Study of Buckling Stability on Tall Tower Truss Structure with All Loads

Transcription

1 Intrnational Journal of Scinc, Tchnology and Socity 06; 4(4): 57-6 htt:// doi: 0.648/j.ijsts ISSN: (rint); ISSN: (Onlin) Study of Buckling Stability on Tall Towr Truss Structur with All Loads Yixiao Qin, Li Zhang, *, Zhngjun ng, Chao Zhang 3 Mchanical Enginring Institution, Taiyuan Univrsity of Scinc and Tchnology, Taiyuan, Shanxi, China Machinry Dsign and Rsarch Institution, Xuzhou Xu Gong Road Construction Machinry CO., LTD, Tianjin, China 3 Machinry Dsign and Rsarch Institution, Hua Dian Havy Industris CO., LTD, Bijing, China addrss: @qq.com (Li Zhang) * Corrsonding author To cit this articl: Yixiao Qin, Li Zhang, Zhngjun ng, Chao Zhang. Study of Buckling Stability on Tall Towr Truss Structur with All Loads. Intrnational Journal of Scinc, Tchnology and Socity. Vol. 4, No. 4, 06, doi: 0.648/j.ijsts Rcivd: May 4, 06; Acctd: Jun 5, 06; ublishd: Jun, 06 Abstract: Towr cran blongs to tall towrs truss structurs, whos bucking instability oftn lad to collas. ast studis focusd on th mast instability undr a singl load, which dosn t aly to th actual condition that towr cran working undr various loads at th sam tim. This ar taking into considration th towr cran lifting wight as wll as various loads lik th hoist tiing momnt, havy vrtical load, wind load, th cntrifugal forc, rotary load of rsistanc and horizontal inrtia forc. Through th ignvalu bucking and nonlinar bucking analysis, w can gt th lifting load whn th hoisting is focusing on a maximum working rang of th arm of th towr and towr bar forc status and th convrgnc ma of stability. This study rovids th comlt sts of th towr stability dsign of towr cran, can b usd as a guidanc or rfrnc for th actual roduct dsign. Kywords: Towr Structur, Buckling Stability, Nonlinarity, Eignvalu Analysis, init Elmnt Mthod. Introduction Th truss towr is th main suorting structur of th towr cran, whos loading condition is quit comlicatd, and analyzing its working condition is sincrly difficult. Undr th influnc of various loads lik th hoist tiing momnt, havy vrtical load, wind load, th cntrifugal forc, rotary load of rsistanc and horizontal inrtia forc, it will roduc th immns strss and dformation much asir. As a towring truss structur, it's ncssary to analyz its stability. With th frqunt accidnts of towr cran, studying in this ara rcntly attractd th attntion of rsarchrs, [-5] studid th stability roblm of two bar truss, [6-9] studid th factors that affct th truss structur of local stability, [0] studid instability of th mast towr cran in static load without wind, undr th condition of changing th amlitud of th loading, [-3] studid th stability of th towr in turbulnt winds. Th towr cran in this ar, for instanc, with th nginring softwar ANSYS to simulat th actual orations undr th fiv most dangrous working condition [4-8], our ar conducts linar bucking and nonlinar buckling analysis rsctivly [9-7], Assuming that th towr cran was working in th most dangrous working condition. Continuously changing th wight and th rang of loads to obtain th rcis towr cran buckling critical loads, in ordr to gt th convrgnc ma of stability, bcaus th ast ars studying in this fild was rar and not nough, on on hand, th rsarch what w studying was of significanc, on th othr hand, It rovids usful basis data for towr cran dsign in ordr to guarant th stability of th cran.. Buckling Analysis Modl on Tall Towr Truss Structur Whthr th finit lmnt modl is rasonabl or not dirctly affcts th accuracy of th analysis rsults, To mak th mast modl rasonabl, th finit lmnt modl should b abl to rflct th charactristics of th towr body structur; loading and constraints of th modl should b consistnt with

2 58 Yixiao Qin t al.: Study of Buckling Stability on Tall Towr Truss Structur with All Loads th ractical nginring situation. Towr structur ntitis and loading should b consistnt with th ral situation. Taking into considration of th largr structural stiffnss at th bottom of th towr, this study assumd fixd baring, to b abl to withstand th bnding momnt. igur. QTZ5 towr cran. Th QTZ5 towr cran is takn as an xaml to modl and conduct buckling analysis. As is shown in igur, th towr cran working rang is from.5m to 35m, th maximum wight is.5t, th nominal wight at th most significant is 0.75t; th main chord is a tub with 00mm outr diamtr cross-sction and 0mm thicknss; all th abdominal rod ar tubs with 00 outr diamtr cross-sction and 5mmthicknss; towr bar matrial is Q35b, luffing sd 0m/min, rotation sd 0.6r/min, hoisting sd 3.5/7m/min. Th towr modl building rocss usd th command stram. irstly, w dfind th ky oints on th standard sction, conncting oints to form th main chord, vntral ol, and dividd it into fin msh. Thn w dfind th lmnt ty and matrial rortis. Considring th structur charactristic and th load of mast towr cran, th BEAM89 sac bam is introducd to mak th lmnt simulation analysis. This unit is a bam that can bar ulling, rssuring, bnding, twisting, furthrmor, with th considration of th shar dformation of Timoshnko bam lmnt, in unit BEAM89 cross-sction rotation and torsion can b in th indndnt introlation. This unit can also b usd with th cross-sction dfind command, which is a convnint, fast, and accurat way to dfin th sction siz. Whn th towr cran lifting th ratd load, th towr main chord should withstand larg tnsil and comrssiv strss, so th towr bar matrial is slctd as Q345b, modulus of lasticity. 0 5 Ma, oisson's ratio is 0.3, dnsity is 7800 kg/m 3. Taking into account th charactristics of towr crans, towr suffrs loads, including wind load, wight of th towr, cntrifugal forc, tiing momnt, torqu and vrtical loads gnratd by th goods, balanc wight and balanc boom in th towr body. This ar slcts four kinds of otntially most dangrous load condition and rformd ignvalu bucking and nonlinar bucking analysis to mast. What ths conditions hav in common is that th car is locatd in th maximum working rang of hoists, vrtical slf wight load rmains unchangd, by incrasing th goods hoist until it rachs th towr yild limit load on th towr. Th diffrncs among th conditions ar listd in tabl and latr contnts, namly diffrnt dirctions of th wind forc, whthr to considr various arts of th rotary inrtia and cntrifugal forc, tc. Ths conditions accuratly dscrit th towr cran stability analysis of th changing of hoisting load and th unchanging rst of th actual load, making th stability analysis rflcts th ral situation and has ractical valu. or comarison, th calculation condition commonly usd in othr documnts and rsults of analysis ar listd as blow. Th fiv load conditions ar as fllow and shown in igur. ) Th arm locatd on th cross-sctional diagonal lin of towr body dos not mov, lifting goods, wind dirction by th balanc of th boom to boom. ) Th arm locatd on th cross-sctional diagonal lin of towr body rotation starting and braking, hanging goods, consistnt with th rotary inrtia forc winds. 3) Th towr arm is aralllld to th two sids of th cross-sction of th towr dos not mov, lifting goods, wind dirction by th balanc of th boom to boom. 4) Th towr arm is aralllld to th two sids of th cross-sction of th towr rotation starting and braking, hanging ratd lifting load, consistnt with th rotary inrtia forc winds. 5) Th towr arm locatd on th cross-sctional diagonal lin, thr is in no wind, static load conditions, which is commonly usd convntional calculation. igur. Diffrnt working conditions of th mast quivalnt loads.

3 Intrnational Journal of Scinc, Tchnology and Socity 06; 4(4): Condition i Tabl. Th calculation condition and th quivalnt loads. Equivalnt loads/n Gc Gc wi n l w w In tabl, th symbol indicats that th load incrass with th hoist. Good load G, boom wight G, balanc h wight G, dynamic load cofficint φ and dynamic slf-wight load cofficint φ can gt th vrtical loads at th to nods of th towr. G = G / 4 = ( φ G + φ G + φ G ) / 4 () c cz h b Gc = Gcz / 4 = ( Gh + Gb + G) / 4 () Th goods, th wight of cran trolly, th arm cntr of gravity, balanc arm focus and arm fram bat fac form to rotary cntr distanc of hart ar rsctivly lh, ld, l, l f and th towr width a, by th cargo load G h, th towr cran boom wight cran countr wight bnding. G d, wight balanc boom wigh b Gb and G can solv th quivalnt forc of = M / a = ( φg l + φg l φg l w h h d d d b φg l ) / a / ( = M a = G l + G l G l w h h d d d b G l ) / a = M / a = ( φg l + φg l φg l w3 3 h h d d d b φg l ) / a / ( 4 = M 4 a = G l + G l G l w h h d d d b G l ) / a w5 w (3) (4) (5) (6) = (7) By turning th start-sto institutions causd th tangntial inrtial forc of goods, th tangntial inrtial forc of boom fram chb h chb d, th tangntial inrtial forc of balanc arm chb, and arm fram of wind load quivalnt forc of torqu T n. w, gnrats = T / a = ( l + l + l n n chbh h chbd d chbb + l ) / a w f rom th abov comonnts quality m i, cran rotary angular vlocity ω and cntroid to th lvl of th rotary cntr distanc γ, cntrifugal forc can b obtaind. i (8) h L = Li (9) i G Th wind rssur of working status П, th windward ara A and wind factor K c, ld to th towr wind load of ach standard sction. =.K A, w KcП A w c П = (0) With QTZ5 towr cran aramtrs in abov all, th quivalnt load data ar shown in tabl. 3. Mast Towr Cran Stability Analysis 3.. Eignvalu Buckling Analysis Th structur undr crtain load will b in a stabl quilibrium stat, whn th load rachs a crtain valu, with a small incrmnt, th quilibrium will b brokn; th structur will go from original quilibrium stat, through th unstabl quilibrium stat and rachs a nw stabl quilibrium stat. This rocss is th instability or buckling, and th corrsonding load is calld th buckling load or critical load. Th lmnt stiffnss matrix that is only dtrmind by th strss stat is calld th gomtric stiffnss matrix, dnotd as K σ. or any known initial strss stat, aftr a solving for th gomtric stiffnss matrix K σ, with alication of th load factor λ to chang initial strss, gomtric stiffnss matrix changs to λ K σ. Undr linar conditions, gomtric stiffnss matrix K σ and stiffnss matrix dislacmnt function, th quilibrium quation is, K ar not a ( K + λk ) δ = () Assuming a critical stat has bn rachd, thn thr xists a rturbations of configuration δ nar its sha δ, so that th systm is in quilibrium stat undr th sam xtrnal forc, thn, σ ( K + λκ )( δ + δ ) = () Subtracting th abov two quations, σ

4 60 Yixiao Qin t al.: Study of Buckling Stability on Tall Towr Truss Structur with All Loads ( K + λκ ) δ = 0 (3) At this oint, th ignvalu buckling analysis is to solv th gnralizd ignvalu, namly solving th gnralizd ignvalu λ and th dislacmnt ignvctors δ. Eignvalu λ tims outsid-of-structur load gts bifurcation oint critical load, without considring balanc arm fram towr dformation condition, through th constantly adjusting goods load to solv th. Whn th rsulting ignvalu λ dos not qual to, continu to adjust goods load, until th ignvalu λ was quald to. ANSYS analysis and calculation rsults as is shown in tabl. σ cr Tabl. Calculation rsults. Working condition Buckling load/kn Eignvalu Shown in th abov fiv kinds of load cass, cas ignvalu buckling load is th minimum, but th most vulnrabl to instability. Th linar buckling analysis charactristic valu of minimum buckling load 00N is 0 tims mor than dynamic allowd maximum lifting load 7.5φ kn. Eignvalu buckling analysis is a linar analysis, alid to rdict th lastic buckling load of th structur undr idal conditions, but th initial dfcts of th actual structur and th dformation bfor buckling of th structur will mak th load xrincing bucking instability bfor it rachd th thortical buckling load. Thrfor, th critical valu of th cr ignvalu buckling analysis is usually gratr than th non-linar analysis rsults. 3.. Nonlinar Buckling Analysis Th nonlinar analysis and calculation alid th bilinar isotroic hardning BISO modl and th isotroic strngthning Von Miss yild critrion, whil oning th larg dformation, using th load incrmnt mthod to rogrssivly load, th arc-lngth mthod to calculat in th itrativ rocss, with dfault convrgnc conditions. ANSYS analysis rorts buckling convrgnc igur, convrgnt igur s horizontal axis is cumulativ itration numbr, th vrtical axis is absolut convrgnc norm. Convrgnc control is associatd with L norm: L valu is constantly changing during th calculation; if th L is not gratr than th tolranc CRIT, thn convrg. Considring th gomtric and matrial nonlinarity, matrial nonlinarity is xrssd through two continuous linar, also known as bilinar strss-strain rlations. Rod matrial buckling strngth σ s35 = Ma. or all load cass in Tabl, with hoists of th car locatd in th maximum working rang, ANSYS workd out th non-linar convrgnc of towr critical loads undr fiv dangrous load conditions ar rsctivly 40kN, 64kN, 50kN, 8kN, 68kN. Cas has th minimum critical load. As th load gradually adds to 40kN, raching th matrial buckling strngth, furthr incrmnt of load rsults in convrgnc ma dos not convrg and th dformation of th towr cran. ANSYS analysis dos not rovid corrsonding strss cloud figur. Mast towr cran nonlinar convrgnc ma and strss cloud shown in igur 3.

5 Intrnational Journal of Scinc, Tchnology and Socity 06; 4(4): igur 3. Diagrams of nonlinar convrgnc and th towr strss cloud. Tabl 3. Mast towr cran nonlinar convrgnc and strss conditions. Condition Bucking critical load/kn Strss/Ma rom tabl 3, cas has towr bucking critical load as 40kN, 4. tims th maximum allowd dynamic lifting loads 7.5φ kn, but lss than th ignvalu buckling analysis rsult 00 KN, which mans th rsult of th nonlinar analysis valu is lss than th rsults of linar charactristic valu, th linar charactristic valu of critical load can t b usd as th buckling analysis as final rsult. 4. Conclusions () This ar is focusing on th working rortis of towr cran, using th load conditions of dsign scifications and considring all loads, with an incrasing hoist load, analyzing th charactristics of towr cran, linar ignvalu buckling and matrial nonlinar buckling on th high-ris towr truss structur basd on th sac fram modl. Th rsults show that chord is most likly to xrinc instability, whil th critical load from nonlinar buckling analysis is much smallr than th critical load from ignvalu buckling analysis. () In this ar, th study of mast of towr crans is don by ignvalu buckling and nonlinar buckling analysis, whr in, ignvalu buckling analysis th matrial nonlinarity, initial dfcts and dformation bfor buckling ar oftn not includd, thus th rsulting buckling load is an idal load, instad of a ractical load accuratly rflcting th ral situation of mast buckling, taking into considration th structur stability lasticity bhavior and th significant dformation whn doing th

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