Postup pro v\u00fdpo\u010det reakc\u00ed ve svazku<\/h1>\n\n\n\n\n- Za\u010d\u00edn\u00e1me zaveden\u00edm vhodn\u00fdch podp\u016frn\u00fdch reakc\u00ed v m\u00edst\u011b podpory. V\u00edce informac\u00ed o t\u00e9to problematice naleznete v \u010dl\u00e1nku Podp\u016frn\u00e9 reakce<\/a>.<\/li>\n\n\n\n
- Pot\u00e9 zkontrolujeme, zda je nosn\u00edk staticky ur\u010dit\u00fd. V\u00edce informac\u00ed o tom naleznete v \u010dl\u00e1nku Ur\u010ditelnost stavu<\/a>.<\/li>\n\n\n\n
- V dal\u0161\u00edm kroku zap\u00ed\u0161eme rovnice rovnov\u00e1hy. V\u00edce informac\u00ed o tomto postupu naleznete v z\u00e1znamu Rovnov\u00e1\u017en\u00e9 rovnice<\/a>.<\/li>\n<\/ul>\n\n\n\n
Jednodu\u0161e podep\u0159en\u00fd nosn\u00edk - V\u00fdpo\u010det podp\u011brn\u00fdch reakc\u00ed pro nosn\u00edky<\/h2>\n\n\n\n
Za\u010dn\u011bme t\u00edm, \u017ee vezmeme sou\u0159adnicov\u00fd syst\u00e9m a p\u0159edpokl\u00e1d\u00e1me kladnou hybnost proti sm\u011bru hodinov\u00fdch ru\u010di\u010dek.<\/p>\n\n\n\n![\"Zna\u010den\u00ed](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/uklad-wspol.png?resize=629%2C591&ssl=1\")
<\/figure>\n\n\n\nN\u00ed\u017ee uv\u00e1d\u00edm p\u0159\u00edklad diagramu prost\u011b podep\u0159en\u00e9ho nosn\u00edku. Takto naz\u00fdv\u00e1me nosn\u00edk podep\u0159en\u00fd kloubov\u00fdmi podp\u011brami na obou konc\u00edch. Pro tento nosn\u00edk ur\u010d\u00edme reakce na podep\u0159en\u00ed.<\/p>\n\n\n\n![\"jednodu\u0161e](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka_swobodna.png?resize=1024%2C340&ssl=1\")
<\/figure>\n\n\n\nNa v\u00fdkresu nosn\u00edku jsou ji\u017e reakce p\u0159id\u00e1ny. V bod\u011b A tedy m\u00e1me neposuvnou kloubovou podporu, tak\u017ee p\u0159id\u00e1me vodorovnou reakci HA a svislou reakci VA. V bod\u011b B na konci nosn\u00edku m\u00e1me posuvnou kloubovou podporu, tak\u017ee p\u0159id\u00e1me jednu svislou reakci VB. D\u00e1le zkontrolujeme statickou ur\u010ditelnost.<\/p>\n\n\n\nN=R-J-3<\/em>=3-0-3=0 - nosn\u00edk je staticky ur\u010diteln\u00fd
Kde:
N - stupe\u0148 statick\u00e9 nepr\u016fkaznosti
R =3 - po\u010det podp\u016frn\u00fdch reakc\u00ed
J =0 - po\u010det vnit\u0159n\u00edch spoj\u016f
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\u010cas na rovnice rovnov\u00e1hy. Nezapome\u0148te, \u017ee pro rovinnou soustavu sil m\u00e1me t\u0159i rovnice:<\/p>\n\n\n\n
![\"\\F_{ix}](\"https:\/\/s0.wp.com\/latex.php?latex=%5CSigma+F_%7Bix%7D+%3D+0+&bg=ffffff&fg=000&s=2&c=20201002\")
- sou\u010det pr\u016fm\u011bt\u016f sil na osu x<\/p>\n\n\n\n
![\"\\F_{iy}](\"https:\/\/s0.wp.com\/latex.php?latex=%5CSigma+F_%7Biy%7D+%3D+0+&bg=ffffff&fg=000&s=2&c=20201002\")
- sou\u010det pr\u016fm\u011bt\u016f sil na osu y<\/p>\n\n\n\n
![\"\\M_{i}](\"https:\/\/s0.wp.com\/latex.php?latex=%5CSigma+M_%7Bi%7D+%3D+0+&bg=ffffff&fg=000&s=2&c=20201002\")
- sou\u010det moment\u016f v bod\u011b<\/p>\n\n\n\n
Za\u010dn\u011bme prvn\u00ed a nejjednodu\u0161\u0161\u00ed rovnic\u00ed. Sou\u010det pr\u016fm\u011bt\u016f sil na osu x.<\/p>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/swobodna-Fx.png?resize=271%2C51&ssl=1\")
<\/figure>\n\n\n\nProto\u017ee v na\u0161em p\u0159\u00edkladu prost\u011b podep\u0159en\u00e9ho nosn\u00edku nep\u016fsob\u00ed ve sm\u011bru osy x \u017e\u00e1dn\u00e1 slo\u017eka s\u00edly, je reakce HA=0.<\/p>\n\n\n\n
Pot\u00e9 p\u0159ejdeme ke t\u0159et\u00ed rovnici pro sou\u010det moment\u016f v bod\u011b.<\/p>\n\n\n\n
V\u00fdb\u011br bodu je na v\u00e1s. J\u00e1 jsem si vybral bod A.<\/p>\n\n\n\nP\u0159i ur\u010dov\u00e1n\u00ed rovnov\u00e1\u017en\u00fdch rovnic sou\u010dtu moment\u016f je nejlep\u0161\u00ed zvolit bod, ve kter\u00e9m se nach\u00e1z\u00ed jedna z podpor.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nV na\u0161em p\u0159\u00edkladu m\u00e1me na v\u00fdb\u011br bod A nebo B. V\u00fdb\u011brem jedn\u00e9 z podpor zp\u016fsob\u00edme, \u017ee se reakce pro tuto podporu neobjev\u00ed v na\u0161\u00ed rovnici pro moment, proto\u017ee moment je s\u00edla vyn\u00e1soben\u00e1 ramenem. Pokud je rameno nulov\u00e9 (s\u00edla proch\u00e1z\u00ed na\u0161\u00edm bodem A), bude moment t\u00e9to s\u00edly tak\u00e9 nulov\u00fd, tak\u017ee jej m\u016f\u017eeme z rovnice vynechat.<\/p>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/swobodna-moment.png?resize=634%2C108&ssl=1\")
<\/figure>\n\n\n\nV rovnici m\u00e1me:<\/p>\n\n\n\n
\n- Reakce VB vyn\u00e1soben\u00e1 vzd\u00e1lenost\u00ed 12, co\u017e je vzd\u00e1lenost mezi body A a B.<\/li>\n\n\n\n
- S\u00edla F vyn\u00e1soben\u00e1 2, tj. vzd\u00e1lenost s\u00edly F od bodu A.<\/li>\n\n\n\n
- Ohybov\u00fd moment M. Moment nen\u00ed n\u00e1soben vzd\u00e1lenost\u00ed.<\/li>\n\n\n\n
- Souvisl\u00e9 zat\u00ed\u017een\u00ed q se vyn\u00e1sob\u00ed d\u00e9lkou 4, na kterou p\u016fsob\u00ed, a 6, co\u017e je vzd\u00e1lenost st\u0159edu q od bodu A.<\/li>\n\n\n\n
- Na obr. 1 si v\u0161imneme znam\u00e9nek moment\u016f podle toho, co jsme p\u0159edpokl\u00e1dali na za\u010d\u00e1tku.<\/li>\n<\/ul>\n\n\n\n
Po transformac\u00edch z\u00edsk\u00e1me hodnotu s\u00edly VB, tak\u017ee m\u00e1me vypo\u010dtenou reakci kolejnice.<\/p>\n\n\n\n
Nakonec nap\u00ed\u0161eme rovnici rovnov\u00e1hy pro s\u00edly ve sm\u011bru osy y.<\/p>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/swobodna-Fy.png?resize=483%2C113&ssl=1\")
<\/figure>\n\n\n\nV rovnici m\u00e1me:<\/p>\n\n\n\n
\n- VA reakce s kladn\u00fdm znam\u00e9nkem, proto\u017ee n\u00e1vrat VA s\u00edly je v souladu s n\u00e1vratem osy y.<\/li>\n\n\n\n
- Reakce VB s kladn\u00fdm znam\u00e9nkem, proto\u017ee n\u00e1vrat s\u00edly VA je v souladu s n\u00e1vratem osy y.<\/li>\n\n\n\n
- Souvisl\u00e9 zat\u00ed\u017een\u00ed q vyn\u00e1soben\u00e9 4, tj. d\u00e9lka, na kterou p\u016fsob\u00ed.<\/li>\n\n\n\n
- S\u00edla F se znam\u00e9nkem \u00fahybu, proto\u017ee n\u00e1vrat s\u00edly F je opa\u010dn\u00fd k ose y.<\/li>\n<\/ul>\n\n\n\n
Po transformaci a dosazen\u00ed hodnoty VB z\u00edsk\u00e1me hodnotu s\u00edly VA. T\u00edmto zp\u016fsobem jsme vypo\u010d\u00edtali v\u0161echny reakce.<\/p>\n\n\n\n
Jednodu\u0161e podep\u0159en\u00fd nosn\u00edk - V\u00fdpo\u010det podp\u011brn\u00fdch reakc\u00ed pro nosn\u00edky<\/h2>\n\n\n\n
Za\u010dn\u011bme t\u00edm, \u017ee vezmeme sou\u0159adnicov\u00fd syst\u00e9m a p\u0159edpokl\u00e1d\u00e1me kladnou hybnost proti sm\u011bru hodinov\u00fdch ru\u010di\u010dek.<\/p>\n\n\n\n N\u00ed\u017ee uv\u00e1d\u00edm p\u0159\u00edklad diagramu prost\u011b podep\u0159en\u00e9ho nosn\u00edku. Takto naz\u00fdv\u00e1me nosn\u00edk podep\u0159en\u00fd kloubov\u00fdmi podp\u011brami na obou konc\u00edch. Pro tento nosn\u00edk ur\u010d\u00edme reakce na podep\u0159en\u00ed.<\/p>\n\n\n\n Na v\u00fdkresu nosn\u00edku jsou ji\u017e reakce p\u0159id\u00e1ny. V bod\u011b A tedy m\u00e1me neposuvnou kloubovou podporu, tak\u017ee p\u0159id\u00e1me vodorovnou reakci HA a svislou reakci VA. V bod\u011b B na konci nosn\u00edku m\u00e1me posuvnou kloubovou podporu, tak\u017ee p\u0159id\u00e1me jednu svislou reakci VB. D\u00e1le zkontrolujeme statickou ur\u010ditelnost.<\/p>\n\n\n\n \u010cas na rovnice rovnov\u00e1hy. Nezapome\u0148te, \u017ee pro rovinnou soustavu sil m\u00e1me t\u0159i rovnice:<\/p>\n\n\n\n Za\u010dn\u011bme prvn\u00ed a nejjednodu\u0161\u0161\u00ed rovnic\u00ed. Sou\u010det pr\u016fm\u011bt\u016f sil na osu x.<\/p>\n\n\n\n Proto\u017ee v na\u0161em p\u0159\u00edkladu prost\u011b podep\u0159en\u00e9ho nosn\u00edku nep\u016fsob\u00ed ve sm\u011bru osy x \u017e\u00e1dn\u00e1 slo\u017eka s\u00edly, je reakce HA=0.<\/p>\n\n\n\n Pot\u00e9 p\u0159ejdeme ke t\u0159et\u00ed rovnici pro sou\u010det moment\u016f v bod\u011b.<\/p>\n\n\n\n V\u00fdb\u011br bodu je na v\u00e1s. J\u00e1 jsem si vybral bod A.<\/p>\n\n\n\n V na\u0161em p\u0159\u00edkladu m\u00e1me na v\u00fdb\u011br bod A nebo B. V\u00fdb\u011brem jedn\u00e9 z podpor zp\u016fsob\u00edme, \u017ee se reakce pro tuto podporu neobjev\u00ed v na\u0161\u00ed rovnici pro moment, proto\u017ee moment je s\u00edla vyn\u00e1soben\u00e1 ramenem. Pokud je rameno nulov\u00e9 (s\u00edla proch\u00e1z\u00ed na\u0161\u00edm bodem A), bude moment t\u00e9to s\u00edly tak\u00e9 nulov\u00fd, tak\u017ee jej m\u016f\u017eeme z rovnice vynechat.<\/p>\n\n\n\n V rovnici m\u00e1me:<\/p>\n\n\n\n Po transformac\u00edch z\u00edsk\u00e1me hodnotu s\u00edly VB, tak\u017ee m\u00e1me vypo\u010dtenou reakci kolejnice.<\/p>\n\n\n\n Nakonec nap\u00ed\u0161eme rovnici rovnov\u00e1hy pro s\u00edly ve sm\u011bru osy y.<\/p>\n\n\n\n V rovnici m\u00e1me:<\/p>\n\n\n\n Po transformaci a dosazen\u00ed hodnoty VB z\u00edsk\u00e1me hodnotu s\u00edly VA. T\u00edmto zp\u016fsobem jsme vypo\u010d\u00edtali v\u0161echny reakce.<\/p>\n\n\n\n<\/figure>\n\n\n\n<\/figure>\n\n\n\nN=R-J-3<\/em>=3-0-3=0 - nosn\u00edk je staticky ur\u010diteln\u00fd
Kde:
N - stupe\u0148 statick\u00e9 nepr\u016fkaznosti
R =3 - po\u010det podp\u016frn\u00fdch reakc\u00ed
J =0 - po\u010det vnit\u0159n\u00edch spoj\u016f
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<\/figure>\n\n\n\nP\u0159i ur\u010dov\u00e1n\u00ed rovnov\u00e1\u017en\u00fdch rovnic sou\u010dtu moment\u016f je nejlep\u0161\u00ed zvolit bod, ve kter\u00e9m se nach\u00e1z\u00ed jedna z podpor.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n <\/figure>\n\n\n\n\n
<\/figure>\n\n\n\n\n
![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/swobodna-calosc-1.png?resize=639%2C299&ssl=1\")
<\/figure>\n\n\n\n![\"Konzolov\u00fd](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka_wspornik.png?resize=900%2C244&ssl=1\")
<\/figure>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wspornik_fx.png?resize=458%2C118&ssl=1\")
<\/figure>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wspornik-fy.png?resize=496%2C109&ssl=1\")
<\/figure>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wspornik_Ma.png?resize=685%2C125&ssl=1\")
<\/figure>\n\n\n\n![\"Rovnice](\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/calosc_wspornik.png?resize=702%2C367&ssl=1\")
<\/figure>\n\n\n\n