Application of first-order finite similitude in structural mechanics and earthquake engineering

An important experimental approach for the testing of earthquake-resistant structures is scaled experimentation with experimental designs impacted upon by the similitude theory of dimensional analysis. Unfortunately, the type of similitude provided by dimensional analysis seldom applies to complex structures, which is particularly problematic when scaling ratios are large. The issue is one of scale effects where the behaviour of the scaled version of any full-size structure can be markedly different. Recently however a new theory of scaling called finite similitude has emerged in the open literature that confirms that the similitude offered by dimensional analysis is just one of a countable infinite number of alternative possibilities. The new theory of scaling raises the possibility that buildings and structures can be designed and tested in new ways and this aspect is the focus of this paper. Similitude rules for single and two scaled experiments are examined to illustrate the benefits provided by alternative forms of similitude. The two types of similitude examined are termed zeroth order and first order finite similitude, which are shown to be two forms in an infinite number of alternative possibilities efficiently defined using a recursive relationship. The theory of scaling is founded on the metaphysical concept of space scaling yet provides the means to establish all scale dependencies for structural components and high-rise steel buildings along with buildings equipped with nonlinear-fluid viscous dampers for resisting earthquake loading conditions. It is shown through case-studies of increasing complexity how the new theory can be applied to reconstruct full-scale behaviours but also revealed are some of the limitations of the new approach.