Evaluation of the stiffness of beam and frame elements using system identification techniques

Abstract

Traditional methods of~ tructural analysis begin usually by the construction of a mathematical model that best represents the prototype structure. Furthermore, the material and geometric properties of the structure appear in the what is known to be either the stiffness matrix or the flexibility matrix, depending on whether the displacement or the force method is used. The subsequent analysis, ie the determination of the response of the system due to any set of loading condition hinges on the availability of such matrices. However, in situations where such information is absent or cannot be accurately computed, the analysis resorts to approximations which undoubtedly lead to erroneous results or to inaccurate ones at best. This is the case with ageing structures that have been in use for long periods of time or when the construction materials have greatly deteriorated. System identification is a method to improve mathematical modelling. Amethod which overcomes the difficulty resulting from the unknown material and geometric properties through a minimization algorithm is known to some applied science disciplines but not widely known to structural engineers. Helou (1)(2) made his presentation limeted to determinate and indeterminate trusses. The present study is an application of the same principles to beam and framed structures, thus the validity of the derived equations would be established and made general to include any structures. 269