{"id":1023,"date":"2024-09-23T14:59:06","date_gmt":"2024-09-23T12:59:06","guid":{"rendered":"https:\/\/solveredu.com\/?p=1023"},"modified":"2026-01-27T23:49:50","modified_gmt":"2026-01-27T22:49:50","slug":"statyczna-wyznaczalnosc","status":"publish","type":"post","link":"https:\/\/solveredu.com\/cs\/post\/statyczna-wyznaczalnosc\/","title":{"rendered":"Statick\u00e1 ur\u010ditelnost"},"content":{"rendered":"

V tomto p\u0159\u00edsp\u011bvku se dozv\u00edte, co je to stupe\u0148 statick\u00e9 neur\u010ditosti? Jak zjistit, zda je syst\u00e9m (nosn\u00edk, r\u00e1m, vazn\u00edk) staticky ur\u010dit\u00fd. D\u00e1le se dozv\u00edte o mo\u017en\u00fdch p\u0159\u00edpadech podpor, se kter\u00fdmi se v mechanice setk\u00e1v\u00e1me.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Statick\u00fd syst\u00e9m se naz\u00fdv\u00e1 syst\u00e9m, kter\u00fd je stacion\u00e1rn\u00ed. To znamen\u00e1, \u017ee se nem\u016f\u017ee pohybovat p\u016fsoben\u00edm vn\u011bj\u0161\u00edch sil. Pokud se pohybuje, pak se jedn\u00e1 o mechanismus.<\/p>\n\n\n\n

Odv\u011btv\u00ed mechaniky, ve kter\u00e9m se budeme zab\u00fdvat pohybem t\u011bles, je kinematika a dynamika. Statika<\/strong> je ta \u010d\u00e1st mechaniky, ve kter\u00e9 jsou sou\u010d\u00e1sti v klidu, aby tomu tak bylo, mus\u00ed b\u00fdt spln\u011bno n\u011bkolik podm\u00ednek.<\/p>\n\n\n\n

V tomto z\u00e1znamu:<\/p>\n\n\n\n

    \n
  1. Podporuje. Typy a symboly<\/a><\/li>\n\n\n\n
  2. Stupe\u0148 statick\u00e9ho neozna\u010den\u00ed<\/a><\/li>\n\n\n\n
  3. Staticky ur\u010diteln\u00e9 syst\u00e9my<\/a><\/li>\n\n\n\n
  4. Staticky neur\u010dit\u00e9 syst\u00e9my<\/a><\/li>\n\n\n\n
  5. Mechanismy<\/a><\/li>\n<\/ol>\n\n\n\n

    <\/p>\n\n\n\n

    Podporuje. Typy a symboly<\/strong><\/h1>\n\n\n\n

    Aby syst\u00e9m z\u016fstal stacion\u00e1rn\u00ed, mus\u00edme ho podporovat. V \u00faloh\u00e1ch mechaniky se nej\u010dast\u011bji setk\u00e1te s podp\u011brami, jako jsou n\u00e1sleduj\u00edc\u00ed. V diagramech jsou ozna\u010deny podp\u016frn\u00e9 reakce<\/strong> pro individu\u00e1ln\u00ed podporu:<\/p>\n\n\n\n

    \"podpora
    Neposuvn\u00e1 podp\u011bra \u010depu<\/figcaption><\/figure>\n\n\n\n
    \"\"
    Podp\u011bra posuvn\u00e9ho kloubu<\/figcaption><\/figure>\n\n\n\n
    \"\"
    Oprava<\/figcaption><\/figure>\n\n\n\n
    \"\"
    Spole\u010dn\u00fd<\/figcaption><\/figure>\n\n\n\n
    V\u0161echny v\u00fd\u0161e uveden\u00e9 podpory najdete v aplikaci. Kalkula\u010dka Nosn\u00edk\u016f<\/u><\/a> kde si m\u016f\u017eete vyzkou\u0161et zp\u016fsoby podp\u00edr\u00e1n\u00ed nosn\u00edkov\u00fdch syst\u00e9m\u016f.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Statick\u00e9 syst\u00e9my m\u016f\u017eeme rozd\u011blit na dva typy:<\/p>\n\n\n\n

      \n
    1. Staticky determinovateln\u00e9 syst\u00e9my - stupe\u0148 statick\u00e9 nedeterminovanosti takov\u00e9ho syst\u00e9mu je nulov\u00fd.<\/li>\n\n\n\n
    2. Staticky neur\u010dit\u00e9 syst\u00e9my - stupe\u0148 statick\u00e9 neur\u010ditosti takov\u00e9ho syst\u00e9mu je v\u011bt\u0161\u00ed ne\u017e nula.<\/li>\n<\/ol>\n\n\n\n

      Stupe\u0148 statick\u00e9ho neozna\u010den\u00ed<\/strong><\/h2>\n\n\n\n

      Pro v\u00fdpo\u010det stupn\u011b statick\u00e9 nerozli\u0161itelnosti dan\u00e9ho syst\u00e9mu lze pou\u017e\u00edt n\u00e1sleduj\u00edc\u00ed vzorec. Tento vzorec se nejl\u00e9pe pou\u017e\u00edv\u00e1 p\u0159i v\u00fdpo\u010dtu nosn\u00edky<\/strong> i ram<\/strong>.<\/p>\n\n\n\n

      N=R-J-3<\/em>
      Kde:
      N - stupe\u0148 statick\u00e9 nepr\u016fkaznosti
      R - po\u010det podp\u016frn\u00fdch reakc\u00ed. To znamen\u00e1, \u017ee sou\u010det v\u0161ech reakc\u00ed pro na\u0161e podpory
      J - po\u010det vnit\u0159n\u00edch kloub\u016f - pokud nejsou p\u0159\u00edtomny P=0
      3 - po\u010det rovnov\u00e1\u017en\u00fdch rovnic. Ve statick\u00fdch syst\u00e9mech je to 3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      <\/p>\n\n\n\n

      Pro p\u0159\u00edhradov\u00e9 konstrukce<\/strong> pou\u017eijeme n\u00e1sleduj\u00edc\u00ed vzorec:<\/p>\n\n\n\n

      2n = m + r<\/em>
      Kde:
      n - po\u010det uzl\u016f p\u0159\u00edhradov\u00e9 konstrukce
      m - po\u010det p\u0159\u00edhradov\u00fdch prut\u016f (prut\u016f)
      r - po\u010det podp\u016frn\u00fdch reakc\u00ed<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      <\/p>\n\n\n\n

      P\u0159\u00edhradov\u00fd nosn\u00edk je ur\u010diteln\u00fd, pokud je spln\u011bn v\u00fd\u0161e uveden\u00fd vztah. To znamen\u00e1, \u017ee zdvojen\u00fd po\u010det uzl\u016f se mus\u00ed rovnat sou\u010dtu prut\u016f a po\u010dtu reakc\u00ed.<\/p>\n\n\n\n

      Staticky ur\u010diteln\u00fd syst\u00e9m<\/strong><\/h3>\n\n\n\n

      Co je to statick\u00e1 determinovatelnost? Staticky determinovateln\u00fd syst\u00e9m je takov\u00fd, pro kter\u00fd m\u016f\u017eeme vypo\u010d\u00edtat podp\u016frn\u00e9 reakce. Nap\u0159. n\u00e1\u0161 nosn\u00edk nebo bude staticky ur\u010diteln\u00fd, pokud pomoc\u00ed t\u0159\u00ed rovnic rovnov\u00e1hy m\u016f\u017eeme vypo\u010d\u00edtat v\u0161echny reakce. Stupe\u0148 statick\u00e9 neur\u010ditosti je u takov\u00fdch syst\u00e9m\u016f nulov\u00fd.<\/p>\n\n\n\n

      N=0<\/p>\n\n\n\n

      Podle v\u00fd\u0161e uveden\u00e9ho vzorce<\/p>\n\n\n\n

      N=R-J-3 => N=3 - 0 - 3 = 0<\/p>\n\n\n\n

      Kde:<\/p>\n\n\n\n

      R=3 - sou\u010det v\u0161ech reakc\u00ed pro na\u0161e podp\u011bry<\/p>\n\n\n\n

      J=0 po\u010det vnit\u0159n\u00edch kloub\u016f, nen\u00ed p\u0159\u00edtomen<\/p>\n\n\n\n

      3 - po\u010det rovnic rovnov\u00e1hy<\/p>\n\n\n\n

      Pro jednoduch\u00fd p\u0159\u00edhradov\u00fd vazn\u00edk bude v\u00fdpo\u010det vypadat takto:<\/p>\n\n\n\n

      2n = m + r => 2*5 = 7 + 3 => 10 = 10<\/em><\/p>\n\n\n\n

      Kde:<\/p>\n\n\n\n

      n = 5 - po\u010det uzl\u016f<\/p>\n\n\n\n

      m = 7 - po\u010det p\u0159\u00edhradov\u00fdch prut\u016f<\/p>\n\n\n\n

      r = 3 - po\u010det podp\u016frn\u00fdch reakc\u00ed<\/p>\n\n\n\n

      Staticky neur\u010dit\u00e9 syst\u00e9my<\/strong><\/h3>\n\n\n\n

      Staticky nejednozna\u010dn\u00fd syst\u00e9m je takov\u00fd, pro kter\u00fd nejsme schopni vypo\u010d\u00edtat podp\u016frn\u00e9 reakce. Stupe\u0148 statick\u00e9 neur\u010ditosti je u takov\u00fdch syst\u00e9m\u016f v\u011bt\u0161\u00ed ne\u017e nula. Po\u010det nezn\u00e1m\u00fdch podp\u016frn\u00fdch reakc\u00ed je v\u011bt\u0161\u00ed ne\u017e po\u010det rovnov\u00e1\u017en\u00fdch rovnic.<\/p>\n\n\n\n

      N > 0<\/p>\n\n\n\n

      Kde:<\/p>\n\n\n\n

      R=5 - sou\u010det v\u0161ech reakc\u00ed pro na\u0161e podpory<\/p>\n\n\n\n

      J=0 - po\u010det vnit\u0159n\u00edch spoj\u016f, nen\u00ed p\u0159\u00edtomen<\/p>\n\n\n\n

      3 - po\u010det rovnic rovnov\u00e1hy<\/p>\n\n\n\n

      Nosn\u00edk je dvakr\u00e1t staticky neur\u010dit\u00fd - (v\u00fdsledek N=2)<\/p>\n\n\n\n

      Takov\u00fd syst\u00e9m je strnul\u00fd a nem\u00e1 \u0161anci fungovat. Nosn\u00edk pod zat\u00ed\u017een\u00edm nebo p\u0159i zm\u011bn\u011b teploty nem\u00e1 mo\u017enost posunu, jin\u00fdmi slovy nem\u00e1 mo\u017enost pr\u00e1ce.<\/p>\n\n\n\n

      Mechanismy<\/strong><\/h3>\n\n\n\n

      Posledn\u00edm typem syst\u00e9m\u016f, o kter\u00e9m budu hovo\u0159it, jsou syst\u00e9my, kter\u00e9 maj\u00ed mo\u017enost pohybu - mechanismy. M\u00edra statick\u00e9 neur\u010ditosti je u takov\u00fdch syst\u00e9m\u016f z\u00e1porn\u00e1.<\/p>\n\n\n\n

      N < 0<\/p>\n\n\n\n

      N=R-J-3 => N=2-0- 3 = -1<\/p>\n\n\n\n

      To je konec t\u00e9matu o statick\u00e9 nekonvexit\u011b, d\u011bkuji a nev\u00e1hejte si prohl\u00e9dnout dal\u0161\u00ed p\u0159\u00edsp\u011bvky \ud83d\ude0a.<\/p>","protected":false},"excerpt":{"rendered":"

      W tym wpisie dowiesz si\u0119 co to jest stopie\u0144 statycznej niewyznaczalno\u015bci? W jaki spos\u00f3b wyznaczy\u0107 czy uk\u0142ad (belka, rama, kratownica) jest statycznie wyznaczalna. Dodatkowo poznasz mo\u017cliwe przypadki podp\u00f3r z kt\u00f3rymi spotykamy si\u0119 w zadaniach z mechaniki. Uk\u0142adem statycznym nazywamy taki uk\u0142ad, kt\u00f3ry jest nieruchomy. To znaczy, \u017ce nie mo\u017ce si\u0119 porusza\u0107 pod wp\u0142ywem dzia\u0142ania si\u0142 […]<\/p>\n","protected":false},"author":255930052,"featured_media":1040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2},"jetpack_post_was_ever_published":true},"categories":[14815],"tags":[14842,14844,14843],"class_list":["post-1023","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-statyczna-wyznaczalnosc","tag-uklad-statycznie-niewyznaczalny","tag-uklad-statycznie-wyznaczalny"],"jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/pg3flK-gv","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Reakcja-przegubowa-przesuwna-blad.png?fit=753%2C589&ssl=1","_links":{"self":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/1023","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/comments?post=1023"}],"version-history":[{"count":14,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/1023\/revisions"}],"predecessor-version":[{"id":3080,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/1023\/revisions\/3080"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media\/1040"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media?parent=1023"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/categories?post=1023"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/tags?post=1023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}