رفتار سازه نامتقارن تیرهای دوکی شکل Tensairity تحت خمش بار

The load bearing behavior of an asymmetric spindle shaped Tensairity girder is studied experimentally and compared to finite element analyses. The influence of the air pressure on the stiffness of the structure is investigated for homogeneous distributed load, asymmetric distributed load and a local load at the center of the structure. An overall good correlation between experiments and finite element predictions was found. An analytical model based on two coupled ordinary differential equations is presented and solved for the homogeneous distributed load case. The role of the form of the Tensairity girder on the stiffness is investigated by comparing the load-deflection behavior of the asymmetric spindle shaped girder with a cylindrical shaped girder.

Inflatable fabric structures made from plain-woven fabrics combine low weight with compact storage volume, ease to deploy and enhanced damping capabilities. Inflated textile beams (airbeams) can be utilized in a variety of forms to achieve a high level of aesthetics and a free-form design concept and applications ranging from roof structures to inflated airplanes have been demonstrated. In order to understand the load bearing behavior of this unconventional structure, the static response of airbeams under bending loads has been studied [1] and [2]. Basically, the airbeam behaves as a thin-walled tube structure for small loads. For higher loads compressive stresses exceed the pretension of the hull and wrinkling has to be taken into account [3], [4], [5] and [6]. Finite elements for predicting the static response of inflated membrane structures were developed [7] and [8] as well as a Timoshenko beam finite element to predict the deflection and wrinkling load of airbeams at high internal air pressure [9]. A major restriction of airbeams is their poor load bearing capacity which drastically limits their application potential. This deficiency can be overcome by the structural concept Tensairity®, where the airbeam is combined with struts and cables [10]. First applications of Tensairity in the field of civil engineering are roof structures and bridges [11]. In Tensairity, the loads are carried by the struts and the cables while the airbeam stabilizes the system. Thus, minimal cross sections for the compression elements can be used. For example, adding 16% mass to an airbeam by adding a strut and a cable, the stiffness and ultimate load of the airbeam could be increased through the Tensairity concept by a factor 3 and 4, respectively [12]. Investigations of the static response of spindle shaped Tensairity structures to axial compressive loads revealed their potential as columns without [13] and with internal fabric webs [14]. Tensairity beams were studied under 3-point bending [15] revealing the influence of the air pressure on the stiffness of the structure. It was shown that the forces in the compression and tension member can be reliably estimated by simple analytical formulas. An analytical model for Tensairity beams without web under homogeneous distributed bending load has been proposed recently for thin compression members [16]. Some first results of the load-deflection behavior of web-Tensairity beams indicate that an analytical model based on beam theory can be applied in this case [12]. This study is devoted to the investigation of the static response of asymmetric Tensairity spindles to different types of bending loads. The test specimen and the experimental set up are described in Section 2. An analytical model based on the theory of beams on elastic foundation is presented in Section 3. Finite element models, outlined in Section 4, were developed in a commercial finite element code taking into account the textile's orthotropic linear elastic material properties and geometrical non-linearity. Results and discussion are given in Section 5 while Section 6 summarizes the main observations of this study and indicates possible further research.

The load bearing behavior of an asymmetric spindle shaped Tensairity girder with 8 m span was investigated. Homogeneous distributed, asymmetric distributed and central local loads were considered. The beam was tested up to an integrated homogeneous load of 18 kN and a maximal stiffness of almost 0.1 kN/mm was obtained for an air pressure of 40 kPa. The experiments show that the spindle shaped girder is stiffer for all load cases and air pressure values compared to the cylindrical girder. Good correlation was found between experimental and FEM results obtained with a commercial software. However, the use of cables poses some challenge in the numerical modeling as the determination of the initial geometry of the cables is not trivial and the pretension of the cables has a strong influence on the deflection of the girders. The cable design demands also for several assumptions and simplifications in the presented analytical model for the homogeneous distributed load case. Nevertheless, the analytical model can well predict the stiffness of the beam as a function of the air pressure. The linear approximation of the analytical model suggests that the vertical displacement of the compression element of the Tensairity girder is basically the sum of the displacement due to the elasticity of the tension element and the displacement due to the pressure dependent constriction of the inflated hull. The stiffness of the girder can be controlled by the air pressure. Tensairity structures are adaptive structures. For local loads and asymmetric distributed loads, the horizontal force is not constant along the length of the chords and corresponding analytical models are subject of further studies. The tested girders were built for a car bridge to demonstrate the outstanding properties of Tensairity such as compact transport volume, fast set up, light weight and high load bearing capacity. The current study shows that reliable predictions of the structural behavior of Tensairity girders can be obtained with numerical and analytical methods fostering the design of civil engineering applications such as roof structures and bridges.