BUTTERFLY STRUCTURE FOR SPATIAL ENCLOSURES
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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
1
Department of Civil Engineering, National University of Singapore, #02-18, BLK E1A, 1 Engineering Drive 2, Singapore,
117576. Email: tranchitrung@nus.edu.sg
2
Department of Civil Engineering, National University of Singapore, #05-13, BLK E1A, 1 Engineering Drive 2, Singapore,
117576. Email: cveljy@nus.edu.sg
Editor’s Note: Manuscript submitted 26 October 2005; revision received 8 April 2006; accepted for publication 4
September 2006. This paper is open for written discussion, which should be submitted to the IASS Secretariat no later than
August 2007.
SUMMARY
A novel tensioned membrane structure of striking form named as the butterfly-shape structural system has been
proposed. 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 to
investigate 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 the
butterfly structure are discussed. Advantages of such structures are explored and their potential uses for space
enclosure are identified.
Keywords: arch; butterfly structure; cable-strut; deployable structure; membrane structures; spatial structure;
structural efficiency
1. INTRODUCTION conventional shelters using parallel crossed arches.
The inclined arches are arranged as the boundary of
Arches are the primary generators of saddle forms membrane which provides space enclosure. Due to
of tensioned membrane structures. Parallel crossed the inclined arches, the curvature of the membrane
arches are typically used with repeated spacing as increases and thus is more effective in resisting
illustrated in figure 1. This form of structures has loads. In addition, more attractive shapes are
been developed by several manufacturers to be used created rather than regular forms as in parallel
as temporary shelters [1,2,3]. Membrane is crossed-arch structures.
spreaded along and stretched in between crossed
arches, thus having vault-like shape which is Apart from that, the self-weight of inclined arches
formed by almost singly-curved surface. Therefore, helps to tension the membrane during erection.
high prestress needs to be introduced in membrane Hence, membrane can be pre-tensioned by using
(e.g. using hydraulic jack [11]) to provide necessary cables instead of using hydraulic jack. The
surface stiffness for resisting loads. Furthermore, deployability of butterfly structure to open and
end bracings are required to provide lateral stability tension the membrane with the use of inclined
for the crossed arches (figure 1). arches and cables helps to reduce erection time and
cost. The use of deployable cable-strut structures
Peter [10] has introduced the use of very light [4] can provide very large span arches and can be
inclined arch in his Xanadome where the arch is easily transported and erected on site.
kept inclined by fans of cables connected to anchor
points at either side of it. In this paper, another idea Furthermore, by connecting the peaks of two
of using inclined arch, which is restrained by adjacent inclined arches together and replicating
membrane and tensioned cables, is presented. this pair of inclined arches longitudinally, the
Various forms of a butterfly-shape membrane length of the structure can be extended to form a
structure are proposed as an alternative to vault. The lateral stability of structure is provided
VOL. 47 (2006) No. 3 December n. 152
without the need of additional bracings and the When the structure is opened to its final
whole structure can be deployed in an accordion configuration, membrane is stretched to achieve its
mechanism. designed shape and prestress. Cables are tensioned
against the anchor points to pull down the inclined
By combining either identical or different butterfly arches. Hence, the arches are kept inclined in space
structures together, various structural forms of by the balance of forces among the self-weight of
different shape and size for space enclosures can be the arches, tensioning forces in cables and
created. prestressing forces in membrane. Self-weight of
inclined arches helps to reduce the tensioning forces
2. BASIC CONCEPT applied on anchor cables to stretch the membrane. It
also minimizes the requirements for anchor point
Butterfly structure is formed by three major and foundation to prevent significant loss of
components which are the inclined arches, the prestress. On the other hand, membrane also
cables or struts, and the membrane. The key provides lateral restraint to the arches to resist
concept of the structure is to use inclined arches to imposed load.
form the membrane boundary. A typical butterfly Top cables are added in between adjacent inclined
structure is the one with two inclined arches, or two arches when the structure is in the deployed
wings, which looks like a butterfly spreading its configuration (figure 2). These cables are designed
wings as shown in figure 2. to ensure the stability of structure if accidental
damage happens to the membrane. Alternatively,
The inclined arches are pin-connected and free to stability of the inclined arch can be maintained by
rotate about the hinge supports. Membrane is membrane and struts instead of anchor cables. In
attached along these arches, spreading between this case, top cables can be removed as the struts
them to provide space enclosure. A fan of cables is are also designed to support self-weight of the
radiated from the outside anchor point to the arches if damage happens to the membrane. This
connecting joints on each arch. will be discussed in section 6
Membrane
Crossed arches
End bracing
Figure 1. Conventional Tensioned membrane structure using parallel crossed
Top cables Membrane
Arch
Anchor cables
Anchor point
Pin connection at support
Figure 2. Two-wing butterfly structure
JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS
3. VERSATILITY ground beam are connected to the curved trusses to
provide lateral stability. After that, anchoring cables
Based on the design concept as described, various can be removed to provide clearance at the two
forms of butterfly structure can be achieved by
entrances.
combining the inclined arches in different ways to
suit the shape and size of applications.
Top cables
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 (a)
triangle and square grids respectively. Anchor cables
Top cables
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 Anchor cables
(b)
other at center of membrane to pull the fabric
upward as illustrated in figure 4. These valley Figure 3. Three-wing (a) and four-wing (b) butterfly
structures
cables help to increase the clear height of the
structure and to provide greater articulation form of
Valley cables
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 (a)
5a). This design provides lateral stability to the Valley cables
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.
(b)
Alternatively, the cable-fans can be replaced by a Figure 4. Three-wing (a) and four-wing (b)
system of truss and struts to provide clear entrances butterfly structures with valley cables
at the two ends (figure 5b). The inclined arches at
the two ends are designed as a plane curved truss to Similarly, it is possible to create multiple three-
increase their stiffness. When the structure is pulled wing and four-wing butterfly structures (see figure
to its final configuration, the inclined struts on 6) based on the same assembly process described
VOL. 47 (2006) No. 3 December n. 152
above. By combining different butterfly structures jointed together by using end plates and bolt
together, many structural forms of various shape connections. The arch can be made of high strength
and size can be achieved. 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.
(a) Stabilized by cable-fans Anchor cables
membrane
Curved truss
R
Cable
Ha
arch
Hc
Inclined
struts α
a
(b) Stabilized by inclined struts Ground beam
Figure 5. Multiple two-wing butterfly structure
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
Figure 6. Multiple three-wing butterfly structure tensioning forces can be adjusted. Besides anchor
cables, butterfly structure has top cables, valley
4. STRUCTURAL CONCEPT cables and boundary cables. The roles of top and
valley cables are mentioned in section 3. Boundary
One of the main structural elements of butterfly cables are used at the edge of membrane for
structure is the inclined arch. The shape of arches is reinforcing and facilitating membrane erection. Top
chosen to be semi-circular to compensate the low and valley cables are high strength strands while
clear height Hc of structure due to the slope of arch boundary cables can be stainless steel of Kevlar
and the curvature of membrane. The radius R of wire rope.
each arch is equal to its span length. The inclination Membrane can be PVC coated polyester or PTFE
angle α of the arch depends on the requirement of coated fiberglass fabric depending on the
clear height and covered area. Two-wing butterfly requirement of each application. PVC coated
structure needs small inclination angle to increase polyester fabric has high flexibility, relative high
the covering area. Butterfly structures with more strength and low price. PTFE coated fiberglass
than two wings often need larger inclination angle fabric offers greater tensile strength and life
to increase the peak height Ha of the inclined arches expectancy at the expense of higher cost. The
and the clear height Hc of structures. Optimal membrane is divided into patterns parallel to the
inclined angle α will be studied in section 8. main curvature. With the patterning layout, strips
are cut from fabric rolls and then welded together to
The radius R of arch, inclination α, peak height Ha form the membrane shape.
and clear height Hc are illustrated in figure 7. The
arch is divided into a number of segments so they The foundations should be strong enough to prevent
can be easily transported. These segments are significant loss of prestress in anchor cables and
JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS
thus in membrane. If the ground is weak, the use of deployment. Due to the joint constraint at peaks and
ground beam will minimize the time and cost for the slidability of the arches, the whole structure can
preparing the foundation. In addition, the use of be deployed simultaneously by pushing the bottom
ground beam makes the structure easily relocatable. of two end arches outward. The deployment
Figure 8 shows a display model of two-wing mechanism of the structure is similar to that of an
butterfly structure with the use of ground beam. accordion as illustrated in figure 10.
Apart from that, in multiple two-wing butterfly
structure, ground beam provides the track for In folded configuration, all arches are gathered
structure to slide during the deployment. 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 8. Display model of a two-wing butterfly (figure 10c).
structure
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 up (a) Arches are installed upright
vertically. 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 (b) Arches are rotated about the
are rotated to their designed inclination angle, the hinge support
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 (c) Membrane is stretched to final
of an accordion movement. The joints at peaks of configuration
the two connecting arches are designed to allow
Figure 9. Deployment process of three-
them to rotate perpendicular to their plane. The
wing butterly structure
arches are slided along the ground beam during theVOL. 47 (2006) No. 3 December n. 152
constructed from two strut-pyramids and four
Temporary struts scissor-like elements as shown in figure 11.
Deployment concept of strut-pyramid was
explained by Liew & Tran [9] and Vu et al [13]
(a) Arches are installed while the scissor-like element is a well known
upright 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
(b) Arches are slided along ground beam
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-
(c) Membrane is stretched to final configuration stressing the central add-in cable.
Figure 10. Deployment process of Deployment of the arch is relied on deployment of
multiple two-wing butterfly structure modules. When the arch is deployed, all modules
are deployed simultaneously due to joint constraint.
The deployment process of the cable-strut arch is
6. DEPLOYABLE CABLE-STRUT ARCHES
illustrated in figure 12.
AS “BUTTERFLY WING”
Figure 13 shows the configuration of a two-wing
For arch with span over 30m, space truss should be butterfly structure using deployable cable-strut arch.
used for the arch to enhance its lateral stability. The membrane is attached to upper-middle joints of
However, assembly of conventional space truss is a modules. With the membrane being continuously
time consuming process and thus increasing the attached, the arches are laterally braced along their
cost of site labour for construction. Vu et al. [4] has length.
introduced four types of deployable cable-strut
structures which are capable of rapid transportation In order to avoid the obstruction to the entrances of
and erection on site yet having equivalent weight structure, the center cable-fan is replaced by two
and structural efficiency as space truss. In this side cable-fans as shown in figure 13. Each cable-
paper, a deployable cable-strut structure is proposed fan, including a safety strut, is radiated from the
for large span arch of butterfly structure to ensure anchor point to the upper middle joints of the arch.
rapid site erection and ease of transportation. Although the safety struts are subjected to tension
forces, they are designed to resist the self-weight of
The arch is formed by several identical cable-strut the arch to prevent catastrophic collapse due to
modules connected together. Each module is accidental damage in the membrane. The top cables
Cables Top joint
restraint the
deployment Top pyramid
Middle joints
Locked by add-
in cable
Scissor-like
elements Underneath Bottom joint
pyramid
(a) Stowed state (b) Deployed state (c) Final configuration locked
by central cable
Figure 11. Module configuration and deployment (Vu et al. [4,13])JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS
Figure 12. Deployment of a cable-strut arch
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
Hinge not only reduces the erection time but also helps
Safety
Pyramid supporting to increase the span of the arch, thus the covering
struts
area of membrane is widened. Hence, larger clear
Figure 13. Two-wing butterfly space can be created.
structure using deployable cable-
7. PARAMETRIC STUDIES
therefore can be removed. The feet of the truss
One of the important design parameters of
arches are assembled with a group of four struts
which forms an upside-down pyramid. The vertex butterfly structure is the inclination angle α of the
of strut-pyramid is pinned to the ground supports arch with respect to the ground plane (figure 14).
so that the arches are able to rotate about the Different inclination angles generate different
supports (figure 13). weights of arch and covered areas of the structure.
Optimal inclination angle should provide the
The height of arch is in proportion to its span. lightest weight of arch with respect to covered
Therefore, unlike small span steel tube arch, area of the structure. Due to the requirements of
deployable truss arch can be either semi-circular clear height and covered area of applications as
Wu
hu
h
hl
D
α
10m Wl
Front side
Wc
hu
h
hl
D
30m
Crossed side
Figure 14. Configuration of two-wing butterfly structure with 14 modules and span = 30mVOL. 47 (2006) No. 3 December n. 152
well as the architectural aesthetic, the inclined and wind downward pressure of 0.15kN/m2 are
angle should not be too small or too large. Thus, adopted for the design of two-wing butterfly
in this paper, parametric studies are carried out for structure [16]. The wind forces are applied
arch with inclination ranging from 40 to 60 perpendicular to the membrane surface.
degree.
Due to the eccentricity of scissor-like elements
The number of module and the span/depth ratio of meeting at the central joint, square hollow
the cable-strut arch are also the important design sections are preferred for all struts of arch to resist
parameters. The common way to evaluate torsion/moment arising from joint eccentricity.
Struts are made of steel of design strength
the structural efficiency of the cable-strut arch is 275N/mm2 and modulus of elasticity
to study its weight-to-strength ratio. In this paper, 210000N/mm2. Cable are high strength strand
the weights of all structural elements that are with breaking stress 1089 N/mm2 and modulus of
designed to resist predetermined load combination elasticity 145000 N/mm2.
is used as a basis for comparing the cable-strut
arches of different inclination angles, numbers of PVC coated polyester fabric is used for membrane
module and span/depth ratios due to its high flexibility. The fabric has a
breaking tensile strength of 84000 N/m and
These parametric studies are carried out on a 30m modulus of elasticity of 420000 N/m in both warp
span two-wing butterfly structure using and weft directions. Prestress are introduced to the
deployable cable-strut arch of semi-circular shape membrane fabric to stabilize it, pull out wrinkles,
as shown in figure 14. The corresponding length and prevent the fabric from slackening when
of the arch is 47.12m. Distance between the experiencing loads. Prestress level in the
adjacent arch supports is 10m. Safety struts are membrane should not be lower than minimum
connected at the upper-middle joints of the second requirement while ensuring that the stresses
modules with respect to supports. The inclination induced in membrane by applied loads should not
angles α studied are 40, 45, 50 and 60 degree. The exceed allowable stress which is 1/4 to 1/8 of
span/depth ratios h/L are chosen to be 15, 20 and breaking strength. Commonly, membrane
25 while the numbers of module are 8, 10, 12 and prestress ranges from 10-20% of allowable stress.
14. In this case, prestress level of 150daN/m is
applied in two major curvature directions of the
The ratio between upper/lower inclination heights membrane surface.
(hu , hl) and upper/lower modular widths (Wu, Wl)
is kept unchanged at 0.1, i.e. hu/Wu = hl/Wl = 0.1. Membrane analysis is a geometrically nonlinear
The upper width Wu, lower width Wl and depth h problem. Conventional nonlinear analyses that
of the arch are determined directly from capture the nonlinear response of membrane
parameters of span/depth ratio and number of separately from the supporting system [5] are
module. Due to the deployment constraint of the inadequate when the structure is subject to
module, the length D of scissor-like elements in significant deflection [8]. In this study,
two perpendicular plane of the module should be geometrically nonlinear response behaviour of
equal (figure 14). Therefore, the crossed-width Wc membrane with support flexibility effect is
of the module is also dependant on the parameters captured directly using nonlinear analysis
of span/depth ratio and number of module. software developed by Gerry [7]. More details on
this geometric nonlinear analysis can be found in
The upper/lower inclination heights (hu , hl), Refs. [6,9].
upper/lower modular widths (Wu, Wl), depth h,
length D of scissor-like element and crossed- The following procedure has been adopted for the
width Wc are defined as illustrated in figure 14. design of butterfly structure.
For membrane structures, wind force is often the 1. Only one section size is selected for each
predominant loading on fabric roof. Based on the group of struts and cables in the structure.
saddle shape of the membrane surface and wind 2. Form-finding process is performed using
speed of 35m/s which is commonly used in South Force density method to find the initial
East Asia region, wind uplift force of 0.45kN/m2 equilibrium shape of structure [6].JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS
3. Geometric nonlinear analysis [9] is performed significantly as compared to the self-weight
with two load combinations of wind uplift and reduction.
wind pressure to calculate member forces.
4. Section capacity and member buckling of Parametric studies also show that the optimum
struts and cables are checked against the number of module falls in range of 12 to 14 while
ultimate limit state. Membrane stress is the optimum span/depth ratio occurs around 19 to
checked whether any part is under 21 as illustrated in figure 16
compression or exceeded allowable stress.
Maximum deflection of the supporting Since the major action in the arch is compression
structure is checked against serviceability force, the effective length of struts has significant
limit state. In this study, the maximum influence on their strength. For the same number
deflection limit of L/200 is adopted. of module, the increase of span/depth ratio
reduces the buckling length of struts in the arch,
5. Resize members if necessary and repeat from resulting in small member size required and thus
step 2. lower self-weight. When the span/depth ratio
becomes large, the arch becomes slender in plane
The membrane shape of structure after form and serviceability limit will govern the design.
finding is shown in figure 14 Hence larger member sizes are required, resulting
in higher self-weight. The minimum weight of
8. OPTIMAL DESIGN PARAMETERS
structure occurs at span/depth ratio of 19 to 21.
Parametric studies show that the optimum Different number of module also influences the
self-weight of structure significantly. The increase
inclination angle α of the arch occurs at about 45
in number of modules will reduce the buckling
degree (figure 15). For small inclination angle, the
length of struts but also increase the number of
membrane area is large, resulting in large applied
joints and members. On the other hand, crossed
wind load and thus large forces induced in
width Wc of module also reduces with the increase
structural members of the arches. As a result,
in number of module, causing the arch to be
large member sizes of struts are required, leading
slender out of plane. Therefore, it can be seen
to the high self-weight of the arches. When
from figure 16 that self-weight of structure is
inclination angle increases, the covered area and
reduced considerably when number of module
membrane area are reduced. However, the
increases from 8 to 12 due to the decrease in
decrease of member forces in arches due to
member buckling length. However, the self-
loading reduced is more significant and thus
weight of structure does not reduce much and
resulting in smaller ratio of self-weight/covered
starts increasing with the increase in number of
area of the structure. When inclination angle
module. Apart from that, larger number of module
exceeds 45 degree, the ratio of self-
will create more connections and thus inverse the
weight/covered area starts to increase in spite of
fabrication cost. Therefore, optimum number of
the decrease of member forces. This is because
module falls in range of 12 to 14.
the covered area of membrane is narrowed
15.50
Total self-weight (kg/m2)
15.00
14.50
14.00
13.50
13.00
35 40 45 50 55 60 65
Inclined angle a (degree)
Figure 15. Self-weight versus inclination angle of two-wing butterfly structure with span of 30m, 12 modules,
span/depth = 20VOL. 47 (2006) No. 3 December n. 152
24 8 modules
10 modules
22 12 modules
Total self-weight (kg/m2)
14 modules
20
18
30m
16
14
45°
12
10 15 20 25 30
Span/depth ratio
Figure 16. Self-weight versus span/depth ratio for different number of module of two-wing butterfly
structure with span of 30m and α = 45°
20.00
Total self-weight (kg/m 2)
18.00
16.00
30m
14.00
45°
12.00
1.4 1.6 1.8 2 2.2 2.4
W/H ratio
Figure 17. Self-weight versus W/H ratio of two-wing butterfly structure with span of 30m andα = 45°
The relationship between average width/gross a. Ground beam, if required, is laid out and
height ratio (W/H) of module and self-weight of secured to the ground using anchor bolts.
the studied two-wing butterfly structure can be
deduced as shown in figure 17. The gross height b. Tube arches are assembled from segments
and average width are defined as H = hu + h + hl on the ground. For deployable truss arch,
and W = (Wu + Wl)/2 respectively (figure 17). It the arch is laid on its side and deployed on
can be seen that optimum W/H ratio is about 1.7. the ground from bundle to its final
This ratio can be used as reference to determine configuration (figure 18).
the optimum number of module and span/depth
ratio for different butterfly structures. c. All arches are raised up and kept standing
vertically by using temporary masts and
9. ASSEMBLY cables.
The assembly process of butterfly structure takes d. Membrane and valley cables (if any) are
place in the following subsequent steps: loosely attached to the arches.JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS
e. Arches are gradually sloped down by using 10. COST IMPLICATION
temporary masts. Cables fans are then
tensioned by turn-buckles against anchor Construction time is one of the factors which have
points until achieving design prestress in great influence to the cost of a structure. Due to its
concave direction of membrane (figure deployability, butterfly structure possesses the
19). advantage of rapid erection compared to
conventional structures. In addition, cranes and
f. Safety struts (if any) are assembled. Edge scaffolds which are the major expense of
cables and valley cables (along convex construction are often not necessary for erecting
curvature, if any) are tensioned until the butterfly structure. With the use of deployable
design prestress in convex direction of cable-strut arch, rapid erection of large span
membrane is achieved (figure 19). 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
Figure 18. Side deployment of the cable- aims at military and emergency applications
strut arch 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.
Anchor Parametric studies were carried out on 30m span
cables
of two-wing butterfly structure using deployable
Edge cables truss arch of semi-circular shape. It is found that
Figure 19. Pretensioning of membrane using optimum inclination angle of the arch is about 45
cables degree while optimum number of module and
span/depth ratio of the arch fall in ranges of 12 toVOL. 47 (2006) No. 3 December n. 152
14 and 19 to 21 respectively. The module average [7] Gerry D’Anza, Forten2000: a system for
width/gross height ratio of 1.7 can be used as Tensile Structures - Design and
reference to determine optimal design parameters Manufacturing, Baku Group DT, Italia,
of different butterfly structures in order to achieve 2002.
lightweight design.
[8] Li J. J., Chan S. L., An integrated analysis
Due to the light weight of membrane structure, of membrane structures with flexible
butterfly structure can be packed and shipped in supporting frames, Finite Elements in
standard containers. Furthermore, the Analysis and Design, 40, 2004, p.529-540.
deployability of butterfly structure allows it to be
[9] Liew J.Y.R., Tran T.C., Novel deployable
erected rapidly on site. A novel deployable
strut-tensioned membrane structures,
tension-strut structure has been proposed for large
Journal of the International Association for
span arch to ensure the rapid erection and
Shell and Spatial Structure, Paper accepted
transportation of butterfly structure. The structure
for publication in Vol 47, No. 1, 2006.
is thus cost effective by saving construction time
and manpower. [10] Peter D., Xanadome, Patent Application No.
PCT/GB01/00539, 2001.
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