{"id":2200,"date":"2026-10-15T02:19:59","date_gmt":"2026-10-15T01:19:59","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/engenharia\/torcao-de-eixo\/"},"modified":"2026-10-15T02:19:59","modified_gmt":"2026-10-15T01:19:59","slug":"torcao-de-eixo","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/engenharia\/torcao-de-eixo\/","title":{"rendered":"Tor\u00e7\u00e3o de eixo"},"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\">Verifique a tens\u00e3o de cisalhamento e o \u00e2ngulo de tor\u00e7\u00e3o em um eixo circular<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2200\" data-favorite-title=\"Tor\u00e7\u00e3o de eixo\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/engenharia\/torcao-de-eixo\/\" data-favorite-excerpt=\"Calcule a tens\u00e3o de cisalhamento m\u00e1xima e o \u00e2ngulo de tor\u00e7\u00e3o de um eixo circular maci\u00e7o ou vazado. Informe o torque, as dimens\u00f5es, o comprimento e o m\u00f3dulo de cisalhamento para verificar um projeto de eixo em segundos.\" 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\/torcao-de-eixo\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2200\" data-post=\"2200\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Carregamento<\/span><\/div><div class=\"field is-single has-term\" id=\"input-2\"><label for=\"field-2\">Torque aplicado (T)<\/label><div class=\"term\">T<\/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=\"torque_aplicado_t\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1000\" min=\"0\" value=\"1000\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"nm\" selected>N\u00b7m<\/option><option value=\"knm\">kN\u00b7m<\/option><option value=\"lbft\">lb\u00b7ft<\/option><option value=\"lbin\">lb\u00b7in<\/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-2\">Torque constante transmitido pelo eixo.<\/small><\/div><div class=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">Geometria do eixo<\/span><\/div><div class=\"field is-single\" id=\"input-4\"><label for=\"field-5\">Tipo de eixo<\/label><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"tipo_de_eixo\"><option value=\"solid\" selected>Eixo circular maci\u00e7o<\/option><option value=\"hollow\">Eixo circular vazado (tubo)<\/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><div class=\"field is-single has-term\" id=\"input-5\"><label for=\"field-6\">Di\u00e2metro externo (D)<\/label><div class=\"term\">D<\/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=\"dimetro_externo_d\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 40\" min=\"0\" value=\"40\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/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-6\">Di\u00e2metro externo da se\u00e7\u00e3o transversal do eixo.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-6\" hidden><label for=\"field-8\">Di\u00e2metro interno (d)<\/label><div class=\"term\">d<\/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=\"dimetro_interno_d\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 20\" min=\"0\" value=\"20\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/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-8\">Somente para eixo vazado: di\u00e2metro do furo. Deve ser menor que o di\u00e2metro externo.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-7\"><label for=\"field-10\">Comprimento do eixo (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=\"comprimento_do_eixo_l\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/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-10\">Comprimento do eixo entre o ponto de aplica\u00e7\u00e3o do torque e a extremidade fixa.<\/small><\/div><div class=\"is-single field\" id=\"input-8\"><span class=\"font-semibold\">Material<\/span><\/div><div class=\"field is-single has-term\" id=\"input-9\"><label for=\"field-13\">M\u00f3dulo de cisalhamento (G)<\/label><div class=\"term\">G<\/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_cisalhamento_g\" id=\"field-13\" aria-describedby=\"calc-info-13\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 80\" min=\"0\" value=\"80\"\/><div class=\"grid grid-cols-1\"><select id=\"field-14\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"gpa\" selected>GPa<\/option><option value=\"mpa\">MPa<\/option><option value=\"psi\">psi<\/option><option value=\"ksi\">ksi<\/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-13\">M\u00f3dulo de elasticidade transversal do material do eixo. Valores t\u00edpicos: a\u00e7o \u2248 80 GPa (11,6\u00b710\u2076 psi), alum\u00ednio \u2248 27 GPa, cobre \u2248 45 GPa.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2200\">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 tor\u00e7\u00e3o<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Tens\u00e3o m\u00e1xima de cisalhamento (\u03c4max)<\/span><span class=\"result-term\">\u03c4max<\/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 is-column\" id=\"output-2\"><span class=\"field-title\"><span>\u00c2ngulo de tor\u00e7\u00e3o (\u03c6)<\/span><span class=\"result-term\">\u03c6<\/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><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=\"2200\" 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 de tor\u00e7\u00e3o de eixo<\/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\\[ J = \\frac{\\pi D^4}{32} \\quad (\\text{maci\u00e7o}) \\qquad J = \\frac{\\pi (D^4 - d^4)}{32} \\quad (\\text{vazado}) \\]\n\\[ \\tau_{max} = \\frac{T \\cdot c}{J}, \\quad c = \\frac{D}{2} \\qquad \\varphi = \\frac{T \\cdot L}{J \\cdot G} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(T\\) \u2014 torque aplicado (N\u00b7m)<\/li>\n<li>\\(D\\) \u2014 di\u00e2metro externo do eixo (m)<\/li>\n<li>\\(d\\) \u2014 di\u00e2metro interno (furo) de um eixo vazado (m)<\/li>\n<li>\\(c\\) \u2014 dist\u00e2ncia do centro \u00e0 superf\u00edcie externa (m)<\/li>\n<li>\\(J\\) \u2014 momento polar de in\u00e9rcia da se\u00e7\u00e3o transversal (m\u2074)<\/li>\n<li>\\(G\\) \u2014 m\u00f3dulo de cisalhamento (m\u00f3dulo de elasticidade transversal) do material (Pa)<\/li>\n<li>\\(L\\) \u2014 comprimento do eixo entre o ponto de aplica\u00e7\u00e3o do torque e a extremidade fixa (m)<\/li>\n<li>\\(\\tau_{max}\\) \u2014 tens\u00e3o de cisalhamento m\u00e1xima na superf\u00edcie externa (Pa)<\/li>\n<li>\\(\\varphi\\) \u2014 \u00e2ngulo de tor\u00e7\u00e3o ao longo do comprimento \\(L\\) (rad)<\/li>\n<\/ul>\n<p>As duas primeiras express\u00f5es descrevem a tor\u00e7\u00e3o de um eixo circular: a tens\u00e3o de cisalhamento cresce linearmente do zero, no centro, at\u00e9 um m\u00e1ximo na superf\u00edcie externa, e o eixo torce-se em um \u00e2ngulo proporcional ao torque e ao comprimento, e inversamente proporcional \u00e0 rigidez \u00e0 tor\u00e7\u00e3o \\(JG\\).<\/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>Tor\u00e7\u00e3o de eixo \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> um eixo de a\u00e7o maci\u00e7o com di\u00e2metro \\(D = 40\\) mm e comprimento \\(L = 1\\) m transmite um torque constante de \\(T = 1000\\) N\u00b7m. O m\u00f3dulo de cisalhamento do a\u00e7o \u00e9 \\(G = 80\\) GPa.<\/p>\n<p>\\[ J = \\frac{\\pi (0.04)^4}{32} = 2.513 \\times 10^{-7}\\ \\text{m}^4 \\]<\/p>\n<p>\\[ \\tau_{max} = \\frac{1000 \\times 0.02}{2.513 \\times 10^{-7}} = 79.6 \\times 10^6\\ \\text{Pa} \\approx 79.6\\ \\text{MPa} \\]<\/p>\n<p>\\[ \\varphi = \\frac{1000 \\times 1}{2.513 \\times 10^{-7} \\times 80 \\times 10^9} = 0.04974\\ \\text{rad} \\approx 2.85^\\circ \\]<\/p>\n<p><strong>Resultado:<\/strong> a tens\u00e3o de cisalhamento m\u00e1xima \u00e9 de aproximadamente 79,6 MPa (\u2248 11,5 ksi) na superf\u00edcie externa, e o eixo torce cerca de 2,85\u00b0 (0,0497 rad) ao longo de seus 1 m de comprimento \u2014 ou seja, cerca de 2,85\u00b0 por metro.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora de tor\u00e7\u00e3o de eixo<\/h2>\n<ol>\n<li>Informe o <strong>Torque aplicado (T)<\/strong> e selecione a unidade \u2014 N\u00b7m, kN\u00b7m, lb\u00b7ft ou lb\u00b7in.<\/li>\n<li>Escolha o <strong>Tipo de eixo<\/strong>: circular maci\u00e7o ou circular vazado (tubo). Para um eixo vazado, informe tamb\u00e9m o <strong>Di\u00e2metro interno (d)<\/strong>, que deve ser menor que o di\u00e2metro externo.<\/li>\n<li>Informe o <strong>Di\u00e2metro externo (D)<\/strong> e o <strong>Comprimento do eixo (L)<\/strong> com suas respectivas unidades (mm, cm, m, in ou ft).<\/li>\n<li>Informe o <strong>M\u00f3dulo de cisalhamento (G)<\/strong> do material \u2014 a\u00e7o \u2248 80 GPa, alum\u00ednio \u2248 27 GPa, cobre \u2248 45 GPa \u2014 e escolha a unidade (GPa, MPa, psi ou ksi).<\/li>\n<li>Leia os resultados: a <strong>tens\u00e3o de cisalhamento m\u00e1xima (\u03c4max)<\/strong> em MPa, ksi e psi, e o <strong>\u00e2ngulo de tor\u00e7\u00e3o (\u03c6)<\/strong> em graus, radianos, graus por metro e graus por p\u00e9.<\/li>\n<\/ol>\n<h2>O que \u00e9 tor\u00e7\u00e3o de eixo?<\/h2>\n<p>Quando um torque \u00e9 aplicado a um eixo \u2014 como ocorre em todo eixo de transmiss\u00e3o, linha de acionamento, coluna de perfura\u00e7\u00e3o ou eixo de h\u00e9lice \u2014, o material \u00e9 torcido. Cada se\u00e7\u00e3o transversal gira em rela\u00e7\u00e3o \u00e0 vizinha, e essa rota\u00e7\u00e3o encontra resist\u00eancia nas tens\u00f5es de cisalhamento distribu\u00eddas pela se\u00e7\u00e3o. Para eixos circulares (maci\u00e7os ou com furo conc\u00eantrico), a an\u00e1lise \u00e9 exata e simples: a tens\u00e3o de cisalhamento varia linearmente do zero, no centro, at\u00e9 um m\u00e1ximo na superf\u00edcie externa \u2014 \u00e9 por isso que eixos e tubos rompem ou escoam primeiro por fora.<\/p>\n<p>Duas grandezas importam na verifica\u00e7\u00e3o \u00e0 tor\u00e7\u00e3o. A primeira \u00e9 a <strong>tens\u00e3o de cisalhamento m\u00e1xima<\/strong>, \\(\\tau_{max} = Tc\/J\\): ela deve permanecer abaixo da tens\u00e3o de cisalhamento admiss\u00edvel do material. Para a\u00e7os d\u00facteis, o limite de escoamento ao cisalhamento fica entre 0,5 e 0,6 vezes o limite de escoamento \u00e0 tra\u00e7\u00e3o, e um coeficiente de seguran\u00e7a adequado \u00e9 aplicado sobre esse valor. A segunda \u00e9 o <strong>\u00e2ngulo de tor\u00e7\u00e3o<\/strong>, \\(\\varphi = TL\/JG\\): mesmo um eixo suficientemente resistente pode torcer demais, causando desalinhamento, vibra\u00e7\u00e3o, efeito mola em sistemas de controle ou erro de posicionamento em acionamentos de precis\u00e3o.<\/p>\n<p>O termo geom\u00e9trico \\(J\\), o momento polar de in\u00e9rcia, cresce com a quarta pot\u00eancia do di\u00e2metro. Dobrar o di\u00e2metro de um eixo maci\u00e7o reduz a tens\u00e3o e a tor\u00e7\u00e3o por um fator de 16. \u00c9 por isso que os eixos vazados s\u00e3o t\u00e3o eficientes: remover o material pouco solicitado pr\u00f3ximo ao centro custa pouqu\u00edssima rigidez, mas economiza bastante peso \u2014 por isso eixos de transmiss\u00e3o, eixos de rolos e muitas pe\u00e7as aeroespaciais s\u00e3o tubos.<\/p>\n<p>&lt;Ao interpretar o resultado, compare \\(\\tau_{max}\\) com a tens\u00e3o de cisalhamento admiss\u00edvel do material e \\(\\varphi\\) com o limite de tor\u00e7\u00e3o admiss\u00edvel. Como regra pr\u00e1tica tradicional, eixos de m\u00e1quina s\u00e3o limitados a cerca de 1\u00b0 de tor\u00e7\u00e3o em um comprimento de 20 di\u00e2metros; acionamentos de precis\u00e3o e linhas de transmiss\u00e3o longas costumam exigir limites muito mais r\u00edgidos.<\/p>\n<h2>Premissas, limita\u00e7\u00f5es e dicas pr\u00e1ticas<\/h2>\n<ul>\n<li><strong>Apenas se\u00e7\u00f5es circulares.<\/strong> As f\u00f3rmulas s\u00e3o exatas para eixos circulares maci\u00e7os ou vazados com furo conc\u00eantrico. Se\u00e7\u00f5es n\u00e3o circulares (barras retangulares, rasgos de chaveta, eixos estriados) torcem de maneira muito diferente e exigem m\u00e9todos pr\u00f3prios.<\/li>\n<li><strong>Eixo uniforme, torque constante.<\/strong> O c\u00e1lculo assume se\u00e7\u00e3o transversal constante, um \u00fanico material e um torque que n\u00e3o varia ao longo do comprimento. Para eixos escalonados ou v\u00e1rios torques aplicados, calcule cada trecho separadamente e some os \u00e2ngulos de tor\u00e7\u00e3o.<\/li>\n<li><strong>Comportamento el\u00e1stico linear.<\/strong> As tens\u00f5es devem permanecer abaixo do limite el\u00e1stico; o resultado n\u00e3o prev\u00ea escoamento nem colapso pl\u00e1stico.<\/li>\n<li><strong>Rasgos de chaveta, furos e ressaltos<\/strong> concentram tens\u00f5es. Um eixo real com rasgo de chaveta ou ressalto pode sofrer tens\u00f5es locais de 1,5 a 3 vezes o valor nominal; portanto, considere fatores de concentra\u00e7\u00e3o de tens\u00e3o em projetos cr\u00edticos.<\/li>\n<li><strong>Verifique os dois crit\u00e9rios.<\/strong> Um eixo curto e robusto normalmente \u00e9 governado pela tens\u00e3o; um eixo longo e esbelto, pelo \u00e2ngulo de tor\u00e7\u00e3o. Lembre-se tamb\u00e9m de que um eixo longo pode falhar por flambagem ou por velocidade cr\u00edtica (whirling) \u2014 uma verifica\u00e7\u00e3o relacionada \u00e9 a nossa <a href=\"https:\/\/wpcalc.com\/pt\/engenharia\/carga-flambagem-euler\/\">calculadora de carga cr\u00edtica de flambagem de Euler<\/a>.<\/li>\n<li>Para eixos que tamb\u00e9m recebem cargas de flex\u00e3o (engrenagens, correias, polias), superponha as tens\u00f5es de flex\u00e3o obtidas em uma an\u00e1lise de viga \u2014 veja as calculadoras de <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-center-point-load\/\">viga biapoiada com carga pontual no centro<\/a> e <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-uniform-load\/\">viga biapoiada com carga uniformemente distribu\u00edda<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calcule a tens\u00e3o de cisalhamento m\u00e1xima e o \u00e2ngulo de tor\u00e7\u00e3o de um eixo circular maci\u00e7o ou vazado. Informe o torque, as dimens\u00f5es, o comprimento e o m\u00f3dulo de cisalhamento para verificar um projeto de eixo em segundos.<\/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-2200","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\/2200","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=2200"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2200\/revisions"}],"predecessor-version":[{"id":2579,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2200\/revisions\/2579"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}