LATTICE TOWER DYNAMIC RESPONSE CALCULATION TO HUMAN INDUCED LOADS: CASE STUDY

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1 Proceedngs of the Interntonl Conference Innovtve Mterls, Structures nd Technologes do: 0750/scconstrs0407 LATTICE TOWER DYNAMIC RESPONSE CALCULATION TO HUMAN INDUCED LOADS: CASE STUDY Lg Gle, Ivrs Rdnsh, Dertment of Structurl Mechncs, culty of Constructon, Rg Techncl Unversty, Azenes st 6, LV-048 Rg, Ltv E-ml: uthor); Abstrct A ste by ste lgorthm of lght-weght lttce tower dynmc resonse clculton method to tycl humn nduced tme vryng horzontl lods s resented n ths work for the frst tme The develoed lgorthm of the method s bsed on the reserches resented n the revous works of the uthors on the subject The clculton method tself s bsed on the generlly cceted desgn rocesses for low frequency structures when t s convenent to consder the mum level of the resonnt resonse tht cn be nduced by erson under reeted footfll nd to lmt t to the ccetble level The lgorthm ws led to fnd theoretclly the ek ccelerton mltudes of vbrton on n ctul 6m hgh lght-weght lttce observton tower n Jurml, Ltv wth eccentrc structurl confgurton The theoretclly obtned results showed good greement wth the exermentl dt found n revous exerments The clculton lgorthm could be consdered s useful tool for the structurl desgners when undertkng the desgn of lght-weght slender ublc observton towers Keywords: lttce tower, observton tower, dynmc resonse, humn nduced lods, footfll, wlkng hrmonc, fundmentl frequency, ek ccelerton, comfort level Introducton Nowdys the servceblty crter often govern contemorry structurl desgn Structures such s lghtweght edestrn brdges, slender floors, grndstnds nd long sn strs re rone to vbrtons cused by humn ctvtes (Žvnovć et l 005, eldmnn et l 004, Ctbs et l 004, Dougll et l 008, Kerr, Bsho 00) Lttce tower tye structures re lso remrkbly flexble, low n dmng nd lght n weght tht results n structures tht re suscetble to humn nduced vbrtons (Gle 0) Trdtonlly for such tye of structures dynmc nlyss s erformed to evlute only wnd nduced vbrtons nd effects on the structure But n res wth low sesmcty nd reltvely low wnd lods the humn nduced dynmc lods re determntve n slender lght-weght observton tower desgn n cse there s requrement to stsfy servceblty crter comfort of the structure users Humn wlkng nduces dynmc tme vryng forces whch hve comonents n vertcl, lterl nd longtudnl drectons tht re due to ccelertng nd decelertng of the mss of ts body (Gronley, Perry 984) In the cse of edestrn brdges, vbrtons re mnly nduced n trnsverse drecton nd re bsclly cused by the edestrn lterl comonent of lod Vbrtons of the edestrn brdges re reltvely well studed; consequently the desgn recommendtons hve been develoed to ensure n dequte edestrn comfort Unlke edestrn brdges, the observton towers re subjected to both edestrn lod trnsverse nd longtudnl comonent But there s lck of understndng nd ndequte desgn nformton of the buldng codes, regrdng the slender tower dynmc resonse to humn nduced lods An lgorthm of the methodology for clculton of mum resonse of structure to tycl humn nduced lods s resented n the er Ths could be useful mterl for the structurl engneers workng n the ndustry nd undertkng the desgn of ublc observton towers s ny other desgn nformton regrdng ths subject s not vlble yet The ossblty to redct the vbrton mltudes of the lttce observton towers gves the desgners confdence bout the dynmc behvour of structure n servce nd therefore llows to desgn more nterestng structures from n rchtecturl ont of vew Methodology of tower resonse clcultons The develoed lgorthm of the methodology for clculton of mum resonse of structure to tycl humn nduced lods s bsed on the exermentl nd theoretcl nvestgtons ublshed n revous ers of the uthors (Gle 0, Gle, Rdnsh 0, Gle, Rdnsh 0, Gle, Rdnsh 0b) The verfcton of the develoed methodology s erformed by comrng the theoretclly nd exermentlly obtned results of the structures mum resonse nd resented n the next secton s cse study rom the theoretcl ont of vew, ccordng to the generlly cceted desgn rocesses for low frequency structures t s convenent to consder the mum level of the resonnt resonse tht cn be nduced by erson under reeted footfll nd to lmt t to the ccetble level Bsed on ths rncle the followng rocedure cn be used to determne whether the desgned lttce observton tower fulfls the servceblty requrement: ccetble comfort level of users of the structure Ste : To determne the nut rmeters Inut rmeters needed for clculton re geometry of the structure nd structurl elements, dynmc rmeters of the observton tower (fundmentl nd nturl frequences, mode shes, tower self-weght, stffness nd dmng rto), men weght of the vstors (recommended G=746N), lmt on number of the tower 4

2 vstors t once to be verfed, number of subsequent successve stes n ( footfll concdng wth the nturl frequency of the structure) If the structure s generlly symmetrc nd hs unform stffness nd mss dstrbuton long ts heght, t s ossble to use the nlytcl method resented n (Gle, Rdnsh 0) to determne the mode shes nd corresondng nturl frequences Otherwse use of EM model s rorte Ste : To determne the most ossble desgn stutons Resonse to humn movement nduced lods should be ssessed when the fundmentl frequency of lttce observton tower s less thn Lttce structures wth hgher fundmentl frequences re usully too stff to be consderbly excted by tycl humn nduced dynmc wlkng lods Theoretcl cng frequency f when one of the fve ossble cses emerges should be found ccordng to Tble where f n s the fundmentl frequency of the structure nd DL s dynmc lod fctor - the ourer coeffcent of the relevnt wlkng hrmonc Tble Theoretcl cng frequency nd corresondng dynmc lod fctor Cse 4 5 Equton f f n f 0 5 f f n f / f / 5 Recommended DL vlue urther nlyss should be erformed for the cses when cng frequency s n the followng rnge: 0 f () Ste : Determne the equvlent number of ersons The hghest resonse of the tower cn be reched when comct grou of vstors moves long the heght of the structure (Gle, Rdnsh 0) Equvlent number of eole n the grou, whose relevnt wlkng hrmonc frequency s close to the nturl frequency of the structure, should be found ccordng to the followng equtons: 000m 005 m 0649 m 0845, () 0005 m 08 m 49, () where: - equvlent number of ersons n the grou wth ntended robblty of not beng exceeded; - equvlent number of ersons n the grou wth ntended robblty of not beng exceeded; m rel number of vstors Ste 4: Mxmum dynmc force nd ts lcton to structure Mxmum force from the selected number of tower vstors for hrmonc nd the relevnt desgn stuton should be led horzontlly t the lst str flght level nd s defned s follows: lt or long csenr H G DL sn( f t), (4) eq where: f csenr -frequency of the wlkng force hrmonc for desgn stuton under consderton, ; DL lt or long- dynmc lodng fctor of th hrmonc for lterl or longtudnl wlkng force comonent; G - men weght of the vstor, N Lod lcton durton t n second deends on the selected number of subsequent successve stes n Smultneously other four hrmoncs wth relevnt frequency ccordng to Tble should be led when fundmentl frequency of tower s below Ste 5: Determne the ek ccelerton from led dynmc lodng The ek ccelertons for the rto between relevnt wlkng hrmonc ngulr frequency nd the fundmentl ngulr frequency W/w n should be determned n the rto rnge of 08 W/w n to tke nto ccount stochstc nture of the lodng The men vlue of ek ccelerton men of rto z=w/w n rnge cn be clculted ccordng to the equton (5): men,,5 0,8 zd z, (5) where: men - men ek ccelerton, m/s ; (z) - ek ccelerton t tme t, m/s ; z=w/w - the rto between relevnt wlkng hrmonc nd the excted nturl frequency; t=n/w - tme fter n subsequent successve stes, s; w - consdered nturl frequency of the tower, rd/sec Ste 6: Lmtng the men ek ccelerton The vbrton resonse cn be consdered stsfctory when the obtned men ek ccelerton multled by the weghtng fctor W d does not exceed lmtng vlue of 0 m/s Weghtng fctor W d s defned s follows: 0 for f W d (6) for f, f where: f consdered nturl frequency of the structure A lmtng vlue of 0m/s s only the recommended vlue (mjorty of eole wll erceve moton) It cn be further modfed by fctors tht tke nto ccount the tye nd locton of the rtculr structure, the requred comfort level or other fctors 4

3 Cse study A clculton exmle s resented to serve s verfcton of the develoed methodology nd lso rctcl gude for the ek ccelerton clculton of lght-weght lttce observton tower resonse to humn nduced lods The further clculted men ek ccelerton comred to the exermentlly obtned ccelerton n cse of 7 vstors scendng the exstng steel tower of eccentrc structurl confgurton (locted n Dzntr, Ltv) (g ) Ste : To determne the nut rmeters To evlute the nturl frequences nd the crtcl mode shes of the exstng tower theoretclly, three dmensonl fnte element model creted by the commercl structurl nlyss softwre STRAP 5 hs been used The structure conssts of the brced nner core wth dmensons of 500 x 500 mm, mde from tubes wth the cross secton of 00 x 00 x 8, nd the outer core wth dmensons of 440 x 440 mm, mde from tubes wth cross secton of 40 x 40 x 5 The outer core hs no vertcl brcng, s t ws requred by the rchtecturl concet The nner nd outer cores re connected together only by steel strs At the level of 5 m there s ltform for sghtseers The totl heght of the tower s 648 m The ltform s lced offset from the centrl core fnte element model djusted ccordngly for more recse tower resonse clcultons Then clculted nturl frequences of the frst three mode shes re s follows: st mode she s couled torsonl nd flexurl wth nturl frequency of 0770; nd mode she s frst flexurl wth nturl frequency of 0790; rd mode she s frst torsonl wth nturl frequency of 57 The numercl vlues obtned from detled tower - D modellng re usully uer bonds on frequency becuse of the effects of connecton nd foundton flexblty (Mdugul 00) The lttce tower tye structure s senstve to the ccurcy of the smulton thus cre should be tken when modellng t In terms of nert, the vrous lght weght ttchments to the tower re not sgnfcnt f t does not exceed 0% of the tower weght tself (Khedr 998), therefore weght of the grou of vstors on the tower usully cn be neglected Also dmng rto s tken from the exermentl results: x=% The men weght of vstors s ssumed 746 N nd weght of the tower s clculted 70 kg/m Number of subsequent successve stes n s tken s four (recommended vlue n revous reserches of the er uthors) Ste : To determne the most ossble desgn stutons The ossble desgn stutons re nlysed n Tble by fndng cng frequency when one of the wlkng hrmoncs concdes wth the fundmentl frequency of the tower Tble Desgn stuton nlyss Cse Wlkng hrmonc st longtudnl nd longtudnl st lterl 4 rd lterl 5 5 th lterl Pcng frequency f=076 f=076/= 08 f=076 = 5 f=076 /= 05 f=076 /5= 0 Notes Smll robblty (cng too slow) Imossble (cng too slow) Should be checked Smll robblty (cng too slow) Imossble (cng too slow) g Observton tower of eccentrc structurl confgurton locted n Jurml, Ltv Due to the eccentrclly lced vstor s ltform mode she wth the lowest frequency s torsonl wth the centre of rotton outsde of the tower s geometry Mode shes re not well serted undmentl frequency of the tower tht ws used n clcultons ws determned from the dynmc testng of structure The stffness of the Anlyss revels tht most lkely cse wll relze when st hrmonc of lterl force comonent concdes wth the fundmentl frequency of structure Due to the secfc chrcter of the structure nd fundmentl frequency well below the rest of the hrmoncs lso should be led to the fnte element model smultneously The dvntge of usng fnte element clculton s tht ll relevnt wlkng hrmoncs cn be led t once 44

4 Ste : Determne the equvlent number of ersons The next ste s to fnd the equvlent number of ersons n the grou, whose wlkng frequency s close to the fundmentl frequency of structure (equtons () nd ()): 000m 005 m 0649 m 0845, m 08m Ste 4: Mxmum dynmc force nd ts lcton to structure Mxmum force of ech hrmonc from grou of 7 eole wth ntended robblty of not beng exceeded led to the lst flght of strs nd ccordng to equton (4): eq long 9 H G DL N, eq long H G DL N, 7 H G DL N, H G DL N, H G DL N Ech lod s led horzontlly n the rorte drecton nd chnges ccordng to the sne wve: sn( f ) csenr t Lod lcton durton t n seconds deends on the selected number of subsequent successve stes n: n t, (7) f or exmle, the ek vlue of tower t ccelerton should be found t tme ntervl t f the ngulr frequency rto of W lt/w n=08 s consdered: n 4 t f Ste 5: Determne the ek ccelerton from led dynmc lodng Clculted vlues for the rto between relevnt wlkng hrmonc ngulr frequency nd the fundmentl ngulr frequency W lt/w n n the rto rnge of 08 W/w n re resented n the Tble The rest of the hrmoncs were lso led to the fnte element model wth the relevnt lodng frequency ccordng to Tble to get ek ccelerton ( t) Clculted ek ccelerton vlues demonstrte tht mum ccelerton mltude sn t necessrly reched when lodng frequency of rtculr cse s mtched exctly wth the fundmentl frequency of the structure The rto rnge z covers lso other oorly serted nturl frequences of the structure As well s dfferent energy nut of the rest of wlkng hrmoncs to the totl vbrton of the structure hs been tken nto ccount Tble Pek ccelerton wth ntended robblty of not beng exceeded from st lterl wlkng force hrmonc Lodng frequency f / , Rto of ngulr frequences z lt n Pek ccelerton t tme ntervl t ( z) m/s , Tme fter n subsequent successve stes, s Then the ek ccelerton men vlue n the rto rnge of 08 W/w n wth ntended robblty of not beng exceeded cn be clculted ccordng to the equton (5): men,,5 0,8 zd z 09 m / s Rto between the equvlent number of ersons wth ntended robblty of nd not beng exceeded ccordng to ste s: H eq 8 r 6 H 5 eq Thus clculted ek ccelerton wth ntended robblty of not beng exceeded s: r m / s Ste 6: Lmtng the men ek ccelerton The vbrton resonse cn be consdered s stsfctory when the ek ccelerton multled by the weghtng fctor W d does not exceed lmtng vlue of 0m/s In ths cse the weghtng fctor W d= ccordng to (6), therefore ek vlue of ccelerton s consderbly more thn 0m/s Comrson of the results Theoretclly obtned results of observton tower to ltform vbrton mltude of ek ccelerton were comred wth the exermentlly obtned ccelerton mltude The exermentl setu, condtons nd rocedure re descrbed n the revous work of the uthors (Gle, Rdnsh 0) Comrson of the obtned results s summrzed n Tble 4 45

5 Tble 4 Comrson of theoretclly nd exermentlly obtned results Clculted ek ccelerton Exermentl ek ccelerton men 09 m / s 09m s ex / ex 00% ex 00% 0 m/ s -8% In ths cse the greement wth the exermentl result s exct f the of ntended robblty not beng exceeded s consdered It s exlcble wth the fct tht durng exerment test ersons were sked to try to ntentonlly synchronze ther cng frequency between ech other The ek vlue of ccelerton s consderbly more thn lmtng 0m/s nd eole wll erceve moton strongly, therefore most of them wll feel uncomfortble whle vstng the observton tower The ctul comlnts from vstors bout the tower s excessve vbrtons snce the tower ws oened on My of 00, confrm t Conclusons A ste by ste lgorthm hs been roosed to clculte lght-weght lttce tower dynmc resonse to tycl humn nduced tme vryng horzontl lods The develoed lgorthm s bsed on the revous fndngs bout the stochstc nture nd mgntude of the humn lodng, the effect of serte wlkng hrmoncs on the totl vbrton, unfvourble locton of lodng nd crtcl desgn stutons, tycl mode shes nd frequences of lttce observton towers, the resonse of the structure nduced by grou of eole, rmeters tht mostly nfluence the structure resonse to humn nduced lodng nd fndngs bout humn comfort crter The clculton method s bsed on the generlly cceted desgn rocesses for low frequency structures It s consdered the mum level of the resonnt resonse of the tower tht cn be nduced by erson under reeted footfll Grou lodng of the vstors s hndled through the use of the equvlent number of ersons whose one of the wlkng frequences concdes wth the nturl frequency of the structure The lgorthm ws led to fnd the ek ccelerton mltudes of ctul 6 m hgh lght-weght lttce ublc observton tower wth eccentrc structurl confgurton The theoretclly obtned ek ccelerton ws n n excellent greement wth the exermentl dt or the frst tme use of the develoed clculton lgorthm rovdes ossblty to ssess the ctul mum vbrton ccelerton level roduced by the movement of tower vstors nd comre t to the lmtng ccelerton vlue tht ensures fulflment of servceblty lmt stte requrements It llows settng lmt on the number of tower vstors tht s justfed by the clcultons or lterng the structurl rrngement durng the desgn stge f requred References Ctbs, C; Gul, M; Szk, H O, 00 Dynmc Testng nd Anlyss of ootbll Stdum In Proceedngs of the IMAC - XXVIII Dynmcs of Cvl Structures 00, lord USA, Jcksonvlle, 4, 95-0 Dougll, J W; Blkeborough, A; Cooer, P et l, 008 Dynmc erformnce requrements for ermnent grndstnds subject to crowd cton: Recommendtons for mngement, desgn nd ssessment London Insttuton of Structurl Engneers, 54 eldmnn, M; Heynemeyer, Ch; Butz, Chr et l, 004 Desgn of floor structures for humn nduced vbrtons JRC Scentfc nd Techncl Reort EUR 4084 EN, 64 Gle, L; Rdnsh, I, 0 Eccentrc lttce tower resonse to humn nduced dynmc lods In Proc of the 9th Interntonl Congress on Sound nd Vbrton 0, 9-46 Gle, L; Rdnsh, I, 0b Humn Induced Dynmc Lodng on Strs In Proceedngs of Interntonl Conference on Cvl nd Constructon (ICSCE 0), Stockholm, 0, 67, 66-6 Gle, L, 0 Anlyss of Dynmc Prmeters of Observton Towers n Ltv In Proceedngs of the 9th Interntonl Scentfc nd Prctcl Conference: Envronment, Technology, Resources, Ltv, Rezekne, 0- June, Gle, L; Rdnsh, I, 0 Lttce tower dynmc erformnce under humn nduced dynmc lods In Proceedngs of the th Interntonl Conference: RASD 0: Recent Advnces n Structurl Dynmcs, Itly, Pz, - July, 0, -5 Gronley, J K; Perry, J, 984 Gt nlyss technques Physcl Thery, 6, 8-88 Kerr, S C; Bsho, N W M, 00 Humn nduced lodng on flexble strcses Engneerng Structures,, 7-45 htt://dxdoorg/006/s04-096(00)0000- Khedr, M A, 998 Sesmc Anlyss of Lttce Towers Ph D Thess Dertment of Cvl Engneerng nd Aled Mechncs McGll Unversty Montrel, Cnd, 4 Mdugul, M K S, 00 Dynmc Resonse of Lttce Towers nd Guyed Msts Amercn Socety of Structurl Engneers, US 57 Žvnovć, S; Pvc, A; Reynolds, P, 005 Vbrton servceblty of footbrdges under humn-nduced exctton: A lterture revew Journl of Sound nd Vbrton, 79(-), -74 htt://dxdoorg/006/jjsv Acknowledgements Ths work hs been suorted by the Euroen Socl und wthn the roject Suort for the mlementton of doctorl studes t Rg Techncl Unversty 46