砖石古建筑的动力可靠度分析-曹书文

395201310SichuanBuildingScience2012-03-191979－。[e-mail]710055。。。TU34A1008－1933201305－193－04DynamicreliabilityevaluationofmasonryhistoricalconstructionCAOShuwenLIUJunqingZHAODongZHANGWeixiMAOXiaofeiSchoolofScienceXi'anUniversityofArchitecture＆TechnologyXi'an710055ChinaAbstractInthispaperthedynamicreliabilityofmasonryhistoricalconstructionsubjectedtonon-stationaryrandomearthquakeisevaluatedbynumericalmethod．Thestochasticdynamicanalysisisperformedbyusingmodalsuperpositionmethodtoobtainthepowerspectraldensityofrandomresponses．Thedetaildynamicreliabilityformulationsaredevelopedthroughthefirstexcursionfailurecriterion．Atlastthedynamicreliabilityofthemasonryhistoricalconstructionundertheeffectoffrequentearthquakeandrareearthquakearededuced．Themethodinthispaperprovidesreferencetothedynamicreliabilityofcomplexstructures．KeywordsYuhuangpaviliondynamicreliabilitypowerspectraldensitynon-stationaryrandomearthquakefirstexcursionfailurecri-terion0。。。。。。1、。。123。。2XtnXt1Xt2…XtnnGauss。391。Sωt=Ψ2tS¨xgω1Ψ2tS¨xgω。2Clough-PenzienClough-PenzienS¨xω=1+4ξ2gω/ωg21－ω/ωg22+4ξ2gω/ωg2×ω/ωf41－ω/ωf22+4ξ2fω/ωf2×S02ξgωgξf、ωfS0。ΨtAminAng2Ψt=t/ta2t≤ta1ta＜t＜tbe－at－tbt≥t{b3tatba。21。1Table1Parametervaluesoftimeenvelopfunctionta/stb/sa/s－1Ⅰ0．55．50．45Ⅱ0．87．00．35Ⅲ1．29．00．25Ⅳ1．612．00．153M¨x+Cx+Kx=－M¨xg4M、CK、。K－ω2M=05ω=ω1ω2…ωNT。K－ω2MΦj=06Φj=φ1jφ2j…φNjT。x=ΦU7U。74Sxω=∑qj=1∑qk=1γjγkH*jωHkωjTkS¨xgω8γjjjj“*”Hjωj。jσ2xjt=ψ2t∫∞－∞Sxjωdω=ψ2tσ2xj9jσ2xjt=ψ2t∫∞－∞ω2Sxjωdω=ψ2tσ2xj104XtXt0T。Possion。Xt0T－bb3Ps－bbT=exp－2σx·πσxexp－b22σ2()x[]T11σ2x、σ2x·XtX·t。9、1040≤t≤t1Pbt=exp－2σxπσx∫t0exp－b22σ2xt/t1[]4d{}t12－1t1≤t≤t2Pbt=exp－2σxπσx∫t10exp－b22σ2xt/t1[]4d{t+∫tt1exp－b22σ2xd()}t12－2t2≤t≤T49139Pbt=exp－2σxπσ{x∫t10exp－b22σ2xt/t1[]4dt+∫t2t1exp－b22σ2()xdt+∫tt2exp－b22σ2xexp－2at－t2[]d}t12－351373。19881。1Fig．1ThefeatureofYuhuangpavilion18.17m。、2。2Fig．2ThesectionandtheplanofYuhuangpavilion。8、、、。。5．12。2。2Table2Parametervaluesofmaterials/MPa25000．3012350．175．2GB50011—2001《》2001GB18306—2001《》70.10gⅢ0.45s。2ωg=16.664Hzξg=0.792ωf=0.260Hzξf=0.742S0=2.086×10－4m2·s－3S0=81.466×10－4m2·s－3T50%T=ln2/a+tb－ta/槡2131T=10．924s。5．3ANSYS。yyPSDsPS-Dv3aby3cd。yy4aby4cd。。5912013No.53Fig．3Powerspectraldensityofdisplacementandvelocityunderfrequentearthquake4Fig．4Powerspectraldensityofdisplacementandvelocityunderrareearthquake33。12－1～35。3Table3Variancesofdisplacementandvelocityσ2x/mm2σ2x/mm/s21．300．950．690．4850．9537．0627．0018．286．795．016．063．86266．36196．84237．19151．275Fig．5Reliabilityoftopdisplacement5。61。27。3。1．—M．2001．2．J．200528182-85．3．M．1998．4．J．200832488-92．5．J．20013435-9．6．J．2006231082-85．69139