{"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":"wykresy-sil-wewnetrznych","status":"publish","type":"post","link":"https:\/\/solveredu.com\/ja\/post\/wykresy-sil-wewnetrznych\/","title":{"rendered":"\u5185\u90e8\u529b\u30c0\u30a4\u30a2\u30b0\u30e9\u30e0"},"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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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\/ja\/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-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 belka, rama czy kratownica. Belka swobodnie podparta 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: Si\u0142y wewn\u0119trzne w belkach. Narysujemy wykresy si\u0142 dla belki z rysunku poni\u017cej Jak pami\u0119tasz zaczynamy od sprawdzenia statycznej wyznaczalno\u015bci oraz wyznaczenia reakcji dla belki. N=R-J-3gdzie:N &#8211; stopie\u0144 [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1223,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_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},"jetpack_post_was_ever_published":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\/ja\/wp-json\/wp\/v2\/posts\/1192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/comments?post=1192"}],"version-history":[{"count":27,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts\/1192\/revisions"}],"predecessor-version":[{"id":3075,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts\/1192\/revisions\/3075"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/media\/1223"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/media?parent=1192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/categories?post=1192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/tags?post=1192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}