** ƙwararrun ƙwararrun kayan tarihi:** labarin yana adana hanyoyin tarihi, ƙididdiga, teburi da zane-zane a fagen tsattsauran ra’ayi, amma ba aiki ba ne, ƙididdigewa a tsaye, hujjar ƙarfin lodi, shirin taro ko kimanta ginin da ke akwai. Goyon baya, tazara, lodi, haɗakar ayyuka, lissafi, kayan aiki, haɗin kai, kwanciyar hankali, gajiya, girgizar ƙasa da matakan gini dole ne a ƙaddara don takamaiman abu bisa ga ingantattun ma’auni. Injiniyoyin da ke da izini an ƙirƙira su kuma bincika su masu ɗaukar kaya.
A yau, Savo Kusić yana mai da hankali kan gilashin katako, itace-aluminum Taga, Taga na al’ada, kofa da buƙatun magana. Wannan labarin ya kasance a matsayin tarihin tarihi kuma baya wakiltar tayin ƙira, lissafi ko aiwatar da gine-gine.
** Formules da Alamu:** an canza kalmomin lissafi a cikin rubutu ta hanyar lambobi daga tushen da aka bincika kuma suna iya ƙunshi kurakurai na rubutu ko OCR. Kada a shigar da su cikin lissafi ba tare da kwatantawa da tushe mai tushe ba, raka’a dubawa, alamu, zato da yanayin iyaka.
Haske mai sauƙi
Goyon bayan halayen, lokacin lanƙwasawa, nakasu da kuma lokacin tsaye M0-yanki don wasu lokuta masu yawan faruwa akai-akai ana bayar da su a cikin tebur1.
Maɗaukaki na yau da kullun tare da rundunonin runduna
Tare da lodi mai ma’ana (Fig.1) lissafin ya fi sauƙi don aiwatarwa ta hanyar ginshiƙai biyu na ƙari a cikin nau’i na tebur. Dangane da alaƙar da ke tsakanin kaya, ƙarfin juzu’i da lokacin
_Qn = Qn+1+ Pn da Mn+1/_λ __= Mn/_λ + Qn+1
Ƙarfin mai jujjuyawar a cikin filin n yana farawa da farko, yana farawa daga ƙarfin juzu’i a tsakiyar katako, sannan lokacin lanƙwasawa a wasu wuraren da suka fara daga ƙimar Mi/λ.
Siffa.1tare da teburi masu taimako.
Lokacin da nauyin ya kasance asymmetrical, kuma nisan ƙarfin ya zama daidai, tebur masu zuwa sun dace da lissafi (fig.2). Duk wani nauyin asymmetric zai iya zama bisa ga fig.3maye gurbinsu da nauyin antimetric guda ɗaya, wanda sau da yawa yana da amfani sosai a cikin lissafi. Maimakon rundunonin Pi da P’i a cikin yanayin ɗaukar nauyi, dakarun (Pi+P’i)/2a maki i da i’, kuma a cikin yanayin ɗaukar nauyi, ƙarfin (Pi-P’i)/2a aya i da karfi -(Pi-P’i)/2a point i’. Lokacin da aka ƙayyade halayen goyan baya a ƙarƙashin lodin antymetric, ƙarfin juzu’i da lokacin lanƙwasawa kuma ana iya ƙaddara a cikin tebur.
Siffa. 2.
Siffa.3.
Matsar da lodi
Ana samun lokacin lanƙwasawa a wuri i ta hanyar zane ta amfani da polygon mai ƙarfi da sarƙoƙi don wani kaya da aka bayar. Ana iya zana polygon sarkar kamar yadda aka nuna a fig.4. Don ƙayyade mafi ƙarancin matsayi na kaya don lokacin a wuri i, ana motsa goyon baya a ƙarƙashin kaya (Fig.5) har sai an tantance max η__i, daga inda aka samu max_Mi_ = H * max_η__i_. Mafi girman ƙarfin juzu’i a wurin i ana samun lokacin da aka motsa lodi ta yadda ƙarfin farko ya kai aya i. Ana iya samun shi daga polygon na sojojin a cikin fig.6: max_Oi_ =1_/l_ * ∑Pibi. A-polygon sarkar polygon ne tare da tazarar sandar sanda H = l, wanda aka zana don tsarin motsi na rundunonin da aka tattara lokacin da ƙarfin farko ya kasance akan goyan baya b.
Siffa.4.
Siffa.5.
Siffa.6.
** Matsar da kaya: ** zaɓi na matsayi mai dacewa da haɗuwa da nauyin motsi ya dogara da manufar tsarin, tsarin aiki, tasiri mai mahimmanci da ka’idoji masu dacewa. Hanyar zane-zane na tarihi bai isa ba hujjar mafi ƙarancin yanayin ginin zamani.
Bracket tare da haɗin gwiwa
Nau’in lodi
Na farko, halayen goyon baya da dakarun da ke cikin haɗin gwiwa an ƙaddara su daga yanayin ma’auni da kuma yanayin haɗin gwiwa. Sa’an nan, lokacin lanƙwasawa da ƙarfin juzu’i don faranti na goyan baya ɗaya za’a iya ƙididdige su azaman katako mai sauƙi, ko katako tare da rataye. Sl.7yana nuna sakamakon lodin faranti uku tare da rungumar ƙarfi. Layin sojojin da ke jujjuyawa suna wucewa a kan haɗin gwiwa a matsayin akai-akai, da kuma lokacin layi ba tare da raguwa ba, idan babu wani karfi mai karfi a cikin haɗin gwiwa.
Siffa.7.
Don nauyin da aka rarraba daidai a kan dukkanin goyon baya, ana samun wasu manyan bambance-bambance tsakanin lokutan akan goyon baya da kuma mafi yawan lokuta a cikin filayen, bisa ga ma’auni na tsawon lokaci da matsayi na haɗin gwiwa, fig.8. Idan a cikin yanayin tallafi tare da haɗin gwiwa tare da buɗewa sama da biyu (fig.9) kuma tare da jeri daidai l na filayen tsakiya zaɓi kewayon filayen ƙarshen l1=0,8535_l_ da matsayi na haɗin gwiwa c=0,1465_l_, sannan tare da nauyin da aka rarraba daidai, ana samun cewa iyakar ƙimar lokutan akan tallafi da a cikin filayen suna daidai da juna, M=0,0625_gl_2. Idan filayen ƙarshen suma suna da kewayon l, to max_M_= garesu0,0957_gl_2.
Siffa.8.
Siffa.9.
Layukan Tasiri
A cewar fig.10Layukan tasiri na Mi da Qi tsakanin maki a da b iri ɗaya ne da layin tasirin katako mai sauƙi. Ana ƙaddamar da gaba na layin tasiri ta hanyar matsayi na goyon baya da haɗin gwiwa waɗanda ke wakiltar manyan sanduna da tsaka-tsakin sarkar kinematic da aka ƙirƙira ta hanyar cire madaidaicin adadi a aya i. Hakazalika, ana ƙaddara layin tasiri na Mr da Qr suna farawa daga katakon da aka goyan baya a maki g1 da c. Load da katako tare da wuce gona da iri akan sashi _ag1_bashi da wani tasiri akan lokatai da jujjuyawar ƙarfi a aya r. Layukan tasiri na lokuta da ƙarfin juzu’i a wuraren da suka wuce (k da v) ana samun sauƙin samu lokacin da aka ƙayyade ordinates don matsayi na kaya a cikin haɗin gwiwa.
Siffa.10.
** Samfurin goyan baya da haɗin gwiwa: ** ainihin ƙaƙƙarfan haɗin gwiwa, daidaitawar tallafi, sharewa, ɓarna, rashin daidaituwa da jerin taro na iya canza rarraba ƙarfi idan aka kwatanta da ƙirar da aka dace. Dole ne a daidaita zato tare da cikakkun bayanan gini kuma a tabbatar da duk matakan da suka dace.
Ruku’u akan haɗin gwiwa guda uku
Tare da ɗorawa na sabani na baka akan haɗin gwiwa guda uku, ana iya tantance halayen goyan bayan ta hoto. Sakamako R1 runduna masu aiki wanda bisa ga fig.11aiki akan farantin hagu dole ne ya daidaita tare da amsa Kb1, wanda layin harin dole ne ya wuce ta hanyar haɗin gwiwa g, kuma ta hanyar amsawa Ka1. Haka kuma akwai Ka2 da Kb2, saboda R2. Tare da tasirin lokaci guda na R1 da R2 ana samun su ta hanyar ƙaura daidai gwargwado da tari na ƙarshe na Ka da Kb da matsi na haɗin gwiwa G.
Siffa.11.
Tare da bayani na nazari, yana da dacewa don aiwatar da lissafin musamman don a kwance kuma musamman don ɗaukar nauyi.
Horizontal load
A kwance lodi a cikin fig.12yana haifar da martani
Siffa.12.
inda C da D sune abubuwan da suka shafi amsawa a cikin hanyar da ke haɗa maki a da b. ∑H = C*cos_a_ – D_cos_a + ∑W =0. Dakarun da ke aiki su ne:
Ni = -Asin__φ__i – Ccos(φ__i-a) – Wmcos__φ__i_,_
Qi = +Acos__φ__i – Csin(φ__i-a) – Wmsin__φ__i,
Mi = A__x__i _– Ccosa*_y__i – Wm(hi-hm).
lodi a tsaye
Nauyin tsaye na baka akan haɗin gwiwa guda uku a cikin fig.13yana haifar da halayen A0kuma B0, waɗanda suke daidai da halayen ɗan ƙaramin katako na span l, da bugun kwance C = cosa = Dcosa = H = Mg0/f (1), inda Mg0 lokaci akan ƙaramin katako a cikin sashe g. Tare da abubuwan da aka gyara a tsaye C da D sassan a tsaye na ƙarshe na halayen sune A = A0 + H_tg_a; B = B0- H_tg_a. Idan axis na baka yana da murabba’in parabola, yi = f xi x’i/la lb, to ga cikakken nauyin da aka raba daidai g t/m (Fig.14) Mi=0, Qi=0.
Siffa.13.
Siffa.14.
Layukan Tasiri
Tasirin layi don amsawa A0 da B0 daidai suke da layin tasiri na katako mai sauƙi. Ana samun layin tasiri don matsawar kwance H bisa ga lissafin (1) daga layin tasiri na dan lokaci Mg0 saukin katako, fig.15. Layin tasiri na lokacin lanƙwasawa Mi ya ƙunshi layin tasiri tare da Mi0 da H, ana ninka na ƙarshe ta -yi. Waɗannan layukan masu tasiri guda biyu an dora su a kan madaidaiciyar ab’ a matsayin layin sifili, daga inda aka zana sassan aa’ = xi da bb’ = -lb yi/f. Bambancin da aka nuna ta motsi ai’g’b yana wakiltar layin tasiri na ƙarshe na Mi. Mai raba ko sifili na layin tasirin da ya dace da babban sandar farantin ig ana samun shi ta hanyar haɗin layin ai da bg. Hakanan za’a iya amfani dashi don gina layin tasiri, inda aka gabatar da sauƙi mai sauƙi na span a - n. Ga baka wanda axis shine murabba’in murabba’i, nauyin da aka rarraba daidai ba ya haifar da lokacin lanƙwasawa, don haka jimlar tasirin layin dole ne ya zama sifili.
Siffa.15.
A cikin fig.16Layukan tasiri na Qi da Ni an sami su ta wurin madaidaicin madaidaicin layukan tasiri na Qi0 da H. Game da ab’ a matsayin layin sifili, duka layukan tasiri a wannan yanayin layin tasiri ne na katako mai sauƙi. Don gina ko sarrafa layukan masu tasiri, ana iya amfani da sassan nQ da nN na layin bg da layin da aka zana ta cikin layi daya a nan, bi da bi. na yau da kullun ga tangent ɗin da ya mamaye kusurwar φ__i tare da kwance. A cikin yanayin baka mai ban sha’awa tare da haɗin gwiwa guda uku, jimillar layin tasiri don ƙarfin juzu’i dole ne ya zama daidai da sifili.
Siffa.16.
** Arches da bugun kwance a kwance:** Matsayin haɗin gwiwa, joometry na axis, tsaurin tushe da kuma yarda da halayen kwance suna da mahimmanci ga halayen tsarin. Canza goyan baya, tashin hankali, rataye ko lokacin hawa na iya canza kwararar runduna; zane mai kyawu na tarihi bai isa ba don aiwatarwa ko gyarawa.
Arch mai tauri tare da katako da shingen rataye
lodi a tsaye
Halayen tsaye yayin lodin faranti masu tsattsauran ra’ayi na goyan bayan faifan ƙididdiga masu ƙarfi tare da katako, goyan bayan rataye da arches akan haɗin gwiwa guda uku da tashin hankali a cikin siffa.17a to f ana samun su daga ma’auni A0 =1/ l * ∑Pnbn da B0 =1/ l * ∑Pnan lokacin da aka sanya A don tsarin a da d_0 = A+K’‘l, B0 = B+K’’r da sauran tsarin A = A0, B= B0. Amsoshin A da B na tsarin a da d ana tantance su daga:
A = A0 - K’l = A0- H(tgal-tg__δ)
B = B0 - K’’r = B0- H(tgar+tg__δ)
Siffa.17.
Don tsarin a, d, e da f, abin da ke kwance shine C=0, kuma ga tsarin b shine E=0. Ƙaƙwalwar kwance, ko ƙaddamarwa a kwance H na tsarin a zuwa d, sassan da ke kwance na karfi a cikin arc na tsarin e da karfi a cikin tashin hankali na tsarin f an ƙaddara bisa ga ma’auni (1). Tebu mai zuwa yana ƙunshe da bayyani na halayen tallafi da ƙarfi a cikin sanduna Sn da Zn don tsarin ɗaiɗaikun.
Horizontal load
Idan ƙarfin kwance W yayi aiki akan faranti a nesa c daga haɗin gwiwa g (Fig.17da kuma e) halayen tallafi da yake haifarwa sune:
Layukan Tasiri
Ana samun layukan tasiri na rundunonin ƙwanƙwasa bisa ga kamanceceniya a cikin halayen waɗannan tsarin da sauƙi mai ma’ana uku. Don baka mai sanda mai kauri a ƙarƙashin baka (Langer beam) a cikin fig.18Ana nuna layukan tasiri na U2, D4 da L4. Karfi cikin sanda _U2_An samu daga lokacin2bel na sama: U2 = M2/h. Daga yanayin ∑V=0mun D4 = Q40/sin__φ – Mg0/f haka4/dan__φ. Hakanan daga yanayin ∑V=0yana biye ( lodi akan ƙananan bel) L4 = -Q50+ Mg0/f * da4.
Siffa.18.
Idan nodes na baka mai haɗe-haɗe uku tare da ƙaƙƙarfan katako mai ƙarfi (fig.19) kwanta a kan square parabola kuma idan haɗin gwiwa ya ta’allaka ne a cikin axis na katako, sa’an nan tare da daidai rarraba kaya g t/m lokacin lanƙwasawa shine M=0a wuraren ratayewa, da M_= g__λ__2/8a tsakiyar filin tsakanin masu rataye.
Siffa.19.
** Masu ratayewa, masu tayar da hankali da masu taurin kai:** waɗannan abubuwan da haɗin gwiwar su na iya zama masu kula da rashin ƙarfi, damuwa na biyu, gajiya, lalata, asarar prestress da yanayin taro. Ba a aiwatar da musanya su, ƙarfafawa ko cire su ba tare da aikin wucin gadi da na ƙarshe na jiha ba.
Frame yana goyan bayan
Siffa.20.
Sl.20yana nuna zanen lokaci na firam mai maɗaukaki uku tare da rataye da rataye da rataye saboda cikakken kaya da aka raba daidai. Ana samun layin tasiri na lokacin Me bisa lafazin Me \ = -Hh + Mk, ta hanyar babban matsayi na layin tasiri don bugun kwance H (tare da mai ninka \ -h) kuma don lokacin lanƙwasawa Mk akan overhang.
A cikin yanayin da ba a daidaita ba na tallafi na ma’auni, ana iya sauƙaƙa lissafin sau da yawa ta hanyar rarraba nauyin a cikin nau’i mai ma’ana da anti-symmetric loading, fig.21. Wannan gaskiya ne musamman ga goyan bayan firam a cikin fig.22kuma23, wanda ke nuna zane-zane na lokacin saboda ƙarfin da aka tattara a wani matsayi na musamman na goyon baya na sama. Ana iya fahimtar nauyin da ke kwance a tsayin joist a matsayin antimetric. Tunda za’a iya ɗaukar nauyin kwance na ƙananan strut a matsayin kayan aiki mai mahimmanci don ƙididdige ƙayyadaddun matsuguni a kwance na sub-strut, za’a iya kammala shi nan da nan daga lokacin saman saman zuwa wanda gefen sub-strut yana motsawa yayin ɗaukar nauyi. Ana samun waɗannan ƙaura ta hanyar haɗa jihohin ma’auni na antimetric. Saboda haka, ga lokuta a cikin fig.22kuma23layin layi yana motsawa zuwa dama.
Siffa.21.
Siffa.22.
Siffa.23.
** Frames da ƙaura:** Ƙarshen jagorancin ƙaura daga zane mai kyau ba ya maye gurbin duba nakasawa, sakamako na biyu, kwanciyar hankali, taurin haɗin gwiwa, tushe da abubuwan da ba su da ƙarfi. Ana duba jahohin iyakan ɗaukar nauyi da sabis akan cikakken samfurin.
Tasirin sararin samaniya
Siffa.24.
Dome na Schwedler (fig.24) da kuma grid grid dala (fig.25), a matsayin wani lamari na musamman na Schwedler’s dome inda meridians ba su da hutu, tare da m benaye da n gefe, ya ƙunshi m \ * n meridional rods S, (m+1)n sandunan zobe R da m*n sandunan zobba D. Kamar yadda adadin nodes k=(m+)1)n goyon baya yana ƙayyade daidai lokacin da adadin goyan bayan a =3ku =2n, wannan shine lokacin da kowane sawun jigon ya sami goyan baya akan madaidaiciyar cibiyar nauyi tare da goyan bayan a tsaye da a kwance. Idan sandunan ƙananan zoben sun faɗi, ana buƙatar madaidaicin matsayi mai goyan baya uku a cikin kowane juzu’i. Ya kamata a yi la’akari da yin amfani da tsarin tallafi na kwance. Hanyoyi na dogara ga fig.26ba daidai ba ne aka zaba domin yana yiwuwa a zana wani tsari na igiya mara jituwa.
Siffa.25.
Trapezoid da aka samar da sandunan meridian da sandunan zobe za a iya daure su da K\ -cikowa. Ya kamata a yi la’akari da sakamakon nodes a matsayin nodes na lebur lattice. Ana iya canja wurin kaya ta manyan nodes kawai. Load ɗin P na tsaye wanda ke kai hari a kumburin zai bazu zuwa wani sashi _Ks=Ps/_λ a cikin alkiblar meridian kuma zuwa cikin ɓangaren kwance _H=Pa/_λ. An kara ruguza bangaren da ke kwance a cikin sassan da ke kan sandar zobe _Kl=Hc/a=Pc/λ _i Kr=Hb/a=Pb/λ.
Hakazalika, an ƙayyade abubuwan Kl da Kr na madaidaicin ƙarfi na kwance W, ta yadda tsarin lodin da aka nuna a fig.27. Ba a nuna abubuwan da aka haɗa X a cikin hanyar sandunan meridian a cikin hoton ba.
Siffa.26kuma27, bi da bi.
Lokacin da goyan bayan da nauyin P suke da simmetrically cyclically, to, dakarun Kl sun yi daidai da rundunonin Kr, don haka diagonals ba su da damuwa yayin da dakarun da ke cikin sandunan meridian su ne:
_S1= -P1s/_λ; S2= (P1+P2)s/λ; S3= (P1+P2+P3)s/λ
kuma a cikin sandunan zobe:
_Ri = Pib/_λ
Ana iya aiwatar da lissafin dome na Schwedler ta hanya ɗaya lokacin da aka fahimci kowane bene a matsayin dala. Baya ga rundunonin aiki P da W, sojojin da ke cikin sandunan S da D na bene na sama yakamata a gabatar da su azaman dakarun waje, bi da bi. abubuwan da suka hada da su a cikin shugabanci na sandar meridian da sandunan zobe. Yayin da a cikin dala ta lattice ana jin tasirin ƙarfin da aka tattara guda ɗaya kawai a cikin sandunan faranti biyu da ke kusa da su, a cikin yanayin dome na Schwedler tasirin tasirinsa ya kai ga yawan sanduna masu girma. A cikin fig.24sandunan da aka damu saboda karfin P a cikin zobe na tsaye suna alama.
Tsarin sararin samaniya da gidaje: kwanciyar hankalin waɗannan tsarin ya dogara da aikin sararin samaniya, tallafi, rashin daidaituwa na geometric, buckling na sanduna, taurin nodes, yarda na wucin gadi da jerin taro. Zane mai lebur ko daidaitattun daidaikun mutane baya tabbatar da daidaiton duniya, ajiyar kaya ko aminci yayin ɗagawa.