Response Control Effect of Steel Building Structure Using Tuned Viscous Mass Damper

Transcription

1 Response Control Effect of Steel Buldng Structure Usng Tuned Vscous Mass Damper Y. Sugmura, W. Goto, H. Tanzawa, K. Sato & T. Nnomya NTT FACILITIES, INC. T. Nagasaku NTT Urban Development Co. K. Sato NTT FACILITIES RESEARCH INSTITUTE, INC. SUMMARY: The authors have proposed a new sesmc response control system called the Tuned Vscous Mass Damper (TVMD). Ths system s composed of arrangng vscous dampng element and nertal mass element n parallel and connectng sprng element n seres, and can get effcent energy absorpton effect because the moton of vscous dampng element s expanded by tunng mass element and sprng element of damper to those of structure. Ths paper shows an applcaton of the newly developed TVMD to a steel buldng structure. Frst, the outlne of ths system and a desgn method based on fxed ponts theory s shown, and next, a desgn example of ths system appled to a steel buldng structure s presented. Lastly, the response control effect and an advantage of ths system on a practcal desgn are llustrated. Keywords: Tuned vscous mass damper, Passve response control, Sesmc response, Response control effect 1. INTRODUCTION Many knds of measures usng dampers have been developed and utlzed to control sesmc response of buldng structures. Dampers commonly used are made use of energy absorpton effect of metal materal or vscous materal. On the other hand, response control usng nertal mass element has been studed, whch gets nertal force due to the relatve acceleraton, but not due to the absolute acceleraton (Furuhash & Ishmaru 004, Isoda, Hanzawa & Tamura 009). Sato et al. has proposed a new sesmc response control system called the Tuned Vscous Mass Damper (Sato, Kurta & Inoue 007, Sato el al. 008, Ikago, Sato & Inoue 01). Ths system s composed of arrangng vscous dampng element and nertal mass element n parallel and connectng sprng element n seres, and can get effcent energy absorpton effect because the moton of vscous dampng element s expanded by tunng mass element and sprng element of damper to those of structure to be controlled (Fg 1.1.). vscous dampng element nertal mass element support sprng element Fgure 1.1. Dynamcal Model of the Tuned Vscous Mass Damper Sesmc Response Control System In general, the effectveness of controllng wnd-nduced response of buldng structure usng mass element lke the Tuned Mass Damper (TMD) s recognzed, but t could be unrealstc to control sesmc response of buldng structure by mass element. The reason of ths s that the amount of supplemental mass becomes very large, whch s requred to control response suffcently. However a

2 damper has been developed whch can amplfy mass effect apparently by means of ball-screw mechansm transformng lnear moton to rotatonal moton, therefore t has become possble to get more effcent response control effect by ths damper as the same scale and weght as usual ones. The nertal mass element whch s used n the TVMD has an apparent mass amplfyng mechansm to obtan a large supplemental mass effect lke ths (Fg 1.., Kda et al. 011). cross roller bearngs frcton materal ball nut ball screw nternal cylnder coned dsk slcone ol cylndrcal flywheel Fgure 1.. Rotary Dampng Tube wth Inertal Mass ball jont Ths paper shows an applcaton example of the newly developed TVMD to a steel buldng structure. Frst, the outlne of ths system and a desgn method based on fxed ponts theory s shown, and next, a desgn example of ths system appled to a steel buldng structure s presented. Lastly, the response control effect and an advantage of ths system on a practcal desgn are llustrated.. OUTLINE OF BUILDING AND STRUCTUAL PLAN The buldng ncorporated wth the TVMD system s located at Tohoku area n Japan, and combnes the functon of offce and the others. The frames consst of steel and the columns are CFT (concrete fxed tube).ths buldng has sesmc response control systems to upgrade sesmc safety of structure and facltes n the buldng (Fg..1.). As for X drecton, t has tradtonal vscous dampers at lower floors and the TVMD system at upper floors. As for Y drecton, t has a Connect-Wall-Damper System n addton to tradtonal vscous dampers (The Buldng Center of Japan 011). Vscous Damper Tuned Vscous Mass Damper Tuned Vscous Mass Damper 5 14F Vscous Damper Y Connect-Wall-Damper System Vscous Damper X 1 4F Y4 Frame Fgure.1. Framng Plan and Elevaton

3 3. TUNED VISCOUS MASS DAMPER RESPONSE CONTROL SYSTEM 3.1. Outlne of TVMD Response Control System The TVMD response control system s composed of arrangng vscous dampng element and nertal mass element n parallel and connectng support sprng element n seres (Fg 1.1.), and can get effcent energy absorpton effect because the moton of vscous dampng element s expanded by tunng mass element and sprng element of damper to those of structure to be controlled. Rotary dampng tube wth nertal mass (Fg 1..) has large mass as nertal mass element, and also has the functon of vscous dampng element. The TVMD system s formed by ncorporatng ths damper to a buldng structure through a support member whch has relevant stffness lke steel or rubber. 3.. Optmum Response Control Desgn Method based on the Fxed Ponts Theory In ths secton, a desgn method of ths system (the optmum response control desgn method) whch s based on the fxed ponts theory s presented (Sato et al. 008). Here we concern about the mult-degree-of-freedom system wth the TVMD system, m sk, m rk, c dk, k bk represent kth story s mass of the prmary structure, kth story s nertal mass, vscous dampng coeffcent and support member s stffness of th mode damper respectvely. And x sk and n represent kth story s relatve dsplacement of the prmary structure from the ground, and number of stores of the prmary structure respectvely. The optmum response control desgn method s as follows. 1) Gve kth story s nertal mass of th mode damper m sk accordng to the target of response control. ) Calculate the equvalent mass M and the equvalent mass between nodes M r by egenvalue problem analyss of the prmary structure. Here, u sk and β represent kth story s element of th mode egenvector and th mode partcpaton factor respectvely. M r = n { msk ( usk ) } k = 1 M = m 3) Calculate mass rato μ. β (3.1) n [ { ( )} ] ( us1) + mrk usk us( k 1) r1 β k= β (3.) μ M M (3.3) = r 4) Calculate optmum tunng frequency rato β opt and optmum dampng rato ς opt. β opt μ = μ ς opt 3(1 1 4 μ ) = (3.4, 3.5) 4 5) Get the support member stffness k bk and vscous dampng coeffcent c dk. Here, ω n represents th mode crcular frequency of the prmary structure. k ( β ω ) c bk = mrk opt n dk opt rk opt n = ς m β ω (3.6, 3.7) About the amount of m sk n procedure 1), although t can be decded by tral run, some desgn methods whch use numercal optmzaton have been also presented (Ikago, Sugmura, Sato, Inoue 010, Ikago, Sugmura, Sato, Inoue 011).

4 4. DESIGN OF TUNED VISCOUS MASS DAMPER 4.1. Ground Moton Acceleraton for Desgn Ground moton acceleratons used n structural desgn are shown below (Table 4.1.). EL CENTRO-NS, TAFT-EW, HACHINOHE-NS are observed records and they are normalsed to be 5cm/s and 50cm/s (Level 1 and Level respectvely) of ther maxmum velocty. KOKUJI-R,K,H are artfcal earthquake acceleratons used n structural desgn of some buldngs n Japan. Fg 4.1. shows the velocty response spectra of these acceleratons. Table 4.1. Ground Moton Acceleraton for Desgn Ground Moton Acceleraton for Desgn Max of Acceleraton (cm/s ) Level 1 Level 1 EL CENTRO-NS (1940) TAFT-EW (195) HACHINOHE-NS (1968) KOKUJI-R(Phase Angle:random) KOKUJI-K(Phase Angle:JMA-KOBE) KOKUJI-H(Phase Angle:HACNIHOHE-NS) EL CENTRO-NS TAFT-EW HACHINOHE-NS KOKUJI-R KOKUJI-K KOKUJI-H Sv(cm/sec) Crteron n Structural Desgn Perod(sec) Fgure 4.1. Velocty Response Spectra Table 4.. shows the sesmc crteron n structural desgn of ths buldng. In ths desgn, structural frames are supposed not to be damaged aganst Level earthquake. Table 4.. Sesmc Desgn Crteron Level 1 Level Shear Force Shear Force to Allowable Stress Desgn Elastc Lmt Strength Inter-story Drft Angle R 1/50 R 1/15 Ductlty Factor μ 1.0 μ Desgn Parameter of Tuned Vscous Mass Damper The desgn of the TVMD system s based on the optmum response control desgn method (see 3..). In ths desgn, the TVMDs are tuned to the 1st mode of the prmary structure. Inertal mass of damper s set to be 5,400ton. Table 4.3. shows the desgn parameters. The mass rato 1 μ presented by Eqn.3.3. becomes Table 4.3. Desgn Parameter of Tuned Vscous Mass Damper ( each 1 damper ) Inertal Mass Vscous Coeffcent Stffness Restrcted Force 5, kg 7,300kN/(m/s) 68,600kN/m 1,00kN

5 4.4. Installaton Method of the Tuned Vscous Mass Damper The TVMD s consttuted lke Fg 4.. to realze above parameters. As for support member, t s planned that a rubber member s to be a perod adjustment member and nstalled through a steel brace. The materal of the rubber member s a natural rubber (G6), and the form s szed at 400mm x 400mm, the thckness s 4mm, and 4 peces are used n each damper. Stffness of a sequental sprng whch conssts of the rubber and the steel braces s desgned to be the target stffness shown n Table 4.3. Here, the controllng of the stffness of the total system s very mportant, t s supposed to be easy to control t by the stffness of the rubber member tended to be domnant to the total stffness. On the other hand, nertal mass of 5,400 ton s realzed by a steel weght whch dameter s 600mm, length s 800mm, thckness s 50mm and actual mass s 560kg by mass amplfyng effect. Beam BH End H Center Column (CFT) Brace H Vscous Mass Damper Support Member BH Natural Rubber (G6) Inner plate moves wth upper brace Stopper aganst sde movement Sde Vew Outer plates move wth dampers Vew from Above Fgure 4.. Installaton Method of Damper 5. MODAL DAMPING AND FREQUENCY CHARACTERISTICS 5.1. Natural Perod and Modal Dampng In ths secton, the change of the whole system by ncorporatng the TVMDs to the prmary system s confrmed. The prmary system s smply modelled to equvalent shear model, and nonlnear vscous damper s substtuted to lnear property n ths study (Fg 5.1. and Table 5.1.). The nherent dampng of the prmary structure s set to be stffness proportonal and provded 0.0 dampng rato to the 1st mode. Table 5.. and Table 5.3. present the natural perods and modal dampng ratos by complex egenvalue problem analyss respectvely. The case wthout damper and the case wth only the vscous damper at lower floors n the buldng are shown for comparson n addton to the case wth all dampers. Although the number of whole system modes ncreases from 14 to 4 by ncorporatng the TVMDs, t can be seen that the modes whose perods are near each other arse from the 1st mode to

6 the 11th mode. These modes correspond to the 1st mode of the other cases, and the 1 and hgher modes of all damper cases correspond to the and hgher modes of other cases. On the other hand, t can also be seen that the modal dampng ratos of the 1st and the 11th mode of all damper case become 14%, and they are larger than that of the other cases. Prmary Structure (14 nodes) Tuned Vscous Mass Damper 10 story Vscous Damper 4 story Fgure 5.1. Study Model Table 5.1. Parameter of the Prmary Structure and Dampers Prmary Structure Damper Mass Vscous Stffness Mass Vscous Coeffcent Coeffcent Stffness ton(= 10 3 kg) kn/(m/s) kn/m ton(= 10 3 kg) kn/(m/s) kn/m Table 5.. Natural Perod Vscous Damper (Lower)+ No Damper Vscous Damper (Lower) Tuned Vscous Mass Damper (Upper) Mode Perod(sec) Mode Perod(sec) Mode Perod(sec) 1st.03 1st.00 1st.0 nd rd th th th th th th th th 1.69 nd 0.79 nd th rd rd th 0.4 4th 0.3 4th th 0.8 5th 0.7 5th th 0.

7 Table 5.3. Modal Dampng Rato No Damper Vscous Damper (Lower) Vscous Damper (Lower)+ Tuned Vscous Mass Damper (Upper) Mode Dampng Rato Mode Dampng Rato Mode Dampng Rato 1st 0.0 1st st 0.14 nd 0.1 3rd 0.1 4th 0.1 5th 0.1 6th 0.1 7th 0.1 8th 0.1 9th th th 0.14 nd 0.05 nd 0.1 1th 0.1 3rd rd th th th th th th th Frequency Characterstcs In ths secton, the magnfcaton factor aganst harmonc nput s confrmed. Fg 5.. presents the magnfcaton factor of nter-story deformaton of each story to the ground dsplacement. 1st nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 1th 13th 14th Magnfcaton Factor (Inter-story/Ground) Magnfcaton Factor (Inter-story/Ground) Magnfcaton Factor (Inter-story/Ground) nd Perod 3rd Perod 1st Perod No Damper Vscous Damper(Lower) Vscous Damper (Lower)+ Tuned Vscous Mass Damper (Upper) Perod(sec) Fgure 5.. Magnfcaton Factor of Dsplacement

8 It appears clearly that the magnfcaton factor across wde range s reduced equally by ncorporatng the vscous dampers. On the other hand, the magnfcaton factor of the tuned mode (=the 1st mode n ths desgn) s reduced ntensvely and those of other modes are not almost changed when the TVMDs are ncorporated. Ths means that the TVMD can rase the dampng of arbtrary mode. 6. SEISMIC RESPONSE CONTROL EFFECT 6.1. Analyss Model Fg 6.1. presents the dynamc analyss model for sesmc response calculaton. The vscous dampers are modelled by Maxwell Model. The TVMD dampers are modelled by 3-elements model and a sprng element represents a rubber member. Y X Beam Beam Brace Column Damper Damper Column Brace Damper Damper Vscous Damper Tuned Vscous Mass Damper Fgure 6.1. Dynamc Analyss Model 6.. Maxmum Response aganst Ground Moton The maxmum responses of ths buldng aganst ground moton used n desgn are shown n Fg. 6.. Each response satsfes the crteron n structural desgn accordng to the response control effect of both the TVMDs and the vscous dampers Advantage n Practcal Desgn on the TVMD Sesmc Response Control System The TVMD has a problem that ts damper force could ncrease compared wth other vscous damper when both dampers have equal response control effect. To solve ths problem, t s shown that the damper force can be reduced by nstallng the force restrcton mechansm wthout reducton of response control effect (Kda et al. 011). Fg 6.3. shows the comparson of maxmum sesmc response due to the exstence of the force restrcton mechansm aganst the TAFT-EW Level nput. The force of restrcton s set to be 1,00 kn, and t corresponds tmes of maxmum damper force when t s not restrcted. Here, the case n whch the TVMDs are exchanged wth the vscous dampers ncorporated n lower floor s shown for comparson. It can be seen that the Force-Restrcted

9 TVMD can reduce the damper force wth lttle reducton of response control effect, and the Force-Restrcted TVMD can obtan equal response control effect wth smaller damper force compared wth the vscous damper. In ths applcaton example, the damper forces decrease about 0.7 tmes compared wth tradtonal vscous damper. Ths can cause a reasonable desgn of frame structure. Level 1 Level EL CENTRO-NS TAFT-EW HACHINOHE-NS KOKUJI-R KOKUJI-K KOKUJI-H R=1/50 0 1/500 1/50 Inter-story Drft Angle (rad.) R=1/15 0 1/50 1/15 Inter-story Drft Angle (rad.) Shear to Allowable Stress Desgn Shear (kn) Elastc Lmt Strength Shear (kn) Fgure 6.. Maxmum Sesmc Response z15 z14 z13 z1 z11 z10 z9 z8 z7 z6 z5 z4 z3 z z1 No Damper Tuned Vscous Mass Damper z15 R=1/15 z14 z13 z1 z11 z10 z9 z8 z7 z6 z5 z4 z3 z z1 0 1/50 1/15 3/50 Inter-story Drft Angle (rad.) Shear (kn) Force-Restrcted Tuned Vscous Mass Damper Vscous Damper Elastc Lmt Strength z15 z14 z13 z1 z11 z10 z9 z8 z7 z6 z5 z4 z3 z z Damper Force (kn) Fgure 6.3. Comparson of Maxmum Sesmc Response due to Damper System Dfference

10 7. CONCLUSIONS Ths paper shows the applcaton example of the newly developed TVMD to a steel buldng structure. Frst, a desgn method and an nstallaton method of ths system are shown, and next, the sesmc response control effect of ths system s presented by analysng natural perod, modal dampng rato, frequency characterstcs and sesmc response. Lastly, an advantage of ths system on a practcal desgn s llustrated. The conclusons we obtaned here are as follows. (1) Very large mass effect can be obtaned accordng to the TVMD system. In ths applcaton example, a mass rato for the whole buldng becomes about 7% by ncorporatng dampers whch holds 5,400ton mass effect. ()Dampng of arbtrary mode wthn structure can be rased ntensvely accordng to the TVMD system. In ths applcaton example, dampng of the 1st mode whch s domnant to sesmc response of buldng structure s rased effectvely, and t becomes about the 14% dampng rato by complex egenvalue problem analyss. (3)It can be got suffcent sesmc response control effect by combnng the TVMD system whch can rase dampng of arbtrary mode wth the tradtonal vscous dampers. (4)The damper force of the TVMD can be decreased wthout reducton of response control effect by usng force restrcton mechansm of ths system. In ths applcaton example, the damper forces decrease 0.7 tmes compared wth tradtonal vscous damper. Ths can cause a reasonable desgn of frame structure. REFERENCES Furuhash T., Ishmaru S. (004). Mode Isolaton By Inertal Mass Study on response control by nertal mass No.1. Journal of Structural and Constructon Engneerng Archtectural Insttute of Japan. 576, (n Japanese). Isoda K., Hanzawa T., Tamura K. (009). A Study on Response Characterstcs of a SDOF Model wth Rotatng Inerta Mass Dampers. Journal of Structural and Constructon Engneerng Archtectural Insttute of Japan. 64, (n Japanese). Sato K., Kurta S., Inoue N. (007). Optmum Response Control of 1-DOF System Usng Lnear Vscous Damper wth Inertal Mass and ts Kelvn-type Modelng. Journal of Structural Engneerng. 53B, (n Japanese). Sato K., Sugmura Y., Nakamnam S., Kda H., Inoue N. (008). Vbraton Tests of 1- Response Control System Usng Inertal Mass and Optmzed Soft Sprng and Vscous Element. The 14th World Conference on Earthquake Engneerng. Paper ID Ikago K., Sato K., Inoue N. (01). Sesmc Control of Sngle-degree-of-freedom Structure usng Tuned Vscous Mass Damper. Earthquake Engneerng and Structural Dynamcs. 41:3, Kda H., Watanabe Y., Nakamnam S., Tanaka H., Sugmura Y., Sato K., Ikago K., Inoue N. (011). Full-Scale Dynamc Tests of Tuned Vscous Mass Damper wth Force Restrcton Mechansm and Its Analytcal Verfcaton. Journal of Structural and Constructon Engneerng Archtectural Insttute of Japan. 665, (n Japanese). The Buldng Center of Japan (011). Complex Comuncaton Buldng ncorporated wth Effcent Semc Response Control Systems. The Buldng Letter Techncal Report. 547, (n Japanese). Ikago K., Sugmura Y., Sato K., Inoue N. (010). Optmum Sesmc Response Control of Multple Degree of Freedom Structures usng Tuned Vscous Mass Dampers. The Tenth Internatonal Conference on Computatonal Structures Technology. Paper 164 Ikago K., Sugmura Y., Sato K., Inoue N. (011). Sesmc Dsplacement Control of Multple-degree-of-freedom Structures usng Tuned Vscous Mass Dampers, The 8th Internatonal Conference on Structural Dynamcs EURODYN