{"id":1192,"date":"2024-09-23T14:59:18","date_gmt":"2024-09-23T12:59:18","guid":{"rendered":"https:\/\/solveredu.com\/?p=1192"},"modified":"2026-01-27T23:44:35","modified_gmt":"2026-01-27T22:44:35","slug":"diagrammes-des-forces-internes","status":"publish","type":"post","link":"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/","title":{"rendered":"Diagrammes des forces internes"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\" id=\"foo\">W tym wpisie dowiesz si\u0119:<\/p>\n\n\n\n<ol id=\"3hvyjwissryvig230824\" class=\"wp-block-list\">\n<li><a href=\"#aaeaq\">Czym s\u0105 wykresy si\u0142 wewn\u0119trznych<\/a><\/li>\n\n\n\n<li><a href=\"#3aqpk\">Jakie si\u0142y wewn\u0119trzne rysujemy na wykresie<\/a><\/li>\n\n\n\n<li><a href=\"#5uhrd\">Wykres si\u0142 wewn\u0119trznych &#8211; belka swobodnie podparta<\/a><\/li>\n\n\n\n<li><a href=\"#3mli8\">Wykres si\u0142 wewn\u0119trznych &#8211; belka utwierdzona<\/a><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\u200b<strong>Wykresy si\u0142 wewn\u0119trznych<\/strong> to graficzna reprezentacja si\u0142 przekrojowych powstaj\u0105cych w naszym uk\u0142adzie (np. w belce, kratownicy czy ramie). Si\u0142y te powstaj\u0105 pod wp\u0142ywem dzia\u0142aj\u0105cego obci\u0105\u017cenia.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h1 id=\"3aqpk\" class=\"wp-block-heading has-large-font-size\">Wykresy si\u0142 wewn\u0119trznych &#8211; rodzaje<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"98k94\">Wyr\u00f3\u017cniamy nast\u0119puj\u0105ce <strong>wykresy si\u0142 wewn\u0119trznych<\/strong>:<\/p>\n\n\n\n<ul id=\"7hkjpwissryvig230836\" class=\"wp-block-list\">\n<li>wykres si\u0142 normalnych &#8211; N<\/li>\n\n\n\n<li>wykres si\u0142 tn\u0105cych &#8211; V<\/li>\n\n\n\n<li>wykres moment\u00f3w gn\u0105cych &#8211; M<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"aiomg\">Zasady rysowania wykres\u00f3w si\u0142 wewn\u0119trznych dla wszystkich struktur s\u0105 takie same. Nie wa\u017cne czy to belka, rama czy kratownica.<\/p>\n\n\n\n<h2 id=\"5uhrd\" class=\"wp-block-heading\">Belka swobodnie podparta<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"cefhr\">Aby m\u00f3c narysowa\u0107 wykres si\u0142 musimy najpierw te si\u0142y obliczy\u0107. Ze zrozumieniem metody wyznaczania si\u0142 wewn\u0119trznych w belkach pomo\u017ce ten wpis: <a href=\"https:\/\/solveredu.com\/post\/sily-wewnetrzne-w-belkach\/\" target=\"_blank\" rel=\"noreferrer noopener\">Si\u0142y wewn\u0119trzne w belkach<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"edl3a\">Narysujemy wykresy si\u0142 dla belki z rysunku poni\u017cej<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"829\" height=\"248\" data-attachment-id=\"1194\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/belka1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?fit=829%2C248&amp;ssl=1\" data-orig-size=\"829,248\" 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=\"belka1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?fit=300%2C90&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?fit=829%2C248&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?resize=829%2C248&#038;ssl=1\" alt=\"\" class=\"wp-image-1194\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?w=829&amp;ssl=1 829w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?resize=300%2C90&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka1.png?resize=768%2C230&amp;ssl=1 768w\" sizes=\"auto, (max-width: 829px) 100vw, 829px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"bjmm7\">Jak pami\u0119tasz zaczynamy od sprawdzenia <a href=\"https:\/\/solveredu.com\/post\/statyczna-wyznaczalnosc\/\" target=\"_blank\" rel=\"noreferrer noopener\">statycznej wyznaczalno\u015bci<\/a> oraz <a href=\"https:\/\/www.solveredu.com\/post\/obliczanie-reakcji-podporowych-dla-belek\" target=\"_blank\" rel=\"noreferrer noopener\">wyznaczenia reakcji dla belki<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table class=\"has-theme-6-background-color has-background has-fixed-layout\"><tbody><tr><td><em>N=R-J-3<\/em><br>gdzie:<br>N &#8211; stopie\u0144 statycznej niewyznaczalno\u015b\u0107<br>R &#8211; liczba reakcji podporowych. Czyli suma wszystkich reakcji dla naszych podp\u00f3r<br>J &#8211; liczba przegub\u00f3w wewn\u0119trznych &#8211; je\u015bli nie wyst\u0119puj\u0105 P=0<br>3 &#8211; liczba r\u00f3wna\u0144 r\u00f3wnowagi. W uk\u0142adach statycznych wynosi 3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"677\" height=\"311\" data-attachment-id=\"1196\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/reakcje1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1.png?fit=677%2C311&amp;ssl=1\" data-orig-size=\"677,311\" 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=\"reakcje1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1.png?fit=300%2C138&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1.png?fit=677%2C311&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1.png?resize=677%2C311&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1196\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1.png?w=677&amp;ssl=1 677w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1.png?resize=300%2C138&amp;ssl=1 300w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"57qf5\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kiedy mamy policzone reakcje podporowe, mo\u017cemy przej\u015b\u0107 do wyznaczania <a href=\"https:\/\/solveredu.com\/post\/sily-wewnetrzne-w-belkach\/\">si\u0142 wewn\u0119trznych<\/a> w przedzia\u0142ach. B\u0119dziemy mieli 3 przedzia\u0142y w naszej przyk\u0142adowej belce. Dla ka\u017cdego przedzia\u0142u zapisujemy r\u00f3wnanie na <strong>si\u0142\u0119 normalna N(x)<\/strong>, <strong>si\u0142\u0119 tn\u0105c\u0105 T(x)<\/strong> oraz <strong>moment gn\u0105cy M(x)<\/strong>. Warto\u015bci poszczeg\u00f3lnych si\u0142 s\u0105 funkcj\u0105 x, co oznacza \u017ce mo\u017cemy podstawi\u0107 dowoln\u0105 warto\u015b\u0107 x z naszego przedzia\u0142u i otrzymamy wynik. Do narysowania wykres\u00f3w wystarcz\u0105 nam jedynie pocz\u0105tek i koniec przedzia\u0142u. W ten spos\u00f3b obliczymy tzw. <em>punkty charakterystyczne<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Poni\u017cej znajdziesz zapisane r\u00f3wnania oraz obliczone pocz\u0105tki i ko\u0144ce przedzia\u0142\u00f3w dla naszej belki.<\/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:#fefefe\"><tbody><tr><td>\u200b\u200bSchemat belki, wszystkie obliczenia oraz wykresy si\u0142 wewn\u0119trznych s\u0105 wygenerowane w moim <a href=\"https:\/\/www.solveredu.com\/kalkulator-belek\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>kalkulatorze belek<\/strong><\/a>. Mo\u017cesz stworzy\u0107 wykresy belek online oraz uzyska\u0107 szczeg\u00f3\u0142owe rozwi\u0105zanie dla ka\u017cdej belki statycznie wyznaczalnej. <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 id=\"5d8fj\" class=\"wp-block-heading\">Przedzia\u0142 1<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"579\" height=\"315\" data-attachment-id=\"1690\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/span1_1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?fit=579%2C315&amp;ssl=1\" data-orig-size=\"579,315\" 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=\"span1_1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?fit=300%2C163&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?fit=579%2C315&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?resize=579%2C315&#038;ssl=1\" alt=\"obliczanie sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1690\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?w=579&amp;ssl=1 579w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?resize=300%2C163&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_1.jpg?resize=18%2C10&amp;ssl=1 18w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"e6tn2\">Maj\u0105c obliczone si\u0142y dla pierwszego przedzia\u0142u podejmijmy pr\u00f3b\u0119 narysowania wykres\u00f3w. Poni\u017cej na Rys. 5. nanios\u0142em punkty charakterystyczne dla N, T i M w pierwszym przedziale. Nast\u0119pnie te punkty \u0142\u0105czymy liniami.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Je\u015bli funkcja N(x), T(x) lub M(x) jest: <br>1. Sta\u0142\u0105 warto\u015bci\u0105 niezale\u017cn\u0105 od x to wykres jest <strong>lini\u0105 poziom\u0105<\/strong> <br>2. Funkcj\u0105 liniow\u0105 od x to wykres jest <strong>lini\u0105 prost\u0105 przechylon\u0105 pod k\u0105tem<\/strong><br>3. Funkcj\u0105 kwadratow\u0105 od x to wykres jest <strong>parabol\u0105<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1022\" height=\"859\" data-attachment-id=\"1689\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wyk1_1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?fit=1022%2C859&amp;ssl=1\" data-orig-size=\"1022,859\" 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=\"wyk1_1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?fit=300%2C252&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?fit=1022%2C859&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?resize=1022%2C859&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1689\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?w=1022&amp;ssl=1 1022w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?resize=300%2C252&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?resize=768%2C646&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_1.jpg?resize=14%2C12&amp;ssl=1 14w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"7p06s\">W przedziale 1 mamy<strong> lokalne maksimum<\/strong> momentu gn\u0105cego. Jest to najwy\u017cszy punkt paraboli. Jak go wyznaczy\u0107? Bardzo prosto. Jest to miejsce w kt\u00f3rym warto\u015b\u0107 si\u0142y tn\u0105cej wynosi zero.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"748\" height=\"262\" data-attachment-id=\"1701\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/mmax-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?fit=748%2C262&amp;ssl=1\" data-orig-size=\"748,262\" 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=\"Mmax\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?fit=300%2C105&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?fit=748%2C262&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?resize=748%2C262&#038;ssl=1\" alt=\"maksymalny moment gn\u0105cy, SolverEdu\" class=\"wp-image-1701\" style=\"width:512px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?w=748&amp;ssl=1 748w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?resize=300%2C105&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Mmax.jpg?resize=18%2C6&amp;ssl=1 18w\" sizes=\"auto, (max-width: 748px) 100vw, 748px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"bh0rr\">Po wyznaczeniu wsp\u00f3\u0142rz\u0119dnej xmax obliczamy warto\u015b\u0107 momentu gn\u0105cego dla tej wsp\u00f3\u0142rz\u0119dnej M1(xmax) = 34.613 [kNm]<\/p>\n\n\n\n<h3 id=\"4d30i\" class=\"wp-block-heading\">Przedzia\u0142 2<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"821\" height=\"310\" data-attachment-id=\"1691\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/span1_2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?fit=821%2C310&amp;ssl=1\" data-orig-size=\"821,310\" 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=\"span1_2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?fit=300%2C113&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?fit=821%2C310&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?resize=821%2C310&#038;ssl=1\" alt=\"obliczanie sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1691\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?w=821&amp;ssl=1 821w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?resize=300%2C113&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?resize=768%2C290&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_2.jpg?resize=18%2C7&amp;ssl=1 18w\" sizes=\"auto, (max-width: 821px) 100vw, 821px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"doaab\">W przedziale drugim robimy dok\u0142adnie to samo co w pierwszym. Nanosimy punkty i \u0142\u0105czymy je liniami. Powstaj\u0105 nam kolejne cz\u0119\u015bci wykres\u00f3w, kt\u00f3re pokaza\u0142em na rys.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1014\" height=\"832\" data-attachment-id=\"1692\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wyk1_2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?fit=1014%2C832&amp;ssl=1\" data-orig-size=\"1014,832\" 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=\"wyk1_2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?fit=300%2C246&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?fit=1014%2C832&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?resize=1014%2C832&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1692\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?w=1014&amp;ssl=1 1014w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?resize=300%2C246&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?resize=768%2C630&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_2.jpg?resize=15%2C12&amp;ssl=1 15w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"es2ql\">Zwr\u00f3\u0107 uwag\u0119 ,\u017ce funkcja momentu gn\u0105cego w drugim przedziale nie jest ju\u017c funkcj\u0105 kwadratow\u0105, wi\u0119c wykres jest liniowy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"cs6ol\">Przedzia\u0142 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fad9o\">W trzecim ostatnim przedziale mamy nast\u0119puj\u0105ce warto\u015bci 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=\"586\" height=\"280\" data-attachment-id=\"1693\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/span1_3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?fit=586%2C280&amp;ssl=1\" data-orig-size=\"586,280\" 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=\"span1_3\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?fit=300%2C143&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?fit=586%2C280&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?resize=586%2C280&#038;ssl=1\" alt=\"obliczanie sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1693\" style=\"width:620px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?w=586&amp;ssl=1 586w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?resize=300%2C143&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span1_3.jpg?resize=18%2C9&amp;ssl=1 18w\" sizes=\"auto, (max-width: 586px) 100vw, 586px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1006\" height=\"844\" data-attachment-id=\"1694\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wyk1_3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?fit=1006%2C844&amp;ssl=1\" data-orig-size=\"1006,844\" 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=\"wyk1_3\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?fit=300%2C252&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?fit=1006%2C844&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?resize=1006%2C844&#038;ssl=1\" alt=\"\" class=\"wp-image-1694\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?w=1006&amp;ssl=1 1006w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?resize=300%2C252&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?resize=768%2C644&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1_3.jpg?resize=14%2C12&amp;ssl=1 14w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"durgs\">Tak oto narysowali\u015bmy kompletne wykresy si\u0142 przekrojowych si\u0142a normalna N(x), si\u0142a tn\u0105ca T(x) oraz moment zginaj\u0105cy M(x).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Czasem spotyka si\u0119 wykresy momentu gn\u0105cego z odwr\u00f3cone. Czyli warto\u015bci dodatnie s\u0105 poni\u017cej a warto\u015bci ujemne powy\u017cej osi poziomej.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9qp5t\">Poni\u017cej umie\u015bci\u0142em wykresy uzyskane z <a href=\"https:\/\/www.solveredu.com\/kalkulator-belek\" target=\"_blank\" rel=\"noreferrer noopener\"><u><strong>kalkulatora belek<\/strong><\/u><\/a>. Jak widzisz wszystkie warto\u015bci s\u0105 identyczne. Takie wykresy generuje w\u0142a\u015bnie moja aplikacja do obliczania belek.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"703\" height=\"924\" data-attachment-id=\"1208\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wykresy1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy1.png?fit=703%2C924&amp;ssl=1\" data-orig-size=\"703,924\" 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=\"wykresy1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy1.png?fit=228%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy1.png?fit=703%2C924&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy1.png?resize=703%2C924&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce swobodnie podpartej, SolverEdu\" class=\"wp-image-1208\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy1.png?w=703&amp;ssl=1 703w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy1.png?resize=228%2C300&amp;ssl=1 228w\" sizes=\"auto, (max-width: 703px) 100vw, 703px\" \/><\/figure>\n\n\n\n<h2 id=\"3mli8\" class=\"wp-block-heading\">Belka utwierdzona (wspornik)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"1tbd6\">Poni\u017cej przyk\u0142ad, kt\u00f3rym si\u0119 zajmiemy.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"930\" height=\"266\" data-attachment-id=\"1209\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/belka2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?fit=930%2C266&amp;ssl=1\" data-orig-size=\"930,266\" 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=\"belka2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?fit=300%2C86&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?fit=930%2C266&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?resize=930%2C266&#038;ssl=1\" alt=\"belka utwierdzona\" class=\"wp-image-1209\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?w=930&amp;ssl=1 930w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?resize=300%2C86&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/belka2.png?resize=768%2C220&amp;ssl=1 768w\" sizes=\"auto, (max-width: 930px) 100vw, 930px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"7brs6\">Podobnie jak w belce swobodnie podpartej, aby narysowa\u0107 wykres musimy obliczy\u0107 si\u0142y wewn\u0119trzne.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9id9d\">zaczynamy od sprawdzenia <a href=\"https:\/\/solveredu.com\/post\/statyczna-wyznaczalnosc\/\">statycznej wyznaczalno\u015bci<\/a> oraz <a href=\"https:\/\/www.solveredu.com\/post\/obliczanie-reakcji-podporowych-dla-belek\" target=\"_blank\" rel=\"noreferrer noopener\">wyznaczenia reakcji dla belki<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-theme-1-color has-theme-6-background-color has-text-color has-background has-link-color has-fixed-layout\"><tbody><tr><td><em>N=R-J-3<\/em><br>gdzie:<br>N &#8211; stopie\u0144 statycznej niewyznaczalno\u015b\u0107<br>R &#8211; liczba reakcji podporowych. Czyli suma wszystkich reakcji dla naszych podp\u00f3r<br>J &#8211; liczba przegub\u00f3w wewn\u0119trznych &#8211; je\u015bli nie wyst\u0119puj\u0105 P=0<br>3 &#8211; liczba r\u00f3wna\u0144 r\u00f3wnowagi. W uk\u0142adach statycznych wynosi 3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"423\" height=\"240\" data-attachment-id=\"1211\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/reakcje-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje-2.png?fit=423%2C240&amp;ssl=1\" data-orig-size=\"423,240\" 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 2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje-2.png?fit=300%2C170&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje-2.png?fit=423%2C240&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje-2.png?resize=423%2C240&#038;ssl=1\" alt=\"obliczanie reakcji belka utwierdzona SolverEdu\" class=\"wp-image-1211\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje-2.png?w=423&amp;ssl=1 423w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje-2.png?resize=300%2C170&amp;ssl=1 300w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"8udv5\">Kiedy mamy policzone reakcje podporowe, mo\u017cemy przej\u015b\u0107 do wyznaczania <a href=\"https:\/\/solveredu.com\/post\/sily-wewnetrzne-w-belkach\/\" target=\"_blank\" rel=\"noreferrer noopener\">si\u0142 wewn\u0119trznych<\/a> w przedzia\u0142ach. B\u0119dziemy mieli 2 przedzia\u0142y w naszej przyk\u0142adowej belce utwierdzonej. Dla ka\u017cdego przedzia\u0142u zapisujemy r\u00f3wnanie na <strong>si\u0142\u0119 tn\u0105c\u0105 V(x)<\/strong> oraz <strong>moment gn\u0105cy M(x)<\/strong>. Tym razem pomijamy obliczanie i rysowanie wykresy si\u0142 normalnych N(x).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\u200bW niekt\u00f3rych belkach nie ma potrzeby wyliczania si\u0142 normalnych, poniewa\u017c warto\u015b\u0107 jest zerowa dla ca\u0142ej belki. S\u0105 to belki, w kt\u00f3rych nie wyst\u0119puje sk\u0142adowa pozioma obci\u0105\u017cenia.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"8hlsr\">Poni\u017cej znajdziesz zapisane r\u00f3wnania oraz obliczone pocz\u0105tki i ko\u0144ce przedzia\u0142\u00f3w dla naszej belki.<\/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>\u200b\u200bSchemat belki, wszystkie obliczenia oraz wykresy si\u0142 wewn\u0119trznych s\u0105 wygenerowane w moim <a href=\"https:\/\/www.solveredu.com\/kalkulator-belek\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>kalkulatorze belek<\/strong><\/a>. Mo\u017cesz stworzy\u0107 wykresy belek online oraz uzyska\u0107 szczeg\u00f3\u0142owe rozwi\u0105zanie dla ka\u017cdej belki statycznie wyznaczalnej. <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 id=\"5d8fj\" class=\"wp-block-heading\">Przedzia\u0142 1<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"213\" data-attachment-id=\"1696\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/span2_1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?fit=458%2C213&amp;ssl=1\" data-orig-size=\"458,213\" 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=\"span2_1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?fit=300%2C140&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?fit=458%2C213&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?resize=458%2C213&#038;ssl=1\" alt=\"obliczanie sil wewn\u0119trznych w belce utwierdzonej, SolverEdu\" class=\"wp-image-1696\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?w=458&amp;ssl=1 458w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?resize=300%2C140&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_1.jpg?resize=18%2C8&amp;ssl=1 18w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"b1jbu\">Maj\u0105c obliczone si\u0142y dla pierwszego przedzia\u0142u rysujemy wykresy. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1014\" height=\"795\" data-attachment-id=\"1698\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wyk2_1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?fit=1014%2C795&amp;ssl=1\" data-orig-size=\"1014,795\" 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=\"wyk2_1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?fit=300%2C235&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?fit=1014%2C795&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?resize=1014%2C795&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce utwierdzonej, SolverEdu\" class=\"wp-image-1698\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?w=1014&amp;ssl=1 1014w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?resize=300%2C235&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?resize=768%2C602&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_1.jpg?resize=15%2C12&amp;ssl=1 15w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<h3 id=\"35snu\" class=\"wp-block-heading\">Przedzia\u0142 2<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"953\" height=\"209\" data-attachment-id=\"1697\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/span2_2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?fit=953%2C209&amp;ssl=1\" data-orig-size=\"953,209\" 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=\"span2_2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?fit=300%2C66&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?fit=953%2C209&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?resize=953%2C209&#038;ssl=1\" alt=\"obliczanie sil wewn\u0119trznych w belce utwierdzonej, SolverEdu\" class=\"wp-image-1697\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?w=953&amp;ssl=1 953w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?resize=300%2C66&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?resize=768%2C168&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/span2_2.jpg?resize=18%2C4&amp;ssl=1 18w\" sizes=\"auto, (max-width: 953px) 100vw, 953px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"a966f\">W przedziale drugim robimy dok\u0142adnie to samo co w pierwszym. Nanosimy punkty i \u0142\u0105czymy je liniami. Powstaj\u0105 nam kolejne cz\u0119\u015bci wykres\u00f3w, kt\u00f3re pokaza\u0142em na rys.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1005\" height=\"797\" data-attachment-id=\"1699\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wyk2_2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?fit=1005%2C797&amp;ssl=1\" data-orig-size=\"1005,797\" 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=\"wyk2_2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?fit=300%2C238&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?fit=1005%2C797&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?resize=1005%2C797&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce utwierdzonej, SolverEdu\" class=\"wp-image-1699\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?w=1005&amp;ssl=1 1005w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?resize=300%2C238&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?resize=768%2C609&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk2_2.jpg?resize=15%2C12&amp;ssl=1 15w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"3j6mn\">I to koniec. Mamy gotowe wykres si\u0142 tn\u0105cych i moment\u00f3w gn\u0105cych.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"c23tr\">Poni\u017cej umie\u015bci\u0142em wykresy uzyskane z <a href=\"\/kalkulator-belek\" target=\"_blank\" rel=\"noreferrer noopener\">kalkulatora belek<\/a>. Jak widzisz wszystkie warto\u015bci s\u0105 identyczne.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"894\" height=\"841\" data-attachment-id=\"1221\" data-permalink=\"https:\/\/solveredu.com\/fr\/post\/wykresy-sil-wewnetrznych\/wykresy2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?fit=894%2C841&amp;ssl=1\" data-orig-size=\"894,841\" 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=\"wykresy2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?fit=300%2C282&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?fit=894%2C841&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?resize=894%2C841&#038;ssl=1\" alt=\"wykresy sil wewn\u0119trznych w belce utwierdzonej, SolverEdu\" class=\"wp-image-1221\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?w=894&amp;ssl=1 894w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?resize=300%2C282&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy2.png?resize=768%2C722&amp;ssl=1 768w\" sizes=\"auto, (max-width: 894px) 100vw, 894px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"cra11\">To wszystko w tym wpisie po\u015bwi\u0119conym rysowaniu wykres\u00f3w si\u0142 wewn\u0119trznych w belkach. Dzi\u0119ki.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym wpisie dowiesz si\u0119: \u200bWykresy si\u0142 wewn\u0119trznych to graficzna reprezentacja si\u0142 przekrojowych powstaj\u0105cych w naszym uk\u0142adzie (np. w belce, kratownicy czy ramie). Si\u0142y te powstaj\u0105 pod wp\u0142ywem dzia\u0142aj\u0105cego obci\u0105\u017cenia. Wykresy si\u0142 wewn\u0119trznych &#8211; rodzaje Wyr\u00f3\u017cniamy nast\u0119puj\u0105ce wykresy si\u0142 wewn\u0119trznych: Zasady rysowania wykres\u00f3w si\u0142 wewn\u0119trznych dla wszystkich struktur s\u0105 takie same. Nie wa\u017cne czy to [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1223,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","jetpack_post_was_ever_published":false,"_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},"categories":[14806],"tags":[],"class_list":["post-1192","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bez-kategorii-pl"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wyk1.2-1.png?fit=789%2C673&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-je","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/posts\/1192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/comments?post=1192"}],"version-history":[{"count":27,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/posts\/1192\/revisions"}],"predecessor-version":[{"id":3075,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/posts\/1192\/revisions\/3075"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/media\/1223"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/media?parent=1192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/categories?post=1192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/fr\/wp-json\/wp\/v2\/tags?post=1192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}