Assessing Key Structural Stiffness of Existing Space Trusses Based on Optimized Simple Static Loadings

Abstract

A novel method of simple static loadings is developed for existing space trusses to assess the key structural stiffness, which provides the main resistance to the structural deformation caused by the load that dominates the deformation check in the structural design. For a space truss under a given dominant load, the structural displacement can be characterized by the generalized displacements along a few eigenvectors, which form a so-called key set, of the stiffness matrix of its numerical (finite-element) model. When the stiffness of the space truss deteriorates, the structural displacement can still be described by the pseudo-generalized displacements along those eigenvectors included in the key set and a small number of their adjacent eigenvectors. Moreover, the pseudo-generalized displacement can be approximately expressed as a linear combination of the generalized displacements along its neighboring eigenvectors included in the key set. Any combination coefficient can be estimated by the measured nodal displacements of the existing (deteriorated) structure under a constructed simple static load. The strategies for selecting the loaded degrees of freedom and optimizing the magnitude of loads are proposed. The selection of the measured degrees of freedom of displacement responses caused by the simple load is also discussed. For two illustrative space trusses with randomly assigned member stiffness deviations, the deterioration of their key structural stiffness is evaluated by comparing the displacement, which is indirectly obtained by simple static loadings, of the existing structure and that of the numerical model. The accuracy and validity of the proposed method are verified.