Improvements Study On The Equivalent Damping Ratio Model Of Capacity Spectrum Method

Pushover analysis method is a static analysis method essentially, which is alsoan important mean of the implementation based on the seismic design ofperformance. By this method, the analysis sequence of plasitic hinge and the damagestates of the structure subjected to seismic actions could be simulated. Capacityspectrum method is commonly used in Pushover analysis method to calculate thestructure performance points.The precision of estimating seismic response structureis influenced greatly by the determination of equivalent damping ratio in capacityspectrum method. In order to make the capacity spectrum method coinse andeffective and to ensure the estimation on the performance point of the structure morereasonable, the relevant study is conducted in this paper. The improved model ofequivalent damping ratio applied in capacity spectrum method is provided. The maincontents are following:1. First of all, the basic principle of the Pushover method, and the concept,principle and the steps of capacity spectrum method are introduced in details. Thecurrent researches of equivalent damping ratio are summarized in details.2. The safety of capacity spectrum method of ATC-40is verified. A three-storyreinforced concrete frame structure is designed, and analyzed by capacity spectrummethod and nonlinear time history analysis method respectively. By contrast, It canbe seen that the maximum of story drift rotations from capacity spectrum method issmaller than that from nonlinear time history analysis method when the normalizedresponse spectrums of ground motions are fitting the design response spectrum verywell, in other words, the structure seismic response is underestimated by capacityspectrum method. By investigating its reason, it’s found that the equivalent dampingratio of capacity spectrum method is based on the maximum displacement ofhysteretic energy dissipation, but under the real seismic actions, the seicmicresponse is not always following the maximum displacement hysteretic relationshipreaction. Hence the equivalent damping ratio is estimated so highly that the seismicresponse is underestimated.3. It’s studied on seismic response underestimation by capacity spectrummethod of ATC-40. To keep consistent with pushover method analysis model, thesingle degree of freedom analysis model is employed to obtain the spectrumdisplacement Sdand spectrum acceleration Sacurve, by a large number of nonlineartime history analysis in that seismic actions are selected considering different site-classes, far-field and near-field site conditions. Then Sd-Sacurves have beencompared with that obtained from nonlinear time history analysis and the oneobtained from design spectrum reducted by the existing seven methods of equivalentdamping ratio used in capacity spectrum method respectively. It’s found that theexisting equivalent damping ratio method is not suitable capacity spectrum method.Thus when the design spectrum is converted into the demand spectrum to fit Sd-Sacurves in time history analysis by altering the damping ratio, the equivalent dampingratio curves with ductility coefficient are obtained. Finally the improved equivalentdamping ratio model of capacity spectrum method is provided.4. The capacity spectrum method with the improved equivalent damping ratioabove mentioned is employed is reffered to as the capacity spectrum method in thispaper. To verify the accuracy of this method in the actual structures,5-story and7-story reinforced concrete frame structures are designed. Then3-story,5-story,7-story strctures are analyzed respectively with the Pushover method and thenonlinear time history analysis method. The time history analysis of three structuresare conducted subjected to different seismic actions according to GB50011-2010Code for Seismic Design of Buildings. The Pushover analysis of three structures areconducted by capacity spectrum method in ATC-40and the capacity spectrummethod in this paper respectively. By comparing the results of the maximum ofdisplacements and the story drift rotations of the Pushover method with those of thetime history analysis, it’s found that if the influence coefficients of sesmic actionsnormalized reponse spectrum and those of the corresponding design spectrum in thestructure natural vibration period are fitting relatively well, the seismic response ofthe capacity spectrum method in this paper is estimated well relatively.