Mphamvu zanthawi zonse pa ndodo zowongoka ndi ndodo zokhota pang’ono
Tanthauzo la mphamvu zodulira gawo
Tiyerekeze kuti ndodo yolunjika yanyamula ndi mphamvu za njira zosiyanasiyana, zomwe tingoganiza kuti zonse zili mu ndege imodzi (ndege ya mphamvu) yomwe imadutsa mu mzere wa ndodo (mzere wolumikiza malo a pakati pa magawo odutsana).
Chith. 1
Kuti tiwerenge zovuta zomwe zimagwira ntchito mu gawo lina la mtanda n – n (chith. 1), ndikofunikira kudziwa mphamvu imene imadutsa kudzera mu mtanda umenewu kuchokera pa mbali imodzi ya ndodo kupita ku ina. Mwachiwonekere, pa kukula ndi malo imafanana ndi zotsatira za mphamvu zonse zomwe zimakhudza mbali imodzi ya ndodo. Zotsatirazi zimagawanika kukhala zigawo mu dongosolo la ma koordinati lomwe x-osi yake imagwirizana ndi osi ya ndodo, ndipo z-osi yake ndi mzere womwe ndege ya mtanda imadula ndege ya mphamvu. Chigawo cholowera m’bali ya osi z chimatchedwa mphamvu ya transversal Q kapena Qz ndipo pa giridi yosavuta chimawerengedwa kuti chili ndi chizindikiro chabwino ngati kumanzere kwa mtandawo chili cholozera mmwamba, ndipo kumanja chili cholozera pansi.
Ndodo ikakhota, ma axis a ma coordinates x ndi z amakhala ndi njira ina mu gawo lililonse ndipo nthawi zonse motero kuti x-axis ndi tangenti ku axis ya ndodo. Ngati ndege imene axis ya ndodo ili mmenemo siyofanana ndi ndege ya mphamvu, kapena ngati axis ya ndodo ndi khota ya m’mlengalenga, zotsatira za mphamvu kumanzere kwa gawo zimakhala ndi chigawo chachitatu, mphamvu yodutsana Qy. Ndi N, Qz ndi Qy kukula ndi njira ya mphamvu yomwe imadutsa kudzera mu gawo zatsimikizika, koma osati malo ake. Pachifukwa ichi ziyeneranso kudziwika ma moment ake okhudza ma axis a ma coordinates. Pa kupindika kwa ndege, ndikokwanira kuti moment ya kupindika M kapena My idziwike. M’njira yambiri kwambiri pamawonekera moment ina ya kupindika Mz ndi moment yozungulira x-axis, Mx.
Mphamvu ndi ma momeni asanu ndi limodzi amene afotokozedwa m’mbuyomu amatchedwa dzina limodzi loti „presečne sile“. Kuzindikira kwawo ndi imodzi mwa ntchito zazikulu za statiki ya zomangamanga.
Pakati pa katundu wogawidwa mosalekeza p (kukula: mphamvu pa unit ya kutalika), mphamvu zam’mbali Q ndi moment ya kupinda M pali ubale wosavuta pa nkhani ya kupinda kosalala. Ndipotu, kuchokera ku chikhalidwe cha kusalingana cha chinthu chimodzi cha ndodo (chith. 2) timapeza
dQ + p dx = 0,
dM = Q dx;
choncho
Q = dM/dx,
p = - dQ/dx = - d2M/dx2. (1a, b)
Chith. 2
Kugawa kwa zovuta za normal
Ngati ndodo imanyamulidwa ndi mphamvu ya axial yokha, mu gawo lake pamapezeka kupsinjika kwa normal komwe kumagawidwa mofanana σ (ndodo yotambasulidwa, kapena yopanikizidwa). Ngati kuphatikiza apo pamawonekera momenti ya kupinda, kupsinjika kumeneku kuyenera kugawidwa mosalingana mwanjira inayake, kotero kuti zotsatira zake zisadutse kachiwalo ka gawo. Kuti adziwe kugawidwaku, chiphunzitso chaumisiri cha kupinda sichiyambira pa yankho lolimba la ma equation oyambira, koma chimachotsa gawo lina la ma equation amenewa ndi lingaliro lovomerezeka lomwe pa nkhani imodzi yosavuta kwambiri limakwaniritsidwanso molimba. Nkhani yapaderayi ndi kupinda kwa ndodo ya prismatic yowongoka popanda mphamvu za transversali (sl. 3). Zinthu zonse za ndodoyo zomwe zili kutali mokwanira ndi mathero ake zimakhala ndi kusintha kofanana, ndipo kuchokera pamenepo zimatsatira mwachindunji kuti axis ya ndodo imasanduka arc ya bwalo ndipo ndege zonse za ma cross-section zomwe poyamba zinali zowongoka ku axis ya ndodoyo, pakusintha zimatsalira zosalala, chifukwa iliyonse mwa izo ndi ndege ya symmetry ya mbali zoyandikana za ndodo yosinthika. Mwachibadwa pamabwera lingaliro lakuti ma cross-section amakhala pafupifupi osalala ngakhale momenti ya kupinda ndi cross-section ya ndodoyo sizikhala zokhazikika, koma zimasintha pang’onopang’ono m’litali mwa ndodo. Lingaliro limeneli lotchedwa Navier-ova hypothesis ndi maziko a chiphunzitso cha kupinda.
Chith. 3
Kukula kwa zovuta zachibadwa
When a straight beam element is bent, one part of its “fibers”, that is, material lines parallel to the axis of the bar, is stretched, while the other part is shortened (fig. 4). Between these two parts lie the neutral fibers z=0, whose length does not change during bending. Let the radius of curvature of these fibers in the bent state be ϱ and let it lie in the x-z plane. From fig. 4 m it can be read
Δ dx/z = _dx/_ϱ
ndipo kuchokera pamenepo kuwerengera kukula kwa kutambasuka kwa ulusi pa mtunda z kuchokera pa axis yopanda katundu, komwe kuli
ε = Δ dx/dx = _z/_ϱ
ndipo potengera lamulo la Hooke-waponso kumakhala kupsinjika
σ _= Ez/_ϱ (2)
Chith. 4
Kupsinjika uku kumakhala kofanana ndi mtunda kuchokera ku ma neutral fibers. Zotsatirazi zikugwirizana ndi lingaliro lakuti musanalandire kusintha, ulusi wonse wa element ya ndodo unali wa utali wofanana, choncho ndodo poyambirira inali yowongoka, kapena osachepera ndi kupindika kochepa kwambiri kotero kuti mphamvu ya kupindika inganyalanyazidwe. Mzere umene wosanjikiza wa neutral ndi ndege ya gawo zimadutsirana umatchedwa neutral axis. Timauvomereza ngati y-axis (sl. 5). Malo a neutral axis mu gawo lodutsa amapezeka kuchokera ku chikhalidwe cha kufanana kwa mphamvu mu njira ya x-axis: ngati mphamvu ya normal N=0 (kupindika popanda mphamvu ya normal), ndiye chotsatira cha mphamvu zamkati chofotokozedwa kudzera mu ma stress a normal m’gawolo chiyeneranso kukhala zero:
Integral pa mbali yakumanja ndi nthawi ya static ya malo poyerekezera ndi y-olumikiza. Kuti ikhale yofanana ndi ziro, olumikizayu ayenera kukhala limodzi mwa ma axis a pakati pa kulemera.
Moment M yomwe imayambitsa kusintha kwake imakhala ndi zigawo zokhudza ma osi y ndi z m’lifupi mwa mtanda (chith. 5):
Gawo (3)
pomwe Iy, Iyz ndi ma equatorial ndi centrifugal moments of inertia a gawo pokhudzana ndi ma axis otchulidwa.
Chofunika kwambiri ndi nkhani yapadera pamene Mz=0. Nkhaniyi imachitika pamene Iyz=0, ndiko kuti, pamene y ndi z ndi ma axis akuluakulu a inertia a gawo. Izi zikutanthauza kuti ndege ya kupinda yomwe yatengedwa pano ngati x-z-ndege imagwirizana ndi ndege yomwe moment ya kupinda M=My imagwira ntchito, ndiko kuti, ndi ndege ya mphamvu.
Chith. 5
Ngati kuchokera ku ma equation (2) ndi (3) _E/_ϱ ichotsedwa, mawonekedwe opezera kupsinjika pa kupinda kowongoka (Iy=I) amapezeka:
σ = M/I * z (4)
kwa malo a m’mphepete 1 ndi 2 makamaka ndi:
σ1 = M/I * h1 = M/W1, σ2 = - M/I * h2 = - M/W2. (5)
Makhalidwe W1,2 = I/h1,2 (miyeso: utali ku mphamvu ya zitatu) amatchedwa ma momeni olimbana. Ngati olamulira a mphamvu ya pakati pa horizontal alinso olamulira a symmetry a gawo, ndiye W1 = W2, choncho mavuto a m’mphepete amakhala ofanana pa mtengo weniweni.
Mzere wa elastiki
Mth. 6
Kufunika kwa maumboni omwe tafotokoza pamwambapa kumalumikizidwa ndi lamulo la Hooke. Izi zimafuna kuti σ << E, choncho malinga ndi (2) h << ϱ. Komabe kupindika kungakhale kwakukulu kotero kuti ϱ ikhale ya kalasi yomweyo ndi utali wa ndodo l. Kwa ndodo zopindika zomwe zimagwiritsidwa ntchito pa zomangamanga, vutoli silichitika; nthawi zonse ϱ imakhala yayikulu kwambiri kuposa l ndipo motero kupinda w << l (chith. 6). Ndiye pafupifupi zimagwira ntchito kuti:
1/ ϱ = - d2w/dx2 = -w’’
ndipo potengera (3):
w’’ = - M/EI.
Equation iyi ndi chikhalidwe cha kufanana (1b) zimapanga dongosolo la ma equation osiyana a ndodo yopindika. Pogwiritsa ntchito kuchotsa zinthu, zingachepetsedwe kukhala equation imodzi ya dongosolo lachinayi:
wIV = + p/EI
kapena, ngati moment ya inertia ndi yosinthika:
(EIw’’)’’ = +p.
Kuphatikiza zinthu izi kungapezeke mawonekedwe a mzere wa elastiki pamene katundu waperekedwa ndi p=p(x) ndipo pamene pa ndodo iliyonse milandu iwiri ya malire imadziwika. Pa izi, osachepera ziwiri ziyenera kukhudza kusintha kwa mawonekedwe. Kuti mudziwe zambiri onani nkhani Statika građevinskih konstrukcija.
M’mtima mwa mtanda
Ngati axis yopanda katundu yadula chigawo chopingasa, imagawa mu gawo la kukokera ndi gawo la kukakamiza. Kwa zinthu zokhala ndi mphamvu yochepa pa kukokera, funso limabuka kuti mphamvu ya kukakamiza iyenera kugwira kuti, ngati m’gawo lopingasa palibe malo amene akuyenera kukhala ndi kukokera. Malo amene mphamvu imakhala yolunjikamo ndiye amangokhala m’dera lotchedwa mtima wa chigawo. Malire a mtimawu mwachionekere ndi malo a ma point, omwe ma axis awo opanda katundu amafika pa chigawo chopingasa ngati tangenti mozungulira. Ndi ichi pamodzi apatsidwanso kumangidwa kwake.
Mtunda wa malire a nucleus kuchokera ku centroid, poyeza m’njira iliyonse, tidzauza ndi k ndi index yofanana ndi njira imeneyo. Pa ma axis aakulu a inertia malinga ndi equation
σ = N/F + Mz/Iz y + My/Iy z (6)
mawu ake ndi awa:
ky = i2z / ey, kz = i2y / ez. (7)
Pa gawo lozungulira lokhala ndi radius r, mtunda wa pakati pa mphamvu ndi k = r/4, ndipo pa mphete yozungulira (ma radius: wakunja R, wamkati r) k = (R2 + r2) / 4R.
Kwa rectangle (chith. 7) ndi ky = 1/6 b, kz = 1/6 h. Choncho, pokhudzana ndi katundu pa gawo la rectangle m’gawo limodzi mwa ma plane a symmetry (koma kokha pamenepo) zokwanira kuti resultant igwere m’chigawo chapakati cha kutalika kapena m’lifupi mwa cross-section, ndipo zipsinjo mu gawo zikhale ndi chizindikiro chimodzi.
Chith. 7
Kupinda m’dera la pulasitiki
Pamene m’mitsempha yakunja ya ndodo yopindidwa yafika pa malire a kutuluka, mphamvu yake yonyamula siyatha komabe, chifukwa pamene mitsempha yakunja ikusinthika mwa pulasitiki pa kupsinjika kosasintha, m’magawo amene ali pafupi ndi nkhwangwa ya pakati, kumene malire a kutuluka sanakwaniritsidwebe, kupsinjika kumawonjezeka, ndipo motero chimawonjezekanso nthawi ya kupinda imene gawo limatha kulandira.
Ngati njira yeniyeni ya ma diagram a kupanikizika ndi kusintha imadziwika, ndondomekoyi kwa zigawo zosamala kawiri (kutalika h) ingatsatidwe mosavuta pa mawerengedwe mwa njira yakuti, poganiza kuti zigawo zimakhalabe zathyathyathya, kuchokera ku ma diagram a kupanikizika ndi kusintha pamakhazikitsidwa kugawa kwa kupanikizika σ chifukwa cha kupinda komwe kumafanana ndi kusintha komwe kwatengedwa kwa ulusi wakumapeto ε__r ndipo kuchokera pamenepo, mwa kuphatikiza, pamakhazikitsidwa momenti ya kupinda. Ngati izi zachitika pa ε__r zosiyanasiyana ndipo kumbali inayo kuwerengedwa kupindika koyenera kwa mzere wa kupendekera w’’ = 2 ε__r / h, amapezeka mndandanda wa mfundo zomwe kudzera mwa izo mungajambule mzere womwe umapereka kugwirizana pakati pa momenti ya kupinda ndi kupindika M = M(w’’); kugwirizanaku sikulinso kwa mzere, ndipo tikadziwa kumeneku n’zotheka kudzera mu graphical integration kudziwa mzere wa kupendekera womwe ukufanana ndi kugawa kopatsidwa kwa ma momenti. Ngati gawo silili lofanana, mawerengedwe amakhala ovuta kwambiri, chifukwa pa chilichonse ε__r ziyenera kudziwika komanso malo a axis ya neutral.
Chith. 8
Kuwerengera kumakhala kosavuta mpaka pang’ono ngati, kuwonjezera pa kufanana kwa gawo, tingaganizirenso kulumikizana kosavuta pakati pa zovuta ndi ma dilatation mogwirizana ndi chith. 8. Kenako zovuta chifukwa cha kupindika pambuyo pa kupitirira malire a kusungunuka zili ndi kugawa komwe kwasonyezedwa pa chith. 9 ndipo momeni wa kupindika ndi:
ndipo kupindika kwa mzere wa deflection kumapezeka pamene equation (2) igwiritsidwa ntchito pa gawo la cross-section lomwe ma stress ake ali m’dera la elastic w’’ = σf / Ez’. Ngati mawonekedwe a cross-section pa z’ iliyonse yosankhidwa akudziwika, ma integral angawerengedwe. Mwachitsanzo, pa nkhani yosavuta kwambiri ya cross-section ya rectangle yokhala ndi m’lifupi b ndi msinkhu h ndi
Ngati pano z’ ifotokozedwa pogwiritsa ntchito w’’, timapeza
Pa I-mitundu ndi ofanana nawo, njira ya M-w’’ curve m’gawo la pulasitiki imakhala yathyathyathya kwambiri ndipo momenti imene kufalira kumayamba ndiye pafupifupi yofanana ndi momenti yayikulu kwambiri ya kupinda yomwe mtanda ungathe kupirira. Choncho kufunika kwa kupinda kwa pulasitiki m’kumanga sikuli pakuwonjezera momenti ya kupinda yomwe mtanda unganyamule, koma pa kuti kusokonekera kwakukulu kwa m’deralo komwe kumachitika pa malire a kufalira kungayambitse kusintha kwabwino kwa kagawidwe ka mphamvu m’makina osatsimikizika statically.
Chith. 9
Izi zingafotokozedwe ndi chitsanzo cha mtolo wopitirira pa mipata iwiri. Tiyeni mtolo (chith. 10) ukhale ndi mipata ya utali wofanana, gawo lokhazikika, ndipo ukhale wanyamulidwa ndi katundu wogawidwa mofanana. Pamenepo, asanafike malire a kusungunuka, momenti pa chithandizo MB = _pl_2/8. Ngati katundu p uwonjezedwa mpaka momenti mu gawo la chithandizo ifike pa mtengo Mf pamene kusungunuka kumayamba, pakuwonjeza katundu kupitirira apo, kupindika pa malo amenewo kudzawonjezekanso popanda kuwonjezeka kooneka kwa momenti. Izi zimapanga chomwe chimatchedwa plastični zglob, ndiko kuti mtolowo pansi pa katundu wowonjezera umakhala ngati pali cholumikizira pamwamba pa chithandizo chapakati. Katundu ungapitirire kuwonjezedwa mpaka kusungunuka kuyambenso pamalo a momenti yayikulu kwambiri m’mipata. Kuonjezanso kwa momenti ya kupinda sikuthekanso ndipo mphamvu yonyamula ya mtolowo imatha. Katundu umene pansi pake chikhalidwechi chimachitika chimatchedwa katundu womaliza.
Mkuyu. 10
Mwachidule, tingayembekezere kuti mu dongosolo limene lili statically indeterminate ka n kawiri, kuyenera kuwoneka (n+1) ma hinge a pulasitiki asanakhale kuti dongosololi likhoza kusuntha ndipo motero lifike malire ake a mphamvu yonyamula. Komabe, lamuloli lili ndi zosiyana mbali zonse ziwiri. Monga chitsanzo chomwe chatchulidwa chikuwonetsa, pa malire a mphamvu yonyamula ma hinge awiri atsopano a pulasitiki angawonekere nthawi imodzi (m’magawo onse awiri), moti dongosolo limene linali lisasunthe limasanduka mwadzidzidzi dongosolo lokhala ndi madigiri awiri a ufulu. Kumbali ina, n’zotheka kuti ngakhale ndi ma hinge a pulasitiki ochepa kuposa (n+1) mphamvu yonyamula ithe pa malo ena, mwachitsanzo pamene mu mlatho wopitilira gawo limodzi lokha likalephera. Chith. 11 chikuwonetsa mmene zimenezi zingachitikire mu dongosolo limodzi lokhala statically indeterminate kaŵiri lomwe liri ndi n=2 ma hinge a pulasitiki. Ngati pa mbali ya kumanja ya chonyamulira awonjezeredwa gawo lachinayi, chonyamuliracho chimakhala statically indeterminate katatu, choncho ma hinge a pulasitiki (n-1) okha ndi okwanira kuti gawo la kumanzere lokha lifikitsidwe ku malire a mphamvu yonyamula.
Chith. 11
Kupsinjika kwa kukamila pakupinda
Kuwerengera koyambirira
Chith. 12
Mikangano yachibadwa σ, ndiko kuti mikangano yomwe imawoneka kwenikweni chifukwa cha kupindika si mikangano yokhayo mu ndodo yopindika, koma pamodzi nayo pamawonekeranso mikangano ya kumeta chifukwa cha mphamvu yodutsa. Popeza chinthu chachikulu cha chiphunzitso chaumisiri cha kupindika ndi chakuti kusintha kwa mawonekedwe chifukwa cha mikangano ya kumeta kumanyalanyazidwa, izi zingadziwike kokha kuchokera ku chikhalidwe cha kufanana. Kuti ichi chiikidwe, chigawo cha mtanda cha mtengo dx chimadulidwa, monga mmene zasonyezedwera pa chith. 12, ndi ndege yopingasa m’magawo awiri, ndipo chikhalidwe cha kufanana cha mphamvu zopingasa zomwe zikugwira pa gawo lotsika chimakhazikitsidwa. Kumbali ya kumanzere pali mphamvu zamkati zoyimiridwa ndi mikangano σ chifukwa cha kupindika, zomwe ziyenera kuphatikizidwa kuchokera ku z’ = z kufika ku z’ = h2
Pa mbali ya kumanja pali ma stress omwewo, koma owonjezeka ndi diferensiyali mogwirizana ndi momenti yoyendera M + dM. Kusiyana kwa mphamvu pa mbali ziwiri za elementiyo kuyenera kukhala m’malingaliro oyenera ndi mphamvu chifukwa cha ma stress a shear τ omwe amachita pa malo a gawo loyima t dx:
Apa integral imayimira static moment ya gawo la cross-section lotengedwa ndi ndege yopingasa ya cross-section poyerekeza ndi axis ya pakati pa gawo. Imawonetsedwa ndi S. Ndi dM/dx = Q kuchokera ku zofunikira za kusiyana kwa mphamvu timapeza:
τ = QS/It. (8)
According to the principle of conjugacy of shear stresses, this is at the same time the value of the vertical shear stress acting in the cross-sectional area and which, together with S and t, is a function of z.
Chith. 13
Chith. 13.1
Equation (8) imapereka data yodalirika pa magawo onse okhala ndi makoma oonda ngati ndege yodulira siyayikidwa mofanana ndi neutral axis, koma m’njira ya makulidwe a khoma. Choncho I-profile imadulidwa kudutsa pa rebra ndi kudutsa pa flange, zomwe zimapatsa kugawa kwa ma stress komwe kwasonyezedwa pa chith. 13.1. Pa ring cross-section (chith. 13) ma shear stresses amagawidwa mofanana poyerekeza ndi vertical diameter ndipo kumanzere ndi kumanja pa neutral line amafika pa maximum
τ = Q / πrt.
Ngati gawo ladulidwa pa malo apamwamba kwambiri kapena otsika kwambiri, kapangidwe ka ma stress a shear sasintha; komabe, ngati ladulidwa pa kumapeto kumanja kwa diameter yopingasa (chith. 14), shear stress pa malo amenewo ndi wofanana ndi zero, pomwe mtengo wake umakhala kawiri pa kumapeto kumanzere kwa diameter yomweyo.
Chith. 14
Zigawo zonse
Pa magawo olimba a mawonekedwe aliwonse, vuto la mikangano yokameta limagwirizana kwambiri ndi nkhani ya torsion. Equation yofunikira (8) panthawiyi salinso yodalirika. Pa gawo lozungulira lokhala ndi utali wozungulira r equation (8) imapereka
τ = 4Q / 3__πr2
monga mtengo wapakati wa kupsinjika kwa kusenda m’mphepete mwa mzere wosalowerera ndale, ndipo mtengo wolondola ndi wokwera ndi magawo ochepa okha pa zana.
Malo a kudula
Ngati pa U-chigawo ma shear stresses awerengedwa monga tafotokozera pamwambapa, amapezeka kugawika kwa kupsinjika komwe kukuwonetsedwa pa sl. 15. Zotsatira za mphamvu zamkati zofanana ndi transverse force Q. Kuchokera pa chithunzichi tingawone malo ake poyerekezera ndi chigawocho, ndiye kuti sichidutsa pa centroid ya chigawo, ndipo sichigona mu ndege ya rib. Ngati mphamvu ya transverse yoŵerengedwa potengera mphamvu zakunja ilibe malo owonetsedwa pa sl. 15, chonyamulira sichimangokhalira kupindika kokha, koma komanso torsion.
Ngati pa mtanda womwewo wa kudutsa atsimikizidwe chotsatira chimene chigwirizana ndi ma kupsinjika a sheya pa katundu wina wopingasa, amapeza mzere wa kukhudzidwa wa mphamvu yopingasa ya transversale. Pamalo pamene mizere iwiri imeneyi imadutsana pali mfundo yodziwika ya mtanda womwewo wa kudutsa, imene imatchedwa središte smicanja M. M’onyamulira, ma kupsinjika chifukwa cha torsion sapezeka pamene malo a središta smicanja a ma mtanda onse a kudutsa ali pa mzere umodzi, ndipo katundu yonse yokhotakhota ku axis ya ndodo imadutsa pa mzerewo. Mosiyana ndi zimenezo, mphindi ya katundu uliwonse poyerekezera ndi mzere umene umalumikiza malo a središta smicanja imayimira sheya ya torsion.
Chith. 15
Mphamvu ya transverse pa kupinda
Nkhani ya luso ya kupinda imakhazikika pa kunyalanyaza kusintha kwa mawonekedwe chifukwa cha ma nkhawa a kumeta. Choncho, imatha kugwiritsidwa ntchito kwenikweni pa ndodo zopyapyala, kumene kunyalanyazaku n’kovomerezeka ndipo kumene mphamvu yopingasa ilibe mphamvu yowoneka pa kupinda.
Komabe, zomwe zachitika zasonyeza kuti chiphunzitso chaumisiri cha kupindika chingagwiritsidwe ntchito ndi kupambana kwina pa zonyamulira zazifupi, zazitali, zomwe kwenikweni sizinalinganizidwepo. Pamenepa pamafunika kuti zotsatira za kusintha chifukwa cha zovuta zosenda, zomwe m’chiphunzitsochi zasiyidwa, ziganiziridwenso pambuyo pake, ngakhale pafupifupi.
Mofanana ndi zovuta za kusenda τ chifukwa cha mphamvu zoyendera m’mbali ndi kusuntha kofanana γ_’ =_ τ_/G_ kumagawidwa mosalingana pa gawo. Chifukwa chake, mtengo wake wapakati γ umayikidwa, ndipo umafufuzidwa moti mphamvu yotere yodutsa m’mbali pa mtengo wapakati uwu wa kupindika imachitira pa chigawo cha girizi dx ntchito ya kupindika yofanana ndi yomwe ikanapezeka ngati ntchito za zovuta zosenda zikanaphatikizidwa pa zinthu za voliyumu payekha zomwe zimapanga gawo la girizi lozindikiridwalo:
kumene
Integral ingawerengedwe pamene dongosolo la ma shear stress pa gawo ladziwika. Popeza shear stress zonse zimayenderana ndi Q/F, mtengo wake umafanana ndi Q2/F2 * F, choncho tikayika kuti uli κ__Q2/F, timapeza
γ = κ__Q / GF.
Konstanti κ amatchedwa koefishenti ya kugawa kwa ma stress a shear. Kwa ma cross-section a rectangolo ndi κ=1,2.
Chith. 16
Pamene coefficient κ ikudziwika, ndipo motero kutsetsereka kwapakati γ, kungawerengedwe kupinda kowonjezera wQ, komwe kumachitika chifukwa cha mphamvu zodutsa, komwe kuyenera kuwonjezeredwa pa kupinda w: chifukwa malinga ndi chith. 16 ndi
ndipo chifukwa cha Q = dM/dx:
pomwe nthawi yokhazikika ya kuphatikiza imapezeka kuchokera ku chimodzi mwa mikhalidwe ya malire.