Nonlinear interaction design provisions using spectral superposition

The problem of enforcing two-variable nonlinear interaction code provisions within a spectral superposition approach to design, is addressed. An analytical procedure based on the linearization of the interaction curve through a set of tangents or secants is developed. Safety with respect to the interaction curve is approximated by requiring safety with respect to that set of straight lines. For calculating the required estimators, the cross-estimator based formula for estimators of the linear combination of variables, derived in a companion paper, is used.The analytical method developed was shown to be equivalent to a graphical method proposed by Gupta, based on inscribing an estimator ellipse within the interaction curve. The analytical method is more straightforward and handles the directional maximum in single-component excitation, which the graphical method does not. The analytical method is much easier to apply. However, if a study calls for actually drawing the estimator ellipse, straightforward construction methods are presented, making unnecessary a cumbersome equivalent modal response approximation that had been suggested. The inherent antisymmetry of the spectral superposition formula, and its implications, are discussed. The effect of static loading and of symmetry of the interaction curve is also analyzed.Within the analysis of an example, the work required for the application of the procedure for nonlinear interaction for design purposes is discussed. It is found that its implementation can be achieved through a very simple function written for any standard numerical computation software package. The example also makes quite apparent the advantages of the analytical over the graphical method.The application example, which considers the design of a concrete column in a simple 10-storey building structure, shows the overconservativeness of a design based only in the standard estimators. The design criterion used in the example is that of the most unfavorable direction of a single-component earthquake. [Copyright &y& Elsevier]