PILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS

Transcription

1 Asia-Pacific Coferece o FRP i Structures (APFIS 2007) S.T. Smith (ed) 2007 Iteratioal Istitute for FRP i Costructio PILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS T.B. Peg *, J.Z. Li ad L.C. Fa Departmet of Bridge Egieerig, Togji Uiversity, Chia. ptb@mail.togji.edu.c, 1239, Sipig Road, Shaghai, P.R.Chia, ABSTRACT Experimetal ad theoretical studies have show that steel-reiforced rubber bearigs ormally used for small to medium spa bridges ca be replaced by FRP rubber isolator without ay risk. The equivalet dampig ad shear deformatio capacity of FRP rubber isolators are superior to those of steel-reiforced rubber bearigs, ad the seismic isolatio requiremet of commo small to medium spa bridge structures ca be satisfied by this kid of isolator. I order to exted the applicatio of FRP rubber isolator as a kid of practical seismic isolator, this paper presets a theoretical approach to the horizotal shear force of rectagular FRP rubber isolators. The relatio betwee total horizotal shear force ad the shear strai of rectagular FRP rubber isolators is derived. The iflueces of plae dimesios, material properties, ad rubber ad FRP plate parameters of the isolator o the horizotal shear force of rectagular FRP rubber isolators are studied. It is show that the horizotal shear behaviour of rectagular FRP rubber isolators ca be desiged to satisfy the seismic isolatio requiremet of small to middle spa bridges, ad the shear deformatio capacity of FRP rubber isolator is preferable. KEYWORDS FRP rubber isolator, horizotal shear behaviour, seismic isolatio INTRODUCTION Vibratio is a commo atural pheomeo, which will be foud almost everywhere i egieerig, such as the effect of gust o tall buildigs, the effect of wave o ships, the effect of groud motio i earthquakes o structures, etc. Vibratio is disadvatageous to idustrial equipmets ad apparatus, log duratio vibratio ad oise accompaied are harmful to huma health, ad structures ad compoets may be destroyed uder itese vibratio. Three vibratio cotrol strategies are regarded as basic priciples to reduce the vibratio amplitude, ad prevet oscillator (for example, equipmet, apparatus, huma, structures ad compoets) from damage. The first oe is to separate the oscillator from the vibratio source to cut off the vibratio trasfer, ad the secod oe is to reduce the vibratio by eergy dissipatio, the last oe to detue the structure, which meas to brig the resoace frequecies of the structure far away from the excitatio frequecies. Several traditioal techiques are adopted to realize the three vibratio cotrol strategies, such as rubber block, metal sprig, air sprig, oil damper. But all these techiques have their iheret shortcomigs which restrict their usage withi very arrow limits. For rubber block ad air sprig, the iferior load bearig capacity ad eergy dissipatio capacity are the mai shortcomigs. For metal sprig, lower abilities to isolate high frequecy vibratio, to isolate soud ad to dissipate vibratio eergy are the mai weakesses. Ad oil damper is limited by its large size, complicated cofiguratio, ad iability to sustai vertical load. So they are seldom used aloe as qualified isolators, especially for seismic isolatio. At the ed of last cetury, FRP rubber isolator was developed (Kelly, 1999), which cosists of elastomeric layers boded to iterleavig FRP plates. High stiffess of reiforcemets restrais the lateral expasio of elastomeric layers ad results i higher compressio stiffess tha a ubouded elastomeric layer i the vertical directio ormal to the layer. Thus, a lamiated elastomeric bearig ca provide high vertical rigidity to sustai gravity loadig, while still providig the same horizotal flexibility of a ubouded rubber. 443

2 FRP rubber isolator has ot oly the same advatages as rubber block, such as light weight, small size, the ability to isolate high frequecy vibratio ad soud, ad the ability to reduce the vibratio alog the axial, trasverse ad rotatioal directio at the same time, but also has relatively large eergy dissipatio capacity ad reliable vertical rigidity to sustai gravity loadig. So it is regarded as a proper isolator for idustrial equipmets ad structures to vibratio ad seismic isolatio. Because it is less tha 10 years sice FRP rubber isolator was developed, experimets to support the horizotal shear behaviour ivestigatio are isufficiet ad usystematic, ad the mechaical model ad aalysis method for shear behaviour have ot bee established. It is very importat to ivestigate seismic isolatio performace of FRP rubber isolator ad establish the mechaical model for applicatio of the isolator to seismic desig of equipmets ad structures. I this paper, horizotal shear force of a rectagular FRP rubber isolator is ivestigated theoretically, ad the relatio betwee horizotal shear force ad shear strai is derived. Iflueces of plae dimesios, material properties, ad rubber ad FRP plate parameters of the isolator are studied. It is show that horizotal shear behaviour of FRP rubber isolator ca satisfy the idustrial equipmets ad structures to vibratio ad seismic isolatio. DERIVATION OF HORIZONTAL SHEAR FORCE FORMULA I the daily service, isolators work i the state of compressio-shear, so horizotal shear force studied here is also uder compressio state. For a isolator made of rubber layers (which are paited black i Figure 1) reiforced by steel plates (which are paited white i Figure 1), because of the large bedig stiffess of rigid plates, the state of compressio-shear is so called, pure shear. All the steel plates remai plai, ad all the rubber layers deformed i shear. Figure 1. Compressio-shear behavior of a steel-plates reiforced isolator For a FRP rubber isolator made of rubber layers (which are paited black i Figure 2) reiforced by FRP plates (which are paited white i Figure 2), durig the compressio-shear test, FRP plates remai plai oly for smaller shear deformatio. Ad for larger shear deformatio, the edge of FRP plates ad rubber layers will bed as show i Figure 2, ad the separatio of the edge of isolator from the supportig plates will be observed. Figure 2. Compressio-shear behavior of a FRP rubber isolator I the aalysis several hypotheses ot very rigorous but acceptable are suggested, (1) Ifluece of vertical compressio to horizotal shear behaviour is egligible; (2) The material behaviour of rubber is assumed to be liear elastic; (3) Plae-sectio assumptio is applicable. We assume the iitial legth, width ad height of a rectagular isolator equal a, b ad h, respectively, ad it is composed of rubber layers of thickess t ad -1 FRP plates of thickess t f. Whe the isolator deforms alog the directio of the width b, the horizotal shear stiffess is the relatio betwee the shear force ad the correspodig horizotal shear deformatio. Firstly, the isolator is divided ito three parts accordig to their APFIS

3 differet deformatio states as show i Figure 3. The first part is the cetral prism with a cross sectio of parallelogram shape, which will deform ito rectagular shape uder compressio shear test. The other two parts are the side prisms with a cross sectio of right triagle shape, which will deform ito sector shape uder compressio shear test as show i Figure 3. Figure 3. The iitial ad deformed shapes of the three parts of a isolator If the horizotal displacemet of the isolator is x, the x = tγ, (1) where, γ is the shear strai of each rubber layer of the cetral prism. The the two legs of the right triagle equal x-tγ/2 ad h, respectively, ad the base lie ad height of the parallelogram are b-x ad h. so it is show that all the base lies of the three parts are fuctios of x. Uder compressio shear test, the total horizotal shear force T icludes three parts, T 1 to make the cetral part ito rectagle ad double T 2 to make the side parts ito sector shapes, which meas T = T1+ 2T2 (2) For the cetral prism, the relatio betwee horizotal shear force T 1 ad horizotal displacemet x is T1 = abgγ axgγ, (3) where, G is the shear modulus of the rubber layer. x Figure 4. The horizotal displacemet x of a side prism For a side prism, the horizotal displacemet x uder T 2 ca be divided ito two parts: shear displacemet d 1 ad bedig displacemet d 2 as show i Figure 4. x = d1+ d2 (4) Shear displacemet ca be calculated based o the plae-sectio assumptio. T2 2T2 d1 = t γ1 = t = (5) xag /2 agγ Bedig displacemet d 2 ca be calculated accordig to the rotatio agle θ i of the ed of each plate. d1 d2 APFIS

4 1 d2 = t siθ + t siθ (6) i f i i= 1 i= 1 Ad T 2 equals the summatio of the horizotal shear forces of all the layers ad each layer, which are assumed to bed like a catilever beam with a cocetrated load applied at the ed. The the followig equatio ca be got. T 2EI 1 2EI f f r r 2 = taθi Vi = taθi θ ta 2 i + θi θ 2 i i= 1 li i= 1 li 1 taθi θ i taθi θ i 2EI r r 2E 2 fi f 2 i= 1 li i= 1 li = + where E r ad E f is the elastic modulus of the rubber layers ad FRP plates. To simplify the aalysisθ i is assumed to be the same for all the layers, ad Eqs (6) ad (7) ca be rewritte as: where, d2 = h siθ (8) T2 = 2ErIr + 2E 2 fi f 2 taθ θ i= 1 li i= 1 li at at 1 f = 2Er + 2E ta f θ θ t γ i= 1 ( i 2 ) 12t γ i= 1 i 3 1 a 1 t f 1 A = Et ta ta 2 r + E 1 2 f θ θ = θ θ γ i= 1 ( i 2 ) t i= 1 i γ 3 1 a 1 t 1 f A= Et + E 1 2 f i= 1 ( i 2 ) t i= 1 i Ad for rubber layers ad FRP plates, l i equal (i-1/2)tγ ad itγ, respectively. Substitutig Eqs (5), (8) ad (9) ito Eq (4), the relatio betwee T 2 ad x ca be obtaied. A x 2T2 x 2T2 T2 = ta arcsi arcsi 2 (10) γ h agγh h agγh The substitutig Eqs (3) ad (10) ito Eq (2), the relatio betwee total horizotal shear force T ad the shear strai γ ca be obtaied. 2 2A agγbt agγbt T abgγ + atgγ 2 ta arcsi arcsi = 0 (11) γ agγh agγh (7) (9) INFLUENCES OF DESIGN PARAMETERS ON THE HORIZONTAL SHEAR FORCE For Eq (11), explicit solutio of T could ot be foud, so a program is writte to calculate the umerical solutio of Eq (11). I the followig part a series of umerical solutios are give to illustrate the iflueces of all the desig parameters o the horizotal shear force. Iflueces of Plae Dimesios a ad b The iflueces of isolator legth a ad isolator width b o the horizotal shear force are show i Figure 5a ad 5b. It is show that the factor does ot chage the shape ad the tred of the relatio but scales up ad dow the force for each shear strai γ. APFIS

5 (a) Ifluece of the isolator legth a (b) Ifluece of the isolator width b Figure 5. Ifluece of plae dimesios a ad b Iflueces of Material Properties G, E ad E f I Eq (11), the shear modulus of the rubber layer G appears alog with isolator legth a, so they have almost the same effect o the horizotal shear force. It is show i Figure 6a that the larger the shear modulus is, the larger the shear force will be. The elastic modulus of rubber layers E ad that of FRP plates E f oly appears i the A term ad have direct ifluece o the bedig displacemet d 2. As show i Figure 6b ad 6c, the iflueces of E ad E f o the horizotal shear froce is almost egligible. (a) Ifluece of shear modulus of rubber layers G (b) Ifluece of elastic modulus of rubber layers E (c) Ifluece of elastic modulus of FRP plates E f Figure 6. Ifluece of material properties G, E ad E f APFIS

6 Iflueces of Rubber ad FRP Plate Parameters, t ad t f Number of rubber layers ad thickess of rubber layers t appear i the third term of Eq (11) as a multiplyig factor, so ad t have almost the same effect as show i Figures 7a ad 7b. It is show that the larger ad t are, the less the shear force is. Thickess of FRP plates t f has almost the same effect as elastic modulus of FRP plates E f. It is show i Figure 7c that the horizotal shear force becomes larger with the icrease of t f for small γ. But for larger γ the relatio betwee T ad t f becomes complex as show Figure 7c, but geerally T is ot sesitive to the chage of t f. (a) Ifluece of umber of rubber layers (b) Ifluece of thickess of rubber layers t (c) Ifluece of thickess of FRP plates t f Figure 7. Ifluece of rubber ad FRP plate parameters, t ad t f As previously stated, all 8 parameters have very distict iflueces o the horizotal shear properties, ad their effects ca be geeralized i Table 1. I Table 1 positive correlatio meas that value of horizotal shear property to be iflueced icreases whe that of the variable icreases, egative correlatio meas that value of horizotal shear property to be iflueced decreases whe that of the variable icreases, without correlatio meas that value of horizotal shear property ad that of the variable are idepedet. Table 1. Relatio betwee the 8 parameters ad the horizotal shear force Variables Relatio betwee the 8 variables ad the horizotal shear force isolator legth a positive correlatio isolator width b positive correlatio shear modulus of rubber layers G positive correlatio elastic modulus of rubber layers E positive correlatio elastic modulus of FRP plates E f positive correlatio umber of rubber layers egative correlatio thickess of rubber layers t egative correlatio almost positive correlatio for small γ ad without correlatio thickess of FRP plates t f for larger γ APFIS

7 Amog the above 8 parameters, a, b, G, ad t ca chage the horizotal shear properties remarkably, ad they are prefered parameters to desig isolators to satisfy the oise ad vibratio cotrol demad. CONCLUSIONS I order to exted the applicatio of FRP rubber isolator as a kid of practical seismic isolator, this paper presets a theoretical approach to the horizotal shear behaviour of rectagular FRP rubber isolators. The relatio betwee total horizotal shear force T ad the shear strai γ of rectagular FRP rubber isolators is derived. The ifluece of plae dimesios, material properties, ad rubber ad FRP plate parameters of the isolator o the horizotal shear force of rectagular FRP rubber isolators are studied. It is show that the horizotal shear behaviour of rectagular FRP rubber isolators ca be desiged to satisfy the seismic isolatio requiremet of small to medium spa bridges, ad the shear deformatio capacity of FRP rubber isolator is preferable. ACKNOWLEDGMENTS The authors gratefully ackowledge the fiacial support provided by the Natural Sciece Foudatio of Chia (Natioal Key Project No ). REFERENCES Kelly, J.M. (1999). Aalysis of fiber-reiforced elastomeric isolator. Joural of Seismology ad Earthquake Egieerig, 2, Kelly, J.M. ad Takhirov, S.M. (2001). Aalytical ad Experimetal Study of Fiber-Reiforced Elastomeric Isolators. PEER Report 2001/11, Pacific Earthquake Egieerig Research Ceter, Uiversity of Califoria, Berkeley. Kelly, J.M. ad Takhirov, S.M. (2002). Aalytical ad experimet study of fiber-reiforced strip Isolators. PEER Report 2002/11, Pacific Earthquake Egieerig Research Ceter, Uiversity of Califoria, Berkeley. Moo, B.Y., Kag, G.J., Kag, B.S. ad Kelly, J.M. (2002) Desig ad maufacturig of fiber reiforced elastomeric isolator for seismic isolatio. Joural of Materials Processig Techology , Moo, B.Y., Kag, G.J., Kag, B.S., Kim, G.S. ad Kelly, J.M. (2003) Mechaical properties of seismic isolatio system with fiber-reiforced bearig of strip type. Iteratioal Applied Mechaics, Vol. 39, No Tasi, H.C. ad Kelly, J.M. (2001). Stiffess aalysis of fiber-reiforced elastomeric isolators. PEER Report 2001/05, Pacific Earthquake Egieerig Research Ceter, Uiversity of Califoria, Berkeley. Tasi, H.C. ad Kelly, J.M. (2002). Stiffess aalysis of fiber-reiforced rectagular seismic isolators. Joural of Egieerig Mechaics, ASCE, 128, Tasi, H.C. ad Kelly, J.M. (2002). Bedig stiffess of fiber-reiforced circular seismic isolators. Joural of Egieerig Mechaics, ASCE, 128, Tasi, H.C. (2004). Compressio stiffess of ifiite-strip bearigs of lamiated elastic material iterleavig with flexible reiforcemets. Iteratioal Joural of Solids ad Structure 41, Tasi, H.C. ad Kelly, J.M. (2005) Bucklig load of seismic isolators affected by flexibility of reiforcemet. Iteratioal Joural of Solids ad Structures 42, APFIS

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