Irodcio o Earhqake Egieerig Respose Aalysis Pro. Dr.-Ig. Uwe E. Dorka Sad: Sepemer 03
Modelig o ildigs masses lmped i loors rames wih plasic higes Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig
Soil-Srcre Ieracio srcre wih soil i FE ad BE simpliied model odary elemes From Clogh, Pezie (3) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 3
Modelig o ridges spersrcre, earigs ad colms wih FE mliple ase ip Model wih 0 dyamic DOFs maser ode 3 DOF x y 3 46 86 33 5 3 4 5 x y x 5 5 9 95 30 46 5 6 7 8 9 y y z y 0 z Rayleigh-dampig: C am K a w w w D w D w w w D w D w w 86 9 3 4 x y x y wih D =D =5% yields w =00.06 ad w =49.44 a = 0.5075958 = 0.0035458 95 30 5 6 7 8 x y y z 33 9 y 0 z Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 4
Earhqake Loadig lmped MDOF-syem wih rigid ase raslaio (horizoal case) Reerece axis v m v c v k v 0 v v j v g j where direcio cosie, or ildigs ypicall "" m v c v k v p e From Clogh, Pezie (3) e p m j v g Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 5
Descripio o o-liear ehavior Hyseresis models (D) o-degradig models Biliear Model Triliear Model Ramerg-Osgood model From Wakaayashi () Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 6
Descripio o o-liear ehavior Hyseresis models (D) Degradig Models Piecewise liear model (Clogh ad Johso) Triliear Takeda model or rc-memers From Wakaayashi () Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 7
Descripio o o-liear ehavior Hyseresis models (D) Slip-Type Models Dole iliear model y Taaashi ad Kaea Slip-ype model From Wakaayashi () Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 8
Descripio o o-liear ehavior Example or slip-ype hyseresis model (ricio coecio wih mliple sops) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 9
Descripio o o-liear ehavior D Hyseresis Model (D Boc-Whe) From Pradlwarer, Schëller, Dorka (7) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 0
Time Hisory Aalysis Time Discreizaio Dyamic eqilirim: M d d x C d d x Kx r p( ) wih r : vecor o o-liear resorig orces Shape cios or discreizig x i ime: / ; ; / wih: / Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig
Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig Weighed Residal Formlaio d K C M W d d d d d d d d d d d d * * * p r * ; ; Wd d W Wd d W Weighig cio W:
3-Poi Recrrece Scheme Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 3 * * * K C M K C M K C M 0 r G * * 0 p K C M K C M K C M K C M G wih:
Sailiy ad Accracy Sailiy ad Accracy Solio or liear SDOFsysem: ad is recrre orm: yields a characerisc eqaio: y( ) Ye y Ye e Ye y m c k m c m c k 0 k exac solio: sale solio wih merical dampig: Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 4
Sailiy ad Accracy period elogaio merical dampig T/T /T 0.5 0. 5 codiioally sale ewmark scheme wiho merical dampig Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 5
ewo-raphso Ieraio G 0 r Sice he respose r a ime + is o kow, a ieraio wihi each ime sep is reqired o solve his eqaio: From Chopra (4) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 6
ewo-raphso Ieraio From Chopra (4) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 7
Examples o ime hisory Respose o liear SDOF-sysem wih T=0,5 s ad z=0 o El Cero grod moio s 0 0 w elasic resisig orce oal acceleraio o he mass peak vale o elasic resisig orce peak vale o oal acceleraio weigh o mass From Chopra (4) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 8
Examples o ime hisory From Chopra (4) y y o y o ormalized yield sregh m y dciliy acor Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 9
Examples o ime hisory Respose o elasoplasic sysem wih T=0,5 s, z=0 ad y=0,5 o El Cero grod moio deormaio resisig orce expressed as acceleraio ime iervalls o yieldig yield sregh orce-deormaio relaio (hyseresis) From Chopra (4) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 0
Examples o ime hisory Deormaio respose ad yieldig o or sysems de o El Cero grod moio; T=0,5 s, z=5% ad y=- 0,5-0,5 ad 0,5 From Chopra (4) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig
Respose Specra viscosly damped SDOF oscillaor From Meskoris (5) From Peerse () m d k m yf m -solvig his eqaio or varios w ad z, oly or oe speciic accelerogramm -he maximm asole acceleraio o his solio gives s he azissa or he ollowig diagramm w w y F where: Eigereqecy: Dampig raio: k w m d m w Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig
Respose Specra give y EC 8 The acceleraio respose specra i EC 8 are give wih respec o he ssoil classes Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 3
Respose Specra give y EC 8 Compariso o elasic ad ielasic respose specra From Meskoris (5) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 4
Modal Aalysis liear eqaios o moio or a MDOF, homogeeos, damped case wih his modal marix, he eqaios o moio ca e rasorm io modal coordiaes or or a damped case wih grod acceleraio m k 0 solvig he eigevale prolem gives s he modal marix F F F F F3... F T T F m F F k F 0 M K 0 T T T T F m F F c F F k F F mj F M C K F ow we have copled eqaios o moio or SDOFsysems i modal coordiaes Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 5
Modal Aalysis These eqaios cold e solved i kow ways, so we ge solios i modal coordiaes i he ime domai Wih he modal marix we are ale o rasorm hese solios ack io local coordiaes j F j Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 6
Modal Aalysis sig Respose Specra The modal resposes aai heir peaks a diere ime isas. How do we have o comie hese peak vales? S S Sperposiio o asole vales j j S Sj j Sqare Roo Sm o Sqare (SRSS) j k S S S jk j jk k correlaio coeicie Complee Qadraic Comiaio (CQC) Pro. Dr.-Ig. Dorka Irodcio o Earhqake Egieerig 7
Reereces () Wakaayashi Desig o Earhqake-Resisa Bildigs McGraw-Hill Book Compay () Peerse Dyamik der Bakosrkioe Vieweg (3) Clogh, Pezie Dyamics o Srcres McGraw-Hill (4) Chopra Dyamics o Srcres Preice Hall (5) Meskoris Badyamik Ers & Soh (6) Ziekiewicz The Fiie Eleme Mehod McGraw-Hill Book Compay (7) Pradlwarer, Schëller, Dorka Reliailiy o MDOF-sysems wih hysereic devices, i Egieerig Srcres, Vol. 0, 998 Elsevier