The research of applied pushover method in the earthquake resistance analysis of soil-structure interaction system

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1 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha The research o appled pushover method the earthquae resstace aalyss o sol-structure teracto system Lu Lpg, Xa Ku ad Cao Xua Assocate Proessor,College o Cvl Egeerg, Chogqg Uversty, Chogqg, P.R.Cha Graduate studet, College o Cvl Egeerg, Chogqg Uversty, Chogqg, P.R.Cha Emal: Lulpg@cqu.edu.c,zhhllp@.com ABSTRACT : The o-lear earthquae resstace aalyss o sol-structure teracto system s complex. The tme hstory aalyss method o o-lear earthquae resstace aalyss s a well tted method, ut t s dcult to use ecause o the complexty o aalyss model ad ucerta put o earthquae moto. As a smpled method, pushover method has ee wdely appled the capalty evaluato o structure earthquae resstace. I the paper the pushover method was appled to study sesmc ehavor o rame-shearwall structure cosdered sol-structure teracto. The plae rame-shearwall structure o tall uldg was tae as a research model, the structure was smulated y eam elemet, ad the groud was smulated y parameter model. rstly the o-lear tme hstory aalyss method was adopted to aalyses the top dsplacemet, story drt ad the order o yeld o the model. The ased o the result o the o-lear tme hstory aalyss method, the applcalty o pushover method sol-structure teracto system was studed. ally pushover method was appled to aalyss the structure earthquae resstace capalty o rame-shearwall structure cosdered sol-structure teracto. KEYWORDS: pushover method; earthquae resstace aalyss; tall uldg; sol-structure teracto. Itroducto The study o sol-structure dyamcs teracto (arevated as ) has attracted wdly atteto,ad has gotte a lots o useul results(lu Lpg ). The ma method o study or s tme-hstory aalyss method. Ths method ca ota structure status at ay tme, whch s regarded as oe o the est methods or the study o. But ecause o the complextythe o aalyss model, the dculty o dealg wth computg data the ucertaty o groud moto ad so o to lmt ts use. Statc pushover aalyss method s a smpled calculato method o structural olear resposes, most o cases t ca get more ormato tha statc elastc ad dyamc aalyss(yag Pu ). The pushover method has e appled the study o y domestc ad aroad researcher. Wag Megu etc. (5) studed the easlty that appled pushover method to aalyss o ramewor structure cosderg. The plae ramewor aalyss model was made, ad the sol was smulated y sprg. The lateral load mode ad target dsplacemet were studed. Ad vered the easlty that appled pushover method to study o ramewor structure cosderg y a example. Wag egxa etc. () trasormed a system to a equvalet SDO system through twce equvalece, ad the pushover method cosderg eects (arevated as PA) was put orward. Cheg Qgju etc. (7) adopted the capacty spectrum method to perorm olear statc sesmc respose aalyss or hgh-rse rame structures wth group ples restg o atural oudato sols, the pushover aalyss model o sol-ple-structure teracto system was estalshed, group ples smulated y sprgs ad group ples stess determed y Daves method. It s ecessary that study the easlty o appled pushover method to aalyss o rame-shearwall structure cosderg. I the paper, the easlty o appled pushover method to aalyss o rame-shearwall structure cosderg s studed ased o others research results. The plae rame-shearwall structure o tall uldg was tae as a research model, the super-structure was smulated y eam elemet, ad the groud was smulated y parameter model. rstly the o-lear tme hstory aalyss method was adopted to aalyses the

2 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha top dsplacemet, drt dsplacemet ad the order o yeld o the model. The ased o the result o the o-lear tme hstory aalyss method, the applcalty o pushover method sol-structure teracto system was studed. ally pushover method was appled to aalyss the structure earthquae resstace capalty o rame-shearwall structure cosderg.. Pushover aalyss method or rame-shear wall structure cosderg. The prcple ad hypothess o statc pushover aalyss method Statc pushover aalyss method s a smpled method or olear sesmc respose aalyss. Oe o smulatg lateral erta orces s put o the aalyzg model ad s elarged step y step tll the structure gets to a target dsplacemet, the the structure sesmc ehavor s evaluated. The hypothess o statc pushover aalyss are: () Sesmc respose o a structure s related to equvalet sgle-degree-o-reedom system. Ths mples that sesmc respose o structure s oly cotrolled y rst vrato mode. () Deormato alog the structure s expressed y shape vector. O the process o sesmc, shape vector eeps varat despte o the magtude o structural deormato. () loor stess tsel plae s te, the stess out o plae ca ot e cosdered. The prcple o statc pushover aalyss method s: () Structure s smpled as a equvalet sgle-degree-o-reedom system. The maxmum elastc dsplacemet o the eect o ortcato level sesmc s calculated, whch s tae as the target dsplacemet. () Two-dmesoal or three-dmesoal model s ult or structural aalyss. () Sesmc acto s smpled as verted tragular dstruto, uorm dstruto or dstruto, the taes t or calculato model o structure. ()Usg load cremet to carry out olear statc aalyss tll the structural pea dsplacemet gets to target dsplacemet. (5)d out plastc hge tmely ad mody total stess matrces cotuously o the process o appg. ()e the structure gets to target dsplacemet, structural teral orce ad deormato ca e used as earg capacty ad deormato requremet o structure. Otag earg capacty ad deormato requremet o structure successvely the comparg to permssle value, thus evaluates structure or ts sesmc ehavor.. Aalyss model o the rame-shear wall structure cosderg couplg eam rame The aalyss model s show gure. It s a smpled plae model that upper structure cosst o shearwall, couplg eam ad rame, ad the ase s smpled to a rgd mass loc, the sol s smulated y a level sprg ad a rotato sprg. The parameters o sprgs are determed y the statc stess o the ured rectagular oudato. The upper rame eam ad rame colum s smulated y eam elemet. Because the shell elemet s t provded plastc hge SAP, the shear walls s smulated y eam elemet to cosder the platc perormace o shear walls. The qualty matrc created y reactor-qualty method.. Statc stess o the ured rectagular oudato The parameters o sprgs g. are determed y the statc stess o the ured rectagular oudato. The statc stess o the ured rectagular oudato adoted the shear wall K gure Pushover aalyss model o rame-shearwall structure cosderg K Kh

3 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha ollowg ormula whch gve y lterature (Pas A 9). Statc stess o the surace oudato: Horzotal stess: GB.5 Khy [.( L/ B) +.( L/ B) +.] ν (.) Rocg stess: GB KφX [.( L/ B) +.] ν (.) Statc stess o the ured oudato: horzotal stess: s.. Khy Khy[ + [. + ]( E/ B) ] + L/ B (.) Rocg stess: s. KφX KϕX[ + E/ B+ [ ]( E/ B)].5 + L/ B (.) the ormula, G s shear modulus o the sol, ν s posso rato o the sol,b s hal legth o the short sde o the rectagular oudato,ls hal legth o the log sde o the rectagular oudato,e s depth o oudato.. Lateral load mode I the pushover aalyss o the structure ased o rgd oudato hypothess, there are three lateral load modes such as tragular dstruto, uorm dstruto ad dstruto. I the most case uses the lear dstruto such as tragular dstruto ad uorm dstruto whch maly represets the eect o the rst vrato mode, ad usually appled to regular low-rse uldg. e the uldg layer creases, the hgh vrato mode luece shoule e cosdered, the olear lateral load mode eeds to use.the lateral load mode o the rame-shearwall structure cosderg s deret rom rgd oudato hypothess. Besdes o horzotal erta orces o superstructure, the horzotal erta orces o oudato must e cosdered. I the paper, the lateral load method recommeded y lterature (Wag Megu 5) s adopted. Regards the rgd oudato as a loor, ad cludes loor's superstructure to compose a (+) structure system. The lateral load modes o the rame-shearwall structure cosderg are show as the ollow: ()Uorm dstruto W (.5) W + W W W + W (.) I aove equato, W, W expresses the oudato wegh ad the th loor's weght separately., ad represets the th layer s horzotal load cremet, the oudato cetrod s horzotal load cremet ad the asemet shearg orce cremet separately. ()Tragular dstruto (.7) + WZ

4 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha + WZ (.) I the ormula, h s the alttude that the th loor leaves the asemet; Z s the alttude that the rgd loc cetrod away rom the asemet. () Curve dstruto (.9) + WZ whch, + WZ. ( T <.5 s) T (.5s T.5 s). ( T.5 s) (.) (.) easlty study o appled pushover method to aalyss o rame-shearwall structure cosderg Comparatve aalyss was used to study the easlty o appled pushover method to aalyss o rame-shearwall structure cosderg. The relato etwee the results o plae model rame-shellwall structure cosderg, whch gotte y o-lear tme hstory aalyss method ad pushover method was otaed. The the easlty o pushover methods or the system was studed The examples o story reorce cocrete ramewor-shearwall structure were desged ased o the model show g.. The heght o Storey s m, the dstace o colum s m, the let-edge spa s layouted shear walls, the rght three spas are arraged colums, the eams etwee the ramewor ad shear walls are regarded as rgd l. I order to study the eect o shear wall, two aalyss models were desged, oe wth more shear walls ad aother wth less shear walls, mared as Model ad Model, respectvely. I the two models, the colums secto are. mx.m ad the eams secto ad the l eams are.mx.7m. The shear wall secto s. mxm Model, ad. mxm Model. The stregth grade o cocrete s C, the stregth o reorcg steel ar the eams, colums ad shear walls s HRB5, ad strrup s HPB5. The sze o oudato s m m m, ad the qualty s to. The dstace etwee ature cetrod ad ass o the oudato s.5m. The Ste classcato s II, ad the correspodg parameters o sol are: desty o sol ρs Kg/ m, posso ratoν s.5, shear wave velocty s s 9m/s. The atsesmc classcato s grade, ad ad the correspodg parameter o asc desg accelerato o groud moto s.g. Accordg to these parameters, the examples were desged. or gotte the result o aove examples calculated y o-lear tme-hstory aalyss, two actual sesmc waves ad oe artcal sesmc wave were selected accordg to the Code or Sesmc Desg o Buldgs (GB5-). The pea accelerato was adjusted to the maxmum accelerato o the rare earthquae correspodg grade o atsesmc classcato, that s.g. The the average o the result calculated y three sesmc waves was tae as the al result. The three sesmc waves are show gure.

5 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha Accelerato(m/s ) Tme(s) Accelerato (m/s ) Tme(s) Accelerato(m/s ) (a) USA7 () USA5 (c) S gure Sesmc waves or o-lear tme-hstory aalyss Tme(s) Three lateral load modes, verted tragle dstruto, uorm dstruto ad dstruto, were used statc pushover aalyss method or aove examples. Comparg the cocluso otaed y deret lateral load modes o pushover mothod wth that otaed y o-lear tme-hstory aalyss method, the results are show gure to gure 7. tragular uorm tmehstory Dsplacemet(mm) gure Story pea dsplacemet o Model calculated y deret methods tragular uorm tmehstory Dsplacemet(mm) gure Story pea dsplacemet o Model calculated y deret methods tragular uorm tmehstory tragular uorm tmehstory Dsplacemet(mm) 5 dsplacemet(mm) gure 5 Story drt o Model calculated y deret methods gure Story drt o Model calculated y deret methods (a) tragular lateral load () uorm lateral load (c) lateral load (d) tme hstory load gure7 Plastc hges dstruto o superstructure

6 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha Compared the results calculated y pushover method ad tme hstory method (gure to gure7), t s showed that there are a lttle deret ut the treds are same, ad there s o est three purshover lateral load mode. Thereore, the pushover aalyss method s sutale or sesmc aalyss o rame-shear wall structure cosdered sol-structure teracto, ut three ds o lateral load patters whch are sutale or sesmc aalyss o rame-shear wall structure cosderg sol-structure teracto eed urther study. Applcato o pushover method to study sesmc ehavor o rame-shearwall structure cosderg I the part, the sesmc ehavor o rame-shearwall structure cosderg was studed y pushover method. Two type o model were estalsed, oe was cosdered (arevated as ) ad the other was ot cosdered (arevated as ). models was the same models (Model ad Model ) show Part. models(mared as Model ad Model ) were desged ased o models. As rgd-plastc ad sprg was sutracted, xed coecto set o the ottom o colum ad shearwall, Model was chaged to Model, ad Model was chaged to Model. Compared the calculated results o two type o model, the sesmc ehavor o rame-shearwall structure cosderg was studed. To reveal the eect o sol-structure teracto, the Ste classcato s I, ad the correspodg parameters o sol are: desty o sol ρs Kg/ m, posso ratoν s.5, shear wave velocty s s m/s. The atsesmc classcato s grade 7, ad ad the correspodg parameter o asc desg accelerato o groud moto s.5g. Accordg to these parameters, the examples were desged. The pushover method was used models ad models. The lateral load mode was tragular dstruto, uorm dstruto ad dstruto respectvely. The average o story pea dsplacemet ad the average o story drt, calculated or the results o three lateral load mode, were regard as the al results. The plastc hges dstruto o superstructure was the results calculated y uorm lateral load. The results o comparatve aalyss are show gure to Dsplacemet(mm) gure Story pea dsplacemet o model compared wth model s Dsplacemet(mm) gure 9 Story pea dsplacemet o model compared wth model s Dsplacemet(mm) gure Story drt o model compared wth model s Dsplacemet(mm) gure Story drt o model compared wth model s

7 The th World Coerece o Earthquae Egeerg Octoer -7,, Bejg, Cha (a) model (NOS-) () model (NOS-) (c) model () (d) model () gure Plastc hges dstruto o superstructur uder uorm lateral load The results dcate that the story pea dsplacemet ad story dt o the structure are reduced as cosdered, ad the order ad dstruto o plastc hges are ale etwee the s results ad s result, ut the degree o plastc hges s decreased. The smlar cocluso has ee show the lterature (Lu Lpg ). 5. Cocluso () The results o pushover aalyss method s a lttle deret rom that o tme-hstory aalyss. But the tred o the story pea dsplacemet, story drt ad plastc hges dstruto, calcluated y two methods, s the same. So the pushover methods ca e appled or sesmc aalyss o rame-shearwall structure cosdered. ()Compared to covetoal olear statc aalyss method, the pushover method cosdered has ts partcularty. It s ecessary to study the determato method o lateral load mode or pushover method. ()Tragular dstruto, uorm dstruto ad dstruto three lateral load mode, whch s the est lateral load mode or purshover method s eeded study. () The story pea dsplacemet ad story dt o the structure are reduced as cosdered, ad the order ad dstruto o plastc hges are ale etwee the s results ad s result, ut the degree o plastc hges s decreased. Reereces Lu Lpg. (). Study o Ple-Sol-Superstructure Elasto-plastc Dyamc Iteracto uder the Horzotal Earthquae Acto. Ph.D.Dssertato o Chogqg Uversty. Yag Pu, L Ygm, Wag Yayog, La Mg. (). Statc Push-over Aalyss Method s Amelorato. Joural o Buldg Structures :, 7-5. Wag Megu, Wag Jawu. (5). Studes o Pushover Aalyss Method or Hgh-Rse rame Structure Cosderg Sol-Structure Iteracto. Earthquae Resstat Egeerg ad Retrottg,7-. Wag egxa, Ou Jpg.(). Pushover Aalyss Procedure or System Cosderg Eects ased o Capacty Spectrum Method. Earthquae Egeerg ad Egeerg rato :5, -9. Che Qgju, HE Xaoa. (7). Aalyss o Sol-Ple-Structure Iteracto System Based o Capacty Spectrum Method. Chses Quarterly o Mechacs :, -. Pas A, Kausel E. (9). Approxmate ormulas or dyamc st-esses o rgd oudatos. Sol Dyamcs Ad Earth-quae Egeerg 7:, -7.