An algorithm for calculating the feasible pre-stress of cable-struts structure

• An algorithm to find the feasible pre-stress is proposed.
• Three types of cable-struts structures are selected to demonstrate the algorithm.
• The algorithm can update the geometry for the feasible pre-stress.
• The algorithm can consider loads during the design of the pre-stress.
• The feasible pre-stress of the cable-struts structure is obtained directly.

A cable-struts structure consists of tension-only cables and compression-only struts. The structural rigidity comes from the pre-stress. To determine the feasible pre-stress for the cable-struts structure efficiently and accurately, the paper first defines the three states for the cable-struts structure based on the loads applied, develops the fuzzy relationship between the internal force and the pre-stress under different states, and studies various essential conditions for the feasible pre-stress. Second, the paper gives a Newton iteration method to update the pre-stress and a simple method for updating the geometry based on the geometrical difference under different states and subsequently develops a process to find the feasible pre-stress, combining the pre-stress updating method with the geometry updating method. Last, the paper selects three types of cable-struts structures as illustrative examples, a traditional Geiger dome, a new form of Geiger dome and a Kiewitt dome with multiple self-stress modes, and successively calculates their feasible pre-stress using the proposed method. The results indicate that the proposed method is able to search for the feasible pre-stress for cable-struts structures efficiently and accurately; it can calculate not only the pre-stress without loads but also the pre-stress considering loads, and it can change the geometry for the feasible pre-stress. Meanwhile, the method is successful in obtaining the feasible pre-stress for the Kiewitt dome with multiple self-stress modes without the optimal process.