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Analysis of cable membrane structures fajman P., Maca J., Polak M




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ANALYSIS OF CABLE MEMBRANE STRUCTURES


Fajman P., Maca J., Polak M.

Department of Mechanics, Czech Technical University in Prague

CZ-166 29 Praha 6, Ceska republika, Thakurova 7


The use of light weight cable-membrane structures is widely accepted and their use is continuously increasing in projects that require coverage of large areas such as storage buildings, exhibition halls and stadia. In the field of exhibition structures especially they have proved to be extremely successful and a considerable number of novel designs have been introduced during the last twenty years. Cable-membrane structures have been used for: roofs and enclosures for buildings such as theatres and music stages; entrance driveways; parking areas; walkways; stadia or domes; airports; exhibition areas; temporary protection tents; circus or conventional tents; warehouses for storage and other innovative purposes. The reasons for their wide acceptance include the following (Topping and Ivanyi 2007):

  • They are light weight and can be transported at a relatively low cost;

  • These structures can be used to cover large areas at very competitive costs per unit area;

  • These structural forms result in structures that can be fully stressed since there is no need
    to consider bending or buckling which results in very efficient use of the materials used;

  • These structures may be prefabricated and can be manufactured in the most efficient
    method;

  • These structures can become very attractive architectural landmarks.

Traditional building from bricks, concrete, steel and wood is the most common in the Czech Republic. Investors prefer these materials due to better durability. The most widespread opinion is that textile structures are short-term and expensive solutions. Recently the behaviour is changed. Architects who try to design unusual and original structures use fabric textiles for airy roofing.

The integration of the architectural and engineering design becomes apparent in many cable-membrane projects. The role of materials development and testing should not be underestimated, for these are essential for realisation of innovative designs. Manufacturers and construction firms have also played a significant role in the development of new technology.

The role of computational methods in the development of cable-membrane structures is less clear but it is evident that without computational methods many of the most innovative structures could not have been realised. Key to the further development of membrane structures is the development of new techniques for the computer modelling including the full environmental life cycle simulation, the development of new materials and design standards.

Very important part of the design process is the verification of the computational model by experimental results. The method for determination of actual level of stresses in cables and membrane has been developed. The method is based on static and dynamic non-destructive experiments.

The device for determination of the force in the anchorage cable of the membrane will be created. This device will be connected with the monitored cable, the force Fp needed for the transversal deflection Aw of the cable will be measured electronically. The value of the axial force N will be evaluated on-line based on the relation between N, Fp and w. This relation is also influenced by the stiffness of the investigated cable and the stiffness of the connection between the cable and the membrane. Therefore, calibration will be done for commonly made cables and membranes to add these influences to the relation between N, Fp and w. The second order theory is used for non-destructive measurement. If the cable is considered as perfectly flexible, then axial forces N can be calculated from the measured transverse displacements w and forces Fp. It is possible to use a simple equation



(1)

The equipment is connected to the measured cable, which is subjected to deflection. Constructed equipment measures the values of transverse displacements w and forces Fp in some steps (Fig. 2). The force values were obtained with a frequency 10Hz during the measurements. In reality the bending stiffness of the investigated cable has an influence on the value of axial force. That effect can be eliminated by trial test. The calibration measurements were provided in the laboratory of the Experimental Centre (FCE CTU). We got values N, Fp and w. Obtained dependencies among the type of cable N, Fp and Aw were used during the following practical measurements on real structures. In compliance with expectations the cable forces obtained from measurements were smaller than theoretical forces calculated from Equation 1. The difference is about 8.8%.







The original method, which was tested at CTU, allows determining membrane stresses in different directions. It is necessary to restrict the part of canvas with evident boundary conditions. Further, the device for determination of the force in the membrane has been developed (see Fig. 3). This device will demarcate the area on the membrane. The value of the membrane loading Fm can be evaluated on-line and it is based on the relation between Fm and the natural frequency of the demarcated area. The stresses in the membrane are usually not the same in different directions. The arrangement of the device is designed to take this influence into account.




Designed method was used in practice. The roof of tram stop Barrandov in Prague was checked. The structure is shown in Fig. 2 and 3. A stop was built in 2002 and the maintenance of prestress was made in 2004. The measurement took place in 2009 and the dependencies of axial forces on transverse displacements were obtained.

The forces in cables were obtained from 1500 values, which were statistically evaluated. The values were taken for transversal displacements bigger than 1 Omm. Evaluated force values are in Table 1.

The natural frequency and corresponding forces in textile membrane are given in Table 2. Forces are indicated for a unit width of canvas.






Table 1 Forces in cables Table 2 Forces in membrane


The data obtained from developed equipments and devices in the experimental part of the project could be used for the verification of computational models of the cable-membrane structures. The comparison of the results from computational models and from experiments carried out on simple membrane structures in the laboratory and also on real structures in situ has been done.

The designed method of measurements of forces in cables is simple and sufficiently accurate. The error without calibrating is about 8% and the error with calibrating is about 2%. The measurement of textile membrane has an error less than 5%.

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