4] can provide very large span arches and can be
easily transported and erected on site.
Furthermore, by connecting the peaks of two
adjacent inclined arches together and replicating
this pair of inclined arches longitudinally, the
length of the structure can be extended to form a
vault. The lateral stability of structure is provided
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VOL. 47 (2006) No. 3 December n. 152
Anchor cables
Top cablesArch Membrane
Anchor pointPin connection at support
Figure 2.Two-wing butterfly structure
without the need of additional bracings and the
whole structure can be deployed in an accordion
mechanism.
By combining either identical or different butterfly
structures together, various structural forms of
different shape and size for space enclosures can be
created.
2. BASIC CONCEPT
Butterfly structure is formed by three major
components which are the inclined arches, the
cables or struts, and the membrane. The key
concept of the structure is to use inclined arches to
form the membrane boundary. A typical butterfly
structure is the one with two inclined arches, or two
wings, which looks like a butterfly spreading its
wings as shown in figure 2.
The inclined arches are pin-connected and free to
rotate about the hinge supports. Membrane is
attached along these arches, spreading between
them to provide space enclosure. A fan of cables is
radiated from the outside anchor point to the
connecting joints on each arch.
When the structure is opened to its final
configuration, membrane is stretched to achieve its
designed shape and prestress. Cables are tensioned
against the anchor points to pull down the inclined
arches. Hence, the arches are kept inclined in space
by the balance of forces among the self-weight of
the arches, tensioning forces in cables and
prestressing forces in membrane. Self-weight of
inclined arches helps to reduce the tensioning forces
applied on anchor cables to stretch the membrane. It
also minimizes the requirements for anchor point
and foundation to prevent significant loss of
prestress. On the other hand, membrane also
provides lateral restraint to the arches to resist
imposed load.
Top cables are added in between adjacent inclined
arches when the structure is in the deployed
configuration (figure 2). These cables are designed
to ensure the stability of structure if accidental
damage happens to the membrane. Alternatively,
stability of the inclined arch can be maintained by
membrane and struts instead of anchor cables. In
this case, top cables can be removed as the struts
are also designed to support self-weight of the
arches if damage happens to the membrane. This
will be discussed in section 6
End bracing
Crossed archesMembrane
Figure 1. Conventional Tensioned membrane structure using parallel crossed
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3. VERSATILITY
Based on the design concept as described, various
forms of butterfly structure can be achieved by
combining the inclined arches in different ways to
suit the shape and size of applications.
For applications of large area in two dimensions,
inclined arches are arranged in regular polygon to
create the boundary for stretching the membrane
between the arches. Each inclined arch is called a
wing of the structure. Figure 3 shows the butterfly
structures with three and four inclined arches (or
three and four wings) which are arranged in regular
triangle and square grids respectively.
Basically, the larger the area needs to be covered,
the more inclined arches the structure requires.However, butterfly structures with more than two
wings have fairly low profile in elevation and flat
membrane surface at the center (figure 3).
Therefore, small valley cables are required to
connect the peak of each arch and to meet each
other at center of membrane to pull the fabric
upward as illustrated in figure 4. These valley
cables help to increase the clear height of the
structure and to provide greater articulation form of
membrane at the center. This helps to drain off rain-
water from the structure.
The inclined arches provide an alternative form to
the conventional shelter using equally spaced
crossed arches. Each inclined arch is sloped
downward to the adjacent arch so that their peaks
meet at a tangent and are connected together (figure
5a). This design provides lateral stability to the
whole structure without the need of bracing.
Furthermore, with the use of ground beam, the
whole structure can be pulled and deployed to
reduce the construction time and cost. Deployment
mechanism of the structure will be discussed in the
subsequent section.
Alternatively, the cable-fans can be replaced by a
system of truss and struts to provide clear entrances
at the two ends (figure 5b). The inclined arches at
the two ends are designed as a plane curved truss to
increase their stiffness. When the structure is pulled
to its final configuration, the inclined struts on
ground beam are connected to the curved trusses to
provide lateral stability. After that, anchoring cables
can be removed to provide clearance at the two
entrances.
(a)
(b)
Figure 3.Three-wing (a) and four-wing (b) butterflystructures
Similarly, it is possible to create multiple three-
wing and four-wing butterfly structures (see figure
6) based on the same assembly process described
Top cables
Top cablesAnchor cables
Anchor cables
Valley cables
(a)
(b)
Figure 4.Three-wing (a) and four-wing (b)butter l structures with valle cables
Valley cables
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VOL. 47 (2006) No. 3 December n. 152
(a) Stabilized by cable-fans
(b) Stabilized by inclined struts
Inclined
struts
Curved truss
Ground beam
Figure 5.Multiple two-wing butterfly structure
Anchor cables
above. By combining different butterfly structures
together, many structural forms of various shape
and size can be achieved.
4. STRUCTURAL CONCEPT
One of the main structural elements of butterfly
structure is the inclined arch. The shape of arches is
chosen to be semi-circular to compensate the low
clear height Hc of structure due to the slope of arch
and the curvature of membrane. The radius R of
each arch is equal to its span length. The inclination
angle of the arch depends on the requirement of
clear height and covered area. Two-wing butterflystructure needs small inclination angle to increase
the covering area. Butterfly structures with more
than two wings often need larger inclination angle
to increase the peak height Ha of the inclined arches
and the clear height Hc of structures. Optimal
inclined angle will be studied in section 8.
The radius R of arch, inclination , peak height Ha
and clear height Hc are illustrated in figure 7. The
arch is divided into a number of segments so they
can be easily transported. These segments are
jointed together by using end plates and bolt
connections. The arch can be made of high strength
steel or alloy aluminum to reduce self-weight.
Tubular members are employed for the arches due
to their superior performance in resisting
compression and torsional forces. For very large
span arch, deployable truss is employed and will be
discussed in detail later.
Figure 7.Side elevation of butterfly structure
Anchor cables are arranged symmetrically in fan-
shape. Each inclined arch is pulled by three or more
anchoring cables depending on its applications.
Twin cables can be used for anchoring cables to
improve the resilience of the structure to accidental
damage of cables. Anchor cables are connected to
anchor point through turnbuckles so that the
tensioning forces can be adjusted. Besides anchorcables, butterfly structure has top cables, valley
cables and boundary cables. The roles of top and
valley cables are mentioned in section 3. Boundary
cables are used at the edge of membrane for
reinforcing and facilitating membrane erection. Top
and valley cables are high strength strands while
boundary cables can be stainless steel of Kevlar
wire rope.
Membrane can be PVC coated polyester or PTFE
coated fiberglass fabric depending on the
requirement of each application. PVC coated polyester fabric has high flexibility, relative high
strength and low price. PTFE coated fiberglass
fabric offers greater tensile strength and life
expectancy at the expense of higher cost. The
membrane is divided into patterns parallel to the
main curvature. With the patterning layout, strips
are cut from fabric rolls and then welded together to
form the membrane shape.
The foundations should be strong enough to prevent
significant loss of prestress in anchor cables and
Figure 6. Multiple three-wing butterfly structure
a
R
arch
membrane
Cable
Ha
Hc
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thus in membrane. If the ground is weak, the use of
ground beam will minimize the time and cost for
preparing the foundation. In addition, the use of
ground beam makes the structure easily relocatable.
Figure 8 shows a display model of two-wing
butterfly structure with the use of ground beam.
Apart from that, in multiple two-wing butterfly
structure, ground beam provides the track for
structure to slide during the deployment.
5. MECHANISM FOR DEPLOYMENT
Deployment of butterfly structure is made possible
by rotating the arches perpendicular to their plane
by providing a rotatable pin at the supports.
In folded configuration, all arches are raised upvertically. During deployment process, the arches
are rotated outward gradually by using temporary
masts so as to open the membrane. When
membrane is stretched, it will restrain the rotation
of the arches. The tensioned membrane thus is
acting as the deployment restraint of the butterfly
wing. Anchor cables then are used to pull the arches
to tension the membrane further. When the arches
are rotated to their designed inclination angle, the
membrane will achieve its designed prestress.
Anchor cables are secured to the anchor points to
lock the deployment of the structure. Figure 9
illustrates the deployment process of a three-wing
butterfly structure.
For multiple two-wing butterfly structure, the
deployment is performed efficiently in the manner
of an accordion movement. The joints at peaks of
the two connecting arches are designed to allow
them to rotate perpendicular to their plane. The
arches are slided along the ground beam during the
deployment. Due to the joint constraint at peaks and
the slidability of the arches, the whole structure can
be deployed simultaneously by pushing the bottom
of two end arches outward. The deployment
mechanism of the structure is similar to that of an
accordion as illustrated in figure 10.
In folded configuration, all arches are gathered
vertically (figure 10a). The two center arches are
translationally restrained while the rest are able to
slide along the ground beam. During the
deployment process, the two end arches are pushed
outward while kept vertically by temporary struts
(figure 10b). The whole structure thus will open in
accordion manner and membrane between the
arches is stretched accordingly. When the structure
is deployed to its final configuration, all supporting
arches are fixed to the ground beam. The two end
arches then are gradually sloped down. After that,
cables are tensioned against the anchor points to
achieve the design prestress in the membrane
(figure 10c).
(b) Arches are rotated about the
hinge support
(c) Membrane is stretched to final
configuration
Figure 9.Deployment process of three-wing butterly structure
(a) Arches are installed upright
Figure 8.Display model of a two-wing butterflystructure
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VOL. 47 (2006) No. 3 December n. 152
6. DEPLOYABLE CABLE-STRUT ARCHES
AS BUTTERFLY WING
For arch with span over 30m, space truss should be
used for the arch to enhance its lateral stability.
However, assembly of conventional space truss is a
time consuming process and thus increasing the
cost of site labour for construction. Vu et al. [4] hasintroduced four types of deployable cable-strut
structures which are capable of rapid transportationand erection on site yet having equivalent weight
and structural efficiency as space truss. In this
paper, a deployable cable-strut structure is proposed
for large span arch of butterfly structure to ensure
rapid site erection and ease of transportation.
The arch is formed by several identical cable-strut
modules connected together. Each module is
constructed from two strut-pyramids and four
scissor-like elements as shown in figure 11.
Deployment concept of strut-pyramid was
explained by Liew & Tran [9] and Vu et al [13]while the scissor-like element is a well known
deployable X-frame proposed by Escrig [14,15].
The joints are specially designed so that they allow
each strut connected to them to rotate freely in a
prescribed plane (figure 11). Therefore, the module
can be folded and deployed efficiently. The
deployment of each module is constraint by the top
and bottom layers of cables as illustrated in figure
11. The final configuration of the module after
deployment is stabilized by attaching and pre-
stressing the central add-in cable.
Deployment of the arch is relied on deployment of
modules. When the arch is deployed, all modulesare deployed simultaneously due to joint constraint.
The deployment process of the cable-strut arch is
illustrated in figure 12.
Figure 13 shows the configuration of a two-wing
butterfly structure using deployable cable-strut arch.
The membrane is attached to upper-middle joints of
modules. With the membrane being continuously
attached, the arches are laterally braced along their
length.
In order to avoid the obstruction to the entrances ofstructure, the center cable-fan is replaced by two
side cable-fans as shown in figure 13. Each cable-
fan, including a safety strut, is radiated from the
anchor point to the upper middle joints of the arch.
Although the safety struts are subjected to tension
forces, they are designed to resist the self-weight of
the arch to prevent catastrophic collapse due to
accidental damage in the membrane. The top cables
Figure 10. Deployment process of
multiple two-wing butterfly structure
(a) Arches are installed
(c) Membrane is stretched to final configuration
(b) Arches are slided along ground beam
Temporary struts
Scissor-like
elements
Top pyramid
Locked by add-
in cable
Underneath
pyramid
Cablesrestraint the
deploymentMiddle joints
Top joint
Bottom joint
Figure 11. Module configuration and deployment (Vu et al. [4,13])
(a) Stowed state (b) Deployed state (c) Final configuration lockedby central cable
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30m
hu
h
hl
Wc
D
Crossed side
Figure 14.Configuration of two-wing butterfly structure with 14 modules and span = 30m
10m
Wu
Wl
hu
h
hlD
Front side
therefore can be removed. The feet of the truss
arches are assembled with a group of four struts
which forms an upside-down pyramid. The vertex
of strut-pyramid is pinned to the ground supports
so that the arches are able to rotate about the
supports (figure 13).
The height of arch is in proportion to its span.
Therefore, unlike small span steel tube arch,
deployable truss arch can be either semi-circular
or arc shape depending on the clear height
requirement of applications. For very large span
enclosure, the membrane may be reinforced by
small valley cables running between the arches, so
that it will be supported at closer interval.
The use of deployable cable-strut system for arch
not only reduces the erection time but also helps
to increase the span of the arch, thus the coveringarea of membrane is widened. Hence, larger clear
space can be created.
7. PARAMETRIC STUDIES
One of the important design parameters of
butterfly structure is the inclination angle of the
arch with respect to the ground plane (figure 14).
Different inclination angles generate different
weights of arch and covered areas of the structure.
Optimal inclination angle should provide the
lightest weight of arch with respect to covered
area of the structure. Due to the requirements of
clear height and covered area of applications as
Figure 12. Deployment of a cable-strut arch
Figure 13. Two-wing butterfly
structure using deployable cable-
Pyramid supporting
HingeSafetystruts
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VOL. 47 (2006) No. 3 December n. 152
well as the architectural aesthetic, the inclined
angle should not be too small or too large. Thus,
in this paper, parametric studies are carried out for
arch with inclination ranging from 40 to 60
degree.
The number of module and the span/depth ratio of
the cable-strut arch are also the important design
parameters. The common way to evaluate
the structural efficiency of the cable-strut arch is
to study its weight-to-strength ratio. In this paper,
the weights of all structural elements that are
designed to resist predetermined load combination
is used as a basis for comparing the cable-strut
arches of different inclination angles, numbers of
module and span/depth ratios
These parametric studies are carried out on a 30mspan two-wing butterfly structure using
deployable cable-strut arch of semi-circular shape
as shown in figure 14. The corresponding length
of the arch is 47.12m. Distance between the
adjacent arch supports is 10m. Safety struts are
connected at the upper-middle joints of the second
modules with respect to supports. The inclination
angles studied are 40, 45, 50 and 60 degree. The
span/depth ratios h/L are chosen to be 15, 20 and25 while the numbers of module are 8, 10, 12 and
14.
The ratio between upper/lower inclination heights
(hu , h l) and upper/lower modular widths (Wu, Wl)is kept unchanged at 0.1, i.e. hu/Wu = hl/Wl = 0.1.The upper width Wu, lower width Wland depth hof the arch are determined directly from
parameters of span/depth ratio and number of
module. Due to the deployment constraint of the
module, the length D of scissor-like elements intwo perpendicular plane of the module should be
equal (figure 14). Therefore, the crossed-width Wcof the module is also dependant on the parameters
of span/depth ratio and number of module.
The upper/lower inclination heights (hu , hl),upper/lower modular widths (Wu, Wl), depth h,length D of scissor-like element and crossed-width Wc are defined as illustrated in figure 14.
For membrane structures, wind force is often the
predominant loading on fabric roof. Based on the
saddle shape of the membrane surface and wind
speed of 35m/s which is commonly used in South
East Asia region, wind uplift force of 0.45kN/m2
and wind downward pressure of 0.15kN/m2
are
adopted for the design of two-wing butterfly
structure [16]. The wind forces are applied
perpendicular to the membrane surface.
Due to the eccentricity of scissor-like elements
meeting at the central joint, square hollowsections are preferred for all struts of arch to resist
torsion/moment arising from joint eccentricity.
Struts are made of steel of design strength
275N/mm2
and modulus of elasticity
210000N/mm2. Cable are high strength strand
with breaking stress 1089 N/mm2
and modulus of
elasticity 145000 N/mm2.
PVC coated polyester fabric is used for membrane
due to its high flexibility. The fabric has a
breaking tensile strength of 84000 N/m and
modulus of elasticity of 420000 N/m in both warpand weft directions. Prestress are introduced to the
membrane fabric to stabilize it, pull out wrinkles,
and prevent the fabric from slackening when
experiencing loads. Prestress level in the
membrane should not be lower than minimum
requirement while ensuring that the stresses
induced in membrane by applied loads should not
exceed allowable stress which is 1/4 to 1/8 of
breaking strength. Commonly, membrane
prestress ranges from 10-20% of allowable stress.
In this case, prestress level of 150daN/m is
applied in two major curvature directions of the
membrane surface.
Membrane analysis is a geometrically nonlinear
problem. Conventional nonlinear analyses that
capture the nonlinear response of membrane
separately from the supporting system [5] are
inadequate when the structure is subject to
significant deflection [8]. In this study,
geometrically nonlinear response behaviour of
membrane with support flexibility effect is
captured directly using nonlinear analysis
software developed by Gerry [7]. More details on
this geometric nonlinear analysis can be found in
Refs. [6,9].
The following procedure has been adopted for the
design of butterfly structure.
1. Only one section size is selected for eachgroup of struts and cables in the structure.
2. Form-finding process is performed usingForce density method to find the initial
equilibrium shape of structure [6].
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Figure 15. Self-weight versus inclination angle of two-wing butterfly structure with span of 30m, 12 modules,
span/depth = 20
13.00
13.50
14.00
14.50
15.00
15.50
35 40 45 50 55 60 65
Inclined angle a (degree)
Totalself-weight(kg/m
2)
3. Geometric nonlinear analysis [9] is performedwith two load combinations of wind uplift and
wind pressure to calculate member forces.
4. Section capacity and member buckling ofstruts and cables are checked against the
ultimate limit state. Membrane stress ischecked whether any part is under
compression or exceeded allowable stress.
Maximum deflection of the supporting
structure is checked against serviceability
limit state. In this study, the maximum
deflection limit of L/200 is adopted.
5. Resize members if necessary and repeat fromstep 2.
The membrane shape of structure after form
finding is shown in figure 14
8. OPTIMAL DESIGN PARAMETERS
Parametric studies show that the optimum
inclination angle of the arch occurs at about 45
degree (figure 15). For small inclination angle, the
membrane area is large, resulting in large applied
wind load and thus large forces induced in
structural members of the arches. As a result,
large member sizes of struts are required, leading
to the high self-weight of the arches. When
inclination angle increases, the covered area and
membrane area are reduced. However, thedecrease of member forces in arches due to
loading reduced is more significant and thus
resulting in smaller ratio of self-weight/covered
area of the structure. When inclination angle
exceeds 45 degree, the ratio of self-
weight/covered area starts to increase in spite of
the decrease of member forces. This is because
the covered area of membrane is narrowed
significantly as compared to the self-weight
reduction.
Parametric studies also show that the optimum
number of module falls in range of 12 to 14 while
the optimum span/depth ratio occurs around 19 to
21 as illustrated in figure 16
Since the major action in the arch is compression
force, the effective length of struts has significant
influence on their strength. For the same number
of module, the increase of span/depth ratio
reduces the buckling length of struts in the arch,
resulting in small member size required and thus
lower self-weight. When the span/depth ratio
becomes large, the arch becomes slender in plane
and serviceability limit will govern the design.
Hence larger member sizes are required, resulting
in higher self-weight. The minimum weight of
structure occurs at span/depth ratio of 19 to 21.
Different number of module also influences the
self-weight of structure significantly. The increase
in number of modules will reduce the buckling
length of struts but also increase the number of
joints and members. On the other hand, crossed
width Wc of module also reduces with the increasein number of module, causing the arch to be
slender out of plane. Therefore, it can be seen
from figure 16 that self-weight of structure is
reduced considerably when number of moduleincreases from 8 to 12 due to the decrease in
member buckling length. However, the self-
weight of structure does not reduce much and
starts increasing with the increase in number of
module. Apart from that, larger number of module
will create more connections and thus inverse the
fabrication cost. Therefore, optimum number of
module falls in range of 12 to 14.
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VOL. 47 (2006) No. 3 December n. 152
The relationship between average width/gross
height ratio (W/H) of module and self-weight ofthe studied two-wing butterfly structure can be
deduced as shown in figure 17. The gross height
and average width are defined asH = hu + h + hl
and W= (Wu + Wl)/2 respectively (figure 17). Itcan be seen that optimum W/Hratio is about 1.7.This ratio can be used as reference to determine
the optimum number of module and span/depth
ratio for different butterfly structures.
9. ASSEMBLY
The assembly process of butterfly structure takes
place in the following subsequent steps:
a. Ground beam, if required, is laid out andsecured to the ground using anchor bolts.
b. Tube arches are assembled from segmentson the ground. For deployable truss arch,
the arch is laid on its side and deployed onthe ground from bundle to its final
configuration (figure 18).
c. All arches are raised up and kept standingvertically by using temporary masts and
cables.
d. Membrane and valley cables (if any) areloosely attached to the arches.
Figure 16. Self-weight versus span/depth ratio for different number of module of two-wing butterfly
structure with s an o 30m and = 45
12
14
16
18
20
22
24
10 15 20 25 30
Span/depth ratio
Totalself-weight(kg/m2)
8 modules10 modules
12 modules14 modules
30m
45
12.00
14.00
16.00
18.00
20.00
1.4 1.6 1.8 2 2.2 2.4
W/H ratio
Totalself-weight(kg/m2
)
Figure 17. Self-weight versus W/H ratio of two-wing butterfly structure with span of 30m and = 45
30m
45
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e. Arches are gradually sloped down by usingtemporary masts. Cables fans are then
tensioned by turn-buckles against anchor
points until achieving design prestress in
concave direction of membrane (figure
19).
f. Safety struts (if any) are assembled. Edgecables and valley cables (along convex
curvature, if any) are tensioned until the
design prestress in convex direction of
membrane is achieved (figure 19).
10. COST IMPLICATION
Construction time is one of the factors which have
great influence to the cost of a structure. Due to its
deployability, butterfly structure possesses the
advantage of rapid erection compared to
conventional structures. In addition, cranes andscaffolds which are the major expense of
construction are often not necessary for erecting
butterfly structure. With the use of deployable
cable-strut arch, rapid erection of large span
structures can be accommodated with aesthetic
appearance.
High strength fabric is often costly. The anticlastic
curvature of butterfly structure enables the use of
lighter and lower strength fabric since the tension
in the materials is reduced as a result of the
surface curvature. The temporary impermanent
character of the structure also lowers the cost of
assembly, requiring less labour force involved.
The structure can be conveniently dismantled and
reused. With the use of ground beam, the whole
structure can be moved on wheels on hard
surfaces so that it can be relocated.
The lightweight and flexibility character of
membrane structure enables butterfly structure to
be packed and shipped in standard containers,
resulting in lower transportation cost. Butterfly
structure can be used for large space enclosure
such as amphitheatres, exhibition halls, etc. It also
aims at military and emergency applications
which often require rapid installation on site.
11. CONCLUSIONS
A new form of tensioned membrane structures has
been introduced. Based on the concept of inclined
arches, different butterfly-shape structures can be
created. By combining either identical of different
butterfly structures in an accordion manner, many
structural forms of various shape and size can be
achieved.
Parametric studies were carried out on 30m span
of two-wing butterfly structure using deployable
truss arch of semi-circular shape. It is found that
optimum inclination angle of the arch is about 45
degree while optimum number of module and
span/depth ratio of the arch fall in ranges of 12 to
Figure 18. Side deployment of the cable-strut arch
Edge cables
Figure 19.Pretensioning of membrane usingcables
Anchorcables
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VOL. 47 (2006) No. 3 December n. 152
14 and 19 to 21 respectively. The module average
width/gross height ratio of 1.7 can be used as
reference to determine optimal design parameters
of different butterfly structures in order to achieve
lightweight design.
Due to the light weight of membrane structure,
butterfly structure can be packed and shipped in
standard containers. Furthermore, the
deployability of butterfly structure allows it to be
erected rapidly on site. A novel deployable
tension-strut structure has been proposed for large
span arch to ensure the rapid erection and
transportation of butterfly structure. The structure
is thus cost effective by saving construction time
and manpower.
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