PASSIVE VIBRATION-CONTROL CONCEPT FOR TRUSS FRAME STRUCTURES

Transcription

1 PASSIVE VIBRATION-CONTROL CONCEPT FOR TRUSS FRAME STRUCTURES T.Takeuch 1) 1) Assocate Professor, Dept. of Archtecture & Buldng Engneerng, Tokyo Insttute of Technology, Japan Abstract: Truss frame generally had to be desgned elastcally even aganst large sesmc force, because of fragle characterstcs led by member bucklng. In ths paper, damage tolerant desgn for truss frame structures usng energy dsspaton members n crtcal postons are dscussed. Detaled desgns for hghrse rack warehouses and communcaton towers are studed and tested, followed by smple method for evaluatng the effect of these members. 1. INTRODUCTION In sesmc area, plastc desgn wth moment frames have been popular for long tme, wth the concept of ductle characterstcs led by plastc-hnges on bendng beam ends. On the other hand, truss frame structures, popularly used for long-span roofs or ndustral facltes, had to be desgned elastcally aganst desgn loads, because of less-ductle characterstcs due to the axal member s bucklng. However, desgnng truss structures elastcally aganst large earthquake s not economc, not elegant n desgn, and remanng rsks for fragle collapse n the event of sesmc level exceedng the desgn crtera. Recently, passvely controlled buldngs have become popular n Japan, and varous types of passve energy dsspaton devces are put n practcal use. Many of them are ncorporated wthn moment frames, achevng damage tolerant desgn, whch keeps man structures n elastc even wth great earthquake. The same concept can be appled for truss frame structures by ncorporate energy dsspaton members n crtcal postons, plastcze them frstly whle other truss members are kept before bucklng, and control entre structure ductle (Fg.1). Ths desgn concept wll enable truss frame structures to be slender, elegant, economc and safe from bucklng even n heavy sesmc areas. Bucklng Energy Dsspaton Member (Hysteretc Damper) Fgure 1. Damage Tolerant Concept for Truss Frame

2 PIN Type-A: All Pn Supported RING BRC Type-B: 1-BRC and -Sprng SPRING Type-C: 3-BRC BRC Type-D: BRC Removed from C Fgure. Rack Structure and Supportng Optons In ths paper, above desgn concept s appled to practcal desgn of hgh-rse automatc rack warehouse and communcaton tower usng hysteretc energy-dsspaton members, ntroducng ther detals and effects.. APPLICATION FOR RACK WAREHOUSES The hgh-rse automatc rack warehouse are composed of 5m hgh, 5 lnes of 1.3m-.m wde trussed structures connected each other at ther top by horzontal beams (Fg.). Each lne of trusses s ndependent between the ground level and the top to keep spaces for vertcal cranes, the aspect ratos of each set of trusses reaches to. As dagonal braces stffen the frames n longtudnal drecton, ths transverse drecton s crtcal n strength and deflectons. Walls are attached on the sde trusses and roofs are on top beams, the rack structure tself composes the warehouse frame. The crtcal members aganst horzontal forces are the base-chords of the trusses, and bucklng of these members lead to the collapse of entre structure. For the sake of ductle desgn, these chords are replaced by Bucklng-Restraned Columns (BRC; e.g. Unbonded Braces), whch perform as axal elasto-plastc dampers. In ths study, four types of truss structures as shown n Fgure are studed. Type-A: Normal truss structure whose bases are all pn-supported. Type-B: Sde base chords of the center truss are replaced by BRC, whle other chords are supported by pn or sprng to concentrate reacton forces nto BRC. Type-C: Sde chords of all trusses except for sde trusses are replaced by BRC. P/Py Core Plate Bucklng Restraner Axal Stran (%) (a)bucklng Restraned Column (Unbonded Brace) and ts Hystress Loop Plastc Hnge (b) Dog-bone Plastc Hnges at Top Beams Dsh Sprng Anchor Bolt Fgure 3 Detals of the Rack Structure (c)dsh Sprngs at Anchor Bolts

3 Type-D: All BRC are removed from Type-C. In Type-B and Type-C, axal yeldng of BRC and plastc hnges of the top beams decde collapsng mechansm of the entre structure. The sde trusses are kept n elastc whle BRC are gong nto plastc, and pull back the structure from resdual deformaton after earthquake beng fnshed. Detaled desgn of each part s shown n Fgure 3. Detal of BRC at bases are n Fgure 3(a). The base-sde chords of the truss are replaced by Unbonded Braces, whch are composed of core plates and concrete-flled tube restraner (Fujmoto et.al. 199). Because of restraner keep core-plate from bucklng even n plastc zone, they show symmetrcal hysteretc loops and excellent characterstcs as energy dsspaton members. They are connected to the truss members wth bolts, whch enables replacement of BRC after earthquake. The top beams have dog-bone shape at truss sdes, whch realzes stable plastc hnges (Fg.3(b)). For sprng supports n Type-B frame, dsh sprngs are nserted for anchor bolts at column bases (Fg.3(c)). To verfy the performance of these structures aganst large sesmc vbratons, tme-hstory analyses are carred out on each types of structure. The analytcal models are two-dmensonal composed of each member as beam element, consderng axal forces and bendng moments. For sesmc vbratons, El Centro NS, Taft EW, Hachnohe NS, and Artfcal wave usng ste ground condtons are used for desgn loads wth the level of 5 cm/sec n maxmum velocty. The maxmum responses for Type-A, Type-B and Type-C are shown n Fgure. In shear forces, addtonal forces of each lne of trusses are shown. In story drft, horzontal dsplacement of the sde trusses, whch are the most crtcal n each truss, are represented. The ultmate capacty of the frame s about 5 kn at base, and maxmum response at Type-A frame exceeds the ultmate capacty. Ths means Type-A frame wll collapse wth foresad sesmc vbraton caused by the bucklng of base columns. On the other hand, maxmum story drft s about mm n 335mm unt Type-A: All Pn Supported Type-B: 1-BRC -Sprng Type-C: 3-BRC Shear Force ( ) ( ) TAFT UlTIMATE TAFT UlTIMATE TAFT Ul TIMATE 3 5 SHEAR FORCE (kn) NG Story Drft Fgure Effects of Energy Dsspaton Devces TAFT TAFT TAFT DEFLECTION (cm)

4 δ Α δ D δ δ δ δ Fgure Maxmum Response Converson Q Α Type-A Fgure 5 Rgd Q D Type-D Models for Stffness Evaluaton Pn Q 5 3 (kn) Bucklng Bucklng Bucklng Type-A Type-C Type-D heght, whch s acceptable for the lmt of 1/ n drft angle. In type-b, maxmum shear forces are reduced to about 75% of Type-A, whch secure some margn n strength. Maxmum dsplacement n each story s slghtly reduced to about 9%. In Type-C, the reducton effect of BRC s more sgnfcant, and the maxmum shear forces are reduced to about 55% of Type-A. Maxmum dsplacement s reduced to about %. Consequently, ntroducton of BRC s effectve to reduce maxmum shear forces and avod local bucklng at base chord members. The more BRC are ntroduced, the more reducton effect s obtaned. Although reductons n deflecton are not sgnfcant, they are also contrbutes to decrease the deflecton of the entre structure. 3. ESTIMATION OF RESPONSE REDUCTION EFFECTS In ths secton, a smple method for estmatng the maxmum response of the frames wth energy dsspaton members, usng lnearzaton technques are proposed. When each set of truss s modeled as an equvalent fragle sngle member, a end of truss wth energy dsspaton elements on sde chords can be modeled as a plastc hnge n the equvalent sngle member. Then the entre truss frames can be modeled as equvalent beamcolumn frames wth plastc hnges as Fgure 5. Smplfed response estmaton methods developed for moment frames wth dampers (Kasa et.al. 199) can be appled to truss frames, whch enable easy structural desgn avodng try-and-error bass study n prelmnary stages. In ths secton, response of Type-C frame s estmated usng stffness of Type-A and D frames. When each type of frames are plotted by horzontal forces (Q) and dsplacement (δ), ther relatonshp can be led as shown n Fgure. Where, Q s the shear force at the base, and δ s the equvalent dsplacement defned as followng. N m δ (1) δ = 1 = N = 1 m δ δ (cm) Fgure 7 Q-δ Relatonshp by Pushover Analyses In these frames, δ s represented by the dsplacement at the heght of -75% of the total heght. In Fg., Type-D has much lower stffness than Type-A, and Type-C s consdered to have the same stffness as Type-A whle BRC s elastc, then transferred to the same stffness as Type-D after BRC yeldng. Pushover analyses n Fgure 7 proves ths assumpton. In ths condton, the equvalent stffness rato of Type-C/ Type-D s the functon of µ=δ c /δ y, where δ c s the maxmum deflecton of Type-C, and δ y s the deflecton

5 where BRC start yeldng, expressed as followng. K () Ceq Kd KA / KD 1 = 1+ = 1+ KD KDµ µ The equvalent dampng rato can be estmated as the followng equaton by takng the average of ntegral to the maxmum ampltude (Kasa et.al 199). (1 + Kd/ K D) µ + Kd/ KD KA/ K D µ + KA/ KD 1 (3) hceq = h + ln = h 1 + ln 1 πµ πµ 1 Kd/ KD KA/ KD (1 + Kd / K D) µ + ( KA / K D) µ where, T A : own perod of Type-A, T D : own perod of Type-D. Consequently, to estmate the maxmum response of Type-C, the followng two steps are requred. 1) Response of Type-A ( n Fg.) s estmated by response spectrums. Where T A >.sec, the response of Type-D ( n Fg.) s estmated by Q beng multpled by (T A /T D ), and δ beng multpled by (T D /T A ). (Step1) ) Response of Type-C ( n Fg.7) s estmated wth the effect of K Ceq /K D and h Ceq. (Step). In detal, the response of Type-C/Type-A s expressed by the followng equatons. Shear force and dsplacement response rato s, respectvely : a C = T K δ A C eq C D = D TD K D h a h A TD K δa D TA K (, 5) C eq where, D = + 5h 1+ 5h 1 T M δ Fgure Comparson of Proposed Estmaton and Tme-Hstory Analyses A, D A, D = 1 A, D = π M = N QA, D h C eq mδ = 1 The evaluated responses by these equatons are calculated n spread sheets, and maxmum shear forces and story drft led by ths results are plotted wth tme-hstory analyses n Fgure. In these fgures, dotted lne s evaluated response wthout dampers (Type-A), and sold lne s response wth dampers (Type-C), both led by the proposed method, and marks are the results of tme-hstory analyses.. From these comparson, the results of proposed evaluaton method s consdered to be consstent wth the results of tme-hstory analyses. In Fg.7, the crtcal deflectons of Type-A,C, D frames are 35cm, 7cm, and 7cm respectvely, and the rate of safety n each structure estmated by proposed evaluaton s 1.1 n Type-A, 1. n Type-D, and.3 n Type-C. Ths means the frame wth almost collapse lmt (Type-A) s mproved n performance to more than double-safe frame just by replacng base chords to BRC (Type-C). From these studes, proposed evaluaton method s consdered to be effectve for decdng the sutable volume and poston of energy dsspaton members n prelmnary desgn stages. Advantage of ths method ncludes that no elasto-plastc analyses or tme-hstory analyses are requred, and sutable amount of energy dsspaton members s drectly gven wthout try-and-error analyses. Tme-Hstory (Type-C) Tme-Hstory (Type-A) Proposed Estmaton (Type-A) Proposed Estmaton (Type-C) 3 5 Shear Force (kn) N mδ Tme-Hstory (Type-C) Proposed Estmaton (Type-C) Proposed Estmaton (Type-A) Tme-Hstory (Type-A) Story Drft (cm) (7,, 9)

6 APPLICATION FOR COMMUNICATION TOWERS Instead of replacng column, replacng dagonal members to bucklng restraned members s another way to reduce sesmc responses. In ths secton, applcaton for communcaton towers are dscussed and tested. The concept of structural system s shown n Fg.9, whch s planned as sesmc refnement. The towers are usually desgned aganst wnd forces, however, sesmc response accelerated by standng buldngs can be exceed the wnd forces. In ths study, crtcal dagonal members are replaced by Bucklng Restraned Braces (BRB), ams at savng all other members from bucklng. BRB Load GPL 375 GPL Dagonal BRB or ( Column ) Beam 17 GPL 335 (a) Communcaton Tower on (b) Test Specmen Buldng Fgure 9 Applcaton for Communcaton Towers To verfy the realty of energy dsspaton mechansm, three types of real-sze mock-up tests are carred -out usng sngle truss elements conssts of a chord, a beam, and a dagonal member. In the exstng tower, all truss members have ppe (CHS) sectons (Type-TO). In strengthen renforcement opton, concrete s n-flled wthn the dagonal member (Type-TC). In BRB renforcement opton, dagonals are replaced by BRB whose yeld strength are meetng wth the bucklng strength of orgnal ppe dagonals (Type-TA). Each truss s cyclcally loaded up to 1/5 story drft. The confguraton of the test s shown n Fg., the detal of BRB n Fg.11, and loadng program s shown n Fg.. concrete core plate core plate kn Ol Jack Pn Load Cell Dagonal BRB or Conc. Inflled Beam Fgure 11 Detal of BRB Story Drft Angle (%) Column Pn Tenson Fgure Test Confguraton Compresson Fgure Loadng Program

7 The test results for Type-TO, Type-TC, Type-TA are shown n Fg,13, and 15, respectvely. In each fgure, (a) are load-relatonshp of truss structures, (b) are axal force-deformaton of dagonal members, (c) are fgures at the end of tests. For Type-TO, story drft up to 1/ s accepted by slp of connecton bolts, then the dagonal started bucklng at 1st 1/5 cycle n compresson. elbow was created at nd 1/5 cycle n compresson, and torn off at 1st 1/5 cycle n tenson. The maxmum axal force to start bucklng was about kn. For Type-TC, bucklng strength was ncreased more than kn, the gusset plate at dagonal-to-beam connecton was buckled to out-of-plane drecton. From ths result, t s found that only strengthen dagonal member wll cause collapse n other parts as connectons. For Type-TA, BRB keeps ts maxmum force between kn and kn, and shows qute stable and symmetrcal hysteress loop up to 1/5 story drft both n Fg.15(a) and 15(b). After 3rd 1/5 cycles, BRB fractured at ts core plate. Ther cumulatve plastc deformaton and dsspated energy untl ts fracture are shown n Fg. and Fg.17, respectvely. The cumulatve equvalent stran (axal deformaton / length) capacty n BRB dagonal (Type-TA) was about 5.5 tmes of normal ppe tests (Type-TO). The dsspated energy untl fracture s also has the same tendency. From these results, replacement of dagonals to BRB s consdered to have the best performance as sesmc refnement and savng other members. P (KN) - N (KN) Bucklng - Story Drft Jack Dsp (mm) Fgure 13(a ) Type-TO P-δ (mm) Fgure 13(b) Type-TO N-δ Β Fgure 13(c) Dagonal bucklng G.PL Bucklng - Story Drft Jack Dsp (mm) (mm) Fgure (a ) Type-TC P-δ Fgure (b) Type-TC N-δ Β - Fgure (c) G.PL bucklng Story Drft Jack Dsp (mm) Fgure 15(a) Type-TA P-δ (mm) Fgure 15(b) Type-TA N-δ Β Fgure 15(c ) Dagonal at Test End

8 Type-TO Tenson Compresson Type-TO Tenson Compresson Type-TC Type-TC Type-TA Type-TA Cumulatve Stran Capacty (%) Fgure Cumulatve Equvalent Stran Capacty untl Fracture Dsspated Energy (knm) Fgure 17 Dsspated Energy untl Fracture 5. CONCLUSIONS Concept of damage-tolerant desgn for truss frames wth elasto-plastc energy dsspaton members are ntroduced, and applcatons for hgh-rse automatc-rack warehouse and communcaton towers are descrbed. Usng lnearzaton technques, the smple method for evaluatng maxmum response of rack warehouse structures aganst large earthquake s proposed, and compared wth tme-hstory analyses. Also cyclc loadng tests for the truss for communcaton towers are carred out wth real-sze mock-ups. By these studes, the followng ponts become clear. 1) In truss frames, ncorporatng energy dsspaton members (e.g. bucklng restraned members) nto crtcal postons n truss frames are effectve to mprove the performance of the rack warehouse structure aganst large earthquake. In the case of 5m hgh rack warehouse structures, replacng /13 base chords to BRC reduces the maxmum shear forces to 75%, and replacng /13 base chords to BRC reduces the maxmum shear forces to 55%. ) The above reducton effects evaluated by proposed evaluaton method are consstent wth tme-hstory analyses, and effectve to predct maxmum responses. For the proposed method requres only elastc analyses, t s useful for decdng the volume of energy-dsspaton members n prelmnary desgn stages. 3) From the real sze cyclc-loadng tests modelng communcaton towers, replacement of dagonals to BRB s consdered to have the best performance as energy dsspaton system. strengthenng dagonal ppes by nfllng concrete wll ncrease the bucklng strength, however, other members or connectons mght be crtcal nstead. BRB frame has stable hysteress loop, and has over 5 tmes of cumulatve stran than normal ppe dagonal. References Fujmoto, M., Wada, A., Saek, E., Takeuch, T., & Watanabe, A., (199), Development of Unbonded Braces, Quarterly Column, pp Kasa, K., Fu, Y. & Watanabe A., (199) Two Types of Passve Control Systems for Sesmc Damage Mtgaton, ASCE Journal of Structural Engneerng Takeuch, T. & Aok, H., (), Desgn of Vbraton-Controlled Buldng, II-, Desgn Recommendaton for the Buldng wth Passve Energy Dsspaton Devces, Japan Structural Consultants Assocaton, Syokokusya Kasa, K., & Joda, A., (), Dynamc property, Behavor, and Ther Smplfed Estmaton Rules for a Passve Control System wth Stud-Type Vscoelastc Damper, J. Struct. Constr. Eng., A.I.J., No.55, pp.5-13 Takeuch, T., Kasa, K., Oohara, K., Kmura, Y., & Nakajma, H., (), Performance Evaluaton and Desgn of Passvely Controlled Buldng usng Equvalent Lnearzaton, Struct. Eng.World Congress, Nagoya, T--a- Watanabe, H., Zhu, L., Suzuk, K., Maeda, Y., & Takeuch, T., (), A Sesmc Behavor of Steel Truss Structure Loaded wth Sldng Baggages, Proceedngs of Annual Meetng of A.I.J., No. -7, pp.31-3 (S-II) T.Uchyama, T.Takeuch, K.Suzuk, Y.Ookouch, T.Ogawa, S.Kato (), Sesmc Refnment for Communcaton Toewrs, Proceedngs of Annual Meetng of A.I.J. Kanto,.3