A NOVEL PASSIVE ENERGY DISSIPATION SYSTEM FOR FRAME-CORE TUBE STRUCTURE

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1 Te Sevent Asia-Pacific Conference on Wind Engineering, November 8-, 009, Taipei, Taiwan A NOVEL PASSIVE ENERGY DISSIPATION SYSTEM FOR FRAME-CORE TUBE STRUCTURE Zeng-qing Cen and Zi-ao Wang Director, Wind Engineering Researc Center, Hunan University Cangsa 4008, Cina, zqcen@nu.cn P.D Student, Wind Engineering Researc Center, Hunan University Cangsa 4008, Cina, ziaowang@gmail.com ABSTRACT Te classical outrigger cantilevering from te core tube or sear wall connected to te perimeter columns directly, wic can make te perimeter columns participate in te overall bending resistance. Terefore, te lateral stiffness of te structure will get improved. A new energy-dissipation system for suc structural system is studied, in wic te outrigger and perimeter columns are separate, and vertical viscous dampers are equipped between te outrigger and perimeter columns to make full use of te relative big displacement of tese two components. Te effectiveness of proposed system is evaluated by means of te modal damping ratio based on te proposed simplified model. Controllable outrigger damping system based on MR dampers and real-time ybrid simulation are undergoing. KEYWORDS: FRAME-CORE TUBE STRUCTURE, OUTRIGGER, VISCOUS DAMPER, MODAL DAMPING RATIO Introduction Te buildings ave continued to soar skyward wit te development of material and construction tecnology. However, flexible structures may fall victim to excessive levels of vibration under te action of wind, adversely affecting serviceability and occupant comfort. To ensure te functional performance of flexible structures, various design modifications are possible, ranging from alternative structural systems and aerodynamic modifications to te utilization of passive and active control devices [Kareem et al. (999)]. Passive supplemental damping systems strategies for ig rise building, including te viscous damper, viscoelastic dampers and tuned mass dampers, are well understood and are widely accepted by te engineering community as a means for mitigating te effects of dynamic loading [Kareem et al. (999), Spencer and Nagarajaia (00)]. It as been sown tat incorporation of viscous dampers in te structure can be a very effective means of reducing unwanted vibrations [Soong and Spencer (00)]. From a design point of view, tis means two questions ave to be answered: (I) wat are good locations for placing te dampers in te structure and (II) wat are te optimal damping constants resulting in minimized vibrations [Engelen et al. (007)]. Tere is a vast of optimization strategy to deal wit tese two questions [Garcia and Soong (00), Liu et al (005), Lavan and Levy (006)], owever, no matter wat kind of optimization approaced is adopted; tere is still one pysical limitation for viscous damper applied in ig rise building. Generally, te dampers are equipped between stories, but te relatively small storey drift and velocity as restricted te damper performance. One of common structural system for ig rise building is frame-core tube structure wit outriggers, wic as become a popular approac to improve te efficiency of te core system by simply engaging te exterior columns to aid in resisting part of te overturning moment resulting from lateral loads, since it was deeply studied by Smit (98). It is obvious tat te

2 outriggers mainly focus on te static design of wind. To furter improve te dynamic response of structure, a new damping system tat adding viscous dampers between outriggers and perimeter column is first presented by [Jeremla (006)]. Smit and Willford (007) as developed a similar system wit [Jeremla (006)], and successfully applied te outrigger damping system to a ig rise building in Pilippine [Willford et al (008)]. Te outrigger damping system is well described in figure and [Smit and Willford (008)]. Figure : Te damped outrigger Figure : Te layout of outrigger damping system A simplified model wit one outrigger in a frame-core tube structure is adapted to evaluate te effectiveness of tis energy dissipation system, and te outrigger location and damping constant of linear viscous damper is analyzed based on parametric analysis, wic can be a good reference for te preliminary design of suc kind of structure.. Simplified analysis model It is well known tat te deformation of te core due to external orizontal load sows similar caracteristics wit te cantilever beam. As a result, a simplified model of te core-to-perimeter-column outrigger system is proposed, in wic te building core is modeled as a uniform cantilever beam, and te outrigger, located atα, is assumed to be massless and infinitely rigid. Te intrinsic damping of te structure is omitted. Te only damping source for te structural system is from te two dampers wit damping constant c d equipped between te outrigger and te perimeter columns. Te calculation diagram is sown in figure. Figure : Te calculation diagram of passive energy dissipation system. SDOF model To get te single degree of freedom (SDOF) model, only one assumed mode is defined. wxt (, ) = φ( xqt ) ( ), and it satisfies te boundary condition φ (0) = 0, φ (0) = 0. For any random virtual displacement δ wxt (, ) of structure, te following equation is establised:

3 δw+ δ W=0, () were δ W and δw represent te virtual work of practical and inertia force respectively. And te equation can be calculated as follows: δw = Mδw ( x, t) dx M δw ( α, t) () d 0 Mδw ( x, t) dx = EIφ ( x) q( t) φ ( x) δq( t) dx = EIq( t) δq( t) ( φ ( x)) dx () dsin( w ( α, t)) Mdδw ( α, t) = ecde φ ( α) δq( t) dt ec qt qt ec qt qt dφ ( α ) ( ) φ ( α ) δ ( ) = d( φ ( α )) ( ) δ ( ) δw = ρawxt (, ) δwxtdx (, ) = ρa φ( xqt ) ( ) φ( x) δqtdx ( ) = ρaqt ( ) δqt ( ) φ ( xdx ) (5) Defining = ρ φ ( ), = d ( φ ( α )), = ( φ ( )) 0 0 as te modal mass, M A x dx C e c K EI x dx damping and stiffness, respectively, te following equation tat represents te SDOF model can de derived as: Mq () t + Cq () t + Kq() t = 0 (6) From te Eq.6 and te definition of modal damping, some conclusions can be drawn: te equivalent damping of structure as been amplified as a result of term e ; te rotational angle of core at te outrigger location also as a great effect. It seems tat te bigger damping constant is, te bigger modal damping is. However, wen te damping is large enoug, it acts as a rigid link, and it won t dissipate energy at all. Terefore, SDOF model can only be used as qualitative analysis, and te precise MDOF model is needed to carry out quantitative analysis.. MDOF model To accelerate te convergence rate of assumed sape metod, te static deformation due to external damping force is cosen to be te first mode sape [Jonson et al (00)], so te static deformation of core due to a moment at te outrigger location is adopted as te first mode sape. Te non-dimension form of all te mode sapes is assumed as: x 0 x a x i φ ( x) = φ i( x) = ( ) i =,,..., n (7) x a a a x Te equation of motion for system free vibration based on generalized displacement can be written as: Mq + Cq + Kq = 0 (8) were te mass M, and stiffness matrix K is easily to be determined as follows: ( ) φ ( ) M ij = ρaφi x j x dx 0 Kij = EIφ i ( x) φ j ( x) dx 0 Te rotational angle of core can be expressed as: (4) (9)

4 n β( x, t) = φ i( x) qi( t) (0) i= Assume tere is a virtual angle δβ wen te angle is β. If β is quite small, we avesin β β. Ten, te virtual work tat damper force made due to te virtual angle δβ can be computed as: n n de ( sin β ) δw = Mdδβ = ecd δβ = e c dβδβ = e cd φ i( α) q i( t) φ i( α) δqi( t) () dt i= i= Terefore, te supplemental damping matrix C can be derived as: C = c e φ α φ α i = : n, j = : n (). FE model ( ) ( ) ij d i j To validate te result of MDOF model, a finite-element approac as been adopted wic states te governing equation of te system in te following form: M f { U } + Cf { U } + K f { U} = 0 () A standard two-node beam element wit two degrees of freedom for eac node is considered in tis study. Te element stiffness and mass matrix are symmetrical and expressed as: 6L 6L 4L 6L L EI k e = (4) L 6L 4L 56 L 54 L ρ AL 4L L L M e= (5) L 4L Te global stiffness matrix and mass matrix are omitted ere; te damping matrix is given as follows: ce d i= j= ( m ) C f = (6) ij 0 else were m represents te node number were te dampers are attaced. It is noticed tat in C matrix, only one position as real value, and all te left is equal to zero. f Parametric analysis To get te modal information, te complex-modal analysis for bot MDOF model and FE model is needed. Te state matrix of system derived from assumed mode sape metod and FE metod can be expressed respectively as: 0 I 0 I Am = ; A f = (7) M K M C M K M C f f f f According te previous researc [Smit et al. (98) and Smit et al. (007)] and te rotational angel mode sape of classical cantilever beam, te outrigger location α is cosen as 0.6 in te next analysis. Te building model parameters are set as: A EI E e ρ = 85000(Kg m); = 4 (Nm ); = 40(m); = 5(m). Based on te comparisons between te MDOF model and FE model, it is found tat wen te number of assumed mode sapes n equals to 8, it is enoug to reac te same accuracy as

5 te FE model wit 50 degrees-of-freedom for te first fort modes. Figure 4 as sown te calculation result of structural natural frequency and modal damping wit te canging damping constant of linear viscous damper, in wic,,, 4 represent te corresponding mode number. From te figure, one interesting penomenon can be seen tat te structure sows modes sift wit te increasing of damping constant, and te iger modes gradually move to its nearest lower modes. As pointed out in te researc of [Engelen et al. (007)], wen te natural frequencies of a structure wit zero damping constant and infinity damping constant of damper are quite close to eac oter, a modest modal damping is acieved, or te critical modal damping will be expected and te modes sift accordingly. Terefore, te structural system described in tis paper is quite different from te cable damping system [Jonson et al (00)], in wic te damper is always added on te position close to te support, and te frequency canging is quite small for two limiting conditions tat one is witout damper, and te oter is wen damper works as te rigid link. Natural frequency(hz) Mode damping ratio Damper coefficients(0 8 Nm/s) Damper coefficients(0 8 Nm/s) Figure 4: Te natunal frequency and modal damping wit different damper coefficients Conclusions and furter researc A novel energy dissipation system tat vertical viscous dampers are equipped between te outrigger and perimeter columns is studied, wic can acieve te amplified damping ratio. It is expected to effectively improve te dynamic performance of structure at te expense of static stiffness and strengt. Te modal caracteristic of te structural system is teoretically analyzed based on te simplified model by parametric analysis, wic can provide useful reference for te preliminary design of frame-core tube structure. However, te nonlinear time istories analysis is still needed to validate te final design in te engineering practice. To furter evaluate te effectiveness of te system, te control performance of building wit te proposed outrigger damping system excited by wind is undergoing. Acknowledgements: Te second autor greatly acknowledges te partial support of Cinese Scolarsip Council and suggestions from Professor Spencer in University of Illinois at Urbara-Campaign. Te autors would also like to tank ARUP for providing te details of damped outrigger system tey developed. References Engelen, K., Ramon, H., Saeys, W. et al. (007), Positioning and tuning of viscous damper on flexible structure, Journal of Sound and Vibration, 04,

6 Te Sevent Asia-Pacific Conference on Wind Engineering, November 8-, 009, Taipei, Taiwan Garcia, D. L., and Soong, T. T. (00), Efficiency of a simple approac to damper allocation in MDOF structures, Journal of structural control, 9, 9-0. Jeremla, C. (006), Application of damping in ig-rise building, Massacusetts Institute of Tecnology. Jonson, E. A., Cristenson, R. E. and Spencer, B. F. (00), Semi-active damping of cables wit sag, Computer-Aided Civil and Infrastructure Engineering, 8,-46. Kareem, A., Kijewski, T. and Tamura, Y. (999), Mitigation of Motion of Tall Buildings wit Recent Applications, Wind and Structures, (), 0-5. Lavan, O., and Levy, R. ( 006), Optimal design of supplemental viscous dampers for linear framed structures, Eartquake Engineering and structural dynamics, 5(), Liu, W., Tong, M., and ; and Lee, G. C. (005), Optimization Metodology for Damper Configuration Based on Building Performance Indices, ASCE Journal of Structural Engineering, (), Smit, B. S. and Salim, I. (98), Parameter study of outrigger-braced tall building structures, Journal of Structural Division, ASCE, 6, Smit, R. J. and Willford, M. R. (007), Te damped outrigger concept for tall buildings, Te Structural Design of Tall and Special Buildings, 6, Smit, R. J. and Willford, M. R. (008), Damped outriggers for tall buildings, Te ARUP Journal,, 5-. Soong T T, Spencer B F. Supplemental energy dissipation: state of art and state of practice, Engineering Structures, 00, : Spencer, B. F. and Nagarajaia S., (00), State of te art of structural control, ASCE Journal of Structural Engineering, 9(7), Willford, M., Smit. R., Scott, D., et al. (008), Viscous dampers come of age, Structure magazine, 6, 5-8.