Okuqukethwe kwengcweti yenqolobane: umbhalo namafomula adlulisa isethulo sethiyori esingokomlando futhi akuyona iphrojekthi, ukubala okumile, ukuhlolwa kwamandla okuthwala umthwalo, ukuhlolwa kwesici esikhona, noma imiyalelo yokwakha noma yokuvuselela. Ukuqokwa, ukuqagela kanye namaphethini alinganiselwe kufanele kuhlolwe kuqhathaniswa nesistimu ethile, impahla, ijometri, izimo zemingcele namazinga asebenzayo. Ukubalwa kokugoqa, ukuzinza, ukukhathala, amalunga nokucindezeleka ngenxa yokugoba okuvinjiwe kufanele kwenziwe unjiniyela onelayisensi, ngokulawula okuzimele lapho kudingeka.

Namuhla, i-Savo Kusić igxile emafasiteleni okhuni, amafasitela okhuni-aluminium, amafasitela ngokwezifiso, umnyango kanye nezicelo zekhotheshini. Lesi sihloko sihlala siyingobo yomlando yobungcweti futhi asimeleli isevisi yedizayini yesakhiwo.

Ithiyori kaSaint-Venant ye-torsion (i-torsion yamahhala)

Isibalo esihlukile

Induku eqondile ye-Cantilever eduze kwe-eksisi engu-x elayishwe umzuzu wokuzungeza u-M ekugcineni kwamahhala

Sl.1

Vumela induku eqondile imiswe kwenye yeziphetho zayo x=0futhi mayilayishwe ngakolunye uhlangothi ngomzuzu wokuhlushwa M (isig.1). Khona-ke isigaba ngasinye saso sizungeza nge-engeli ethile α(x) eduze komugqa othile ohambisana ne-eksisi yenduku, esizoyithatha njenge-eksisi x-. Uma zonke izigaba zilingana nenye, noma yimuphi umugqa oqondile ohambisana ne-eksisi ka-x uzodlulela kukhoyili, futhi i-engeli α izolingana nebanga elisuka ekugcineni okungaguquki: α=ϑx, lapho okuphuma khona ingxenye endizeni yesigaba ivela (Fig.2):

v = - r a isono__ψ = - ϑ x z,

w = r a cos__ψ = ϑ x y.  (1a)

Inani ϑ libizwa ngokuthi i-torsion angle (ubukhulu: ubude-1, ukuzungezisa ngobude beyunithi). I-engeli ye-torsion ilingana nenkathi ye-torsion M:

ϑ = M/GJT.   (2)

Ingxenye enqamulayo yenduku enezixhumanisi zika-y no-z, i-radius nezingxenye zengcindezi yokugunda

Fig. 2

I-proportionality factor GJT, ukuqina kwe-torsional, ilingana nomkhiqizo we-shear modulus G kanye ne-factor JT, emele umphumela womumo nosayizi wesigaba.

Lokhu kujikeleza kwesigaba akukona ukuphela kokuguqulwa kwenduku. Ngaphezu kwalokho, kukhona futhi ukugoba kwesigaba esiphambanayo, okungukuthi ekuthuthweni u ekuqondeni kwe-x-eksisi, enobukhulu obufanayo bamaphuzu ahambisanayo azo zonke izigaba eziphambanayo futhi ngenxa yalokho kuwumsebenzi wezixhumanisi endizeni yesigaba, futhi ngenye indlela ilingana nomthwalo M_i-engeli M.

u = u(y,z) = ϑ ∙ φ(y,z), dφ/dx=0.  (1b)

Uma izinkulumo ezingenhla zethulwa ezilinganisweni ezihambisanayo zokususwa, kutholwa ukuthi izingcindezi ezivamile eziyinhloko zilingana noziro, kushiya izingcindezi zengxenye ezimbili kuphela τxy kanye no-τxz:

Izibalo zezingxenye zokucindezeleka kwe-shear tau xy kanye ne-tau xz ezivezwa ngokuya ngokugudluka kanye nomsebenzi wokuguquguquka

Eyodwa.3

I-equation ehlukile yenkinga ye-torsion itholakala ngokusekelwe kuzibalo (3) ukubeka:

Ibhalansi Emibili Ehlukile Nezilinganiso Ezihambisanayo Zenkinga Ye-Torsion

Eyodwa.4nami4b

kanye nokuxazulula lezi zibalo ezihlukile kokungaziwa τxy kanye ne-τxz ngokwethula umsebenzi wengcindezi F(y,z) othi:

τxy = - dF/dz,   τxz = + dF/dy.  (5)

Ngalokhu, i-equation (4a) aneliseke ngokufanayo, futhi kusukela kuzibalo (4b) kutholwa isibalo esidingekayo somehluko

d2F/D2+ d2F/dz2=2G__ϑ (6)

Isimo somngcele esidingekayo ukuze kuxazululwe isixazululo esiyingqayizivele salesi sibalo sitholakala ekufuneni ukuthi akukho ukucindezeleka kwe-shear emvilophini yenduku, okuvela kuyo, ngenxa yemvelo ehlangene yokucindezeleka kwe-shear, kulandela ukuthi ukucindezeleka endizeni yesigaba akumele kube nengxenye ehambisana nayo eduze kwe-contour. Kusukela lapha, fig.2:

dy/dz = _τxy/_τxz = - (dF/dz) / (dF/dy)

ngakho-ke

dF/dy dy + dF/dz dz =0,

okungukuthi, umehluko ophelele womsebenzi F kumelwe ube uziro, okungukuthi, kumelwe ube F=i-const. eduze kwekhonta.

Uma ingxenye inekhonsathi eyodwa kuphela, ingavele ibekwe F= kuyo0, ngoba ngomsebenzi we-voltage, empeleni sinesithakazelo kuphela kokuphuma kokunye, i-adbitrary additive constant ayidlali indima. Ezigabeni ezinekhonsathi engaphezu kweyodwa, lolu daba luyinkimbinkimbi kakhulu.

Njengoba kubonakala ku-equation (5) umphumela wokucindezelwa kwe-shear τxy kanye no-τxz endaweni engafanele yomgwaqo ilingana ngobukhulu negradient yomsebenzi wokucindezeleka F, kodwa incike kuwo, okungukuthi inokuqondisa kwe-tangent kulayini F=const.

Ngokuxazulula i-equation ehlukile (6)) ama-voltage τ njengemisebenzi ye-y, z kanye no-ϑ ayatholakala. Umsebenzi wokubala, yiqiniso, ukunqunywa kwe-orsion angle ϑ kanye nokucindezeleka, ikakhulukazi ukucindezeleka okukhulu njengomsebenzi womzuzu wokuvivinya umzimba, ngakho-ke, ukunqunywa kokuqina kwesigaba JT kusukela ku-equation (2) kanye ne-torque yokumelana WT = Mmaxτ. Ukuthola lokhu, kuyadingeka kuphela ukuveza M njengomsebenzi we-F:

Isisho esiphelele somzuzu wokucindezeleka phezu kwezingxenye zokucindezeleka nomsebenzi F

Kokubili ukufinyezwa kwalokhu okubalulekile, okufanele kuthathwe kuso sonke isigaba, kungaguqulwa ngokuhlanganisa ingxenye. Uma, isibonelo, eyokuqala ihlanganisa kuqala kulayini z=const. ukusuka endaweni yokukhonkolo y=y1 kuze kube y=y2 (isib.3) futhi ucabangele ukuthi kuwo womabili amaphuzu F=0, iyatholakala

Ukuhlanganiswa kwengxenye yetemu nokususelwe kokusebenza kwengcindezi F phakathi kwemikhawulo y1kanye y2

Inani elifanayo litholakala kokubalulekile kwesibili, ukuze

Iphethini ye-torsion moment M njengengxenye ephindwe kabili yomsebenzi wokucindezeleka F

Eyodwa.7

Ingxenye enqamulayo engafanele enomugqa ovundlile phakathi kwamaphoyinti omngcele y1kanye y2

Sl.3

Ezinye izimo zezigaba ezigcwele

I-equation ehlukile (6) isibalo esilinganayo sethiyori engaba khona. Ngakho-ke, ukuze kuxazululwe inkinga ye-torsion esimweni se-cross-section engafanele, izindlela ze-theory engenzeka ziyatholakala, ezivumela ukuthi ihlale itholakala. Lezi zindlela, nokho, ngokuvamile ziyinkimbinkimbi kakhulu ukuthi zingasetshenziswa ezimweni ezingazodwana ezivela ekusebenzeni. Ngakho-ke, ithebula elilandelayo libonisa imiphumela yezibalo ezinjalo zezigaba eziningana.

Ithebula lezinto zokuqina kanye nezikhathi zokumelana nezimo eziqinile nezingenalutho eziyindilinga, i-elliptical kanye nezigaba eziwunxande

Ezingxenyeni eziphambanayo eziseduze nesiyingi, JT=F ingafakwa4/40_Ip_, lapho F kuyindawo futhi Ip iyinkathi ye-polar ye-inertia yesigaba.

Qaphela kumafomula namathebula: izinkulumo namanani ezithombeni eziskeniwe kugcinwa njengomthombo womlando. Umbhalo we-OCR, amamaki wenkomba nokuskena akuthembekile ngokwanele ukubala. Ngaphambi kokusetshenziswa, ifomula ngayinye, iyunithi, i-coefficient kanye nendawo yokuqinisekisa kufanele ihlolwe emthonjeni osemthethweni osemthethweni kanye nezinga elivumelekile.

Ukufana nolwelwesi

Usizo oluhle lokulinganisa ukucindezeleka kwe-torsional, futhi ngesikhathi esifanayo inqubo yokuzimisela kwabo okunembile inikezwa isifaniso phakathi komsebenzi wokucindezeleka F wenkinga ye-torsional kanye nomthwalo oguquguqukayo we-membrane. Makube nokuvuleka okumaphakathi odongeni oluyisicaba lomkhumbi oluqondana nendawo enqamulayo yenduku elayishwe ku-torsion. Lapho ulwelwesi lweluliwe phezu kwalokhu kuvuleka futhi ukucindezela okuncane okweqile p kubangelwa emkhunjini, ulwelwesi luyaqhuma ngaphandle, ukuze ukuchezuka kwalo ξ(y,z) kwenelise isibalo esihlukanisayo.

Isibalo esihlukile sokuchezuka kolwelwesi olulayishwe ingcindezi

lapho N kuwukungezwani kwendawo kulwelwesi olubangelwa amandla e-capillary (ubukhulu: amandla ngeyunithi ngayinye ubude). Lesi sibalo sihambisana nesibalo (6), kanye nesimo somngcele ξ=0kuyafana nomsebenzi we-voltage. Ngale ndlela, umsebenzi we-voltage F(y,z) ungatholakala kusetshenziswa lesi sibuko esinolwelwesi futhi ngaleyo ndlela kuxazululwe inkinga ye-torsion. I-stress τ ihambisana nomthambeka we-membrane ngokuphathelene nendiza y-z-, ngakho-ke indawo ewumqansa kakhulu yilapho induku evezwe ku-torsion inokucindezeleka okukhulu kwe-shear.

Ijiyomethri ye-I-section ihlukaniswe yaba onxande abathathu abanendingilizi eqoshiwe endaweni ehlangene yombambo nonyawo

Sl.4

Umdwebo we-alpha coefficient kuye ngesilinganiso sobukhulu bezingxenye zesigaba se-I

Sl.5

Le nqubo ye-membrane ifaneleka kakhulu ukuthola amaphethini acishe abe yizingxenye ezinezindonga ezincane. Lapho, isibonelo, isigaba se-I sihlukaniswa ngokomkhiwane.4kuma-rectangles amathathu futhi ngayinye yazo isifaniso ne-membrane senziwa ngokuhlukana, isamba semiqulu ye-protrusions ewumphumela sizoba sincane kancane kunomthamo ohambelana ngempela nomsebenzi we-voltage. Ngakho-ke, uma ubukhulu bungu-b1 kanye b2 encane, cishe

JT =2JT1+ JT2,

lapho JT1 kanye JT2 izici zokuqina zonxande abangabodwana abangabalwa ngokusekelwe kuthebula1. Indlela engcono itholakala uma i-JT ibekwe ubambo2 = a2b32/3, ngakho-ke, lapho ubambo lubhekwa njengengxenye yonxande olude kakhulu. Inani elinembe nakakhulu litholwa ngokusho kwe-Trayer kanye no-March\ kusuka

JT =2JT1+1/3a2b32+2 D4,

lapho D kuwububanzi besiyingi esikhulu kunazo zonke esibhalwe kufig.4, futhi α ingathathwa emkhiwaneni.5. Engxenyeni ye-T itholakala ngokufanayo

JT = JT1+JT2+ α D4,

lapho JT2 ingxenye yenani elibalwe ngokwethebula1okwe a=2_a2_, b=b2. Okwezigaba ze-L (Fig.6) kuyafana nalokho

JT = JT1+ JT2+ β D4

lapho JT1 ngoba ingalo ewugqinsi ithathwa ngqo etafuleni1, ngenkathi JT2 ngoba umlenze ozacile ubalwa njengengxenye T, futhi β uthathwa emkhiwaneni.7.

Ijiyomethri yesigaba L enobukhulu bemilenze, ukujiya kanye ne-radius yokujikeleza

Fig. 6

Umdwebo we-coefficient ye-beta kuye ngesilinganiso sobukhulu besigaba L

Sl.7

Lapho kubalwa ukucindezelwa, umzuzu we-torsional uhlukaniswa ngonxande abakhona: ingxenye ewela kuma-flanges M.1=M JT2/JT; ukucindezelwa kokugunda bese kubalwa endaweni emaphakathi yohlangothi olude lonxande ngamunye ngokusekelwe etafuleni1. Okukhulu kakhulu kwalokhu kugcizelela akufanele kube ukucindezelwa kokugunda okukhulu okuvela esigabeni. Okungukuthi, uma i-engeli yesigameko ingafinyeziwe, τ=∞ itholakala kuleyo ndawo, ukuze irediyasi encane kakhulu yokuzungezisa, kulindeleke ukucindezelwa kwe-shear okuphezulu kakhulu lapha.

Inothi Lobunjiniyela: ubunye bezibalo be-engeli ye-acute ekahle akuyona ilayisensi yokulinganisa imininingwane yangempela ngale phethini elinganiselwe iyodwa. Ijiyomethri eyindilinga yangempela, ukubekezelelana, ipulasitiki, amashisela, izingcindezi ezisalelayo, ukuzinza kwendawo nokukhathala kudinga ukumodela okufanele kanye nokuqinisekiswa kochwepheshe.

Okwe-engeli yohlangothi olulodwa ugqinsi lwalo oluseceleni okungu-t ngokuya ngokuthi Trefftz\ kusekuzungezweni kobubanzi r:

Iphethini yobukhulu bokucindezelwa kwe-shear ekuzungezeni kwesigaba sekhona

lapho nge τ0 imakwe umkhawulo kagesi olinganiselwe obalwa ngomlenze ngamunye ngokusekelwe kunqubo echazwe lapha. Ku-radii enkulu ezungezayo, τ= ingatholwa2__τ0.

Amapayipi Anezindonga Ezincane (Amaphethini ka-Bradt)

Emapayipini anezindonga ezincane, ulwelwesi oluqhumayo lunomumo oboniswe kufig.8, equkethe indiza ngaphezu kwesikhala esingenalutho ngaphakathi kwepayipi kanye nendawo ezungezile ezungezile futhi elele ngaphezu kwengxenye ephumelelayo yodonga lwamapayipi; le ndawo ethambekele kufanele ibe ngaphezulu uma izindonga zamapayipi zincane endaweni efanele. Kulesi simo, ukucindezelwa kwe-shear kusakazwa ngokulinganayo phezu kobukhulu bezindonga futhi kuhambisana ngokuphambene nobukhulu bezindonga, okungukuthi shear force T = τt ayishintshi eduze komjikelezo wesigaba.

Isifaniso se-membrane sengxenye evaliwe enezindonga ezincanyana enendawo eyisicaba futhi etshekile ngaphezu kodonga lwamapayipi

Sl. 8

I-elementi engaphezulu t_∙ds_ ithola ingxenye yesikhathi se-torsional

dM = t_∙ds∙τ∙h,_

ngakho-ke isikhathi esiphelele

Iphethini yesikhathi sokunyakaziswa kwengxenye evaliwe enezindonga ezincane ngaphezu kwamandla okugunda nendawo evalekile

Eyodwa.8

lapho i-FR surface imbozwe umugqa ophakathi omakwe ngemigqa namachashazi emkhiwaneni.8. Itholakala lapha

Iphethini yokucindezela okukhulu kwe-shear esigabeni esivaliwe esinezindonga ezincane

Eyodwa.9- Iphethini yokuqala Bredt\

Ukuqina kwe-torsional kutholakala kalula lapho umsebenzi wokuguquguquka uvezwa ngakolunye uhlangothi ngokusebenzisa i-torsional angle kanye ne-torsion angle futhi ngakolunye uhlangothi ngokucindezela kwe-shear. Ngale ndlela, kutholwa intonga yobude l

Isibalo somsebenzi wokuguquguquka wentonga evezwa umzuzwana, i-angle yokuguquguquka nokucindezelwa kokugunda

ngakho-ke, ukwethula inani lika-τ ngokuvumelana nesibalo (8),

I-equation yomsebenzi wokuguquka ngemva kokwethula inkulumo ka-Bredt yengcindezi yokugunda

okungukuthi, ngokuqhathanisa ne-equation (2):

Isisho sika-Bradt sokuqina kokuqina kwengxenye evaliwe enezindonga ezincanyana zogqinsi oluguquguqukayo

Eyodwa.10

Uma ubukhulu bezindonga bufana nxazonke, khona-ke kulula (2. Iphethini ka-Bredt):

Isisho sika-Bradt sokuqina kokuqina kwengxenye evaliwe yobukhulu obulinganayo bodonga

Eyodwa.11

Ukucindezelwa okuvamile ekunyakazeni ngenxa yokugoba kwesigaba

Amagama ayisisekelo kanye nesibalo esihlukile

Ukususwa kwengxenye u, isibalo (1b), inquma ukugoba kwezigaba ezindizeni zazo. Uma umzuzu we-torsion ungashintshi, lokhu kugoba kuyefana kuzo zonke izigaba futhi izingcindezi ezijwayelekile σx aziveli.

Ezimweni eziningi, ukugoba kwe-cross-section, okufanele kuvele ngesisekelo _St. Ithiyori kaVenant ayinakwenzeka. Uma umzuzu we-torsional ushintsha kungazelelwe esigabeni esisodwa esiphambanayo, ukugoba kobukhulu obuhlukile bekuzokwenzeka nhlangothi zombili zesigaba esiphambanayo, futhi ukuqhubeka kokuguqulwa kuzophazamiseka. Umkhawulo owodwa wenduku ungaboshelwa kangangokuthi ukugoba kwesigaba kukhishwe ngokuphelele kulelo phuzu. Ezimweni ezinjalo, kufanele kwenziwe isichibiyelo _St. Imibono kaVenant. Ukucindezelwa okungeziwe okungu-σx kuhlangothi lwe-eksisi yenduku namandla okugunda okungeziwe T (izingcindezi zokugunda T/t) avela erothini, okuphakeme kakhulu esigabeni lapho ukuqhubeka kokuguqulwa kwephulwa khona futhi ehla kakhulu ngebanga ukusuka kulesi sigaba. Endabeni yezinduku eziqinile namashubhu, lo mbono uyinkimbinkimbi, futhi ama-voltages angeziwe ayancipha ngokushesha kangangokuthi ukuzimisela kwabo akuzuzisi ezimweni eziningi. Ezindongeni ezivulekile zephrofayili enezindonga ezincane, lokhu kulungiswa kubaluleke kakhulu futhi kungabalwa kalula.

Umugqa omaphakathi wesigaba esivulekile esinezindonga ezincane ezinezixhumanisi, isikhungo sokujikeleza nebanga eliphansi

Sl.9

Sl.9ikhombisa umugqa lapho kuphambana khona indawo ephakathi yodonga kanye nendiza yesigaba (umugqa omaphakathi wesigaba). O iyisikhungo sokuzungezisa okuhlobene kwezigaba ezimbili ezincikene. Uma ibanga labo lingu-dx, i-engeli ye-torsion ithi ϑ dx, ngakho-ke indawo engafanele yomugqa omaphakathi idlula u ϑ dx. Lokhu kususwa kunengxenye rt ϑ dx ekuqondeni kwe-tangent eya esigabeni, futhi kuwukushelela kwe-elementi yendawo emaphakathi yodonga (kucatshangelwa ukuthi _u=_φϑ):

γ=__ϑ (rt + d__φ/ds).

Njengoba ingcindezi yokugunda endaweni emaphakathi yodonga inguziro, kufanele futhi kube γ=0, ngakho-ke

Isisho esiphelele somsebenzi we-curvature fi eduze komugqa omaphakathi wesigaba esivuliwe

Le phethini iqukethe amapharamitha amathathu aphikisayo: umsuka lapho ubude be-arc s bubalwa khona kanye nezixhumanisi ezimaphakathi nokuzungezisa okuhlobene O, lapho okuthi rt kuncike khona. Indawo yokuqala lapho kubalwa khona ubude be-arc s ingakhethwa ukuze inani elimaphakathi lokugoba libe nguziro:

Isimo sokuthi inani elichazayo lomsebenzi wokugoba endaweni ephambanayo lilingana noziro

futhi izixhumanisi zesikhungo O zinganqunywa ngendlela yokuthi izikhathi ngenxa yokugoba kwesigaba zibe uziro:

Izimo ezimbili ezibalulekile zezikhathi ezinguziro zomsebenzi wokugoba ngokuya ngezixhumanisi y kanye no-z

Kungaboniswa ukuthi isikhungo sokuzungezisa kunqunywa ukuthi siqondane nesikhungo sokugunda esi lapha kuchazwe futhi kuchazwe ngenye indlela.

Uma ukugoba kwesigaba esichazwe yilawa maphethini kuvinjwe ngokuphelele noma kancane, ukucindezelwa okujwayelekile okuthi σx kuhlangothi lwe-eksisi yenduku kufanele kuvele. Ukuhlola eduze kubonisa ukuthi lokhu kucindezeleka kungathathwa njengokulingana nomsebenzi we-curvature φ: σx=k__φ, lapho φ incike kuphela ku-s naku-k kuphela ku-x. Ngokomthetho kaHooke:

σx = E_∂u/∂x = Eφ dϑ/dx_, (12)

kufanele kube k=E d__ϑ/dx. Izingcindezi ezijwayelekile σx zibizwa ngokuthi izingcindezi zesigaba. Ngokucabangela ukulinganisa okungenhla, bakha uhlelo lokulinganisa lwamandla esigabeni ngasinye, uhlelo lwamandla ngenxa yokugoba kwesigaba.

Itorque ephelele iqukethe izingxenye ezimbili: eyodwa yazo M1=I-GJT__ϑ ivela ngenxa yokucindezelwa kokushefa okunikezwe ngu-St. Ithiyori ka-Venant, kanye nenye ethi M2 kwenzeka ngenxa yokugoba kwesigaba:

Izibalo ezihlukile zenani eliphelele lesikhathi sokuvivinya umzimba ne-Saint-Venant nengxenye egobile

Eyodwa.13

Isikhathi somkhakha we-inertia njengengxenye yesikwele somsebenzi wokugoba ngokuqina kodonga

Njengoba isikhathi M sinikezwa njengomsebenzi othi x, lesi sisho simelela isibalo esihlukile se-engeli ye-torsion ϑ. Uma le zibalo isixazululiwe, M ingabalwa1 kanye no-M2, ngakho-ke zonke izingcindezi nezinkinga.

Isixazululo nezinhlelo zokusebenza

Lapho umzuzu we-torsion M uhlala njalo, isisombululo esijwayelekile se-equation (13) yilokhu:

Isixazululo esivamile se-engeli ye-torsion ehlukanisiwe nezilinganiso ezihlanganisayo C1kanye no-C2

Ukuhlanganisa okungaguquki C1, C2 kufanele kunqunywe kusukela ezimeni zemingcele emibili.

a) Isiphetho esiboshwe ngokuqinile x=0(fig.1)

Ekugcineni ngu-u≡0, ngakho ngokusekelwe esilinganisweni (1b) ϑ=0. Uma induku iyinde kakhulu (αl>>1), bese C1=0kanye C2= -M/GJT. Endabeni yezinduku ezimfushane, ukubonakala kokucindezeleka ngenxa yokugoba kwesigaba kuthinteka isimo ekugcineni kwenduku. Uma ukugoba kwesigaba kungavinjelwanga kuleyo ndawo, kuzoba khona okuthi σx≡0kanye ne-dϑ/dx=0. Itholakala lapha

Izinkulumo zokuhlanganisa okungaguquki C1kanye no-C2induku enemibandela yomngcele

b) Umthwalo we-Symmetrical torsion ngokusho komkhiwane.10

Engxenyeni yesokunxele yenduku, umzuzu wokuvivinya umzimba ngu--M/2, futhi kwesokudla +M/2. Endabeni ye-torsion yamahhala, izigaba ezingakwesokunxele nangakwesokudla phakathi kwenduku zizosonteka ngokuphambene, ngakho-ke ukuqhubeka kwe-deformation ngeke kugcinwe. Ngakho-ke, endaweni x=0sonke isikhathi sokuvivinya umzimba kufanele sidluliselwe ngokucindezeleka okwenzeka ngenxa yokugoba kwesigaba esiphambene, ngakho-ke kulesi sigaba esiphambene M1=0ngakho-ke ϑ=0. Kuleli qophelo, uhlelo lwamandla lusebenza ukuze kuqinisekiswe ukuthi isigaba sihlala siqondile, nakuba izingxenye ezilele kude nendawo ephakathi kwejika lenduku. Uma, ngaphezu kwalokho, kudingeka ukuthi iziphetho zenduku zibe nezingcindezi σx≡0, isimo somngcele owodwa sitholakala engxenyeni ngayinye yenduku, ngakho-ke iyingxenye efanele

Isixazululo se-engeli ye-Torsion sengxenye yenduku elayishwe ngokulinganayo

Induku eboshiwe emikhawulweni yomibili futhi ilayishwe isikhashana esinyakazayo phakathi

Fig. 10

c) Umzuzu wangaphandle M endaweni engafanele (isib.11)

Kulokhu, ikhambi elithi ϑ lazo zombili izingxenye zenduku kufanele libhalwe ngokuhlukana, ukuze kuvele ingqikithi yama-constants amane C.1, C2, C3, C4. Ngaphezu kwalokho, izikhathi zokuhlushwa Ma, Mb nazo azaziwa. Izibalo eziyisithupha ziyatholakala: umbandela wokuqhubeka we-ϑ (okuvezwa ngu-u) kanye no-dϑ/dx (okuvezwa ngu-σx) endaweni yokulayisha, umbandela owodwa ekupheleni kwenduku (isb. ukuqinisa okuqinile ϑ=0, noma ukugoba okungaphazanyiswa, dϑ/dx=0), isimo sebhalansi ngezikhathi ezithile -Ma+Mb=M futhi ekugcineni isimo sokuthi izigaba zokugcina azijikelezi ngokuhloniphana: ∫ ϑdx =0.

Induku eboshwe kuzo zombili iziphetho ngesikhashana endaweni engafanele kanye nomdwebo wokusabela kuka-Ma kanye no-Mb

Sl.11

Inothi lokugcina: ukukhethwa kwemodeli ye-torsion kuncike engxenyeni evulekile noma evaliwe, ubuncane, indlela yokusekela, indawo yokufaka isikhashana kanye nethuba lokugoba mahhala. Ngesici sangempela, umkhawulo wokuthwala umthwalo kanye nokusevisa uthi, imininingwane yendawo, amalunga, ukukhathala nokuzinza kufanele kuhlolwe, hhayi nje ifomula eyodwa ehlukanisiwe ku-athikili.