Tuned liquid dampers simulation for earthquake response control of buildings

Size: px

Start display at page:

Download "Tuned liquid dampers simulation for earthquake response control of buildings"

Morris Newman
6 years ago
Views:

Tuned liquid dampers simulation or earthquake response control o buildings T. Novo, H. Varum, F. Teixeira-Dias & H. Rodrigues Universidade de Aveiro, Aveiro M.J. Falcão Silva & A.

1 Tuned liquid dampers simulation or earthquake response control o buildings T. Novo, H. Varum, F. Teixeira-Dias & H. Rodrigues Universidade de Aveiro, Aveiro M.J. Falcão Silva & A. Campos Costa aboratório Nacional de Engenharia Civil, isboa. Guerreiro Instituto Superior Técnico, isboa SUMMARY: This paper is ocused on the study o an earthquake protection system, the Tuned iquid Damper (TD), which can, i adequately designed, reduce earthquake demands on buildings. This positive eect is accomplished taking into account the oscillation o the ree surace o a luid inside a tank (sloshing). The behaviour o an isolated Tuned iquid Damper, subjected to a sinusoidal excitation at its base, with dierent displacement amplitudes, was studied by inite element analysis. The eiciency o the TD in improving the seismic response o an existing building, representative o modern architecture buildings in southern European countries was also evaluated based on linear dynamic analyses. Keywords: Tuned iquid Damper, TD, earthquake protection systems, energy dissipation, numerical simulation, sloshing.. INTRODUCTION Recent earthquakes have dramatically revealed that research in earthquake engineering should be directed towards the evaluation o the vulnerability o existing buildings, generally devoid o adequate structural characteristics. Its strengthening should be made aiming at the reduction o its vulnerabilities, consequently reducing the associated risk to acceptable levels. The study and development o new strengthening techniques and/or the improvement o seismic perormance is undamental so as to avoid signiicant economic losses, as well as human lives, in uture events. Tuned iquid Dampers (TDs) have been used as passive or semi-active control devices in a wide range o applications, such as tall buildings and high-rise structures. TDs are passive energy absorbing devices that have been suggested or controlling vibrations o structures under dierent dynamic loading conditions. A TD consist on a rigid tank with a shallow luid. This luid, that can be water or another luid, is inside the tank that is rigidly connected to the structure. Tuning the undamental sloshing requency o the TD to the structure s natural requency causes sloshing and breaking waves at the resonant requencies o the combined TD-structure system which allows the dissipation o signiicant amounts o energy. TDs have already been studied by other research groups or application as earthquake response controlling device in buildings. In act, a rectangular TD can allow sloshing to occur in any direction and, when properly designed, its inherent behaviour properties under dynamic loading can make it a good solution in the reduction o bi-directional earthquake demands in buildings. The global mechanism o controlling vibrations in structures with TDs is based on the phenomena o luid sloshing and wave breaking. These phenomena dissipate part o the energy induced by earthquakes. The undamental sloshing requency o the luid in the TD should be close to the natural requency o the structure i the TD is to dissipate energy eiciently. The recent growing interest in liquid dampers or application in large structures can be associated to their potential advantages, such as: low cost when compared to other solutions, easy installation in existing building structures, minimal maintenance costs, may be employed or temporary use, beneit

2 dynamic eect in uni- or bi-directional earthquake excitations, and eectiveness even or small amplitude vibrations.. PROBEM FORMUATION The inclusion o TDs in structures can improve its behaviour, especially when subjected to dynamic actions, such as wind and earthquakes. When TDs are rigidly linked to a building structure, which is subjected to a dynamic action, luid sloshing originates pressures that change the dynamic characteristics o the structure and its response to dynamic loads. The hydrodynamic horizontal impulses applied by the steady state luid on the tank side walls act as an auto-equilibrated system, neglecting higher-order terms and shear orces on the structure. When the structure is subjected to dynamic actions, luid sloshing induces non-equilibrated impulsive loads in both tank side walls corresponding to the development o lateral shear orces in the structure o the building, F ind. These shear orces can be calculated, at any time instant t, as a unction o the hydrostatic pressure on the tank side walls perpendicular to the direction o ground motion (equivalent to hydrostatic pressure at the same instant). Thereore, these orces depend on the height o luid close to the tank side walls [Sun, 99]. The building structure s shear orce induced by luid sloshing can be expressed as: F ind r g b ( h h ) = ( h + η ) ( h η ) ) r g b = (.) r l e e where is the density o the luid, b is the tank width and, h r and h l are the surace elevations at the right and let side walls o the tank, respectively. Figure... Schematic representation o the orces induced to the structure due to luid sloshing in a TD [Novo, 008]. The lateral shear orces induced to the structure can be considered to be dependent only on the hydrostatic pressure, because this is signiicantly higher to the inertial loads originated by the horizontal acceleration o luid sloshing in the tank and by riction orces acting on the tank side walls and bottom. Thereore, in this study, these two loads were neglected. It is then considered that liquidinduced horizontal loads can be calculated rom the sum o total pressures acting on the right and let side walls o the tank. According to Fig.. the hydrostatic pressures are dependent on the ree surace height o the luid at each side wall o the TD [Sun, 99]. 3. FUID MOVEMENT MATHEMATICA MODE iquid sloshing movement into a horizontal and low depth surace involves non-linearities. Non-linear models, supported by the shallow water wave theory and based on partial dierential equations under the speciied initial and boundary conditions, can be solved using numerical methods. However, these

3 approaches requently lead to high numerical instabilities. These equations are the result o both continuity relations and two-dimensional Navier-Stokes equations [Sun et. al, 99]. A linear analytical model is applied in this work, where the linear solution or liquid sloshing in the tank is simulated applying the long wave theory, based on dissipative and dispersive non-linear studycases. This theory is used associated with integration techniques, in order to obtain the transerence s unction expression in a simple analytical orm. As previously presented Fig... shows the liquid sloshing in a tank, which is subjected to a horizontal motion x, in OX direction. The local Cartesian coordinate system (OXZ) has to be considered above the steady ree luid s surace and its origin is placed at the let side wall o the tank. The length o the tank is designated by and the average liquid depth is h. In an one-dimensional approach, liquid sloshing in the tank can be expressed by two non-dimensional partial dierential equations (PDE), where a straight line is applied and the u(x,t) variable is eliminated, and so the expression or the elevation o the ree surace becomes [epelletier e Reichelen, 988]: η( x, t ) = Re k sin κ x cos k e i σ t n =0 ( )n sin a n x [ Re n e Sn t ] (3.) The undamental linear sloshing requency o the TD (w) can be given by [Fujino et. al., 99]: ω = π g tanh π h (3.) where is the length o the tank, h is the liquid height and g is the acceleration o gravity. 4. NUMERICA SIMUATION OF A TD The inite element method (FEM) was used to evaluate the eiciency o the proposed tuned liquid damper model and to study the characteristics o the liquid sloshing mechanism in a TD when subjected to a sinusoidal dynamic excitation at its base or dierent displacement amplitudes. ANSYS CFXTM was the inite element analysis tool used to test the eiciency o the TD. The inite element mesh o the tank was generated and the problem boundary conditions and the particular properties o the luid were deined [Novo, 008].The optimized inite element mesh (Fig. 4.) adopted in these analyses has 693 tetrahedral elements with an element average dimension o 8 mm. Figure 4.. Finite element mesh o the TD (with 693 tetrahedral elements) [Novo, 008]. The same tank dimensions and TD parameters were used or all the analyses. The dynamic load applied to the tank was imposed by a sinusoidal motion law o the accelerations applied directly on the tank base. The sinusoidal acceleration imposed along the OX direction, which simulates the direction o ground motion, is given by:

4 ( t) a y = K g sin π (4.) where K is the constant acceleration amplitude and is the natural requency o the building. Gravity acceleration is considered along the O Z direction (a z =9.8 m/s ) and no acceleration is considered along the O Y direction (a x =0 m/s ).Considering the acceleration law: ( t) = A sin( π t) x c (4.) and integrating twice, leads to: x c 4 π ( t) = x ( t) = A sin( π t) (4.3) Thus, the displacement amplitude can be calculated with the expression: A D = 4 π c A c = D ( 4 π ) (4.4) The values o A c and K are listed in Table 4.. According to equations (4.) and (4.): K = g A c (4.5) Table 4.. Amplitude values or A c and K The dissipated energy and corresponding equivalent damping were calculated to evaluate the eiciency o the tuned liquid damper. The dissipated energy or all simulations was calculated and compared to the input energy o the system. For one speciic load cycle, the energy introduced in system is calculated with the ollowing expression [Uang e Bertero, 998]: E i = m x( t)dt (4.6) The energy dissipated per cycle can be evaluated determining the interior area o a cyclic response o the TD in terms o lateral orce versus horizontal displacement. For one speciic cycle o the TD s response, the energy dissipation is determined by the ollowing expression [Uang e Bertero, 998]: E d = Fx ( t)dt (4.7) For a chosen cycle, it is possible to estimate the equivalent damping coeicient through the ollowing expression: Area o the cicle ζ = eq π Fmáx Dmáx (4.8)

5 where F max. is the maximum orce (due to hydrostatic pressure) and D max is the maximum horizontal displacement o the tank. In what concerns the obtained results, Fig. 4. shows the orce-displacement response o the TD or cyclic loading amplitude o 5 mm. Fig. 4.3 shows the evolution o the input and dissipated energy components or a cyclic loading corresponding to an imposed displacement amplitude o 5 mm. Figure 4.. Force-displacement behaviour or a cyclic loading amplitude o 5 mm. Figure 4.3. Input and dissipated energy evolutions or a cyclic loading corresponding to an imposed displacement amplitude o 5 mm. For all the analyses perormed, corresponding to displacements imposed in the -00 mm amplitude range, the evolution o the ratio between the input energy and the dissipated energy is shown in Fig In Fig are plotted, or each displacement amplitude the maximum ratio between the dissipated energy and the input energy (Fig. 4.5a), as well as the estimated equivalent damping, which gives an indication o the TD eiciency.! " Figure 4.4. Ratio between the input and dissipated energy. # $% Figure 4.5. Eiciency o the TD as a unction o the cyclic loading amplitude, in terms o: (a) maximum ratio between the dissipated energy and the input energy and (b) the estimated equivalent damping.

6 5. DESIGN OF A TD FOR AN EXISTING BUIDING For the applications carried out in the scope o this paper, and having in mind a speciic building, the ground motion considered was deined only along one horizontal direction. The building chosen or this study is representative o the modern Portuguese architecture, namely the buildings designed and built in the 950s, when earthquake design was still not considered in the national standards. This representative building has nine-storeys. The option or this case-study is justiied by the moderate to high local seismic hazard o the isbon region and by the signiicant number o buildings with this typology designed and built in Southern European cities in that period. The procedure adopted or the design o the tuned liquid dampers or the studied building was as ollows: i) The building irst natural requency in the longitudinal direction measured in-situ [Miranda et. al, 005] was =.08 Hz. The sloshing requency o the luid is equalled to the irst natural requency o the building: ω = = Τ π (5.) where Τ is the natural period o the structure and is the corresponding angular requency. ii) In terms o linear requency (in Hz) the equation o sloshing requency o the luid (equation 3.3), can be rewritten as ollows: = g π π h tanh (5.) Imposing a ratio between the height o the luid, h, and the length o the tank,, equal to 0.5, [Fujino et al., 99], and substituting the values or the structure under analysis in equation (5), the ollowing non-linear system o equations can be obtained as a unction o h and :.08 = 9.8 π h tanh π and h = 0.5 (5.3) In the scope o this work, it was assumed that the width b o the TD is equal to its length, leading to a quadrangular geometry in plan. This geometry guarantees that the TD will behave equally on both horizontal directions, as opposed to a rectangular tank. From the literature review, no rule or proposal was ound or the height limitation o the TDs. Thereore, on the present case-study it was considered, =0.3m and h =0.044 m. 6. CASE STUDY The eiciency o the TD in the improvement o the seismic response o an existing building was evaluated and the main results are presented in the next. The studied building was presented in Section 5. The linear analyses were perormed with a inite element analysis program (SAP 000 TM ). According to the building dimensions, the structure properties and the TD dimensions and its characteristics, the number o TDs needed to guarantee the required perormance was estimated, in terms o energy dissipation o the structure-td system. The mass o the luid in each tank is m = h b, where is the mass density o the luid and h, b and are the tank dimensions. The number o tanks required, N, was determined with the ollowing relation [Banerji et. al, 000]: m N = µ m e (6.)

7 where µ is the mass ratio between the liquid and the structure (typically varying between and 5%), m s is the mass o the structure and m is the mass o the luid in each tank. The luid chosen or this analysis is water. The total mass o the building is 3863 ton. Consequently, according to equation (6.), the number o tanks needed or each mass ratio considered in this study is listed in Table umped mass method Table 6.. Amplitude values or A c and K &!' ( )*+ Simpliied methods can be ound in the literature to simulate the behaviour o tuned liquid dampers. The lumped mass method and the linear wave theory are such methods. With the lumped mass method [Housner and Brady, 963] method, the wall o the TD is assumed to be rigid. Hydrodynamic pressure caused by liquid sloshing in the tank due to the dynamic loading is considered separately as impulsive pressure and sloshing pressure. The impulsive pressure is proportional to the tank acceleration, but with opposite direction. The sloshing pressure is related to the height o the wave and to the sloshing requency o the liquid. Thereore, both hydraulic pressures can be simulated by two equivalent masses linked to the tank. Fig. 6.. shows a schematic representation o the lumped mass model, in which M 0 is the mass rigidly connected to the tank at an elevation H 0 above its base and M represents the impulsive mass attached to springs with stiness k at elevation H. k M k h M0 H H 0 Figure 6.. umped mass model or a rectangular TD. For rectangular tanks, these parameters can be estimated by [Newmark and Rosenblueth, 97]: M M o tanh = ( 3 * ( / )/ h ) 3 * ( / ) / h m (.6 * h /( / ) ) M 0.83 tanh =.6 * h /( / ) (6.) (6.3) H 0 m = 0.38 h + α M0 (6.4) m ( / ) ( / ) (m ( / ) H = + β h M H h M h (6.5)

8 3 g M h k = m (6.6) where M is the total mass o the contained luid, =.0 and =.33 are parameters due to the hydrodynamic moment on the tank base and h is the liquid height. 6.. Damping o surace wave in a rectangular tank The damping o surace waves in a rectangular tank was studied by Miles [Miles, 967], who suggested that the dissipation coeicient can be corrected by a actor +h/b+s, where b is the tank width. With this correction actor, the energy dissipation due to the luid riction on the lateral side walls and the liquid surace contamination is taken into account. Friction due to the side wall boundary layer is assumed to be the same as that o the bottom boundary layer. S is a surace contamination actor that can vary between 0 and. S= will be used in this study, which corresponds to a ully contaminated surace [Sun, 99] ζ = ν ω h + + S b h g h (6.7) 6.3. Proposed mechanical model The steps adopted or the simpliied simulation o the passive energy dissipation system based on TDs in the Structural Analysis Program [Novo, 008] are briely described in the next paragraphs. Each TD group is simulated by a macro-model, as ollows: i) A damper type link was deined in order to simulate the equivalent damping (ζ) properties o the TD; ii) Each link is connected to the structure with bar elements with stiness k (according to expression 6.6); and iii) Concentrated masses were introduced at the ends o the macro-model to simulate the static mass and at the centre to simulate the dynamic mass. To simpliy the analysis, and due to the large number o TDs needed or the passive energy dissipation system designed in this study, each macro-model corresponds to a set o TDs. The schematic representation o the macro-model developed in SAP to simulate a group o TDs is shown in Fig.6.. M 0 / (nº TDs) M (nº TDs) M 0 / (nº TDs) Figure 6.. Schematic representation o the macro-model used to represent a set o TDs with the proposed model [Novo, 008] Ground motion This study was perormed or a set o synthetic ground motions artiicially generated, or a moderate

9 risk scenario, according to a non-stationary stochastic inite ault seismological simulation model based on random vibration [Rodrigues et. al, 007]. The considered ground motions relect both the close and distant earthquake scenarios and were deined or several return periods. Distant earthquake scenarios were considered or this study and three artiicial earthquakes were generated or each return period [Carvalho et. al, 008] Numerical results The envelope lateral displacement proiles and the maximum inter-storey drit proiles or 475 and 975 years return period are shown in Fig. 6.3 to Fig Each proile represents the average, or the dierent earthquakes, o the results or each return period considered. Figure 6.3. Envelope lateral displacement (475yrp). Figure 6.4. Maximum inter-storey drit proiles (475yrp). Figure 6.5. Envelope lateral displacement (975yrp). Figure 6.6. Maximum inter-storey drit proiles (975yrp). 7. CONCUDING REMARKS The main objective o this paper was to analyse the eiciency o quadrangular tuned liquid dampers in controlling the response o building structures when subjected to earthquake ground motions. To characterize the TDs, as well as the liquid sloshing mechanism, a TD was studied using a reined inite element model. The TD studied was designed or a requency o.08 Hz and subjected to sinusoidal excitations at its base with displacement amplitudes between and 00 mm. From the analysis o the obtained results it can be concluded that, or a sinusoidal cyclic loading, the behaviour o the studied TD is globally eicient, signiicantly increasing the energy dissipation and the corresponding equivalent damping o the global system. The TD is more eective in reducing the

10 structural demands or structures with lower natural periods, as the building structure here studied with a natural period close to s, representative o a large number o existing buildings in many countries around the world. Finally, it can be concluded that TDs can be adopted as eective measures or reducing building structural demands to earthquake input motions. However, these innovative structural protection systems have to be urther studied by shaking table experimental tests and in-situ assessment o their perormance on existing structures. Additionally, the architectonic implications associated to this type o rehabilitation measures should be considered in each speciic case. Concerning the assessment o the perormance o TDs by experimental shaking table testing, it was developed at NEC acility a study that aimed to deine TDs linear and non-linear behavior when subjected to random vibrations o increasing amplitude [Falcão Silva, 00]. Besides that, a considerable eort was also made in what concerns numerical simulations o the behaviour o TDs when isolated or included in SDOF and MDOF structural systems.. REFERENCES Banerji, P.; Murudi, M.; Popplewell, (000) N., Tuned iquid Dampers or controlling earthquake response o structures, Earthquake Engineering and Structural Dynamics; v. 9, pp Carvalho, A.; Zonno, G.; Franceschina, G.; Bilé Serra J.; Campos Costa, A., (008)Earthquake shaking scenarios or the metropolitan area o isbon, Soil Dynamics and Earthquake Engineering, v. 8, n. 5, pp Falcão Silva, M.J. (00). Sistemas de Protecção Sísmica: Uma abordagem baseada no desempenho de Amortecedores de íquido Sintonizados, PhD Thesis, Instituto Superior Técnico, Universidade Técnica de isboa. Fujino, Y.; Sun,.M.; Pacheco, B.M.; Chaiseri, P., (99). Tuned iquid Damper (TD) or Suppressing Horizontal Motion o Structures, Journal o Engineering Mechanics, v. 8, n. 0, pp Housner, G.W.; Brady, A.G. (963).Natural Periods o Vibrations o Buildings, Proceedings o the American Society o Civil Engineering, 89 (EM4), pp epelletier, T.G.; Raichlen, F., (988). Nonlinear oscillations in Rectangular Tanks, Journal o Engineering Mechanics, v. 4, n., pp. -3. Miles, J.W., (967). Surace Wave Damping in Closed Basins, Proceedings o the Royal Society o ondon, A 97, pp , 967. Miranda,.; Rodrigues, H.; Fonseca, J.; Costa, A. G. (005). Relatório de inspecção, Faculdade de Engenharia da Universidade do Porto Newmark, M.N.; Rosenblueth, E., (97). Fundamentals o Earthquake, Prentice-Hall, Inc. Novo, T., (008). Melhoramento da resposta sísmica de ediícios com recurso a TDs, MSc Thesis, University o Aveiro. Rodrigues, H.; Varum, H.; Costa, A., (007). Avaliação da vulnerabilidade e reorço sísmico de um ediício representativo da arquitectura moderna em Portugal, SÍSMICA 007-7º Congresso de Sismologia e Engenharia Sísmica. Sun,.M. (99). Semi-Analytical Modelling o Tuned iquid Damper (TD) with Emphasis on Damping o iquid Sloshing, PhD, University o Tokyo. Sun,.M.; Fujino, Y.; Pacheco, B.M., (99). Modelling o Tuned iquid Damper (TD), Journal o Wind Engineering and Industrial Aerodynamics, v. 4-44, pp , 99. Uang, C.M.; Bertero, V.V., (998). Use o energy as a design criterion in earthquake-resistant design, College o Engineering, University o Caliornia at Berkeley.

STRUCTURAL CONTROL USING MODIFIED TUNED LIQUID DAMPERS

STRUCTURAL CONTROL USING MODIFIED TUNED LIQUID DAMPERS A. Samanta 1 and P. Banerji 2 1 Research Scholar, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India, 2 Professor,