Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 98 The use of helical spring and fluid damper isolaion sysems for bridge srucures subjeced o verical ground acceleraion A. Parvin 1 and Z. Ma 2 1 A/Professor, Deparmen of Civil Engineering, Universiy of Toledo, OH 4366-339 USA Email: aparvin@eng.uoledo.edu 2 Former Grad. Suden, Deparmen of Civil Engineering, Universiy of Toledo, OH 4366-339 USA Received 17 May 21; revised 22 July 21; acceped 24 July 21 ABSTRACT In his sudy a combinaion of helical springs and fluid dampers are proposed as isolaion and energy dissipaion devices for bridges subjeced o earhquake loads. Verical helical springs are placed beween he supersrucure and subsrucure as bearings and isolaion devices o suppor he bridge and o eliminae or minimize he damage due o earhquake loads. Addiionally, horizonal helical springs are placed beween he abumens and bridge deck o save he srucure from damage. Since helical springs provide siffness in any direcion, a muli-direcional seismic isolaion sysem is achieved which includes isolaion in he verical direcion. To reduce he response of displacemen, nonlinear fluid dampers are inroduced as energy dissipaion devices. Time hisory analysis sudies conduced show ha he proposed bridge sysem is sufficienly flexible o reduce he response of acceleraion. The response of displacemen due o provided flexibiliy is effecively conrolled by he addiion of energy dissipaion devices. KEYWORDS Seismic isolaed srucures; dynamic analysis; verical moion; helical spring. 1. Inroducion Seismic isolaion reduces he response of a srucure during an earhquake by inroducing flexibiliy and energy dissipaion capabiliies. Generally, horizonal ineria forces cause he mos damage o a srucure during an earhquake. Since he magniude of he verical ground acceleraion componen is usually less han he horizonal ground acceleraion componen, verical seismic loads are no considered in he design of mos srucures. The verical acceleraion is ypically aken as wo hirds of he horizonal acceleraion componen for he same response specral curve. However, recen observaion and analysis of earhquake ground moion have shown ha he verical moion in bridges should no be compleely ignored. Researchers compiled records and phoographs of damage and failures of buildings and bridges due o high verical moion. Raios of peak verical-o-horizonal acceleraion have been recorded as high as 1.6, while he convenional design assumpion is.67 [1]. Damage from Kalamaa, Greece (1986), Norhridge, CA (1994), and Kobe, Japan (1995) due o purely verical effecs is repored, along wih he high verical -o-horizonal acceleraion raios. No many researchers address verical moion in heir sudies. Among he few who have, Buon e al. [2] invesigaed he effec of verical ground acceleraion on six bridge ypes and hey recommended crieria for inclusion or exclusion of verical ground moion in he design and analysis of bridges. Their sudy was limied o bridges wih no base isolaion and energy dissipaion devices. Waisman and Grigoriu [3] sudied he influence of he verical seismic 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 99 componen on a fricion-pendulum ype base-isolaed bridge. Their model was limied o a single span, and single degree-of-freedom sysem. Saadeghvaziri and Fouch [4] invesigaed he behavior of reinforced concree highway bridges ha were no isolaed and were subjec o combined verical and horizonal earhquake moions. They concluded ha i is imporan o include he verical componen of ground acceleraion moion in he design of highway bridges. Mos research sudies in bridge isolaion, where he verical ground moion is negleced, include heoreical and experimenal analysis of various acive and passive isolaors (for horizonal plane moions) ha are no muli-direcional and are complex in some cases. Among such recen sudies, Xue e al. [5] proposed a new sysem ermed he Inelligen Passive Vibraion Conrol (IPVC), which conains boh passive (isolaion) and inelligen, or acive (damping) elemens. During small earhquakes, only he passive sysem is uilized. During large earhquakes, he acive sysem is riggered by displacemen limiaions. Furher experimenal and analyical resuls on passive/acive conrol of a bridge, which employs sliding bearings wih recenering springs for isolaion, and servo-hydraulic acuaors acivaed by absolue acceleraion records, are repored by Nagarajaiah e al. [6]. This sysem allows for a sliding sysem wih higher fricion o be implemened wihou fear of high acceleraion response. Yang e al. [7] presened analyical models for rubber and sliding bearings coupled wih acuaors for bridges. The verical moion in he bridge is crucial. The uplif from he verical moion may cause loss of conac followed by impac, which is likely o lead o higher mode response and large axial forces in he piers. Exising bridge bearings including elasomeric bearings and lead rubber bearings among ohers are designed o only provide isolaion in he horizonal plane. For insance, in some cases, using only horizonal isolaion may provide sufficien proecion agains an earhquake. However, in cerain oher cases, where verical ground acceleraion is significan, a muli-direcional isolaion sysem, which possibly employs helical springs may be required. This sudy involves novel bridge bearings consising of helical springs and viscous dampers o achieve a muli-direcional seismic isolaion sysem, which also provides conrolled flexibiliy in he verical direcion. In he proposed configuraion of he isolaed bridge (Fig.1), he deck and girders can be considered o be floaing on helical spring bearings. Helical springs, which have boh verical and shear siffness, are designed o suppor verical loads, including he selfweigh of he bridge, providing he mechanism o accommodae movemen in all direcions. To proec he bridge deck and abumen from damage by an earhquake in he longiudinal direcion, helical springs are also insalled beween he deck and abumens. Addiionally, fluid dampers are added verically a he locaions of he inerface beween he supersrucure and is supporing pier and abumen o conrol he response of displacemen during an earhquake. The combinaion of helical springs and fluid dampers is expeced o provide an efficien flexible seismic isolaion and energy dissipaion device ha reduces he response of he sysem. The following secions discuss he mahemaical models for he damper and helical spring of he bridge model. A numerical analysis sudy for he verical response of he bridge wih he proposed isolaion sysem, is hen presened followed by he conclusions. 2. Characerizaion of elemens in proposed isolaion sysem Two fundamenal isolaion and energy dissipaion elemens presened in his secion include he helical spring and he fluid damper, respecively. The helical spring possesses siffness in all direcions. Is siffness can be cusomized according o design requiremens. Compared o a non-isolaed bridge, a spring-suppored bridge is relaively flexible in he verical direcion, allowing vibraion in he verical direcion wih no damage o he srucure. The helical spring 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 1 can grealy reduce he relaive response of acceleraion. Oher advanages of using helical springs include high load carrying capaciy, linear load versus deflecion curve, nearly unlimied lifeime service (if provided wih suiable corrosion proecion), and consan properies wih ime [8]. These combined properies make he helical spring a very suiable elasic elemen wih a resoring force. However, he helical spring has lile damping effec [9]. If addiional damping is required for pracical purposes, supplemenal damping devices can be combined wih he springs or used separaely. The helical spring follows a linear relaionship where elasic force is proporional o relaive deformaion. The relaionship beween saic force and relaive deformaion of a helical spring is: Fv = kvv, (1a) where k v is he verical siffness of spring, and v is he relaive deflecion in verical direcion. The shear siffness is aken as 4% ~ 5% of he verical siffness [8,1]. In he shear direcion, a similar relaionship is aken as: Fs = k su = ηkvu, (1b) where k s is he shear siffness of helical spring, u is he relaive deflecion in shear direcion, and η is he raio coefficien and is equal o 4% ~ 5%. The spring siffness is linear for saic or dynamic analysis, which is a significan simplifying facor for he numerical analysis. Fluid dampers have been used or proposed for srucures as energy dissipaion devices during he pas hree decades. Taylor and Consaninou [11] repored muliple episodes of high capaciy fluid damping devices being used in buildings, bridges and relaed srucures, which were originally invened and developed o aenuae he shock and blas effecs in miliary equipmen. Consaninou e al. [12] sudied he effec of various passive energy dissipaion sysems used in buildings. The fluid damping level can be up o 2%~5% of criical, hus grealy decreasing he response of displacemen [11,13]. The oupu force of he fluid damper is insensiive o emperaure. This propery allows greaer versailiy in he applicaion of hese devices. In addiion, here are also noeworhy advanages in insallaion, operaion and mainenance of he fluid dampers and hey have been proven o be reliable and cos effecive. The oupu force of he fluid damper a any ime is ypically represened as: P = C u! r d, (2) where!u is he velociy of he pison rod, C d is he damping coefficien, and r is he exponen coefficien, ranging from.1 o 1.8 as manufacured [14]. The pison rod sroke and he damping oupu force are mechanical characerisics of he fluid damper. The pison rod movemen is limied o is sroke. Therefore, he displacemen of he damped sysem should no be greaer han he maximum sroke of he fluid damper. The fluid damper can provide damping in is axial direcion only. To eliminae he damage caused by non-axial forces o he damper, a roller is placed a he end of he pison rod. Damping raio is used as a measure o evaluae he damping level of a muli-mode damped sysem, and can be obained for any mode as: Edi ξ i =, (3) πesi where ξ i is he damping raio of he ih mode, E di is he oal energy dissipaed by he fluid damper per cycle, and E si is he oal elasic energy of he sysem per cycle for he ih mode. 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 11 For a srucure subjeced o dynamic loading, he equivalen damping raio hroughou he complee duraion of he loading is: j ξ = (4) π F D j P D j j where P j is he damping force, F j is he elasic force, and D j is he response of displacemen a any jh ime sep. Equaion (4) will be used in his sudy as he basic formula o evaluae he damping raio, which will be an approximaion if he forces and displacemens are solved numerically. Harmonic moion is a special case of Equaion (4). I is noed ha for a linear fluid damper, he damping raio is independen of ampliude of moion. For a non-linear case, he damping raio generally reduces wih increasing ampliude of moion. Srucural sysem damping is anoher facor ha affecs he dynamic performance of he srucure. This damping is defined as he resisance o moion provided by he inernal fricion of he maerials. The fricion develops as he molecules forming he maerials are forced across one anoher when he srucure moves relaively. However, evaluaion of sysem damping canno be easily performed in pracice. Usually, some percenage of criical damping is aken insead [15]. 3. Modeling of bridge For dynamic analysis, he isolaed bridge (Fig.1) can be modeled as a coninuous beam for simpliciy. Since his model is flexible in he verical direcion, i canno be considered as a rigid block in ha direcion. The enire verical load is carried by helical spring bearings. Fluid dampers are placed a he locaion of he bearings and do no suppor he verical load. Their funcions are o dissipae seismic energy, suppress possible resonance, and limi displacemens. If a group of springs and dampers is employed a one locaion of he bridge, he resulan siffness as well as he damping of he springs and dampers need o be calculaed for a paricular direcion. Fluid dampers provide damping in only one direcion, while helical springs have siffness in all direcions. j j verical longiudinal isolaor abumen damper pier damper abumen Figure 1. Two-Span Box Girder Bridge Prooype The displacemen mehod is used o consruc he relaionship beween he force and deformaion of a deformable body. The derivaion follows he ypical procedure of marix srucural analysis for he bridge model [16,17]. In his model, he oal siffness marix K c is found by adding he supporing spring siffness o he diagonal elemen of he global siffness marix a he corresponding degrees-of-freedom. 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 12 A consisen approach for mass accouns for ranslaional, as well as roaional degrees-offreedom, while he lumped mass approach only considers he ranslaional degrees-of-freedom. Since he roaional componen of earhquake ground moion is no considered in mos cases, he moion in roaional degrees-of-freedom would no be excied. Addiionally, in he lumped mass bridge model, he amoun of roaions compared o ranslaions are insignifican. Hence, he roaional degrees-of-freedom are excluded from he siffness marix. The saic siffness equaion, which is F = K c in marix form, is pariioned as: K vv K vθ v Fv =, K θv K θθ θ Fθ where v and θ represen ranslaion and roaion, respecively. (5) If F = θ in Equaion (5), hen θ = K 1 θθ K θ v v. Subsiuing ino he firs submarix in Equaion (5) yields: 1 ( K vv K vθ Kθθ K θv ) v = Fv or Kv = F v, (6) 1 where K= K vv K vθ KθθKθ v v is he ranslaion siffness marix. Only hose degrees-offreedom relaed o ranslaion are reained. Therefore, he condensed marix becomes compaible for use wih he diagonal lumped mass marix M. The sysem damping marix is expressed as: T 1 C = ( Mφ[ φ Mφ] ) c s m T ([ φ Mφ] 1 T φ M), where φ is he modal shape marix and c m is he generalized modal damping marix. (7) The diagonal damping marix when fluid dampers are placed a he bearings in he verical direcion is represened by C d. The damping forces of fluid dampers are deermined by he damping coefficien, he damping exponen, and he velociy of he pison. The dynamic equaion of he base-isolaed bridge model in he verical direcion has he following nonlinear form: M W! CsW! CdW! r + + + KW = MW! g, (8) where W!! g is he acceleraion of he earhquake ground moion, WWW,!,!! are he vecor of verical displacemen, velociy and acceleraion, respecively. Among numerous direc inegraion mehods o solve for he nonlinear response in Equaion (8), he Newmark inegraion mehod appears o be he mos effecive wih he smalles numerical errors. In he Newmark mehod, he acceleraion is assumed o be linear for he ime o +. For he ime inerval, following relaions are assumed: W! + = W! + [( 1 β ) W!! + βw! + ] and (9a) 1 2 W + = W + W! + [( α ) W!! ], 2 + αw! + (9b) where α and β are parameers used o achieve he inegraion accuracy and sabiliy. In he case of α = 1 and β = 1, he consan-average-acceleraion mehod will yield uncondiional 4 2 sabiliy in he ieraion procedure. 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 13 From Equaions (9a) and (9b), W! + and W!! + can be solved in erms of W + as follows:!! 1 1 ( )! 1 W W W W ( ) W!! (1a) + = + 1 and 2 α α 2α W! = W! + 1 β ) W!! + β W!. (1b) + ( + To obain he soluion for displacemen, velociy and acceleraion a ime +, he equilibrium Equaion (8) is rewrien as: r M W!! + + CsW! + + CdW! + + KW + = M( W! g ) +. (11) Since CW! r d + is a nonlinear erm, subsiuing Equaions [1a] and [1b] ino Equaion [11] will no yield linear simulaneous equaions wih respec o W +. Hence W + canno be solved direcly. To avoid using he ieraion echnique o solve he displacemen vecor a each ime sep, he nonlinear erm W! r + is expanded a ime by a Taylor series as shown in he following equaion: r r r 1 W! W! r diag( W! )( W! W! + = + + ), (12) where i is assumed ha he high order erms can be negleced wihou loss of accepable accuracy and diag is an operaor o diagonalize a vecor o a marix. By subsiuing Equaions (1a), (1b), and (12) in Equaion (11), a linear equaion wih respec o W + a each ime sep is obained as: ~ ~ K W + = P, (13) + 1 β rβ K = K + M + C + C diag( W! 2 m d α α α ~ P M( W!! ) + Ma + C a + C a ~ r 1 + = g + M s Cs d C d 1 1 1 a M = W ( 1), 2 + W! + W! α α 2α β β a W ( 1) W! β C s = + + ( 1) W!!, and α α 2α β r r r 1 1 r 1 a W W! β diag( W! ) W! ( 1) W!! C d r (1 ) diag( W! = + + β β ) W!!. α α 2α Afer W + is solved from Equaion (13), W!! + and W! + can be obained from Equaions (1a) and (1b), respecively. Since he velociy and acceleraion a ime + have been expressed in erms of heir previous values a ime afer he displacemen a ime + is known, he ieraion procedure can be performed sep-by-sep wih any given iniial condiions. In he above analysis, i can be shown ha he nonlinear problem has been simplified o be an approximaely linear problem by employing a Taylor series expansion o he nonlinear erm of he damping force a each ime sep. Nex he displacemens a each ime sep are solved direcly, and herefore he sep-by-sep direc inegraion mehod can be implemened. 4. Descripion of he proposed bridge model A flexible sysem will be less suscepible o damage when subjeced o an earhquake exciaion. However, here is concern over he issue of isolaion for an ideally flexible sysem. In pracice, he bridges need o be designed wih sufficien amoun of srengh and siffness o resis he service load. The basic facors including he spring siffness involved in engineering design are aken ino consideraion for he wo-span bridge model in his sudy. The span lengh ),, 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 14 is based on he coninuous beam model. Once he span lengh is decided, he size of he cross secion can be calculaed by applying raffic load as a live load plus he dead load of he bridge model, assuming he maerial is concree. Noe ha he deflecion under normal bridge loading mus be conrolled and can be he deerminan for he bridge siffness. From he poin of seismic isolaion, he bearings are expeced o be as flexible as possible. Since he large displacemen due o flexibiliy can be effecively reduced by fluid dampers, he spring siffness will be mainly deermined by operaional loading. The siffness of he springs can be calculaed based on he reacion a he bearing and he saic selemen limi (fluid dampers are no accouned for carrying he load). Also he kineic deflecion change beween raffic load on and off he bridge should be considered as a facor o deermine he spring siffness. Based on he above analysis, a wo-span coninuous concree slab and box girder bridge illusraed in Fig.1 is employed as a model o demonsrae he isolaion effecs of helical springs and fluid damper sysems. This bridge is suppored and isolaed by helical springs posiioned in he verical direcion as bearings. Helical springs are also insalled longiudinally a boh ends beween he abumen and he deck o proec he bridge from impac load. Fluid dampers are locaed beween he supersrucure and subsrucure in he verical direcion where necessary. The lengh of he bridge model is 58.5 m (192 f) for each span. AASHTO HS2-44 ruck loading is used for he live load. The dead weigh of he bridge supersrucure is esimaed o be 2.138x1 4 kg/m (14.357 kip/f). The ypical cross-secion of he bridge box girder has a widh of 12.95m (42.5 f) and a heigh of 2.36 m (7.75 f). The momen of ineria in he verical direcion is 66.4 m 4 (1.594x1 8 in 4 ). Under he presumed oal load, he maximum deflecion of he bridge is approximaely 1 mm (4 in), and he deflecion change beween raffic on and off he bridge is limied o less han 6 mm (.24 in). The siffness of he helical springs is defined by he following, where he shear siffness is assumed o be 4% of he verical siffness: Verical siffness of he spring placed a end bearing 4.9 1 4 kn / m (32. 95 kip / f ). Verical siffness of spring placed a he middle bearing is 14. 7 1 4 kn / m (98.716 kip / f ). Verical siffness of he spring placed a he abumen is 1 3 kn / m (. 672 kip / f ). Fig.2 illusraes his wo-span bridge, which is simplified as a five-lumped-mass model when analyzed numerically. The appropriae damping force relaion, in accordance wih he manufacurer provided daa for he damper, is seleced as (Fig.3).75 P = 1V (14) where V is he velociy of he pison rod [18]. Fig.4 gives he diagram of he damping forcedisplacemen relaionship for he case of harmonic moion wih period π and 2π. The enclosed loop areas are he oal energies ha can be dissipaed by he damper in one cycle of harmonic moion. For differen periods, he damper has a differen area. When he sysem is subjeced o he earhquake moion, he loops will no be symmerical shapes. However, he energy dissipaion capabiliy indicaed by he diagram could be useful in selecing he parameers for he fluid damper. damper Figure 2. Lumped Mass Bridge Model spring damping force (kn) 8 7 6 5 4 3 2 1.1.2.3.4.5 velociy (m/s) Figure 3. Damping Force-Velociy Relaionship of Seleced Fluid Damper 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 15 damping force (1 3 kn).6.4.2 -.3 -.2 -.1.1.2.3 -.2 -.4 period=+ period= 2π -.6 displacemen (m) Figure 4. Harmonic Damping Force-Displacemen Relaionship 5. Verical response of he bridge Among he sofware ools o perform he required numerical analysis for srucures wih proecive devices agains earhquakes, he 3-D BASIS by Nagarajaiah e al. [19] is noeworhy. This ool has he capabiliy o analyze various hybrid isolaion configuraions for hreedimensional seismic moion. Alhough his numerical analysis sofware covers modeling of various combinaions of isolaors and energy dissipaion devices, i assumes he isolaion devices are rigid in he verical direcion. This model of isolaion devices is more applicable for approximaion of elasomeric bearing behavior, which is almos incompressible, and has large verical siffness, while he shear siffness is no more han one percen of he verical siffness. In our sudy, he MATLAB TM sofware package is employed o obain he responses of he bridge model illusraed in Fig.1. The bridge is subjeced o he verical componens of he Norhridge and El Cenro earhquakes. Iniially, isolaed sysems wih various damping raios are considered o observe he effec of damping level on he sysem. During he nex sep, verical response of he isolaed and undamped, isolaed and damped, and non-isolaed bridge models are compared o observe he isolaion effec of coil springs in he bridge model wih or wihou dampers. In he bridge model, he naural frequency of he firs mode in he verical direcion is 1.56 Hz. The Norhridge verical ground moion, wih peak acceleraion of.799 g, and El Cenro verical ground moion wih peak acceleraion of.21 g are used as inpu exciaions (Fig. 5). The sysem damping raio is assumed o be wo percen of he criical. ground acceleraion (g).2.15.1.5 -.5 1 2 3 4 5 6 -.1 -.15 -.2 -.25 duraion (second) 1 2 3 4 5 6 7 -.2 (a) El Cenro (b) Norhridge Figure 5. Verical Ground Acceleraions ground acceleraion.8.6.4.2 -.4 -.6 -.8 duraion (second) 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 16 Iniially, he effec of fluid dampers placed a he bridge bearing on he verical response of he isolaed bridge sysem was sudied. Maximum responses and damping level of all he undamped and damped cases for Norhridge and El Cenro earhquakes are compared in Table 1. For he Norhridge earhquake, he undamped responses a mid-span of he bridge model are illusraed in Fig.6. The maximum response of acceleraion a mid-span is.796 g and he dynamic deflecion is over 78 mm (3in ). To reduce he displacemen response, fluid dampers are used for he bridge model. For he damped case wih one fluid damper placed a each bearing, responses of he bridge model are shown in Fig.7. The maximum response of midspan displacemen in he damped case reduces 4.5% from 78. 6 mm (3 in ) o 46. mm (1.84 in ) of he undamped case. The maximum response of mid-span velociy and acceleraion also decreases 23.7% and 34.3%, respecively, when he fluid damping level is 9.16%. Fluid dampers exhibi excellen damping effecs for he bridge model. The damping force versus displacemen loop of he damper a he middle bearing is illusraed in Fig.8. Unlike he curves in Fig.3, he shape of he loop is no symmeric. The acceleraion versus displacemen hyseresis of he lumped mass a mid-span of damped case bridge model is shown in Fig. 9. The maximum response of displacemen is reduced o 46.8 mm (1.84 in ) and he maximum response of acceleraion is also as small as.523 g. Table 1 Maximum Verical Responses of he Bridge Model Earhquake Locaion Damping Displacemen (mm) Velociy (mm/s) Acceleraion (g) Fluid Damping (%) Norhridge Undamped 76.3 7.4.749 End bearing 1 damper 44.8 521.6.53 9.16 2 dampers 32.3 432.4.463 19.35 Undamped 78.6 727.9.796 Mid-span 1 damper 46.8 555.3.523 9.16 2 dampers 36.1 54.7.473 19.35 Undamped 75.9 696.6.748 Cener bearing 1 damper 45.2 546..541 9.16 2 dampers 36.5 515..63 19.35 El Cenro Undamped 23. 233.1.225 End bearing 1 damper 1.7 19..128 13.3 2 dampers 7.6 75.5.115 28.36 Undamped 23.7 239.5.24 Mid-span 1 damper 11.9 118..139 13.3 2 dampers 9. 11.5. 153 28.36 Undamped 22.8 233.1.223 Cener bearing 1 damper 11.9 12.3.147 13.3 2 dampers 9.3 96..163 28.36 8 6 8 6.8.6 displacemen (mm) 4 2-2 -4-6 -8 1 2 3 4 5 6 7 duraion (s) velociy (mm/s) 4 2-2 -4-6 -8 1 2 3 4 5 6 7 duraion (s) (a) (b) (c) Figure 6. (a) Displacemen; (b) Velociy; (c) Acceleraion Responses a Mid-Span (Norhridge, Undamped) acceleraion (g).4.2 -.2 -.4 -.6 -.8 1 2 3 4 5 6 7 duraion (s) 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 17 5 6.6 4 3 4.4 displacemen (mm) 2 1-1 1 2 3 4 5 6 7-2 velociy (mm/s) 2 1 2 3 4 5 6 7-2 acceleraion (g).2 1 2 3 4 5 6 7 -.2-3 -4-4 -.4-5 duraion (s) -6 duraion (s) (a) (b) (c) Figure 7. (a) Displacemen; (b) Velociy; (c) Acceleraion Responses a Mid-Span (Norhridge, Damped) -.6 duraion (s) 6 4 damping force (kn) 2-6 -4-2 2 4 6-2 -4-6 -8 displacemen (mm) Figure 8 Damping Force-Displacemen Loop a Middle Bearing (Norhridge).6.4 acceleraion (g).2-6 -4-2 2 4 6 -.2 -.4 -.6 displacemen (mm) Figure 9 Damping Force-Displacemen Loop a Middle Bearing (Norhridge) The damping raio is increased by placing wo fluid dampers a each bearing. The reducion in response is minimal when he number of dampers was doubled. The fluid damping raio for his case is 19.35%. Therefore, o reduce he response by adding more fluid dampers o he sysem is almos of no use when damping raio has reached a cerain value. The reducion of responses canno be solely achieved by dampers. The analysis for he case of he El Cenro verical componen leads o similar phenomena. The only difference is ha he maximum responses are less significan due o he smaller peak ground acceleraion. The maximum undamped response of displacemen a mid-span is 23.7 mm (.93 in ) and he acceleraion is.24 g. The response of displacemen, velociy and acceleraion for he case wih one damper placed a each bearing decreases by 49.8%, 5.7%, 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 18 and 42.1%, respecively, where he fluid damping level is 13.3%. When wo dampers were used a each bearing, he response of displacemen and velociy a mid-bearing had minimal reducion while he acceleraion a mid-bearing slighly increased. This resul is expeced, since damping is effecive in reducing he displacemen. As a rade-off, he response of he acceleraion would increase wih a decrease in displacemen. As menioned previously, damping is more efficien in reducing he displacemen of an undamped sysem. For he damped sysem, using more han one damper decreases he response of displacemen very lile and even increases he response of acceleraion. Therefore, o achieve an ideal effec one can use a more flexible sysem such as helical springs in combinaion wih dampers o reduce he response. Of paricular ineres is he response a he mid-span of he bridge subjeced o verical earhquake ground moion. Convenional bearings have oo much siffness in he verical direcion and canno resis verical moion. The verical response of acceleraion a mid-span would be significan, especially in he even of he Norhridge earhquake wih is large verical ground acceleraion. The spring bearings show he promise of providing he flexibiliy needed in he verical direcion. Nex, o show he isolaion effecs of he spring bearing, he isolaed and non-isolaed responses a he cener bearing and a he mid-span of bridge model subjeced o Norhridge and El Cenro verical ground acceleraion are compared in Table 2. In he non-isolaed case, he bridge girder becomes flexible relaive o he rigid suppors. There is a significan difference beween he response of acceleraion a he bearing and a he mid-span. For he non-isolaed case, he response of he acceleraion can be over 2g for he bridge when subjeced o a srong ground moion such as he Norhridge earhquake. In addiion, he maximum acceleraion a mid-span is also larger han he undamped isolaed acceleraion response. Even in he even of an earhquake wih small peak verical ground acceleraion, such as El Cenro, he acceleraion a he bearing is as low as.2 g while he acceleraion a he mid-span is over.5 g. Table 2. Maximum Verical Responses of Isolaed and Non-Isolaed Bridge Model Equake Locaion Damping Displacemen (mm) Velociy (mm/s) Acceleraion (g) Fluid Damping (%) Norhridge isolaed+undamped 76.3 7.4.749. Bearing isolaed+damped 45.2 546..541 9.16 non-isolaed...792. isolaed+undamped 78.6 727.9.796. Mid-span isolaed+damped 46.8 555.3.523 9.16 non-isolaed 7.8 451. 2.3. El Cenro isolaed+undamped 23. 233.1.225. Bearing isolaed+damped 11.9 12.3.147 13.3 non-isolaed...28. isolaed+undamped 23.7 239.5.24. Mid-span isolaed+damped 11.9 118..139 13.3 non-isolaed 1.9 127.9.56. Therefore, if he bridge is no flexible enough in he verical plane, he response of acceleraion can be greaer han he ground acceleraion, even hough he response of displacemen a midspan is negligible. For he isolaed undamped case, he acceleraion responses are reduced over 5% a mid-span of he bridge compared o he non-isolaed case for boh earhquakes, resuling 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 19 in reduced ineria force on he bridge srucure. The isolaed damped case is of more pracical significance as he response of displacemen and velociy due o he increase in he flexibiliy from he isolaion device can be reduced over 5%. This is done by he addiion of over 1% damping raio wihou causing over-damping as may be he case in a linear damped sysem. For he isolaed cases, he maximum response of acceleraion hroughou he bridge span is limied o.54 g for Norhridge and.2 g for El Cenro. Hence, he bridge is proeced from verical ground moion by inroducing spring bearings which resul in a more flexible bridge sysem. The large response of displacemen due o spring flexibiliy can effecively be reduced by damping. Fig.1 illusraes hree cases of maximum verical dynamic deflecion shape hroughou he bridge model occurring a he same ime. I can be observed ha he verical deflecion hroughou he span lengh of isolaed bridge model has less variaion han he non-isolaed one, and ha he relaive deflecion is reduced which is likely o resul in reducion of sresses. dynamic deflecion (mm) -1 2 4 6 8 1 12 isolaed/1 damper -2 isolaed/undamped nonisolaed isolaed/2 dampers -3-4 -5-6 -7-8 span lengh (m) 6. Conclusions Figure 1. Verical Deflecion of Bridge Model Throughou Span In order o achieve beer proecion for he bridge subjeced o srong verical ground moion, helical springs are used as bearings wih fluid dampers as energy dissipaors. The bridge model is suppored on spring bearings in lieu of convenional rigid bearings. The spring-suppored bridge is modeled o be much more flexible in he verical direcion. I is concluded ha he response of acceleraion in an isolaed damped bridge model, paricularly a he mid-span, has been grealy reduced up o 75% compared o he non-isolaed case. Therefore, he ineria forces induced by acceleraion response in he bridge srucure are also reduced which in urn benefis he srucural design. In addiion, he damage from he deflecion gap beween he inspan and bearing is alleviaed because of he flexibiliy due o he spring bearings. The larger response of displacemen of he bridge hroughou he span, as a radeoff of he flexible spring bearings, can be effecively reduced by adding fluid dampers o he isolaion sysem. In general, bridge srucures have damping levels less han 1% criical. The damping level of a srucural sysem isolaed by fluid dampers could be over 2% wih more energy absorbed, offering a dramaic reducion in deflecion a no cos of increase in base shear. I is noed ha exra damping becomes less efficien a higher damping levels. Reducion of response will hardly be achieved by only adding more dampers, especially in a less flexible bridge sysem. The siff sysem is more sensiive o he ground acceleraion exciaion and he response of acceleraion is greaer han he flexible sysem. Use of helical springs as bearings 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse
Inernaional Elecronic Journal of Srucural Engineering, 2 ( 21) 11 will cerainly provide addiional flexibiliy for he bridge srucural sysem in which he displacemens are conrolled by dampers. The proposed bridge sysem is effecive in grealy reducing he srucural responses and relaive deflecion. Acknowledgmens Financial suppor of his projec has been provided by he Naional Science Foundaion, Gran No. CMS-952772. All earhquake ground moion records were made available from he Universiy of Souhern California via World Wide Web, and from he Universiy of California a Berkeley via Gopher. REFERENCES 1. Papazoglou, A.J., and Elnashai, A.S. 1996. Analyical and Field Evidence of he Damaging Effec of Verical Earhquake Ground Moion. Earhquake Engineering and Srucural Dynamics, 25: 119-1137. 2. Buon, M.R. Cronin, C.J., and Mayes, R.L. 1999. Effec of Verical Ground Moions on he Srucural Response of Highway Bridges. Mulidisciplinary Cener for Earhquake Engineering Research Repor 99-7, Sae Universiy of New York a Buffalo, Buffalo, NY. 3. Waisman, F., and Grigoriu, M. 1994. Effeciveness of Vibraion Isolaion Sysems for Bridges. Proceedings of he Firs World Conference on Srucural Conrol. Los Angeles, CA, Vol.1, pp. 3-39. 4. Saadeghvaziri, M., and Fouch, D.A. 1991. Dynamic Behavior of R/C Highway Bridges Under he Combined Effec of Verical and Horizonal Earhquake Moions. Earhquake Engineering and Srucural Dynamics, 2: 535-549. 5. Xue, S., Kuria, S., and Tobia, J. 1997. Mechanics and Dynamics of Inelligen Passive Vibraion Conrol Sysem. Journal of engineering Mechanics 123:323-327. 6. Nagarajaiah, S., Reinhorn, A., and Riley, M.A. 1993. Conrol of Sliding-Isolaed Bridge wih Absolue acceleraion Feedback. Journal of engineering Mechanics, 119: 2317-2332. 7. Yang, J.N., Kawashima, K., and Wu, J.C. 1995. Hybrid Conrol of Seismic-Excied Bridge Srucures. Earhquake Engineering and Srucural Dynamics, 24:1437-1451. 8. GERB Schwingungsisolierungen GmbH&Co., KG. 1994. Vibraion Isolaion Sysems. 9h Ediion, Berlin, Germany. 9. Hueffmann, G.K. 1991. Proecion of Spring Suppored Equipmen Agains Seismic Exciaion. Seismic, Shock, and Vibraion Isolaion, PVP, 222: 45-5. 1. Waller, R.A. 1969. Building on Springs. Pergamon Press, UK. 11. Taylor, D.P., and.consaninou, M.C. 1995. Tesing Procedures for High Oupu Fluid Viscous Dampers Used in Building and Bridge Srucures o Dissipae Seismic Energy. Shock and Vibraion, 2: 373-381. 12. Consaninou, M.C., Soong, T.T., and Dargush, G.F. 1998. Passive Energy Dissipaion Sysems for Srucural Design and Rerofi. Mulidisciplinary Cener for Earhquake Engineering research Monograph No. 1, Sae Universiy of New York a Buffalo, Buffalo, NY. 13. Soong T.T., and Consaninou M.C. 1994. Passive and Acive Srucural Vibraion Conrol in Civil Engineering, Springer Verlag, Wien-New York. 14. Makris, N., Consaninou, M.C., and Hueffmann, G.K. 1991. Tesing and Modeling of Viscous Dampers. Seismic, Shock, and Vibraion Isolaion, PVP, 222: 51-56. 15. Clough, R.W., and Penzien, J. 1993. Dynamics of Srucures. 2nd Ediion, McGraw-Hill, New York. 16. Azar, J.J. 1972. Marix Srucural Analysis. Pergamon Press, UK. 17. Weaver, W., and Gere, J.M. 199. Marix Analysis of Framed Srucures. Third Ediion, Van Nosrand Reinhold, New York. 18. Delis, E.A., Malla, R.B., Madani M., and Thompson, K. J. 1996. Energy Dissipaion Devices in Bridges Using Hydraulic Dampers. Proceedings of Srucures Congress XIV, ASCE, Chicago, IL, Vol. 2, pp.1188-1196. 19. Nagarajaiah, S., Reinhorn, A.M., and Consaninou, M.C. 1991. 3D-Basis Nonlinear Dynamic Analysis of Three-Dimensional Base Isolaed Srucures: Par II. Mulidisciplinary Cener for Earhquake Engineering Research Repor 91-5, Sae Universiy of New York a Buffalo, Buffalo, NY. 21 EJSE Inernaional. All righs reserved. Websie: www.civag.unimelb.edu.au/ejse