Zindikirani Zofunika Zaukadaulo ndi Chitetezo: Awa ndi mawu ophunzitsira zakale, osati mawerengedwe osasunthika, kapangidwe kake, kapena buku la momwe amagwirira ntchito. Mafomula, zitsanzo zothandizira ndi zojambula zidasamutsidwa kuchokera pazomwe zidayambika popanda kutsimikizira akatswiri kapena kutengera malamulo amasiku ano. Mphamvu yonyamulira, kukhazikika, katundu, zida, zolumikizira ndi maziko a chinthu china chake ziyenera kutsimikiziridwa ndi mainjiniya ovomerezeka ogwirizana ndi miyezo yovomerezeka, deta ya geotechnical ndi momwe zimakhalira. Zithunzizo ndi zamaphunziro ndipo sizikuyimira mapulojekiti otsimikizika a Savo Kusić.
Kuwerengera kosasunthika ndi kapangidwe kazinthu zothandizira sizili gawo lazoperekedwa ndi anthu. Zomwe zidapangidwa pakadali pano ndi mazenera amatabwa, mazenera a matabwa a aluminiyamu ndi zitseko. Pazenera linalake kapena polojekiti ya pakhomo, mukhoza kutumiza pempho la quotation.
Mapangidwe ndi magawano a chonyamulira
Zinthu zothandizira: kukhazikika kwamkati ndi kunja
Zinthu zonyamula ndi:
Simple rods zomwe zimatha kutumiza mphamvu zokhazikika kapena zopondereza zomwe mzere wake wowukira umagwirizana ndi axis ya ndodo. Izi zikutanthawuza kuti ndodo zomwe zili muzitsulo zimamangiriridwa ndi mfundo zomwe palibe kumenyana, ndipo mphamvu zakunja zimamenyana ndi mfundozo. Zothandizira zomwe zimakhala ndi ndodo zosavuta zimatchedwa trusses.
Zomata zolimbana ndi kupindika - mizati - imatha kufalitsa mphamvu zonse zomwe mizere yawo yowukira imagwirizana ndi nsonga ya ndodo, ndi mphamvu zomwe mizere yawo yowukira imayenderana ndi nsonga ya ndodoyo kapena mokhomerera. Miyendo imalandira mphamvu zowoneka bwino, mphamvu zodutsa, mphindi zopindika ndipo, munthawi yomwe wapatsidwa, mphindi za torsion. Amene ali ndi mfundo amatha kumangidwa ndi mahinji kapena ndi ngodya zolimba.
Zothandizira ndi zomangira zimalepheretsa chithandizo kupita kumalo okhazikika mu ndege kapena danga. Thandizo lirilonse limatha kutumiza mphamvu kumbali ina yomwe imadutsa mu node yoyimitsidwa. Ngati pali chithandizo chimodzi chokha mu node yothandizira - malo othandizira - amatchedwa movable bear ya chithandizo cha malo. Ngati mfundoyo ithandizidwa ndi zothandizira ziwiri, imatchedwa immovable bed ya flat support, kapena space carrier line. Bedi loyima la chithandizo cha danga limafunikira zothandizira zitatu.
Kutsina kulikonse kwa ndodo yosapindika kumatha kutumiza mphindi yotsina ili mundege inayake. Nthawi zambiri, chotengera chosasunthika chimalumikizidwa ndi cholumikizira, kotero kuti pakakhala chithandizo chathyathyathya pali zogwirizira ziwiri ndi chingwe chimodzi, ndipo pakakhala chithandizo chapamalo pali zogwirizira zitatu ndi zingwe zitatu. Kusuntha ndi kusinthasintha kwa kukula kwinakwake kumatha kuchitika pamalo othandizira ndi kukanikiza.
Nambala yofunikira ya zinthu zokhazikika kwa chithandizocho imapezeka kuchokera kuzinthu zokhazikika mkati ndi kunja. Thandizo ndi internally stable pamene malo apakati-chipinda cha node za chithandizo amatsimikiziridwa ndi chiwerengero chokwanira cha ndodo kotero kuti chikhoza kusinthidwa kokha pamene zina kapena ndodo zonse zimasintha kutalika. Thandizo lokhazikika lamkati lokhazikika limatchedwa rigid plate. Thandizo limakhala lakunja kapena lokhazikika pamene malo apakati a mfundo ndi malo awo molingana ndi mfundo zokhazikika za ndege, kapena danga lingasinthe pokhapokha pakusintha kwa kutalika kwa ndodo, kuyenda kwa zothandizira kapena kuzungulira kwa clamping.
Mabulaketi athyathyathya
Chiwerengero chochepa cha ndodo zomwe zimafunikira kuti chikhazikike chamkati ndi chiwerengero chochepa cha ndodo ndi zothandizira zomwe zimafunika kuti pakhale bata lakunja la truss ndi s rods, a zothandizira ndi k node ndi:
s =2k -3
s + ndi =2k, (3 ≤_ a)
Mkhalidwe woyamba umakwaniritsidwa pamene chithandizo chimapangidwa kuyambira ndodo imodzi mwa kulumikiza mfundo zina ndi ndodo ziwiri iliyonse, momwe ndodo zomwe mfundo imodzi imagwirizanitsidwa sayenera kugona pamzere wowongoka womwewo.
Bracket yokhala ndi s1 ndodo zosavuta, s2 ndodo zolephera kupindika, e ngodya zolimba, a1 amathandiza, a2 pinches ndi k nodes ndi zamkati, kapena zokhazikika kunja pamene:
s1+s2+ e ≥ 2k -3
s1+s2+ ndi + a1+ a2 ≥2k, (a=a1+ a2≥3)
Sl.1
Ngodya iliyonse yolimba imatha kusinthidwa ndi ndodo yosavuta. Ngati mu mfundo imodzi i ndodo zimagwirizana mwamphamvu, chiwerengero cha ngodya zolimba mu mfundoyo ndi i-1. Pamene zowonjezera za ndodo (ma consoles) zimawerengedwa ngati ndodo, mapeto aulere ayenera kuwerengedwa ngati mfundo. Chingwe mu mkuyu.1ndi s1=9, s2=7, e=5(chalembedwa pachithunzichi) ndi k=12mkati mwake ndi chokhazikika. Pamene ngodya zolimba4ndi5tiyeni tilowe m’malo mwake ndi zolumikizira ndi ndodo zosavuta, zomwe zalembedwa ndi mizere yosweka pachithunzichi, ndiye s1=11, s2=7, e=3, pamene chiwerengero cha node sichinasinthe.
Sl.2ndi i2b
Ngati mu chithandizo chimodzi ndi chiwerengero chochepa chothandizira, ndodo za munthu kapena ngodya zolimba zimasinthidwa ndi zothandizira kapena zomangira, chithandizocho chimataya kukhazikika kwake mkati, mkuyu.2ndi, b. Pazithandizo zotere pali zotheka zina za momwe kukhazikika kungayesedwe. Ngati p ndi chiwerengero cha mbale zolimba za chithandizo popanda kukhazikika kwa mkati, pamene ziyenera kudziwidwa kuti ndodo imodzi yosavuta kapena ndodo yosagwirizana ndi kupindika imakumana ndi kukhazikika kwa mkati ndipo imatha kumveka ngati mbale yolimba, ndipo ngati z ndi chiwerengero cha kusagwirizana mumagulu, kukhazikika kwakunja kumafuna kuti: a + z_3p. Kuchuluka kwa zochitika zapakatikati pamgwirizano womwe mbale imamangiriridwa (mkuyu.3,4,5) ndi z=2(_ndi-_1).
Sl.3ndi4, motero
Sl.5
Frame mu mkuyu.6ndi kasanu ndi kamodzi mosawerengeka. Ngati zowonjezera, zomwe zilibe mphamvu pamlingo wa static indeterminacy, zimawerengedwa ngati ndodo, ma angles okhwima omwe amamangiriridwa nawo ku dongosololi ayeneranso kuganiziridwa ndipo mapeto aulere a overhangs ayenera kuwerengedwa ngati node (s=7, e=6, a=9, k=8). Pazothandizira zamitundu iyi, njira yoyenera yoyesera kukhazikika kwamkati ndi kunja ndi:
3_s_ ≥3k-3;3s+a ≥3k, (a≥3).
Pa nthawi yomweyi, zodutsa siziyenera kuwerengedwa ngati ndodo. Nthawi zambiri, pazifukwa zotere, njira yachangu kwambiri yofikira pakutsimikiza za kuchuluka kwa kusakhazikika kwa chithandizo ndikudula ndodo kapena kusaphatikiza zochulukira mpaka mosakayika, chithandizo chokhazikika chokhazikika chitsalira. Ndi zigawo zitatu zomwe zasonyezedwa mkuyu.7magawo atatu osasunthika (mphamvu yanthawi zonse, mphamvu yodutsa, mphindi yopindika) sizikuphatikizidwa.
Ngati m’modzi n0-nthawi zosawerengeka zosawerengeka zokhazikika ndodo zonse mu node zimalumikizidwa mwamphamvu, kuchuluka kwa static indeterminacy ndi
n =n0+2s – k.
Mth. 6
Sl.7
Zothandizira zamalo
Chiwerengero chocheperako chothandizira ma gridi apakati ndi a=6. Zinthu zotsatirazi zikugwira ntchito pakukhazikika kwamkati ndi kunja:
s ≥3k -6; s + ndi ≥3k, (a≥6).
Mkhalidwe wokhazikika wamkati umakwaniritsidwa pamene, kuyambira pa mbale imodzi ya katatu, mfundo zina mumlengalenga zimamangidwa ndi ndodo zitatu, zomwe siziyenera kugona mu ndege imodzi. Mwa njira iyi, spatial grid ya mtundu woyamba imapangidwa, chikhalidwe chake ndi chakuti nthawi zonse imakhala ndi mfundo imodzi yomwe ndodo zitatu zokha zimamangidwa, ndipo zimasunga izi ngakhale pamene mfundoyo ndi ndodo zofananira zimachotsedwa.
Kuphatikiza apo, ma gridi opangira malo amatha kupangidwa mwa kulumikiza mbale za triangular kotero kuti mbale ziwiri ndi ziwiri zimagwirizanitsidwa ndi ndodo zisanu ndi chimodzi, pomwe node iliyonse imalumikizidwa ndi mbale zoyandikana ndi ndodo ziwiri. Kulumikizana kwa mbale ziwiri kapena ma gridi okhazikika amkati amkati amatha kuzindikirika pogwiritsa ntchito cholumikizira chimodzi ndi ndodo zitatu zomwe sizidutsa mgululi. Pomaliza, mbale zitatu zamakona atatu zitha kulumikizidwa nazo12za ndodo ndi izo ndi po4ndodo pakati pa mbale iliyonse. Kwa mkati, kapena kukhazikika kwakunja kwa zothandizira zapakati pomwe ndodo zonse zimangiriridwa mwamphamvu ndikupindika ndi kupindika, mikhalidwe iyenera kukwaniritsidwa.
6s ≥6(k-1);6s + ndi ≥6k
Choncho, chonyamulira mu mkuyu.8ndi24times statically indeterminate, zomwe, monga kale, zingatsimikizidwe mosavuta pamene ndodo zinayi zopingasa zadulidwa ndipo mwa njira iyi zosadziwika zisanu ndi chimodzi zimachotsedwa mu kudula kulikonse (1mphamvu yabwinobwino,2transverse mphamvu,2 mkupindika ndi1mphindi ya torsional). Ngati tichotsa maulumikizidwe a f poyika zolumikizira mu ndodo kapena zolumikizira, ndiye kuti mikhalidwe yokhazikika ndi:
6s - f ≥6(k-1);6s – f + a ≥6k.
Sl. 8
Katundu ndi machitidwe: statics ntchito
Pankhani ya zothandizira lathyathyathya, mphamvu zakunja ziyenera kugona mu ndege yothandizira, pazithandizo za malo, zikhoza kukhala ndi malo osagwirizana. Mu trusses, amaganiziridwa kuti katundu akuukira pa mfundo.
Mphamvu zogwira ntchito zimayambitsa kukana kwa maelementi akunja, kuyankhidwa kwa zochirikiza C pothandizira ndi kukanikiza kamphindi E mumatsina. Zotsutsana za zinthu zamkati zothandizira - mphamvu zodutsa - ndi: mphamvu za axial S mu ndodo zosavuta; mu ndodo zosagwirizana ndi kupindika ndi kupindika mphamvu zachilendo kapena zautali N, mphindi zopindika M, mphindi zopindika kapena zopindika T ndi mphamvu zodutsa Q. Kukaniza kwa zinthu kungayambitsenso kusintha kwa kutentha ndi kumasuka kwa zothandizira.
Kukula kwazinthu zamtundu uliwonse ndikuzindikira ma voltages omwe amawoneka mwa iwo ndi ntchito ya Material Resistance. Pozindikira zikhalidwe zokhazikika, zinthu zomwe zimagwiritsidwa ntchito ndizofunika pokhapokha kuti katundu wokhazikika amadalira. Zina mwazinthuzo zimaganiziridwa pokhapokha pokhudzana ndi chikoka cha kayendetsedwe ka chithandizo kapena kusintha kwa kutentha (kutsika, kutuluka) kapena pamene ma deformation amafunika kuwerengedwa. Nthawi zambiri, ma girders amayenera kuyesedwa pamilandu yosiyanasiyana yolemetsa yomwe siyenera kuchitika nthawi imodzi (katundu wokhazikika, katundu wothandiza, katundu wamphepo, chipale chofewa). Poganiza kuti ma deformations zotanuka ndi ang’onoang’ono kotero kuti akhoza kunyalanyazidwa poyerekezera ndi miyeso ya dongosolo - ndipo nthawi zambiri ndi choncho - mfundo ya superposition ikugwira ntchito, malinga ndi zimene munthu katundu milandu ndi zikoka zina akhoza kufufuzidwa payokha ndi mawerengedwe mfundo za malo amodzi kapena geometric zedi anawonjezera palimodzi, ndi kukonza zina za makhalidwe kudzera m’malo okhazikika chitetezo ndi zosinthika coefficient. zosasangalatsa).
Zotsimikizika zokhazikika
Ma equation osadziwika komanso omwe alipo
Mu latisi yodziwika bwino, a machitidwe a zothandizira ndi s axial mphamvu sizikudziwika, kutsimikiziridwa komwe kulipo pamene latisi ili ndi k node.2_k_ equation (∑X=0ndi ∑Y=0) mu ndege i3k equation mu danga. Mu chithandizo chathyathyathya, zosadziwika zitha kuchepetsedwa kukhala s1 mphamvu za axial za ndodo zosavuta, s2 mphamvu zanthawi zonse za ndodo zosagwirizana ndi kupindika, e kupindika m’makona olimba, a1 kachitidwe kothandizira ndi a2_nthawi zopumira. Mphamvu zodutsa ziyenera kutsimikiziridwa kuyambira nthawi yomwe ili kumapeto kwa ndodo ndi mphamvu zakunja zomwe zimagwira ntchito pakati pa mfundozo. Pamalo omwe i ndodo zolumikizidwa molimba zimayambira kumalo oyandikana nawo, ndikokwanira kudziwa i-1 moment - yomwe imagwirizana ndi kuchuluka kwa ngodya zolimba - chifukwa kuti mudziwe mphindi ina yosadziwika mu node iliyonse yotere pali chikhalidwe chofanana ∑M=0. Kuti mudziwe s1 +s2 + e + a1 + a2 zosadziwika zikadalipo2_k mikhalidwe yofananira.
Zofunikira pakuwongolera mphamvu zakunja pazothandizira zosalala
Zochita za mbale zimathandizira kupumira pa choyimira chimodzi chosunthika (mkuyu.9) amapezedwa mojambula pogwiritsa ntchito ma polygons amphamvu. Mzere wa kuukira kwa mphamvu B umadziwika ndipo uli ndi chitsogozo chothandizira panthawiyo, ndipo mzere wa kuukira kwa mphamvu Ka uyenera kudutsa pamphambano za mphamvu B ndi P. Zimawerengedwa kuchokera ku chikhalidwe Ma =0,H =0ndi Mb =0amatsimikiziridwa pang’onopang’ono ndi mphamvu B, C ndi A. Kupumitsa mbale pazitsulo zitatu zosunthika (mkuyu.10) ndi zolondola pokhapokha mizere yoyankhayo sinadutse nthawi imodzi. Zochita zimatsimikiziridwa momveka bwino pogwiritsa ntchito ma polygons okakamiza kapena mwachiwerengero pogwiritsa ntchito ma equation amphindi poyerekeza ndi pomwe mizere yowukira iwiri ndi iwiri idutsana.
Sl.9
Mkuyu. 10
Pankhani ya zothandizira zokhazikika popanda kukhazikika kwamkati, kuwonjezera pa mikhalidwe ya mphamvu yakunja yonse, mikhalidwe yamagulu imayambitsidwanso, yomwe imasonyeza kufunikira kuti mafupa sangalandire mphindi zopindika. Choncho, kuukira mzere anachita Ka atatu-hinged chimango mu Mkuyu.11 mora amadutsa mu mgwirizano g, ndipo mbale yoyenera ikhoza kukhala yofanana pokhapokha mphamvu zitatu zomwe zikugwira ntchito (P, Kb ndi mphamvu mu mgwirizano = Ka) zimadutsa nthawi imodzi. Kuti mupeze mikhalidwe yofananira yomwe ili ndi imodzi yokha yosadziwika, ndikwabwino kuwerengera ndi zigawo zosunthika zamachitidwe A ndi B ndi zigawo C ndi D pamzere wolumikiza mfundo zothandizira. Kuchokera pa chikhalidwe Mb =0ndi Ma =0mphamvu A ndi B amapezedwa, ndipo kuchokera mikhalidwe ya olowa Mg =0kwa mphamvu zomwe zimamenyana ndi mbale yakumanzere, mphamvu ya C imapezeka, ndipo mphamvu zomwe zili pa mbale yoyenera, zimakakamiza D. Mofananamo, machitidwe a mafelemu othandizira amatsimikiziridwa mumkuyu.12. Kwa katundu woperekedwa apa, njira yofulumira kwambiri yopezera zotsatira ndi zojambula. Bracket yokhala ndi zolumikizira molingana ndi mkuyu.13. Zigawo zopingasa za mphamvu zakunja zomwe zimalimbana ndi chithandizo zimalandiridwa ndi bedi loyima, mphamvu F imachokera ku ∑H=0. Plate II imathandizidwa pa mfundo g1_ndi _ Mr2 pa mbale I ndi III, ndi mbale IV mu _g3_pa III. Mphamvu zoima m’malo olumikizirana G1, G2, G3 ndi zomwe E zimatsimikiziridwa kuchokera ku mgwirizano wa mbale II kapena IV, ndiyeno zotsatira za sitepe ndi sitepe A, B, C ndi D zimatsimikiziridwa.
Sl.11ndi12, motero
Sl.13
Kutsimikiza kwa makulidwe okhazikika amkati
Axial Forces S ya ndodo zosavuta, monga lamulo, zimaganiziridwa ngati zabwino pamene zili mphamvu, komanso zoipa pamene zili mphamvu zokakamiza. Mofananamo, chizindikiro cha mphamvu yachibadwa N mu mtengo chimatsimikiziridwa. Mphamvu yachibadwa Ni pa nsonga i ndi chigawo chofananira ndi tangent ku nsonga ya mtanda pa mfundo i ya chotsatira R cha mphamvu zonse zomwe zimagwira pamtengo kumbali imodzi ya mfundo i. Mphamvu yodutsa Qi ndi chigawo chodziwika bwino ku axis ya ndodo pa mfundo ndi zofanana ndi zotsatira, ndipo mphindi yopindika Mi ndi mphindi ya zotsatira (mkuyu 14). Kutsimikiza kwa kuchuluka kwa N, Q ndi M kumachitika nthawi zonse kuchokera ku mphamvu zamunthu ndi zigawo zake zofananira ndi perpendicular kwa olamulira a ndodo popanda kudziwa chotsatira R. Msonkhano wa mayendedwe abwino akuwonetsedwa mkuyu. 15.
Mth. 14 ndi 15, motsatira
Popeza momwe kuthandizira kumatsimikiziridwa mowonekera, mphamvu zabwinobwino, mphindi zopindika ndi mphamvu zodutsa zimatha kuzindikirika kuchokera ku polygon yamphamvu ndi dongosolo lomwe mphamvu zimaperekedwa ndi malo. Mwachitsanzo, mu gawo lamanzere la chimango chamitundu itatu mumkuyu. 11Chigawo choyimirira cha mphamvu Ka ndi mphamvu yabwinobwino (yopanda), yopingasa ndi mphamvu yodutsa (yopanda), ndi Mi = Kari mphindi yopindika, yolakwika pamene mphindi zoyambitsa kupsinjika mkati zimawonedwa ngati zabwino.
Mikhalidwe ∑X= iyenera kukwaniritsidwa mu node iliyonse yomwe ndodozo zimakokedwa0, ∑Y=0. Ma gridi omwe amapangidwa m’njira yosavuta - polumikiza mfundo ndi ndodo ziwiri - nthawi zonse amakhala ndi mfundo imodzi pomwe ndodo ziwiri zokha zimakumana. Pochotsa mfundo zoterezi, izi zimasungidwa. Kuwerengera mphamvu za axial mu ndodo kungathe kuchitidwa pothetsa ma equation awiri ndi awiri osadziwika.
Yankho lazithunzi limapezeka popanga force plan (Cremana plan) molingana ndi mkuyu.16. Mphamvu zakunja P1 ku P6 imirirani mulingo. Mphamvu mu ndodo Si zimatsimikiziridwa pang’onopang’ono kuyambira pomwepa1ndi kupita ku mfundo monga momwe zalembedwera. Kuyika chizindikiro kwa mphamvu kumachitidwanso motsatira ndondomeko yomwe atsimikiziridwa. Node iliyonse imafanana ndi poligoni ya mphamvu ndi njira yopitilira muvi, komwe zizindikiro za mphamvu mu ndodo zimatsatira. Ngati gawo lapangidwa kupyolera mu chithandizo ndipo ngati pa malo omwe ndodozo zimadulidwa mphamvu zomwe zimagwira ntchito mu ndodozo zimagwiritsidwa ntchito ngati mphamvu zakunja, mbali iliyonse ya lattice imakhala yofanana. Pa izi, ndondomeko ya Culmann's imalembedwa, yomwe mphamvu mu ndodo yosasinthasintha imatha kuzindikirika mopanda mphamvu zina.
Sl.16
M’mawunikidwe avuto lokhazikitsa ma equation ndi amodzi osadziwika, njira ya Ritter ndiyofunikira kwambiri. Latisi imadulidwa kuti ndodo zitatu zikhudzidwe ndi odulidwawo. Mphamvu zomwe zili m’mipiringidzo yachigawo zimagwiritsidwa ntchito ku gawo lililonse la truss ngati mphamvu zomangika, kuchokera ku node kupita ku gawo. Mikhalidwe yofananira imagwira gawo lililonse la latisi. Kuphatikizika kwa ndodo ziwiri ndi ziwiri zodumphadumpha ndi nthawi yomwe mukuzindikira mphamvu mu ndodo yachitatu (mfundo Ritter’s). Ngati ri ndi mtunda wa mphamvu Si kuyambira pomwe i, ndipo Mi ndi mphindi ya mphamvu yogwira ntchito ndi machitidwe a zothandizira pokhudzana ndi mfundo i, ndiye kuti mphamvu mu ndodo imaperekedwa ndi mawu.
Si = ± Mi/ri
Sl.17
Sl.18
Malinga ndi mkuyu.17ndi18mphamvu mu ndodo zopingasa ndi:
On = -Mn/rn; Ku-1= Mwa-1/rn-1;
Dn = Md/rd; Ln = Mv/rv.
Pamene zojambulazo sizipereka kulondola kokwanira, malo a mphindi d ndi v ndi mtunda rd ndi rv ayenera kuwerengedwa. Pakuwerengera mphamvu D ndi L, mawu otsatirawa ndi abwino kwambiri, momwe mawonekedwe okhawo a gululi amawonekera ngati mphindi (mkuyu.19,18):
D = (Mu/hu – M(o)/ho) * (d/λd), (35)
Ln = ± Ql ± (Mn tgβn + M’n tgγn)/hn.
Kwa ma lattice okhala ndi malamba ofanana, mphamvu za D ndi L zitha kupezeka mwachindunji kuchokera kumphamvu yodutsa:
D = Q/tchimo__φ_; L=±Q
Sl.19
Kusuntha katundu ndikuwongolera mizere
Ngati chithandizocho chikulemedwa ndi katundu wosuntha, mphamvu zowonongeka pamtunda wokhazikika pakati pa wina ndi mzake, ndiye kuti mayeserowo ayenera kuchitidwa pa most unfavorable load positions. Kwa mtengo wosavuta pazithandizo ziwiri, mphamvu yayikulu kwambiri yodutsa Qmax ingapezeke pogwiritsa ntchito A-polygon, ndi mphindi yayikulu yopindika Mmax pogwiritsa ntchito polygon yamaunyolo pamachitidwe amphamvu omwe chithandizocho chimayenda.
Mukazindikira chikoka chamtundu umodzi wokhazikika kapena wa geometric, komanso katundu Pm=1yomwe imayendayenda pa lamba wonyamulira wa chonyamulira, pa malo aliwonse olemetsa m amagwiritsidwa ntchito pansi pa mphamvu, kuchokera ku mzere umodzi wa ziro, mtengo wowerengedwa ηm wa kukula kofunikira. Mzere wolowa kumapeto kwa ma ordinates ndi line of influence. Mizere yopindika Mi ndi mphamvu yopingasa Qi pa nsonga i ya mtengo womwe umathandizidwa pa mfundo a ndi b ndi mizere yowongoka ga ndi gb yomwe zigawo zake zokhotakhota ndi aa’ = xi (=M’i= za _A).1) ndi bb’ = x’i (=M’‘i kwa B=1) (chith.20). Mzere wa chikoka cha mphamvu A waperekedwa ndi mzere gb, womwe mayendedwe ake pa olamulira oima ndi a aa’=1.
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Mzere wachikoka pamtundu uliwonse wokhazikika wa chithandizo chodziwika bwino chimakhala ndi mizere yowongoka yogwirizana ndi mbale zolimba za unyolo wokakamizidwa wa kinematic wopangidwa ndi kusakhalapo kwa kuchuluka komwe kwafunsidwa. Mizereyo imadutsa m’mizeremizere kudzera m’malo amphindi, kapena kudzera m’malo omwe mbalezo zimakokedwa. Dera lomangidwa ndi mzere wa ziro, mzere wa chikoka ndi ma ordinates awiri amatchedwa dera lachikoka. The divider (zero point of the influence line) amagawaniza mbali zabwino ndi zoyipa za chikoka.
Monga ηm ikuyimira mphamvu yosuntha Pm=1pa kuchuluka kofunikira Z, ndi Pmηm chikoka cha mphamvu Pm, pomwe dongosolo la mphamvu P limayambitsa chikoka Z=∑Pη. Miyezo yocheperako yamphamvu maxZ ndi minZ idzapezedwa pomwe njira yosunthika yamphamvu zolumikizidwa ikakhazikitsidwa kotero kuti mphamvu zazikuluzikulu zichulukitsidwe ndi magulu akulu kwambiri. Pamene malo oyipa kwambiri sakudziwika motsimikiza, chikoka kuchokera pamzere wachikoka chiyenera kuwerengedwa mbali ndi mbali kwa malo osiyanasiyana olemetsa (njira yobwerezabwereza).
Pa katundu wogawidwa pang’ono mofanana p t/m ndi Z = _∫_p dx η = pF, pamene F ndi kukula kwa chizindikiro cha gawo lokhudzidwa. Pakulemera pang’ono kwautali wocheperako c ndi mawonekedwe a rectilinear a mzere wachikoka (Chith.58) katunduyo aziyika kuti η1 = η2(c1= cxi/l; c2= cx’i/l), kotero timapeza Z = pc (ηi + η1)/2. Posamutsa katundu wosalunjika, mzere wa chikoka uli pakati pa ma ordinates ηn ndi ηn+1 kusintha mu mzere wowongoka, mkuyu.21.
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