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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.

REFERENCES

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butterfly 4 spacial

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