{"id":1357,"date":"2024-09-23T14:58:54","date_gmt":"2024-09-23T12:58:54","guid":{"rendered":"https:\/\/solveredu.com\/?p=1357"},"modified":"2026-01-27T23:52:36","modified_gmt":"2026-01-27T22:52:36","slug":"rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania","status":"publish","type":"post","link":"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/","title":{"rendered":"Tens\u00e3o estaticamente indeterminada - Tarefas"},"content":{"rendered":"<p class=\"wp-block-paragraph\" id=\"foo\">Nesta entrada:<\/p>\n\n\n\n<ol id=\"pevmu3319\" class=\"wp-block-list\">\n<li><a href=\"#6o6iq\"><u>M\u00e9todo de solu\u00e7\u00e3o para tarefas estaticamente indeterminadas<\/u><\/a><\/li>\n\n\n\n<li><a href=\"#hp40j28774\"><u>Exemplo de uma solu\u00e7\u00e3o para uma tarefa de for\u00e7a concentrada<\/u><\/a><\/li>\n\n\n\n<li><a href=\"#y33sc54589\">Exemplo de solu\u00e7\u00e3o de uma tarefa de carga cont\u00ednua<\/a><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"pkfv52319\">A tens\u00e3o normal induzida por for\u00e7as de tra\u00e7\u00e3o e compress\u00e3o em uma barra prism\u00e1tica foi discutida na entrada <a href=\"https:\/\/solveredu.com\/pt\/post\/tensao-e-compressao-axial\/\">Tens\u00e3o e compress\u00e3o<\/a>. Nesta postagem, tratamos de exemplos estaticamente determin\u00e1veis, ou seja, exemplos em que t\u00ednhamos apenas uma rea\u00e7\u00e3o de suporte e pudemos determin\u00e1-la a partir da condi\u00e7\u00e3o de equil\u00edbrio.<\/p>\n\n\n\n<h1 id=\"6o6iq\" class=\"wp-block-heading has-large-font-size\">Tarefas estaticamente indeterminadas<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"cnyux9403\">Agora veremos exemplos que s\u00e3o um pouco mais dif\u00edceis, ou seja, estaticamente n\u00e3o determinantes. Essas s\u00e3o tarefas em que a barra \u00e9 fixada em ambas as extremidades (pode-se dizer que ela est\u00e1 imprensada entre duas paredes n\u00e3o deslizantes). Nesse caso, temos duas for\u00e7as de rea\u00e7\u00e3o desconhecidas dessas restri\u00e7\u00f5es e apenas uma equa\u00e7\u00e3o de equil\u00edbrio, portanto, \u00e9 por isso que falamos de exemplos estaticamente n\u00e3o equ\u00edvocos.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"569\" data-attachment-id=\"1360\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?fit=1028%2C571&amp;ssl=1\" data-orig-size=\"1028,571\" 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=\"przyklad\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?fit=1024%2C569&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?resize=1024%2C569&#038;ssl=1\" alt=\"\" class=\"wp-image-1360\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?resize=1024%2C569&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?resize=300%2C167&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?resize=768%2C427&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad.jpg?w=1028&amp;ssl=1 1028w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Equa\u00e7\u00f5es de equil\u00edbrio<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"455\" height=\"61\" data-attachment-id=\"1362\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/fxx\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/fxx.jpg?fit=455%2C61&amp;ssl=1\" data-orig-size=\"455,61\" 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=\"fxx\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/fxx.jpg?fit=455%2C61&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/fxx.jpg?resize=455%2C61&#038;ssl=1\" alt=\"\" class=\"wp-image-1362\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/fxx.jpg?w=455&amp;ssl=1 455w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/fxx.jpg?resize=300%2C40&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/fxx.jpg?resize=450%2C61&amp;ssl=1 450w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Condi\u00e7\u00e3o geom\u00e9trica<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"441\" height=\"77\" data-attachment-id=\"1363\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/delta-l\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/delta-L.jpg?fit=441%2C77&amp;ssl=1\" data-orig-size=\"441,77\" 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=\"delta L\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/delta-L.jpg?fit=441%2C77&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/delta-L.jpg?resize=441%2C77&#038;ssl=1\" alt=\"\" class=\"wp-image-1363\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/delta-L.jpg?w=441&amp;ssl=1 441w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/delta-L.jpg?resize=300%2C52&amp;ssl=1 300w\" sizes=\"auto, (max-width: 441px) 100vw, 441px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fzirg23835\">Nesse caso, usamos <strong>condi\u00e7\u00e3o geom\u00e9trica<\/strong>. Essa condi\u00e7\u00e3o afirma que o alongamento total da barra deve ser zero. Como as duas extremidades da barra n\u00e3o podem se mover (elas est\u00e3o presas), a deforma\u00e7\u00e3o total do nosso sistema \u00e9 igual a \"0\".<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"v52lp29905\">Voc\u00ea pode se deparar com tarefas em que a barra esteja posicionada verticalmente. N\u00e3o importa em termos do m\u00e9todo de solu\u00e7\u00e3o, seguimos exatamente o mesmo caminho.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"8s4bm29843\">Quando se trata do n\u00famero de fragmentos em que dividimos nossa barra, dois fatores s\u00e3o importantes:<\/p>\n\n\n\n<ul id=\"v0xyv44071\" class=\"wp-block-list\">\n<li>mudan\u00e7a de carga - for\u00e7a adicional ou carga cont\u00ednua<\/li>\n\n\n\n<li>altera\u00e7\u00e3o na \u00e1rea da se\u00e7\u00e3o transversal ou na rigidez do material (m\u00f3dulo de Young)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"8bayo47344\">Esses dois fatores influenciam a quantidade de deforma\u00e7\u00e3o de nossa barra.<\/p>\n\n\n\n<h2 id=\"9w9kz104495\" class=\"wp-block-heading has-large-font-size\">Tens\u00e3o estaticamente indeterminada - Tarefas<\/h2>\n\n\n\n<h3 id=\"hp40j28774\" class=\"wp-block-heading\">Exemplo de uma solu\u00e7\u00e3o para uma tarefa de for\u00e7a concentrada<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"6m0e029283\">Como primeiro exemplo, resolveremos uma tarefa com uma barra carregada por uma \u00fanica for\u00e7a concentrada. A barra consistir\u00e1 em duas partes com diferentes \u00e1reas de se\u00e7\u00e3o transversal. A tarefa ser\u00e1 resolvida com s\u00edmbolos sem dados num\u00e9ricos, o que \u00e9 comum nesse t\u00f3pico de tarefa.<\/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-5-background-color has-text-color has-background has-link-color has-fixed-layout\" style=\"color:#ffffff\"><tbody><tr><td>Todos os exemplos usados nesta postagem foram criados e calculados em meu <a href=\"\/pt\/calculadora-de-forcas-normais\/\" target=\"_blank\" rel=\"noreferrer noopener\">Calculadora de alongamento<\/a>. Convido-o a experimentar o aplicativo, com a ajuda dele voc\u00ea determinar\u00e1 as for\u00e7as normais, a tens\u00e3o normal e o alongamento ou encurtamento da barra.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"318\" data-attachment-id=\"1364\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad1_1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?fit=1123%2C349&amp;ssl=1\" data-orig-size=\"1123,349\" 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=\"przyklad1_1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?fit=1024%2C318&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?resize=1024%2C318&#038;ssl=1\" alt=\"C\u00e1lculo de rea\u00e7\u00e3o, tarefa estaticamente indeterminada, SolverEdu\" class=\"wp-image-1364\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?resize=1024%2C318&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?resize=300%2C93&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?resize=768%2C239&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_1.jpg?w=1123&amp;ssl=1 1123w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"lnpha49294\">A figura acima mostra o exemplo que resolveremos. Vamos come\u00e7ar denotando as rea\u00e7\u00f5es em Ra e Rb nos suportes. Como lembrete, a express\u00e3o das rea\u00e7\u00f5es \u00e9 arbitr\u00e1ria e n\u00f3s decidimos como tom\u00e1-las.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"emg5w9907\">Na pr\u00f3xima etapa, escrevemos a equa\u00e7\u00e3o de equil\u00edbrio para as for\u00e7as na dire\u00e7\u00e3o horizontal e a condi\u00e7\u00e3o geom\u00e9trica. Em nosso caso, teremos dois intervalos de A at\u00e9 a aplica\u00e7\u00e3o da for\u00e7a F e do ponto de aplica\u00e7\u00e3o da for\u00e7a F at\u00e9 o ponto B. Em seguida, elaboramos as f\u00f3rmulas para os alongamentos das se\u00e7\u00f5es L1 e L2. Depois de substituir as quantidades conhecidas para as for\u00e7as N1 e N2 nos respectivos intervalos e o produto de E e A e assimilar o total a zero, podemos calcular a rea\u00e7\u00e3o Ra. Em seguida, depois de substituir a rea\u00e7\u00e3o Ra na condi\u00e7\u00e3o de equil\u00edbrio, obtemos Rb.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"575\" height=\"609\" data-attachment-id=\"1366\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad1_21\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_21.jpg?fit=575%2C609&amp;ssl=1\" data-orig-size=\"575,609\" 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=\"przyklad1_21\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_21.jpg?fit=575%2C609&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_21.jpg?resize=575%2C609&#038;ssl=1\" alt=\"C\u00e1lculo de rea\u00e7\u00e3o, tarefa estaticamente indeterminada, SolverEdu\" class=\"wp-image-1366\" style=\"width:470px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_21.jpg?w=575&amp;ssl=1 575w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_21.jpg?resize=283%2C300&amp;ssl=1 283w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"hzoxz34568\">Na pr\u00f3xima etapa, agora que sabemos o valor das rea\u00e7\u00f5es de suporte, podemos determinar as for\u00e7as normais (axiais), as tens\u00f5es normais e a deforma\u00e7\u00e3o de cada compartimento. Essa etapa do c\u00e1lculo j\u00e1 est\u00e1 descrita na entrada <a href=\"https:\/\/solveredu.com\/pt\/post\/rozci%C4%85ganie-i-%C5%9Bciskanie\/\" rel=\"noreferrer noopener\" target=\"_blank\"><u>Tens\u00e3o e compress\u00e3o<\/u><\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"661\" height=\"890\" data-attachment-id=\"1367\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad1_311\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_311.jpg?fit=661%2C890&amp;ssl=1\" data-orig-size=\"661,890\" 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=\"przyklad1_311\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_311.jpg?fit=661%2C890&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_311.jpg?resize=661%2C890&#038;ssl=1\" alt=\"for\u00e7as normais, tens\u00f5es normais, alongamento , membro estaticamente indeterminado , SolverEdu\" class=\"wp-image-1367\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_311.jpg?w=661&amp;ssl=1 661w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_311.jpg?resize=223%2C300&amp;ssl=1 223w\" sizes=\"auto, (max-width: 661px) 100vw, 661px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"1yeki49398\">Conhecendo todas as quantidades, podemos desenhar gr\u00e1ficos mostrando a mudan\u00e7a nessas quantidades para cada intervalo. Os gr\u00e1ficos est\u00e3o inclu\u00eddos na figura abaixo.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"870\" height=\"949\" data-attachment-id=\"1369\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad1_4\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_4.png?fit=870%2C949&amp;ssl=1\" data-orig-size=\"870,949\" 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=\"przyklad1_4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_4.png?fit=870%2C949&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_4.png?resize=870%2C949&#038;ssl=1\" alt=\"Diagrama de for\u00e7as normais, tens\u00f5es normais, alongamento, membro estaticamente indeterminado, SolverEdu\" class=\"wp-image-1369\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_4.png?w=870&amp;ssl=1 870w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_4.png?resize=275%2C300&amp;ssl=1 275w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad1_4.png?resize=768%2C838&amp;ssl=1 768w\" sizes=\"auto, (max-width: 870px) 100vw, 870px\" \/><\/figure>\n\n\n\n<h3 id=\"y33sc54589\" class=\"wp-block-heading\">Exemplo de solu\u00e7\u00e3o de uma tarefa de carga cont\u00ednua<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"58k0u54592\">O pr\u00f3ximo exemplo que examinaremos \u00e9 uma tarefa com uma barra com uma carga cont\u00ednua de q=4 kN\/m. A barra consistir\u00e1 em duas partes com diferentes \u00e1reas de se\u00e7\u00e3o transversal. Desta vez, a tarefa ser\u00e1 resolvida com base em dados num\u00e9ricos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"azff061906\">A tarefa tamb\u00e9m ser\u00e1 resolvida com <a href=\"https:\/\/solveredu.com\/pt\/calculadora-de-forcas-normais\/\">Calculadora de alongamento<\/a> para resolver esse tipo de tarefa.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"892\" data-attachment-id=\"1370\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad2_1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_1.jpg?fit=630%2C892&amp;ssl=1\" data-orig-size=\"630,892\" 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=\"przyklad2_1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_1.jpg?fit=630%2C892&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_1.jpg?resize=630%2C892&#038;ssl=1\" alt=\"C\u00e1lculo de rea\u00e7\u00e3o, tarefa estaticamente indeterminada, SolverEdu\" class=\"wp-image-1370\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_1.jpg?w=630&amp;ssl=1 630w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_1.jpg?resize=212%2C300&amp;ssl=1 212w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"z9q5o54605\">A figura acima mostra o exemplo que resolveremos. Vamos come\u00e7ar denotando as rea\u00e7\u00f5es em Ra e Rb nos suportes. Como voc\u00ea pode ver, a barra est\u00e1 posicionada verticalmente para mostrar a voc\u00ea como resolver essa tarefa e como desenhar gr\u00e1ficos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"q0jhs54608\">Na pr\u00f3xima etapa, escrevemos a equa\u00e7\u00e3o de equil\u00edbrio e adicionamos uma condi\u00e7\u00e3o geom\u00e9trica. Em nosso caso, teremos dois intervalos de A at\u00e9 o in\u00edcio da carga q e desse ponto at\u00e9 o ponto B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5q8nn76615\">Em seguida, elaboramos as f\u00f3rmulas para os alongamentos dos segmentos L1 e L2. Depois de substituir as quantidades conhecidas para as for\u00e7as N1 e N2 nos intervalos correspondentes. Como voc\u00ea pode ver no segundo compartimento, onde h\u00e1 uma carga cont\u00ednua, usamos a integral do quociente da for\u00e7a normal pelo produto do m\u00f3dulo de Young e da \u00e1rea da se\u00e7\u00e3o transversal para determinar o alongamento.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"3q1i476989\">Ap\u00f3s resolver essa express\u00e3o, obtemos a rea\u00e7\u00e3o Ra. Em seguida, ap\u00f3s substituir a rea\u00e7\u00e3o Ra na condi\u00e7\u00e3o de equil\u00edbrio, obtemos Rb.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"680\" height=\"623\" data-attachment-id=\"1371\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad2_2_11\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_2_11.jpg?fit=680%2C623&amp;ssl=1\" data-orig-size=\"680,623\" 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=\"przyklad2_2_11\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_2_11.jpg?fit=680%2C623&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_2_11.jpg?resize=680%2C623&#038;ssl=1\" alt=\"C\u00e1lculo de rea\u00e7\u00e3o, tarefa estaticamente indeterminada, SolverEdu\" class=\"wp-image-1371\" style=\"width:430px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_2_11.jpg?w=680&amp;ssl=1 680w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_2_11.jpg?resize=300%2C275&amp;ssl=1 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"uml0c54612\">Na pr\u00f3xima etapa, agora que sabemos o valor das rea\u00e7\u00f5es de suporte, podemos determinar as for\u00e7as normais (axiais), as tens\u00f5es normais e a deforma\u00e7\u00e3o de cada compartimento. Essa etapa do c\u00e1lculo j\u00e1 est\u00e1 descrita na entrada <a href=\"https:\/\/solveredu.com\/pt\/calculadora-de-forcas-normais\/\" target=\"_blank\" rel=\"noreferrer noopener\"><u><strong>Tens\u00e3o e compress\u00e3o<\/strong><\/u><\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"580\" height=\"721\" data-attachment-id=\"1372\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad2_3_111\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_3_111.jpg?fit=580%2C721&amp;ssl=1\" data-orig-size=\"580,721\" 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=\"przyklad2_3_111\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_3_111.jpg?fit=580%2C721&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_3_111.jpg?resize=580%2C721&#038;ssl=1\" alt=\"for\u00e7as normais, tens\u00f5es normais, alongamento , membro estaticamente indeterminado , SolverEdu\" class=\"wp-image-1372\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_3_111.jpg?w=580&amp;ssl=1 580w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_3_111.jpg?resize=241%2C300&amp;ssl=1 241w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5w7w054619\">Conhecendo todas as quantidades, podemos desenhar gr\u00e1ficos mostrando a mudan\u00e7a nessas quantidades para cada intervalo. Os gr\u00e1ficos est\u00e3o inclu\u00eddos na figura abaixo.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"697\" data-attachment-id=\"1374\" data-permalink=\"https:\/\/solveredu.com\/pt\/post\/rozci%c4%85ganie-%c5%9bciskanie-statycznie-niewyznaczalne-zadania\/przyklad2_4\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?fit=1186%2C807&amp;ssl=1\" data-orig-size=\"1186,807\" 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=\"przyklad2_4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?fit=1024%2C697&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?resize=1024%2C697&#038;ssl=1\" alt=\"Diagrama de for\u00e7as normais, tens\u00f5es normais, alongamento, membro estaticamente indeterminado, SolverEdu\" class=\"wp-image-1374\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?resize=1024%2C697&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?resize=300%2C204&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?resize=768%2C523&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad2_4.jpg?w=1186&amp;ssl=1 1186w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"iuexm2329\">Como pode ser visto, o alongamento no final da barra \u00e9 zero, confirmando que resolvemos bem a tarefa. Isso conclui a entrada Tens\u00e3o indeterminada est\u00e1tica compressiva - tarefas.<\/p>","protected":false},"excerpt":{"rendered":"<p>W tym wpisie: Napr\u0119\u017cenie normalne wywo\u0142ane si\u0142ami rozci\u0105gaj\u0105cymi i \u015bciskaj\u0105cymi w pr\u0119cie pryzmatycznym zosta\u0142o om\u00f3wione we wpisie Rozci\u0105ganie i \u015bciskanie. W tym wpisie zajmowali\u015bmy si\u0119 przyk\u0142adami statycznie wyznaczalnymi, czyli takimi gdzie mieli\u015bmy tylko jedn\u0105 reakcj\u0119 podporow\u0105 i byli\u015bmy w stanie j\u0105 wyznaczy\u0107 z warunku r\u00f3wnowagi. Zadania statycznie niewyznaczalne Teraz zajmiemy si\u0119 przyk\u0142adami nieco trudniejszymi, czyli [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1377,"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":[14815,14816],"tags":[14862,14860,14861],"class_list":["post-1357","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","category-wytrzymalosc-materialow","tag-pret-roziagany","tag-rozciaganie-sciskanie","tag-statycznie-niewyznaczalne"],"jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/pg3flK-lT","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1.jpg?fit=1028%2C571&ssl=1","_links":{"self":[{"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/posts\/1357","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/comments?post=1357"}],"version-history":[{"count":14,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/posts\/1357\/revisions"}],"predecessor-version":[{"id":3083,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/posts\/1357\/revisions\/3083"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/media\/1377"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/media?parent=1357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/categories?post=1357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/pt\/wp-json\/wp\/v2\/tags?post=1357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}