DESIGN OF ROOF ISOLATION SYSTEMS WITH VARIABLE FRICTION DAMPERS

Transcription

1 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin DESIGN OF ROOF ISOLATION SYSTEMS WITH VARIABLE FRICTION DAMPERS Y. Riov 1 nd G. Agrnovich 1 Senior Lecturer, Dept. of Civil Engineering, Ariel University Center of Smri, Ariel. Isrel Emil: riovt@riel.c.il Associted Professor, Dept. of Electricl Engineering, Ariel University Center of Smri, Ariel. Isrel ABSTRACT : Using tuned mss dmpers is well nown nd effective wy to protect uildings from erthques, winds nd other types of dynmic excittions. Severl structures with tuned msses hve demonstrted enhnced ehvior. Sometimes the tuned mss displcements reltive to the roof is ig enough, nd in order to decrese it supplementl dmpers re used. Another disdvntge of tuned mss dmpers is tht they contriute to the sttic lods cting on the uilding. A more effective wy llowing similr improvement in structurl dynmic response is implementtion of roof isoltion systems, which require no dditionl mss. The current study is imed to investigte roof isoltion system incorporting vrile friction dmpers (VFD). The vrile friction dmpers hve re-centering cpcity nd limit displcements of the isolted roof prt reltive to the upper floor diphrgm. A method for selection of the dmpers properties is proposed. A numericl exmple hs een crried out on six-story frme uilding sujected to three nturl erthque records. A structure with the proposed system hs n enhnced seismic ehvior nd proves the effectiveness of the VFD in limiting the isolted roof prt displcements. KEYWORDS: tuned mss, vrile friction dmper, seismic response, selection of dmpers properties

2 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin 1. INTRODUCTION Using supplementl dmpers for virtion reduction hs een thoroughly investigted in the pst few decdes. Vrious dmping devices were proposed in order to improve the structurl response to erthques nd to limit the dmge cused to the structurl elements. These devices dissipte energy in vrious wys, such s y yield of mild steel (Tyler, 1995, Tsi et l., 1993), sliding friction (Pll et l., 1993), viscoelstic ehvior of polymers (Bergmn et l., 1993), movement of piston in viscous fluid (Constntinou nd Symns, 1993, Seleemh nd Constntinou, 1997), etc. A wide review of pssive energy dissiption pplictions in uildingd hs een done y Soong nd Drgush (1997). Tuned mss dmpers (TMD) consisting of mss nd spring-dshpot hve een widely used in structurl pplictions in order to reduce response of uildings nd ridges to wind, erthque, trffic (lie pedestrins or rilwy trins) nd other types of dynmic lods. These systems were proposed out hundred yers go nd re nown s clssic solutions for improving dynmic ehvior of structures (Copr, 1995, Hrt nd Wng, 000). An dvntge of TMD is tht it is very simple nd requires no ostructions closing the structurl ys lie in the cse of using supplementl dmpers connected etween the floor diphrgms. A mss in TMDs is tuned in resonnce with the structures dominnt frequency llowing significnt reduction in structurl dynmic response. Depending on the mss rtio, the tuning frequency nd the dmping cpility the reduction in structurl seismic response cn e very significnt. The improvement of seismic performnce ccording is confirmed y theoreticl nd prcticl investigtions (Nwrotzy, 006). Mny reserchers in the lst three decdes hve developed modern effective method for selection of optiml prmeters of TMD systems (Wrurton, 1981, Sde et l., 1997). Roof isoltion is specil type of TMD. It ws proposed y Villverde nd Mosqued (1999) in order to overcome the disdvntges of conventionl TMD systems lie reltively lrge mss, spce required for instlltion, lrge reltive displcements of the mss cused y setting it in resonnce with the structures dominnt frequency. The ide ws to use portion of the roof mss s the mss of the sorer. Elstomeric erings usully used in se isoltion systems (Kelly, 1993) were proposed to e used together with viscous dmpers insted of springs in order to reduce the mss displcement nd to provide dditionl energy dissiption. Lter Villverde (00) hs investigted 13 story uilding to gin insight into the size of the erings nd dmpers needed to uild n sorer, to estimte the mximl roof displcement nd to prove the effectiveness of the proposed solution. The uthors propose n lterntive roof isoltion system, incorporting vrile friction dmpers (Riov et l., 006) insted of viscous ones nd elstomeric erings. The proposed system is simple nd hs the sme effect. A method for selection of vrile friction dmpers prmeters is developed.. THE ROOF ISOLATION SYSTEM AND SELECTION OF ITS PARAMETERS A uilding with roof isoltion system RIS) ws descried in detils y Villverde (00). A schemtic view of n RIS proposed in this study is shown in Figure 1. The system consists of n isolted roof sl (1), roof em (), column (3), uxiliry em (4), sliding support (5) nd vrile friction dmper (6). The dmper is imed to limit the isolted roof. prt displcement reltive to the un-isolted one. According to Sde et l. (1997), it is possile to otin the prmeters of tuned mss dmper s follows: f 1 = 1+Φ m Φ m 1 ξ (..1) 1+Φ m

3 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin ξ m ξ =Φ + (.) 1+ m 1+ m where f is frequency rtio, Φ denotes the mplitude corresponding to the mss of the structure tht supports the ppendge in the mode shpe of the structure without the ppendge corresponding to the frequency ω, which is nturl frequency of multi degree of freedom structure (equl to the nturl virtion frequency of the sorer, ω ), m is sorer mss, ξ nd ξ re the sorer nd the structures dmping rtios, M is the generlized mss of the structure. Figure 1. A roof isoltion system with vrile friction dmper Villverde (00) hs demonstrted tht the ove explined method cn e successfully used for design of RIS. In this cse the sorer mss is prt of the roof one, nd ccording to this vlue the sorer s stiffness nd the viscous dmper s dmping coefficient should e defined. Following Villverde (00), the dmping rtio for the RIS is otined from Eq. (). The dmping coefficient nd the systems stiffness re otined s follows: c = ξ ω m (.3) ω = f m (.4) 3. BASIC LAYOUT AND FEATURES OF A VARIABLE FRICTION DAMPER A vrious friction dmper (VFD) proposed to e used s prt of RIS hs een developed erlier y Riov et l., (006). It consists (Figure ) of rectngulr section tue (7), doule wedge (8), two elstic strip elements (9), nd olted connection clip (10). The wedge lies prtly inside the tue nd cn move c nd forth long its xis. The strips hve cntilever sttic scheme nd re fixed to the tue y the connection clip, forming n elstic strip system. The stiffness of this system my e regulted y chnging the loction of the connection clip long the tue. The free ends of the cntilever strips re in contct with the inclined surfce of the wedge. Figure. A vrile friction dmper

4 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin The dmping force, F D, cn e otined s function of wedge displcement, x, s follows (Riov et l., 006): F D = x / (C u + C v cot α) (3.1) where α is the wedge inclintion ngle, f strip elements, is the friction coefficient on the surfce etween the wedge nd the elstic C u = δ 1 / tn (α + ρ) + δ 11 nd C v = δ / tn (α + ρ) + δ 1 (3.) ρ = rc tn f (3.3) δ ij (i = 1;, j = 1;) re the elstic strip elements flexiility coefficients; 1 nd re the horizontl nd verticl directions, respectively. 4. DESIGN OF A ROOF ISOLATION SYSTEM WITH VARIABLE FRICTION DAMPERS As it ws mentioned ove, vrile friction dmper is proposed to e used s prt of RIS insted of elstomeric isoltors nd viscous dmpers (Villverde, 00). A method for selection of VFD prmeters yielding equivlent structurl seismic response (lie in the cse of RIS with isoltors nd viscous dmpers) is proposed. Assuming tht the ehvior of uilding with viscous dmped RIS incorporting isoltors nd of tht with VFDs is similr, the following two demnds my e ten into ccount for otining the VFD properties: - the mximum isolted roof displcements reltive to the unisolted roof prt should e equl; - the energy dissipted in RIS with isoltors nd viscous dmpers nd in tht with VFD re equl. Let d(t) = d mx cos(π f t) e the isolted roof displcement reltive to the unisolted prt of the roof. Here f = ω /π is the first nturl virtion mode frequency, d mx is the mximum isolted roof displcement reltive to the unisolted prt of the roof. Then the energy dissipted in the RIS cn e otined s follows: E RIS 1 f 0 1 f c ( t) d( t) dt= c d& ( t) dt= π fcd mx 0 = f & (4.1) where nd c re stiffness nd dmping coefficients clculted ccording to Equtions (3) nd (4), f c is the dmping force developed in the viscous device. The theoreticl reltion etween the displcement, trnsferred to the VFD, nd the resulting dmping force is governed y Eq. 5. The friction force chnges sign when loding of the dmper is followed y unloding. Therefore the corresponding lines hve different slopes: slope L for loding nd slope U for unloding (Figure 3). Figure 3. Reltion etween the dmping force nd the displcement in VFD (Riov et l., 006). Let the isector of the ngle etween the upper nd the lower slopes equls the RIS stiffness coefficient. In other words let

5 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin U + L = (4.) Hence the VFD coefficients my e defined y mens of new prmeter D (0 D < 1) using the following equtions: L = ( 1+ D), = (1 D) (4.3) U The energy dissipted in the VFD cn e otined s follows: P VFD 1 4 f 1 f L U D = d( t) d& L ( t) dt+ d( t) d& U ( t) dt = d mx = d mx (4.4) f By equting the Eqns (4.1) nd (4.4), D 4π = (4.5) Eqns. (4.5) nd (4.3) llow otining prmeters of VFD which will yield seismic response of structure with isolted roof similr to tht with RIS proposed y Villverde (00). f c 5. NUMERICAL EXAMPLE To exmine the efficiency of the proposed RIS with VFD nd the method for selection of the VFD prmeters, numericl simultion of six story uilding ws crried out. A sher frmed structure with stiff ems ws nlyzed (Figure 4). The structure is steel frme. Steel ASTM A36 iss used for ll shpes of columns nd grids. The nturl frequencies of the uilding re 1.083,.9, 4.799, 9.596, 7.93, nd Hz. Figure 4. A six-story structure used for numericl nlysis An initil dmping rtio of % ws ssumed for ll virtion modes of the structure without the RIS. The following three nturl seismic excittions were used s input in order to exmine the ehvior of the structure:

6 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin El Centro S00E, 1940, Koe NF17, 1995, nd Hchinohe The response of the structure ws nlyzed for the following three cses: Cse 1. Uncontrolled structure; Cse. A structure with RIS incorporting elstomeric erings nd viscous dmpers (Villverde 00); Cse 3. A structure with the proposed RIS including VFD. All simultions were performed with routines written in MATLAB (Plm, 003, Tewri, 00) using the improved fst simultion method (Agrnovich t l., 004). According to the method descried y Villverde 4 (00), the following optiml RIS prmeters were otined for the selected structure: m = g-mss, = N/m, c = N sec/m. Following Eqn. (4.4), D= nd ccording to Eqn. (4.3), L = 5330 N/m, U = 1750 N/m. Pe vlues of floor solute displcements under the selected erthques re presented in Figure 5. It should e noted tht for ll erthques the pe response of the structure with the RIS is significntly improved compred to tht of the uncontrolled one. The reductions in the pe solute displcements of the structure with the RIS compred to the uncontrolled one vries from 33% to 50% (see Figure 5). El Centro Hchinohe Koe Figure 5. Pe solute displcements of the uilding

7 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin 6. CONCLUSIONS Vrile friction dmpers were proposed to e used s prt of roof isoltion system. A method for selection of dmpers prmeters ws developed. It ws imed to yield similr structurl response to erthques lie in the cse when roof isoltion systems incorporting elstomeric erings nd viscous dmpers re used. Selection of VFD properties is sed on the ssumption tht: the mximum isolted roof displcements reltive to the unisolted roof prt nd the energy dissipted in RIS with isoltors nd viscous dmpers nd in tht with VFD re equl. Numericl simultion of six-story steel frme with two ind of roof isoltion systems ws crried out in order to prove the efficiency of the proposed method. The uilding s response to three nturl erthque records ws clculted. It ws shown tht using roof isoltion llows significnt reduction in structurl response. Asolute pe floors displcements were reduced up to 50% in structure with roof isoltion system compred to n uncontrolled one. Energy dissipted under the selected erthques in the roof isoltion system with vrile friction dmper ws similr to tht in roof isoltion system with elstomeric erings nd viscous dmpers. The pe displcements of the isolted roof prt reltive to the unisolted one were lmost the sme for oth cses. There ws no significnt chnge in the pe se sher forces of the structure with two types of roof isoltion systems. Hence the proposed method my e effectively used for design of structures with roof isoltion systems incorporting vrile friction dmpers, providing enhnced structurl response to erthques. 7. REFERENCES Agrnovich, G., Riov, Y. nd Blostotsy, B. (004). A Method for Fst Simultion of Seismiclly-Excited Active Controlled MDOF Structures. Journl of Structurl Control nd Helth Monitoring 11, pp Bergmn, D. M., Hnson, R. D. (1993). Viscoelstic Mechnicl Dmping Devices Tested t Rel Erthque Displcements. Erthque Spectr 9:3, Chopr, A.K. (1995). Dynmics of Structures. Theory nd Applictions to Erthque Engineering, Prentice Hll, NJ. Constntinou, M.C., nd Symns, M.D. (1993). Experimentl Study of Seismic Response of Buildings with Supplementl Fluid Dmpers. The Structurl Design of Tll Buildings., Hrt, G.C. nd Wng, K. (000). Structurl Dynmics for Structurl Engineers, Willey, NY. Kelly, J.M. (1993). Erthque Resistnt Design with Ruer, Springer, London. Nwrotsy, P. (006). Tuned-Mss Systems for the Seismic Retrofit of Buildings. 7-th Interntionl Congress on Advnces in Civil Engineering, Istnul, Turey, pper No Pll, A., Vezin, S., Proulx, P., nd Pll, R. (1993). Friction Dmpers for Seismic Control of Cndin Spce Agency Hedqurters. Erthque Spectr 9:3, Plm W. J. III. (003). Introduction to MATLAB 7 for Engineers, McGrw-Hill Science, NY. Riov, Y., Blostotsy, B. nd Ishov, Y. (006). Theoreticl Model nd Lortory Testing of Vrile Friction Dmper. Europen Erthque Engineering 0:1,

8 World Conference on Erthque Engineering Octoer 1-17, 008, Beijing, Chin Sde, F., Mohrz, B., Tylor, A.W. nd Chung, R.M. (1997). A Method of Estimting the Prmeters of Tuned Mss Dmpers for Seismic Applictions. Erthque Engineering nd Structurl Dynmics 6:6, Seleemh, A. A., nd Constntinou, M. C. (1997). Investigtion of Seismic Response of Buildings with Liner nd Nonliner Fluid Viscous Dmpers. Tech. Rep. NCEER , Ntionl Center of Erthque Engineeing Reserch, Stte University of New Yor t Bufflo, N.Y. Soong, T.T., nd G.F. Drgush, (1997). Pssive energy dissiption systems in structurl engineering, Wiley, New Yor. Tewri, A. (00). Modern Control Design With MATLAB nd SIMULINK, John Wiley & Sons, NY. Tsi, K. C., Chen, H. W., Hong, C. P., nd Su, Y. F. (1993). Design of Steel Tringulr Plte Energy Asorers for Seismic-Resistnt Construction. Erthque Spectr 9:3, Tyler, R. G. (1985). Further Notes on Steel Energy-Asoring Element for Brced Frmewors. Bulletin of New Zelnd N`tionl Society for Erthque Engineering 18:3, Villverde, R. (00). Aseismic Roof Isoltion System: Fesiility Study with 13 Story Building. ASCE Journl of Structurl Engineering 18:, Villverde, R. nd Mosqued, G. (1999). Aseismic Roof Isoltion System: Anlyticl nd She Tle Studies. Erthque Engineering nd Structurl Dynmics 8:3, Wrurton, G. B., (1981). Optimum sorer prmeters for minimizing virtion responses., Erthque Engineering nd Structurl Dynmics 9, 51-6.