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Seminar Report 2011

TENSAIRITY 1.INTRODUCTION

The fascination of pneumatic structures begins with the fascination of the sky. On solid ground, pneumatic structures had a first breakthrough as shelters for radar devices after world war 11. The shelter needed to be lightweight, mobile, and deployable in short time and without any metallic parts, ideal requirements for pneumatic structures. Light weight structures are a challenge for the structural engineer and an important step towards a sustainable architecture. The essence of engineering lightweight structures is a careful design of the horse flow within the structure such that minimal material is use for the specific task. Cables under tension are the most efficient way of structural use since the cable strength is independent of the length of cable and solely dependent on the material. However, whenever there is tension, there is compression too. And for compression length matters. The danger of buckling demands for larger cross sections and thus for more materials. As a result columns are heavier and thicker. Pyramids in Egypt, the columns of greek temples,the arches and domes of the romans etc are based on same structrural principle,compression.These buildings used up incredible resources both in terms of money,material and human power.From a structural point of view, compression principle of these buildings has a severe disadvantage:buckling.Buckling couples the load bearing capacity.of a structure with its length.The longer the column,either the less load it can bear,or the larger the diameter needs to be.larger cross sections mean more material which often cannot be utilized to yield limit, thus a waste of resources. The tent structures that are used for housing are light and deployable . Fabrics and ropes , the important elements of tent structure , relay on tension, structurally the most efficient use of a material. The load bearing capacity of example a cable is independent of its length and solely determined by the material properties and cross sectional area. Where tension is, there is

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compression too. Tent structures need poles. And these poles have to with stand buckling . The goal of good light weight structural engineering is to find the optimal interplay between tension and compression. Tension and compression are evenly balanced in the new structural concept TENSARITY. The main advantages of tensairity structures are light weight, fast errection and dismantling and small storage and transportation volume.Given this properties, tensairity is ideally suited for wide span roof structures as well as deployable structures as tents and temporary bridges.

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2.TENSAIRITY 2.1 BASIC PRINCIPLE The basic Tensairity beam consists of three major parts: a cylindrical airbeam under low pressure, a compression element tightly connected to the airbeam and two cables running with different helicity in a spiral form around the airbeam (Fig. 2.1). The cables are connected to each end of the compression element closing the force flow between cables and compression element. The role of the compressed air is to pretension the cables and to stabilize the compression element against buckling. In Tensairity the airbeam has solely a stabilizing function which is the reason that Tensairity can operate with low air pressure. The loads are carried by the cables and the compression element. Therefore, the load bearing capacity of a Tensairity structure is determined by the dimensions of the cables and the compression element. Since no buckling problem arises in the compression element, the material of both the cable and the compression element can be used to the yield limit and therefore in its most efficient way. This is the reason for the outstanding light weight properties of Tensairity.

Fig 2.1 The basic elements of a Tensairity beam.

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2.2 TENSAIRITY BEAM The fundamental Tensairity beam consists of a cylindrical air beam, a compression strut tightly connected with the air beam and two cables spiralled around the air beam and attached at each end with the compression strut. While the cables are pretensioned by the air beam, the buckling problem in the compression strut is avoided due to the stabilization by the air beam. As for a beam on an elastic foundation, the buckling load in the compression strut of the Tensairity girder is independent of its length but relies on the pressure in the air beam.Compression element is of different materials. Steel, aluminium, wood and composite. For composites, sandwich constructions, wood or other anisotropic materials the element is more appropriate. The numerical calculation of the loaddeflection curve for various Tensairity beams with 30 m span is With identical span, slenderness and materials, the Tensairity beam deflects six times less then the original topology under the same load.Air beams are generally made of fabrics and the membrane is able to resist to traction load only. From a material point of view, the cable can be generally considered as elastic. However, the geometry of the cable is involved. The node of the cable element slay on geodesic curve: the shortest path connecting two points on a given surface. The cable, in fact, would naturally find that position .In the case of a cylinder this curve is obviously a spiral. It is very important to place initially the nodes of the cable elements exactly on the geodesic line. Otherwise large cable displacements are engaged even with small live loads.The cable is supported by the membrane through contact elements: these elements have four nodes: one connected to the cable and the others connected to the membrane. Contact elements have a nonlinear response: very rigid spring type response when compression occurs, no reaction if the cable tends to go away from the membrane. Tensairity has inherently a very good damping behaviour. No external dampers must be added to the structure in the case of a 72 meters span footbridge.

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3.ADVANTAGES OF TENSAIRITY STRUCTURES

One problem of Tensairity, and all pneumatic structures, is that the membrane can be damaged leading to an air leak. For Tensairity, we can overcome this problem in several ways. First, as we only have small air pressure, the effect of a hole in the membrane is not so critical. Second, Tensairity beams in civil engineering applications will always be connected to a fan or compressor. This pressure control system is designed such that it can maintain the pressure in the tube even if there are small holes in the membrane. Third, the Tensairity beam can be designed such that it will not collapse under its own weight even with zero pressure by taking advantage of the bending stiffness of the compressive element.

4.TENSARITY AND BIONICS

Very often, nature and technology are considered as two opposite. A very interesting aspect of pneumatic structures is that they are a biological technology. Pressure induced stability is common in nature .The green tissue of plants is stabilized by the turgur, the cell pressure in plants which is 5-10 bar, remarkably high. ‘Equisetum gigantenum‘ is an example of a turger-stabilized system. Pressure induced stability has also been found in worms, in the starfish-feet and sharks. However all these biological system use liquid s as pressurized media while tensarity mainly operates with gases.

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5. ANALYSIS The non-linear geometric and non-linear material analysis must be executed in several steps to reach convergence. In the first phase only the pressure load is applied, using if required the additional spring elements for the membrane as aid. Cables should be prestressed so that all contact elements work during the first phase. The resulting stresses and displacements are the initial values for the second phase where the live load is added to the structure. Live loads should be applied in small subsequent steps. Failure of the structure can be reached in two different ways: First the yield stress is reached, generally in the compression element, or second buckling occurs as demonstrated. For the first case it is enough to get the element resulting stresses under a specified load and verify that they are in the acceptable range. It is not useful to use failure criteria or elastic-plastic constitutive laws for the materials. In Tensairity there is no possibility to redistribute stresses over other structural elements. The structure is statically determinate so the anisotropic nonlinear elastic law is enough. For buckling, the determination of the maximum load is more difficult and involves the bisection method of the Newton-Raphson algorithm. The software divides the load into steps until the critical load is approached. The last converged load-step is approximately the solution. Using the arc-length searching algorithm the real maximum could be determined but generally the difference is not relevant for design purposes.

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Fig.5.1.Buckling of compression element near the support of the tensairity beam

6. APPLICATIONS 6.1 TENSAIRITY DEMONSTRATION BRIDGE As a first demonstration of the power of Tensairity we built a small car bridge with 8 m span and 3.5 tons maximal load (Fig. 6.1). The supporting structure of the bridge is given by two parallel cylindrical Tensairity beams with a diameter of 50 cm each. The membrane of the Tensairity beam is standard PVC coated polyester fabric. Steel cables with 6 mm diameter were used. Due to the moving local load of the car, an extra set of cables winding twice around the tube is added to stiffen the structure in the first and last quarter of the bridge. The compression element is made of a carbon sandwich for demonstration and test purposes. Aluminum or steel would have worked equally well. The two Tensairity beams are covered with wood plates to drive on. These plates do not have any structural function. The working pressure in the tubes as shown in Figure 11 was 400 mbar. Each complete Tensairity beam weights 98 kg. The weight of a HEB steel girder with the same load bearing capacity is 320 kg. A simple air beam with the same dimensions would need a pressure of almost 15 bar for the same load bearing capacity.

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Fig6.1. Tensairity demonstration bridge with 8 m span and 3.5 tons maximal load

The design of the bridge was done in two steps. In a first step, the dimensions of all components were calculated based on our analytical model . In a second step, the bridge was modeled with FEM for fine tuning of the structure. The commercial software ANSYS 7.1 was used [PED04a]. The mesh model of a single 8 m Tensairity beam as well as the calculated longitudinal stress of the membrane are shown in Fig6.2.

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Seminar Report 2011 Fig6.2. FE analysis of the 8 m Tensairity beam. The mesh (top) and the calculated longitudinal membrane stress (bottom) are shown

Next to the light weight property, the fast and easy set up of Tensairity structures is an other important advantage. Assembling of the Tensairity beams of the bridge is very easy. The membrane has to be rolled out, the compression element stuck together and connected with the membrane in this case by means of a keder. In the next step, the cables are positioned and connected with the compression element. Finally, air is pumped into the membrane and the Tensairity beam is complete. The beam can be designed such that no screws or rivets are needed for the assembling allowing a very fast set up. The dismantled Tensairity beam of the bridge can be compactly stored and easy transported. Membrane and cables can be rolled together. The only bending stiff material is the compression element. Here we have divided the compression element into two parts of 4 m each (Fig. 6.3). If transport of the whole beam in a small box is desired, the compression element can be divided into shorter sections. Therefore Tensairity is ideally suited for deployable and temporary structures as tents, shelters and temporary bridges, too.

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Seminar Report 2011 Fig6.3. Dismantled Tensairity beam of the 8 m span bridge. The compression element on the right is the only bending stiff element, which can be divided in short pieces if compact transport in a box is needed

We have also performed ultimate load tests with the Tensairity beams of the demonstration bridge. A frame was constructed to fix the Tensairity beam while it was put under load by means of a hydraulic piston. Two cases were investigated: a central load in the middle of the structure and a load at one quarter of the structure (Fig. 5.4, left). At the central position we were not able to break down the structure due to the limited extension of the piston. However, the maximal applied load was 30 kN. The beam operated still in a completely elastic range as all deformations were reversible by unloading of the structure

Fig6.4. Limiting load test of the Tensairity beam with 8 m span.

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Seminar Report 2011 Deformation of the beam at themaximal applied load of 35 kN shortly before failure (left). Shear failure of the compression element (right).

The measured deformation of the beam for a given load at the quarter position is shown in Fig6.5. An overpressure of 1.2 bar was applied for this test. A maximal load of 35 kN was determined. Slightly above 35 kN, the compression element failed due to the high shear forces at the end of the wooden beam used to distribute the high local forces of the hydraulic piston (Fig. 6.4, right). The membrane remained intact during failure and the airbeam was still air tight. Thus, the Tensairity beam still had a significant load bearing capacity after failure. The experimentally investigated ultimate load of the Tensairity beam was close to the theoretically estimated value. An other important lesson learnt from these tests is, that the limit of the Tensairity structure seems to be predictable. The bending and deformation of the beam at 35 kN was such that a near failure was obvious simply by looking at the structure. This good natured failure behavior is an other advantage of Tensairity structures. The Tensairity test bridge fulfilled all the expectations of this new technology. It clearly demonstrates that real loads can be carried by Tensairity with low structural weight and small overpressure. The basic Tensairity concept of pressure induced stabilization of compression elements has been confirmed. Theory, FE-analysis and the experimental model are in good agreement proofing the soundness of the technology. Compact storage, fast set up and good natured failure behavior in the expected range are other important advantages demonstrated by the test bridge. Based on these properties one can anticipate the huge potential of Tensairity for light weight civil engineering applications such as wide span structures and temporary buildings.

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Fig 6.5 Measured load versus deflection at the piston for the Tensairity beam with 8 m span from the demonstration bridge. The data is for the load at the quarter position(Fig. 6.4, left).

5.2 PARKING GARAGE ROOF While the cylindrical shape was the first Tensairity form investigated, further studies have revealed that spindle shaped Tensairity girders are more efficient and applications such as the roof over the parking garage in Montreux rely on the spindle shape. This membrane roof is supported by 12 Tensairity girders with a span up to 28m. Steel has been used for the upper and lower chord of the Tensairity girder. The same silicon coated glass fiber fabric is used for the covering as well as for the Tensairity girders. The air pressure in the beams is about 100 mbar. The architects in the roof in Montreux made intensive use of the intriguing lightning possibilities of Tensairity. Spotlights with color changing capabilities are mounted on each end of the Tensairity beams. The light shines through glassy end plates into the pneumatic structure and illuminates the Tensairity girders from inside in a surprisingly SSET Karukutty

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Seminar Report 2011 homogeneous way. The color of each Tensairity beam can be dynamically changed and controlled by software enabling interesting light patterns over the whole roof structure.

Fig.6.6 The roof over the parking garage in Montreux

6.3 TENSARITY GIRDERS The machine aspect of Tensairity structures can give a different look on civil engineering structures. In civil engineering, the girder for e.g. a roof structure is designed to withstand the total load which is the sum of the dead load and the live load. While the dead load is constant, the live load is often variable and can depend on wind and snow conditions. In light weight structures, the live load normally dominates the dead load and thus mainly defines the design of the structure. Such a girder is therefore designed for a maximal live load which is normally given by the building regulations. Most of the structures never experience the maximal load during their life time. The

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Seminar Report 2011 price for a nevertheless relative security is that most structures are under almost all conditions way to strong and way too heavy. A Tensairity girder can be adapted to the current load situation simply by pressure variation. This enables an important safety concept for Tensairity. The idea is to design the Tensairity structure in such a way that the load-bearing capacity of the bending stiff elements in the girder is large enough to carry the dead load of the structure even with zero overpressure. This can easily be realized in spindle-shaped Tensairity girders, where the upper and lower chord can be made identical to carry both compression and tension. The role of the compressed air is then to guaranty the stability of the structure under changing live load conditions. In a structure like the parking garage in Montreux, the maximal live load is in the order of a factor 10 higher than the dead load. Thus the philosophy, inherent structural integrity for dead load, adaptiveness to live load can have a real impact on the design and weight of the structure. Since such designed structures do not fail even with zero overpressure under the dead load plus eventually some predefined value of live load, they are not prone to vandalism. Even in case of a complete pressure loss in the Tensairity girder due to a damage in the membrane, there is in almost any case enough time to evacuate people from the building and to take measure to restore the structural integrity, since high live load events are very rare. And since an unusual pressure loss can be even detected by the naked eye, problems with the structural integrity of Tensairity are easy to detect. This is in striking contrast to many conventional structures, where a structural failure often comes completely unexpected. Another possible advantage of the adaptiveness of Tensairity is in scaffolding for e.g. bridges, where the deflection of the scaffold can be kept constant under increasing load by increasing the pressure.

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6.4 TENSARITY ACTORS The adaptiveness of Tensairity enables to use the structure as an actor, where the machine character of this new structural element becomes most obvious. One possible design of a Tensairity actor is a cantilever as shown in Fig. 6.7. The Tensairity cantilever is similar to the set up of Fig. 2.1. However, the compression element lies at the lower side of the airbeam and the two cables spiral only half way around the airbeam. The compression element is made flexible to a certain amount to increase the range of lift of the actor. In Fig. 6.7 on the left, the load still touches the ground and the overpressure in the actor is almost zero. In Fig. 6.7 in the middle, the pressure is increased and an intermediate state of the lift process is shown. Finally, the Tensairity cantilever reaches its final straight position for a higher pressure value as shown in Fig. 6.7 on the right. By releasing the pressure, the load will drop down again under its weight. The lift process is therefore reversible and cycles can be driven. An interesting feature of the actor is, that the highest pressure is needed for the straight position, where the bending moments due to the load are maximal and the forces in the compression and tension element are maximal, too. As the pressure is needed for the stabilization of the compression element against buckling, the stabilization effect increases with the increasing force on the compression element during the lifting process. The Tensairity effect adapts in a constructive way to the changing load conditions.

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Fig 6.7. Demonstration prototype of a Tensairity actor. The load is lifted by increasing the pressure in the Tensairity cantilever.

7. CONCLUSION However, the solution of the vulnerability of pneumatic structures would follow the path of nature: a self repairing membrane.In fact, the self repair mechanisms of plants have been studied and the result give important inputs for a technical solution. These bionics can bring an important added value to Pneumatic Structures and Tensarity Pneumatic Structures have many advantages but also some shortcomings. The research of prospective concepts has freed Pneumatic Structure technology from its shape restrictions by advancing the web technology. Tensarity the most recent development by Air light Ltd. eliminates the sorrows drawback of the limited load capacity of pneumatic structures. These two major improvements of pneumatic structures open up exciting possibilities. Due to its properties tensarity is termed as “biological” technology, hopping that the self-repairing mechanism can be introduced in tensairity structures, leading to a great achievements.

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8.REFERENCES 1. Luchsinger, R.H., Pedretti, A., Steingruber, P. and Pedretti, M., (2008), “The New Structural Concept Tensairity”, New Building materials and construction world, vol.63, no.6, pp.188-195. 2. Luchsinger, R.H., Pedretti, A., Steingruber, P. and Pedretti, M.,(2004), “Light Weight Structures With Tensairity”, New Building materials and construction world, vol.34, no.5, pp.80-81 3. Reinhard, A., Luchsinger, R.H. and Pedretti, M., (2004), “Pressure induced stability: from pneumatic structures to Tensairity”, Journal of Bionics Engineering, vol.1, no.3, 141-148 4. www.tensairity.com, Accessed on 9-8-2008. 5. R.luchsinger @prospective concepts .ch , Accessed on 9-8-2008.

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