BUTTERFLY STRUCTURE FOR SPATIAL ENCLOSURES

Transcription

1 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, tranchitrung@nus.edu.sg 2 Department of Civil Engineering, National University of Singapore, #05-13, BLK E1A, 1 Engineering Drive 2, Singapore, cveljy@nus.edu.sg Editor s Note: Manuscript submitted 26 October 2005; revision received 8 April 2006; accepted for publication 4 September This paper is open for written discussion, which should be submitted to the IASS Secretariat no later than August 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 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 of membrane 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 and tension 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

2 VOL. 47 (2006) No. 3 December n. 152 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 Membrane Crossed arches End bracing Figure 1. Conventional Tensioned membrane structure using parallel crossed Arch Top cables Membrane Anchor cables Anchor point Pin connection at support Figure 2. Two-wing butterfly structure

3 JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS 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 rainwater 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. Anchor cables (a) Top cables Top cables Anchor cables (b) Figure 3. Three-wing (a) and four-wing (b) butterfly structures Valley cables (a) Valley cables (b) Figure 4. Three-wing (a) and four-wing (b) butterfly structures with valley cables Similarly, it is possible to create multiple threewing and four-wing butterfly structures (see figure 6) based on the same assembly process described

4 VOL. 47 (2006) No. 3 December n. 152 above. By combining different butterfly structures together, many structural forms of various shape and size can be achieved. 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. (a) Stabilized by cable-fans Anchor cables Curved truss membrane R Cable Inclined struts (b) Stabilized by inclined struts Ground beam Ha arch α a Hc Figure 5. Multiple two-wing butterfly structure Figure 7. Side elevation of butterfly structure Figure 6. Multiple three-wing butterfly structure 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 H c 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 α of the arch depends on the requirement of clear height and covered area. Two-wing butterfly structure 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 H a of the inclined arches and the clear height H c of structures. Optimal inclined angle α will be studied in section 8. The radius R of arch, inclination α, peak height H a and clear height H c are illustrated in figure 7. The arch is divided into a number of segments so they can be easily transported. These segments are Anchor cables are arranged symmetrically in fanshape. 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 anchor cables, 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

5 JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS 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. Figure 8. Display model of a two-wing butterfly structure 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). 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 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 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. (a) Arches are installed upright (b) Arches are rotated about the hinge support 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 (c) Membrane is stretched to final configuration Figure 9. Deployment process of threewing butterly structure

6 VOL. 47 (2006) No. 3 December n. 152 (a) Arches are installed upright Temporary struts (b) Arches are slided along ground beam (c) Membrane is stretched to final configuration Figure 10. Deployment process of multiple two-wing butterfly structure 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] has introduced four types of deployable cable-strut structures which are capable of rapid transportation and 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 prestressing the central add-in cable. Deployment of the arch is relied on deployment of modules. When the arch is deployed, all modules are 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 of structure, the center cable-fan is replaced by two side cable-fans as shown in figure 13. Each cablefan, 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 Cables restraint the deployment Top joint Top pyramid Middle joints Locked by addin 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])

7 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. Hinge Pyramid supporting Figure 13. Two-wing butterfly structure using deployable cable- Safety struts 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 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 covering area 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 α 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 W u h u h α 10m D W l h l Front side W c h u h 30m D Crossed side h l Figure 14. Configuration of two-wing butterfly structure with 14 modules and span = 30m

8 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 30m span 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 α studied are 40, 45, 50 and 60 degree. The span/depth ratios h/l are chosen to be 15, 20 and 25 while the numbers of module are 8, 10, 12 and 14. The ratio between upper/lower inclination heights (h u, h l ) and upper/lower modular widths (W u, W l ) is kept unchanged at 0.1, i.e. h u /W u = h l /W l = 0.1. The upper width W u, lower width W l and depth h of 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 in two perpendicular plane of the module should be equal (figure 14). Therefore, the crossed-width W c of the module is also dependant on the parameters of span/depth ratio and number of module. The upper/lower inclination heights (h u, h l ), upper/lower modular widths (W u, W l ), depth h, length D of scissor-like element and crossedwidth W c 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/m 2 and wind downward pressure of 0.15kN/m 2 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 hollow sections are preferred for all struts of arch to resist torsion/moment arising from joint eccentricity. Struts are made of steel of design strength 275N/mm 2 and modulus of elasticity N/mm 2. Cable are high strength strand with breaking stress 1089 N/mm 2 and modulus of elasticity N/mm 2. PVC coated polyester fabric is used for membrane due to its high flexibility. The fabric has a breaking tensile strength of N/m and modulus of elasticity of N/m in both warp and 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 each group of struts and cables in the structure. 2. Form-finding process is performed using Force density method to find the initial equilibrium shape of structure [6].

9 JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS 3. Geometric nonlinear analysis [9] is performed with two load combinations of wind uplift and wind pressure to calculate member forces. 4. Section capacity and member buckling of struts and cables are checked against the ultimate limit state. Membrane stress is checked 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 from step 2. The membrane shape of structure after form finding is shown in figure OPTIMAL DESIGN PARAMETERS Parametric studies show that the optimum inclination angle α 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, the decrease 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 selfweight/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 W c of module also reduces with the increase in 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 module increases from 8 to 12 due to the decrease in member buckling length. However, the selfweight 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 Total self-weight (kg/m 2 ) Inclined angle a (degree) Figure 15. Self-weight versus inclination angle of two-wing butterfly structure with span of 30m, 12 modules, span/depth = 20

10 VOL. 47 (2006) No. 3 December n. 152 Total self-weight (kg/m 2 ) Span/depth ratio 45 8 modules 10 modules 12 modules 14 modules 30m Figure 16. Self-weight versus span/depth ratio for different number of module of two-wing butterfly structure with span of 30m and α = Total self-weight (kg/m 2 ) m 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 height ratio (W/H) of module and self-weight of the studied two-wing butterfly structure can be deduced as shown in figure 17. The gross height and average width are defined as H = h u + h + h l and W = (W u + W l )/2 respectively (figure 17). It can be seen that optimum W/H ratio 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 and secured to the ground using anchor bolts. b. Tube arches are assembled from segments on the ground. For deployable truss arch, the arch is laid on its side and deployed on the ground from bundle to its final configuration (figure 18). c. All arches are raised up and kept standing vertically by using temporary masts and cables. d. Membrane and valley cables (if any) are loosely attached to the arches.

11 JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS e. Arches are gradually sloped down by using temporary 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. Edge cables 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 and scaffolds 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. Figure 18. Side deployment of the cablestrut arch 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. Anchor cables Edge cables Figure 19. Pretensioning of membrane using cables 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

12 VOL. 47 (2006) No. 3 December n 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 [1] Rubb Building Systems. Website: [2] Global Shelters. Website: [3] Big Top Manufacturing. Website: [4] Vu K.K., Liew J.Y.R., and Anandasivam K. 2005, Deployable Tension-Strut Structures: from concept to implementation, Journal of Constructional Steel Research, Vol. 62, Issue 3, p [5] Shaeffer R.E., Tensioned fabric structures: a practical introduction, American Society of Civil Engineers, Task Committee of Tensioned Fabric Structures, [6] Tran T.C., Liew J.Y.R., Effect of support flexibility on Tensioned fabric structures, In the Proceedings of The 17th KKCNN Symposium on Civil Engineering, Thailand, December 13-15, 2004, p [7] Gerry D Anza, Forten2000: a system for Tensile Structures - Design and Manufacturing, Baku Group DT, Italia, [8] Li J. J., Chan S. L., An integrated analysis of membrane structures with flexible supporting frames, Finite Elements in Analysis and Design, 40, 2004, p [9] Liew J.Y.R., Tran T.C., Novel deployable strut-tensioned membrane structures, Journal of the International Association for Shell and Spatial Structure, Paper accepted for publication in Vol 47, No. 1, [10] Peter D., Xanadome, Patent Application No. PCT/GB01/00539, [11] Philip, D., Stressed membrane space enclosure, U.S. Patent No , [12] British Standard Institute, BS 5950, Part 1, Code of practice for design: Rolled and welded sections, BSI, [13] Vu K.K., Tran T.C., Liew J.Y.R., and Anandasivam K., In the Proceedings of Deployable tension-strut structures: Design guildlines, Adaptable 2006 Congress, Eindhoven, the Netherlands. [14] Escrig F. and Valcarcel J., Expandable space frame structures, International Journal of Space Structures, Vol. 8, No. 1&2, 1993, p [15] Escrig F., Valcarcel J. and Sanchez J., Deployable cover on a swimming pool in Seville, Journal of the International Association for Shell and Spatial structure, Vol 37, No. 1, 1996, p [16] Forster B., European Design Guide for Tensile Surface Structures, Tensinet, 2004.