CASE STUDIES ON PERFORMANCE BASED SEISMIC DESIGN USING CAPACITY SPECTRUM METHOD

Transcription

1 CAE TUDIE ON PERFORMANCE BAED EIMIC DEIGN UING CAPACITY PECTRUM METHOD T NAGAO, H MUKAI An D NIHIKAWA 3 UMMARY Ths research ams to show the proceures an results of Performance Base esmc Desgn usng Capacty pectrum Metho (CM) for Ductle teel tructures. Two 9-story bulngs, A an B for examples, whch are rgly jonte steel structures wth the same confguraton were esgne uner fferent sesmc performance crtera. Bulng A was esgne to satsfy the mnmum requrements, whch are escrbe as "Lfe-safety aganst severe EQ (earthquake)" an "ervceablty after moerate EQ". Bulng B was esgne to have one more requrement as "Reparablty after severe EQ", whch ncates hgher sesmc performance. CM s the proceure where the eman spectra an the capacty of the structure met n the Acceleraton Dsplacement Response pectrum (ADR) format at the performance pont, whch escrbes a fferent level of sesmc esgn crtera. The results were evaluate by the elasto-plastc mult-mass tme-hstory sesmc response analyses usng real EQ recors. The bulng performance mprovement can be one wth a slght expense of steel weght. INTRODUCTION "Lfe-safety aganst severe EQ (earthquake)" an "ervceablty of the structure after moerate EQ" were the stanar sesmc esgn crtera. After the 995 Kobe EQ, t becomes wely recognze that some partcular bulng shoul am to hgher levels of sesmc esgn crtera such as Reparablty or ervceablty when severe EQ occurs. Responng to these current emans, the Performance Base esmc Desgn s ntene to be ntrouce to the Japanese Bulng tanar Law as a near future esgn proceure, however, etals are not yet clear. Ths paper ams to show the proceures an results of Performance Base esmc Desgn usng Capacty pectrum Metho (CM) for uctle moment resstng steel frames. CONCEPT OF PERFORMANCE BAED EIMIC DEIGN UING CM Capacty pectrum Metho (CM) The Capacty pectrum Metho s a graphcal an approxmate metho use to compare the bulng capacty an an earthquake eman, as shown n Fg.. An earthquake eman s represente by a response spectrum curve. 3 tructural Engneerng Dept., Nhon ekke Inc., hnjuku, Tokyo, JAPAN Emal:nagao-t@nhonsekke.co.jp tructural Engneerng Dept., Nhon ekke Inc., hnjuku, Tokyo, JAPAN tructural Engneerng Dept., Nhon ekke Inc., hnjuku, Tokyo, JAPAN

2 Conventonally t s represente by a (acceleraton response)-t (pero) relatonshps for fferent ampng levels. However, n CM t s expresse by an Acceleraton ( a )-Dsplacement ( ) Response pectrum (ADR) format, n ths the T -axs s converte to the -axs where the raal lnes from the orgn n the ADR format represent the pero n the form of ω ( =( ) π ). / T The lateral force resstng capacty of the bulng s represente by the story shear-force to nter-story rft relatonshps ( curve) obtane from pushover analyses. Q δ Q δ The secant moulus (the raal lne from the orgn) n the curve represents an equvalent lnear system wth an equvalent hysteress ampng (substtute ampng) whch reflects the effect of nelastc behavor. The substtute ampng h cause by nelastc behavor s ncate here by hbata metho [] as follows; h =. + h e µ () h =. where, : elastc ampng for steel moment frame,an, µ : uctlty rato e When both curves are plotte on ADR format, the pont of ntersecton approxmates the response an the performance of the structure for a partcular earthquake, ths s calle a performance pont. Acceleraton pectrum a Fg. : Concept of CM Fg. 3: Performance Base esmc Desgn usng CM ubsttuton from Mult-Degree of Freeom system to ngle-degree of Freeom system As shown n Fg., a Mult-Degree of Freeom system (MDF) s substtute by a ngle-degree of Freeom system (DF) uner the followng assumptons. Frstly, the strbuton pattern of the lateral splacements (rfts ) of MDF resembles to ts frst natural moe of vbraton, an seconly the equvalent heght of the substtute DF s etermne from the heght at { u } β of the MDF, where, β = (cm/s ) h =5% h =% ( π ) ω = T (cm) Dsplacement pectrum ncates the frst natural moe of vbraton. Bulng Capacty Performance Pont T T Deman pectrum ubsttute Acceleraton a (=Q B / M) (cm/s ) h =5% h =8% h =% evere EQ Moerate EQ Performance Pont R * R 3 R R Crtera Crtera 3 Equvalent Drft Angle /H eq Crtera (ra.) ncates the partcpaton factor of the frst natural moe, an { } u

3 Q δ The set of curves of MDF etermne from pushover analyss s substtute to the global forcesplacement relatonshp of DF usng the followng equatons [5]. T N = N = m δ π () P δ M N = = N = m δ m δ (3) Performance Levels of Bulng Table : esmc Desgn Crtera For Rear EQ. (5 years of Return pero) For Moerate EQ. (5 years of Return pero) pecal level (Grae ) ervceable () ervceable / Non-amage Hgh level (Grae ) Reparable () ervceable tanar level (Grae 3 ) Lfe-safe (3) Reparable / ervceable () ervceable level s that when the partcular bulng systems are able to operate, therefore the structural elements ha lghtly-amage or non-amage. () Reparable level s that when the bulngs are able to be reuse, therefore the structural elements behave n the nelastc regon but wthn the lmte eformaton causng slght resual eformatons. (3) Lfe-safe level s that when the bulngs o not collapse, therefore the structural elements are heavly amage up to ts eformaton capacty. A strbuton P β { u } β u = Q B M st natural moe of vbraton H eq H MDF Fg. : ubsttutng from MDF to DF DF a QB M = (4) 3

4 a = (5) ω A T = + α α + 3 T (6) where, T = π / ω : funamental pero of the substtute structure (DF) M : substtute mass of the DF whch corresponng to effectve mass of the st moe of MDF Q : base-shear force B a : substtute acceleraton response (DF) : substtute splacement response of DF whch correspons to the splacement at eq of MDF : rft of the -th story of MDF A strbuton δ P : lateral force apple to the -th story of MDF whch s etermne from ω : funamental crcular velocty of the substtute structure (DF) N : number of stores of MDF H eq : equvalent heght of DF corresponng to the heght β { u} = of the MDF A : horzontal shear force strbuton etermne n current Japanese esmc Desgn Coe (MDF) N N w / = = α = w : the non-mensonal mass of -th floor, where w ncates weght of -th floor Target Performance: Performance levels of bulngs are conventonally classfe nto 3 categores, as shown n Table, whch can be efne numercally by the maxmum splacement response [4]. ubsttute ampng s selecte from 5 to 8% for severe EQ, an to 5% for moerate EQ n the CM. For uctle moment resstng steel frames, Reparablty after severe EQ (crtera ) s represente as the maxmum splacement response less than R, as shown n Fg.3, whch s assume here as. ra. of substtute rft angle ( / H eq ) by severe EQ wth 8% ampng to realze a slght resual splacement. Lfe-safety after severe EQ (crtera ) s represente less than R (assume here.5 ra.) by severe EQ wth 8% ampng, an ervceablty after moerate EQ (crtera 3) s less than R3 (assume here as.5 ra. ) by moerate EQ wth % ampng. tructural members were selecte by tral-an-error metho untl meetng the target performance through the funamental pero, the substtute rft angle, an the substtute acceleraton response. Moel Frame : CAE TUDY Two 9-story offce bulngs A an B, whch are rgly jonte steel structures wth the same confguraton, were esgne uner fferent sesmc performance crtera. Bulng A( W=7kg/m ) was esgne to satsfy the mnmum requrements, whch are escrbe as "Lfe-safe aganst severe EQ" an "ervceable after moerate EQ", corresponng to tanar level n Table. Bulng B( W=83kg/m ) was esgne to have one more requrement of "Reparable after severe EQ", whch ncates hgher sesmc performance corresponng to Hgh level n Table. The structure s 5x5spans wth 9mx9m spannng, as shown n Fg.4 [], an average weght of the bulng (the ea +lve loa per unt floor area) s about 55kg/m. Columns are col forme rectangular hollow sectons, H 4

5 an beams are H-shape rolle sectons, as shown n Table 4 (materal propertes are both JI N49), whch are selecte to realze the weak beam type collapse mechansm wth uctle behavor. tory R/9 9/8 Table : tructural Members for Moel Frame Bulng A Bulng B Column Beam Column Beam Box-45x6 H-5x5x9x6 Box-5x9 H-6x5x9x6 8/7 Box-45x9 H-5x5x9x6(9) Box-5x H-6x5xx9 7/6 H-5x5x9x9() H-6x5xx9() 6/5 H-6x5xx(5) 5/4 Box-45x H-6x5xx9() Box-6x5 H-7x5xx(5) 4/3 3/ H-7x5x4x5(8) / Box-5x5 H-7x5x4x9() Box-6x8 H-75x5x4x5(8) ( ) ncates the external en (at the connecton to external column) of Beam member (Unt: mm) (a) tructural Elevaton (b) tructural Plan Fg. 4: Moel Frame Pushover Analyss: Pushover analyss was performe uner the followng assumptons; ) Lateral shear force strbuton s A ncate n Eq(6). ) Benng stffness of beams are evaluate as composte beams wth concrete slab. 3) Benng, shear, an axal eformatons are consere n beams an columns. 4) Deformatons of panel zone are neglecte. 5) Column-bases are fxe. 6) Perfect b-lnear characterstcs are assume n the plastc hnges of beams at M p (full plastc moment), an of columns at M pc (reuce plastc moment ue to axal force). 7) Yel strength ( σ y )=3.63 tonf/cm (% ncrease from nomnal value) was use for structural members. tory shear force to nter-story rft relatonshps ( Q δ curves) for each story are shown n Fg.5. Plastc hnges occurre, as shown n Fg.6, frstly at the beam-ens, an fnally at the column bases, whch ncates the weak beam type collapse mechansm. The hysteress characterstcs are moele as tr-lnear. 5

6 The frst nflecton pont of ths moel (here efne as µ =) s etermne as the frst yelng of a partcular beam, especally at the rear en of the long-span beam cause by vertcal loa, an the secon nflecton pont s etermne at a stage close to the collapse mechansm (the thr stffness of ths moel s almost ). tory-hear Force (tonf) 3 8F 9F Moerate EQ by CM Inter-tory Drft (cm) 7F F F 3F 4F 5F 6F evere EQ by CM tory-hear Force (tonf) 4 3 9F 8F Moerate EQ by CM Inter-tory Drft (cm) 7F F F 3F 4F 5F 6F evere EQ by CM (a) Blg. A (b) Blg. B Fg.5 : tory-hear Force to Inter-tory Drft Relatonshp RFL RFL 9FL 8FL 7FL 6FL 5FL 4FL 3FL FL FL 8FL 7FL 6FL 5FL 4FL 3FL FL FL 9 FL X X X3 X4 X5 X6 X X X3 X4 X5 X6 (a) Blg. A (b)blg. B Deman pectra an Capacty of Bulngs Fg. 6: Plastc Hnge Pattern The eman spectra an the capactes of the bulngs are escrbe n ADR format ( a - agram), as shown n Fg.7.The eman spectra for severe EQ (5years of return pero) wth 5 to 8%t ampng an moerate EQ (5years of return pero) wth %ampng are erve from reference [3], whch are apple to Tokyo area wth meum soft sol conton.the capacty of the bulngs are etermne as global loaeformaton relatonshps through Eq() to Eq(5). The performance ponts obtane from CM are summarze n Table 3. 6

7 The loa-eformaton curve of Blg. A satsfes the crtera, however oes not satsfy the crtera. The Blg.B satsfes the both crtera. H Although the substtute rft angles ( / eq ) of the Blg. B corresponng to severe EQ s over /, the * resual rft angle ( R ) s less than /5 (.ra.), whch s consere to mantan the Reparblty. The fferences between Blgs. A an B n the terms of unt steel weght s only 5%. Unt steel weght (W ) Table 3: Results of CM evere EQ (5years of return pero) Moerate EQ (5years of return pero) * * (gal) R (ra.) a (gal) R (ra.) *) a ( = Q B / M ) / H eq (ra.) ( = Q B / M ) / H eq (ra.) Blg. A 7 kg/m Blg. B 83 kg/m *) W : total steel weght of columns an beams ve by the total floor area of the bulng ubsttute Drft Angle /H eq (cm/s ) (ra.) h =5% Deman pectrum Accelaraton pectrum a h =8% Blg.B Blg.A El Centro N (h=5%) Taft EW (h=5%) Kobe (NTT) N (h=5%) Performance Pont Crtera Crtera Dsplacement pectrum (cm) Fg. 7: Results of CM Table 4: Input EQ Waves Input EQ Waves Recore Max. Recore Max. Tme Duraton Use Max. Acceleraton Acceleraton Velocty Corresponng to Vmax=5cm/sec El Centro 94 N Taft 95 EW Kobe (NTT) 995 N Tme Hstory Dynamc Response Analyss: The results obtane through CM (a metho of approxmate analyss) were evaluate by a more precse elastoplastc mult-mass tme-hstory sesmc response analyss usng real EQ recors. The restorng force characterstcs are assume for normal-tr-lnear, an the EQ recors are, as shown n Table 4, scale to 5cm/sec as of maxmum velocty ( V max =5cm/sec) corresponng to severe EQ. 7

8 To evaluate the characterstcs of the nput EQ waves, as shown n Fg.7, the response spectra wth 5% ampng were plotte n ADR format ( a - agram). In spte of ranomness of ther spectra, ther envelope s smlar (however quanttatvely larger) to the smoothe esgn spectrum use n CM. Performance ponts obtane by CM are shown n Fg.5. The maxmum response of splacement (rft angle) an uctlty, shown n Fg.8, are larger than the results obtane from CM, because the CM represents the average behavor of MDF as DF. tory R (ra.) Fg. 8: Maxmum Drft Angle ( R ) an Ductlty Rato ( µ ) Response Conclusons are summarze as follows; tory CONCLUION. Performance base sesmc esgn can be attane through CM uner approprate assumptons.. Up-grang of bulng performance can be obtane by a slght expense of steel weght (only 5% of steel weght ncrease was enough n ths case). 3. Results obtane through CM are consstent wth the results usng more exact tme-hstory sesmc response analyss. 4. CM shows the average response of Mult-Degree of Freeom system, therefore, the response concentraton to the partcular story shoul be avoe n the esgn proceures such as a control of collapse mechansm, a control of strength rato between beam to column, etc. REFERENCE Blg.A Blg.B El Centro N Taft EW Kobe(NTT) N CM. T.Hasegawa et.al., Comparson between sesmc performance of U steel permeter an Japanese spatal moment resstng frames(part to 3), Annual Conferences of AIJ, 998, C-pp A.hbata an M.A.ozen., ubsttute structure metho for sesmc esgn n R/C, Journal of Earthquake Engneerng an tructural Dynamcs, vol.8, 98, pp Archtectural Insttute of Japan, Recommenatons for Loas on Bulng, 993, AIJ 4. tructural Engneers Assocaton of Calforna, Performance Base esmc Engneerng of Bulngs, VIION, 995 Kuramoch et.al., esmc Evaluaton of Bulngs by Acceleraton Response pectrum at Engneerng Berock (Part 6) Converson to ngle Degree of Freeom, Annual Conferences of AIJ, 999 8