Keywords: form-finding, cable net, force density method, FEM.

Light weight cable-net structures are stable three dimensional mechanical structures which maintain their form due to an intricate relationship with forces. A key step in the design of cable net structures is to determinate their states of prestress and the geometrical configurations, known as form-finding. Various methods have been used for the form finding of cable net structures and different methods would lead to different forms and balance prestress states.

In this paper, the research on form-finding computing of a cable-net structure joined to steel trusses is presented. Four form-finding principles and two computing methods are introduced to get the objective configuration.

Four form-finding principles for cable net structures are proposed in the paper:

1. All members have equal forces, which gets the equal stress distribution in cable net structures and the form is called the minimum surface in mathematics.
2. All members have equal lengths, which is for uniform material preparation.
3. All end members have equal forces, which is for uniform force control in construction.
4. Equal forces or equal member lengths are in every weft and longitudinal cable, which make a relatively convenient construction.

Two computing methods are carried out to realize the principles. One is the finite element method. A numerical model for short cable members is set up. Forces are controlled and the original lengths are changeable in some tension-only members, which could simulate the slipping effect of the pretension process in construction. Other tension-only members in cables have definite changeless original length in the initial model, whose tension forces is varied based on form finding analysis.The other is a mixed method with FEM and force density method. The form-finding process divides into two steps. The finding of configurations of cable net structures is completed by force-density method first and then the force distribution in steel trusses is completed induced by cable net structures. Different iterative rules are applied to get different configurations and force distributions of the cable net and truss structure.

The steel structure of the Chinese marine museum is composed of two crossed steel grid trusses linked by a spatial curved truss arch. Two pieces of double curved cable net structures are joined to the arch and the edge members of the grid truss. The height of the structure is 58m, and the height of the cable net structure is 40m.The up two form-finding methods and different objective principles are used. The configurations and pre-stress distributions of the mixed structure are compared.

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