THE ROLE OF FABRICS IN TENSAIRITY - Eawag-Empa Library

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integrity of Tensairity structures can be easily checked by a simple pressure sensor or even by the naked eye. The combination of an airbeam and a cable-strut structure enables new safety concepts for Tensairity far outreaching the safety of conventional pneumatic structures. 3. BASIC TENSAIRITY The basic principles of Tensairity have been described by Luchsinger et al. [3]. As a structural analogy, a Tensairity girder can be compared with a truss girder. Both structures have an upper and a lower chord. In Tensairity, however, the airbeam takes over the role of the vertical and diagonal struts of the truss [4]. The struts in the truss have essentially three functions: load transfer from the upper to the lower chord, reduction of the buckling length of the chord under compression and transfer of shear forces by the diagonal struts. In Tensairity, the load transfer from the upper to the lower chord is accomplished by the pretensioned fabric of the airbeam. Note, that a compressive force is transmitted by a fabric. The buckling length of the chord under compression is reduced due to the stabilization by the airbeam in Tensairity. The chord can be viewed as a beam on an elastic foundation. The buckling length is then a function of the bending stiffness of the chord and the spring constant of the foundation, which in the case of Tensairity is determined by the over pressure [5]. A proper choice of the bending stiffness and the over pressure can lead to a buckling load which is higher than the yield load of the chord, a property we call buckling free compression. Thus, load transfer from the upper to the lower chord and reduction of the buckling length can be well taken over by the airbeam. The transfer of shear forces in Tensairity is less obvious and subject of further studies. In the basic Tensairity model the fabric is treated as an inextensible hull. The non-linear and non-isotropic fabric behavior is not taken into consideration in these models. This approximation is justified to understand the basic concepts of Tensairity. However, the fabric properties do certainly influence the behavior of Tensairity structures. Understanding the fabric specific behavior of Tensairity is important to gain deeper insight into the potential of this new structure. With increasing size of the applications of Tensairity, where testing of a 1:1 prototype is not feasible and a reliable numerical analysis is crucial, a detailed physical model including the fabric specific properties based on experimental and theoretical studies is needed (Fig. 3). Figure 3. The experimental set up for the study of the behavior of Tensairity beams. 4
3. FABRIC EFFECTS IN TENSAIRITY Tensairity beams have essentially the shape of a cylinder or a spindle [6]. The fabric is stressed both in the hoop and longitudinal direction due to the internal over pressure. The ratio of the hoop stress and the longitudinal stress in a cylinder is 2:1. For slender spindles, approximately the same ratio is found. The magnitude of the stress is determined by the over pressure and the radius of the cylinder. Since the fabric in Tensairity is in a biaxial stressed state, biaxial tests are important to investigate the fabric properties for Tensairity. In Figure 4 left, the force-strain response in the warp direction is shown for a biaxial test of a polyamide based fabric [7]. A force controlled load profile with a ratio of 2:1 in warp and weft direction is applied for five load cycles. The total applied force varies between 1.25 kN and 7.5 kN in the warp direction and half of that value in the weft direction. The fabric shows an initial response in the first cycle and gradually converges in further cycles. The load-displacement response of a Tensairity beam under bending load is shown in Fig. 4 right. A spindle shaped Tensairity girder with 5 m length and a central diameter of 0.5 m is used for this experimental investigations in the laboratory (Fig. 3). The fabric of the Tensairity girder is identical to the fabric of the biaxial test. Since this fabric is not airtight, a thin PU foil is embedded. An over pressure of 150 mbar is applied for this test. The upper and lower chords of the Tensairity test beam are made of aluminum. In the experiment, a central bending load is applied by means of a hydraulic piston in three load cycles ranging from 0 kN to 0.9 kN. The fabric adapts to the new load condition during the first load cycle. The load-displacement responses of the second and third load cycle are almost identical. The Tensairity girder also shows a pronounced hysteresis indicating energy dissipation. This hysteresis has to be attributed to the air beam, since the aluminum chords of the Tensairity girder have an elastic behavior. It can result from the fabric or from energy dissipation into the compressed air. The details behind the hysteresis are not yet understood and are subject of further studies. It is in any case an interesting aspect regarding the dynamic properties and damping behavior of Tensairity girders. force [kN] 8 6 4 2 Biaxial fabric test 0 0 1 2 3 strain [%] 4 5 6 load [kN] Figure 4. Experimental data of a biaxial fabric test (left) and a Tensairity beam under central bending load (right). 5 1.2 1 0.8 0.6 0.4 0.2 0 Tensairity beam p = 150 under mbar bending load -0.2 0 10 20 30 40 50 displacement [mm]
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THE ROLE OF FABRICS IN TENSAIRITY - Eawag-Empa Library

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