Ngā pēhanga noa i ngā tokotoko tika me ngā tokotoko he iti te kōpiko
Whakamārama o ngā kaha wāhanga-tapahi
Me whakaarohia he rākau tōtika e kawengia ana e ngā kaha aronga kōwhiringa, ā, ko tā te whakapae anake ko te katoa kei roto i te rererangi kotahi (rererangi kaha) e whakawhiti ana i te aho o te rākau (te rārangi e hono ana i ngā pokapū taumaha o ngā wāhanga whakawhiti).
Wh. 1
Kia tātaihia ai ngā ngānati e mahi ana i tētahi wāhanga whakawhiti n – n (wh. 1), me mōhio te kaha e whakawhitia ana mā tēnei wāhanga mai i tētahi wāhanga o te rākau ki tētahi atu. E tino ōrite ana taua kaha, i runga i tōna nui me tōna tūnga, ki te putanga whakakotahi o ngā kaha katoa e pā ana ki tētahi wāhanga o te rākau. Ka wawahia taua putanga whakakotahi hei wāhanga i roto i tētahi pūnaha taunga e ū ana te tuaka x ki te tuaka o te rākau, ā, ko te tuaka z te rārangi e motu ai e te papa o te wāhanga whakawhiti te papa o ngā kaha. Ko te wāhanga i te ahunga o te tuaka z ka kīia ko te kaha whakawhiti Q rānei Qz, ā, mō te kurupae māmā ka whakaarotia he pai mēnā kei te taha mauī o te wāhanga he ahunga whakarunga, ā, kei te taha matau he ahunga whakararo.
Ina kōpiko te rākau, he rerekē te ahunga o ngā tuaka ruruku x me z i ia wāhanga whakawhiti, ā, i ngā wā katoa ko te x-tuaka he pātata ki te aho o te rākau. Mēnā kāore te rererangi e takoto ai te aho o te rākau e hāngai ana ki te rererangi o ngā kaha, ā, mēnā rānei he ānau mokowā te aho o te rākau, ka whai wāhanga tuatoru anō te hua o ngā kaha kei te taha mauī o te wāhanga whakawhiti, arā, te kaha whakawhiti Qy. Mā N, Qz me Qy ka tautuhia te rahi me te aronga o te kaha e tukuna ana mā te wāhanga whakawhiti, engari ehara i tōna tūranga. Hei tēnei, me mōhio hoki ōna pūkaha e pā ana ki ngā tuaka ruruku. Mō te piko papatahi, ka ranea kia mōhiotia te pūkaha piko M rānei My. I te take whānui rawa, ka puta mai tētahi atu pūkaha piko Mz me te pūkaha huri mō te x-tuaka, Mx.
Ko ngā kaha me ngā taipana e ono kua tautuhia i te whakamāramatanga o mua ka kīia ngātahitia he “kaha wāhanga whakawhiti”. Ko tā rātou whakatau tētahi o ngā mahi matua o te statics o ngā hanganga hanga.
I waenga i te kawenga kua tohaina tonutia p (āhuatanga: kaha ia wae roa), te kaha whakawhiti Q me te taipana piko M, he hononga māmā kei te take o te piko papatahi. Arā, mai i te tikanga taurite o tētahi huānga o te rākau (wh. 2) ka puta
dQ + p dx = 0,
dM = Q dx;
no reira
Q = dM/dx,
p = - dQ/dx = - d2M/dx2. (1a, b)
Fig. 2
Kōtuitanga o ngā ngānati noa
Mēnā ka utaina te tokotoko ki te kaha ā-axial anake, ka puta i te wāhanga ko te āheinga noa σ kua tohatoha ōrite anake (tokotoko tō, kōpeke rānei). Ki te puta anō he moment piko, me tohatoha koretake ēnei āheinga i ētahi huarahi, kia kore ai tā rātou hua kotahi e haere mā te pokapū taumaha o te wāhanga. Hei whakatau i tēnei tohatoha, kāore te ariā hangarau o te piko e tīmata i te otinga tino tika o ngā whārite taketake, engari ka whakakapi i tētahi wāhanga o aua whārite ki tētahi whakapae e āhei ana te whakaae, ā, i tētahi take tino māmā kotahi ka tino tutuki hoki. Ko taua take motuhake ko te piko o tētahi tokotoko prismatic tika kāore he mahi a ngā kaha whakawhiti (whaka. 3). Ko ngā wāhanga katoa o te tokotoko e tino tawhiti ana i ōna pito ka pāngia e te hurihanga kotahi, ā, ka hua tonu ake i konei ka huri te tuaka o te tokotoko hei āwhiowhio porowhita, ā, ka noho papatahi tonu ngā paparanga katoa o ngā wāhanga whakawhiti i noho poutū i te tuatahi ki te tuaka o te tokotoko i te wā e pā ana te whakarerekētanga, nā te mea ko ia paparanga he paparanga hangarite mō ngā wāhanga tata o te tokotoko kua whakarerekētia. E mārama ana te whakapae e noho tata papatahi tonu ngā wāhanga whakawhiti ahakoa kāore te moment piko me te wāhanga whakawhiti o te tokotoko e pūmau, engari e āta rerekē haere ana i te roanga o te tokotoko. Ko tēnei whakapae, e kīia nei ko te Navier-ova hipoteza, te pūtake o te ariā piko.
Whaka. 3
Te nui o ngā taumahatanga noa
Ina piko tētahi huānga tika o te kurupae, ka tōia tētahi wāhanga o ōna “muka”, arā, ngā rārangi rauemi e whakarara ana ki te tuaka o te tokotoko, engari ka whakapotohia tētahi atu wāhanga (wh. 4). Kei waenganui i ēnei wāhanga e rua ko ngā muka kūpapa z=0, kāore ō rātou roa e huri i te wā e piko ana. Me kī ko te pūtoro kōpiko o ēnei muka i te āhua piko he ϱ, ā, kei roto ia i te rererangi x-z. Mai i te wh. 4 m ka taea te pānui
Δ dx/z = _dx/_ϱ
ā, mai i reira ka tātaihia te whakaroanga o ngā muka i te tawhiti z mai i te tuaka kūpapa, arā
ε = Δ dx/dx = _z/_ϱ
nō reira, i runga i te ture a Hooke- ka puta te mānukanuka
σ _= Ez/_ϱ (2)
Whakaahua. 4
E taurite ana tēnei pēhanga ki te tawhiti mai i ngā muka kūpapa. E hāngai ana taua hua ki te whakapae i mua i te rerekētanga he ōrite te roa o ngā muka katoa o te huānga rākau, nā reira i mua rā he tika te rākau, i te iti rawa rānei he iti rawa te kōpiko kia taea ai te whakakore i te pānga o te kōpiko. Ko te rārangi e whakawhiti ai te paparanga kūpapa me te paparanga tapahanga ka kīia ko te tuaka kūpapa. Ka whāia e mātou hei y-tuaka (sl. 5). Ka whiwhi te tūranga o te tuaka kūpapa i te tapahanga whakawhiti mai i te tikanga taurite o ngā kaha i te aronga o te x-tuaka: mēnā ko te kaha pūnoa N=0 (piko kāore he kaha pūnoa), me kore hoki te hua o ngā kaha o roto e whakaaturia ana mā ngā pēhanga pūnoa i te tapahanga:
Ko te taurangi i te taha matau ko te momeniti statika o te mata e pā ana ki te tuaka y. Kia kore ai e ōrite ki te kore, me noho tēnei tuaka hei tētahi o ngā tuaka pūtake-pūtake.
Ko te taipana M e whakaohooho ana i te deformation he ōna wāhanga e pā ana ki ngā tuaka y me z i te paparangi o te wāhanga (wh. 5):
Wae. (3)
i reira ko Iy, Iyz ngā taipana porowhita me ngā taipana pākahukahu o te wāhanga e pā ana ki ngā tuaka kua tohua.
Ko te take motuhake tino nui ko te wā Mz=0. Ka puta tēnei take ina Iyz=0, arā, ina ko y me z ngā toki matua o te koretake o te whitinga. Ko te tikanga, ko te rererangi piko kua whakaaetia i konei me te x-z-rerangi e ōrite ana ki te rererangi e mahi ai te taipana piko M=My, arā ki te rererangi o ngā kaha.
Wh. 5
Mēnā ka whakakorea te _E/_ϱ i ngā whārite (2) me (3), ka puta te tauira hei whakatau i ngā taumahatanga i te piko taurite (Iy=I):
σ = M/I * z (4)
mō ngā ira mata 1 me 2 anake, ko te:
σ1 = M/I * h1 = M/W1, σ2 = - M/I * h2 = - M/W2. (5)
Ko ngā rahinga W1,2 = I/h1,2 (āhuatanga: te roa ki te kaha tuatoru) e kīia ana he momeniti ātete. Ki te mea ko te tuaka tōpuni whakapae hoki te tuaka hangarite o te whiti, kātahi W1 = W2, ā, he ōrite ngā taumahatanga mata i te uara pūmau.
Rārangi rapa
Fig. 6
E herea ana te hiranga o ngā tauira kua kōrerohia ake nei ki te ture a Hooke. E tono ana tēnei kia σ << E, nō reira e ai ki (2) h << ϱ. Heoi anō, ka āhei tonu te piko kia pēnei te rahi, arā ka ōrite te ϱ ki te roa o te tokotoko l. I ngā tokotoko piko e whai pānga ana ki te hanganga whare kāore tēnei āhuatanga e puta; he nui ake tonu te ϱ i te l, nō reira he iti rawa te piko w << l (fig. 6). Nā reira, āhua pēnei te ture e whai ake nei:
1/ ϱ = - d2w/dx2 = -w’’
i runga anō i (3):
w’’ = - M/EI.
Ko tēnei whārite me te tikanga taurite (1b) e hanga ana i te pūnaha whārite rerekē o te tokotoko kōpiko. Mā te whakakore ka taea te whakaiti ki tētahi whārite kotahi o te raupapa tuawhā:
wIV = + p/EI
rānei, i te take he rerekē te momeniti o te inersia:
(EIw’’)’’ = +p.
Mā te whakauru ka kitea te āhua o te rārangi hāngū ina hoatu te utanga p=p(x) ā, ina mō ia take o te rākau e mōhiotia ana ngā tikanga rohe e rua. I ēnei, me pā te iti rawa e rua ki te huringa. Mō ngā kōrero taipitopito tirohia te tuhinga Statika građevinskih konstrukcija.
Kākano o te wāhanga whiti
Mēnā ka whakawhiti te tokotoko kūpapa i te tapahanga whiti, ka wehea e ia ki te rohe tō me te rohe kōpeke. Ki ngā rauemi he iti te kaha tō, ka ara ake te pātai ki hea me pā mai te kaha kōpeke, mēnā kāore e āhei kia puta he tō i tētahi wāhi o te tapahanga whiti. Ka herea te tūnga o te wāhi pānga o te kaha ki tētahi rohe e kīia nei ko te ngākaunui o te tapahanga. Ko te rohe o taua ngākau ka kitea tonutia hei wāhi āhuahanga o ngā pūwāhi e pā ana ngā tokotoko kūpapa ki te tapahanga whiti i te paenga katoa. Nā konei anō hoki ka tohua tōna hanga.
The distance of the core boundary from the centroid, measured in any direction, shall be denoted by the k index corresponding to that direction. For the principal axes of inertia according to the equation
σ = N/F + Mz/Iz y + My/Iy z (6)
ko ngā kīanga e whai ake nei:
ky = i2z / ey, kz = i2y / ez. (7)
Mō te whitinga porowhita me te pūtoro r, ko te tawhiti o te pūtake ko k = r/4, ā, mō te mowhiti porowhita (ngā pūtoro: o waho R, o roto r) k = (R2 + r2) / 4R.
Mō te tapawhā (wh. 7) ko ky = 1/6 b, kz = 1/6 h. Nō reira, i te utanga o tētahi wāhanga tapawhā i roto i tētahi o ngā rererangi hangarite (engari i taua wā anake) he rawaka kia pā mai te huanga ki te tuatoru waenga o te teitei, o te whānui rānei o te wāhanga whiti, kia ōrite ai te tohu o ngā taumahatanga i te wāhanga.
Whaka. 7
Piko i te rohe kirihou
Ina kua tae te rohe rere i ngā muka o waho o te tokotoko piko, kāore anō kia pau tana kaha kawe, nā te mea i te wā e whakakori kirihou ana ngā muka o waho i raro i te ahotea pūmau, ka piki te ahotea i ngā wāhanga e tata ake ana ki te tuaka kūpapa, kāore anō kia tae te rohe rere ki reira, ā, mā reira hoki ka piki te taipana piko ka taea e te whiti te kawe.
Mēnā e mōhiotia ana te rere tika o te hoahoa o ngā pēhanga me ngā whakaroanga, ka taea te whai ā-tauranga i te tukanga mō ngā wāhanga e rua ngā hangarite (teitei h) mā te tango, i raro i te whakapae e noho papatahi tonu ana ngā wāhanga, i te hoahoa pēhanga me te whakaroanga te tohatoha o ngā pēhanga σ nā te piko e hāngai ana ki tētahi whakaroanga kua whāia o ngā muka mutunga ε__r, ā, mā te tuitui mai i reira ka whakatauria te taimana piko. Ki te mahia tēnei mō ngā ε__r rerekē, ā, i tētahi atu taha ka tātaihia te kōaro e hāngai ana o te rārangi kōpiko w’’ = 2 ε__r / h, ka puta he huinga ira ka taea te tō mai he rārangi e whakaatu ana i te hononga i waenga i te taimana piko me te kōaro M = M(w’’); kāore tēnei hononga i te rārangi ā-tonu, ā, ina mōhiotia ka taea, mā te tuitui ā-whakaahua, te kimi i te rārangi kōpiko e hāngai ana ki tētahi tohatoha taimana kua tautuhia. Ki te kore te wāhanga e hangarite, ka uaua ake te tātaitanga, nā te mea mō ia ε__r me whakatau anō te tūnga o te tuaka kūpapa.
Whaka. 8
Ka māmā ake te tātai mēnā, hei tāpiri atu ki te hangarite o te wāhanga whakawhiti, ka whakaarohia hoki he hononga māmā i waenga i ngā pēhanga me ngā toronga, e ai ki te wh. 8. Nō reira, ko ngā pēhanga nā te piko, i muri i te hipanga o te rohe tuku, he tohatoha tā te wh. 9, ā, ko te taipana piko ko:
ā, ka whiwhi te kōpiko o te rārangi piko ina whakamahia te whārite (2) ki te wāhanga o te whiti e noho ai ngā ahotea i te rohe rapa w’’ = σf / Ez’. Ki te mōhiotia te āhua o te whiti mō ia z’ kua tangohia, ka taea te tātai i ngā tāuru. Hei tauira, mō te take māmā rawa o tētahi whiti ā-whiti tapawhā tōtika me te whānui b me te teitei h ko
Ki te whakaaturia i konei te z’ mā te w’’, ka whiwhi
Mō ngā wāhanga I me ērā rite, he āta hōrapa ake anō te āhua o te ānau M-w’’ i roto i te rohe kirihou, ā, i taua wā ko te taipana e tīmata ai te rerenga he āhua ōrite ki te taipana piko nui rawa atu ka taea e te wāhanga te kawe. Nō reira, kāore te hiranga o te piko kirihou i roto i te hanga e takoto ana i te whakapikinga o te taipana piko ka taea e te wāhanga te kawe, engari i te mea ka taea e te whēru nui ā-rohe e puta ana i te paearu rerenga te arahi ki tētahi panonitanga pai o te tohanga kaha i ngā pūnaha kāore i te mōhiotia te tau o ngā tautoko.
Whakaahua 9
Ka taea tēnei te whakamārama mā te tauira o tētahi kaikawe tonutanga mō ngā ātea e rua. Me kī he ōrite te roa o ngā ātea o te kaikawe (sl. 10), he wāhanga whiti pūmau, ā, e utaina ana ki te utanga tohatoha ōrite. Nā reira, i mua i te taenga ki te rohe rerenga, ko te taipana kei runga ake i te tautoko MB = _pl_2/8. Ki te whakanuia nuitia te utanga p kia tae ai te taipana i te wāhanga tautoko ki te uara Mf e tīmata ai te rerenga, ka piki tonu te kōpiko i taua wāhi i te pikinga anō o te utanga, engari kāore e tino piki te taipana. Ka hangaia te mea e kīia nei he hononga kirihou, arā, ka whanonga te kaikawe i raro i te utanga tāpiri me te mea nei he hononga kei runga ake i te tautoko waenga. Ka taea tonu te whakanui i te utanga kia tīmata anō ai te rerenga ki te wāhi o te taipana nui rawa atu i te ātea. Kāore e taea te whakanui ake anō i te taipana piko, ā, kua pau te kaha kawe o te kaikawe. Ko te kawenga e puta ai tēnei āhua ka kīia ko te utanga rohe.
Fig. 10
I te nuinga ka taea te tūmanako, i roto i tētahi pūnaha n ngā wā ā-wātea pateko, me puta mai (n+1) ngā pūtuitanga kirihou i mua i te noho pūkoro o te pūnaha, ā, mā reira ka tae ki tōna pae kawe. Heoi, he ōkawa ōna wehenga ki ngā taha e rua. Pērā i tā te tauira i kōrerotia e whakaatu ana, i te pae kawe ka puta wā kotahi ngā pūtuitanga kirihou hou e rua (i ngā wāhi e rua), kia huri ohorere ai tētahi pūnaha kāore anō kia pūkoro ki tētahi pūnaha e rua ngā tohu herekore. Ki tētahi atu taha, ka taea hoki kia whai ka pau ā-rohe te kaha kawe ahakoa he iti iho i (n+1) ngā pūtuitanga kirihou, hei tauira, ina ngoikore noa iho tētahi wāhi i tētahi kaikawe haere tonu. E whakaatu ana te āhua 11 me pēhea e taea ai tēnei i tētahi pūnaha he rua ngā wā kore pateko me n=2 ngā pūtuitanga kirihou. Mēnā ka tāpiritia he wāhanga tuawhā ki te taha matau o te kaikawe, ka noho toru ngā wā kore pateko o te kaikawe, nō reira e ranea ana (n-1) ngā pūtuitanga kirihou hei kawe i te wāhanga mauī anake ki te pae kawe.
Whak. 11
Ngā taumahatanga kutikuti i te piko
Tātai taketake
Fig. 12
Ko ngā mānukanuka noa σ, arā, ko ngā mānukanuka e tino puta mai ana nā te piko, ehara i te mānukanuka anake i te tokotoko kōpiko, engari ka puta hoki ngā mānukanuka kutikuti nā te pānga o te kaha whakawhiti. Nā te mea ko te āhuatanga matua o te ariā hangarau o te piko ko te wareware ki ngā panonitanga nā ngā mānukanuka kutikuti, ka taea ēnei mā te tikanga taurite anake te whakatau. Kia whakatakotoria ai tēnei, ka tapahia te huānga kurupae dx, pēnei i tā te wh. 12 e tohu ana, mā tētahi papa whakapae kia rua ngā wāhanga, ā, ka whakatakotoria te tikanga taurite o ngā kaha whakapae e pā atu ana ki te wāhanga raro. I te taha mauī ko ngā kaha ā-roto e whakaaturia ana e ngā mānukanuka σ nā te piko, me tāpiri mai i te z’ = z ki te z’ = h2
I te taha matau ka mahi ngā tōpū ōrite, engari kua nui ake mā te rerekētanga e ai ki te taipana piko e hāngai ana M + dM. Me taurite te rerekētanga i waenga i ngā kaha i ngā taha e rua o te huānga ki te kaha nā ngā tōpū kutikuti τ e mahi ana i te mata wāhanga whakapae t dx:
I konei, ko te integala e tohu ana i te momeniti pateko o tētahi wāhanga o te tapahanga whiti kua wehea e tētahi rererangi whiti whakapae, e pā ana ki te aake pūtake o te tapahanga. Ka tohua ki te S. Mai i te dM/dx = Q e ai ki te āhua taurite ka riro mai:
τ = QS/It. (8)
E ai ki te kaupapa o te piringa o ngā pēhanga kutikuti, koinei anō hoki te rahi o te pēhanga kutikuti poutū e mahi ana i te mata o te whitinga, ā, e, me S me t, he mahi nō z.
Fig. 13
Wh. 13.1
Ko te whārite (8) e tuku ana i ngā raraunga pono mō ngā tapahanga angiangi-taiepa katoa mēnā kāore te paparangi tapahanga e whakatakotoria whakarara ki te tuaka kūpapa, engari ki te ahunga o te matotoru o te taiepa. Nō reira ka tapahia whakawhiti te kōtaha I mā te web me te flanše, ā, ka puta te tohatoha taumahatanga e whakaaturia ana i te whak. 13.1. I te tapahanga ā-mowhiti (whak. 13) ka tohaina hangarite ngā taumahatanga kutikuti e pā ana ki te whata poutū, ā, ki mauī, ki matau o te rārangi kūpapa ka tae ki te mōrahi
τ = Q / πrt.
Ki te tapahia te whiti i te wāhi teitei rawa, iti rawa rānei, kāore e rerekē te tohatoha o ngā ahotea kutikuti; engari, ki te tapahia i te pito matau o te whānui whakapae (wh. 14), ka rite te ahotea kutikuti i taua wāhi ki te kore, ā, ka takirua tōna uara i te pito mauī o taua whānui anō.
Whaka. 14
Ngā wāhanga mārō
I ngā wāhanga kī o tētahi āhua kōwhiringa ka piri tata te raru o ngā ahotea kutikuti ki te take o te kōiriiri. Kāore anō te whārite māmā (8) e tino pono i taua take. Mō te wāhanga porowhita o te pūtoro r ka hoatu e te whārite (8)
τ = 4Q / 3__πr2
hei uara toharite o te pēhanga kutikuti i te taha o te tuaka kūpapa, ā, he iti noa iho te uara tika, mō ētahi ōrau ruarua noa iho, te nui ake.
Te pokapū kutikuti
Mēnā ka tatauhia ngā ahotea kutikuti mō te U-whiti i runga i te tikanga kua whakamāramatia i runga ake nei, ka riro ko te tohatoha ahotea e whakaaturia ana i te sl. 15. Ko te hua whakakotahi o ngā kaha ā-roto hāngai ko te kaha whakawhiti Q. E kitea ana i te whakaahua tōna tūranga e pā ana ki te whiti, arā, kāore ia e haere mā te pokapū o te whiti, kāore hoki e takoto i te rererangi o te rīpene poutū. Mēnā kāore te kaha whakawhiti i tātaihia i runga i ngā kaha o waho i te tūranga e whakaaturia ana i te sl. 15, kāore te kaikawe e utaina ki te piko anake, engari ki te tōronga anō hoki.
Mēnā ka whakatauria mō te wāhanga-whiti kotahi anō te hua whakakotahi e hāngai ana ki ngā taumahatanga kutikuti mō tētahi utanga whakapae, ka whiwhi te rārangi pānga o te kaha whakawhiti whakapae. I te wehenga o ēnei rārangi pānga e rua ka kitea te ira āhuatanga mō taua wāhanga-whiti, e kīia ana ko te pokapū kutikuti M. Kāore e puta ngā taumahatanga nā te huri wiri i roto i te kaikawenga ina kei runga i te rārangi kotahi ngā pokapū kutikuti o ngā wāhanga-whiti katoa, ā, ka haere ngā kawenga katoa e poutū ana ki te tuaka o te tokotoko mā taua rārangi. Ki te kore, ko te taipana o ia kawenga e pā ana ki te rārangi e hono ana i ngā pokapū kutikuti ka tohu i te kutikuti toromuri.
Fig. 15
Te pānga o te kaha whakawhiti ki te piko
E hāngai ana te ariā hangarau o te piko ki te whakaarokore i ngā pāheketanga nā ngā taumahatanga kutikuti. Nō reira, ka taea tonu te whakamahi ki ngā tokotoko angiangi, arā, he tika tēnei whakaarokore i reira, ā, kāore te kaha whakawhiti e tino whai pānga ki te piko.
Heoi anō, kua whakaaturia e te wheako ka taea te whakamahi me ētahi angitū i te ariā hangarau o te piko ki runga i ngā kaikawenga poto, teitei hoki, ahakoa kāore rawa i hoahoatia mō rātou. I reira ka kitea te hiahia kia whakaarohia anō, ahakoa he tata noa iho, te pānga o te whakarerekētanga nā ngā taumahatanga kutikuti, i tēnei ariā i whakarērea.
Pēnei anō me ngā taumahatanga kutikuti τ nā ngā kaha whakawhiti, ka tohaina koretika hoki ngā retiretanga e hāngai ana γ_’ =_ τ_/G_ puta noa i te wāhanga-whiti. Nā reira ka whakaurua tō rātou uara toharite γ, ka whakatauria kia pēnei ai ka mahia e te kaha whakawhiti i tēnei uara toharite o te whakarerekētanga he mahi whakarerekē i runga i te huānga kurupae dx he ōrite ki tērā e puta ana mā te whakakotahi i ngā mahi a ngā taumahatanga kutikuti ki ngā huānga rōrahi takitahi e waihanga ana i te huānga kurupae kua tirohia:
i reira ka
Ka taea te tātai i te tāuru ina mōhiotia te tohatoha o ngā taumahatanga kutikuti puta noa i te wāhanga. I te mea he ōrite katoa ngā taumahatanga kutikuti ki te Q/F, nō reira he ōrite hoki tōna uara ki te Q2/F2 * F, ā, mā te whakatakoto he κ__Q2/F, ka riro
γ = κ__Q / GF.
Ko te pūmau κ e kīia ana ko te tāupe tohatoha o ngā ahotea kutikuti. Mō ngā wāhanga tapawhā, κ=1,2.
Fig. 16
Ina mōhiotia te taupū κ, ā, mā reira hoki te paheke toharite γ, ka taea te tātai te piko tāpiri wQ, i hua mai i te mahi a ngā kaha whakawhiti, me tāpiri ki ngā piko w: nā te mea, e ai ki te whika 16 ko
nā reira, nā te Q = dM/dx:
i reira ka puta te pūmau whakauru mai i tētahi o ngā tikanga tapa.