Evaluation of secondary and higher order response facets in response spectrum analysis

Abstract

In structural dynamics, designers are concerned not only with primary or first order response facets, i.e. those directly involved in the problem formulation, but also with others which will be generically called higher order facets since they are obtained as linear combination of lower order ones. Direct application of linear combination formulae of lower order facets does not make much sense in the context of Response Spectrum Analysis. In fact, it is usually conservative and anyway unrealistic, the only known thing about the lower order variables being their peak values which are not simultaneous. This paper presents an effective method for treating the results of a Response Spectrum Analysis without adding undesirable conservatism. This method leads to exact peak values of any higher order facets whenever the linear combination coefficients are known a priori. If they are not — as, for example, in the case of obtaining principal stresses — the higher order facet peak value can also be evaluated with enough accuracy. Finally, it permits to find out sets of compatible values of several facets of the same order, affecting the same or different points of the structure, thus enlarging the scope of the Response Spectrum Analysis method which is supposed to provide only maxima regardless of the fact that they usually are not simultaneous. This last capability being of paramount importance when deciding about the structure's capacity to undergo the excitation.