** Zolemba za akatswiri a zakale: ** zolemba ndi mafomuwa amapereka mbiri yakale ndipo si ntchito, kuwerengera kosasunthika, kufufuza mphamvu zonyamula katundu, kuwunika kwa chinthu chomwe chilipo, kapena malangizo omanga kapena kukonzanso. Mapangidwe, malingaliro ndi njira zofananira ziyenera kuyang’aniridwa ndi dongosolo, zinthu, geometry, malire ndi miyezo yoyenera. Kuwerengera kwa torsion, kukhazikika, kutopa, mafupa ndi kupsinjika chifukwa cha kupindika koletsedwa kuyenera kuchitidwa ndi mainjiniya omwe ali ndi chilolezo, ndikuwongolera pawokha pakufunika.

Masiku ano, Savo Kusić amayang’ana kwambiri mazenera amatabwa, mazenera a matabwa a aluminiyamu, mazenera amwambo, khomo ndi zopempha za mawu. Nkhaniyi idakali ngati mbiri yakale ndipo siyikuyimira ntchito yokonza mapulani.

Chiphunzitso cha Saint-Venant cha torsion (kuzunzika kwaulere)

Equation yosiyana

Cantilever mowongoka ndodo motsatira x-axis yodzaza ndi mphindi yovutitsa M kumapeto kwaulere

Sl.1

Lolani ndodo yowongoka ikhale pa imodzi mwa malekezero ake x=0ndipo mulole kuti ikwezedwe kumapeto kwina ndi mphindi yakuzunzika M (mkuyu.1). Kenako gawo lililonse limazungulira ndi ngodya inayake α(x) mozungulira mzere wina wofanana ndi axis ya ndodo, yomwe tidzatenge ngati x-axis. Ngati magawo onse ali ofanana wina ndi mzake, mzere uliwonse wowongoka wofanana ndi x-axis udzadutsa mu koyilo, ndipo ngodya α idzakhala yolingana ndi mtunda kuchokera kumapeto kokhazikika: α=ϑx, pomwe gawo lomwe limasamutsidwa mu ndege ya gawolo limatuluka (Chith.2):

v = - ndi tchimo__ψ = - ϑ x z,

w = r a cos__ψ = ϑ x y.  (1a)

Kuchuluka ϑ kumatchedwa angle ya torsion (dimension: kutalika-1, kuzungulira pautali wagawo). Ngodya ya torsion ikufanana ndi mphindi ya torsion M:

ϑ = M/GJT.   (2)

Gawo lodutsa la ndodo yokhala ndi ma y ndi z, ma radius ndi zida zometa ubweya

Sl.2

The proportionality factor GJT, kuuma kwa torsional, ndi ofanana ndi mankhwala a shear modulus G ndi chinthu JT, chomwe chimayimira zotsatira za mawonekedwe ndi kukula kwa gawolo.

Kuzungulira kwa gawoli sikuli kokha kusinthika kwa ndodo. Kuphatikiza apo, palinso kupindika kwa gawolo, mwachitsanzo, kusuntha u molunjika x-olamulira, omwe ali ndi kukula komweko kwa mfundo zofananira za magawo onse am’mbali ndipo chifukwa chake ndi ntchito yokhayo yolumikizirana mu ndege ya gawolo, ndipo mosiyana ndi katundu _M_Mlingo:

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

Ngati mawu omwe ali pamwambawa alowetsedwa m’magawo ofananirako akusamuka, zimapezedwa kuti kupsyinjika kwakukulu kuli kofanana ndi ziro, ndikusiya zigawo ziwiri zokha txy ndi τxz:

Equations of shear stress components tau xy ndi tau xz zosonyezedwa potengera kusamuka kwawo ndi ntchito ya warping

Mmodzi.3

Kusiyana kosiyana kwa vuto la torsion kumachitika potengera ma equations (3) kuika:

Kulingana Kuwiri Kosiyana ndi Kugwirizana kwa Vuto la Torsion

Mmodzi.4ndi i4b

ndi kuthetsa ma equation osiyanitsa awa a osadziwika txy ndi τxz poyambitsa ntchito yopanikizika F(y,z) kuti:

txy = - dF/dz,   τxz = + dF/dy.  (5)

Ndi izi, equation (4a) kukhutitsidwa chimodzimodzi, komanso kuchokera ku equation (4b) chiwerengero chofunikira chosiyana chimapezeka

d2F/D2+ d2F/dz2=2G__ϑ (6)

Mkhalidwe wamalire womwe umafunika kuti pakhale yankho lapadera la equation iyi umachokera ku zofunikira kuti palibe kumeta ubweya wa ubweya pa envelopu ya ndodo, yomwe, chifukwa cha conjugate chikhalidwe cha kukameta ubweya wa ubweya, ndiye kuti kupanikizika mu gawo la ndege sikuyenera kukhala ndi chigawo chimodzi chogwirizana ndi contour. Kuchokera apa, mkuyu.2:

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

choncho

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

i.e. kusiyanitsa kwathunthu kwa ntchito F kuyenera kukhala ziro, ndiko kuti, F=const. m’mphepete mwa contour.

Ngati gawolo lili ndi mizere imodzi yokha, ikhoza kuikidwa F= pamenepo0, chifukwa ndi ntchito yamagetsi, yomwe timangokonda zokhazokha, zowonjezera zowonjezereka sizigwira ntchito. Kwa magawo omwe ali ndi mizere yopitilira imodzi, nkhaniyi ndi yovuta kwambiri.

Monga tawonera mu equation (5) zotsatira za kumeta ubweya wa ubweya τxy ndi τxz pa mphambano yokhazikika ndizofanana mu kukula kwa gradient ya ntchito yopanikizika F, koma ndi perpendicular kwa izo, i.e. ili ndi kalozera kakang’ono ku mzere F=const.

Pothetsa equation yosiyana (6)) ma voltages τ monga ntchito za y, z ndi ϑ apezedwa. Ntchito yowerengera, ndithudi, kutsimikiza kwa torsion angle ϑ ndi kupsinjika maganizo, makamaka kupsinjika kwakukulu monga ntchito ya mphindi yowonongeka, motero, kutsimikiza kwa kuuma kwa gawo JT kuchokera ku equation (2) ndi torque yotsutsa WT = Mmaxτ. Kuti mupeze izi, ndikofunikira kufotokoza M ngati ntchito ya F:

Mafotokozedwe ophatikizika a mphindi yakuzunzika pa zigawo za kupsinjika ndi ntchito ya kupsinjika F

Zophatikiza zonse ziwiri zaphatikizidwezi, zomwe ziyenera kutengedwa pagawo lonselo, zitha kusinthidwa ndi kuphatikiza pang’ono. Ngati, mwachitsanzo, woyamba wa iwo aphatikizana koyamba pamzere z=const. kuchokera pomwepa y=y1 mpaka y=y2 (chith.3) ndikuganiziranso kuti mu mfundo zonse ziwirizi F=0, wapezedwa

Kuphatikizika kwapang’ono kwa mawuwa ndi chochokera ku ntchito ya kupsinjika F pakati pa malire y1ndi y2

Mtengo womwewo umapezeka kuchokera ku gawo lachiwiri, kotero kuti

Chitsanzo cha mphindi ya kuzunzika M ngati gawo limodzi la magawo awiri a kupsinjika F

Mmodzi.7

Ndime yodutsana mopanda malire yokhala ndi mzere wopingasa pakati pa nsonga zamalire y1ndi y2

Sl.3

Nkhani zina za zigawo zonse

Kusiyana kwa equation (6) ndi inhomogeneous equation ya chiphunzitso chomwe chingatheke. Choncho, kuti athetse vuto la torsion pa nkhani ya chigawo chopanda malire, njira zamaganizo zomwe zingatheke zilipo, zomwe zimathandiza kuti zizipezeka nthawi zonse. Njirazi, komabe, nthawi zambiri zimakhala zovuta kwambiri kuti zigwiritsidwe ntchito pazochitika zomwe zimangochitika. Choncho, tebulo lotsatirali likuwonetsa zotsatira za kuwerengera koteroko kwa zigawo zingapo.

Tchubu la zinthu zowuma ndi kukana kwanthawi yopumira pazigawo zolimba ndi zopanda kanthu zozungulira, zozungulira komanso zamakona anayi

Pazigawo zozungulira pafupi ndi zozungulira, JT=F ikhoza kuyikidwa4/40_Ip_, pomwe F ndi malo ndipo Ip ndi nthawi ya polar ya inertia ya gawoli.

Zindikirani pa mafomu ndi matebulo: mawu ndi zofunikira pazithunzi zosakanizidwa zimasungidwa ngati mbiri yakale. Zolemba za OCR, index marks ndi scan sizodalirika mokwanira kuwerengera. Musanagwiritse ntchito, fomula iliyonse, gawo, coefficient ndi gawo lovomerezeka liyenera kuyang’aniridwa ndi gwero lovomerezeka laukadaulo ndi muyezo wovomerezeka.

Kufananiza ndi nembanemba

Thandizo labwino pakuyerekeza kupsinjika kwa torsional, ndipo nthawi yomweyo njira yodziwira molondola imaperekedwa ndi kufanana pakati pa ntchito ya nkhawa F ya vuto la torsional ndi kupatuka kosinthika kwa nembanemba. Lolani kuti pakhale kutseguka kwapakati pakhoma lathyathyathya la chotengera chomwe chimagwirizana ndi gawo lopingasa la ndodo yodzaza ndi torsion. Nembanembayo ikatambasulidwa pachitseko ichi ndipo kupanikizika kwakung’ono p kumachitika muchombo, nembanembayo imatuluka kunja, kotero kuti kupotoza kwake ξ(y,z) kukhutitsa kusiyana kwa equation.

Kuphatikizika kosiyana kwa kupatuka kwa nembanemba yodzaza mphamvu

kumene N ndiko kugwedezeka kwa pamwamba pa nembanemba komwe kumachitika chifukwa cha mphamvu za capillary (miyeso: mphamvu pa kutalika kwa unit). Equation iyi ikugwirizana ndi equation (6), ndi chikhalidwe cha malire ξ=0ndizofanana ndi ntchito yamagetsi. Mwanjira iyi, ntchito yamagetsi F (y, z) ikhoza kupezeka pogwiritsa ntchito galasi ili ndi nembanemba ndikuthetsa vuto la torsion. Kupsyinjika τ kumagwirizana ndi kutsetsereka kwa nembanemba pokhudzana ndi y-z-ndege, kotero malo otsetsereka ndi omwe ndodo yomwe imawululidwa ku torsion imakhala ndi kupsinjika kwapamwamba kwambiri.

Geometry ya gawo la I lagawidwa m’makona atatu okhala ndi bwalo lolembedwa pamgwirizano wa nthiti ndi phazi

Sl. 4

Chithunzi cha alpha coefficient kutengera chiyerekezo cha miyeso ya magawo a gawo la I

Sl.5

Kachitidwe ka nembanemba kameneka ndi koyenera kwambiri kupeza njira zofananira ndi magawo amipanda yopyapyala. Pamene, mwachitsanzo, gawo la I lagawidwa molingana ndi mkuyu.4pa makona atatu ndipo kwa aliyense wa iwo fanizo ndi nembanemba ikuchitika padera, kuchuluka kwa voliyumu ya protrusions chifukwa adzakhala pang’ono chabe ang’onoang’ono kuposa voliyumu kuti kwenikweni mogwirizana ndi voteji ntchito. Choncho, pamene makulidwe ali _b1_ndi b2 yaying’ono, pafupifupi

JT =2JT1+ JT2,

ku _jt1_ndi JT2 stiffness factor of individual rectangles that can be counted based on the table1. Njira yabwino imapezeka pamene JT yayikidwa panthiti2 = a2b32/3 Choncho, nthitiyo ikatengedwa ngati mbali ya rectangle yaitali kwambiri. Mtengo wolondola kwambiri umapezeka molingana ndi Trayer ndi March\ kuchokera

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

kumene D ndi m’mimba mwake wa bwalo lalikulu kwambiri lolembedwa monga momwe tawonetsera mkuyu.4, ndi α akhoza kutengedwa kuchokera mkuyu.5. Kwa gawo la T limapezeka chimodzimodzi

JT = JT1+ JT2+ D4,

ku jt2 theka la mtengo wowerengedwa molingana ndi tebulo1za a=2_a2_, b=b2. Kwa magawo a L (mkuyu.6) ndizofanana ndi izi

JT = JT1+ JT2+ β D4

ku jt1 chifukwa mkono wokhuthala umatengedwa kuchokera patebulo1, pamene JT2 pakuti mwendo wocheperako umawerengedwa ngati gawo la T, ndipo β watengedwa kuchokera mkuyu.7.

geometry ya gawo la L yokhala ndi kukula kwa miyendo, makulidwe ndi utali wozungulira

Mth. 6

chithunzi cha beta coefficient kutengera chiyerekezo cha miyeso ya L-gawo

Sl.7

Powerengera kupsinjika, mphindi yopindika imagawidwa m’makona anayi: gawo lomwe limagwera pama flanges M.1=M JT2/JT; kupsinjika kwa kukameta ubweya kumawerengedwa pakatikati pa mbali yayitali ya rectangle iliyonse kutengera tebulo1. Kupsyinjika kwakukulu kumeneku sikuyenera kukhala kumeta ubweya wambiri komwe kukuwonekera mu gawoli. Momwemo, ngati ngodya ya zochitika sizinazungulidwe, τ=∞ imapezeka pamalo amenewo, kotero kuti kwa kagawo kakang’ono kwambiri kozungulira, kumeta ubweya wapamwamba kwambiri kungayembekezere pano.

Chidziwitso Chaukatswiri: masamu amodzi a angle yowoneka bwino si chilolezo choyerekeza mwatsatanetsatane ndi njira iyi yokha. Ma geometry enieni ozungulira, kulolerana, pulasitiki, ma welds, kupsinjika kotsalira, kukhazikika kwapafupi ndi kutopa kumafunikira kutengera koyenera komanso kutsimikizira kwa akatswiri.

Kwa ngodya ya mbali imodzi yomwe makulidwe ake am’mbali ndi t molingana ndi Trefftz\ ali pakuzungulira kwake r:

Chitsanzo cha kumeta ubweya wambiri pamakona ozungulira gawo

ku t0 yakhala chizindikiro champhamvu kwambiri chowerengera mwendo uliwonse malinga ndi ndondomeko yomwe yafotokozedwa apa. Kwa radii yokulirapo yozungulira, τ= ikhoza kutengedwa2__τ0.

Mapaipi Opyapyala (Mipangidwe ya Bradt)

Mu mipope yopyapyala yokhala ndi mipanda, nembanemba yophulika imakhala ndi mawonekedwe omwe akuwonetsedwa mkuyu.8, yomwe imakhala ndi ndege pamwamba pa dzenje mkati mwa chitoliro ndi malo otsetsereka omwe amazungulira ndipo amakhala pamwamba pa gawo logwira ntchito la khoma la chitoliro; malo okhotakhotawa ayenera kukhala otsetsereka ngati makoma a chitoliro ndi ocheperako pamalo oyenera. Pachifukwa ichi, kumeta ubweya wa ubweya kumagawidwa mofanana pa makulidwe a makoma ndipo ndi mosiyana ndi makulidwe a makoma, i.e. shear force T = τt sikusintha mozungulira gawolo.

Chifaniziro cha mamemba cha gawo lotsekedwa lokhala ndi mipanda yopyapyala yokhala ndi malo athyathyathya komanso opendekera pamwamba pa khoma la chitoliro

Sl. 8

Mbali ya pamwamba t_∙ds_ imalandira gawo la mphindi yovutitsa

dM = t_∙ds∙τ∙h,_

kotero mphindi yonse ili

Panoni ya kamphindi kakang’ono ka mipanda yopyapyala yokhala ndi mipanda yotseka pamwamba pa mphamvu yometa ubweya ndi malo otsekeredwa

Mmodzi.8

kumene FR pamwamba imaphimbidwa ndi mzere wapakati wodziwika ndi mizere ndi madontho mumkuyu.8. Imapezedwa kuchokera pano

Chitsanzo cha kupsyinjika kwakukulu kwa kumeta ubweya m’gawo lotsekedwa ndi mipanda yopyapyala

Mmodzi.9- Choyambirira cha Bredt\

Kuuma kwa torsional kumapezeka makamaka pamene ntchito yopindika imawonetsedwa mbali imodzi kudzera mumphindi ya torsional ndi angle ya torsion komanso mbali inayo kudzera kupsinjika kwa kukameta ubweya. Mwanjira iyi, imapezeka ngati ndodo yautali l

Equation of the deformation work of the rod element yosonyezedwa ndi mphindi, torsion angle and shear stress

kotero, kuyambitsa mtengo wa τ molingana ndi equation (8),

Kuphatikizika kwa ntchito yosintha pambuyo poyambitsa mawu a Bredt okhudza kukameta ubweya

ndiko kuti, poyerekeza ndi equation (2):

Mawu a Bradt okhudza kuuma kwapang’onopang’ono kwa gawo lotsekeka la mipanda yopyapyala ya makulidwe osiyanasiyana

Mmodzi.10

Ngati makulidwe a makomawo ndi ofanana pozungulira, ndiye kuti ndizosavuta (2. Chithunzi cha Bredt):

Mawu a Bradt a kuuma kwapang’onopang’ono kwa gawo lotsekedwa la makulidwe ofanana a khoma

Mmodzi.11

Kupsinjika kwanthawi zonse pakugwedezeka chifukwa chakupindika kwa gawo

Mawu oyambira ndi ma equation osiyana

Kusintha kwa zigawo u, equation (1b), imatsimikizira kupindika kwa magawo kuchokera ku ndege zawo. Nthawi ya torsion ikakhazikika, kupindika uku kumakhala kofanana m’magawo onse ndipo kupsinjika kwanthawi zonse σx sikuwoneka.

Nthawi zambiri, kupindika kwa gawoli, komwe kuyenera kuchitika pamaziko a _St. Lingaliro la Venant silingatheke. Ngati mphindi yokhotakhota isintha mwadzidzidzi mumtanda umodzi, kupindika kwa kukula kosiyana kudzachitika mbali zonse za gawolo, ndipo kupitiliza kwa mapindikidwewo kungasokonezedwe. Mapeto amodzi a ndodo amatha kutsekedwa kotero kuti kupindika kwa gawolo sikumaphatikizidwanso pamenepo. Zikatero, kusinthidwa kuyenera kupangidwa _St. Malingaliro a Venant. Kupsyinjika kowonjezera σx molunjika ku nsonga ya ndodo ndi mphamvu yowonjezera yometa ubweya T (kumeta kumeta T/t) kumawonekera mu ndodo, yomwe ili yokwera kwambiri mu gawo lomwe kupitiriza kwa kupunduka kwathyoka ndi komwe kumachepa kwambiri ndi mtunda wa gawoli. Pankhani ya ndodo zolimba ndi machubu, chiphunzitsochi ndi chovuta, ndipo zowonjezera zowonjezera zimachepa mofulumira kotero kuti kutsimikiza kwawo sikuli kopindulitsa nthawi zambiri. Kwa ndodo zotseguka zokhala ndi mipanda yopyapyala, kuwongolera uku ndikofunikira kwambiri ndipo kumatha kuwerengedwa mosavuta.

Pakati pagawo lotseguka lokhala ndi mipanda yopyapyala yokhala ndi zolumikizira, pakati pa kuzungulira ndi mtunda wautali

Sl.9

Sl.9akuwonetsa mzere womwe pakati pa khoma ndi gawo la ndege likudutsa (mzere wapakati wa gawolo). O ndiye pakati pa kasinthasintha wachibale wa magawo awiri oyandikana. Ngati mtunda wawo uli dx, mbali ya torsion ndi ϑ dx, kotero kuti malo osakanikirana apakati amachoka u ϑ dx. Kusamuka kumeneku kuli ndi chigawo rt ϑ dx molunjika ku gawolo, ndipo ndikutsetsereka kwa gawo lapakati pakhoma (poganizira kuti _u=_φϑ):

γ=__ϑ (rt + d__φ/ds).

Popeza kumeta ubweya pakati pa khoma ndi zero, kuyeneranso kukhala γ=0, ndiye chifukwa chake

Mafotokozedwe ophatikizika a ntchito yopindika fi pakatikati pa gawo lotseguka

Chitsanzochi chili ndi magawo atatu osagwirizana: chiyambi chomwe kutalika kwa arc s kumawerengedwera ndi makonzedwe apakati a kasinthasintha wachibale O, pomwe rt amadalira. Poyambira pomwe kutalika kwa arc s kuwerengedwera kumatha kusankhidwa kuti mtengo wopindika ukhale ziro:

Mkhalidwe woti mtengo wopendekera pagawo lopingasa ndi wofanana ndi ziro

ndipo ma coordinates apakati O angadziwike m’njira yoti mphindi chifukwa cha kupindika kwa gawolo ndi ziro:

Zinthu ziwiri zophatikizika za mphindi ziro za ntchito yopindika molingana ndi y ndi z

Zitha kuwonetsedwa kuti center of rotation potero imatsimikiziridwa kuti ikugwirizana ndi shear center yomwe ili pano kufotokozedwa ndi kufotokozedwa mwanjira ina.

Ngati kupindika kwa gawo lomwe lafotokozedwa ndi machitidwewa kupewedwa kwathunthu kapena pang’ono, kupsinjika kwanthawi zonse σx molunjika kumtunda kwa ndodo kuyenera kuwonekera. Kuyang’ana mozama kukuwonetsa kuti kupsinjika kumeneku kungatengedwe kukhala kolingana ndi ntchito yopindika φ: σx=k__φ, pomwe φ imadalira s ndi k pokha pa x. Malinga ndi lamulo la Hooke:

σx = E_∂u/∂x = Eφ dϑ/dx_, (12)

iyenera kukhala k=E d__ϑ/dx. Kupsinjika kwanthawi zonse σx kumatchedwa kupindika kwa gawo. Poganizira ma equation omwe ali pamwambapa, amapanga dongosolo lofanana la mphamvu mu gawo lirilonse, dongosolo la mphamvu chifukwa cha kupindika kwa gawolo.

Torque yonse imakhala ndi magawo awiri: imodzi mwazo M1=GJT__ϑ imayamba chifukwa cha kumeta ubweya wonyezimira woperekedwa ndi St. Malingaliro a Venant, ndi ena M2 zimachitika chifukwa cha kupindika kwa gawolo:

Kufanana kosiyana kwa mphindi yakuzungulira kwathunthu ndi Saint-Venant ndi gawo lopindika

Mmodzi.13

Mphindi ya gawo la inertia monga chophatikizika cha masikweya a ntchito yopindika ndi makulidwe a khoma

Popeza nthawi M yaperekedwa ngati ntchito ya x, mawu awa akuyimira equation yosiyana ya ngodya ya torsion ϑ. Equation iyi ikathetsedwa, _M ikhoza kuwerengedwa1_ndi M2, motero kupsinjika ndi zovuta zonse.

Yankho ndi ntchito

Pamene mphindi ya torsion M imakhala yokhazikika, yankho lalikulu la equation (13) ndi:

General solution of the torsion angle differential equation with integration constants C1ndi C2

Kuphatikiza kokhazikika C1, C2 ziyenera kutsimikiziridwa kuchokera ku malire awiri.

a) Mapeto omangika mwamphamvu x=0(chith.1)

Pamapeto pake ndi u≡0, kutengera equation (1b) ϑ=0. Ngati ndodoyo ndi yayitali kwambiri (αl>>1), ndiye C1=0ndi c2= -M/GJT. Pankhani ya ndodo zazifupi, maonekedwe a kupsinjika maganizo chifukwa cha kupindika kwa gawolo kumakhudzidwa ndi chikhalidwe chomwe chili kumapeto kwa ndodo. Ngati kupindika kwa gawo sikuletsedwa pamalopo, padzakhala σx≡0ndi dϑ/dx=0. Imapezedwa kuchokera pano

Mafotokozedwe a kuphatikiza kokhazikika C1ndi C2kwa ndodo yokhala ndi malire

b) Symmetrical torsion load malinga ndi mkuyu.10

Pa theka lakumanzere la ndodo, mphindi yopindika ndi -M/2, ndi kumanja +M/2. Pankhani ya torsion yaulere, zigawo za kumanzere ndi kumanja kwapakati pa ndodo zikanakhala zokhotakhota mosiyana, choncho kupitiriza kwa kusinthika sikungasungidwe. Chifukwa chake, pamalo x=0mphindi yonse ya torsion iyenera kusamutsidwa kudzera muzopsinjika zomwe zimachitika chifukwa cha kupindika kwa gawolo, chifukwa chake mu gawo ili M.1=0ndipo chifukwa chake ϑ=0. Panthawiyi, kachitidwe ka mphamvu kakuchitapo kanthu kuti chigawocho chikhale chowongoka, ngakhale kuti zigawo zomwe zili kutali kwambiri ndi pakati pa ndodo. Ngati, kuwonjezera apo, pamafunika kuti malekezero a ndodo akhale ndi zopsinjika σx≡0, malire amodzi akupezeka pa theka lililonse la ndodo, choncho ndi theka loyenera

Torsion angle solution ya theka la ndodo zopakidwa molingana

Ndodo yomangika mbali zonse ziwiri ndikudzazidwa ndi mphindi yopumira pakati

Mkuyu. 10

c) Mphindi yakunja M pamalo osagwirizana (mkuyu.11)

Pachifukwa ichi, yankho ϑ la mbali zonse ziwiri za ndodo liyenera kulembedwa mosiyana, kotero kuti zonse zinayi zokhazikika C ziwonekere.1, C2, C3, C4. Kuphatikiza apo, nthawi zozunzika Ma, Mb sizikudziwikanso. Ma equation asanu ndi limodzi alipo: chikhalidwe chopitilira ϑ (chofotokozedwa ndi u) ndi dϑ/dx (chofotokozedwa ndi σx) pamalo olemetsa, chikhalidwe chimodzi kumapeto kwa ndodo (mwachitsanzo, kulimba kolimba ϑ=0, kapena kupinda mosasokoneza, dϑ/dx=0), chikhalidwe cha kusanja ndi mphindi -Ma+Mb=M ndipo potsiriza chikhalidwe chakuti zigawo zomalizira sizimazungulirana wina ndi mzake: ∫ ϑdx =0.

Ndodo yomangika mbali zonse ziwiri ndi mphindi pamalo osagwirizana ndi chithunzi cha zomwe Ma ndi Mb

Sl.11

** Cholemba chomaliza: ** kusankha kwachitsanzo cha torsion kumadalira gawo lotseguka kapena lotsekedwa, kuwonda, njira yothandizira, malo olowera kamphindi komanso mwayi wopindika kwaulere. Pazinthu zenizeni, malire onyamula katundu ndi ntchito, tsatanetsatane wamba, zolumikizira, kutopa ndi kukhazikika ziyenera kuyang’aniridwa, osati njira imodzi yokhayokha kuchokera m’nkhaniyo.