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In this paper, the static and dynamic behavior of a cable-stiffened arch is investigated by means of numerical and experimental methods. The pre-tension introducing experiment, the loading experiment and the free vibration experiment are carried out and the experimental results are compared with the numerical analysis. From the pre-tension introducing experiment, it is shown that pre-tension of a cable can be effectively introduced through using length-adjustable struts and a reversed process method. In the loading experiment, the loading ability of the cable-stiffened arch is examined and it is found that the buckling load of the experimental model increases greatly when cable is used. Natural frequency and mode damping ratio from the first mode to the fourth mode are measured by means of the free vibration experiment. Damping ratio increases greatly when cable is used. It is also found that the amplitude of displacement and the pre-tension of cable have influences on the damping ratio.

The usages of tension elements, such as membrane, cables, tension rods and so on, can be classified into three categories. The first one is that tension elements are used as main structural elements in “tension-only” structures, for example, cable nets or tension membrane structures. The shape of a “tension-only” structure should be carefully designed so that pre-tension can be introduced into every part of the structure. The soap experimental method, which was used by F. Otto in shape-finding design in previous times, now can be carried out by using numerical calculation. The second usage of tension elements is found in “tension–compression” structures in which all elements are pin-jointed and no moment exists. Tensegrity [1] or tensegric structure [2] and tension truss [3] belong to this class, or are typical examples of this class. A “tension–compression” structure becomes stable only when pre-tension is introduced. In order to obtain a “tension–compression” structure which can be pre-tensioned, a shape-finding process is also necessary. The third usage of tension elements can be found in cable-stiffened structures, which is the focus of this paper. In a cable-stiffened structure, tension elements are used to stiffen a primary stable structure, which can be a column, a beam or even a single layer lattice shell. Structural properties, such as buckling load, stiffness, stabilization, etc., can be improved greatly through stiffening primary structures with tension elements. For example, a stayed column is much more effective in resisting buckling than a simple column [4], or the maximum moment in a beam can be reduced greatly if a beam string structure is used. For large span space structures, tensegric systems can be used to stiffen thin-walled domical domes [5] and supplementary self-equilibrated tension units are effective in stiffening lattice shells to obtain larger buckling load [6]. A pre-stressed dome with cable stiffeners was numerically investigated [7] and [8], and it was found that the buckling load of the dome increased when stiffeners were used. Many real cable-stiffened structures, a glass grid roof is one example, can be found in [9]. Because the primary structure itself is usually stable, no shape-finding process is necessary in designing a cable-stiffened structure. Tension elements are usually pre-tensioned so that they can be used as compression elements. Several theoretical methods for calculating self-equilibrated stress mode and analyzing pre-tension introducing processes have been suggested [10] and [11]. It is not easy to get both the shape and tension under control in a real construction process. The deformation of a structure in the pre-tension introducing process will cause the change of tension in other cables. A pre-tension introducing method that will not cause large deformation of the structure and can introduce pre-tension effectively is usually expected. In general, there are two kinds of methods for pre-tension introduction. The first one, which is here named as method A for convenience, is that pre-tension is introduced one cable at a time and little tension by little tension until the designed pre-tension is reached. Method A depends on the designer’s experience in determining the introducing order and the pre-tension value of every introducing step. Though no complicated calculation is necessary for method A, many steps are usually needed and the pre-tension introduction is time-consuming. The second one, i.e. method B, is called the reversed progress method. By considering the final shape in which pre-tension has already been introduced and calculating tension in other cables through slacking off one cable in a reverse order of the pre-tension introducing process, the pre-tension that should be introduced into cables in every step is obtained. Generally, the pre-tension introduction can be finished in one turn. Method B is very efficient though an accurate reversed progress calculation is needed [12]. In order to analyze the structural response under wind or earthquake, the dynamic characteristics of a structure, damping ratio for example, are necessary. There are a few reports on the damping ratio of tension structures, which mainly come from cable-stayed bridges [13] and [14]. For space structures, few data on natural frequency and damping ratio from direct measurement can be found [15]. Damping ratio of a practical structure is influenced by many factors, such as friction, foundation conditions, roof materials, and so on. Also, measured damping ratio is influenced by measuring methods and data analyzing methods. Until now, few investigations on the damping property of tension structures can be found. To investigate the basic behavior of a cable-stiffened system, the authors of this paper have carried out numerical and experimental studies on a cable-stiffened column [16]. In this paper, we apply the cable-stiffened system to an arch as shown in Fig. 1. In order to study the suggested cable-stiffened arch, an experimental model with a 1/10 scale of a designed arch is investigated for (1) the pre-tension introducing process, (2) the loading behaviors and (3) the free vibration. In the pre-tension introducing experiment, two models with different introducing systems, i.e. model A for pulling cables and model B for elongating struts, are used. In the loading experiment, several kinds of loading conditions are set and different pre-tensions are used. In the end, the free vibration experiment is carried out in order to obtain the damping ratio of the experimental model. Natural vibrations from the first mode to the fourth mode are stimulated and the corresponding natural frequencies and damping ratios are measured.Numerical analyses for the pre-tension introducing process simulation and the loading–displacement calculation are carried out using geometrically nonlinear FEM. Results from the experiments and the numerical analysis are compared in the paper. Before the details of the experiments are described, the numerical method used in this paper is summarized.

A new kind of structure system consisting of stiffening cables is suggested in the paper. To investigate the static and dynamic behaviors of the new system, the pre-tension introducing experiment, the loading experiment and the free vibration experiment are carried out. The experimental model comes from a lightweight membrane roof structure using a 1/10 scale. Pre-tension introduction method A through modifying tension in cables step by step cannot be recognized as an effective method because too many steps are needed in the introducing process and tension in cables should be monitored. But the pre-tension introduction analysis with high accuracy is not needed in this method. Pre-tension introduction method B by using the reversed process method can be recognized as an effective method because pre-tension can be introduced in one step. The reversed process calculation with high accuracy is necessary in method B. The buckling load of the arch increases greatly after it is stiffened by cables. In the loading experiment, along with the increase of load, tension in some cables disappears. As a result, the stiffness of the system becomes lower. But no sudden drop of the stiffness of the system is observed in the experiment when only several cables lose their tension. Imperfections in shape and pre-tension of cable have an apparent effect on loading behavior in the experiment, which should be carefully examined in designing such a kind of structure system. The damping ratio of a practical structure depends on many factors, such as the structure system, the detail of joints, the foundation condition, and so on. The damping ratio obtained from measurement of a practical structure varies not only with the detail of the structure itself, but also with the vibration amplitude, the measuring method and the data processing method. As a result, it is difficult to find out how the damping ratio is influenced by different factors. In this paper, in order to investigate the influence of cable on the damping property of the system, an experimental model is designed, which excludes the outside damping such as friction in joints. By using such a model, the natural frequencies and the damping ratios of the first mode to the fourth mode are measured with high accuracy through the free vibration experiment. The influence of the pre-tension and the displacement amplitude on the natural frequency and the damping ratio of the cable stiffened arch model has been studied carefully. Through using stiffening cables, not only the loading ability of the system is improved, but also an additional damping effect is provided. This paper shows some important experimental data about damping ratios of the cable-stiffened structures, which is a currently seldom investigated area.