Ƙididdigar tsarin: tallafi da daidaituwa

** Muhimmiyar Bayanin Fasaha da Tsaro:** Wannan rubutun ilimi ne, ba madaidaicin lissafi ba, ƙirar gini, ko littafin aiki. An canza tsarin tsari, ƙirar goyan baya da zane daga ainihin abun ciki ba tare da ƙwararrun ƙwararru ko daidaitawa ga ƙa’idodin yau ba. Ƙarfin ɗaukar nauyi, kwanciyar hankali, lodi, kayan aiki, haɗin gwiwa da tushe don takamaiman abu dole ne a ƙayyade ta injiniyan farar hula da aka ƙware bisa ingantattun ma’auni, bayanan geotechnical da ainihin yanayin tsarin. Misalai na ilimi ne kuma ba sa wakiltar ayyukan da aka tabbatar na Savo Kusić.

Ƙididdigar ƙididdiga da ƙira na tsarin tallafi ba sa cikin sabon tayin jama’a na kamfani. Mahimmancin samarwa na yanzu ya ƙunshi gilashin katako, itace-aluminum Taga da kofofin al’ada. Don takamaiman aikin taga ko kofa, zaku iya aika buƙatar magana.

Tsari da rarraba mai ɗaukar kaya

Abubuwan tallafi: kwanciyar hankali na ciki da na waje

Abubuwan da ake ɗauka sune:

Sauƙaƙan sanduna masu iya watsa ƙarfi ko matsawa kawai waɗanda layin harinsu ya zo daidai da axis na sandar. Wannan yana buƙatar sandunan da ke cikin kullin an ɗaure su tare da haɗin gwiwar da ba su da rikici, kuma sojojin waje suna kai hari ga kullin. Tallafin da ya ƙunshi sanduna masu sauƙi kawai ana kiransa trusses.

Sticks mai juriya da lankwasawa - katako - na iya watsa dukkan rundunonin da layin harinsu ya zo daidai da axis na sandar, haka nan kuma dakarun da layin harin suka yi daidai da axis na sandar ko kuma suka karkata zuwa gare ta ba bisa ka’ida ba. Ƙunƙwasa suna karɓar ƙarfi na al’ada, ƙarfin juyewa, lokacin lanƙwasawa kuma, a cikin yanayin da aka bayar, lokacin toshewar. Ana iya ɗaure waɗanda ke cikin kulli ko ta hanyar kusurwoyi masu tsauri.

Taimako da ƙugiya suna hana goyon baya motsawa zuwa ƙayyadaddun wurare a cikin jirgin sama ko sarari. Kowane goyan baya yana da ikon watsa ƙarfi a wani takamaiman shugabanci wanda ke wucewa ta kullin da aka dakatar. Idan akwai goyon baya ɗaya kawai a cikin kumburin da aka goyan baya - wurin goyan baya - ana kiransa motsi mai ɗaukar nauyi na goyan bayan sarari. Idan kumburin yana goyan bayan goyan baya biyu, ana kiransa immovable bed na goyan bayan lebur, ko gadon layi mai ɗaukar sarari. Kwancen gado na tallafin sararin samaniya yana buƙatar tallafi uku.

Kowane tsunkule na sanda mai juriya yana iya watsa lokacin tsinke a cikin wani jirgin sama. A mafi yawan lokuta, an haɗa igiyar da ba za ta iya motsi ba zuwa maƙala, ta yadda a yanayin goyon bayan lebur ɗin akwai goyon baya biyu da ɗaki ɗaya, kuma a yanayin goyon bayan sararin samaniya akwai goyon baya uku da maɗaukaki uku. Motsa jiki da jujjuyawar ƙayyadaddun girman na iya faruwa a wuraren goyan baya da ƙwanƙwasa.

Ana samun adadin abubuwan da ake buƙata don kwanciyar hankali na tallafi daga yanayin kwanciyar hankali na ciki da waje. Taimakon yana internally stable lokacin da tsaka-tsakin matsayi na nodes na goyon baya yana tabbatar da isasshen adadin sanduna ta yadda za’a iya canza shi kawai lokacin da wasu ko duk na sandunan suka canza tsayi. Ana kiran goyan bayan lebur mai tsayayye na ciki rigid plate. Tallafin yana da ƙarfi a waje ko gabaɗaya lokacin da matsakaicin matsayi na nodes da matsayinsu bisa ga tsayayyen maki na jirgin sama, ko sarari na iya canzawa kawai zuwa girman canje-canje a cikin tsayin sanduna, motsi na goyan baya ko juyawa na clamping.

Madaidaicin madaidaicin

Matsakaicin adadin sandunan da ake buƙata don kwanciyar hankali na ciki da ƙaramin adadin sanduna da goyan baya da ake buƙata don kwanciyar hankali na waje na truss tare da s rods, a goyon baya da k nodes shine:

s =2ku -3

s + a =2ku,(3_≤_ a)

Sharadi na farko yana cika lokacin da aka samar da goyan bayan farawa daga sanda ɗaya ta hanyar haɗa ƙarin nodes tare da sanduna guda biyu kowannensu, ta yadda sandunan da aka haɗa kumburi ɗaya ba dole ba ne su kwanta akan madaidaiciyar layi ɗaya.

Baki mai s1 sanduna masu sauki, s2 sanduna masu jure jurewa, e madaidaitan kusurwa, _a1_taimakawa, a2 pinches da k nodes na ciki ne, ko kuma na waje idan:

s1+ s2+ e≥_ 2ku -3

s1+ s2+ e + a1+ a2 ≥2ku (a=a1+ a2≥3)_

Sl.1

Ana iya maye gurbin kowane kusurwa mai tsayi da sanda mai sauƙi. Idan a cikin kulli ɗaya i sanduna suna da alaƙa da juna, adadin madaidaitan kusurwa a cikin wannan kumburin shine i\ -1. Lokacin da aka kidaya overhangs na sanduna (consoles) a matsayin sanduna, ya kamata a ƙidaya iyakar kyauta a matsayin nodes. Bakin a cikin fig.1da s1=9, s2=7, e=5(alama a cikin hoton) da k=12ciki yana da kwanciyar hankali. Lokacin m kusurwa4kuma5bari mu maye gurbinsa da haɗin gwiwa da sanduna masu sauƙi, waɗanda aka yi wa alama da karya layukan da ke cikin hoton, sannan s1=11, s2=7, e=3, yayin da adadin nodes ya kasance ba canzawa.

Sl.2kuma i2b

Idan a cikin goyon baya ɗaya tare da mafi ƙarancin adadin tallafi da ake buƙata, kowane sanduna ko kusurwoyi masu tsauri ana maye gurbinsu da goyan baya ko ƙugiya, tallafin ya rasa kwanciyar hankali na ciki, fig.2a, b. Don irin waɗannan tallafin akwai wasu yuwuwar yadda za’a iya gwada kwanciyar hankali. Idan p shine adadin madaidaicin faranti na tallafi ba tare da kwanciyar hankali na ciki ba, yayin da ya kamata a lura cewa sanda ɗaya mai sauƙi ko sanda mai juriya don lankwasawa ya dace da yanayin kwanciyar hankali na ciki kuma ana iya fahimtar shi azaman farantin m, kuma idan z shine adadin hulɗar haɗin gwiwa a cikin haɗin gwiwa, kwanciyar hankali na waje yana buƙatar cewa: a + z _ ≉3p_. Adadin halayen tsaka-tsaki a cikin haɗin gwiwa wanda aka haɗa farantin (fig.3,4,5) z=2(_kuma-_1).

Sl.3kuma4, bi da bi

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Firam a cikin fig.6sau shida ne a kimiyance. Idan overhangs, waɗanda ba su da tasiri a kan matakin rashin daidaituwa, an ƙidaya su a matsayin sanduna, ƙananan kusurwar da aka haɗa su da tsarin ya kamata a yi la’akari da su kuma a ƙidaya iyakar kyauta na overhangs a matsayin nodes (s=).7, e=6, a=9, k=8). Don waɗannan nau’ikan tallafi, yanayin da ya dace don gwada kwanciyar hankali na ciki da waje shine:

3_s_ 3k-3;3s+a ≥3ku, (a≥3).

A lokaci guda kuma, ba dole ba ne a ƙidaya abubuwan wucewa a matsayin sanduna. Sau da yawa, a irin waɗannan lokuta, hanya mafi sauri don zuwa ga ƙarshe game da matakin rashin ƙayyadaddun goyan baya shine ta hanyar yanke sanduna ko ban da ƙididdige ƙididdiga har sai an sami kwanciyar hankali, tabbataccen ƙayyadaddun tallafi. Tare da sassan uku da aka nuna a cikin fig.7Ba a cire madaidaitan adadi guda uku (ƙarfin al’ada, ƙarfin juzu’i, lokacin lanƙwasawa).

Idan a daya n0-Lokacin da ba a iya tantancewa ba tare da lattice ba duk sandunan da ke cikin nodes ɗin suna da alaƙa da ƙarfi, matakin ƙarancin ƙima yana

_n = n0+2ku - ku

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Yana goyan bayan sararin samaniya

Matsakaicin adadin goyan bayan grid na sararin samaniya shine a=6. Sharuɗɗa masu zuwa sun shafi kwanciyar hankali na ciki da na waje:

s 3ku -6; s + a ≥3ku, (a≥6).

Yanayin kwanciyar hankali na ciki yana cika lokacin da, farawa daga farantin triangular guda ɗaya, ƙarin nodes a cikin sararin samaniya an ɗaure su tare da sanduna uku kowanne, wanda dole ne ba ya kwanta a cikin jirgi ɗaya. Ta wannan hanyar, ana ƙirƙirar spatial grid na nau’in farko, halayensa shine koyaushe yana ɗauke da aƙalla kumburi guda ɗaya waɗanda sanduna uku kawai ke ɗaure, kuma yana riƙe da wannan fasalin koda an cire wannan kumburin tare da daidaitattun sanduna.

Bugu da ƙari, ana iya samar da grid na sararin samaniya ta hanyar haɗa faranti mai siffar triangular ta yadda za a haɗa faranti biyu da biyu tare da sanduna shida, inda kowane kumburi yana haɗa da faranti na kusa da sanduna biyu kowanne. Haɗin faranti biyu ko grid masu tsayayye na ciki biyu ana iya samun su ta hanyar haɗin gwiwa ɗaya da sanduna uku waɗanda ba sa wucewa ta wannan haɗin gwiwa. A ƙarshe, ana iya haɗa faranti na triangular uku da su12na sanduna da kuma cewa tare da po4sanda tsakanin kowane faranti. Don na ciki, ko kwanciyar hankali na waje na goyan bayan sararin samaniya inda duk sanduna ke daure da kyar don lankwasawa da karkatarwa, dole ne a cika sharuɗɗan.

_6ku _≥6(k-1);6s + a ≥6k

Saboda haka, mai ɗauka a cikin fig.8shine24sau statically m, wanda, kamar yadda ya gabata, za a iya tabbatar da mafi sauƙi lokacin da aka yanke sandunan kwance guda huɗu kuma ta wannan hanyar an cire abubuwan da ba a sani ba guda shida a kowane yanke (1karfi na al’ada,2dakarun da ke karkata2 mlankwasawa kuma1lokacin torsional). Idan muka cire haɗin f ta hanyar shigar da haɗin gwiwa a cikin sanduna ko haɗin su, to, yanayin kwanciyar hankali shine:

6s - f 6(k-1);6s - f + a ≥6k.

Sl.8

Load da martani: ayyuka na ƙididdiga

A cikin yanayin goyon baya na lebur, dole ne sojojin waje su kwanta a cikin jirgin sama na goyon baya, a cikin yanayin goyon bayan sararin samaniya, za su iya samun matsayi na sabani. A cikin trusses, an ɗauka cewa nauyin ya kai hari a nodes.

Kungiyoyi masu aiki suna haifar da juriya na external abubuwan, halayen goyan baya C a cikin goyon baya da lokacin tsinke E a cikin pinches. Ƙarfafawar abubuwan internal na tallafi - rundunonin giciye - sune: sojojin axial S a cikin sanduna masu sauƙi; a cikin sanduna masu jure juriya da jujjuyawa na al’ada ko rundunonin tsaye N, lokacin lanƙwasawa M, lokacin murɗawa ko lokacin torsional T da ƙarfin juzu’i Q. Juriya na abubuwan kuma na iya haifar da canje-canje a yanayin zafi da sassauta abubuwan tallafi.

Dimensioning na daidaikun abubuwa da kuma tantance ƙarfin lantarki da ke bayyana a cikin su shine aikin Resistance Material. Lokacin da aka ƙayyade ƙima mai mahimmanci, kayan da aka yi amfani da su yana da mahimmanci kawai har sai nauyin dindindin ya dogara da shi. Sauran kaddarorin kayan ana la’akari dasu ne kawai lokacin da yazo da tasirin motsin tallafi ko canje-canjen zafin jiki (raguwa, kwarara) ko lokacin da ake buƙatar ƙididdige nakasu. Gabaɗaya, ya kamata a gwada girders don lokuta daban-daban waɗanda ba dole ba ne su faru a lokaci guda (nauyin dindindin, kaya mai amfani, nauyin iska, nauyin dusar ƙanƙara). Tsammanin cewa nakasar nakasassu tana da ƙanƙanta da za a iya watsi da su dangane da ma’aunin tsarin - kuma galibi haka lamarin yake - ƙa’idar superposition ta shafi, bisa ga abin da za a iya bincika shari’o’in ɗaukar nauyi da sauran tasirin daban da ƙididdige ƙididdige ƙididdigewa don ƙididdige ƙididdiga ko ƙididdigar lissafi tare, tare da takamaiman gyara dabi’u ta hanyar ƙimar aminci na dindindin ko ma’auni (fasalin ƙima na dindindin). mara kyau).

Tabbatattun abubuwan tallafi

Ba a sani ba kuma akwai daidaitattun daidaito

A cikin ƙayyadaddun ƙayyadaddun ƙayyadaddun ƙayyadaddun lattice, a halayen goyan baya da s axial sojojin ba a san su ba, ƙayyadaddun sa yana samuwa lokacin da lattice yana da nodes k_2_k equation (∑X=0da ∑Y=0) a cikin jirgi i3k equation a sarari. A cikin madaidaicin goyan bayan, ana iya rage abubuwan da ba a sani ba zuwa s1 dakarun axial na sanduna masu sauki, _s2_Rukunin sanduna na yau da kullun masu jurewa lankwasawa, e lokacin lanƙwasawa cikin kusurwoyi masu tsauri, a1 martanin tallafi da _a2_lokacin matsawa. Ya kamata a ƙayyade ƙarfin jujjuyawar daga lokuttan da ke ƙarshen sanduna da sojojin waje da ke aiki tsakanin nodes. A cikin kumburin da i sandunan da aka haɗa da gaske suka fara zuwa nodes ɗin maƙwabta, ya isa sanin i\ -1 moment - wanda yayi daidai da adadin kusurwoyi masu tsauri - saboda don ƙayyade wani lokacin da ba a sani ba a cikin kowane irin wannan kumburi akwai yanayin ma’auni ∑M=0. Don tantance s1 + s2 + e + a1 + a2_Wanda har yanzu ba a sani ba2_k yanayin daidaito.

Sharuɗɗa don ma’auni na ƙarfin waje akan goyan bayan lebur

Martanin farantin yana goyan bayan tsayawa akan kafaffen kafaɗaɗɗen daɗaɗɗen motsi ɗaya (Fig.9) ana samun su ta hanyar hoto ta amfani da polygons mai ƙarfi. An san layin harin da karfi B kuma yana da jagorancin goyon baya a wannan lokacin, kuma layin harin karfi Ka dole ne ya wuce ta hanyar haɗin gwiwar sojojin B da P. An ƙididdige shi daga yanayin Ma =0, H =0da Mb =0a hankali sojojin B, C da A sun ƙaddara su. Ajiye farantin a kan ɗakuna masu motsi uku (fig.10) daidai ne kawai lokacin da layin amsa ba su shiga lokaci ɗaya ba. Ana ƙayyade martani ta hanyar zane ta amfani da polygons mai ƙarfi ko ƙididdigewa ta yin amfani da ma’auni na ɗan lokaci dangane da wuraren da layukan hari biyu da biyu na sojoji ke haɗuwa.

Sl.9

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A cikin yanayin ƙayyadaddun ƙayyadaddun ƙayyadaddun tallafi ba tare da kwanciyar hankali na ciki ba, ban da yanayin ma’auni na ma’auni na waje gaba ɗaya, ana kuma gabatar da yanayi don haɗin gwiwa, wanda ke bayyana buƙatar cewa haɗin gwiwa ba zai iya samun lokacin lanƙwasa ba. Sabili da haka, layin kai hari na dauki Ka na firam mai hawa uku a cikin siffa.11 mora ya wuce ta hanyar haɗin g, kuma farantin dama zai iya kasancewa cikin ma’auni kawai lokacin da rundunonin uku da ke aiki akan shi (P, Kb da karfi a cikin haɗin gwiwa = Ka) sun haɗu a lokaci guda. Domin samun ma’aunin ma’auni mai ƙunshe da ɗaya kaɗai wanda ba a san kowa ba, yana da dacewa don ƙididdigewa tare da madaidaitan sassan halayen A da B da abubuwan C da D tare da layin da ke haɗa wuraren tallafi. Daga yanayin Mb =0da Ma =0ana samun sojojin A da B, kuma daga yanayin haɗin gwiwa Mg =0ga sojojin da suka kai hari kan farantin hagu, ana samun karfi C, kuma ga dakarun da ke kan farantin dama, tilasta D. Hakazalika, an ƙayyade halayen da ke goyon bayan firam a cikin fig.12. Don nauyin da aka bayar a nan, hanya mafi sauri don samun sakamakon shine zane. Bracket tare da haɗin gwiwa bisa ga fig.13. Abubuwan da ke kwance na sojojin waje waɗanda ke kai hari ga tallafin suna karɓar gadon tsaye, ana samun ƙarfin F daga ∑H=0. Ana goyan bayan farantin II a maki _g1_kuma_Mr2_a kan faranti I da III, da farantin IV a cikin _g3_na III. Sojojin tsaye a cikin haɗin gwiwa G1, G2, G3 da amsa E an ƙaddara daga ma’aunin ma’auni na farantin II ko IV, sannan an ƙaddara matakin mataki-mataki halayen A, B, C da D.

Sl.11kuma12, bi da bi

Sl.13

Ƙaddamar da masu girma dabam na ciki

A matsayinka na mai mulki, axial Forces S na sanduna masu sauƙi suna la’akari da kyau lokacin da suke da karfi, da kuma mummunan lokacin da suke da karfi. Hakazalika, an ƙayyade alamar ƙarfin al’ada N a cikin katako. Ƙarfi na al’ada Ni a wurin i shine bangaren da yake daidai da tangent zuwa kusurwar katako a wurin i na sakamakon R na duk dakarun da ke aiki a kan katako a gefe ɗaya na batu i. Ƙarfin jujjuyawar Qi shine ɓangaren al’ada ga ma’aunin sandar a wurin kuma iri ɗaya kuma sakamakon, kuma lokacin lanƙwasawa Mi shine lokacin wannan sakamakon (Fig.14). Ƙididdigar adadin N, Q da M ana yin su akai-akai daga runduna guda ɗaya da kayan aikin su a layi ɗaya kuma daidai da axis na sanda ba tare da tantance sakamakon R ba. An nuna al’ada na ingantattun kwatance a fig.15.

Sl.14kuma15, bi da bi

Tun da an ƙaddara halayen goyan baya ta hanyar hoto, ana iya ƙayyade ƙarfin al’ada, lokacin lanƙwasa da ƙarfin juzu’i daga polygon mai ƙarfi da tsarin da aka ba da ƙarfi ta matsayi. Misali, a cikin ginshiƙin hagu na firam mai ɗaure uku a cikin fig.11bangaren karfi na tsaye Ka shine karfin al’ada (mara kyau), bangaren kwance shine madaidaicin karfi (negative), sannan Mi = Kari lokacin lankwasawa, mara kyau idan lokutan da ke haifar da tashin hankali a ciki ana daukar su tabbatacce.

Sharuɗɗan ∑X = dole ne a cika su a kowane kulli inda sandunan ke rataye0, ∑Y=0. Grids waɗanda aka kafa ta hanya mafi sauƙi - ta hanyar haɗa nodes tare da sanduna biyu kowanne - koyaushe suna da aƙalla kumburi guda ɗaya inda sanduna biyu kawai ke haɗuwa. Ta hanyar cire irin waɗannan nodes, ana kiyaye wannan fasalin. Ana iya aiwatar da lissafin sojojin axial a cikin sanduna ta hanyar warware ma’auni biyu tare da waɗanda ba a sani ba.

Ana samun mafita mai hoto ta hanyar gina force plan (Cremana plan) bisa ga fig.16. Sojojin waje _P1_zuwa P6 tsaye cikin daidaito. An ƙaddara ƙarfin da ke cikin sanduna Si a hankali suna farawa daga wurin1da tafiya daga kumburi zuwa kumburi a cikin tsari da aka lakafta su. Hakanan ana yin alama na dakarun a cikin tsari da aka ƙayyade. Kowane kumburi yayi daidai da polygon na sojoji tare da jagorar kibiya mai ci gaba, daga abin da alamun dakarun da ke cikin sanduna ke bi. Idan an yi wani sashe ta hanyar tallafi kuma idan a wuraren da aka yanke sandunan an yi amfani da dakarun da ke aiki a cikin waɗannan sanduna a matsayin dakarun waje, kowane bangare na lattice yana cikin ma’auni. A kan wannan, ana yin rikodin hanyar Culmann, ta yadda za’a iya tantance ƙarfin da ke cikin sandar sabani ba tare da sauran dakarun ba.

Sl.16

A cikin maganin nazari na matsalar saita daidaito tare da wanda ba a san ko wane ba, tsarin Ritter yana da mahimmanci. Ana yanke latti don yanke sanduna uku ya shafa. Ana amfani da dakarun da ke cikin sandunan sashe zuwa kowane ɓangaren truss a matsayin ƙarfin tashin hankali, daga kumburi zuwa sashe. Sharuɗɗan ma’auni sun shafi kowane ɓangare na lattice. Ƙaddamarwar sanduna biyu da biyu masu haɗakarwa ita ce lokacin lokacin da ake ƙayyade ƙarfin a cikin sanda na uku (Ritter’s point). Idan ri shine nisa na ƙarfin Si daga lokacin batu i, kuma Mi shine lokacin ma’aikata masu aiki da halayen tallafi dangane da batu i, to, an ba da karfi a cikin sanda ta hanyar magana.

Si = ± Mi/ri

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A cewar fig.17kuma18Sojojin da ke cikin sandunan giciye sune:

Ana = -Mn/rn;   un-1= Mn-1/rn-1;

Dn = Md/rd;      Ln = Mv/rv.

Lokacin da ginin hoto bai samar da isasshiyar daidaito ba, dole ne a ƙididdige matsayi na lokacin maki d da v da nisa rd da rv. Don lissafin rundunonin D da L, maganganun masu zuwa sun fi dacewa, wanda kawai abubuwan halayen grid suna bayyana a matsayin maki na lokaci (Fig.19,18):

D = (Mu/hu – M(o)/ho) * (d/λd), (35)

Ln = ± Ql ± (Mn tgβn + M’n tgγn)/hn.

Don gratings tare da bel ɗin layi ɗaya, ana iya samun ƙarfin D da L kai tsaye daga ƙarfin juzu’i:

D = Q/zunubi__φ_;   L=__±Q_

Sl.19

Matsar da kaya da tasirin tasiri

Idan an ɗora goyon baya tare da nauyin motsi, ƙarfin ƙarfafawa a tsaka-tsakin tsaka-tsakin tsakanin juna, sa’an nan kuma gwaje-gwajen ya kamata a yi a most unfavorable load positions. Don sauƙi mai sauƙi akan goyan baya guda biyu, ana iya samun mafi girman ƙarfin juzu’i Qmax ta amfani da A-polygon, kuma mafi girman lokacin lanƙwasawa Mmax ta amfani da polygon sarkar don tsarin ƙarfin da goyon baya ke motsawa.

Lokacin da aka ƙayyade layin tasiri don adadi ɗaya ko na geometric, da kuma nauyin Pm=1wanda ke tafiya tare da bel ɗin da aka ɗora na mai ɗaukar nauyi, don kowane matsayi na m ana amfani da shi a ƙarƙashin ƙarfi, daga layin sifili ɗaya, ƙimar ƙididdigewa ηm na girman da ake buƙata. Layin da ya haɗu da ƙarshen waɗannan ƙa’idodin shine line na tasiri. Layukan tasiri na lokacin lanƙwasawa Mi da ƙarfin juzu’i Qi a wurin i na katakon da aka goyan baya a maki a da b layukan ga da gb ne kai tsaye waɗanda sassansu akan madaidaiciyar goyan bayan sune aa’ = xi (= M’i na A=1) da bb’ = x’i (= M’‘i na B=1) (fig.20). An ba da layin tasiri na ƙarfin A ta layin gb, wanda ke daidaitawa a kan axis a tsaye shine a aa’=1.

Sl.20

Layin tasiri na kowane madaidaicin adadin goyan bayan da aka ƙaddara ya ƙunshi madaidaitan layukan daidai da tsayayyen faranti na sarkar kinematic tilas da aka ƙirƙira ta hanyar keɓance adadin da ake buƙata. Layuka suna haɗuwa a tsaye ta wurin maki nan take, ko kuma ta cikin wuraren da faranti ke jingina. Yankin da ke da iyaka da layin sifili, layin tasiri da ordinates guda biyu ana kiransa yankin tasiri. divider (sifili sifili na layin tasiri) yana rarraba sassa masu kyau da mara kyau na tasirin tasirin.

Kamar yadda ηm ke wakiltar tasirin motsin ƙarfi Pm=1akan adadin da ake buƙata Z, shine Pmηm tasirin ƙarfin Pm, yayin da tsarin runduna P ke haifar da tasirin Z=∑Pη. Za a sami iyakar ƙimar tasirin maxZ da minZ lokacin da aka saita tsarin motsi na rundunonin da aka haɗa ta yadda za a ninka mafi girman rundunoni ta hanyar mafi girma. Lokacin da ba a san matsayi mafi kyau ba tare da tabbacin, tasirin tasiri daga layin tasiri dole ne a lissafta gefe da gefe don matsayi daban-daban na kaya (tsari na maimaitawa).

Domin juzu’i daidai rarraba kaya p t/m shine _Z = _ _∫p dx η = pF, inda F shine alamar girman sashin da ya dace na saman mai tasiri. A wani ɓangaren kaya na iyakataccen tsayin c da siffar rectilinear na layin tasiri (Fig.58) ya kamata a sanya kaya ta yadda η1 =2(c1= cxi/l; c2= cx’i/l), don haka muna samun Z = pc (ηi + η1)/2. A cikin canja wurin kaya kai tsaye, layin tasiri yana tsakanin ordinates ηn da ηn+1 canje-canje a madaidaiciyar layi, fig.21.

Sl.21