{"id":1093,"date":"2024-09-23T14:59:28","date_gmt":"2024-09-23T12:59:28","guid":{"rendered":"https:\/\/solveredu.com\/?p=1093"},"modified":"2026-01-27T23:34:47","modified_gmt":"2026-01-27T22:34:47","slug":"static-equilibrium-equations","status":"publish","type":"post","link":"https:\/\/solveredu.com\/cs\/post\/rownania-rownowagi\/","title":{"rendered":"Rovnov\u00e1\u017en\u00e9 rovnice"},"content":{"rendered":"

V tomto p\u0159\u00edsp\u011bvku najdete informace o:<\/p>\n\n\n\n

    \n
  1. Jak\u00e9 jsou rovnice rovnov\u00e1hy?<\/a><\/li>\n\n\n\n
  2. Rovnov\u00e1\u017en\u00e9 rovnice pro rovinnou soustavu sil (2D)<\/a><\/li>\n\n\n\n
  3. Rovnice rovnov\u00e1hy pro prostorovou soustavu sil (3D)<\/a><\/li>\n<\/ol>\n\n\n\n
    Rovnice rovnov\u00e1hy se pou\u017e\u00edvaj\u00ed k popisu stavu t\u011blesa, kter\u00e9 je v rovnov\u00e1ze. Takov\u00e9 t\u011bleso nem\u011bn\u00ed svou polohu, tj. je v klidu.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Sou\u010det v\u0161ech sil a moment\u016f p\u016fsob\u00edc\u00edch na t\u011bleso v klidu mus\u00ed b\u00fdt v rovnov\u00e1ze, co\u017e matematicky pop\u00ed\u0161eme takto:<\/p>\n\n\n\n

    \"\\F_{ix} - sou\u010det pr\u016fm\u011bt\u016f sil na osu x<\/p>\n\n\n\n

    \"\\F_{iy} - sou\u010det pr\u016fm\u011bt\u016f sil na osu y<\/p>\n\n\n\n

    \"\\M_{i} - sou\u010det moment\u016f v bod\u011b<\/p>\n\n\n\n

    Rovinn\u00e1 soustava (2D) - rovnov\u00e1\u017en\u00e9 rovnice<\/h1>\n\n\n\n

    V\u00fd\u0161e uveden\u00e9 rovnice plat\u00ed v ploch\u00fd syst\u00e9m nap\u00e1jen\u00ed<\/strong>. Pou\u017e\u00edv\u00e1me je k ur\u010den\u00ed reakc\u00ed nosn\u00edk\u016f, r\u00e1m\u016f a vazn\u00edk\u016f. Tyto typy prvk\u016f jsou z\u00e1kladn\u00edmi ot\u00e1zkami statiky. V takov\u00fdch \u00faloh\u00e1ch chceme, aby prvky z\u016fstaly v klidu. Pokud se t\u011blesa pohybuj\u00ed, hovo\u0159\u00edme o jin\u00fdch odv\u011btv\u00edch mechaniky, jako je kinematika nebo dynamika.<\/p>\n\n\n\n

    \"Stupn\u011b<\/figure>\n\n\n\n

    V rovinn\u00e9 soustav\u011b se t\u011bleso m\u016f\u017ee pohybovat ve sm\u011bru x a y a ot\u00e1\u010det se kolem osy z sm\u011brem k n\u00e1m. V rovinn\u00e9 soustav\u011b m\u00e1 t\u011bleso 3 stupn\u011b volnosti. A aby t\u011bleso z\u016fstalo v klidu, mus\u00edme tyto 3 stupn\u011b volnosti vyv\u00e1\u017eit. A pr\u00e1v\u011b k tomuto \u00fa\u010delu pou\u017e\u00edv\u00e1me rovnice rovnov\u00e1hy. Pokud je rovnov\u00e1ha sil x a y a sou\u010det moment\u016f rovna nule, znamen\u00e1 to, \u017ee se t\u011bleso nepohybuje ani neot\u00e1\u010d\u00ed.<\/p>\n\n\n\n

    Specifick\u00fdm typem ploch\u00e9ho syst\u00e9mu je ploch\u00fd syst\u00e9m sb\u00edhav\u00fdch sil<\/strong> (ozna\u010dovan\u00fd tak\u00e9 jako centr\u00e1ln\u00ed syst\u00e9m). Jedn\u00e1 se o soustavu, jej\u00ed\u017e s\u00edly se prot\u00ednaj\u00ed v jednom bod\u011b. V tomto bod\u011b se sb\u00edhaj\u00ed. Pro takovou soustavu jsou podm\u00ednkou rovnov\u00e1hy pouze dv\u011b rovnice:<\/p>\n\n\n\n

    \"\\F_{ix} - sou\u010det pr\u016fm\u011bt\u016f sil na osu x<\/p>\n\n\n\n

    \"\\F_{iy} - sou\u010det pr\u016fm\u011bt\u016f sil na osu y<\/p>\n\n\n\n

    Prostorov\u00fd syst\u00e9m (3D) - rovnov\u00e1\u017en\u00e9 rovnice<\/h2>\n\n\n\n

    Prostorov\u00e9 uspo\u0159\u00e1d\u00e1n\u00ed m\u00e1 o n\u011bco v\u00edce stup\u0148\u016f volnosti. Je jich a\u017e \u0161est. Pro ka\u017ed\u00fd stupe\u0148 volnosti m\u00e1me rovnici popisuj\u00edc\u00ed rovnov\u00e1\u017en\u00fd stav. Dost\u00e1v\u00e1me tedy \u0161est rovnic. V \u00faloh\u00e1ch, kde ur\u010dujeme podp\u016frn\u00e9 reakce v prostorov\u00fdch soustav\u00e1ch, je nalezen\u00ed \u0159e\u0161en\u00ed obt\u00ed\u017en\u011bj\u0161\u00ed, proto\u017ee rovnic je \u0161est.<\/p>\n\n\n\n

    \"\\F_{ix} - sou\u010det pr\u016fm\u011bt\u016f sil na osu x<\/p>\n\n\n\n

    \"\\F_{iy} - sou\u010det pr\u016fm\u011bt\u016f sil na osu y<\/p>\n\n\n\n

    \"\\F_{iz} - sou\u010det pr\u016fm\u011bt\u016f sil na osu z<\/p>\n\n\n\n

    \"\\\u25a0Sigma - sou\u010det moment\u016f kolem osy x<\/p>\n\n\n\n

    \"\\M_{iy} - sou\u010det moment\u016f kolem osy y<\/p>\n\n\n\n

    \"\\M_{iz} - sou\u010det moment\u016f kolem osy z<\/p>\n\n\n\n

    Zapamatujte si tolik rovnic, kolik je maximum nezn\u00e1m\u00fdch. 6 rovnic = max. 6 nezn\u00e1m\u00fdch.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    To znamen\u00e1, \u017ee se t\u011bleso v prostoru m\u016f\u017ee pohybovat t\u0159emi sm\u011bry a ot\u00e1\u010det se kolem t\u0159\u00ed os.<\/p>\n\n\n\n

    \"Stupn\u011b<\/figure>\n\n\n\n

    To je ode m\u011b k t\u00e9matu rovnov\u00e1\u017en\u00fdch rovnic ve statice v\u0161e.<\/p>\n\n\n\n

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

    <\/p>","protected":false},"excerpt":{"rendered":"

    W tym wpisie znajdziesz informacj\u0119 na temat: R\u00f3wnania r\u00f3wnowagi s\u0142u\u017c\u0105 do opisania stanu cia\u0142a kt\u00f3re, jest w r\u00f3wnowadze. Takie cia\u0142o nie zmienia swojej pozycji, czyli jest w spoczynku. Suma wszystkich si\u0142 i moment\u00f3w dzia\u0142aj\u0105cych na cia\u0142o w stanie spoczynku musi si\u0119 r\u00f3wnowa\u017cy\u0107, opisujemy to matematycznie w nast\u0119puj\u0105cy spos\u00f3b: – suma rzut\u00f3w si\u0142 na o\u015b x […]<\/p>\n","protected":false},"author":255930052,"featured_media":1637,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_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","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":true},"categories":[14815],"tags":[14823,14822,14820],"class_list":["post-1093","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-przestrzenny-uklad-sil","tag-plaski-uklad-sil-2","tag-rownania-rownowagi"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/stopnie-swobody_3D_eng.png?fit=947%2C556&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-hD","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/1093","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=1093"}],"version-history":[{"count":17,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/1093\/revisions"}],"predecessor-version":[{"id":3067,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/1093\/revisions\/3067"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media\/1637"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media?parent=1093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/categories?post=1093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/tags?post=1093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}