{"id":899,"date":"2024-09-23T14:59:27","date_gmt":"2024-09-23T12:59:27","guid":{"rendered":"https:\/\/solveredu.com\/?p=899"},"modified":"2026-01-27T23:42:18","modified_gmt":"2026-01-27T22:42:18","slug":"schnittgr%c3%b6%c3%9fen-am-balken","status":"publish","type":"post","link":"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/","title":{"rendered":"Schnittgr\u00f6\u00dfen am Balken"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\" id=\"foo\">W tym wpisie:<\/p>\n\n\n\n<ol id=\"bmwwansmrg0l42233965\" class=\"wp-block-list\">\n<li><a href=\"#6k4jq\">Co to s\u0105 si\u0142y wewn\u0119trzne i rodzaje si\u0142 wewn\u0119trznych<\/a><\/li>\n\n\n\n<li><a href=\"#8bgmc\">Wyznaczanie si\u0142 wewn\u0119trznych dla belki<\/a><\/li>\n\n\n\n<li><a href=\"#14cmf\">Wykresy si\u0142 wewn\u0119trznych.<\/a><\/li>\n<\/ol>\n\n\n\n<h1 id=\"6k4jq\" class=\"wp-block-heading has-large-font-size\">Si\u0142y wewn\u0119trzne w belkach i ich rodzaje<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"bh9jq\">Aby wyt\u0142umaczy\u0107 czym s\u0105 si\u0142y wewn\u0119trzne w belkach pos\u0142u\u017c\u0119 si\u0119 metod\u0105 przeci\u0119cia my\u015blowo. Na rys.1. poni\u017cej mamy most podparty na dw\u00f3ch ko\u0144cach podporami przegubowymi. W miejscu podpar\u0107 wprowadzamy reakcje i ca\u0142y uk\u0142ad jest w r\u00f3wnowadze.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"b29fp\">Gdyby\u015bmy teraz my\u015blowo przeci\u0119li most na dwie cz\u0119\u015bci?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fgq25\">Bez wprowadzenie si\u0142 wewn\u0119trznych w miejscu przeci\u0119cia most si\u0119 zawali i nasz jele\u0144 wpadnie do wody\ud83d\ude0a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"svoc\">Dlatego aby obie cz\u0119\u015bci mostu by\u0142y w r\u00f3wnowadze musimy zast\u0105pi\u0107 oddzia\u0142ywanie fragment\u00f3w mostu poprzez przy\u0142o\u017cenie si\u0142 wewn\u0119trznych.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"939\" height=\"690\" data-attachment-id=\"1574\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/sily-wewnetrzne\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?fit=939%2C690&amp;ssl=1\" data-orig-size=\"939,690\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"sily wewnetrzne\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?fit=939%2C690&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?resize=939%2C690&#038;ssl=1\" alt=\"Si\u0142y wewn\u0119trzne w belkach, SolverEdu\" class=\"wp-image-1574\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?w=939&amp;ssl=1 939w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?resize=300%2C220&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?resize=768%2C564&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?resize=16%2C12&amp;ssl=1 16w\" sizes=\"auto, (max-width: 939px) 100vw, 939px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"deai\">Wyr\u00f3\u017cniamy nast\u0119puj\u0105ce si\u0142y wewn\u0119trzne (przekrojowe):<\/p>\n\n\n\n<ul id=\"t0er2nsmrg0l42233979\" class=\"wp-block-list\">\n<li><strong>N &#8211; si\u0142a normalna<\/strong> (osiowa, pod\u0142u\u017cna) &#8211; w belce to si\u0142a dzia\u0142aj\u0105ca w kierunku poziomym x, r\u00f3wnolegle do osi belki<\/li>\n\n\n\n<li><strong>V &#8211; si\u0142a tn\u0105ca<\/strong> ( poprzeczna) &#8211; w belce to si\u0142a dzia\u0142aj\u0105ca w kierunku pionowym y, prostopadle do osi belki<\/li>\n\n\n\n<li><strong>M &#8211; moment gn\u0105cy<\/strong><\/li>\n<\/ul>\n\n\n\n<h2 id=\"8bgmc\" class=\"wp-block-heading has-medium-font-size\">Wyznaczanie si\u0142 wewn\u0119trznych dla belki<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fcs9m\">Przejd\u017amy do wyznaczania si\u0142 wewn\u0119trznych w belce. Zr\u00f3bmy to na przyk\u0142adzie belki swobodnie podpartej <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"857\" height=\"297\" data-attachment-id=\"1163\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/przedzialy\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzialy.png?fit=857%2C297&amp;ssl=1\" data-orig-size=\"857,297\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przedzialy\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzialy.png?fit=857%2C297&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzialy.png?resize=857%2C297&#038;ssl=1\" alt=\"Schamat belki swobodnie podpartej, SolverEdu\" class=\"wp-image-1163\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzialy.png?w=857&amp;ssl=1 857w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzialy.png?resize=300%2C104&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzialy.png?resize=768%2C266&amp;ssl=1 768w\" sizes=\"auto, (max-width: 857px) 100vw, 857px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"66mag\">Cyframi od 1 do 3 oznaczone zosta\u0142y przedzia\u0142y.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Przedzia\u0142 dodajemy w momencie pojawienia si\u0119 nowego obci\u0105\u017cenia lub podpory.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5bgbv\">Wyznaczanie si\u0142 wewn\u0119trznych b\u0119dziemy robi\u0107 dla ka\u017cdego przedzia\u0142u po kolei. Zanim zaczniemy wyznaczanie si\u0142 musimy najpierw om\u00f3wi\u0107 znakowanie si\u0142 wewn\u0119trznych<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"806\" height=\"337\" data-attachment-id=\"1576\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/m_sign\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?fit=806%2C337&amp;ssl=1\" data-orig-size=\"806,337\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"m_sign\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?fit=806%2C337&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?resize=806%2C337&#038;ssl=1\" alt=\"Znakowanie si\u0142 wewn\u0119trznych w belkach, SolverEdu\" class=\"wp-image-1576\" style=\"width:533px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?w=806&amp;ssl=1 806w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?resize=300%2C125&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?resize=768%2C321&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/m_sign.jpg?resize=18%2C8&amp;ssl=1 18w\" sizes=\"auto, (max-width: 806px) 100vw, 806px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"7p25j\">Na rysunku powy\u017cej przedstawiony jest spos\u00f3b znakowania si\u0142y normalnej, si\u0142y tn\u0105cej oraz momentu gn\u0105cego. Tak skierowane wektory maj\u0105 dodatni\u0105 warto\u015b\u0107 i to musisz zapami\u0119ta\u0107. Wektory skierowane przeciwnie b\u0119d\u0105 mia\u0142y ujemy znak. Jak widzisz inaczej jest z lewej a inaczej z prawej strony belki.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Pami\u0119taj, \u017ce przyj\u0119ty znak momentu gn\u0105cego przy wyznaczaniu reakcji mo\u017ce si\u0119 r\u00f3\u017cni\u0107 tego u\u017cywanego do si\u0142 wewn\u0119trznych. Radz\u0119 oddziela\u0107 te dwa etapy przyjmowania znak\u00f3w momentu gn\u0105cego.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"542\" height=\"344\" data-attachment-id=\"1166\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/znaki3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/znaki3.png?fit=542%2C344&amp;ssl=1\" data-orig-size=\"542,344\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"znaki3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/znaki3.png?fit=542%2C344&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/znaki3.png?resize=542%2C344&#038;ssl=1\" alt=\"Znakowanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1166\" style=\"width:426px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/znaki3.png?w=542&amp;ssl=1 542w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/znaki3.png?resize=300%2C190&amp;ssl=1 300w\" sizes=\"auto, (max-width: 542px) 100vw, 542px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"4kj93\">Dodatkowo jako skojarzenie dodatniego znaku momentu gn\u0105cego z u\u015bmiechni\u0119t\u0105 buzi\u0105 ( wygi\u0119te ko\u0144ce belki tworz\u0105 u\u015bmiech). A znak ujemny tworzy smutn\u0105 min\u0119.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9oed9\">W pierwszej kolejno\u015bci, zanim przyst\u0105pimy do obliczania <strong>si\u0142 wewn\u0119trznych<\/strong> musimy sprawdzi\u0107 <a href=\"https:\/\/solveredu.com\/post\/statyczna-wyznaczalnosc\/\">statyczn\u0105 wyznaczalno\u015b\u0107<\/a> oraz obliczy\u0107 <a href=\"https:\/\/www.solveredu.com\/post\/obliczanie-reakcji-podporowych-dla-belek\" target=\"_blank\" rel=\"noreferrer noopener\">reakcje podporowe<\/a> .<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"4qlf5\">Uk\u0142ad jest statycznie wyznaczalny &#8211; mo\u017cemy przej\u015b\u0107 do obliczania reakcji.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"57shu\">Korzystaj\u0105c z r\u00f3wna\u0144 r\u00f3wnowagi obliczamy warto\u015bci <strong>reakcji podporowych <\/strong>dla belki swobodnie podpartej.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"638\" height=\"344\" data-attachment-id=\"1578\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/reakcje-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje.jpg?fit=638%2C344&amp;ssl=1\" data-orig-size=\"638,344\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"reakcje\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje.jpg?fit=638%2C344&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje.jpg?resize=638%2C344&#038;ssl=1\" alt=\"Obliczanie reakcji w belkach, SolverEdu\" class=\"wp-image-1578\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje.jpg?w=638&amp;ssl=1 638w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje.jpg?resize=300%2C162&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje.jpg?resize=18%2C10&amp;ssl=1 18w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fcajd\">Maj\u0105c poprawnie wyznaczone reakcje podporowe w belce <strong>swobodnie podpartej <\/strong>, mo\u017cemy przyst\u0105pi\u0107 do obliczania si\u0142 wewn\u0119trznych dla poszczeg\u00f3lnych przedzia\u0142\u00f3w.<\/p>\n\n\n\n<figure style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.536), 20px);\" class=\"wp-block-table\"><table class=\"has-theme-2-background-color has-text-color has-background has-link-color has-fixed-layout\" style=\"color:#ffffff\"><tbody><tr><td>\u200bSchemat belki oraz wszystkie obliczenia s\u0105 wygenerowana w moim <a href=\"https:\/\/www.solveredu.com\/kalkulator-belek\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Kalkulatorze Belek<\/strong><\/a>. Mo\u017cesz za jego pomoc\u0105 uzyska\u0107 szczeg\u00f3\u0142owe rozwi\u0105zanie dla ka\u017cdej belki statycznie wyznaczalnej.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 id=\"56dg\" class=\"wp-block-heading\">Przedzia\u0142 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dla pierwszego przedzia\u0142u x nale\u017cy od 0 do 2m. Kolorem niebieskim oznaczy\u0142em <strong>uk\u0142ad znakowania <\/strong>si\u0142 tn\u0105cych i normalnych dla przekroju lewostronnego.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"461\" height=\"331\" data-attachment-id=\"1581\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/przedzial1-5\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.jpg?fit=461%2C331&amp;ssl=1\" data-orig-size=\"461,331\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przedzial1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.jpg?fit=461%2C331&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.jpg?resize=461%2C331&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1581\" style=\"width:386px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.jpg?w=461&amp;ssl=1 461w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.jpg?resize=300%2C215&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.jpg?resize=18%2C12&amp;ssl=1 18w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5e0t\">Si\u0142a normalna N:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"121\" data-attachment-id=\"1584\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/n1-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/N1-1.jpg?fit=268%2C121&amp;ssl=1\" data-orig-size=\"268,121\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"N1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/N1-1.jpg?fit=268%2C121&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/N1-1.jpg?resize=268%2C121&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1584\" style=\"width:242px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/N1-1.jpg?w=268&amp;ssl=1 268w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/N1-1.jpg?resize=18%2C8&amp;ssl=1 18w\" sizes=\"auto, (max-width: 268px) 100vw, 268px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"io9n\">Je\u015bli chodzi o si\u0142\u0119 N1(x) w pierwszym przedziale to wynosi ona -HA (zwrot HA jest przeciwny do naszego uk\u0142adu znakowania st\u0105d znak minus) co po podstawieniu warto\u015bci daje nam 10 [kN]. Warto\u015b\u0107 jest dodatnia, wiec mamy rozci\u0105ganie przekroju. Jak widzisz u\u017cywam zapisu N1(x) co oznacza, \u017ce N1 jest funkcj\u0105 x. mo\u017cemy wstawi\u0107 dowolny x z przedzia\u0142u od 0 do 2 i otrzymamy wynik si\u0142y normalnej dla tej wsp\u00f3\u0142rz\u0119dnej x.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Na potrzeby rysowania wykres\u00f3w si\u0142 wewn\u0119trznych obliczymy punkty charakterystyczne czyli pocz\u0105tek i koniec przedzia\u0142u.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5mqrl\">Si\u0142a tn\u0105ca V:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"236\" height=\"116\" data-attachment-id=\"1585\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/v1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/V1.jpg?fit=236%2C116&amp;ssl=1\" data-orig-size=\"236,116\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"V1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/V1.jpg?fit=236%2C116&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/V1.jpg?resize=236%2C116&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1585\" style=\"width:232px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/V1.jpg?w=236&amp;ssl=1 236w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/V1.jpg?resize=18%2C9&amp;ssl=1 18w\" sizes=\"auto, (max-width: 236px) 100vw, 236px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"39scl\">Si\u0142a tn\u0105ca V1(x) wynosi VA (znak dodatni, zwrot zgodny z naszym znakowaniem si\u0142y tn\u0105cej). Mamy sta\u0142\u0105 warto\u015b\u0107 si\u0142y tn\u0105cej na ca\u0142ym przedziale. Po podstawieniu Va mamy V1=-5.3 [kN]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"csjiu\">Moment gn\u0105cy Mg:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fegq\">Najwa\u017cniejszym etapem rozwi\u0105zywania belek jest wyznaczanie moment\u00f3w gn\u0105cych. Jest to zarazem najtrudniejsza cz\u0119\u015b\u0107 rozwi\u0105zywania zada\u0144 z belek.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"117\" data-attachment-id=\"1586\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/m1-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/M1.jpg?fit=308%2C117&amp;ssl=1\" data-orig-size=\"308,117\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"M1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/M1.jpg?fit=308%2C117&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/M1.jpg?resize=308%2C117&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1586\" style=\"width:292px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/M1.jpg?w=308&amp;ssl=1 308w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/M1.jpg?resize=300%2C114&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/M1.jpg?resize=18%2C7&amp;ssl=1 18w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5211l\">Moment gn\u0105cy jest funkcj\u0105 Va*x. Jak wiemy moment to si\u0142a pomno\u017cona przez rami\u0119. Si\u0142\u0105 jest si\u0142a tn\u0105ca &#8211; rami\u0119 to nasz x. Im dalej jeste\u015bmy od podpory A tym moment od reakcji VA jest wi\u0119kszy. Po podstawieniu za x pocz\u0105tku przedzia\u0142u M1(0)= 0 oraz ko\u0144ca przedzia\u0142u M1(2) = -10.6 [kNm].<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Je\u015bli na pocz\u0105tku lub na ko\u0144cu belki nie ma przy\u0142o\u017conego momentu skupionego<strong> warto\u015b\u0107 momentu gn\u0105cego zawsze b\u0119dzie wynosi\u0107 zero<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"dkt8d\">Pierwszy przedzia\u0142 mamy wyznaczony. Przechodzimy do kolejnego.<\/p>\n\n\n\n<h3 id=\"af3dl\" class=\"wp-block-heading\">Przedzia\u0142 2<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Cz\u0119sto pytacie czy mam uwzgl\u0119dni\u0107 te\u017c si\u0142y z pierwszego przedzia\u0142u czy to pomin\u0105\u0107? Odpowied\u017a brzmi:<\/p>\n<\/blockquote>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\u200bJe\u015bli chodzi o r\u00f3wnania opisuj\u0105ce si\u0142y w ka\u017cdym kolejnym przedziale to <strong>bierzemy pod uwag\u0119 wszystko to co dzieje si\u0119 od pocz\u0105tku belki,<\/strong> czyli si\u0142y z ka\u017cdego poprzedzaj\u0105cego przedzia\u0142u te\u017c bierzemy pod uwag\u0119.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"67ra3\">W drugim przedziale x nale\u017cy od 2 do 6m.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"eh6uh\">Kolorem niebieskim oznaczy\u0142em uk\u0142ad znakowania si\u0142 tn\u0105cych i normalnych dla przekroju lewostronnego.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"776\" height=\"337\" data-attachment-id=\"1587\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/przedzial2-4\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?fit=776%2C337&amp;ssl=1\" data-orig-size=\"776,337\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przedzial2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?fit=776%2C337&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?resize=776%2C337&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1587\" style=\"width:539px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?w=776&amp;ssl=1 776w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?resize=300%2C130&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?resize=768%2C334&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2.jpg?resize=18%2C8&amp;ssl=1 18w\" sizes=\"auto, (max-width: 776px) 100vw, 776px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"7fosk\">Si\u0142a normalna N:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"668\" height=\"343\" data-attachment-id=\"1588\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/span-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span-2.jpg?fit=668%2C343&amp;ssl=1\" data-orig-size=\"668,343\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"span 2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span-2.jpg?fit=668%2C343&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span-2.jpg?resize=668%2C343&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1588\" style=\"width:615px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span-2.jpg?w=668&amp;ssl=1 668w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span-2.jpg?resize=300%2C154&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span-2.jpg?resize=18%2C9&amp;ssl=1 18w\" sizes=\"auto, (max-width: 668px) 100vw, 668px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"633u9\">Je\u015bli chodzi o si\u0142\u0119 N2(x) w drugim przedziale to od warto\u015bci z poprzedniego odejmujemy si\u0142\u0119 F2, mamy -HA-F2. Po podstawieniu warto\u015bci daje nam 0 [kN], czyli nie ma si\u0142y normalnej na tym przedziale.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9nbk4\">Si\u0142a tn\u0105ca V:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"e6thv\">Si\u0142a tn\u0105ca V2(x) do VA dochodzi nam F1 Mamy sta\u0142\u0105 warto\u015b\u0107 si\u0142y tn\u0105cej na ca\u0142ym przedziale, po podstawieniu Va mamy V2= 2.7 [kN]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"dfpa9\">Moment gn\u0105cy Mg:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"8mo4d\">Do Va*x dochodzi nam F1*(x-2) znak momentu od F1 jest dodatni. X jest pomniejszony o 2m czyli o tyle o ile si\u0142a F1 jest oddalona od pocz\u0105tku naszej belki. Rzeczywiste rami\u0119 dzia\u0142ania si\u0142y F1 wynosi (x-2). Po podstawieniu za x pocz\u0105tku przedzia\u0142u M2(2)= -10.6 [kNm] oraz ko\u0144ca przedzia\u0142u M2(6) = 0.2 [kNm].<\/p>\n\n\n\n<h3 id=\"8j2ce\" class=\"wp-block-heading\">Przedzia\u0142 3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"1so1i\">W ostatnim przedziale x nale\u017cy od 6 do 10m.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"7h1cr\">Kolorem niebieskim oznaczy\u0142em uk\u0142ad znakowania si\u0142 tn\u0105cych i normalnych dla przekroju lewostronnego.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"317\" data-attachment-id=\"1589\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/przedzial3-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?fit=1000%2C317&amp;ssl=1\" data-orig-size=\"1000,317\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przedzial3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?fit=1000%2C317&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?resize=1000%2C317&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1589\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?w=1000&amp;ssl=1 1000w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?resize=300%2C95&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?resize=768%2C243&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial3.jpg?resize=18%2C6&amp;ssl=1 18w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"558\" height=\"311\" data-attachment-id=\"1590\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/span3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span3.jpg?fit=558%2C311&amp;ssl=1\" data-orig-size=\"558,311\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"span3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span3.jpg?fit=558%2C311&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span3.jpg?resize=558%2C311&#038;ssl=1\" alt=\"Obliczanie si\u0142 wewn\u0119trznych w belce, SolverEdu\" class=\"wp-image-1590\" style=\"width:620px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span3.jpg?w=558&amp;ssl=1 558w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span3.jpg?resize=300%2C167&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span3.jpg?resize=18%2C10&amp;ssl=1 18w\" sizes=\"auto, (max-width: 558px) 100vw, 558px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"b32a1\">Si\u0142a normalna N:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"esag5\">Je\u015bli chodzi o si\u0142\u0119 N3(x) to jest r\u00f3wna sile N2, nic si\u0119 nie zmienia.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fride\">Si\u0142a tn\u0105ca V:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5d9r9\">We wzorze na si\u0142\u0119 tn\u0105c\u0105 V3(x) dochodzi nam obci\u0105\u017cenie ci\u0105g\u0142e q pomno\u017cone przez d\u0142ugo\u015b\u0107 na jakim wyst\u0119puje, czyli odcinek (x-6). Po podstawieniu za x pocz\u0105tku przedzia\u0142u mamy V3(6)= 2.7 [kN] oraz ko\u0144ca przedzia\u0142u V3(10)= -5.3[kN]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5ukn8\">Moment gn\u0105cy Mg:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ce6go\">W r\u00f3wnaniu na moment mamy wszystko to co w przedziale 2. Dodatkowo dodajemy M oraz odejmujemy warto\u015b\u0107 momentu od obci\u0105\u017cenia ci\u0105g\u0142ego q. Ta warto\u015b\u0107 to g pomno\u017cone przez (x-6) co daje nam si\u0142\u0119 oraz pomno\u017cone przez 0.5*(x-6) czyli rami\u0119 dzia\u0142ania si\u0142y. Znak jest ujemny gdy\u017c moment od g b\u0119dzie dzia\u0142a\u0142 przeciwnie do naszego przyj\u0119tego dodatniego znaku momentu. Po podstawieniu za x pocz\u0105tku przedzia\u0142u M3(6)= 5.2 [Nm] oraz ko\u0144ca przedzia\u0142u M3(10) = 0 [Nm].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fg00u\">I tak zako\u0144czyli\u015bmy wyznaczanie si\u0142 wewn\u0119trznych w naszej belce. Na podstawie otrzymanych wynik\u00f3w sporz\u0105dza si\u0119 wykresy jak na Rys.12 poni\u017cej. Ale o tym w nast\u0119pnym wpisie.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\" id=\"14cmf\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"762\" height=\"878\" data-attachment-id=\"1591\" data-permalink=\"https:\/\/solveredu.com\/de\/post\/sily-wewnetrzne-w-belkach\/wykresy-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy.jpg?fit=762%2C878&amp;ssl=1\" data-orig-size=\"762,878\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"wykresy\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy.jpg?fit=762%2C878&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy.jpg?resize=762%2C878&#038;ssl=1\" alt=\"Wykresy si\u0142y wewn\u0119trznych, SolverEdu\" class=\"wp-image-1591\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy.jpg?w=762&amp;ssl=1 762w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy.jpg?resize=260%2C300&amp;ssl=1 260w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy.jpg?resize=10%2C12&amp;ssl=1 10w\" sizes=\"auto, (max-width: 762px) 100vw, 762px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"99frk\">Dzi\u0119kuj\u0119, do nast\u0119pnego wpisu.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym wpisie: Si\u0142y wewn\u0119trzne w belkach i ich rodzaje Aby wyt\u0142umaczy\u0107 czym s\u0105 si\u0142y wewn\u0119trzne w belkach pos\u0142u\u017c\u0119 si\u0119 metod\u0105 przeci\u0119cia my\u015blowo. Na rys.1. poni\u017cej mamy most podparty na dw\u00f3ch ko\u0144cach podporami przegubowymi. W miejscu podpar\u0107 wprowadzamy reakcje i ca\u0142y uk\u0142ad jest w r\u00f3wnowadze. Gdyby\u015bmy teraz my\u015blowo przeci\u0119li most na dwie cz\u0119\u015bci? Bez wprowadzenie [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1574,"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":[14786],"tags":[],"class_list":["post-899","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bez-kategorii"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sily-wewnetrzne.jpg?fit=939%2C690&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-ev","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/posts\/899","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/comments?post=899"}],"version-history":[{"count":24,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/posts\/899\/revisions"}],"predecessor-version":[{"id":3072,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/posts\/899\/revisions\/3072"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/media\/1574"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/media?parent=899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/categories?post=899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/de\/wp-json\/wp\/v2\/tags?post=899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}