Combination of modal responses consistent with seismic input representation
The well-known modal superposition method for the evaluation of seismic response by the complete quadratic modal combination rule (CQC) is revisited. The most widely used version of the CQC rule utilizes correlation coefficients derived for white-noise excitation and neglects the influence of peak factor variation on the response. Here a simplified procedure for evaluation of correlation coefficients and peak factors consistent with the power spectral density of seismic excitation is proposed. The procedure is based on an approximate analytic expression for direct evaluation of the power spectral density of the excitation consistent with any prefixed response spectrum, and the evaluation of…
Numerical and experimental verification of a technique for locating a fatigue crack on beams vibrating under Gaussian excitation
The stationary vibrations of a beam excited by Gaussian noise are strongly affected by the presence of a fatigue crack. Indeed, as soon as the crack arises the system response becomes non-linear due to crack breathing and a non-Gaussian behaviour is encountered. The paper presents both numerical and experimental investigations in order to assess the capability of the non-Gaussianity measures to detect crack presence and position. Monte Carlo method is applied to evaluate in time domain the higher order statistics of a cantilever beam modelled by finite elements. The skewness coefficient of the rotational degrees of freedom appears the most suitable quantity for identification purpose being …
Combination coefficients for modal pushover analysis
Conventional non-linear static analysis estimates the response peak value by evaluating the pushover curve adopting a distribution of invariant forces proportional to the fundamental vibration mode. In order to include the effect of higher modes, multi-modal push-over analysis has been proposed in literature. Nodal response peak values are obtained by combination of “modal” responses usually by the traditional CQC method, requiring cross correlation coefficients defined for linear systems. In this paper, the accuracy of correlation coefficients for linear systems in predicting the statistical correlation of hysteretic oscillator responses is investigated by the Monte Carlo Simulation conduc…
Recenti sviluppi nei metodi di analisi strutturale per la valutazione della vulnerabilità sismica degli edifici
A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random processes
A method for the evaluation of the response sensitivity of both classically and non-classically damped discrete linear structural systems under stochastic actions is presented. The proposed approach requires the following items: (a) a suitable modal expansion of the response; (b) the derivation in analytical form of the equations governing the evolution of the derivatives of the response (the so-called sensitivity equations) with respect to the parameters that define the structural model; (c) an extensive use of the Kronecker algebra for determining the analytical expressions of the sensitivity of the structural response statistics to non-stationary random input processes. Moreover, a step-…
Non linear and linearized combination coefficients for modal pushover analysis
Current design practice and seismic codes tend to assess seismic demand of buildings by Non linear Static Analysis (NSA), based on the evaluation of the pushover curve. Earlier non-linear static analysis procedure estimate the response peak value by evaluating the push-over curve adopting a distribution of invariant forces proportional to the fundamental vibration mode. In order to include the effect of higher modes several multimodal push-over analysis procedures were proposed in literature. In In the most famous of these, namely Modal Pushover Analysis (MPA), nodal response peak values are obtained by combination of "modal" responses by the traditional SRSS or CQC methods: the use of the …