Namhlanje, i-Savo Kusić igxile kwi ifestile zomthi, iifestile zomthi-aluminiyam, iifestile zesiko, umnyango kunye nezicelo zekoteyishini. Esi sicatshulwa sihlala singuvimba wenkcazo-bungcali yolwakhiwo kwaye ayisosithembiso soyilo olungatshintshiyo, ubalo lozinzo okanye ukubuyisela kwisimo sangaphambili.
Umahluko wenxaki yokugoba ukugoba
Kucingelwa ukuba zonke iingqikelelo zanelisiwe, ngakumbi
- intonga ithe tye ngokupheleleyo
- ukuba umthwalo P usebenza kwi-shaft yentonga
- ukuba amandla ombane ahlala engaphantsi komda wolungelelwaniso
- ukuba i-deformations incinci ngokwaneleyo ukuvumela ukwenza lula okuqhelekileyo kwezibalo.
Ukuba intonga igoba phantsi kwesenzo samandla P kwaye mhlawumbi nangenxa yomthwalo q osebenza kwi-transverse direction, ke iimeko ezaziwayo zokulingana phakathi kwemithwalo yangaphandle kunye nemikhosi kwicandelo kufuneka yaneliswe. Ngaphandle koko, kungokwemvelo ukuba kufuneka kubekho ubudlelwane obaziwayo phakathi kokuguqulwa kunye namandla kwicandelo.
Sl. 1 - Ibhalansi
Kumkhiwane.1intonga yobude egobileyo ds imelwe. Ithambeka le-tangent v’ lincinci ukuze ukuya kuthi ga kulandelelwano lwesibini, ubude bento bunokumiselwa ukuba bulingane noqikelelo ds=dz. Ukongezelela, kwiimvavanyo ezikhankanywe ngezantsi, iimeko apho P iguquka rhoqo kwi-axis yentonga ayiyi kuthathelwa ingqalelo, oko kukuthi amandla aqhelekileyo N≈P=const. Kwiimeko ezintathu ze-equilibrium ezikhoyo kwi-element, inani elithile lamalungu linokungahoywa. Ngeempawu kunye neempawu ezivela kwikhiwane.10hlala ke kuqikelelo lokuqala lwenxaki
N=P, M’=Q, Q’=-q+Pv’’.
Amandla anqamlezayo anokupheliswa, kwaye ke M’‘=Pv’’-q ibambe. Umthetho ka-Bernoulli__M=-EI/R ubonelela ngenxaki elahlekileyo. Ijika le-axis yentonga, njengesiqhelo, ukusuka kwithiyori yokugoba umqadi, yenziwe lula ngolu hlobo lulandelayo.
Kuyenzeka ke ukuphelisa umzuzu wokugoba; kwaye nge M=-EI*v’’ umahluko wenxaki yentonga egobileyo
(EI*v’‘)’’ + Pv’’ = q. (1)
Kwimeko ekhethekileyo yokugoba okungaguqukiyo kokuqina EI=consst. i-equation (1) yenziwe lula, ngoko
EIv’‘’’ + Pv’’ = q. (1a)
Eq. (1) kunye (1a) zinomgca ku-v ngokokwenza lula okukhankanyiweyo.
Ngokwenyani, eyona meko ilula yokugoba okungaguqukiyo EI=const. ibaluleke kakhulu, esebenza njengesiseko sale mizekelo ingezantsi.
Ityala likaEuler
Iingqikelelo zemeko yakudala yokuqhobosha zi, ngaphandle kwezo zinqwenelekayo zikhankanyiwe: p=0, ngoko ke N=const.=P, kunye nokuqina okungaguqukiyo ngaphandle kokukhuhlana, okulele ngqo kwi-axis yentonga. Umahluko oqhelekileyo weequation (1a) lulandelelwano lwesine, lumgca kunye ne-homogeneous ngenxa ye-q=0. Isisombululo ngokubanzi sithi:
v(z) = A_∙_sin__αz + B∙cosαz + C∙z + D, (2)
apho A, B, C, D zizigxina ezine zohlanganiso. Ipharamitha inobungakanani obunomda ngenxa yentelekelelo EI≠0. Ngaphaya koko, α≠0 ye P>0.
Fig. 2
Ukusukela ukuba i-linear differenceeequation (1a) i-homogeneous, le ngxaki ikwasonjululwa ngu-n_∙__v(z)_, apho n iyinto engatshintshiyo engatshintshiyo. Sele isuka kuhlelo lwemathematika lwe-equation yokwahlukana (1a) kunokubonwa ukuba ubungakanani bokugoba v abunakumiselwa. Ukumisela ukudibanisa ukudibanisa A, B, C, D kwimeko Euler\ (umzobo 2) iimeko ze-contour ezilandelayo zikhoyo: Ngenxa yenkxaso echazweyo, umzuzu wokugoba u-zero kuzo zombini iziphelo zentonga, okt.
v=0 kunye M=0 ye z=0
v=0 kunye ne-M=0 ye-z=s.
Ngenxa ye- M=-EI_∙__v’‘_, kulandela ukuba M=0 lixabiso lika-v’’=0, ngoko ke iimeko ezine zecontour zifundeka:
v=0 kunye v’’=0 ye z=0
v=0 kunye v’’=0 ye z=s.
Isisombululo (2) ngaloo ndlela sikhokelela kwiinxaki zemigca ezine:
Nye.3
Ezi equation zine homogeneous zineyokuqala ebizwa ngokuba yi-trivial solution A=B=C=D=0, ehambelana ne-v(z)=0. Intonga engagotywanga v_(z_)=0 yindawo eqhelekileyo yolungelelwaniso olungenasizathu, ingakumbi amaxabiso amancinci omthwalo P. Apha, sinomdla kakhulu kwiimeko apho intonga igoba phantsi kwayo, oko kukuthi v(z)≠0. Ii-equations (3) azinaso sisombululo sincinci A, B, C, D ≠ 0 kuphela ukuba isilawuli se-coefficient silingana no-zero.
Nye. 3a
Ukususela kwimiqathango ye-buckling Δ = α4∙s∙sinαs =0 mog ukubala amaxabiso abalulekileyo PK yomthwalo. Le nxaki yaneliswa kuphela ukuba sono αs =0, oko kukuthi αKms = mπ nge m=1,2,3,… Amaxabiso ahambelanayo Euler's buckling force are PKm=EI_∙_α2Km = EI(MP/s)2. Ngexabiso ngalinye le-m, kufunyanwa amandla athile okubopha. Kwiimeko ezininzi, kuphela eyona incinci kule mikhosi inomdla, kwaye loo nto
PK1=EI(π/s)2.
Kulu guqulelo lulandelayo, kuya kubakho isalathisi m, okanye 1 ikakhulu eshiyiweyo, ebhekiselele kumthwalo ophantsi wemithwalo ebalulekileyo. Umdla ngumgca we-elastic ohambelanayo. Ukusuka kwenye (2) enye B=C=D=0 ifunyenwe. Umqathango oseleyo uthi A∙sin__αs=0. Umgca we-elastic buckling kule meko ingasentla m=1 ngulo, v(z) = A_∙sinπz/s_, apho v(z) yeye-αK resp. PK eigenfunction ehambelanayo. Ubungakanani be A buhlala bungekaqinisekiswa.
Makhe siphinde sijonge yonke indawo yomthwalo. Ngamaxabiso angenasizathu e-P, ngakumbi kwimikhosi P_<_PK1 ngu-v(z)=0, intonga ihlala ithe tye.
Ngokulayishwa “kancinci kancinci” P kuthethwa kwithiyori yakudala yozinzo uthotho olulandelelanayo lobungakanani P, apho uzinzo lwetyala lomthwalo eliqatshelweyo liya kuvavanywa kwakhona kwaye kwakhona kwinqanaba ngalinye lokulayisha P. Ngexesha lovavanyo lozinzo, ubukhulu be-P buhlala bungatshintshanga. Ukuba elinye ilizwe P lizimisele ukuba lizinzile, ngoko umthwalo unyuswa yinto ethile, kwaye ngoko uvavanyo lokuzinza luphinda luphindwe. Olu kuzimisela oluchanekileyo luyimfuneko ukuze kungabikho ukudideka kunye nohlobo lomthwalo, olusisiseko se-Shanley\ isiphumo, apho kukho ukwanda komthwalo ngelixa iziphazamiso ezincinci zisebenza ngexesha elifanayo. Xa uphonononga uzinzo ngokutsho Shanley, kwindawo yeplastiki buckling, amandla amancinane bifurcation kwenzeka kunokuba ngendlela classical ingqalelo.
Ezi ngqwalasela zilandelayo zithatha indlela yokuqala yokunyusa umthwalo: Ngokunyuka kancinci kumthwalo P ngale ndlela, PK ifikelelwe.1=EI_∙(π/s)_2okokuqala ukuya kwindawo enye ye-bifurcation ye-elastic equilibrium, kunye nomgca olula wesine njengomgca we-elastic buckling
v1(z)=f_∙_sin__π__z/s.
f=A ichaza i-amplitude engamiselwanga yomgca weelastiki. Yemithwalo _P*__>_PK1 ngokungqinelana nethiyori yomgca Δ≠0, oko kukuthi ibhalansi ayinakwenzeka apho. Kuphela yemikhosi ephezulu yokubopha PK2 njalo njalo. iyakuba Δ= kwakhona0kwaye ngokunjalo v(z)≠0. Unobangela wesi sigqibo sethiyori, esingahambelani nendlela yokuziphatha yokwenyani, ilele kumgca wolungelelwaniso lwenxaki.
Ukudityaniswa kweentonga ezicinezelweyo ezenziwe ngamacandelo amabini
Sizibekela umda kwizinti ezicinezelweyo ezinamacala amabini, kwaye kwizinti ezicinezelweyo ezenziwe ngamacandelo amathathu nangaphezulu, kuyasebenza ubudlelwane obufanayo.
Sl.3
Ngokohlobo loqhagamshelo olunqamlezileyo, iintonga zelathisi ziyahluka (umkhiwane.3a) kunye neentonga zefreyimu (umkhiwane.3e). Ngaphandle kwamaqhina anqamlezileyo, indawo nganye yentonga ibinokugoba yodwa (umkhiwane.3b). Ukuba ukuzaliswa kubuthathaka, ke intonga enye yebhanti inokugoba ngaphandle kokugoba intonga yonke. Kuba umkhiwane wentonga yenqwanqwa.3c inokuthelekiswa: ekhohlo kwisixokelelwano esinehenjisi, ekunene kumabhanti aqhubekayo; nefiya yentonga.3f ekhohlo kumakhasi oqhagamshelwano athambileyo, ekunene kuqhagamshelo oluqinileyo. Ukusuka apho, kunokubonwa ukuba ukubhitya λ_ kunempembelelo enkulu1_=imiz1/i1_. Kwilungu ngalinye lentonga, ndibekwe1=F1_∙_i12, imiz1 kukwahlukaniswa kwebala (Fig.3), ndi1 ibhekisa kwi-axis1-1(bona Isazobe.4).
Sl.4
I-buckling force of compound rods ehambelana ne-elastic buckling lines of fig.3d, okanye3g ibingumxholo wophando olubanzi lwethiyori. Ukuba intonga yenziwe ngamacandelo awodwa (umzekelo, ngembambo) okanye ukuba udibaniso olunqamlezileyo belusoloko luqhelekile kangangokuba intonga egotywe ukusuka kumalungu amabini ayahlukanga kwisiphumo sayo kwintonga enye, ngoko iyakuba σ__K_=_π__2__E/λ__y__2. Apho ichaza λ__y=sK/iy (Fig.4). Nangona kunjalo, olu xinzelelo lwe-buckling aluyi kufikeleleka ngokupheleleyo ekusebenzeni kuba akukho midibaniso eyaneleyo enqamlezileyo kuloo nto, kwaye i-elastic. Uqikelelo olwanelisayo kwiimeko ezininzi lufunyanwa ukuba sibeka ngokwesiphakamiso F. Engesser\a ukuba ukugoba koxinzelelo lwentonga ecinezelweyo eyenziwe ngamacandelo amabini kuyalingana
σ__K_=_π__2__E/λ__yi__2.
λyi yinto ebizwa ngokuba yi-aldeal slenderness.
Izibophelelo ezinqamlezayo kufuneka zanele ngenani kwaye zomelele ngokwaneleyo ukunyanzela amalungu omabini entonga ukuba asebenze kunye. Ngaphandle koxinzelelo lwesibini, amakhonkco anqamlezayo ahlala engagxininisi nje ukuba intonga ihlala ithe tye. Kungokugoba kuphela apho kufuneka bafumane amandla, kwaye kufuneka bathumele amandla anqamlezayo anyuka ngokugoba. Kwimeko apho i-elastic line
amandla anqamlezayo e-I=const. iyalingana
Q = M’ = - EI∙v’‘’.
Ngomkhiwane. 5 m inokufundwa ngoko nangoko Q(z)=PK∙v’(z). Ixabiso eliphezulu ekupheleni kwentonga
Sl.5
Imidibaniso enqamlezileyo kufuneka ikwazi ukwamkela la mandla anqamlezayo. Ekubeni umthwalo ohambelanayo yi-buckling force PK, kwanele ukuba umda wokuthwala umthwalo ufikeleleke kule nto nakwi-transverse connections - oko kukuthi ngaxeshanye kunye nentonga yonke. Ngokucacileyo, bekungayi kubakho nzuzo ukuba iikhonkco ezinqamlezayo bezinobungakanani obunamandla ngakumbi kunokuba kuyimfuneko ukufumana Q0. Kwelinye icala, amakhonkco anqamlezayo abuthathaka kakhulu anokubangela ukuba intonga ingaphumeleli kwangethuba.
Le nxaki ingentla ayinakusetyenziswa ekuqaleni kuba ubungakanani botolo olunqandayo ayaziwa. Intonga ikwi-equilibrium engakhathaliyo phantsi kwe-PK kwaye inokuthi, ubuncinci kwinqanaba lokuqala lokuqikelelwa, ithathe ixabiso elingenasizathu. Iluncedo ke ngoko, ngokwesiphakamiso sika F. Krohn-a, ukumisela ubungakanani belo buckling maxv apho intonga egobileyo ilahlekelwa ngumthamo wokuthwala ngenxa yokusilela ngenxa yokugoba. Oku kuya kwenzeka ngokuqinisekileyo ukuba indawo yesivuno ifikeleleke kwicala le-concave ye-bend (Fig.6). Ukugoba oku kukhule ngakumbi kwaye amaxesha okugoba ahambelanayo akanakusetyenziswa.
Fig. 6
Uxinzelelo olupheleleyo kwicala le-concave le-bend lihambelana nomkhiwane.6kwizinto ezifanelekileyo zeplastiki
Ukusuka apho kuza eyona swagger inkulu isenokunyamezela
ubuninziQ0 ngamandla anqamlezayo ahambelanayo ekupheleni kwentonga.
Ukuba isetyenziselwa i-σK Tetmeier's ifomu kwaye ubeke σF=3,1t/cm2kunye sK=e/2∙ λy ehambelana iy≈e/2, emva koko Krohn's ixabiso eliqikelelweyo le maxQ lifunyenwe0=F/28(Q kwi t, F kwi-cm2).
Kwimigca engafuniyo ukuxinzezeleka kwe-buckling kufunyenwe
ubuninziQ0=μK∙SK.
I-coefficient μK iyatshintsha kunye ne-slenderness yentonga, nayo ixhomekeke kwizinto eziphathekayo. Xa i-equation ingentla yahlulwe yi-coefficient yokhuseleko ngokuchasene ne-buckling ingabhalwa
dozv__Q=μ∙dozvS.
Ukudityaniswa kweenkqubo zomgca
Kwimeko yeenkqubo zomgca, kuqhelekile ukumisela ubude bokugoba sK=β∙h wentonga ebhijelwe kwiziphelo zombini kwaye amandla ayo okugoba ayi-PK=π xa kuthelekiswa.2EI/s2K nje mkhulu. Ukuthelekisa “ubude bokubopha” kuya kunikwa kule mizekelo ingezantsi.
a) Intonga ibanjelwe kuzo zombini iziphelo (EI=const.)
Sl.7
Kwimeko yomkhiwane.7ye-buckling yi PK=4π2EI/h2=4,0∙PE, ukuthelekisa “ubude bokubopha” sK=h/2kunye nomgca welastiki wokubopha v(z)=D(1-cos2πz/h).
b) Intonga ikhululekile kwelinye icala (umkhiwane.8)
Sl. 8
Kucingelwa ukuba ulwalathiso lwe-P alutshintshi njengoko intonga igoba. Emva koko (EI=consst.)
PK=π2EI/4h2=PE/4, sK=2h
v(z)=D(1-cosπz/2h).
Iimeko zecontour yesiphelo sasimahla z=h zilapha
M=0 okanye v’’=0
Q=M’-Pv’=0 okanye v’’’+a2∙v’=0.
c) Intonga ibotshelelwe kwelinye icala (fig 9)
Sl.9
Ngeemeko zecontour
v=0 kunye v’=0 ye z=0
v=0 kunye v’’=0 ye z=h
ifunyenwe EI=const. imeko buckling
sin_αh - αh∙cos_αh=0_,_
okanye ukulingana
tgα=αh. (4)
Iingcambu zale nxaki yolwandle zifumaneka kwiitheyibhile K. Hayashi's. Awona mandla asezantsi okubopha ngokwetheyibhuli PK1=4,49342/ h2∙ EI =2,046π2EI/h2.
Ubude bokuthelekisa buckling ngu sK = h / √2,046=0,699h.
d) Intonga ebambeneyo kwelinye icala nokuphazamiseka (fig.10)
Fig. 10
Siza kuqwalasela imeko ye-tip displacement yesayizi eqhubekayo. Imiqathango yecontour yaloo nto
v=0kunye v’=0 ye z=0,
v=v1kwaye v’=0 ye z=h.
Yingxaki yokulinganisa kunye nomgca we-elastic
Idinomineyitha yegama eliphambi kwe- {}-izibiyeli ziya kuba ngu-zero kwaye ukunyuswa kwe-buckling kunyuke ngaphezu kwayo yonke imida ukuba P→PK (jonga imeko ye-buckling Eq.4)). Isici sokuziphatha kwentonga ukuba ukugoba phakathi kunye nesiphelo esisezantsi kwintonga ekuqaleni kuncinci kunye nomthwalo okhulayo P kwaye utshintshe uphawu lwabo kuphela kwimithwalo ephezulu. Sl.10ibonisa ukugoba kwisiqingatha sobude.
e) Intonga eqhubekayo kwimihlaba emibini
Sl.11
Kuzo zombini iindawo zesisombululo (umkhiwane.11) siya kusebenzisa useto
Kwaye_. v(z1) = A1∙synαz1+ B1∙cosαz1+C1∙z1+ D1,_
II. v(z2) = A2∙synαz2+ B2∙cosαz2+C2∙z2+ D2.
Ukwenza lula makube (EI)1=(EI)2=EI. Ukufumana ezisibhozo ezigxininisiweyo A1, …, A2, … isebenza njengeemeko zecontour
v=0kunye v’=0 ye z1=0,
v=0kwaye v’=0 ye z2=y,
kwakunye neemeko zotshintsho phakathi kweendawo I no-II
v=0 ye z1=h i ye z2=0,
v’’ (z1=h)=v’(z2=0),
v’’ (z1=h)=v’’(z2=0).
Ii-equations ezinemiqathango zinikwe kwitheyibhile engezantsi
Ngokumisela i-determinant ye-coefficient elingana ne-zero, imeko ye-buckling ifunyenwe
Ubude bokugoba sK=0,878_h_, ngelixa ikhiwane.35mhlawumbi β=0,699. I-buckling force yehla xa ithelekiswa ne2,046:1,297ngenxa yokongezwa kwentsimi yesibini exhonyiweyo. Ukuba elinye ibala belicinezelwe ngaphezulu, ngoko ke amandla okugoba azakuphinda anyuke aye encochoyini.2,04_PE_.
Le nkcazo yembali yeefomyula ayiyona iprojekthi okanye ubungqina bokuzinza kwesakhiwo. Iingqikelelo zeklasiki zelungu elilungileyo elithe ngqo, umthwalo ophakathi kunye nommandla we-elastic awubandakanyi ukungafezeki kokuqala, uxinzelelo olushiyekileyo, i-eccentricity, ukuqina koxhumo, ukungahambi kakuhle kwezinto, ukuzinza kwecala okanye, xa kufanelekile, umlilo, isenzo se-seismic kunye nezigaba zokuhlanganisa. Ubalo lwesakhiwo esilulo kufuneka lwenziwe yinjineli yoluntu egunyazisiweyo ngokwemigaqo nemigangatho esebenzayo.