{"id":2202,"date":"2026-10-15T02:27:38","date_gmt":"2026-10-15T01:27:38","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/engenharia\/viga-biapoizada-carga-central\/"},"modified":"2026-10-15T02:27:38","modified_gmt":"2026-10-15T01:27:38","slug":"viga-biapoizada-carga-central","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/engenharia\/viga-biapoizada-carga-central\/","title":{"rendered":"Viga biapoizada com carga pontual no centro"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Rea\u00e7\u00f5es de apoio, momento fletor e flecha da viga<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2202\" data-favorite-title=\"Viga biapoizada com carga central\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/engenharia\/viga-biapoizada-carga-central\/\" data-favorite-excerpt=\"Calcule as rea\u00e7\u00f5es de apoio, o momento fletor m\u00e1ximo e a flecha no meio do v\u00e3o de uma viga biapoizada com uma carga pontual aplicada no centro. Informe o v\u00e3o, a carga, o m\u00f3dulo de Young e o momento de in\u00e9rcia da \u00e1rea.\" aria-label=\"Adicionar aos favoritos\" data-favorite-icon=\"icon icon-civil\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pt\/engenharia\/viga-biapoizada-carga-central\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2202\" data-post=\"2202\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">V\u00e3o (L)<\/label><div class=\"term\">L<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"vo_l\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"4\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"m\" selected>m<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-1\">Dist\u00e2ncia entre os dois apoios<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Carga pontual (P)<\/label><div class=\"term\">P<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"carga_pontual_p\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1.0E-6\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"kN\" selected>kN<\/option><option value=\"N\">N<\/option><option value=\"lbf\">lbf<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Aplicada no meio do v\u00e3o<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">M\u00f3dulo de elasticidade (E)<\/label><div class=\"term\">E<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"mdulo_de_elasticidade_e\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1.0E-6\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"GPa\" selected>GPa<\/option><option value=\"MPa\">MPa<\/option><option value=\"psi\">psi<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">A\u00e7o \u2248 200 GPa (29.000 ksi), alum\u00ednio \u2248 69 GPa, madeira \u2248 11 GPa<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">Momento de in\u00e9rcia da \u00e1rea (I)<\/label><div class=\"term\">I<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"momento_de_inrcia_da_rea_i\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1.0E-6\" value=\"1000\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"cm4\" selected>cm\u2074<\/option><option value=\"mm4\">mm\u2074<\/option><option value=\"in4\">in\u2074<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Momento de in\u00e9rcia da \u00e1rea da se\u00e7\u00e3o transversal da viga em rela\u00e7\u00e3o ao eixo de flex\u00e3o<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2202\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Resultados da viga<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Rea\u00e7\u00f5es de apoio (em cada apoio)<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Momento fletor m\u00e1ximo<\/span><span class=\"result-term\">M<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Flecha m\u00e1xima (no meio do v\u00e3o)<\/span><span class=\"result-term\">\u03b4<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copiar link para este c\u00e1lculo<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Deixar um coment\u00e1rio<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"2202\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Curti <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">\u00datil <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confuso <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Decepcionado <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Impreciso <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>F\u00f3rmula da viga biapoizada com carga central<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ R = \\frac{P}{2} \\qquad M_{max} = \\frac{P \\, L}{4} \\qquad \\delta_{max} = \\frac{P \\, L^3}{48 \\, E \\, I} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(R\\) \u2014 rea\u00e7\u00e3o de apoio em cada extremidade (N)<\/li>\n<li>\\(P\\) \u2014 carga pontual aplicada no meio do v\u00e3o (N)<\/li>\n<li>\\(L\\) \u2014 v\u00e3o entre os dois apoios (m)<\/li>\n<li>\\(M_{max}\\) \u2014 momento fletor m\u00e1ximo, que ocorre sob a carga (N\u00b7m)<\/li>\n<li>\\(\\delta_{max}\\) \u2014 flecha m\u00e1xima no meio do v\u00e3o (m)<\/li>\n<li>\\(E\\) \u2014 m\u00f3dulo de Young do material da viga (Pa)<\/li>\n<li>\\(I\\) \u2014 momento de in\u00e9rcia da \u00e1rea da se\u00e7\u00e3o transversal (m\u2074)<\/li>\n<\/ul>\n<p>Como a carga atua exatamente no ponto m\u00e9dio entre dois apoios id\u00eanticos, a simetria a divide igualmente entre eles. O momento fletor e a flecha atingem seus valores m\u00e1ximos no meio do v\u00e3o, exatamente onde a carga \u00e9 aplicada.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Viga biapoizada com carga central \u2013 exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> uma viga de a\u00e7o com v\u00e3o de 4 m suporta uma carga pontual de 10 kN no meio do v\u00e3o. A viga tem m\u00f3dulo de Young \\(E = 200\\) GPa e momento de in\u00e9rcia da \u00e1rea \\(I = 1000\\) cm\u2074 = \\(1 \\times 10^{-5}\\) m\u2074.<\/p>\n<p>\\[ R = \\frac{P}{2} = \\frac{10\\,000\\ \\text{N}}{2} = 5\\ \\text{kN} \\]<\/p>\n<p>\\[ M_{max} = \\frac{P L}{4} = \\frac{10\\,000 \\times 4}{4} = 10\\ \\text{kN\u00b7m} \\]<\/p>\n<p>\\[ \\delta_{max} = \\frac{P L^3}{48 E I} = \\frac{10\\,000 \\times 4^3}{48 \\times 200 \\times 10^9 \\times 1 \\times 10^{-5}} \\approx 6.67 \\times 10^{-3}\\ \\text{m} \\]<\/p>\n<p><strong>Resultado:<\/strong> cada apoio recebe 5 kN, o momento fletor m\u00e1ximo \u00e9 de 10 kN\u00b7m no meio do v\u00e3o e a viga sofre uma flecha de aproximadamente 6,67 mm (cerca de 0,26 pol.) no ponto de aplica\u00e7\u00e3o da carga.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Informe o <strong>V\u00e3o (L)<\/strong> \u2014 a dist\u00e2ncia entre os dois apoios \u2014 e escolha a unidade (m ou ft).<\/li>\n<li>Informe a <strong>Carga pontual (P)<\/strong> aplicada no meio do v\u00e3o e selecione a unidade (kN, N ou lbf).<\/li>\n<li>Informe o <strong>M\u00f3dulo de Young (E)<\/strong> do material. O a\u00e7o fica em torno de 200 GPa, o alum\u00ednio em torno de 69 GPa e a madeira em torno de 11 GPa.<\/li>\n<li>Informe o <strong>Momento de in\u00e9rcia da \u00e1rea (I)<\/strong> da se\u00e7\u00e3o transversal da viga em rela\u00e7\u00e3o ao eixo de flex\u00e3o, em cm\u2074, mm\u2074 ou pol.\u2074.<\/li>\n<li>Leia os resultados: as rea\u00e7\u00f5es de apoio, o momento fletor m\u00e1ximo e a flecha m\u00e1xima no meio do v\u00e3o.<\/li>\n<\/ol>\n<h2>O que \u00e9 uma viga biapoizada com carga central?<\/h2>\n<p>Uma viga biapoizada repousa sobre dois apoios \u2014 normalmente uma articula\u00e7\u00e3o (pino) em uma extremidade e um apoio m\u00f3vel (rolete) na outra. Nenhum dos apoios resiste \u00e0 rota\u00e7\u00e3o, de modo que a viga fica livre para fletir e suas extremidades podem girar. Essa \u00e9 uma das simplifica\u00e7\u00f5es mais comuns na engenharia estrutural e mec\u00e2nica: ela descreve com boa precis\u00e3o vigas de piso apoiadas em duas paredes, eixos sobre dois mancais e diversos elementos de m\u00e1quinas e estruturas.<\/p>\n<p>Quando uma \u00fanica carga pontual \\(P\\) \u00e9 aplicada exatamente no meio do v\u00e3o, o problema passa a ser sim\u00e9trico. Cada apoio suporta exatamente metade da carga, ou seja, \\(R = P\/2\\). O momento fletor cresce linearmente do zero em cada apoio at\u00e9 um pico de \\(M_{max} = PL\/4\\) logo sob a carga \u2014 esse \u00e9 o ponto de tens\u00e3o m\u00e1xima na viga, onde a ruptura ou o escoamento come\u00e7aria.<\/p>\n<p>A flecha segue uma rela\u00e7\u00e3o c\u00fabica com o v\u00e3o: \\(\\delta_{max} = PL^3\/(48EI)\\). Dobrar o v\u00e3o multiplica a flecha por oito \u2014 \u00e9 por isso que v\u00e3os longos s\u00e3o muito mais dif\u00edceis de manter r\u00edgidos. O produto \\(EI\\), chamado de <em>rigidez \u00e0 flex\u00e3o<\/em>, mede a resist\u00eancia da viga \u00e0 flex\u00e3o: um material mais r\u00edgido (\\(E\\) maior) ou uma se\u00e7\u00e3o transversal mais alta (\\(I\\) maior) reduzem a flecha. Se voc\u00ea precisar trabalhar separadamente com a rigidez do material, a <a href=\"https:\/\/wpcalc.com\/pt\/engenharia\/frequencia-ressonante-mola-modulo-young\/\">calculadora de m\u00f3dulo de Young<\/a> abrange c\u00e1lculos relacionados \u00e0s propriedades dos materiais.<\/p>\n<p>Ao interpretar o resultado, compare a flecha com o limite admiss\u00edvel da sua aplica\u00e7\u00e3o. Muitas normas de constru\u00e7\u00e3o limitam a flecha de cargas acidentais a \\(L\/360\\) ou \\(L\/240\\) do v\u00e3o; no exemplo de 4 m acima, \\(L\/360 \\approx 11,1\\) mm, de modo que uma flecha de 6,67 mm seria aprovada.<\/p>\n<h2>Hip\u00f3teses e limita\u00e7\u00f5es<\/h2>\n<ul>\n<li>A carga deve atuar <strong>exatamente no meio do v\u00e3o<\/strong>. Para uma carga em posi\u00e7\u00e3o qualquer, as f\u00f3rmulas mudam \u2014 as rea\u00e7\u00f5es passam a ser \\(R_1 = Pb\/L\\) e \\(R_2 = Pa\/L\\).<\/li>\n<li>A viga \u00e9 considerada prism\u00e1tica (se\u00e7\u00e3o transversal constante), homog\u00eanea e linearmente el\u00e1stica \u2014 as flechas s\u00e3o pequenas em compara\u00e7\u00e3o com o v\u00e3o.<\/li>\n<li>O peso pr\u00f3prio da viga \u00e9 desprezado. Se a viga for pesada em rela\u00e7\u00e3o \u00e0 carga aplicada, some-o como carga distribu\u00edda em uma an\u00e1lise separada.<\/li>\n<li>Os apoios s\u00e3o ideais: suportam apenas carga vertical, sem restri\u00e7\u00e3o ou engastamento rotacional.<\/li>\n<li>Considera-se apenas carregamento vertical; cargas horizontais, tor\u00e7\u00e3o e efeitos din\u00e2micos est\u00e3o fora do escopo destas f\u00f3rmulas.<\/li>\n<\/ul>\n<p>Em situa\u00e7\u00f5es din\u00e2micas \u2014 por exemplo, uma massa apoiada em uma viga que funciona como mola \u2014 o resultado est\u00e1tico obtido aqui \u00e9 apenas o ponto de partida. Consulte a <a href=\"https:\/\/wpcalc.com\/pt\/engenharia\/massa-da-mola\/\">calculadora de massa-mola<\/a> e a <a href=\"https:\/\/wpcalc.com\/pt\/engenharia\/frequencia-ressonante-mola\/\">calculadora de frequ\u00eancia ressonante da mola<\/a> para an\u00e1lise de vibra\u00e7\u00f5es.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calcule as rea\u00e7\u00f5es de apoio, o momento fletor m\u00e1ximo e a flecha no meio do v\u00e3o de uma viga biapoizada com uma carga pontual aplicada no centro. Informe o v\u00e3o, a carga, o m\u00f3dulo de Young e o momento de in\u00e9rcia da \u00e1rea.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[84],"class_list":["post-2202","post","type-post","status-publish","format-standard","hentry","category-engenharia","tag-vigas"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2202","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=2202"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2202\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2202"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2202"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}