Performance-Based Plastic Design (PBPD) Procedure

Transcription

1 Performace-Baed Platic Deig (PBPD) Procedure 3. Geeral A outlie of the tep-by-tep, Performace-Baed Platic Deig (PBPD) procedure follow, with detail to be dicued i ubequet ectio i thi chapter ad theoretical utificatio give i the Appedix.. Select a deired yield mechaim ad target drift for the tructure coitet with the iteded performace obective for the deig earthquake hazard. Aume idealized elatic-platic (EP) force-diplacemet behavior ad etimate the yield drift ratio, y, for the tructure.. Etimate the atural period, T, of the tructure ad aumea appropriate vertical ditributio of deig lateral force. 3. With the iformatio i tep ad alog with the deig pectral acceleratio value, S a (Figure -), calculate the deig bae hear, V, by equatig the work eeded to mootoically puh the tructure up to the target drift (o puhover aalyi eeded) to the eergy eeded by a equivalet EP-SDOF to be diplaced up to the ame drift. A ratioal theory of ielatic eimic repoe of EP-SDOF ca be ued here, uch a the idealized ielatic repoe pectra by Newmark-Hall or other a preferred. 4. Modificatio for V i eeded if the force-deformatio behavior of the tructure i differet from the aumed EP behavior, uch a for CBF or other framig ytem. 5. Ue the platic method to deig the tructural member that are expected to diipate the earthquake eergy ielatically (DYM), while keepig the vertical ditributio of lateral tregth of the tructure cloe to the ditributio of deig hear ditributio. Member that are required to remai elatic (o-dym), uch a colum, are deiged by a capacity-deig approach, by accoutig for the trai-hardeig ad material overtregth of the DYM a well a by icludig the frame deformatio (P ) effect a appropriate. 3. Deig Procedure 3.. Target Yield Mechaim Figure 3- how everal typical tructural ytem i the yield mechaim tate ubected to deig lateral force ad puhed to their target platic drift limit. All iela- 7

2 tic deformatio are iteded to be cofied withi the DYM that are part of the elected yield mechaim, uch a platic hige i beam or yieldig ad bucklig of bracig member. Sice the platic hige at colum or wall bae geerally form durig a maor earthquake, the global yield mechaim of thee tructural ytem alo iclude platic hige at thoe locatio. Figure 3- Deirable Yield Mechaim of Typical Structural Sytem 8

3 Performace-Baed Platic Deig (PBPD) Procedure Figure 3- (cotiued) Deirable Yield Mechaim of Typical Structural Sytem 3.. Deig Lateral Force Equivalet tatic deig lateral force i the curret code are obtaied from implified model aumig that the tructure behave elatically ad primarily i the firt mode of vibratio (ATC, 978; Clough ad Pezie, 993; Chopra, 000; BSSC, 003b). However, buildig tructure deiged accordig to curret code procedure are expected to udergo large deformatio i the ielatic rage whe ubected to maor earthquake, thereby leadig to lateral force ditributio that ca be quite differet from thoe give by the code formula. I order to achieve the mai goal of performace-baed eimic deig, i.e., a deirable ad predictable tructural repoe, it i eceary to accout for ielatic behavior of tructure directly i the deig proce. Ulike the force ditributio i the curret code, the deig lateral force ditributio ued i the PBPD method i baed o maximum tory hear a oberved i oliear time-hitory aalyi reult (Chao et al., 007). Thi ew deig lateral force ditributio ha bee foud uitable for MF, EBF, CBF, ad STMF. Aalytical reult have how that: ) frame deiged with thi lateral force ditributio experieced more uiform maximum itertory drift alog the height tha the frame deiged with curret code ditributio; ) thi force ditributio alo give a very good etimate of maximum colum momet demad whe the tructure are repodig to evere groud motio ad deform ito the ielatic rage; 3) higher mode effect are well reflected i the propoed deig lateral force ditributio. Thi lateral force ditributio i expreed a 9

4 F i C V (3-) vi where C ( vi i i ) wh w h T whe i =, + = 0 (3-) i V V i i w h wh T (3-3) I the above equatio, i repreet the hear ditributio factor at level i; V i ad V, repectively, are the tory hear force at level i ad at the top (th) level; w i the eimic weight at level ; h i the height of level from the bae; w i the weight at the top level; h i the height of roof level from bae; T i the fudametal period; F i i the lateral force at level i; ad V i the total deig bae hear Deig Bae Shear The deig bae hear i the PBPD method i derived baed o the ielatic tate of the tructure, with the drift cotrol built i. Therefore, o eparate drift check i eeded after deig. I thi approach the deig bae hear i determied by puhig the tructure mootoically up to a target drift after the formatio of a pre-elected yield mechaim. No actual puhover aalyi i eeded for thi, a will be ee later. The amout of work eeded i aumed a a factor time the elatic iput eergy E( MS v ) for a equivalet EP-SDOF ytem (Houer, 956 ad 960). Houer (960) ued thi approach i order to determie the collape limit tregth of a catilever colum (repreetig a water tower, for example). For implicity, Houer aumed the eergy factor =, a he did ot have a good way of determiig it value at that time. The above-metioed work aume o relatiohip with the actual eergy diipated durig earthquake excitatio, which ha bee ued i eergy-baed procedure a propoed by a umber of ivetigator (Akiyama, 985; Uag ad Bertero, 988). However, thoe procedure have bee foud to be quite cumberome to implemet i commo deig practice. I the PBPD method, the eeded work term ( Ee Ep) i imply ued a a mea to calculate the required deig bae hear by etablihig tie amog the deired yield mechaim, deig drift, force-diplacemet characteritic of the tructure, ad elatic iput eergy from the deig groud motio. Thu, the work-eergy equatio ca be writte a ( Ee Ep) E ( MS v ) (3-4) 0

5 Performace-Baed Platic Deig (PBPD) Procedure where E e ad E p are, repectively, the elatic ad platic compoet of the eergy (work) eeded to puh the tructure up to the target drift. S v i the deig pectral peudo-velocity, ad M i the total ma of the ytem. The eergy modificatio factor,, deped o the tructural ductility factor ( ) ad the ductility reductio factor (R ). Figure 3- how the relatiohip betwee the bae hear (CW) ad the correpodig drift () of the elatic ad correpodig elatic-platic SDOF ytem. Uig the geometric relatiohip betwee the two area repreetig work ad eergy i Figure 3-, Equatio (3-4) ca be writte a CW y ( max y) C euweu (3-5) Figure 3- Structural Idealized Repoe ad Eergy (Work) Balace Cocept for SDOF Equatio (3-5) ca be reduced ito the followig form: eu y ( max y ) eu (3-6) where eu ad max i Figure 3- are equal to R y ad y, repectively. Subtitutig thee term ito Equatio (3-6), the expreio for eergy modificatio factor ca be writte a R (3-7)

6 where i the ductility factor equal to the deig target drift divided by the yield drift ( max / y ), ad R i the ductility reductio factor equal to C eu /C y. It ca be ee from Equatio (3-7) that the eergy modificatio factor i a fuctio of the ductility reductio factor (R ) ad the ductility factor ( ). The method by Newmark ad Hall (98) i ued herei to relate the ductility reductio factor ad the tructural ductility factor for EP-SDOF a how i Figure 3-3 ad Table 3- (Mirada ad Bertero, 994; Lee ad Goel, 00). Plot of the eergy modificatio factor a obtaied from Equatio (3-7) are how i Figure 3-4. For thi purpoe, ay ielatic pectra for EP-SDOF ytem ca be ued a preferred. Table 3- Ductility Reductio Factor (R = C eu /C y ) ad it Correpodig Structural Period Rage Period Rage Ductility Reductio Factor 0 T < T 0 T 0 R = R log T T T 4 R TT T R T T T T R Note: T = 0.57 ec., T T( / ) ec. Figure 3-3 Idealized Ielatic Spectra by Newmark ad Hall for EP-SDOF (98)