**Umxholo wengcali ye-Archival: ** inqaku ligcina iinkqubo zembali, iifomyula, iitheyibhile kunye nemizobo kwintsimi yezakhiwo ezimileyo, kodwa akusiyo iprojekthi, ukubala okumileyo, ubungqina bomthamo womthwalo, isicwangciso sendibano okanye uvavanyo lwesakhiwo esikhoyo. Inkxaso, i-spans, imithwalo, indibaniselwano yezenzo, ijometri, izixhobo, ukudibanisa, ukuzinza, ukukhathala, i-seismicity kunye nezigaba zokwakha kufuneka zimiselwe into ethile ngokwemigangatho esebenzayo. Izakhiwo zokuthwala umthwalo ziyilwe kwaye zihlolwe ziinjineli ezigunyazisiweyo ezinoxanduva.
Namhlanje, i-Savo Kusić igxile kwi ifestile zomthi, iifestile zomthi-aluminiyam, iifestile zesiko, umnyango kunye nezicelo zekoteyishini. Eli nqaku lihlala linjengovimba wembali kwaye alibonisi isibonelelo sokuyila, ukubala okanye ukuphunyezwa kwezakhiwo zokwakha.
Iifomula namanqaku: Iintetho zemathematika kwisicatshulwa zikhutshelwe ngokwedijithali zisuka kumthombo oskeniweyo kwaye zisenokuba neempazamo zokuchwetheza okanye ze-OCR. Akufunekanga bafakwe ekubaleni ngaphandle kokuthelekiswa nomthombo ogunyazisiweyo, iiyunithi zokutshekisha, iimpawu, iingqikelelo kunye neemeko zomda.
Umqadi olula
Inkxaso yokusabela, ixesha lokugoba, iziphene kunye nemizuzu engatshintshiyo ye-M0-umphezulu wezinye iimeko zomthwalo ezenzeka qho zinikwa kwitheyibhile 1.
Umthwalo othe rhoqo kunye nemikhosi egxininisiweyo
Ngokulayisha okulingeneyo (umzobo.1) Ukubala kulula kakhulu ukukuphumeza ngeekholamu ezimbini zokudibanisa ngokohlobo lwetheyibhile. Ngokusekwe kubudlelwane phakathi komthwalo, amandla anqamlezayo kunye nomzuzu
_Qn = Qn+1+ Pn kunye noMn +1/_λ _= Mn/_λ + Qn+1
amandla anqamlezayo kwintsimi n amiselwa kuqala, ukuqala kumandla anqamlezayo embindini womqadi, kwaye ke amaxesha okugoba kwiindawo ezithile ukusuka kwixabiso Mi/λ.
Ikhiwane.1ngeetafile ezincedisayo.
Xa umthwalo u-asymmetrical, kwaye imigama yamandla ilingana, ezi tafile zilandelayo zifanelekile ukubala (umkhiwane.2). Nawuphi na umthwalo we-asymmetric unokuba ngokomkhiwane.3buyisela ngomthwalo omnye we-antimetric, odla ngokuba luncedo kakhulu ekubaleni. Esikhundleni semikhosi Pi kunye ne_P’i_ kwimeko yokulayisha ngokulinganayo, imikhosi (Pi+P’i)/2kumanqaku i kunye i’, kwaye kwimeko ye-antimetric yokulayisha, amandla (Pi-P’i) /2kwindawo i kunye nokunyanzela -(Pi-P’i)/2kwindawo i’. Xa iimpendulo zenkxaso zichongwa phantsi komthwalo we-antimetric, amandla aguquguqukayo kunye namaxesha okugoba nawo anokumiselwa kwitheyibhile.
Ikhiwane. 2.
Fig. 3.
Umthwalo oshukumayo
Umzuzu wokugoba kwindawo i ufunyenwe ngokomzobo kusetyenziswa upholigoni wamandla kunye nekhonkco le polygon kumthwalo onikiweyo. Ikhonkco lepoligoni lingazotywa njengoko kubonisiwe kwifig. 4. Ukumisela eyona ndawo ingathandekiyo yomthwalo wexesha kwindawo i, inkxaso ihanjiswa phantsi komthwalo (umkhiwane 5) kude kube ixabiso eliphezulu η__i lichongiwe, apho max_Mi_ = H * max_η__i_ imiselwe. Amandla amakhulu aguquguqukayo kwindawo i ifunyenwe xa umthwalo ushukunyiswa ukuze amandla okuqala afikelele kwinqanaba i. Inokufumaneka kwipolygon yemikhosi kwifig. 6: max_Oi_ = 1_/l_ * ∑Pibi. I-A-polygon yipholigoni yetsheyini enesithuba seepali H = l, izobelwa inkqubo eshukumayo yamandla agxininisiweyo xa amandla okuqala abekwe phezu kwenkxaso b.
Fig. 4.
Ikhiwane.5.
Ikhiwane. 6.
Imithwalo ehambayo: ukukhethwa kwendawo echaphazelekayo kunye nokudibanisa imithwalo ehambayo kuxhomekeke kwinjongo yesakhiwo, imodeli yesenzo, iimpembelelo ezinamandla kunye nemimiselo esebenzayo. Inkqubo yegraphic yembali ayikho ubungqina obaneleyo beyona meko ingathandekiyo yolwakhiwo lwangoku.
Isibiyeli esinamalungu
Ukulayisha rhoqo
Okokuqala, ukuphendulwa kwezixhaso kunye nemikhosi kumalungu anqunywe kwiimeko zokulingana kunye neemeko zokubambisana. Emva koko, amaxesha okugoba kunye namandla anqamlezayo kwiipleyiti zenkxaso nganye zinokumiselwa njengemiqadi elula, okanye i-boam ene-overhangs. Sl.7ibonisa isiphumo sokulayisha iipleyiti ezintathu ngamandla agxininisiweyo. Umgca wamandla aguquguqukayo udlula amajoyina njengento eqhubekayo, kunye nomgca wexeshana ngaphandle kwekhefu, ukuba akukho mandla agxininisiweyo kwi-joint.
Ikhiwane.7.
Ngomthwalo osasazwa ngokulinganayo kwinkxaso yonke, ulwahlulo oluthile olukhulu phakathi kwamaxesha angaphezulu kwezixhaso kunye namaxesha aphezulu emasimini afunyenwe, ngokwemilinganiselo ye-span kunye nesikhundla samalungu, umkhiwane.8. Ukuba kwimeko yenkxaso enamalungu anemingxuma engaphezulu kwesibini (umkhiwane.9) kunye noluhlu olulinganayo l lwemihlaba ephakathi khetha uluhlu lwemihlaba yesiphelo l1=0,8535_l_ kunye nendawo edibeneyo c=0,1465_l_, emva koko ngomthwalo owabiwe ngokulinganayo, kufunyenwe ukuba amaxabiso omda wemizuzu ngaphezulu kwenkxaso nakwimihlaba ayalingana, M=0,0625_gl_2. Ukuba imihlaba yesiphelo nayo inoluhlu lwe l, ngoko max_M_= kubo0,0957_gl_2.
Ikhiwane.8.
Ikhiwane.9.
Imigca yempembelelo
Ngokwefig. 10 imigca yempembelelo Mi kunye Qi phakathi kwamanqaku a kunye no-b ziyafana nemigca yempembelelo ye-beam elula. Ikhosi eyongezelelweyo yomgca wempembelelo inqunywe yindawo yokuxhasa kunye namajoyina amele izibonda eziphambili kunye nezibonda eziphakathi kwe-kinematic chain eyenziwe ngokususa ubuninzi be-static kwindawo i. Ngendlela efanayo, imigca yempembelelo ka Mr kunye ne Qr imiselwe ukuqala kumqadi oxhaswa kumanqaku g1 kunye c. Umthwalo we-beam kunye ne-overhang kwinxalenye ag1 ayinayo impembelelo kwimizuzu kunye nemikhosi enqamlezayo kwinqanaba r. Imigca yempembelelo yemizuzu kunye nemikhosi eguquguqukayo kwiindawo zokuxhoma (k kunye v) zifumaneka ngokulula xa ulungelelwaniso lwendawo yomthwalo kwindawo edibeneyo.
Fig. 10.
**Imodeli yokuxhasa kunye nokudibanisa: ** ukuqina kwangempela kwamalungu, ukuhlaliswa kwezixhaso, ukucocwa, ukungqubuzana, ukungafezeki kunye nomyalelo wokudibanisa unokutshintsha ukusabalalisa kwamandla xa kuthelekiswa nemodeli efanelekileyo. Iingqikelelo mazingqanyaniswe neenkcukacha zokwakha kwaye zitshekishwe kuzo zonke izigaba ezifanelekileyo.
Izaphetha ezintathu ezidibeneyo
Ekulayishweni ngokungenamkhethe kwe-arch kumalungu amathathu, ukusabela kwezixhasi kunokumiselwa ngomzobo. Isiphumo R1 samandla asebenzayo athi ngokomkhiwane. 11 esebenza kwipleyiti yasekhohlo mayilungelelane ne-reaction Kb1, umgca wayo wohlaselo kufuneka udlule kwijoyini g, kunye ne-reaction Ka1. Ngendlela efanayo, kukho Ka2 kunye Kb2, ngenxa ye-R2. Ngesenzo saxeshanye R1 kunye R2 zifunyanwa ngokufuduswa okufanayo kunye nokupakishwa kwamandla okugqibela okusabela Ka kunye Kb kunye noxinzelelo oludibeneyo G.
Ikhiwane.11.
Ngesisombululo sokuhlalutya, kukulungele ukwenza ukubala ngokukodwa kwi-horizontal kwaye ngokukodwa kwimithwalo ethe nkqo.
Umthwalo othe tye
Umthwalo othe tye kwikhiwane.12kubangela ukusabela
Ikhiwane.12.
apho u-C kunye no-D zingamacandelo empendulo kwicala elidibanisa amanqaku a kunye no-b. ∑H = C*cos_a_ – D_cos_a + ∑W =0. Amandla okucheba akhoyo ngala:
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).
Umthwalo othe nkqo
Umthwalo othe nkqo we-arch kumalungu amathathu kwifig.13kubangela ukusabela A0kunye no-B0, ezilingana neempendulo ze-beam elula ye-span l, kunye ne-horizontal thrust C=cosa = Dcosa = H = Mg0/f (1), apho Mg0 umzuzu kumqadi olula kwicandelo g. Ngamacandelo athe nkqo C kunye D amacandelo athe nkqo eempendulo zenziwa A = A0 + H_tg_a; B = B0 – H_tg_a. Ukuba i-axis ye-arch yiparabola yesikwere, yi = f xi x’i/la lb, ngoko kumthwalo opheleleyo owahlulwe ngokulinganayo g t/m (Fig.14) Mi=0, Qi=0.
Ikhiwane.13.
Ikhiwane.14.
Imigca yempembelelo
Imigca yempembelelo kwiimpendulo A0 kunye ne-B0 ziyafana nemigca yempembelelo ye-beam elula. Umgca wempembelelo ye-horizontal thrust H ifunyenwe ngokwe-equation (1) ukusuka kumgca wempembelelo okwethutyana Mg0 ye-beam elula, umkhiwane. 15. Umgca wempembelelo womzuzu wokugoba Mi uqulathe imigca yempembelelo ene-Mi0 kunye ne-H, apho le yokugqibela iphindaphindwe ngu--yi. Le migca mibini inempembelelo ibekwe ngaphezulu kwindawo ethe tye ab’ njengomgca onguziro, apho amacandelo aa’ = xi kunye no-bb’ = -lb yi/f azotywa khona. Umahluko oboniswe yintshukumo ai’g’b imele umgca wempembelelo yokugqibela ye Mi. I-divider okanye i-zero point of the influence line ehambelana nesibonda esiphambili seplate ig ifunyenwe ngokudibana kwemigca ai kunye bg. Ingasetyenziselwa ukwakhiwa komgca wempembelelo, apho i-beam elula ye-span a - n ingeniswa. Kwimeko ye-arch ene-axis yiparabola yesikweri, umthwalo owabiwe ngokulinganayo awubangeli amaxesha okugoba, ngoko ke indawo epheleleyo yomgca wempembelelo kufuneka ilingane no-zero.
Fig. 15.
Kumkhiwane. 16 imigca yempembelelo ye-Qi kunye ne-Ni ifunyenwe nge-superposition ehambelanayo yemigca yempembelelo ye-Qi0 kunye ne-H. Ngokubhekiselele ku ab’ njengomgca onguziro, yomibini imigca yempembelelo kulo mzekelo imigca yempembelelo yomqadi olula. Kulwakhiwo okanye ulawulo lwemigca enempembelelo, amacandelo nQ kunye nN omgca bg kunye nomgca owenziwe nge-parallel unokusetyenziswa apha, ngokulandelanayo. iqhelekile kwi tangenti egqithe iengile φ__i ngokuxwesileyo. Kwimeko ye-arch parabolic ene-joints ezintathu, indawo epheleleyo yomgca wempembelelo ye-transverse force kufuneka ilingane no-zero.
Fig. 16.
Ii-arches kunye ne-horizontal thrust: indawo yamalungu, ijometri ye-axis, ukuqina kwesiseko kunye nokwamkelwa kweempendulo ezithe tye zibalulekile kukuziphatha kwenkqubo. Ukutshintsha inkxaso, ukuxhatshazwa, i-hanger okanye isigaba sokunyuka kunokutshintsha ukuhamba kwemikhosi; umzobo owenziwe ngokwembali awonelanga ukwenziwa okanye ukubuyisela kwisimo sangaphambili.
I-Arch iqiniswe ngomqadi kunye nesibiyeli esijingayo
Umthwalo othe nkqo
Ukuphendula okuthe nkqo ngexesha lokulayishwa ngokuthe nkqo kweepleyiti eziqinileyo zenkxaso ye-arch eqiniswe ngokwe-statically eqiniswe ngomqadi, izixhaso ezijingayo kunye ne-arches kumalungu amathathu kunye noxinzelelo kwiFig.17a ukuya ku f zifunyanwa kwiinxaki A0 =1/l * ∑Pnbn kunye B0 =1/l * ∑Pnan xa A ibekwe kwiinkqubo a kunye d_0 = A+K’‘l, B0 = B+K’’r kunye nezinye iinkqubo A = A0, B=B0. Iimpendulo A kunye B kwiinkqubo a kunye no-d zimiselwa ukusuka:
A = A0 - K’’l = A0 – H(tgal-tg__δ)
B = B0 – K’’r = B0 – H(tgar+tg__δ)
Ikhiwane.17.
Kwiinkqubo a, d, e kunye f, impendulo ethe tye ithi C=0, kunye nenkqubo b ngu E=0. I-Horizontal thrust, okanye i-horizontal tension H yenkqubo a ukuya ku-d, icandelo elithe tye lamandla kwi-arc yenkqubo e kunye namandla kuxinzelelo lwenkqubo f zimiselwa ngokusekelwe kwi-equation (1). Le theyibhile ilandelayo iqulethe isishwankathelo sokusabela kweenkxaso kunye namandla kwiintonga Sn kunye no-Zn kwisixokelelwano ngasinye.
Umthwalo othe tye
Ukuba amandla axwesileyo W asebenza kwiipleyiti kumgama c ukusuka kwindibaniselwano g (umkhiwane.17kunye e) neempendulo zeenkxaso ezizibangelayo zezi:
Imigca yempembelelo
Imigca yempembelelo yemikhosi yokucheba ifunyenwe ngokusekelwe ekufaniseni ukuziphatha kwezi nkqubo kunye ne-arch elula eneentonga ezintathu. Kwi-arch yentonga ene-arch eqinile phantsi kwe-arch (i-Langer’s beam) kwifig.18Imigca enempembelelo ye U ibonisiwe2_D4 kunye no_L4_. Ukunyanzeliswa kwintonga U2 ifunyenwe kwinqanaba lomzuzu2ibhanti eliphezulu: U2 = M2/h. Ukusuka kwimeko ∑V=0sifumana D4 = Q40/isono__φ – Mg0/f ukuba4/unyana__φ. Kwakhona ukusuka kwimeko ∑V=0ilandela (umthwalo kwibhanti esezantsi) L4 = -Q50+ Mg0/f * ukuba4.
Ikhiwane.18.
Ukuba iindawo ze-arch ezidityanisiweyo ezintathu ezinomqadi oqinileyo wokuqina (umkhiwane.19) lala kwiparabola yesikwere kwaye ukuba umdibaniso ulele kwi-axis yomqadi, ngoko ngomthwalo owabiwe ngokulinganayo g t/m amaxesha okugoba ngu_M_=0kwiindawo zokuxhoma, kunye M=g__λ__2/8embindini webala phakathi kwama-hangers.
Ikhiwane.19.
IiHanger, i-tensioners and stiffeners: ezi elementi kunye noqhagamshelo lwazo zinokuba novakalelo lokungafezeki, uxinzelelo lwesibini, ukudinwa, ukubola, ukulahleka koxinzelelo kunye neemeko zokuhlangana. Ukutshintshwa kwabo, ukuqiniswa okanye ukususwa akwenziwa ngaphandle kweprojekthi yexeshana kunye neyokugqibela.
Isakhelo sixhasa
Ikhiwane.20.
Sl.20ibonisa umzobo womzuzu wesakhelo esineehenjisi ezintathu esinezogquma kunye neebhanti ezixhonyiweyo ngenxa yomthwalo opheleleyo owabiwe ngokulinganayo. Umgca wempembelelo okomzuzwana Me ufunyenwe ngokusekelwe kwintetho Me=-Hh + Mk, ngokubekwa okuphezulu komgca wempembelelo ye-horizontal thrust H (nge-multiplier -h) kunye nomzuzu wokugoba Mk kwi-overhang.
Kwimeko yokulayishwa kwe-symmetric ye-symmetric supports, ukubala kunokuthi kube lula ngokuhlula umthwalo kwi-symmetric and anti-symmetric loading, umkhiwane.21. Oku kuyinyani ngokukodwa kwiinkxaso zesakhelo kwifig.22kwaye23, ebonisa imizobo yomzuzu ngenxa yamandla agxininisiweyo kwindawo engafanelekanga yenkxaso ephezulu. Umthwalo othe tye kumphakamo wejoist unokuqondwa njenge-antimetric. Ekubeni umthwalo othe tyaba we-sub-strut unokuqwalaselwa njengomthwalo obonakalayo wokubala ukufuduka okuthe tye kwe-sub-strut, kunokugqitywa ngokukhawuleza ukusuka kwinqanaba lendawo ukuya kwelinye icala le-sub-strut ehamba ngexesha lomthwalo othe nkqo. Oku kufuduswa kufunyanwa ngokudibanisa i-antimetric equilibrium states. Ke ngoko, kumatyala akufig.22kwaye23umgca ngaphantsi ushukuma uye ekunene.
Ikhiwane.21.
Ikhiwane.22.
Ikhiwane.23.
Iifreyimu kunye nokufuduswa: ukugqitywa kwesalathiso sokufuduka ukusuka kumzobo ochanekileyo awuthathi indawo yokukhangela ukuguqulwa, iziphumo zesibini, ukuzinza, ukuqina kwamalungu, iziseko kunye nezinto ezingenayo. Umda wokuthwala kunye nokunikezelwa kwenkonzo ujongwa kwimodeli epheleleyo.
Iigridi zendawo
Ikhiwane.24.
Idome likaSchweler (umkhiwane.24) kunye nephiramidi yegridi enehemed (Fig.25), njengemeko ekhethekileyo yedome ye-Schwedler's apho i-meridians ingenazo izaphulelo, ezinemigangatho engu-m kunye namacala angu-n, ziqulathe m*n meridional rods S, (m+1)n iintonga zamakhonkco R kunye m*n iirodi zediagonal D. Njengenani leendawo k=(m+1)n inkxaso imiselwa ngokwezibalo xa inani leenkxaso a =3k-s =2n, kulapho unyawo ngalunye lomxholo luxhaswa kumbindi womgca womxhuzulane kunye nenkxaso ethe nkqo nethe tye. Ukuba iintonga zeringi esezantsi ziyawa, ibhodi emileyo enezixhaso ezintathu iyafuneka kwivertex nganye. Ukusetyenziswa kolungelelwaniso lweenkxaso ezithe tye kufuneka kuhlolwe. Izalathiso zenkxaso kwifig.26zikhethwe ngokungachanekanga kuba kunokwenzeka ukuzoba isicwangciso sepali esingachasananga.
Ikhiwane.25.
I-trapezoids eyenziwe ngama-meridian rods kunye ne-ring rods inokuqiniswa kunye K-ukuzaliswa. Iingqungquthela eziphumayo kufuneka zithathwe njengeendawo ze-lattice ecaba. Imithwalo inokugqithiselwa kuphela ngeenodi eziphambili. Umthwalo othe nkqo P ohlasela kwindawo yendibano uya kuchithwa ube licandelo _Ks=Ps/_λ kwicala lemeridian kunye necandelo elithe tye _H=Pa/_λ. Icandelo elithe tye liphinda liboliswe libe ngamacandelo kwicala le-ring rods _Kl=Hc/a=Pc/_λ _i Kr=Hb/a=Pb/_λ.
Ngendlela efanayo, amacandelo Kl kunye Kr amandla arbitral horizontal W azimisele, ukuze isikimu umthwalo eboniswe fig.27. Amacandelo X kwicala le-meridian rods aziboniswa emfanekisweni.
Ikhiwane.26kwaye27, ngokulandelelanayo.
Xa inkxaso kunye nomthwalo P i-cyclically symmetrical, ngoko imikhosi Kl ilingana nemikhosi Kr, ngoko i-diagonals ayigxininisi ngelixa imikhosi kwiintonga ze-meridian:
_S1= -P1s/_λ; S2= -(P1+P2)s/λ; S3= -(P1+P2+P3)s/λ
nasezintongeni zekhonkco.
_Ri = Pib/_λ
Ukubalwa kwedome likaSchwedler kunokuqhutywa ngendlela efanayo xa umgangatho ngamnye uqondwa njengephiramidi yelatisi. Ngaphandle kwamandla asebenzayo P kunye W, imikhosi kwiintonga S kunye D zomgangatho ophezulu kufuneka zingeniswe njengamandla angaphandle, ngokulandelanayo. amacandelo abo kwicala le-meridian rod kunye neentonga zamakhonkco. Ngelixa kwiphiramidi yelathisi impembelelo yamandla enye egxininisiweyo ivakala kuphela kwiintonga zeepleyiti ezimbini ezimeleneyo, kwimeko ye Schwedler's dome impembelelo yayo idlulela kwinani elikhulu kakhulu lezintonga. Kumkhiwane.24iintonga ezigxininisiweyo ngenxa yamandla P kwiringi ye-vertex ziphawulwe.
Iitrasi zendawo kunye needomes: ukuzinza kwezi nkqubo kuxhomekeke ekusebenzeni kwesithuba, inkxaso, ukungafezeki kwejometri, ukubotshwa kweentonga, ukuqina kweengqumba, ukuthotyelwa kwethutyana kunye nolandelelwano lokudibanisa. Umzobo osicaba okanye i-equation yomntu ngamnye ayibonakalisi uzinzo lwehlabathi, ukugcinwa komthwalo okanye ukhuseleko ngexesha lokunyuswa.