Kushandiswa kwema statics: matanda, arches uye trusses

** Archive inyanzvi yezvinyorwa: ** chinyorwa chinochengetedza maitiro ezvakaitika kare, mafomula, matafura uye mifananidzo mumunda wezvimiro zvakagadzikana, asi haisi purojekiti, static calculation, uchapupu hwekutakura mutoro, chirongwa chegungano kana kuongorora kwechivako chiripo. Zvitsigiro, spans, mitoro, musanganiswa wezviito, geometry, zvinhu, zvinongedzo, kugadzikana, kuneta, seismicity uye nhanho dzekuvaka dzinofanirwa kutariswa kune chimwe chinhu zvinoenderana nemaitiro anoshanda. Zvivako zvinotakura zvinhu zvinogadzirwa uye zvinotariswa nemainjiniya ane mvumo.

Nhasi, Savo Kusić inotarisa pa mahwindo emapuranga, wood-aluminium Mahwindo, mahwindo etsika, gonhi uye zvikumbiro zvekotesheni Ichi chinyorwa chinosara sechinyorwa chenhoroondo uye hachimiriri kupihwa kwedhizaini, kuverenga kana kuita kwezvivakwa zvekuvaka.

Mafomula neMaki: mataurirwo esvomhu ari muchinyorwa akatamiswa nedigital kubva kwaakaongororwa uye anogona kunge aine zvikanganiso zvekutaipa kana zveOCR. Ivo havafanirwe kupinzwa mukuverenga pasina kuenzanisa neane chiremera sosi, yekutarisa mayuniti, zviratidzo, fungidziro uye muganhu mamiriro.

Beam iri nyore

Maitikiro ekutsigira, nguva dzekukotama, deformation uye nguva dzakasimba dzeM0-pamusoro kune dzimwe nyaya dzinogara dzichiitika zvinopihwa patafura 1.

Constant load ine concentrated forces

Iine symmetrical kurodha (Fig.1) kuverenga kuri nyore kuita kuburikidza nemakoramu maviri ekuwedzera muchimiro chetafura. Zvichienderana nehukama huri pakati pemutoro, simba rakachinjika uye nguva

_Qn = Qn+1+ Pn uye Mn +1/_λ _= Mn/_λ + Qn+1

simba rinochinjika mumunda n rinotariswa kutanga, kutanga kubva kune rinochinjika riri pakati pedanda, uyezve nguva dzekukotama pane dzimwe nzvimbo kutanga kubva paukoshi Mi/λ.

Fig.1nematafura ebetsero.

Kana mutoro usiri asymmetric, uye nhambwe dzesimba dzakaenzana, matafura anotevera akakodzera kuverenga (fig.2) Chero asymmetric mutoro unogona kuenderana nefig.3tsiva neimwe antimetric mutoro, iyo inowanzo batsira mukuverenga. Panzvimbo pemasimba Pi uye P’i kana iri nyaya yekuenzanisa kurodha, masimba (Pi+P’i)/2pamapoinzi i uye i’, uye mune antimetric kesi yekurodha, simba (Pi-P’i)/2panguva i uye simba -(Pi-P’i)/2panguva i’. Kana maitiro erutsigiro akatemerwa pasi pekurodha antimetric, masimba anochinjika uye nguva dzekukotama zvinogona zvakare kutsanangurwa mutafura.

Fig. 2.

Fig. 3.

Kufambisa mutoro

Nguva yekukotama panzvimbo i inowanikwa zvine graphic uchishandisa simba polygon uye cheni polygon kune yakapihwa mutoro. Cheni yeporigoni inogona kudhirowa sezvinoratidzwa mumufananidzo.4. Kuti uone nzvimbo isina kunaka yemutoro yenguva iri panzvimbo i, rutsigiro runofambiswa pasi pemutoro (Fig.5) kusvika kukosha kwepamusoro η__i kwatarwa, kubva papi max_Mi_ = H * max_η__i_ panowanikwa. Simba guru rinochinjika panzvimbo i rinowanikwa kana mutoro wafambiswa kuitira kuti simba rekutanga risvike pachinhanho i. Inogona kuwanikwa kubva ku polygon yemasimba mune fig.6: max_Oi_ =1_/l_ * ∑Pibi. A-polygoni iketani paporigoni ine pole spacing H = l, yakadhonzwa kuti ifambe yemasimba akasimba kana simba rekutanga riri pamusoro perutsigiro b.

Fig. 4.

Fig.5.

Fig.6.

** Kufambisa mitoro: ** kusarudzwa kwechinzvimbo chakakodzera uye kusanganiswa kwekutakura mitoro kunoenderana nechinangwa chechimiro, chiito chekuita, maitiro ane simba uye mitemo inoshandiswa. Iyo nhoroondo yemifananidzo maitiro haisi humbowo hwakakwana hwemamiriro asina kunaka ekuvaka kwazvino.

Bracket ine majoini

Constant load

Kutanga, maitiro ezvitsigiro uye masimba ari mumajoini anotarirwa kubva pakuenzanisa mamiriro uye mamiriro ezvisungo. Zvadaro, nguva dzekukotama uye masimba anochinjika emahwendefa ega ega ekutsigira anogona kutariswa kunge ari nyore matanda, kana danda rine overhangs. Sl.7inoratidza mhedzisiro yekurodha mahwendefa matatu ane masimba akanyanya. Mutsara wemasimba anochinjika unopfuura pamusoro pemajoini seanogara, uye mutsara wenguva pasina kuputika, kana pasina simba rakadzika mumubatanidzwa.

Fig.7.

Kumutoro wakagovaniswa zvakaenzana pamutsigiro wose, mimwe misiyano mikuru pakati penguva pamusoro pezvitsigiro uye nguva dzepamusoro muminda dzinowanikwa, maererano nereshiyo yespan uye nzvimbo yemajoini, fig.8. Kana iri nyaya yezvitsigiro zvine majoini ane anopfuura maviri kuvhurwa (fig.9) uye nemitsara yakaenzana l yenzvimbo dzepakati sarudza huwandu hwenzvimbo dzekugumisira l1=0,8535_l_ nenzvimbo yemubatanidzwa c=0,1465_l_, zvino nemutoro wakagovaniswa zvakaenzana, unowanikwa kuti miganho yenguva pamusoro pezvitsigiro uye muminda yakaenzana, M=0,0625_gl_2. Kana minda yekugumisira iinewo huwandu hwe l, saka max_M_= kwavari0,0957_gl_2.

Fig.8.

Fig.9.

Mitsetse yepesvedzero

Maererano nemufananidzo. 10 pesvedzero mitsetse ye Mi ne Qi pakati pemapoinzi a na b akafanana nemitsara yekufurira yedanda riri nyore. Iyo imwezve nzira yemutsara wepesvedzero inotarirwa nenzvimbo yezvitsigiro uye majoini anomiririra matanda makuru uye epakati matanda ekinematic chain akagadzirwa nekubvisa iyo static quantity panzvimbo i. Nenzira imwecheteyo, mitsetse yekupesvedzera ye Mr na Qr inotemerwa kutanga kubva padanda rinotsigirwa pamapoinzi g1 na c. Kuremerwa kwedanda rine overhang pachikamu ag1 harina mhedzisiro pane nguva uye masimba anochinjika panzvimbo r. Mitsetse yepesvedzero yenguva uye masimba anochinjika panzvimbo dzekurembesa (k uye v) anowanikwa zviri nyore kana marongero echinzvimbo chemujoini akatemwa.

Fig. 10.

Modhi yezvitsigiro uye majoini: kuomarara chaiko kwemajoini, kugadziriswa kwezvitsigiro, kubvisirwa, kukakavara, kusakwana uye kurongeka kwekusangana kunogona kushandura kugoverwa kwemasimba kana kuenzaniswa nemuenzaniso wakasarudzika. Kufungidzira kunofanirwa kuenderana neruzivo rwekuvaka uye kuongororwa kune ese akakodzera zvikamu.

Uta hutatu hwakabatana

Pakurodha zvisina tsarukano kwearch pamajoini matatu, maitiro ezvitsigiro anogona kutariswa zvakajeka. Mhedzisiro R1 yemasimba anoshanda ayo zvinoenderana nefig. 11 kuita pandiro yekuruboshwe kunofanirwa kuva pakati nepakati nemaitiro Kb1, ane mutsara wekurwisa unofanira kupfuura nemujoini g, uye mhinduro Ka1. Nenzira imwecheteyo, kune Ka2 uye Kb2, nokuda kwe_R2_. Nekuita panguva imwe chete R1 uye R2 anowanikwa nekufamba kwakafanana uye kurongedza kwekupedzisira kuita kwemasimba Ka uye Kb uye kudzvinyirirwa kwemajoini G.

Fig.11.

Nemhinduro yekuongorora, zviri nyore kuita kuverenga kunyanya kune yakachinjika uye kunyanya kune yakatwasuka mitoro.

Horizontal mutoro

The horizontal mutoro muonde.12zvinokonzera maitiro

Fig.12.

apo C na D ndiwo maitiro ekuita mugwara rinobatanidza mapoinzi a na_b_. ∑H = C*cos_a_ – D_cos_a + ∑W =0. Masimba ekugera aripo ndeaya:

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).

Vertical load

The vertical load yearch pamajoini matatu mufig.13inokonzeresa reactions A0uye B0, izvo zvakaenzana nemabatiro edanda riri nyore respan l, uye kurovera kwakachinjika C=cosa = Dcosa = H = Mg0/f (1), uko Mg0 nguva padanda riri nyore muchikamu g. Nezvikamu zvakamira C uye D zvikamu zvakamira zvakamira zvekupedzisira zvezvaitwa zvinoti A = A0 + H_tg_a; B = B0 – H_tg_a. Kana iyo axis yearch iri sikweya parabola, yi = f xi x’i/la lb, zvino kune yakakamurwa zvakaenzana mutoro g t/m (Fig.14) Mi=0, Qi=0.

Fig.13.

Fig.14.

Mitsetse yepesvedzero

Mitsetse yepesvedzero yezvinoitwa A0 uye B0 zvakafanana nemitsara yekufurira yedanda riri nyore. Mutsetse wepesvedzero weiyo horizontal thrust H inowanikwa zvinoenderana neiyo equation (1) kubva kumutsara wepesvedzero yechinguvana Mg0 yedanda riri nyore, fig. 15. Mutsetse wepesvedzero yenguva yekukotama Mi ine mitsetse yepesvedzero ine Mi0 na H, apo iyo yekupedzisira inopetwa ne -yi. Mitsetse miviri iyi ine simba inoiswa pamusoro yakatwasuka ab’ semutsara we zero, kubva panobva padhonzwa zvikamu aa’ = xi uye bb’ = -lb yi/f. Musiyano unoratidzwa nekufamba ai’g’b unomiririra yekupedzisira pesvedzero mutsetse we Mi. Muparadzi kana zero poindi yepesvedzero mutsara unoenderana nedanda guru rendiro ig inowanikwa nekupindirana kwemitsara ai uye bg. Inogonawo kushandiswa pakuvaka mutsara wepesvedzero, apo danda riri nyore re span a - n rinounzwa. Kana ari arch ane axis i square parabola, mutoro wakagovaniswa zvakaenzana haukonzeri nguva dzekukotama, saka nzvimbo yese yerutsvagiro inofanira kuenzana ne zero.

Fig. 15.

Mumuonde. 16 mitsetse yepesvedzero ye Qi ne Ni yakawanikwa nepamusoro-soro yemitsara yesimba ye Qi0 ne_H_. Neruremekedzo kuna ab’ semutsara we zero, mitsara miviri yekupesvedzera iri mune iyi nyaya mitsetse yekupesvedzera yedanda riri nyore. Pakuvaka kana kutonga kwemitsara ine simba, zvikamu nQ uye nN zvemutsara bg uye mutsara wakadhirowewa kuburikidza nea mukuenderana zvinogona kushandiswa pano, zvichiteerana. zvakajairika kune tangent inodarika kona φ__i neyakachinjika. Kana iri parabolic arch ine majoini matatu, nzvimbo yese yerutsvagiro rwesimba rinochinjika inofanira kuenzana ne zero.

Fig. 16.

** Arches uye horizontal thrust: ** nzvimbo yemajoini, geometry yeaxis, kuoma kwenheyo uye kugamuchirwa kwemaitiro akakomberedzwa zvakakosha pamaitiro ehurongwa. Kuchinja kutsigirwa, kushushikana, hanger kana kukwira chikamu kunogona kushandura kuyerera kwemasimba; kudhirowa kwekare hakuna kukwana kuurayiwa kana kugadzirisa.

Arch yakaomeswa nedanda uye rakarembera bracket

Vertical load

Mabatiro epamhepo panguva yekurodha mahwendefa akaomeswa eakatemerwa arch anotsigira akaomeswa nedanda, anorembera zvitsigiro uye arch pamajoini matatu uye kushushikana mumufananidzo.17a kusvika ku f anotorwa kubva kuequations A0 =1/l * ∑Pnbn uye B0 =1/l * ∑Pnan kana A yaiswa kune masisitimu a uye d_0 = A+K’‘l, B0 = B+K’’r uye kune mamwe masisitimu A = A0, B=B0. Zvinoitwa A uye B zvemasisitimu a uye d zvinobva zvatemwa kubva:

A = A0 - K’’l = A0 – H(tgal-tg__δ)

B = B0 – K’’r = B0 – H(tgar+tg__δ)

Fig.17.

Kune masisitimu a, d, e uye f, kuchinjika kunoti C=0, uye yehurongwa b iri E=0. Horizontal thrust, kana kuti horizontal tension H yehurongwa a kusvika d, chikamu chakachinjika chesimba muarc yehurongwa e uye simba mukukakavadzana kwehurongwa f zvinotemerwa zvichibva paequation (1) Tafura inotevera ine mhedziso yemabatirwo ezvitsigiso nemasimba ari mutsvimbo Sn ne_Zn_ kumasisitimu ega ega.

Horizontal mutoro

Kana simba rakachinjika W rikashanda pamahwendefa ari chinhambwe c kubva pamubatanidzwa g (fig.17uye ku e) maitiro ezvitsigiro zvaanokonzera ndezvi:

Mitsetse yepesvedzero

Mitsetse yepesvedzero yemasimba eshear inowanikwa zvichienderana nekufanana kwemaitiro ezvirongwa izvi uye akareruka matatu-hinged arch. Kune arch yetsvimbo ine danda rinoomesa pasi pearch (Langer’s beam) mumuonde.18mitsetse ine simba ye U inoratidzwa2, _D4_uye L4. Simba mutsvimbo U2 inotorwa kubva panguva ino2bhandi repamusoro: U2 = M2/h. Kubva pachimiro ∑V=0tinowana D4 = Q40/sin__φ – Mg0/f izvozvo4/mwanakomana__φ. Zvakare kubva pachimiro ∑V=0inotevera (mutoro pabhandi rezasi) L4 = -Q50+ Mg0/f * izvo4.

Fig.18.

Kana iyo node dzeatatu-akabatanidzwa arch ane yakasimba kuomesa danda (fig.19) rara paskweya parabola uye kana mubatanidzwa uri muaxis yedanda, zvino nemutoro wakagovaniswa zvakaenzana g t/m nguva dzekukotama ndi M=0munzvimbo dzekurembera, uye M=g__λ__2/8pakati pemunda pakati pezvirembera.

Fig.19.

** Hangers, tensioners uye stiffener: ** zvinhu izvi uye zvibatanidzo zvazvo zvinogona kuva nehanya nekusakwana, kushushikana kwechipiri, kuneta, kuora, kurasikirwa kweprestress uye mamiriro egungano. Kutsiva kwavo, kuomesa kana kubviswa hakuitwe pasina purojekiti yenguva pfupi uye yekupedzisira.

Frame inotsigira

Fig.20.

Sl.20inoratidza dhiyagiramu yechinguvana yefuremu ine hinged nhatu ine overhangs uye magidhi akamiswa nekuda kwemutoro wakagovaniswa zvakaenzana. Mutsetse wepesvedzero wenguva Me unowanikwa zvichibva pachirevo Me=-Hh + Mk, nepamusoro pemutsetse wepesvedzero weiyo yakachinjika H (nemupupuri -h) uye nenguva yekukotama Mk pane iyo overhang.

Panyaya yekusapindirana kwekutakura kwezvitsigiro zve symmetric, kuverenga kunogona kurerutswa nekuparadzanisa mutoro mu symmetric uye anti-symmetric loading, fig.21. Izvi ndezvechokwadi kunyanya kune furemu inotsigira mufig.22uye23, iyo inoratidza madhayagiramu enguva nekuda kwesimba rakadzika pane imwe nzvimbo yekusarudzika yerutsigiro rwepamusoro. Iyo yakatwasuka mutoro pakureba kwejoist inogona kunzwisiswa se antimetric. Sezvo kuremerwa kwakatwasuka kweiyo sub-strut kunogona kutorwa semutoro chaiwo wekuverenga kwekumisikidza kwakatwasuka kweiyo sub-strut, inogona kupedzwa nekukasira kubva panguva iyo nzvimbo inoenda kudivi iro sub-strut inofamba panguva yekumira yakatwasuka. Uku kudzingwa kunowanikwa nekubatanidza antimetric equilibrium states. Naizvozvo, kune zviitiko mufig.22uye23pasi panoenda kurudyi.

Fig.21.

Fig.22.

Fig.23.

** Mafuremu uye kutamiswa: ** mhedziso yekutungamira kwekutama kubva kune yakasarudzika dhizaini haitsivi kutarisa kwe deformations, yechipiri-kurongeka mhedzisiro, kugadzikana, kuomarara kwemajoini, hwaro uye zvisina-kutakura zvinhu. Iyo inotakura-yekutakura uye serviceability muganhu nyika inotariswa pane yakazara modhi.

Spatial grids

Fig.24.

Schwedler’s dome (fig.24) uye piramidhi ine hemmed grid (Fig.25), sechiitiko chakakosha che Schwedler's dome apo mameridians haana maburi, ane m pasi uye n mativi, ane m*n meridional rods S, (m+1)n tsvimbo dzemhete R uye m*n diagonal rods D. Senhamba yemanodhi k=(m+1)n tsigiro inotemerwa zvakatemerwa kana nhamba yerutsigiro a =3k-s =2n, ndipo panotsigirwa tsoka yega yega yedingindira pamutsara wepakati wegiravhiti nerutsigiro rwakamira uye rwakachinjika. Kana matanda echindori chepasi akadonha, bhero rakamira rine zvitsigiso zvitatu rinodiwa muvertex imwe neimwe. Iko kushandiswa kwegadziriro yezvitsigiro zvakadzikama kunofanira kuongororwa. Nzira dzekutsigira mufig.26vanosarudzwa zvisizvo nekuti zvinokwanisika kudhirowa hurongwa hwedanda husingapesani.

Fig.25.

Trapezoids inoumbwa nemeridian rods uye mhete dzemhete dzinogona kuomeswa ne K-kuzadza. Manodhi anozobuda anofanirwa kutorwa semanodhi ereti rakatsetseka. Mitoro inogona kutamiswa chete kuburikidza nemanodhi makuru. Mutoro wakatwasuka P unorwisa panzvimbo inozoitwa chikamu _Ks=Ps/_λ munzira yemeridian uye muchikamu chakachinjika _H=Pa/_λ. Iyo yakachinjika chikamu chinooreswa zvakare kuita zvikamu mugwara remhete _Kl=Hc/a=Pc/_λ _i Kr=Hb/a=Pb/_λ.

Nenzira imwecheteyo, zvikamu Kl uye Kr zvechisimba chakananga W zvakatemwa, kuitira kuti chirongwa chekutakura chinoratidzwa mumufananidzo.27. Zvikamu X munzira yemeridian tsvimbo hadzina kuratidzwa pamufananidzo.

Fig.26uye27, zvichiteerana.

Kana tsigiro uye mutoro P zviri cyclically symmetrical, ipapo masimba Kl akaenzana nemauto Kr, saka ma diagonals haana kusimbiswa nepo masimba ari mumeridian rods ari:

_S1= -P1s/_λ;   S2= -(P1+P2)s/λ;   S3= -(P1+P2+P3)s/λ

namapango echindori.

_Ri = Pib/_λ

Kuverengera kwedome raSchwedler kunogona kuitwa nenzira imwechete apo pasi pega pega parinonzwisiswa sepiramidhi yelatisi. Kunze kwemasimba anoshanda P na W, masimba ari mumatanda S ne_D_ epauriri hwepamusoro anofanirwa kuunzwa semasimba ekunze, zvichiteerana. zvikamu zvadzo munzira yemeridian tsvimbo nemhete tsvimbo. Ipo mupiramidhi yelatisi simba resimba rimwe chete rakanyungudutswa rinonzwika chete mumatanda emahwendefa maviri ari padyo, kana iri Schwedler’s dome simba rayo rinosvika kune nhamba yakakura kwazvo yetsvimbo. Mumuonde.24tsvimbo dzinenge dzakatsikirirwa nekuda kwesimba P mumhete ye vertex yamaka.

**Spatial trusses uye domes: ** kugadzikana kwemaitiro aya kunoenderana nekushanda kwenzvimbo, kutsigirwa, kusakwana kwejometri, kuputika kwetsvimbo, kuoma kwemanodhi, kutevedza kwenguva pfupi uye kutevedzana kwekuunganidza. Dhizaini yakatsetseka kana equation yemunhu hairatidze kugadzikana kwepasirese, kutakura mutoro kuchengeterwa kana kuchengetedzeka panguva yekusimudza.