Report - PEER - University of California, Berkeley
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Report - PEER - University of California, Berkeley

Report - PEER - University of California, Berkeley Report - PEER - University of California, Berkeley

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12.07.2015 Views

where, T: natural period of structure(sec.), Sa: acceleration response spectrum atengineering bedrock without surface soil, h: damping coefficient. The earthquakeground motion is used as the standard for evaluating the seismic performance capacityof a structure, which includes the site amplification through the surface soil from thebedrock. A new and simple method of calculating the site amplification from thebedrock is presented in the Guidelines. The standard earthquake motion is basicallythe same as defined in the BSL and does not have an explicit conception of exceedingprobability and regional hazard.On the other hand, the site earthquake motion is the earthquake motion used forevaluating the seismic performance risk of a structure at the construction site. Thelevel and the characteristics are to be calculated based on the site-specific groundcharacteristics as well as the regional seismic activity.5. ESTIMATION OF RESPONSESA variety of analytical methods are supposed to be used for estimating responses ofthe structures, from equivalent linearization to time-history response analysis withdetailed structural models. The principles for the structural and response analyses areprescribed in the Guidelines.The response evaluation procedures covered in the Guidelines may be roughlyclassified as (a)-(d) below:(a) Static nonlinear (pushover) analysis and response estimation based onreduced SDOF system (equivalent linearization),(a) Pushover analysis and reduced SDOF time-history response analysis,(b) (a) and time history response analysis of multiple lumped-mass systems,(c) (a) and nonlinear time history response analysis at the member level,(d) Nonlinear time history response analysis at the member level.The method (a), which is a de facto standard procedure in the Guidelines, may bedescribed more in detail as follows:(1) Static nonlinear analysis of the structure with fixed foundation under anassumed load distribution (pushover analysis) is performed to obtain the equivalentload-displacement relationship of the reduced SDOF system, and the relationshipsbetween the equivalent displacement and the inter-story drift angle, memberdeformation angle (ductility factor) and member force.(2) The limit deformations on the relations corresponding to the limit states(serviceability, reparability I/II, safety) are calculated from damage rates based onmember deformations. The detailed evaluation methods are given in the level 2documents. Also possible errors in the analysis due to higher modes, material strength,shall be taken into account.(3) The earthquake response spectrum at the base of the building is evaluatedfrom the standard earthquake at the engineering bedrock taking into account the soilamplification.31

(4) The inelastic responses ofthe reduced SDF are related to theamplification factors of thespectrum by the equivalentlinearization method, modifiedcapacity spectrum method (CSM),and identify the level of thecapacity earthquake, thedeterministic performance index,defined as the factor when theresponse attains to the limit states.The inelastic responses by CSMcan be calculated numerically orgraphically, as shown in Figure 1,but also it should be noted that theestimated response can explicitlybe formulated by simple equationsbase on the poly-linear relations ofthe spectrum. The CSM forestimation may be modified soS aDemand Spectrafor Inelastic (h eq =15%)for Elastic (h eq =5%)T 5% T 7% Transition CurveT 10%Performance PointT 15% Capacity SpectrumS d5%h eq at Performance Point7% 10% 15%h eqFigure 1. Capacity spectrum method(CSM) for estimation of inelastic responseof SDF.that the equivalent period can be made optimum (shorter) instead of the secantstiffness to the peak as adopted in the new BSL. A factor of 0.82 for the equivalentperiod is recommended, and this can simply be considered by shifting the earthquakespectrum to the longer side by the factor as shown in Figure 2.300T c/α T=1.054sS V(cm /s)T200c=0.864sdT100 c/α TdT c第 Standard 2 種 地 盤 告 示 Earthquake安 全 限 界 スペクトル等 Shifted 価 線 形 化 計 for 算 用 CSM 応 答 スペクトル00.0 0.5 1.0 1.5 2.0 2.5T(s)equivalent stiffnessfor CSMsecant stiffnessto peakpeakresponseFigure 2. Shift of velocity spectrum of the standard earthquake taking optimumequivalent stiffness for CSM instead of secant stiffness to peak displacement.32

where, T: natural period <strong>of</strong> structure(sec.), Sa: acceleration response spectrum atengineering bedrock without surface soil, h: damping coefficient. The earthquakeground motion is used as the standard for evaluating the seismic performance capacity<strong>of</strong> a structure, which includes the site amplification through the surface soil from thebedrock. A new and simple method <strong>of</strong> calculating the site amplification from thebedrock is presented in the Guidelines. The standard earthquake motion is basicallythe same as defined in the BSL and does not have an explicit conception <strong>of</strong> exceedingprobability and regional hazard.On the other hand, the site earthquake motion is the earthquake motion used forevaluating the seismic performance risk <strong>of</strong> a structure at the construction site. Thelevel and the characteristics are to be calculated based on the site-specific groundcharacteristics as well as the regional seismic activity.5. ESTIMATION OF RESPONSESA variety <strong>of</strong> analytical methods are supposed to be used for estimating responses <strong>of</strong>the structures, from equivalent linearization to time-history response analysis withdetailed structural models. The principles for the structural and response analyses areprescribed in the Guidelines.The response evaluation procedures covered in the Guidelines may be roughlyclassified as (a)-(d) below:(a) Static nonlinear (pushover) analysis and response estimation based onreduced SDOF system (equivalent linearization),(a) Pushover analysis and reduced SDOF time-history response analysis,(b) (a) and time history response analysis <strong>of</strong> multiple lumped-mass systems,(c) (a) and nonlinear time history response analysis at the member level,(d) Nonlinear time history response analysis at the member level.The method (a), which is a de facto standard procedure in the Guidelines, may bedescribed more in detail as follows:(1) Static nonlinear analysis <strong>of</strong> the structure with fixed foundation under anassumed load distribution (pushover analysis) is performed to obtain the equivalentload-displacement relationship <strong>of</strong> the reduced SDOF system, and the relationshipsbetween the equivalent displacement and the inter-story drift angle, memberdeformation angle (ductility factor) and member force.(2) The limit deformations on the relations corresponding to the limit states(serviceability, reparability I/II, safety) are calculated from damage rates based onmember deformations. The detailed evaluation methods are given in the level 2documents. Also possible errors in the analysis due to higher modes, material strength,shall be taken into account.(3) The earthquake response spectrum at the base <strong>of</strong> the building is evaluatedfrom the standard earthquake at the engineering bedrock taking into account the soilamplification.31

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