A Note on Damage-Based Inelastic Spectra

Abstract

SUMMARYWhen a structure is subjected to moderate to severe ground motions, a few excursions of the response yield level may take place following the reductions usually enforced in the design forces. These excursions are associated with progressive damage in the structure. Thus, a choice of the design level has to be suitably based on the maximum damage to be allowed in the structure. In this paper, a stochastic technique of developing damage-based non-linear spectra has been proposed for the aseismic design of those structures which can be idealized through Single-Degree-Of-Freedom (SDOF) oscillators. The proposed technique has been illustrated by obtaining the non-linear spectra which can possibly be used for a damage-based design. Along with the spectra, allowable ductility demand which should be supplied through proper sizing and detailing of the members and is compatible with the damage has also been specified. The non-linear SDOF oscillators have been approximated for this purpose by equivalent linear oscillators using a new stochastic linearization technique. The proposed linearization technique has been validated through simulation results in the case of an idealized, non-hysteretic, Elasto-Plastic (EP) model.

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

“…However, such considerations involve computationally intensive iterative numerical schemes requiring the calculation of integrals which are not amenable to analytical treatment, without necessarily yielding results of substantially increased accuracy (see e.g. [23,33,43]). Since simplicity and computational efficiency are primary objectives in the herein proposed approach, the classical statistical linearization method is adopted in all of the ensuing analytical and numerical results to obtain equivalent linear properties by minimizing the squared difference between the nonlinear and the equivalent linear system.…”

“…[23,33,[41][42][43]), while significant research effort has been also devoted in relaxing the aforementioned Gaussian distribution assumption (e.g. [44,45]).…”

“…Equations (22) and (23). It should be clear from the preceding comments that the effective linear properties ω eq and ζ eq obtained through iterative solution of Equations (20) to (23) depend explicitly on the input power spectrum G(ω).…”

“…Furthermore, Basu and Gupta [23] derived inelastic spectra pertaining to certain recorded seismic accelerograms also based on a statistical linearization formulation. This formulation required the minimization of the expected value of the square difference (error) between the considered nonlinear equation of motion and the corresponding (target) equivalent linear with respect to the dynamical properties of the ELS.…”

Statistical linearization based estimation of the peak response of nonlinear systems subject to the EC8 design spectrum

“…Furthermore, Basu and Gupta [6] derived inelastic spectra pertaining to certain recorded seismic accelerograms also based on a statistical linearization formulation. This formulation required the minimization of the error of the mean square of the peak responses between the original nonlinear and an ELS.…”