Keywords: tensile structure, block and tackle, dynamic relaxation, nonlinear analysis, friction, truss arch, suspension system, cable net.

Tensile roofs supported by three and four truss arches have been analysed in the research presented in this paper. Structures with different geometry and with different suspension systems have been compared. In the case of "conventional" suspension the short, individual suspension cables connect the breakpoints of the ridge cables to the joints of the truss arches directly. In the case of a block and tackle suspension system the continuous suspension cables passes through a series of upper and lower pulleys along the supporting arches. The lower pulleys are secured to the ridge cable of the tensile roof; pairs of upper pulleys are secured to the supporting arch. Since the force in the continuous suspension cable is (almost) constant, the supporting arch can be designed to correspond to the pressure line of the arch loads.

The block and tackle suspension system was invented by Árpád Kolozsváry to minimize the bending moment in the supporting arches of tensile roofs [1]. The invention and the first numerical results of the analysis based on idealised, frictionless pulleys were introduced in [2]. Later a more precise numerical procedure based on the well-known dynamic relaxation method [3,4] has been developed by the author [5]. With the help of this procedure the friction between the pulley and its shaft can be also taken into account.

The aim of the current research is to optimize the structure of the roof and the supporting arches. In the current paper the effect of the curvature of the circular supporting truss arches has been analysed on the internal forces of the arches and the displacements of the structure.

The results show that the curvature of the arches has a strong effect on the arch loads and the normal forces in the arch, but its effect on the bending moments is less significant. The optimal geometry of the arches has been determined on the basis of the minimization of the maximum force in the chord members of the truss arches multiplied by the average length of the chord members. On the other hand the results show that by the help of the block and tackle suspension system the bending moment of the supporting arches can be reduced radically, independently of the curvature of the circular arches.

1

Á. Kolozsváry, "Roof Arches without Bending Moments", Patent, WO/2006/136867, 2006.

2

K. Hincz, "Arch-supported Tensile Structures with Very Long Clear Spans", Journal of the International Association of Shell and Spatial Structures, 48(2), 89-98, 2007.

3

A.S. Day, "An Introduction to Dynamic Relaxation", The Engineer, 218-221, 1965.

4

M.R. Barnes, "Form-finding and analysis of prestressed nets and membranes", Computers and Structures, 30, 685-695, 1988. doi:10.1016/0045-7949(88)90304-5

5

K. Hincz, "Nonlinear Analysis of Cable Net Structures Suspended from Arches with Block and Tackle Suspension System, Taking into Account the Friction of the Pulleys", International Journal of Space Structures, 24(3), 143-152, 2009. doi:10.1260/026635109789867643

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