Seismic Performance Enhancement Methodology for Framed Structures using Supplemental Damping

Transcription

1 Vol., Issue.1, pp ISSN: Sesmc Performance Enhancement Methodology for Framed Structures usng Supplemental Dampng K. SAHISH KUMAR 1, R. SUNDARARAJAN, C. ANONY JEYASEHAR 3,. RADHA KRISHNAN 4 & K. MUHUMANI 5 1 (Senor Prncpal Scentst, ASaR Laboratory, CSIR-Structural Engneerng Research Centre, araman, Chenna, Inda) (Professor, Department of Structural Engneerng, Government College of echnology, Combatore, Inda) 3 (Professor, Department of Cvl and Structural Engneerng, Annamala Unversty, Annamala Nagar, Inda) 4 (M.E., Student, Department of Structural Engneerng, Government College of echnology, Combatore, Inda) 5 (Chef Scentst, ASaR Laboratory, CSIR-Structural Engneerng Research Centre, araman, Chenna, Inda) Abstract Supplemental dampng through passve energy dsspaton (PED) devces s often used for enhancng the sesmc performance of a sesmcally defcent structure to reduce the sesmc response under earthquake loadng. Such PED devces are normally ncorporated wthn the frame structure between adjacent floors through dfferent bracng schemes lke dagonal and chevron, so that they effcently enhance the overall energy dsspaton ablty of the sesmcally defcent frame structure n the loadng drecton. hese PED devces functon based on the large and stable energy dsspaton obtaned usng energy dsspaton mechansms lke vsco-elastc and elasto-plastc. hs paper presents a methodology based on the drect dsplacement based desgn (DBD) for desgnng PED devces for provdng supplemental dampng to enhance the energy dsspaton ablty of mult-storey frames subjected to earthquake loadng. Keywords - Sesmc performance enhancement, sesmc retrofttng, dsplacement based desgn, supplemental dampng, passve energy dsspaton devce 1. INRODUCION Recent damagng earthquakes provded powerful remnders of how vulnerable we all are to the forces of nature. Even n an advanced ndustral naton, our bult envronment s stll qute susceptble to natural dsasters. Consequently, one of the prncpal current challenges n structural engneerng concerns the development of nnovatve desgn concepts to better protect structures, along wth ther occupants and contents, from the damagng effects of destructve envronmental forces due to earthquakes. he tradtonal approach to sesmc desgn has been based on provdng a combnaton of strength and ductlty to resst the mposed loads. For major earthquakes, the structural desgn engneer reles upon the nherent ductlty of structure to prevent catastrophc falure, whle acceptng a certan level of damage. In ths tradtonal sesmc desgn, acceptable performance of a structure durng an earthquake s based on the lateral force resstng framed system beng able to absorb and dsspate energy n a stable manner for a large number of cycles. Energy dsspaton occurs n specally detaled ductle plastc hnge regons of beams and column bases whch also form part of the gravty load carryng system. Plastc hnges are regons of concentrated damage to the gravty frame whch often s rreparable. Nevertheless, ths desgn approach s acceptable because of economc consderatons provded, of course, that structural collapse s prevented and lfe safety s ensured. Sometmes, stuatons exst n whch ths tradtonal sesmc desgn approach s not applcable. When a structure must reman functonal after an earthquake, as the case of lfelne structures, the conventonal sesmc desgn approach s napproprate. For such cases, the structure may be desgned wth suffcent strength so that nelastc acton s ether prevented or s mnmal; an approach that s very costly. Moreover, n such structures, specal precautons need to be taken n safeguardng aganst damage or falure of mportant secondary systems whch are needed for contnung servceablty. But ths draw back can be mtgated, and perhaps elmnated, f the earthquake-nduced energy s dsspated n supplemental dampng devces placed n parallel wth the gravty load resstng system. he new approach for mprovng sesmc performance and damage control s that of passve energy dsspaton (PED) systems. hs strategy s attractve for two prmary reasons: 1. Damage due to the gravty load resstng system s substantally reduced, leadng to major reducton n post earthquake repar costs.. Earthquake damaged PED devces can be easly replaced wthout the need to shore the gravty framng. Alternate sesmc performance enhancement strateges [1] have been developed whch ncorporate earthquake protectve systems n the structure. In these systems, mechancal devces are ncorporated nto the frame of the structure to dsspate energy throughout the heght of the structure. he means by whch energy s dsspated s ether yeldng of mld steel, 134 P a g e

2 Vol., Issue.1, pp ISSN: sldng frcton, moton of a pston or a plate wthn a vscous flud, orfce acton of flud or vsco-elastc acton n polymerc materals. In addton to ncreasng the energy dsspaton capacty per unt drft of a structure, some energy dsspaton systems also ncrease the strength and stffness. Such systems nclude the followng types of energy dsspaton mechansms: yeldng, extruson, frcton, vscous and vsco-elastc acton.. MECHANISM OF SUPPLEMENAL DAMPING Fg. 1(a) and Fg. 1(b) show the pushover curves of a lnearly elastc frame and yeldng frame whch s essentally a plot of base shear vs. top floor dsplacement. Smlarly, the correspondng force dsplacement hysteretc loops depct lnear behavor and lmted ablty to absorb energy. Consder the case when energy-dsspatng devces are added to the frame, t s assumed that the connecton detals of the devces are such that nether nelastc acton nor damage occurs n the frame at the ponts of attachment durng sesmc exctaton. It s also assumed that the desgn of the energy dsspaton system s such that t functons properly and dsspates energy throughout the heght of the frame. he ablty of the frame to dsspate energy s substantally ncreased as demonstrated n the force-dsplacement hysteretc loops of the frame. Accordngly, the frame undergoes consderably reduced ampltude of vbraton n comparson to the frame wthout the energy dsspaton system under the same earthquake moton. Whle the energy dsspaton system can acheve a consderable reducton n the dsplacement response, t can also acheve a reducton n the total force exerted on the structure. In general, reducton n force wll not be as much as reducton n dsplacement whch s due to the ncreased strength or ncreased stffness provded by the energy dsspaton system. Comparable reductons n dsplacement and force can be acheved wth systems that do not ncrease the strength or stffness of the structure to whch they are attached. 3. MODELING OF PED DEVICES For analyss of structures wth PED devces, varous mathematcal modelng technques have been developed. Varous models wth ncreased complexty are revewed n Renhorn et al., (1995) [] for PED devces of vscous type. Constantnou and Symans (1993) [3] showed that the Maxwell model s adequate to capture the frequency dependence of the vscous PED devce. It s also shown that, below a cut off frequency of approxmately 4 Hz, the model can be further smplfed nto a purely vscous dashpot model. It s stated n FEMA-73 [4] and FEMA-74 [5] that the dampng force of a vscous PED devce can be modeled to be proportonal to the velocty wth a constant exponent rangng between 0. and.0. In prelmnary analyss and desgn stages, the velocty exponent of 1.0 s recommended for smplcty. In ths study, based on those references, the behavor of vscous PED devce s modeled by a lnear dashpot. Fg.1 (a) Pushover curves and force-dsplacement hysteretc curves of an elastc structure wthout and wth passve energy dsspaton devces Fg.1 (b) Pushover curves and force-dsplacement hysteretc curves of a yeldng structure havng proper plastc hnge formaton, wthout and wth passve energy dsspaton devces 135 P a g e

3 Vol., Issue.1, pp ISSN: be an effectve method for mplementng performance based sesmc desgn utlzng deformaton capacty and ductle detalng standards. In the present study, the general procedure of the DBD documented n the SEAOC Blue Book [7] s appled n reverse order for evaluaton of sesmc performance of an exstng structure. In prncple, the proposed analyss procedures are smlar to the capacty spectrum method [5],[8],[9] n that performance pont s G'( ) A determned as a locaton where the dsplacements demand of Kd the earthquake becomes equal to the plastc deformaton t (1) capacty of the structure. he dfference s on the use of G"( ) A dsplacement spectrum nstead of the so called acceleraton Cd dsplacement response spectrum (ADRS). herefore, the extra t work requred for transformng the capacty and demand curves to ADRS format can be avoded. Although ths may not be a sgnfcant mprovement, t has the advantage of mantanng consstence wth the proposed desgn procedure A typcal vsco-elastc PED devce conssts of thn layers of vsco-elastc materal bonded between steel plates. In practce, the dynamc behavor of vsco-elastc PED devce s generally represented by a sprng and a dashpot connected n parallel [6]. For the lnear sprng-dashpot representaton of the vsco-elastc PED devce, the stffness K d and the dampng coeffcent C d are obtaned as follows: Where, G () and G () are the storage shear modulus and loss shear modulus respectvely; A and t are total shear area and the thckness of the materal respectvely; and s forcng frequency for whch the fundamental natural frequency of the structure s generally utlzed n tme doman analyss. Wth ths sprng-damper dealzaton, the dynamc system matrces of the structure wth added vsco-elastc PED devces can be constructed by superposng the damper propertes to the stffness and dampng matrces of the structure. Fg. represents the mathematcal models of vscous and vscoelastc PED devces employed n ths study. for supplemental dampers. wo nonlnear statc analyss procedures, the step by step and the graphcal procedure, whch correspond to the nonlnear statc procedures A and B of AC-40 [8] respectvely, are proposed for sesmc performance evaluaton of structures (wthout PED devces). he two procedures are summarzed as n the followng subsectons: Fg. (a) Mathematcal model representng vscous PED devce Fg. (b) Mathematcal model representng vsco-elastc PED devce 4. PERFORMANCE EVALUAION USING DISPLACEMEN SPECRUM AND CAPACIY CURVE he drect dsplacement based desgn (DBD), whch focuses on dsplacement as the key desgn parameter, s consdered to Fg. 3 Blnear representaton of a capacty (pushover) curve 4.1 Step by step procedure 1. Obtan base shear versus roof storey dsplacement capacty curve for the frame structure from pushover analyss.. Approxmate the capacty curve by blnear lnes based on equal energy concept (area A 1 = area A ), and determne the quanttes such as effectve elastc stffness K e, elastc natural perod e, base shear at yeld V y, yeld dsplacement Δ y and post-yeld stffness rato α (Fg.3). 136 P a g e

4 Vol., Issue.1, pp ISSN: ransform the roof storey dsplacement coordnate nto pseudo-dsplacement coordnate S d usng the followng relaton: S R d () R Where, Δ R s the roof dsplacement and and R s the modal partcpaton factor and the roof storey component of the fundamental mode respectvely. hs process corresponds to the transformaton of the structure nto an equvalent sngle degree of freedom (SDOF) structure. 4. Assume the frst tral value for the maxmum dsplacement S dm of the equvalent structure, and determne the ductlty factor μ = S dm /S dy. he equvalent dampng rato eq can be obtaned as: eq hen, the effectve dampng for the structure can be obtaned as the sum of the equvalent dampng and the nherent dampng of the structure: (3) eff eq (4) Where, s the nherent dampng for whch 5% of crtcal dampng s generally utlzed. Also, the effectve perod eff correspondng to the maxmum dsplacement can be obtaned as: eff 11 1 e 1 Where, e s the fundamental perod of the structure. 5. Construct the dsplacement response spectrum for desgn earthquake usng the effectve dampng obtaned n the prevous step, and read from the spectrum the next tral value for the maxmum dsplacement S dm correspondng to the effectve perod eff. 6. Repeat the process from step 4 usng the maxmum dsplacement computed n the above step. Once the maxmum dsplacement S dm converges, then convert t nto the maxmum roof dsplacement usng equaton. 7. Carry out pushover analyss untl the roof dsplacement reaches the maxmum value computed above to estmate the maxmum nter-storey drfts. (5) 4. Graphcal procedure 1. Steps 1 & : he same as those of the step by step procedure.. Step 3: Draw dsplacement response spectra wth varous dampng ratos. 3. Step 4: For a seres of ductlty ratos, obtan maxmum dsplacements (S dm = μ. S dy ), effectve perods eff (μ) [Eq.5] and effectve dampng ratos ( eff ) [equatons.3 and 4]. 4. Step 5: Fnd out the pont at whch the effectve dampng rato correspondng to a ductlty rato, obtan n step 4, s equal to the equvalent dampng rato of a dsplacement spectrum crossng the pont [ eff (μ), S dm (μ)]. 5. Step 6: Convert the maxmum dsplacement computed n the above step nto the maxmum roof dsplacement, and carry out pushover analyss untl the roof dsplacement reaches the maxmum value computed above to estmate the maxmum nter-storey drfts. 5. DESIGN PROCEDURE FOR PED DEVICES If the maxmum storey drft of a structure subjected to a codespecfed earthquake load exceeds the desred performance level, the structure needs to be retroftted. Among the varous methods for sesmc retroft, ths study focuses on ncreasng dampng to decrease earthquake nduced structural responses. o ths end, a procedure for estmatng the amount of supplemental dampng requred to satsfy the gven performance objectve s proposed. he basc dea s to compute the requred dampng from the dfference between the total effectve dampng needed to meet the target dsplacement and the equvalent dampng provded by the structure at the target dsplacement. 5.1 Requred dampng to meet target dsplacement he dampng rato of the dsplacement response spectrum that ntersects the pont of the target dsplacement S dt on the dsplacement ordnate (vertcal axs) and the effectve perod eff on the perod ordnate (horzontal axs) corresponds to the total effectve dampng eff for the structure to retan to meet the performance objectve. For structure wth supplemental dampers, the total effectve dampng s composed of the three components: nherent vscous dampng, equvalent dampng of the structure contrbuted from nelastc deformaton of the structural members eq and the dampng requred to be added by the PED devces d. he equvalent dampng of the structure s obtaned from the followng equatons [4]: 1 E VyS DS dt SdyVt eq (6a) 4 E V S for Vscous PED devce S t dt 137 P a g e

5 Vol., Issue.1, pp ISSN: V S S V of storey. he potental energy stored n the mult-storey (6b) structure can be expressed as follows: V S ξ eq yd dt dy td for Vsco-elastc PED devces td Where, V yd = V y + K d S dy, V td = V t + K d S dt and E s and E DS are the stored potental energy n the structure and the energy dsspated by hysteretc behavor of the structural members n the retroftted structure respectvely. sopelas et al., (1997) [10] provdes the contrbuton of the added dampng to the total effectve dampng as ( d. eff )/ e, where d s the supplemental dampng rato. hen the requred supplemental dampng can be computed from the followng equaton: dt eff. d E for Vscous PED devces eff. d N S m eff. d 1 y (10) M * Sdt V (1 ) for Vsco-elastc PED devces M * Sdt V (1 ) K S y d dt (11a) (11b) e d ( eff eq ) (7) Where, the total effectve dampng and the equvalent dampng can be obtaned from the dsplacement response spectrum and from equaton 6 respectvely. 5. Storey-wse dstrbuton of PED devces In mult-storey frame structures, the supplemental dampng computed n the equvalent SDOF system usng equaton 7 should be dstrbuted throughout the stores of the orgnal structure n such a way that the dampng rato for the fundamental mode becomes the requred supplemental dampng d. For ths purpose, the expresson for equvalent dampng (equaton 6) s used agan except that the energy dsspated by the PED devce E DV s used n the numerator nstead of E DS eq 1 EDV 4 E (8) S If the PED devces are placed as dagonal members wth the nclnaton, then, the energy dsspated by the PED devces can be expressed as follows [4]: eff Where, M* s the effectve modal mass and m s the mass of the th storey. By substtutng equaton 9 and 10 nto equaton 8, the dampng rato contrbuted from the PED devces can be expressed as: 1 d 4 N eff. d C cos ( 1 d 1) N m 1 (1) In equaton 1, the left hand sde of the equaton d s obtaned from equaton 7 n the equvalent SDOF system. For vscous devce, the dampng coeffcent of the damper devce n the th storey C d can be determned n equaton 1, whereas for vsco-elastc devce, both C d and K d are the varables that should be determned. hs can be done by usng the relaton K d = (G /G ).C d obtaned from equaton 1. he smplest case s to assume that the PED devces n all storeys have the same capacty, and the dampng coeffcent n ths case can be obtaned from equaton 1 as: C d 1 4 eff, d 4 N 1 d N 1 m cos ( ) 1 (13) E N DV Cd cos ( 1) eff. d 1 (9) Where, eff.d s the secant perod of the retroftted structure; C d and Δ are the dampng coeffcent and the maxmum lateral dsplacement of the th storey respectvely, and N s the number In ths stage, however, the maxmum storey dsplacements, except for the top-storey dsplacement gven as performance lmt state, are known. herefore, the confguraton for lateral storey drfts Δ needs to be assumed n equatons 1 and 13. A smple case s to assume that the maxmum storey drfts are proportonal to the fundamental mode shape or to the pushover curve. he storey-wse dstrbuton pattern for the PED devces also needs to be assumed. For vscous dampers, the 138 P a g e

6 Vol., Issue.1, pp ISSN: desgn process ends here. However, for PED devces wth stffness such as vsco-elastc or hysteretc dampers, teraton s requred, because the added PED devces ncrease system stffness. In that case, the capacty curve of the system needs to be redrawn consderng added PED devces, and the process s repeated untl convergence. 6. DESIGN PROCEDURE FOR PED DEVICE SCHEME he proposed procedure to desgn supplemental dampers for performance based sesmc retroft of exstng structures can be summarzed n the followng steps: 1. Carry out egen value analyss of the structure to obtan natural perods and mode shapes. Usng the mode shapes, perform pushover analyss to obtan top storey versus base shear curve, and transform the pushover curve nto a capacty curve usng equaton. Idealze the curve nto a blnear shape, and read the yeld dsplacement S dy.. Decde a desred target roof dsplacement, and transform t nto the target value n the equvalent SDOF system S dt. Obtan ductlty rato μs dt /S dy, the effectve perod eff (equaton 5) and the equvalent dampng eq (equaton 6) at the target dsplacement. 3. Fnd out the effectve dampng rato correspondng to the dsplacement response spectrum that crosses the pont of the target dsplacement and the effectve perod. hs corresponds to the total demand on dampng mposed by the earthquake. It would be more convenent to start the procedure wth response spectra wth varous dampng ratos. 4. Compute the requred dampng for supplemental dampers from equaton he requred dampng s dstrbuted throughout the storeys usng Equaton 1. he sze of PED devce n each storey s desgned based on the requred dampng allocated to the storey. 6. For structures retroftted wth vsco-elastc PED devces, carry out egen value analyss and redraw the capacty curve of the structure usng the newly obtaned mode shape, and repeat step 1 untl convergence. 7. Check whether the structural members, especally columns, can resst the addtonal axal and shear forces mposed by PED devces. 7. SUMMARY AND CONCLUSIONS he general procedure of the drect dsplacement based desgn (DBD) documented n the SEAOC Blue Book s appled n reverse order for evaluatng the sesmc performance of an exstng structure. Based on whch a methodology s presented for desgnng PED devces of vscous and vscoelastc types for provdng supplemental dampng to enhance the energy dsspaton ablty of mult-storey frames subjected to earthquake loadng. ACKNOWLEDGEMEN he authors wsh to express ther deep apprecaton to Drector, CSIR-SERC, Chenna, for the support and encouragement provded n carryng out the above research work and for the knd permsson to publsh the paper n the Internatonal Journal of Modern Engneerng and Research. REFERENCES [1] J.M. Kelly, R.I. Sknner, and A.J Hene, Mechansm of Energy Absorpton n Specal Devces for Use n Earthquake Resstant Structures, Bull, N.Z., Soc. Earthquake Engneerng, 5(3), 197, [] A.M. Renhorn, C. Le, and M.C. Constantnou, Expermental and Analytcal Investgaton of Sesmc Retroft of Structures wth Supplemental Dampng, Part I: Flud Vscous Dampng Devces (echncal Report, NCEER Natonal Center for Earthquake Engneerng Research, Buffalo, New York, 1995). [3] M.C Constantnou, and M.D. Syman, Expermental Study of Sesmc Response of Buldngs wth Supplemental Flud Dampers, Struct. Des. all Buldngs, (), 1993, [4] Federal Emergency Management Agency (FEMA), NEHRP Gudelnes for the Sesmc Rehabltaton of Buldngs, FEMA-7 (prepared by the Appled echnology Councl for the Buldng Sesmc Safety Councl, Washngton, D.C.,1997a). [5] Federal Emergency Management Agency (FEMA), NEHRP Commentary on the Gudelnes for the Sesmc Rehabltaton of Buldngs, FEMA-74 (prepared by the Appled echnology Councl for the Buldng Sesmc Safety Councl, Washngton, D.C. 1997b). [6].. Soong, and G.F. Dargus, Passve Energy Dsspaton Systems n Structural Engneerng (Wley, New York, 1997). [7] Structural Engneers Assocaton of Calforna (SEAOC), Recommended Lateral Force Requrements and Commentary (Appendx I, Sacramento, Calforna, 1999). [8] Appled echnology Councl (AC), Sesmc Evaluaton and Retroft of Concrete Buldngs, (AC-40, Redwood Cty, Calforna, 1996). 139 P a g e

7 Vol., Issue.1, pp ISSN: [9] S.A. Freeman, Development and Use of Capacty Spectrum Method, Proceedngs of 6 th Natonal Conference on Earthquake Engneerng, Seatle, [10] P. sopelas, M.C. Constantnou, C.A. Krcher, and A.S. Whttaker, Evaluaton of Smplfed Method of Analyss for Yeldng Structures (echncal Report: NCEER , Natonal Center for Earthquake Engneerng Research, State Unversty of New York at Buffalo, Buffalo, New York. 1997). 140 P a g e