Mark Aschheim

The representation of P-Δ effects using Yield Point Spectra

Yield Point Spectra are used to indicate the influence of P- effects on the lateral strengths associated with constant ductility demands. The intensity of P- effects is represented by a new index, termed the effective height, heff. This representation is useful for performance-based seismic design, because the effective height may be estimated accurately using information that is available early in the design process, and varies little as the initial design is further refined. This index is also useful for the evaluation of structures having known properties. An example illustrates design to limit peak displacement response in the presence of P- effects when the initial stiffness is unknown. The design is based on an estimate of the yield displacement and uses heff to represent the intensity of P- effects.  2003 Elsevier Ltd. All rights reserved.

Theory of principal components analysis and applications to multistory frame buildings responding to seismic excitation

Abstract Described herein is a technique of multivariate statistical analysis applied to the post-processing of dynamic response data. The data may represent the linear or nonlinear response of structures, and may be obtained from computed simulations or from the measured response of instrumented structures. When applied to displacement response data, an ordered set of orthonormal mode shapes is obtained. The principal components analysis (PCA) mode shapes coincide with or are related to the elastic mode shapes for linear elastic systems, and depart from these shapes as nonlinear response becomes more prominent. The PCA modes provide an unambiguous and simple description of the ‘predominant’ mode of structures responding to earthquake ground motions, and thus improve the theoretical basis of nonlinear static procedures that use ‘equivalent’ single-degree-of-freedom (SDOF) systems for representing the response of structures subjected to damaging earthquake ground motions (e.g. the capacity spectrum and displacement coefficient methods). Where greater fidelity is desired, the most efficient representations are obtained by including as few PCA modes as are needed for the degree of precision desired. This paper presents the theory of PCA and illustrates its application to a 12-story frame building responding linearly and nonlinearly to earthquake ground motions. ‘Equivalent’ SDOF models of the structure are developed based on the PCA mode shapes, and these are applied to estimate the computed displacement histories.

THE USE OF SIMPLE PULSES TO ESTIMATE INELASTIC RESPONSE SPECTRA

Inelastic response spectra are estimated for elasto-plastic SDOF systems subjected to strong earthquake ground motions by applying the strength reduction factors determined for a simple pulse to the elastic response spectrum of the ground motion. This approach relies upon similarities in the strength reduction factors computed for earthquake ground motions and for short duration pulses. The accuracy of the estimated inelastic spectra obtained using 24 simple pulse waveforms is assessed in order to identify subsets of just several pulse waveforms that are suited for this purpose. Based upon the ground motions and pulses investigated, this approach appears to be equally applicable to short and long duration ground motions and those having near-fault forward directivity features.

AN ALGORITHM FOR COMPUTING ISODUCTILE RESPONSE SPECTRA

The computation of constant ductility (or isoductile) response spectra for single-degree-of-freedom systems can require numerous individual response history analyses. Recognising that the same ductility response may be obtained for different strength oscillators of a given period, greater computational effort is required to reduce the possibility that a desired solution is not overlooked. Even a single solution may not exist if a local discontinuity in the strength-ductility relationship coincides with the desired value of ductility. This paper describes a two-phase algorithm to identify the highest strength solution for which the corresponding ductility equals (or does not exceed) the desired ductility. The first phase adopts a “check-reject” approach to reject intervals of strength where the possibility of unidentified higher-strength solutions is considered to be remote, thereby narrowing the strength interval in which the solution will be found. The second phase identifies a solution within this interval as rapidly as possible using a bisection approach. The algorithm is implemented in the USEE software program. The efficiency and accuracy of the algorithm are demonstrated by comparison to results obtained with other software programs.