{"id":2177,"date":"2025-04-08T15:28:26","date_gmt":"2025-04-08T13:28:26","guid":{"rendered":"https:\/\/solveredu.com\/?p=2177"},"modified":"2025-10-12T13:47:03","modified_gmt":"2025-10-12T11:47:03","slug":"moment-bezwladnosci-kola","status":"publish","type":"post","link":"https:\/\/solveredu.com\/cs\/post\/moment-bezwladnosci-kola\/","title":{"rendered":"Moment setrva\u010dnosti kola - teorie, vzorce a p\u0159\u00edklady v\u00fdpo\u010dtu"},"content":{"rendered":"

Jak\u00fd je moment setrva\u010dnosti?<\/strong><\/strong><\/h1>\n\n\n\n

Moment setrva\u010dnosti je jednou ze z\u00e1kladn\u00edch geometrick\u00fdch veli\u010din popisuj\u00edc\u00edch rozlo\u017een\u00ed hmoty nebo povrchu kolem osy ot\u00e1\u010den\u00ed. Ve stavebn\u00ed mechanice popisuje moment setrva\u010dnosti plochy (tzv. druh\u00fd moment plochy) odolnost pr\u016f\u0159ezu proti ohybu. \u010c\u00edm v\u011bt\u0161\u00ed je moment setrva\u010dnosti, t\u00edm v\u011bt\u0161\u00ed je tuhost prutu.<\/p>\n\n\n\n

Moment setrva\u010dnosti kola - vzorec<\/strong><\/strong><\/h2>\n\n\n\n

Pro kruh (pln\u00fd disk) o polom\u011bru , je moment setrva\u010dnosti povrchu vzhledem k ose proch\u00e1zej\u00edc\u00ed st\u0159edem a kolm\u00e9 na povrch kruhu roven:<\/p>\n\n\n\n

\"I_{x},I_{y}<\/p>\n\n\n\n

Pokud zn\u00e1te pr\u016fm\u011br , m\u016f\u017eete pou\u017e\u00edt transformovan\u00fd vzorec:<\/p>\n\n\n\n

\"I_{x},I_{y}<\/p>\n\n\n\n

P\u0159\u00edklad v\u00fdpo\u010dtu pro kru\u017enici<\/strong><\/p>\n\n\n\n

N\u00ed\u017ee je uveden p\u0159\u00edklad v\u00fdpo\u010dtu momentu setrva\u010dnosti kruhu v na\u0161\u00ed online kalkula\u010dce. Sta\u010d\u00ed vybrat tvar \u201ekruh\u201d, zadat polom\u011br a kalkula\u010dka automaticky vypo\u010d\u00edt\u00e1 hodnotu momentu setrva\u010dnosti.<\/p>\n\n\n\n

\"Moment<\/figure>\n\n\n\n

Moment setrva\u010dnosti p\u016flkruhu - nedostatek symetrie<\/strong><\/strong><\/strong><\/h2>\n\n\n\n

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

Pro p\u016flkruh se vzorec pro moment setrva\u010dnosti li\u0161\u00ed, proto\u017ee \u00fatvar nen\u00ed symetrick\u00fd kolem vodorovn\u00e9 osy. Moment setrva\u010dnosti p\u016flkruhu vzhledem k vodorovn\u00e9 ose proch\u00e1zej\u00edc\u00ed t\u011b\u017ei\u0161t\u011bm p\u016flkruhu:<\/p>\n\n\n\n

\"I_{x}<\/p>\n\n\n\n

Moment setrva\u010dnosti p\u016flkruhu vzhledem ke svisl\u00e9 ose proch\u00e1zej\u00edc\u00ed t\u011b\u017ei\u0161t\u011bm p\u016flkruhu:<\/p>\n\n\n\n

\"I_{y}<\/p>\n\n\n\n

To znamen\u00e1 polovinu momentu setrva\u010dnosti pln\u00e9ho kola.<\/p>\n\n\n\n

P\u0159\u00edklad v\u00fdpo\u010dtu pro p\u016flkruh<\/strong><\/p>\n\n\n\n

N\u00ed\u017ee je uveden p\u0159\u00edklad v\u00fdpo\u010dtu momentu setrva\u010dnosti p\u016flkruhu v na\u0161\u00ed online kalkula\u010dce. Sta\u010d\u00ed vybrat tvar \u201ep\u016flkruh\u201d, zvolit orientaci v rovin\u011b, zadat polom\u011br a polohu st\u0159edu p\u016flkruhu a kalkula\u010dka automaticky vypo\u010d\u00edt\u00e1 hodnotu momentu setrva\u010dnosti.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Trubkov\u00fd profil - lehk\u00fd a pevn\u00fd<\/strong><\/h2>\n\n\n\n

Trubkov\u00e9 profily (tj. prstence) maj\u00ed velmi p\u0159\u00edzniv\u00fd pom\u011br setrva\u010dn\u00e9ho momentu k hmotnosti. D\u00edky dut\u00e9mu vnit\u0159ku si zachov\u00e1vaj\u00ed vysokou tuhost p\u0159i v\u00fdrazn\u011b ni\u017e\u0161\u00ed spot\u0159eb\u011b materi\u00e1lu. Vzorec pro moment setrva\u010dnosti prstence (trubky) s vn\u011bj\u0161\u00edm a vnit\u0159n\u00edm polom\u011brem:<\/p>\n\n\n\n

\"I_{x},I_{y}<\/p>\n\n\n\n

P\u0159\u00edklad v\u00fdpo\u010dtu pro profil potrub\u00ed<\/strong><\/p>\n\n\n\n

N\u00ed\u017ee je uveden p\u0159\u00edklad v\u00fdpo\u010dtu momentu setrva\u010dnosti pr\u016f\u0159ezu potrub\u00ed v na\u0161\u00ed online kalkula\u010dce. Sta\u010d\u00ed vybrat tvar \u201ekruh\u201d, zadat polom\u011br, pot\u00e9 op\u011bt vybrat \u201ekruh\u201d pro otvor zadat pr\u016fm\u011br a vybrat mo\u017enost \u201e\u0159ez\u201d pro vy\u0159\u00edznut\u00ed otvoru. Pot\u00e9 stiskn\u011bte tla\u010d\u00edtko \"solve\" a kalkula\u010dka automaticky vypo\u010d\u00edt\u00e1 hodnotu momentu setrva\u010dnosti.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Jak je vid\u011bt, moment setrva\u010dnosti trubkov\u00e9ho pr\u016f\u0159ezu se v\u00fd\u0159ezem sn\u00ed\u017e\u00ed. Proto\u017ee se v\u0161ak v\u00fd\u0159ez nach\u00e1z\u00ed bl\u00edzko st\u0159edu hmotnosti, je jeho vliv na odpor proti ohybu minim\u00e1ln\u00ed, tak\u017ee pou\u017eit\u00ed materi\u00e1lu je v tomto p\u0159\u00edpad\u011b neefektivn\u00ed. V d\u016fsledku toho vede odstran\u011bn\u00ed t\u00e9to \u010d\u00e1sti pr\u016f\u0159ezu ke zlep\u0161en\u00ed \u00fa\u010dinnosti konstrukce, proto\u017ee umo\u017e\u0148uje lep\u0161\u00ed rozlo\u017een\u00ed materi\u00e1lu v oblastech, kter\u00e9 maj\u00ed v\u011bt\u0161\u00ed vliv na tuhost pr\u016f\u0159ezu.<\/p>\n\n\n\n

Souhrn<\/strong> <\/h2>\n\n\n\n

Moment setrva\u010dnosti je d\u016fle\u017eit\u00fd pro ohybov\u00e9 i deforma\u010dn\u00ed s\u00edly. To je patrn\u00e9 z jejich vzorc\u016f, v nich\u017e je moment setrva\u010dnosti ve jmenovateli:<\/p>\n\n\n\n

Vzorec pro nap\u011bt\u00ed v ohybu:<\/p>\n\n\n\n

\"\\\u25a0sigma<\/p>\n\n\n\n

Vzorec pro pr\u016fhyb konzolov\u00e9ho bal\u00edku zat\u00ed\u017een\u00e9ho silou na konci:<\/p>\n\n\n\n

\"f=<\/p>\n\n\n\n

Moment setrva\u010dnosti kruhov\u00fdch pr\u016f\u0159ez\u016f je charakteristick\u00fd t\u00edm, \u017ee je v obou os\u00e1ch stejn\u00fd. To d\u00e1v\u00e1 smysl, proto\u017ee pr\u016f\u0159ez je symetrick\u00fd v\u016f\u010di os\u00e1m X i Y. Budeme to analyzovat porovn\u00e1n\u00edm s I-nosn\u00edkem, kde se moment setrva\u010dnosti m\u016f\u017ee v jednotliv\u00fdch os\u00e1ch li\u0161it. Pou\u017eit\u00ed t\u00e9to symetrie je v\u00fdhodn\u00e9 v p\u0159\u00edpad\u011b, \u017ee zat\u00ed\u017een\u00ed nep\u016fsob\u00ed v\u017edy pod\u00e9l siln\u011bj\u0161\u00ed osy prutu, proto\u017ee p\u0159edpov\u00edd\u00e1me pevnost prutu bez ohledu na sm\u011br zat\u00ed\u017een\u00ed.<\/p>\n\n\n\n

Momenty setrva\u010dnosti pro dal\u0161\u00ed z\u00e1kladn\u00ed \u00fadaje naleznete v tomto dokumentu. vstup<\/a><\/p>\n\n\n\n

Moment setrva\u010dnosti je kl\u00ed\u010dovou veli\u010dinou p\u0159i pevnostn\u00ed anal\u00fdze konstrukce. Nyn\u00ed zn\u00e1te vzorce pro kruh, p\u016flkruh a trubkov\u00fd profil a na\u0161e kalkula\u010dka v\u00e1m umo\u017en\u00ed prov\u00e9st pot\u0159ebn\u00e9 v\u00fdpo\u010dty rychle a p\u0159esn\u011b.
Vyzkou\u0161ejte n\u00e1\u0161 n\u00e1stroj pro v\u00fdpo\u010det momentu setrva\u010dnosti a vyzkou\u0161ejte si v\u00fd\u0161e uveden\u00e9 v\u00fdpo\u010dty sami.<\/p>\n\n\n\n

\n
Vyzkou\u0161ejte si ji zdarma<\/a><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"

Czym jest moment bezw\u0142adno\u015bci? Moment bezw\u0142adno\u015bci to jedna z podstawowych wielko\u015bci geometrycznych opisuj\u0105cych rozk\u0142ad masy lub powierzchni wok\u00f3\u0142 osi obrotu. W mechanice konstrukcji moment bezw\u0142adno\u015bci powierzchni (inaczej: drugi moment powierzchni) opisuje odporno\u015b\u0107 przekroju poprzecznego na zginanie. Im wi\u0119kszy moment bezw\u0142adno\u015bci, tym wi\u0119ksza sztywno\u015b\u0107 elementu konstrukcyjnego. Moment bezw\u0142adno\u015bci ko\u0142a – wz\u00f3r Dla ko\u0142a (pe\u0142nego dysku) o […]<\/p>\n","protected":false},"author":255930052,"featured_media":2199,"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":false},"categories":[14815],"tags":[14867,14852],"class_list":["post-2177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-moment-bezwladnosci","tag-srodek-ciezkosci"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/04\/kolo-e1760269513848.jpg?fit=620%2C277&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-z7","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/2177","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=2177"}],"version-history":[{"count":39,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/2177\/revisions"}],"predecessor-version":[{"id":2904,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/2177\/revisions\/2904"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media\/2199"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media?parent=2177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/categories?post=2177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/tags?post=2177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}