Karakteristik dinamis struktur domes berelemen membran

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1 Krterst dnms strtr domes berelemen membrn (DYNAMICS CHARACTERISTIC of THE STRUCTURAL DOMES USING SHELL ELEMENT ) SKRIPSI Dn nt Memenh Sebgn Persrtn Memperoleh Gelr Srn Ten Dern Oleh : Dev Sr Prnwt NIM. I.6 JURUSAN TEKNIK SIPIL FAKULTAS TEKNIK UNIVERSITAS SEBELAS MARET SURAKARTA 5 KARAKTERISTIK DINAMIS STRUKTUR DOMES

2 BERELEMEN MEMBRAN (DYNAMICS CHARACTERISTIC of THE STRUCTURAL DOMES USING SHELL ELEMENT ) Dern Oleh : DEVY SARI PURNIAWATI NIM. I 6 SKRIPSI Telh dset nt dperthnn d hdpn Tm Peng Penddrn Flts Ten Unversts Sebels Mret PEMBIMBING I Dset, PEMBIMBING II Ir. AGUS SUPRIYADI, MT SENOT SANGADJI, ST, MT NIP NIP JURUSAN TEKNIK SIPIL FAKULTAS TEKNIK UNIVERSITAS SEBELAS MARET SURAKARTA 5 ALGORITMA KENDALI AKTIF DENGAN KONTROL PID

3 PADA STRUKTUR SDOF (ACTIVE CONTROL ALGORITHM WITH PID CONTROLLER ON SDOF STRUCTURE) SKRIPSI Dern Oleh : DEVY SARI PURNIAWATI NIM. I 6 Dperthnn ddepn Tm Peng Penddrn Flts Ten Unversts Sebels Mret Srrt dn dterm gn memenh slh st persrtn nt mendptn gelr Srn Ten. Pd hr : Sels Tnggl : 5 Jnr 5 Tm Peng Penddrn : Ket : Ir. AGUS SUPRIYADI, MT :.. NIP Anggot : SENOT SANGADJI, ST,MT :.. NIP Anggot : STEFANUS A K, ST, MSc, PhD :.. NIP Anggot : EDY PURWANTO, ST, MT :.. NIP. 6 Mengeth, Dshn oleh :.n Den, Ket Jrsn Ten Spl, Ir. Prnto, MS Ir. Ags Sprd, MT NIP NIP MOTTO

4 Kengnn mns dlh sepert on-on ecl ng dbwn dlm sebh ntng. Semn bn ng dmln n semn membertnn. Hdp dlh rntngn ng hrs dhdp, perngn ng hrs dmenngn, rhs ng hrs dgl, dn ngerh ng hrs dpergnn. Hl ecl membent esemprnn, tp esemprnn bnlh hl ecl. If lfe s rver nd or hert s bot, the wter s flowng sprt eep o flot. Alws welcome thw new mornng wth new sprt, sme on or fce, love n or hert nd good thoghts n or mnd. Forget the mste tht o hve mde, bt don t forget the lesson o lerned. PERSEMBAHAN

5 UNTUK PAPA, MAMA, KEDUA KAKAK, DAN ADIKKU DI YOGYAKARTA ABSTRAK

6 Dev Sr Prnwt, 5, Krterst Dnms Strtr Domes Berelemen Membrn. Jrsn Ten Spl Flts Ten Unversts Sebels Mret Srrt. Strtr domes dlh bngnn lterntf ng thn terhdp gelombng r mpn tenn ngn ng cp besr. Domes g thn terhdp getrn gemp bm dn bh ebrn. B pembtn domes reltf mrh ren td mem blo dn olom. Anlss n bertn nt mengeth bgmn pengrh bent elemen (shell) pd strtr monolthc dome dr beton bertlng dn berp besrn perode getr dn freens lm domes pd onds nforced vbrton. Hsl nlss mennn bhw mods getr dome berelemen shell perseg berbent smetrs dn dome berelemen shell belh etpt terdeforms cp sgnfn d pnc menebbn ed domes tersebt td meml tngt estbln ng cp. Mods getr dome berelemen shell segtg berbent smetrs, hl n mennn bhw dome berelemen shell segtg cp stbl. Besrn perode getr dn freens lm pd fndmentl mode (mods pertm) onds nforced vbrton shell perseg dlh.754 det dn.59 Hz, segtg dlh.758 det dn.59 Hz, belh etpt dlh.747 det dn.45 Hz. KATA PENGANTAR

7 P dn Sr penls pntn e hdrt Thn Yng Mh es, sehngg penls dpt menelesn peneltn dengn dl Krterst Dnms Strtr Domes Berelemen Membrn. Peneltn n bertn nt melengp persrtn memperoleh gelr Srn Ten pd Flts Ten, Jrsn Ten Spl, Unversts Sebels Mret Srrt. Penls ngn mengcpn term sh secr hss epd Bp Ir.Ags Sprd, MT dn Bp Senot Sngd, ST, MT sel pembmbng srps penls sehngg penls dpt menelesn peneltn n dengn b. Semog peneltn n dpt membern mnft bg sem pembc ng bdmn. Srrt, Jnr 5 Penls, DAFTAR ISI

8 HALAMAN JUDUL HALAMAN PERSETUJUAN PEMBIMBING HALAMAN PENGESAHAN HALAMAN MOTTO v HALAMAN PERSEMBAHAN v ABSTRAK v KATA PENGANTAR v UCAPAN TERIMA KASIH v DAFTAR ISI DAFTAR NOTASI DAN SIMBOL DAFTAR TABEL v DAFTAR GAMBAR v DAFTAR LAMPIRAN v BAB I PENDAHULUAN. Ltr Belng. Identfs Mslh. Rmsn Mslh.4 Btsn Mslh.5 Mnft dn Tn 4 BAB II LANDASAN TEORI 5. Tnn Pst 5. Dsr Pemrn 6. Persmn Dfferensl Gern Strtr MDOF 7.4 Sols Mods Getr dn Freens Alm 9.5 Model Elemen Hngg.5. Idelss Mtrs Ken Strtr Segtg 5.5. Idelss Mtrs Ken Strtr Perseg.5. Proses pembentn Persmn Globl Strtr Perhtngn Tegngn Elemen 5 BAB III METODOLOGI PENELITIAN 5

9 . Urn Umm 5. Anlss Model 5. Desrps Domes 5.. Permodeln Strtr 6.4 Metode Anlss 6.5 Kerng Anlss 6.6 Thp Anlss 8 BAB IV ANALISA DAN PEMBAHASAN 4. Anlss Strtr Dome 4.. Strtr Dome Elemen Shell Perseg 4.. Strtr Dome Elemen Shell Segtg Strtr Dome Elemen Shell Belh Ketpt 8 4. Pembhsn 4 BAB V KESIMPULAN DAN SARAN Kesmpln Srn 44 DAFTAR PUSTAKA v LAMPIRAN v DAFTAR TABEL

10 Tbel 4. Tbel Prtsps Mode Tbel 4. Dt Freens Alm dn Perode Getr Tbel 4. Jont Dsplcement Strtr Tbel 4.4 G Dlm dn Tegngn Elemen Shell 5 Tbel 4.5 Dt Freens Alm dn Perode Getr Strtr 6 Tbel 4.6 Jont Dsplcement Strtr 6 Tbel 4.7 G Dlm dn Tegngn Elemen Shell 8 Tbel 4.8 Dt Freens Alm dn Perode Getr Strtr 4 Tbel 4.9 Jont Dsplcement Strtr 4 Tbel 4. G Dlm dn Tegngn Elemen Shell 4 Tbel 4. Perbndngn Nl Jont Dsplcement Msmm 4 Tbel 4. Perbndngn Nl Perode Getr dn Freens Alm 4 Tbel 4. Perbndngn G Dlm dn Tegngn Dlm Shell 4 DAFTAR GAMBAR

11 Gmbr. Model Dome ng Bervrs Gmbr. Desn Elemen Strtrl Dome Gmbr. () Sstem dengn Tg Dert Kebebsn Teredm (b) Free-Bod Dgrm 7 Gmbr. Elemen Segtg Dlm Tg Dmens 4 Gmbr. Elemen Segtg Pd Koordnt Globl 5 Gmbr.4 Elemen Segtg Pd Koordnt Lol 6 Gmbr.5 Elemen Shell Rectnglr dengn Empt Jont Gmbr.6 Elemen Perseg dengn Koordnt Globl Gmbr. Dgrm Ilstrs Globl Peneltn 7 Gmbr. Dgrm Alr Proses Perhtngn Secr Umm 8 Gmbr. Dgrm Alr Perhtngn dengn Kompter 9 Gmbr 4. Crenosphere Stdon d Amer Sert Tngg Msmm dome mencp 5ft dengn dmeter Msmm ft Gmbr 4. Dome dengn Elemen Shell Perseg Gmbr 4. Mods Getr Pertm dengn Perode Getr (T,754 det) Gmbr 4.4 Dstrbs G Shell Msmm pd Tp Tngt Mode Gmbr 4.5 Dstrbs Momen Shell Msmm pd Tp Tngt Mode Gmbr 4.6 Dstrbs G Shell Msmm pd Tp Tngt Mode Gmbr 4.7 Dstrbs Tegngn Shell Msmm pd Tp Tngt Mode Gmbr 4.8 Dome Kc dengn Elemen Shell Segtg 4 Gmbr 4.9 Dome dengn Elemen Shell Segtg 4 Gmbr 4. Mods Getr Pertm dengn Perode Getr (T,758 det) 5 Gmbr 4. Dstrbs G Shell Msmm

12 pd Tp Tngt Mode 5 Gmbr 4. Dstrbs Momen Shell Msmm Pd Tp Tngt Mode 5 Gmbr 4. Dstrbs G Geser Shell Msmm Pd Tp Tngt Mode 6 Gmbr 4.4 Dstrbs Tegngn Shell Msmm Pd Tp Tngt Mode 7 Gmbr 4.5 Dome dengn Elemen Shell Belh Ketpt 8 Gmbr 4.6 Mods Getr Pertm dengn Perode Getr (T,748 det) 8 Gmbr 4.7 Dstrbs G Shell Msmm Pd Tp Tngt Mode 9 Gmbr 4.8 Dstrbs Momen Shell Msmm Pd Tp Tngt Mode 9 Gmbr 4.9 Dstrbs G Geser Msmm Pd Tp Tngt Mode 4 Gmbr 4. Dstrbs Tegngn Shell Msmm Pd Tp Tngt Mode 4 Gmbr 4. Perbndngn Pol Getrn Strtr Domes 4 Gmbr 4. Domes dengn Elemen Shell Belh Ketpt Tmp dr ts 4 DAFTAR LAMPIRAN

13 Lmprn A Lmprn B Hsl Anlss Model A- Model Shell Elemen Perseg A- Model Shell Elemen Segtg A- Model Shell Elemen Belh Ketpt Srt-srt Srps BAB I

14 PENDAHULUAN. Ltr Belng Dome merpn st lterntf bngnn strtrl ng meml bn enggln. Model strtr dome ng sphercl t ellptcl membtn sngt erodnms dlm menhn bebn ngn, torndo, mpn hrrcne pbl dbndngn dengn strtr bs ng cenderng mem bent flt/dtr. Sebh dome mmp menhn ngn hngg bereceptn 5 mph bhn g hrrcne dengn eceptn mph. [] Strtr dome bn dgnn sebg strtr rmh tnggl d pntpnt Amer Sert ren meml ethnn terhdp gelombng r mpn tenn ngn ng cp besr msln sepert bngnn dome d Porth Arthr, Tes. Kenggln ln dr dome dlh ethnnn terhdp getrn gemp bm. Hl n dsebbn oleh ren tn ntr strtr dome dengn ponds ng dbt rgd dn monolth sehngg td terdpt esentrsts ng bs menebbn pntr pd strtr tm. Gmbr.. Model Dome ng Bervrs Strtr dome g sngt preventf terhdp bh ebrn. Monolthc dome ng terbt dr beton tent s thn terhdp pns p bl dbndngn dengn strtr bs ng msh mem elemen dn b.

15 Reso bngnn rs oleh serngg, ts, mpn cng dpt dhndr ren strtr dome terbt dr beton dn monolthc. B pembtnn pn lebh mrh, hl n bs dlht dr desn dome ng td mem elemen tp dn plfond ng dng b onstrsn mencp.. rph tp 94.4 m. Gmbr.. Desn Elemen Strtrl Dome Desn dome ng b dn optml hrs mmp member ethnn strtrl terhdp bebn ngn dn bebn gemp bm. Gemp bm, tnh, dn ponds strtr bsn bergetr pd perode. hngg. det, sedngn ngn pd mmn berhembs dengn perode getr sebesr det t dengn freens lm.5 Hz. Sehngg dperln desn elemen shell dr dome ng tept b berbent trnglr, rectnglr, mpn dmond nt mencp onds getrn strtr ng berd h dr resonns getrn gemp bm mpn bebn ngn.. Identfs Mslh Dome dpt dbt dr bermcm-mcm elemen ml dr beton, beton bertlng, lmnm (logm), bt, bt bt (msonr), polrethne, dn sebgn. Msng-msng bhn meml ethnn dn modls elststs ng berbed sehngg dlm desn dome perl dperhtn pemlhn elemen ng tept sehngg bs dcp desn ng optml dr seg drblts, ethnn strtr, dn eonoms. Model shell element dr strtr dome g perl d nt mendptn desn ng tert, shell element dengn re ng ls dn bent

16 ng h dr segtg n memperlemh strtr ren membern respon dnms dn tegngn ners ng besr st strtr dgncng oleh gemp bm t terten oleh ngn. Berdsrn ltr belng ng telh demn sebelmn m dtemn beberp mslh ng dpt d dntrn dlh tentng pengrh bent t model shell element pd strtr Plne Stress terhdp respon dnms strtr ng berp respon perpndhn (ont dsplcement), freens lm, tegngn membrn dn mods getr.. Rmsn Mslh Bgmn pengrh bent elemen (shell) pd strtr monolthc dome dr beton bertlng : trnglr, rectnglr, t dmond terhdp rterst dnms (freens lm, perode getr, mods getr, dn dsplcement)..4 Btsn Mslh Pd penlsn tgs hr n nlss strtr dbts secr elsts, strtr dome ng dnlss hn smp dengn edn bhw strtr belm menglm ret. Dlm onds elsts beton dpt dnggp sebg bhn ng homogen dn sotrops. Lngp permslhn penlsn srps n dlh sebg bert :. Bngnn sebg bldng hose dtep pnt bertngt d terbt dr beton bertlng. b. Jens dome ng dtn dlh monolthc dengn model hemsphercl. c. Strtr ddsrtssn e dlm bent d dmens, t plne stress d. Dert ebebsn strtr berp MDOF. e. Rso pnng ss-ss elemen shell rectnglr :. f. Rso pnng ss-ss elemen shell trnglr :. g. Rso pnng ss-ss elemen shell dmond :. h. Respon dnms ng dtn dlh sebg bert :. Res perpndhn (ont dsplcement)

17 . Freens lm. Perode getr strtr 4. Tegngn membrn (l, bendng tensle, sher).5 Mnft dn Tn Tn tm dr penlsn srps n dlh nt menwb rmsn mslh ng d, t bgmn mencptn model desn shell element ng terb nt mencptn strtr domes ng meml etn msml terhdp gemp bm dn ngn. Sedngn mnft ng dpt dmbl dlh sebg bert :. Mnft Teorts Unt ddn dsr pengethn d bdng perencnn desn shell element strtr domes hemsphercl ng thn terhdp ngn dn gemp bm. b. Mnft Prts Unt lebh menebrlsn pemn domes hemsphercl berelemen membrn sebg slh st lterntf dlm desn strtr d Indones. BAB II LANDASAN TEORI

18 . Tnn Pst Bebn dnm dlh setp bebn ng besrn, rh t possn berbh menrt wt. Demn pl respon strtr terhdp bebn dnm, t lendtn dn tegngn ng dhsln g menglm perbhn wt, t bersft dnm. (R.W. Clogh & Penzen, 988). Kemdn R.W. Clogh & Penzen (988) g mengtn bhw mslh dnm strtr dlh sft perbhn menrt wt sehngg mslh dnm td mempn penelesn tnggl, sepert pd mslh stts. Anlssn hrs menentn penelesn bertrt-trt ses dengn sem wt ng pentng dlm rwt respon. Jd mslh dnms els lebh omples dn bn ment wt drpd mslh stts. Anlss dnm n dgnn pd strtr-strtr hss t : gedng ng strtrn td bertrn, gedng dengn lonctn bdng m ng besr, gedng dengn tngt en ng td mert, gedng ng tnggn lebh dr 4 m, gedng ng bent, rn, dn penggnnn td mm. (Pedomn Perencnn Kethnn Gemp nt Rmh dn Gedng, 987). Anl K Chopr (995) mentn bhw slh st pls pentng dr teor dnm strtr dlm res gemp dlh nlss respon dr strtr terhdp gern tnh ng dbtn oleh gemp bm. Pd nlss dnm pertm-tm hrslh menentn freens lm dn mods getr strtr sebg prmeter dsr. Metode ng denl nt mslh n dlh penelesn nl egen dn vetor egen dr strtr. (Senot Sngd, 4). Modl Anlss Method dlh metode ng mem stndr mode shpes pd strtr MDOF dengn onds nforced vbrton. Pd onds tersebt n dperoleh st pol/rgm gongn strtr MDOF ng denl secr mm dengn stndr mode shpes, ren respon strtr merpn fngs lngsng ts mode shpes strtr ng bersngtn. (Wdodo. ).

19 Clogh & Penzen (99) mengtn bhw metode n g mempn elemhn t terlet pd penelesn egenproblem nt mencr nl/oordnt mode shpes. Kren proses trnforms dr copled mend ncopled, persmn dfferensl mend ncopled m td dperln mtrs mss, mtr redmn, dn mtrs en. Persmn egenproblem merpn rterst strtr ng berp hbngn ntr mss dn en strtr. Hbngn tersebt n menentn nl freens sdt dn perode getr dr strtr. (Wdodo, ).. Dsr Pemrn Cngng (domes) dlh bent strtrl tg dmensonl ng dn tps ng mempn permn lengng. Permn cngng dpt mempn sembrng bent. Bent ng mm dlh permn ng bersl dr rv ng dptr terhdp st smb (msln permn bol, ellps, erct dn prbol). Bebn bebn ng beer pd permn domes dtersn e tnh dengn menmbln tegngn geser, tr, dn ten pd rh dlm bdng (nplne) permn tersebt. Tpsn permn domes menebbn td dn thnn momen ng berrt. Domes terssn ts elemen elemen shell ng tertt rp membent bh. Elemen elemen shell n sngt tps dengn bentng reltf besr tetp sngt t nt menhn bebn ngn dn gemp bm. Berdsrn defns tersebt, dpt dsmpln bhw dlm strtr domes elemen shell berpern sebg penhn bebn, b bebn mt mpn bebn hdp ng beer pd strtr.konds tersebt menebbn ntegrts domes sngt bergntng pd elemen shell, b bent, rn mpn eteblnn. Pemlhn bent, rn mpn etebln shell ng tept hrs mendn strtr meml en ng cp sehngg meml freens lm tertent ng h dr freens lm ngn dn gemp bm.

20 . Persmn Dfferensl Gern Strtr MDOF Secr mm strtr bngnn gedng tdlh sell dpt dntn ddlm st sstem ng mempn dert ebebsn tnggl (SDOF). Strtr sepert domes dn seensn ng mempn bent fs ontn, m pd strtr strtr sepert t n mempn dert ebebsn t terhngg t dert ebebsn bn (mlt degree of freedom). Dert ebebsn dlh dert ndependens ng dperln nt mentn poss st sstem pd st st, d sstem ebebsn dert bn dlh st sstem ng pn beberp tt ng dpt berpndh secr berbed. Anggpn sepert prnsp sher bldng berl pd strtr dengn dert ebebsn bn (MDOF). Unt memperoleh persmn dfferensl tersebt, m tetp dp prnsp esembngn dnm (dnmc eqlbrm) pd st mss ng dtn. Unt memperoleh persmn tersebt m dmbl model strtr MDOF sepert Gmbr. P (t) P (t) c c c () P (t) (b) Gmbr. () Sstem dengn tg derd ebebsn teredm; (b) Free-Bod Dgrm dmn : m mss strtr c oefssen redmn strtr eceptn reltf en tngt nodl dsplcement p(t) bebn lr st t Berdsrn pd esetmbngn dnm pd free bod dgrm gmbr m n dperoleh :

21 (.) (.) m + c ( ) c ( ) p (t) m ( ) + c( ) ( ) c( ) p (t) m + ( ) + c( ) p (t) (.) Pd persmn tersebt dts tmp bhw esembngn dnm st mss ng dtn ternt dpengrh oleh en, redmn dn smpngn mss sebelm dn sesdhn. Persmn dengn sft sft sepert t mmn dsebt copled eqton, ren persmn persmn tersebt n tergntng st sm dengn ng lnn. Penelesn persmn tersebt hrs dln secr smltn, rtn dengn melbtn selrh persmn ng d. Selntn mensn persmn persmn dts menrt prmeter ng sm (perceptn, eceptn, dn smpngn) sehngg n dperoleh : (.4) (.5) (.6) m + (c + c ) c + ( + ) p(t) m c + (c + c) c + ( + ) p(t) m c + c + p(t) Persmn persmn d ts dpt dtls dlm bent mtrs sebg bert :

22 m m m c c c c c c c c c (t) p (t) p (t) p (.7) Persmn d ts dpt dtls dlm mtrs ng lebh omp : p(t) c m + + (.8) Apbl strtr dengn dert ebebsn bn tersebt den bebn gemp bm m persmn (.8) mend : {} + + g m c m (.9) dmn {}dlh vetor ng st dn g dlh perceptn tnh..4 Sols Mods Getr dn Freens Alm Setp bend meml bent mods dn freens tertent ng dsebt mods getr dn freens lm. Freens meml stn Hertz (Hz), serngl dntn dlm rdn tp stn wt dn dsmboln dengn hrf ltn ω. Freens dpt ddefnsn sebg bnn sls ng dln selm st det. Invers dr freens dlh perode, t wt ng dbthn st bend nt menelesn st sls, dengn stn det (second). Setp bend meml freens lm dengn mlh ng td terbts, tetp ng dperln dlm nlss serngl hnlh ng terendh (fndmentl freqenc). Sedngn mods t mode dlh bent deforms strtr et berger dlm st perode tertent. Mods sngt pentng nt deth ren et mods mncl, berrt d bn energ ng mem st

23 strtr dn membtn bergetr. J energ ng memsn terll bn sehngg melebh psts strtr, m strtr n menglm ernthn ren mpltdo getrnn n mend t terhngg serng dengn wt dn dssl dengn hlngn ntegrts strtr. Angn topn memshn st rmh dr tpn t et ngn menggnn tenn dn ml mengngt tp. Kren strtr domes td meml tp, m ngn td dpt memshn strtr domes. Freens lm ngn ng bersr ntr.5 Hz terlet dlr ngn freens gemp ng bersr ntr.8-5 Hz. Oleh ren t sngtlh pentng nt mengeth pd freens berp sebh domes n bergetr, sehngg strtr domes dpt dbt gr meml mods pertm dengn deforms tertent dn freens tertent ng dnggp lebh b bg en dn ntegrts tertent. Kren sstem berger dengn getrn bebs, dpt dperoleh dengn menghlngn mtrs redmn dn vetor bebn ng denn dr persmn (.8) sehngg dperoleh : m + (.) dmn dlh vetor nol. Mslh nlss getrn terdr dr penentn onds ddlm persmn dts n memngnn terd ger. Unt st sstem MDOF, dsmsn getrn bebs dlh hrmons sederhn, ng dntn sebg : (.) dlm perntn φ n (t) φ n sn(ω + θ) menggmbrn bent sstem (ng td berbh menrt wt; hn mpltdo ng berbh) dn θ dlh sdt fse. Perbhn perpndhn menrt wt dntn dlm fngs hrmons sederhn sn (ωt+θ). Bl dmbl trnn ed dr persmn dts, perceptn pd getrn bebs dlh :

24 ω φ sn (ωt+θ) - ω n (.) dengn mensbsttsn persmn (.) dn (.) e persmn (.) ddptn : ω mφ nsn (ωt+θ)+ φ n sn (ωt+θ) (.) ren bent sns sembrng dn dpt dhlngn persmn dts dpt dtls : (- ω m)φ n (.4) persmn tersebt sell mempn penelesn t berrt (trvl solton) φ n, ng td bergn ren dengn penelesn n berrt td d getrn. Persmn dts mempn penelesn ng berrt (nontrvl solton) : ω m (.5) persmn (.5) dsebt persmn rterst, persmn freens, t egenproblem. Dengn memperls determnn n dperoleh persmn lbr berdert N, dlm prmeter ω nt sstem ng mempn N dert ebebsn. Ke-N r-r persmn n ( ω,ω,ω,...ω N ) mennn freens ntrl dr e-n getrn ng mngn terd pd sstem. Ar dr persmn rterst denl sebg nl rterst, nl norml t nl egen. J freens ntrl getrn ω N dselesn nt mendptn vetor sdh deth, persmn (.4) dpt φ n. Nl egen t nl rterst td membern mpltdo ng pst pd vetor φ n, tetp nl tersebt hn n sebndng ntr ng st dengn ng ln. Sehngg n dperoleh

25 N vetor φ n ng denl sebg pol norml (norml modes) t bent pol ntrl (ntrl mode shpes), t vetor egen (egenvectors)..5 Model Elemen Hngg (Plne Stress) Relts perl strtr ng rmt pd domes dn pd sem strtr pd mmn menntt proses nlss ng rmt dn hmpr td dpt dln, ren pd entnn, strtr sepert n meml mss ng terdstrbs secr ontn pd eselrhn bgnn. Kedn tersebt membt strtr meml dert ebebsn (Degree of Freedom) t DOF ng td terhngg, sehngg mlh omponen perpndhn ng hrs dpertmbngn mend td terhngg pl. Agr perl domes n dpt dnlss dengn lebh mdh nmn tetp mendet perl ng sebenrn, m omponen perpndhn hrs dntn dlm bent mlh terhngg dr oordnt ng sdh ddsretssn. Unt mendsretssn oordnt perpndhn ng n dnlss, eselrhn sstem hrs dbg-bg mend semlh bgn ng tept t elemen-elemen ng perln dengn mdh telh dmengert dn telh dpt dformlsn dlm bent pls onsep mtemts bs dn emdn mert embl sstem strtr sl dr elemen elemen tersebt nt mempelr perln. Pd nlss tgs hr n, model ddsretssn e dlm Plne Stress. Plne Stress dlh edn dmn tegngn norml dn tegngn geser ng teg lrs bdng dsmsn nol (Drl L Logn,986). Jens elemen hngg ng dp nt mendsretssn elemen elemen dlm mengdelssn domes ng n dnlss pd srps n dlh elemen shell, dmn elemen shell ng n dnlss d mcm bent t segtg (trnglr), perseg (rectnglr), dn belh etpt (dmond). Hbngn tegngn dn regngn ng ddsr ts hm Hooe dpt dtls dlm bent sebg bert :

26 (.6) ( ε ) [ C](. σ) ( σ) [ C].( ε) [ D ](. ε) (.7) [ C] dlh opertor mtrs ng menghbngn vetor tegngn ( σ) vetor regngn ( ε ). Sedngn mtrs [ D] [ C] dn sebg mtrs onstttf tegngn (mtrs en mterl), dlh opertor mtrs ng menghbngn vetor tegngn ( σ) dn vetor regngn ( ε ). Mtrs [ ] mtrs [ D] edn merpn mtrs smetrs. C dn Mterl ontn ng dsmsn bersft sotrop, sehngg hbngn ntr tegngn dn regngn dpt dtrnn, b t tegngn bdng mpn regngn bdng. Tegngn bdng ddsrn ts sms bhw : σ γ ε z z z τ γ z z τ z n ddptn omponen tegngn dr regngn: (.8) (.9) σ σ γ E υ υe υ τ G ε ε υe + υ E + υ ε ε (.) Pd persmn (.), G dlh onstnt elststs ln ng dsebt modls geser. Hbngn G terhdp modls elststs (E) dntn :

27 E G ( + υ) (.) persmn (.) dsbstrsn e persmn (.) dperoleh : ( + υ) γ τ E (.) υ dlh ng posson (Posson Rto). Persmn (.8), (.9), dn (.) dsbsttsn e persmn (.7) ddpt hbngn ntr tegngn dn regngn bdng sebg bert : (.) dengn : σ σ τ υ E υ υ υ υ ε ε υ γ υ E υ υ D υ υ υ (.4) [ D] dlh mtrs en mterl tegngn bdng nt Plne Stress..5.. Idelss Mtrs Ken Strtr Segtg

28 Gmbr (.) Elemen Segtg dlm Dmens Sft sft mterl (mterl propertes) ng dperln dlm nlss dengn elemen shell melpt :. Modls elststs (modls of elstct) b. Modls geser (sher nodls) c. Posson s rto, etg mterl propertes dts dgnn nt menghtng en lentr dn geser trnsversl. d. Koefsen espns therml (coeffcent of therml epnson), nt menghtng espns membrn dn regngn lentr therml. e. Mss ens (mss denst), nt menghtng mss elemen. f. Bert ens (weght denst), nt menghtng bert sendr dn bebn grvts.

29 Y X Gmbr (.) Elemen Segtg pd Koordnt Globl Unt mengembngn [ K] ddsrn pd oordnt locl, v v v Gmbr (.4) Elemen Segtg pd Koordnt Lol (,) : omponen dsplcement rh smb v v (,) : omponen dsplcement rh smb Unt persoln n The Assmed Dsplcement Feld dmbl sebg polnoml lner dlm dn nt mpn v : + + (.5)

30 v (.6) selntn prmeter non dmensonl 6...,, tersebt n dntn dlm fngs nodl degrees of freedom d tt nodl,, v v v persmn tersebt dpt dtls dlm bent mtrs : v v v (.7) bl dnvers persmn (.7) mend : v v v. H H A (.8) dmn A : Ls elemen segtg

31 : ½ ( )( ),, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) H (.9) gr lebh smple tt nodl d elemen segtg tersebt bermpt dengn tt wl oordnt lol - sehngg : A ½ ( )( ) ½ H (.) persmn (.5) dn (.6) dpt dtls dlm bent mtrs : v (.) persmn (.) dsbsttsn e persmn (.8) dperoleh : v v v H H A v

32 [ ] { } 6 6 U. N v v v N N N N N N A (.) dengn : N shpe fncton nodl dsplcement vector ( ) N - ( ) + N N (.) menggnn Strn Dsplcement Eqtons dpt dtls sebg bert : [ ] {} 6 6. N. γ ε ε (.4) persmn (.) dsbsttsn e persmn (.4) ddpt : { } [ ]{ } B. ε (.5) sehngg ddpt mtrs en locl :

33 [ ] [ ] [ ][ ]dv B D.. B K v T (.6) dmn nt Plne Stress mtrs en mterl tegngn bdng dpt dlht pd persmn (.4): υ υ υ υ υ υ E D proses ntegrs persmn dts cp pnng, sehngg td dtls secr lengp dsn. Hsl stffness mtr elemen segtg sebg bert : [ ] [ ] [ ] [ ] B D B A t K T (.7) dmn : K mtr en elemen t tebl strtr A ls penmpng elemen D mtrs onstttf (mterl) elemen [ ] β γ β γ β γ γ γ γ β β β A B (.8) [ ] T B Trnspose mtrs [ ] B γ β γ β γ β.5.. Idelss Mtrs Ken Strtr Perseg Elemen Shell (gbngn dr plte dn membrne) dgnn nt memodeln st omponen strtr ng meml etebln lebh ecl dbndngn dmens pnng dn lebrn sepert pd pelt lnt rmh pd

34 mmn. Dsmsn bdng potongn pelt melntng tetp dn td menglm deforms et pelt menglm tegngn. Shell rectnglr dbent oleh empt ont,,, dn 4 dengn spect rto (perbndngn dmens pnng dn lebr) mendet st dn meml enm dert ebebsn tf pd setp ont ng terhbng. Gmbr (.5 ) Elemen Shell Rectnglr dengn Empt Jon Y h g e f X Gmbr (.6) Elemen Perseg pd Koordnt globl nt mengembngn [ K] ddsrn pd oordnt lol,.

35 ,v v h h b h b v g g h g, v e h e e f v f f Gmbr (.7) Elemen perseg pd oordnt lol (,) omponen dsplcement rh smb v (,) omponen dsplcement rh smb (, ) v(, ) (.9) persmn tersebt dpt dtls mend : (, ) + 4bh (.4) [(b )(h ) + (b + ))h ) + (b + )(h + ) + (b )(h ) ] 4 v (, ) + 4bh ( [(b )(h )v + (b + ))h )v + (b + )(h + )v + (b )(h ) ].4) emdn dperoleh nl N Shpe Fncton : ( b )( h ) ( b + )( h ) N N 4bh 4bh v 4 ( b + )( h + ) ( b )( h + ) N N 4 4bh ng dpt dtls edlm bent mtrs : 4bh

36 h h g g f f e e 4 4 v v v v N N N N N N N N v (.4) [ ] { } 8 8. N dengn menggnn dsplcement regngn, dpt dtls sebg bert : [ ] {} 8 8. N. γ ε ε (.4) persmn (.4) dsbsttsn e persmn (.4) mend : { } [ ]{ } B. ε (.44) sehngg ddpt mtrs en lol : [ ] [ ] [ ][ ] h h b b T d d B.t D B K (.45) dmn nt Plne Stress mtrs en mterl tegngn bdng dpt dlht pd persmn (.4): υ υ υ υ υ υ E D

37 proses ntegrs persmn dts cp pnng, sehngg td dtls secr lengp dsn. Hsl stffness mtr elemen segtg sebg bert : T [ K] t A [ B] [ D] [ B] (.46) dmn : K mtr en elemen t tebl strtr A ls penmpng elemen D mtrs onstttf (mterl) elemen (h ) (h ) (h + ) (h + ) B (b ) (b + ) (b + ) (b ) 4bh (b ) (h ) (b + ) (h ) (b + ) (h + ) (b ) (h + ).(.4 7).5.. Proses Pembentn Persmn Globl Strtr Setelh mendptn nl [ K] dr tp-tp elemen, nl [ K] tersebt dgbng nt mendptn nl dsplcement. Penggbngn n dsebt ssemblng pd mtrs en elemen, menggnn metode ng sngt poplr t Drect stffness Method. Persmn globl strtr dlh sebg bert : (.48) { f} [ K].{ d} dmn : { f } [ K] s { d } s globl nodl forces mtrs en strtr globl dsplcement Sebelm srt bts dterpn determnn [ K] s sehngg td dpt d nversn. Tetp setelh srt bts dterpn strtr n bersft mmoble (td berpndh), determnn [ K] s mend sehngg sols bs dln dn ddptn nl dsplcement.

38 Setelh srt bts dterpn persmn (.46) n menghsln set persmn smltn : K K M K n K K M K n L L M L K M K n n mn d d. M d n f f M f n (.49) dengn metode persmn lner progrm SAP dpt menghsln nl dsplcement.{ d} merpn nnown degrees of freedom ng bs dsebt Prmr Unnowns ng merpn prmeter pertm l terhtng dlm metode en..5.4 Perhtngn Tegngn Elemen Unt strtr Plne Stress tegngn msng-msng elemen dlh sebg bert : (.5) { σ} [ D ] [ B] { d} dmn : { σ} Tegngn bdng tp elemen [ D] [ B] mtrs B { d} dsplcement mtrs en mterl

39 BAB III METODOLOGI PENELITIAN. Urn Umm Metodolog dlh cr t prosedr nt menwb rmsn mslh ng telh demn, t nt mengeth pengrh bent t model shell element pd strtr Plne Stress terhdp respon dnms strtr ng berp respon perpndhn (ont dsplcement), freens lm, tegngn membrn dn mods getr.. Anlss Model Permodeln st strtr dlh mengdelssnn sebg st sstem ng terssn dr elemen elemen ng l, ng msh membern eteptn ng cp et perln dnlss dn dengn mlh perhtngn ng ms l. (Wlter, 988). Desrps Domes Strtr dome ng dplh nt dnlss dlh bngnn rmh sebg bldng hose d tep pnt bertngt d berens monolthc dn sphercl berdmeter 6 m dn tngg 8 m.

40 .. Permodeln Strtr Sft sft mterl ng ddelssn dn dgnn sebg prmeter dlm nlss dlh sft dr st mterl tm pembent strtr sln, t mterl beton C65. Sft-sft mterl tersebt dlh sebg bert :. Mss per nt volme (m) 9.6 g/m b. Bert per nt volme (w) N/m c. Modls Elststs (E).57 N/m d. Posson s Rto ( υ). e. Koefsen espns therml 4-6 m/m/ o C.4 Metode Anlss Proses nlss strtr domes td mngn dln tnp progrm ompter ren bnn dert ebebsn (DOF) ng dml strtr n membt mtrs en dn mtrs mss mempn ordo ng besr sehngg menltn perhtngn, ment wt dn rng rt bl perhtngn dln secr mnl. Metode nlss ng dgnn dlh Modl Anlss Method..5 Kerng Anlss Thp nlss ng dln nt mencr pengrh bent t model shell element pd strtr Plne Stress terhdp respon dnms strtr ng berp respon perpndhn (ont dsplcement), freens lm, tegngn membrn dn mods getr dpt drn sebg bert :. Memodeln strtr dome dengn metode elemen hngg, terms pembebnn, dn prmeter pensnn. b. Mengnlss model strtr nt mendptn fereens lm, mods getr, dn dsplcement dr strtr dengn bntn progrm ompter t SAP menggnln Modl nlss Method. c. Membndngn dn mengevls hsl nlss dr etg elemen shell.

41 Ilstrs globl peneltn n bs dgmbrn dlm dgrm sebg bert : STRUKTUR Domes BEBAN Bert sendr Mterl Prmeter Pensnn ANALISIS DINAMIS Modl Anlss RESPON I Freens lm RESPON II Mods Getr RESPON III Dsplcement Gmbr. Dgrm Ilstrs Globl Peneltn

42 .6 Thp Anlss Anls dln dengn lngh-lngh sebg bert : MULAI Dt Strtr (Mterl dn Frme) Pemodeln Strtr Persmn Krterst Freens Ntrl/Perode Getr Anls Dnms Strtr dengn Modl Anlss Respon Perpndhn Strtr SELESAI Gmbr. Dgrm Alr Proses Perhtngn Secr Umm

43 MULAI Dt Strtr (Mterl dn Frme) Pemodeln Strtr Anls Dt (Rn Dt) Otpt : Freens Alm dn Perode Getr Mods Getr, Jont Dsplcement SELESAI Gmbr.5 Dgrm Alr Perhtngn dengn Progrm Kompter Progrm d ts dln berlng-lng dengn vrs model strtr

44 BAB IV ANALISIS DAN PEMBAHASAN 4. Anlss Strtr Dome Setelh seles memodeln shell strtr domes, t perseg, segtg, dn belh etpt dengn bntn progrm SAP ddptn freens lm, perode getr, dsplcement dn bent mods getr. Hsl nlss selengpn dpt dlht pd lmprn A. 4.. Strtr Dome Elemen Shell Perseg Slh st contoh model strtr dome dengn elemen shell perseg : Gmbr 4. Crenosphere Stdm d Amer Sert. Tngg msmm dome mencp 5 ft dengn dmeter msmm ft. Model strtr dome ng dgnn pd nlss n dlh gmbr 4. bert : Gmbr 4. Dome dengn elemen shell perseg Monolthc domes d ts dssn oleh : bh elemen shell, dengn lsn shell msmm pd bgn dsr lengng sebesr.5 m, dn ls derh shell mnmm d pnc dome sebesr.48 m.

45 Hsl nlss ddptn bhw pd mode e- mltf prtsps moden membern pengrh terbesr bg eselrhn mode. M mode e- n dgnn sebg dsr nlss desn strtr dome. Tbel 4. Tbel Prtsps Mode Step Perod UX UY UZ SmUX SmUY SmUZ Tet Sec Untless Untless Untless Untless Untless Untless Mode,759,6956,867,7E-,6956,867,7E- Mode,759,867,6955 9,55E-,87797,87795,5E- Mode,645,5E-,496E- 6,86E-,87797,87795,764E- Mode 4,69 8,698E-,56E- 9,59E-,87797, ,75E- Mode 5,69,79E- 5,4E-,57E-,87797, ,8E- Mode 6,698 7,7E-5,44E- 4,7E-,87797, ,86E- Mode 7,698 4,46E- 5,78E-,4E-,87797, ,87E- Mode 8,5786,94E-,594E- 6,67E-,87797, ,88E- Gmbr 4. Mods getr pertm dengn perode getr ( T.754 det ). Pd mode pertm dome menglm deforms terbesr pd bgn dsr strtr, hl n terd ren ls elemen shell ng lebh besr dbndngn dengn lsn shell d tsn sehngg enn mend lebh ecl. Dt perode getr dn freens lm strtr dlm onds tnp bebn dpt dlht pd tbel d bwh n : Tbel 4. Dt freens lm dn perode getr strtr OtptCse Step Perod Freqenc Tet Tet Sec Cc/sec MODAL Mode,759,598 MODAL Mode,759,598 MODAL Mode,645 5,564

46 Tbel 4. Jont dsplcement strtr U (m) U(m) U (m) R (rd.) R (rd.) R (rd.) msmm,574,5645,64,8774,597,889 mnmm -,564 -,57 -,8 -,56 -,567 -,8 Mods getr strtr pd step mode pertm, ed, dn etg bs dlht perbednn pd gmbr dgrm g dn tegngn dlm shell bert n : Mode e- Mode e- Mode e- Gmbr 4.4 Dstrbs g shell msmm pd tp tngt mode Dr gmbr dts dpt deth mods getr e- dn e- msh smetrs dn tegngn berpst d dsr sebesr 5 ton/m. Pd mode e- mods getr sdh smetrs, grs meredn st dengn ng ln berbed rh perpndhnn. Tegngn terbesr terlet pd tp tp grs merednn sebesr 65 ton/m. Mode e- Mode e- Mode e- Gmbr 4.5 Dstrbs momen shell msmm pd tp tngt mode Mode e- dstrbs momen terbesr terlet pd shell bwh dn momen terbg rt men pnc domes. Mode n msh cp stbl ren deforms strtr sngt ecl. Konds pd mode e- msh sm dengn

47 mode e- tetp strtr sdh terdeforms cp besr e r. Pd mode e- dstrbs momen terbesr terdpt pd grs meredn. Mode e- Mode e- Mode e- Gmbr 4.6 Dstrbs g geser shell msmm pd tp tngt mode Dstrbs g geser terbesr mode e- dn mode e- berpst pd dsr dome dn strtr msh bersft smetrs dn hn terdeforms e nn dn e r. Mode e- sdh bersft smetrs dn g geser terbesr mendet pnc dome. Mode e- Mode e- Mode e- Gmbr 4.7 Dstrbs tegngn shell msmm pd tp tngt mode Mode e- strtr dome msh stbl ren hmpr td terdeforms dn td d dstrbs tegngn ng besr. Hl n dtnn dengn td dn wrn br pd strtr. Mode e- dstrbs tegngn shell terbesr berpst pd dsr dome sebelh r dn strtr sdh ml terdeforms e nn. Mode e- sngt td stbl ren dstrbs tegngn shell terbesr terdpt pd grs merdn meners dr pnc men dsr sehngg menebbn strtr td smetrs. Selntn g dn tegngn msmm mpn mnmm dpt dtbeln sebg bert:

48 Tbel 4.4 G dlm dn tegngn elemen shell Msmm Mnmm F (ton/m) 687, -686,54 M (ton-m/m) 9,6-9,6 V (ton/m) 7,7,8 S Top (ton/m^) 45,7-458,8 S Bottom (ton/m^) 89,6-89, S Averge (ton/m^) 74,54, Strtr Dome Elemen Shell Segtg Slh st contoh model strtr dome dengn elemen shell segtg : Gmbr 4.8 Dome c dengn elemen shell segtg Model strtr dome ng dgnn pd nlss n dlh gmbr 4.9 bert : Gmbr 4.9 Dome dengn elemen shell segtg Monolthc domes d ts dssn oleh : 54 bh elemen shell, dengn lsn shell msmm pd bgn dsr lengng sebesr.6 m, dn ls derh shell mnmm d pnc dome sebesr.84m.

49 Gmbr 4. Mods getr pertm dengn perode getr ( T.758 det ). Pd mode pertm dome td menglm deforms ng sgnfn, hl n terd ren ls elemen shell ng ble sm pd setp bgn sehngg en strtrn mert. Dt perode getr dn freens lm strtr dlm onds tnp bebn dpt dlht pd tble d bwh n : Tbel 4.5 Dt freens lm dn perode getr strtr Step Perod Freqenc Tet Sec Cc/sec Mode,758,59 Mode,7578,59 Mode,5566 7,965 Tbel 4.6 Jont dsplcement strtr U (m) U(m) U (m) R (rd.) R (rd.) R (rd.) msmm,79,786,679,956,956954,744 mnmm -,789 -,7 -,667 -,9564 -,9595 -,58 Mods getr strtr pd step mode pertm, ed, dn etg bs dlht perbednn pd gmbr dgrm g dn tegngn dlm shell bert n :

50 Mode e- Mode e- Mode e- Gmbr 4. Dstrbs g shell msmm pd tp tngt mode Mode e- Mode e- Mode e- Gmbr 4. Dstrbs momen shell msmm pd tp tngt mode Mode e- Mode e- Mode e- Gmbr 4. Dstrbs g geser shell msmm pd tp tngt mode

51 dome. Mode e- terdstrbs mert dn td d wrn br mennn td d g geser shell ng besr. Mode e- Mode e- Mode e- Gmbr 4.4 Dstrbs tegngn shell msmm pd tp tngt mode Dstrbs tegngn shell pd etg mode n hmpr sm dengn dstrbs g shell. Dstrbs terbesr dtnn dengn wrn br dn terecl dengn wrn nng. Bent etg mode n smetrs sehngg strtr msh cp stbl. Selntn g dn tegngn shell msmm mpn mnmm dpt dtbeln sebg bert : Tbel 4.7 G dlm dn tegngn elemen shell Msmm Mnmm F (ton/m) 555, -6, M (ton-m/m) 5,7-4,94 V (ton/m) 4,88,4 S Top (ton/m^) 78,9-955,44 S Bottom (ton/m^) 577, ,4 S Averge (ton/m^) 687,67,79

52 4.. Strtr Dome Elemen Shell Belh Ketpt Model strtr dome dengn menggnn bntn perngt ln nlss strtr dlh sebg bert : Gmbr 4.5 Dome dengn elemen shell belh etpt Adpn monolthc domes d ts dssn oleh : 54 bh elemen shell, dengn lsn shell msmm pd bgn dsr lengng sebesr.44 m, dn ls derh shell mnmm d pnc dome sebesr.898m. Gmbr 4.6 Mods getr pertm dengn perode getr ( T.748 det ). Pd mode pertm dome menglm deforms ng cp sgnfn pd bgn pnc dome, bent elemen ng td stbl berp belh etpt dn mn mengecl d bgn pnc dome.

53 Dt perode getr dn freens lm strtr dlm onds tnp bebn dpt dlht pd tbel d bwh n : Tbel 4.8 Dt freens lm dn perode getr strtr OtptCse Step Perod Freqenc Tet Tet Sec Cc/sec MODAL Mode,747,445 MODAL Mode,748,46 MODAL Mode,677 4,99 Tbel 4.9 Jont dsplcement strtr U (m) U(m) U (m) R (rd.) R (rd.) R (rd.) msmm,57577,46,8589,95,9959,66659 mnmm -,4698 -,87 -,4484 -,47 -, ,6667 Mods getr strtr pd step mode pertm, ed, dn etg bs dlht perbednn pd gmbr dgrm g dn tegngn dlm shell bert n : Mode e- Mode e- Mode e- Gmbr 4.7 Dstrbs g shell msmm pd tp tngt mode Mode e- dn mode e- terdeforms d pnc tetp td terdeforms e nn mpn e r. Sedngn pd mode e- terdeforms e nn. Konds sepert d ts mennn bhw strtr td stbl d pnc dome. Mode e- Mode e- Mode e- Gmbr 4.8 Dstrbs momen shell msmm pd tp tngt mode

54 Dstrbs momen pd strtr dome n mert, dtnn dengn wrn h ng sergm d tp shelln. Wrn h n bersr ntr - 66 tonm. Mode e- Mode e- Mode e- Gmbr 4.9 Dstrbs g geser shell msmm pd tp tngt mode Dstrbs g geser pd etg mode tersebt terbesr terlet pd pnc dome. Konds n dtnn dengn dn perbedn wrn d pnc dome t merh. Wrn merh bersr ntr 4-56 ton/m, sedng wrn ng bersr ntr -4 ton/m. Mode e- Mode e- Mode e- Gmbr 4. Dstrbs tegngn shell msmm pd tp tngt mode Ketg mode tersebt terdstrbs mert dengn wrn ng sm tetp pd mode e- dn mode e- terdeforms besr d pnc. Selntn g dn tegngn shell msmm mpn mnmm dpt dtbeln sebg bert : Tbel 4. G dlm dn tegngn elemen shell Msmm Mnmm F (ton/m) 5447,59-58,4 M (ton-m/m) 89, -57,74 V (ton/m) 445,8,877 S Top (ton/m^) 76849,8-689,96 S Bottom (ton/m^) ,95-7,46 S Averge (ton/m^) 896,47,7

55 4. Pembhsn. Hsl nlss mennn bhw mods pertm strtr domes dengn elemen shell berbent dsr perseg, segtg, dn belh etpt meml deforms ng sedt berbed sepert dtnn pd gmbr bert n : Los deforms Los deforms Los deforms. dome perseg b. dome segtg c. dome belh etpt Gmbr 4. Perbndngn pol getrn strtr domes Gmbr d ts mennn bhw strtr domes dengn elemen shell segtg dn perseg meml smpngn ng td terll besr hl n dsebbn ren bent dsr elemen shelln cp stbl. b. Hsl nlss mennn bent mods getr ng dhsln elemen shell perseg mode e- pd dstrbs g, momen, g geser dn tegngn shell berbent smetrs. Grs merdn st dengn ng ln berbed rh perpndhnn. Kl d lebh lnt elemen shell perseg td meml tngt estbln ng tngg, ren terdpt 4 tt ng bs dbt bermcm mcm rng msln belh etpt. c. Mods getr shell segtg dr mode e- smp mode terhr berbent smetrs. Kl d lebh lnt elemen shell segtg ng meml tt hn bs dbt bdng s. Hl n mennn bhw shell segtg meml tngt estbln ng lebh tngg dr shell perseg. d. Domes dengn elemen shell berbent dsr belh etpt cenderng menglm deforms ng cp besr pd bgn pnc domes, ddg ren perbedn spe rso ss belh etpt bgn bwh dengn bgn pnc t : dengn :4 sehngg elemen shell d pnc lebh td.

56 e. Nl perbndngn ont dsplcement etg strtr dpt dlht pd tbel d bwh n : Tbel 4. Perbndngn nl ont dsplcement msmm Domes shell perseg,574 Domes shell segtg,67 Domes shell belh etpt,8589 Mmm ont dsplcement (m) Tbel d ts mennn bhw Domes berelemen shell belh etpt meml smpngn ng sngt besr, t lebh dr meter. Smpngn n tent sngt berbh bg penghn dome pbl terd gemp t tpn ngn ng cp besr (torndo). f. Dt perode getr dn freens lm strtr mennn ng ng slng mendet, dmn bersr pd nl.74 det t setr,5 hz. Freens lm n cp mn terhdp getrn dnms ngn ng bersr pd nl.5 Hz. Tbel 4. Perbndngn nl Perode getr dn Freens lm Perode Getr (det) Domes shell perseg,759,59 Domes shell segtg,758,59 Domes shell belh etpt,7479,44 Freens Alm (Hz) g. Dt g dlm dn tegngn dlm elemen shell strtr dpt dlht pd tbel bert n : Tbel 4. Perbndngn g dlm dn tegngn dlm shell Domes shell perseg Domes shell segtg Domes shell belh etpt F m. (ton/m) 687, 555, 5447,6 M m. (ton-m/m) 9,6 5,7 89, V m. (ton/m) 7,8 4,88 445,8 S m. (ton/m^) 45,7 78, ,95 Semn besr g dlm ng dthn oleh elemen shell, m semn besr pl ftor emnn ng hrs dnlss dlm desn strtr domes.

57 BAB V KESIMPULAN DAN SARAN 5. Kesmpln Berdsrn nlss ng telh dln terhdp tg model dengn tg tpe shellng berbed, t perseg (rectnglr), segtg (trnglr), dn belh etpt (dmond), dpt dmbl esmpln sebg bert :. Elemen shell perseg mennn mods getr ng smetrs ren pd grs merdn st dengn ng ln berbed perpndhnn. b. Elemen shell belh etpt meml mods getr ng terdeforms besr d pnc domes. c. Elemen shell segtg mennn mods getr ng smetrs dr mode pertm smp terhr. d. Besrn perode getr dn freens lm pd fndmentl mode (mods pertm) onds nforced vbrton shell perseg dlh.754 det dn.59 Hz, segtg dlh.758 det dn.59 Hz, belh etpt dlh.747 det dn.45 Hz. 5. Srn Beberp pembtsn dn penederhnn ng dln dlm nlss n dpt mend bhn pertmbngn pd nlss selntn. Msln mlh model, bent strtr domes ln ng belm d dlm nlss n.

58 DAFTAR PUSTAKA Anonm, 997. Pedomn Penlsn Srps dn Lporn Ker Prte. Srrt: UNS Press. Al, D.D & C, Kspl.. Lmt Stte Anlss of Hemsphercl Domes wth Fnte Frcton. Inggrs, from: Bmbng Shendro. 99. Metode Elemen Hngg dn Aplsn. Yogrt. Clogh, R, W., Joseph Penzen Dnmcs of Strctre. London: Mc- Grw-Hll, Inc. Copr, Anl K Dnmcs of Strctre: Theor nd Applctons to Erthqe Engneerng. New Jerse:Prentce Hll, Inc. Deprtemen Peern Umm, 987. Pedomn Perencnn Kethhn Gemp nt Rmh dn Gedng. Ysn Bdn Penerbt Peern Umm. Gobogng & Wen, En H.. Senstvt Anlss of Cble to Sspense dome strctrl sstem. Chn: Deprtemen of Cvl Engneerng Zhe Chng Unverst Hng Zo. Logn, Drl L A Frst Corse n Fnte Element Method. Boston: PWS Engneerng. Pz, Mro. 99. Dnm Strtr: Teor dn Perhtngn. Eds ed. New Yor: Vn Nostrnd Renhold Compn. Schode, Dnel. 99. Strtr. Yogrt:Erlngg.

59 Svensson, H.S., nd E. Jordet The Concrete Cble Sted Helgelnd Brdge n Norw. Accessed on September 9 th,, from: Wdodo.. Respon dnm Strtr Elst. Yogrt: UII Press. Zmmermn, Jonthn & Robert Bsset. 4. Dome of Home Premers on The Trvel Chnnel. Accssed on September th, 4, from: