Practical calculation of cable-stayed arch bridge lateral stability Wei Lu 1,2,a,,Ding Zhou 2,b,Zhi Chen 1,c

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1 pplie Mechnic n Meril Online: IN: 66-7, Vol , pp oi:0.0/ 0 Trn Tech Publicion, wizerln Prcicl clculion of cble-e rch brige lerl bili Wei Lu,,,,Ding Zhou,b,Zhi Chen,c chool of Civil Engineering & Mechnic, Huzhong niveri of cience n Technolog, Wuhn,Hubei 007,Chin Wuhn Municipl Engineering Deign & eerch Iniue Co.,L, Wuhn,Hubei 005, Chin 06695@qq.com, b c 7769@qq.com Kewor: Cble-e rch brige, lerl bili, energ principle, conrucion proce. brc. long-pn cble-e rch brige i new form of brige rucure h combine feure of cble-e brige wih chrceriic of rch brige. In he preen u, we erive prcicl clculion meho for he lerl ebilizion criicl loing of cble-e rch brige uring he conrucion proce be he energ principle. The vlii of he meho w verifie wih n exmple. The clculion meho provie quick n efficien w o evlue he lerl bili of cble-e rch brige n concree fille eel ubulr rch brige uring he conrucion proce. Inroucion cble-e rch brige i novel compoie rch brige. The min re reie on he rch rucure upplemene b he cble re []. Figure how i rucure. The new rch em i inpire b he cble-hoig conrucion meho of concree fille eel ubulr CFT rch brige. Deigner hink he emporr buckle in he cble-hoig conrucion cn be ue permnen force componen o form cble-e rch brige ogeher wih rch rib. The conrucion bili of rch brige h lw been criicl problem n gine inene enion in he engineering fiel []. In he preen u, we ue he energ principl o euce prcicl formul o clcule he bili of cble-e rch brige uring he conrucion proce. Fig. rucure of cble-e rch brige Derivion of he prcicl clculion formul ic umpion Mn cholr in Chin hve erive he lerl ebilizion criicl loing of cble-e rch brige ug he energ meho. The bic umpion pplie here re he me ecribe in lierure [] n []. In iion, he following umpion re ifie. The hrp rrngemen i pplie o cble which re uniforml rrnge from he rch foo o he op. The effec of he brige eck n upener re ignore. Onl he bili of rch rib egmen uring he hoig proce i coniere. The ouble-rib-hoig cheme i ope. To implif he nli, ume h prere h been pplie when inlling cble n he cble force h been e up. ll righ reerve. No pr of conen of hi pper m be reprouce or rnmie in n form or b n men wihou he wrien permiion of Trn Tech Publicion, ID: , Pennlvni e niveri, niveri Prk, -0/05/6,0:0:57

2 pplie Mechnic n Meril Vol The conrucion bili before he cloe of rch rib i he onl fcor coniere. Hence, fer he hoig of rch rib, rch rib hve been inlle wihin he rc opening ngle rnge of ~. When 0 < < n 0, i i he mximl cnilever hoig ge. 5 The cro n cble beween rib re iribue evenl in he hoie rch rib egmen. The pil eformion geomeric relionhip of cble-e rch [],[] The pil eformion of rch xe w uie. The curve coorine hown in Figure w ue. The fixe coorine em of rnom ie,, in he rch i x, n z. The irecion of z i he ngenil irecion of he curve on he min plne. The cenrl ngle of i. The iplcemen of in he irecion of x, n z i u, v n w, repecivel. The lope i β, γ, θ, n he horizonl cble ngle i. θ γ Fig. The igrm for bili clculion of cble-e rch The lerl eflecion re of he wo ifferenil ie ecion wih ince of roun he n z xe re follow. K The ngleincremen roun he z xi θ γ K z The inceincremen he me ime, he non-reching coniion for n rch correponing o n rch xi uring inclining i w v u ccoring o he iuion h wo rch fee hve no relive ngenil iplcemen coniion w 0, we ge u v Thengleincremen rounhe xi γ θ Theinceincremen Moreover, ccoring o he flexure eformion feure uring he rnvere inbili of rch u rib, we ge γ 5

3 5 uinble Ciie Developmen n Environmen Proecion IV The energ relionhip uring he cble-e rch brige conrucion For cble-e rch in he hinge bounr, he iplcemen funcion i u θ '' '' The bounr coniion of u u 0, θ θ 0 houl be ifie. When, for he cble-e rch in he fixe bounr, he iplcemen funcion i u θ 7 ' ' The bounr coniion of u u 0, θ θ 0 houl be ifie. When, he energ relionhip of rch conrucion proce uring cerin conrucion ge i follow ner he hinge bounr coniion: he lerl flexurl rigii of rib θ u he orionl rigii of rib θ u z he rib elic poenil energ ue o he non-irecion force of cble [5] T ' T k u ' l0 Tm l0 m i clcule ug he impon inegrl formul [6]. mong i, < n he lerl bening rin energ of crobr n he locl bening rin energ of rch rib h h u η h η D D η h D 5The vericl bening rin energ of crobr D D 6he poenil of rch rib uner he effec of exernl lo q 6 9 0

4 q q u q V Hence, he ol energ for he lerl inbili of cble-e rch brige uner he hinge bounr coniion i he imilr iem re merge ccoring o n D m T q D V h k bk k b z η ner he fixe bounr coniion he lerl flexurl rigii of rib u θ 5 he orionl rigii of rib θ z u 6 he rib elic poenil energ ue o he non-irecion force of cble [5] 0 ' 0 ' n T l T u l T k 7 mong i, < n n i clcule ug he impon inegrl formul [6]. he lerl bening rin energ of crobr n he locl bening rin energ of rch rib η η η h h h h D D u D pplie Mechnic n Meril Vol

5 590 uinble Ciie Developmen n Environmen Proecion IV 5The vericl bening rin energ of crobr D D 6he poenil of rch rib uner he effec of exernl lo q 9 q u q V 0 q Hence, he ol rch energ for he lerl inbili of cble-e rch brige uner he fixe bounr coniion i he imilr iem re merge ccoring o n. In he formul, i he lerl flexurl rigii of rib; i he orionl rigii of rib; E b I b i he eck lerl flexurl rigii; h n i he rnverl n ril flexurl rigii of crobr, repecivel; i he horizonl ince of upener; T i he cble preenion force; l 0 i he horizonl ince from he op of he rch; he ngle of cble i ; i he ince beween wo rib; n D i he ince beween wo crobr. The clculion meho for he lerl bili criicl loing of cble-e rch brige uring he conrucion proce The principle of poenil energ i ope. ner he hinge bounr coniion, we ge z k V h 0 i z Obin he homogeneou equion regring o n : h k V η D D i n η D q 6 h q Tn T D m imilrl, obin he homogeneou equion regring o n uner he fixe bounr coniion h 0 0

6 pplie Mechnic n Meril Vol η D h q T i n 6 D n The bove homogeneou equion hve oo mn prmeer, o i i complice o genere he nlicl formul bou q. Therefore, in he prcicl pplicion, he mhemicl ofwre Mhemic i ue for clculion be on he given prmeer n hen pu ino he homogeneou equion. I i more convenien o eermine q ccoring o he coniion h he coefficien eerminn of he equion i Exmple nli Exmple he bic of ouble-rib eck cble-e rch brige re follow. pn, 0m; he brige eck wih, 0m; he rie-o-pn rio, /5; he bening moulu of rib ecion, emp; he her moulu, 7.69e0MP; he bening rigii ou of plne,.7m ; n he orionl rigii,.55m. The cble preenion force i 000KN. The rrngemen i from he rch foo o he op ill he fourfol poin. The cble ngle in ech ie i 0 egree. There re even crobr evenl iribue beween rib of wo rche. The vericl bening rigii of crobr i 0.657m n he ngenil rigii i 0.5 m. The cble-upener-hoig meho i ue uring he conrucion. The hoig cheme i ouble-rib hoig n ouble-rib clog. In ech hlf of he rch, here re ix egmen for hoig. The verge lengh for ech egmen i 0m. For ech hoie rib egmen, crobr n cble re inlle in he mile n he of he egmen. In he prcicl meho, he vlue of prmeer reflec ifferen conrucion ge. The clcule prmeer correponing o ix egmen i.9 о,. о,. о,.5 о, 6. о n 0 о, repecivel. ccoring o hee bic, he Mhemic ofwre i ue o clcule prmeer which re hen pu ino Equion n. ner he coniion h he coefficien eerminn i 0, he lerl ebilizion criicl loing ix conrucion ge i obine,menwhile,he reul clcule b he finie elemen meho i compre wih i Figure. Fig. The lerl ebilizion criicl loing vriou conrucion ge

7 59 uinble Ciie Developmen n Environmen Proecion IV e on Fig., he clcule vlue ug he prcicl meho propoe b he u i bigger hn he vlue clcule ug he finie elemen meho. However, he ifference i no lrge n wihin he rnge of llowble error. I ugge h he prcicl meho we erive i correc n feible. The figure lo inice h he lerl ebilizion criicl loing i grull ecree long wih he incree of rib hoig egmen. The ifference beween he ebilizion criicl loing uner he hinge n fixe bounr coniion i grull reuce. ner he hinge bounr coniion, he lerl ebilizion criicl loing in he mximl cnilever hoig ge i 5KN/m. The rib eel ube eni i 7.6KN/m, n i cn be convere ino he uniforml iribue lo 5.76KN/m. In he cul eign, he elic bili fe fcor of rch brige bili mu be bigger hn ~5. e on he requiremen, he mximl cnilever hoig ge m no be ble o if he bili requiremen. Hence, uring he cul conrucion, rch fee re hinge in he erl ge. fer lifing o cerin egmen, he cloure i performe o form fixe bounr. In he figure, he criicl loing in mximl cnilever hoig ge uner he fixe bounr coniion mee he requiremen. Concluion In he preen u, we erive prcicl meho o clcule he lerl ebilizion criicl loing uring he conrucion proce of ouble-rib cble-e rch brige be on he energ principle. Through he cree exmple, we compre he reul from he propoe meho n he finie elemen meho. The reul implice h ug he propoe criicl loing formul in he preen u voi eblihing he complice finie elemen moel. The inpu of rucure bic prmeer lone cn rpil genere relivel correc reul. I provie n effecive w o preliminril evlue he lerl bili of rucure in he erl ge of conrucion. Moreover, he prcicl meho i lo uible for he bili clculion of ouble-rib CFT rch brige conrucion. eference: [] hiong Luo. Conierion n u of innovive echnique for long-pn cble-e rch brige. [J].rige conrucion, 0056:- [] Yecheng Zhng. eerch on conrucion echnolog of lrge-pn CFT rch brige. [Ph.D. hei D].Zhejing niveri, 00:50-55 [] Hengli.ble clculion of he rch em [M].eijing:Chin Communicion Pre, 979:7-6 [] Guoho Li. bili n vibrion of brige rucure. [M].eijing:Chin ilw Pre, 965:7- [5] Weiling Jin. eerch on lerl bili of long-pn rch brige. [D].Dlin:Dlin niveri of Technolog, 9:5-6 [6] Wei Lu. u on bili of long-pn compoie cble-e rch brige. [D].Wuhun: Wuhn niveri, 00:67-

8 uinble Ciie Developmen n Environmen Proecion IV 0.0/ Prcicl Clculion of Cble-e rch rige Lerl bili 0.0/