Approaches To Determination Of Key Elements In Spatial Structures

The elements whose failure would cause the collapse of more than a limited portion of the structure close to the element in question are defined as key elements. The existing standards for key elements couldn’t meet with the demands for design and maintenance of spatial structure. This paper devotes to explore the approaches to determination of key elements in spatial structure, which is divided as rigid, flexible, and rigid-flexible structure.Combined with the characteristics of rigid structure, based on the perturbation theory in the error analysis, starting from the definition of structural robustness, a new approach to determine key elements was proposed by using the Relative Condition Number of the whole stiffness matrix as the quantitative indicator of structural robustness. Considering the relay effect of progressive collapse, local region for a certain member in structures was defined, then the relay effect from the elements to local region was investigated by calculating the structural strain energy in local region, so as to supplement the integrated indicator R(K).Similarly, combined with the characteristics of flexible structure, a new approach with two steps to determine key elements was also proposed. Namely, under the premise of assuming no displacement shift of nodes happened in newly formed cable-strut tensile system derived from the single cable or strut broken in the original, the first step to determine key elements was based on the principle of whether geometric instability as well as cables slacking in new systems happened or not. Next, under the condition of no displacement large shift of nodes occurred in newly formed cable-strut tensile system, based on the principle of whether the unbalanced load could form self-equilibrated system of forces or not without cables slacking and elements failing, the key elements was further detennined via analysis of whole process for the new system.Again, considering the configuration of rigid-flexible structure, such as the cable suspen dome, the key elements in separated the single-layer shell were determined bythe Relative Condition Number. For the cable-strut sub-system in the cable suspen dome system, the key elements in the sub-system were determined based on the their contribution to the enhancement of the structural stability capacity.