{"id":2063,"date":"2026-10-14T16:44:23","date_gmt":"2026-10-14T15:44:23","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/engenharia\/modulo-de-resistencia-da-secao-2\/"},"modified":"2026-10-14T16:44:23","modified_gmt":"2026-10-14T15:44:23","slug":"modulo-de-resistencia-da-secao-2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/engenharia\/modulo-de-resistencia-da-secao-2\/","title":{"rendered":"M\u00f3dulo de resist\u00eancia da se\u00e7\u00e3o de vigas"},"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\">Calcule as propriedades da se\u00e7\u00e3o para flex\u00e3o de vigas<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2063\" data-favorite-title=\"M\u00f3dulo de resist\u00eancia\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/engenharia\/modulo-de-resistencia-da-secao-2\/\" data-favorite-excerpt=\"Calcule o m\u00f3dulo de resist\u00eancia el\u00e1stico e o momento de in\u00e9rcia da \u00e1rea para se\u00e7\u00f5es retangulares, circulares, tubos ou perfis I\/H. Digite as dimens\u00f5es, escolha o formato e obtenha as propriedades em rela\u00e7\u00e3o ao eixo forte de flex\u00e3o.\" 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\/modulo-de-resistencia-da-secao-2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2063\" data-post=\"2063\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Forma da se\u00e7\u00e3o transversal<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"forma_da_seo_transversal\"><option value=\"rect\" selected>Ret\u00e2ngulo<\/option><option value=\"circle\">C\u00edrculo maci\u00e7o<\/option><option value=\"tube\">Tubo circular oco<\/option><option value=\"isec\">Perfil I \/ H<\/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 has-term\" id=\"input-2\"><label for=\"field-2\">Largura (b)<\/label><div class=\"term\">b<\/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=\"largura_b\" id=\"field-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"100\" min=\"0.01\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" 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><\/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><div class=\"field has-term\" id=\"input-3\"><label for=\"field-4\">Altura (h)<\/label><div class=\"term\">h<\/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=\"altura_h\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"200\" min=\"0.01\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" 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><\/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-4\">Altura medida paralelamente ao eixo de flex\u00e3o<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">Di\u00e2metro (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_d\" id=\"field-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"50\" min=\"0.01\" value=\"50\"\/><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><\/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><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-8\">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-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"100\" min=\"0.01\" value=\"100\"\/><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><\/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><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-10\">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-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"80\" min=\"0.01\" value=\"80\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" 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><\/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><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-12\">Altura total (h)<\/label><div class=\"term\">h<\/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=\"altura_total_h\" id=\"field-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"200\" min=\"0.01\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-13\" 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><\/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><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-14\">Largura da flange (b)<\/label><div class=\"term\">b<\/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=\"largura_da_flange_b\" id=\"field-14\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"100\" min=\"0.01\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-15\" 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><\/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><div class=\"field has-term\" id=\"input-9\" hidden><label for=\"field-16\">Espessura da flange (tf)<\/label><div class=\"term\">tf<\/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=\"espessura_da_flange_tf\" id=\"field-16\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0.01\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-17\" 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><\/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><div class=\"field has-term\" id=\"input-10\" hidden><label for=\"field-18\">Espessura da alma (tw)<\/label><div class=\"term\">tw<\/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=\"espessura_da_alma_tw\" id=\"field-18\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"6\" min=\"0.01\" value=\"6\"\/><div class=\"grid grid-cols-1\"><select id=\"field-19\" 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><\/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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2063\">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> Propriedades da se\u00e7\u00e3o<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Momento de in\u00e9rcia da \u00e1rea<\/span><span class=\"result-term\">Ixx<\/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>M\u00f3dulo de resist\u00eancia el\u00e1stico<\/span><span class=\"result-term\">Sxx<\/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 is-column\" id=\"output-3\"><span class=\"field-title\"><span>F\u00f3rmula e observa\u00e7\u00f5es<\/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=\"2063\" 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>M\u00f3dulo de resist\u00eancia<\/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\\[ S_{xx} = \\frac{I_{xx}}{c} \\qquad \\sigma_{max} = \\frac{M}{S_{xx}} \\\\\\ I_{xx} = \\frac{b h^{3}}{12} \\ \\text{(ret\u00e2ngulo)} \\qquad I_{xx} = \\frac{\\pi d^{4}}{64} \\ \\text{(c\u00edrculo maci\u00e7o)} \\\\\\ I_{xx} = \\frac{\\pi \\left(D^{4} - d^{4}\\right)}{64} \\ \\text{(tubo oco)} \\qquad I_{xx} = \\frac{b h^{3} - \\left(b - t_{w}\\right)\\left(h - 2 t_{f}\\right)^{3}}{12} \\ \\text{(perfil I \/ H)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(S_{xx}\\) \u2014 m\u00f3dulo de resist\u00eancia el\u00e1stico em rela\u00e7\u00e3o ao eixo centroidal horizontal (x\u2013x) (mm\u00b3 ou in\u00b3)<\/li>\n<li>\\(I_{xx}\\) \u2014 momento de in\u00e9rcia da \u00e1rea em rela\u00e7\u00e3o ao mesmo eixo (mm\u2074 ou in\u2074)<\/li>\n<li>\\(c\\) \u2014 dist\u00e2ncia do eixo neutro \u00e0 fibra mais afastada: \\(c = h\/2\\) ou \\(c = D\/2\\)<\/li>\n<li>\\(b\\) \u2014 largura (ou largura da mesa, no caso de um perfil I)<\/li>\n<li>\\(h\\) \u2014 altura total da se\u00e7\u00e3o<\/li>\n<li>\\(d\\) \u2014 di\u00e2metro (c\u00edrculo maci\u00e7o) ou di\u00e2metro interno (tubo)<\/li>\n<li>\\(D\\) \u2014 di\u00e2metro externo do tubo<\/li>\n<li>\\(t_{f},\\ t_{w}\\) \u2014 espessuras da mesa e da alma de um perfil I \/ H<\/li>\n<li>\\(M\\) \u2014 momento fletor aplicado; \\(\\sigma_{max}\\) \u2014 tens\u00e3o m\u00e1xima de flex\u00e3o<\/li>\n<\/ul>\n<p>O m\u00f3dulo de resist\u00eancia mede a efici\u00eancia com que uma se\u00e7\u00e3o transversal resiste \u00e0 flex\u00e3o: quanto maior \\(S_{xx}\\), menor a tens\u00e3o de flex\u00e3o gerada por um determinado momento.<\/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>M\u00f3dulo de resist\u00eancia \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> uma viga de madeira com se\u00e7\u00e3o retangular de 100 mm de largura e 200 mm de altura, carregada de modo a flexionar em torno do eixo forte.<\/p>\n<p>\\[ I_{xx} = \\frac{b h^{3}}{12} = \\frac{100 \\times 200^{3}}{12} = 66{,}666{,}667 \\ \\text{mm}^{4} \\approx 160.2 \\ \\text{in}^{4} \\]<\/p>\n<p>\\[ S_{xx} = \\frac{I_{xx}}{h\/2} = \\frac{66{,}666{,}667}{100} = 666{,}667 \\ \\text{mm}^{3} \\approx 40.68 \\ \\text{in}^{3} \\]<\/p>\n<p><strong>Resultado:<\/strong> \\(I_{xx} \\approx 6.67 \\times 10^{7}\\) mm\u2074 e \\(S_{xx} \\approx 6.67 \\times 10^{5}\\) mm\u00b3 (40,68 in\u00b3). Um momento fletor de 10 kN\u00b7m produziria, portanto, uma tens\u00e3o m\u00e1xima de \\(\\sigma = 10^{7} \/ 666{,}667 \\approx 15.0\\) N\/mm\u00b2 (MPa).<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Selecione o <strong>formato da se\u00e7\u00e3o transversal<\/strong>: Ret\u00e2ngulo, C\u00edrculo maci\u00e7o, Tubo circular oco ou Perfil I \/ H. Apenas os campos de dimens\u00f5es relevantes para o formato escolhido s\u00e3o exibidos.<\/li>\n<li>Digite as dimens\u00f5es nos campos vis\u00edveis \u2014 por exemplo, <strong>Largura (b)<\/strong> e <strong>Altura (h)<\/strong> para um ret\u00e2ngulo, ou <strong>Di\u00e2metro externo (D)<\/strong> e <strong>Di\u00e2metro interno (d)<\/strong> para um tubo.<\/li>\n<li>Escolha a unidade (mm, cm, m ou in) de cada dimens\u00e3o. Os resultados seguem o sistema de unidades que voc\u00ea digitou, com a convers\u00e3o para o outro sistema mostrada entre par\u00eanteses.<\/li>\n<li>Leia o <strong>momento de in\u00e9rcia da \u00e1rea<\/strong> e o <strong>m\u00f3dulo de resist\u00eancia el\u00e1stico<\/strong> no painel de resultados, junto com a f\u00f3rmula exata usada para o seu formato.<\/li>\n<\/ol>\n<h2>O que \u00e9 o m\u00f3dulo de resist\u00eancia?<\/h2>\n<p>Quando uma viga flexiona, o material mais afastado do eixo neutro \u00e9 o mais solicitado, enquanto o material sobre o eixo neutro praticamente n\u00e3o sofre tens\u00e3o de flex\u00e3o. O <strong>m\u00f3dulo de resist\u00eancia el\u00e1stico<\/strong> \\(S\\) expressa quanta mat\u00e9ria \u201ceficaz\u201d a se\u00e7\u00e3o posiciona longe desse eixo. Ele \u00e9 definido como o momento de in\u00e9rcia da \u00e1rea dividido pela dist\u00e2ncia at\u00e9 a fibra mais afastada, \\(S = I\/c\\), e liga o momento fletor \u00e0 tens\u00e3o por meio da f\u00f3rmula da flex\u00e3o \\(\\sigma = M\/S\\).<\/p>\n<p>A consequ\u00eancia pr\u00e1tica \u00e9 simples: para o mesmo momento aplicado, um m\u00f3dulo de resist\u00eancia maior significa uma tens\u00e3o m\u00e1xima de flex\u00e3o menor. \u00c9 por isso que os perfis I e H s\u00e3o t\u00e3o comuns \u2014 ao concentrar material nas mesas, longe do eixo neutro, eles alcan\u00e7am um \\(S\\) elevado com relativamente pouco material. Dobrar a altura de uma viga retangular, por exemplo, multiplica seu m\u00f3dulo de resist\u00eancia por cerca de quatro.<\/p>\n<p>Todas as propriedades aqui s\u00e3o calculadas em rela\u00e7\u00e3o ao <strong>eixo forte x\u2013x<\/strong> (o eixo horizontal que passa pelo centroide), que \u00e9 a orienta\u00e7\u00e3o usual das vigas em aplica\u00e7\u00f5es de piso e cobertura. A se\u00e7\u00e3o tamb\u00e9m pode ser carregada em torno do eixo fraco y\u2013y; nesse caso, o m\u00f3dulo de resist\u00eancia ser\u00e1 consideravelmente menor \u2014 para um ret\u00e2ngulo, \\(S_{yy} = h b^{2}\/6\\).<\/p>\n<p>Para transformar o resultado em uma verifica\u00e7\u00e3o de projeto, combine-o com o momento fletor do seu caso de carregamento. Se voc\u00ea conhece a carga atuante na viga, nossas calculadoras de <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-uniform-load\/\">viga biapoiada com carga uniformemente distribu\u00edda<\/a> ou de <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-center-point-load\/\">carga concentrada no centro<\/a> fornecem o momento m\u00e1ximo; divida-o por \\(S_{xx}\\) para obter a tens\u00e3o de pico e compare-a com a tens\u00e3o admiss\u00edvel do seu material.<\/p>\n<h2>Premissas, limita\u00e7\u00f5es e dicas pr\u00e1ticas<\/h2>\n<ul>\n<li><strong>Apenas comportamento el\u00e1stico.<\/strong> Os resultados pressup\u00f5em que o material permanece abaixo do limite de escoamento. No dimensionamento pl\u00e1stico, deve-se usar o m\u00f3dulo de resist\u00eancia pl\u00e1stico (que \u00e9 maior que o el\u00e1stico).<\/li>\n<li><strong>Se\u00e7\u00f5es homog\u00eaneas e sim\u00e9tricas.<\/strong> As f\u00f3rmulas pressup\u00f5em um \u00fanico material e um formato duplamente sim\u00e9trico, de modo que o eixo neutro passa pelo centroide. Vigas mistas (por exemplo, concreto\u2013a\u00e7o) exigem uma an\u00e1lise de se\u00e7\u00e3o transformada.<\/li>\n<li><strong>Raios de concord\u00e2ncia e detalhes s\u00e3o ignorados.<\/strong> Perfis I laminados reais t\u00eam raios de concord\u00e2ncia e mesas levemente inclinadas, por isso os valores tabelados em cat\u00e1logo diferem do c\u00e1lculo idealizado em alguns por cento.<\/li>\n<li><strong>A orienta\u00e7\u00e3o importa.<\/strong> Digite a altura medida na dire\u00e7\u00e3o da flex\u00e3o. Um ret\u00e2ngulo de 100 \u00d7 200 usado deitado (flexionando em torno do eixo fraco) tem apenas um quarto do m\u00f3dulo de resist\u00eancia da mesma se\u00e7\u00e3o posicionada em p\u00e9.<\/li>\n<li><strong>Verifica\u00e7\u00e3o do tubo.<\/strong> Em um tubo oco, o di\u00e2metro interno deve ser menor que o di\u00e2metro externo; paredes muito finas podem ainda ser governadas pela flambagem local, e n\u00e3o pela tens\u00e3o de flex\u00e3o.<\/li>\n<li><strong>A flex\u00e3o n\u00e3o \u00e9 tudo.<\/strong> Uma viga tamb\u00e9m pode falhar por cisalhamento, flecha excessiva ou flambagem lateral com tor\u00e7\u00e3o. Elementos esbeltos comprimidos tamb\u00e9m devem ser verificados com a <a href=\"https:\/\/wpcalc.com\/en\/engineering\/euler-buckling-load\/\">calculadora de carga de flambagem de Euler<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calcule o m\u00f3dulo de resist\u00eancia el\u00e1stico e o momento de in\u00e9rcia da \u00e1rea para se\u00e7\u00f5es retangulares, circulares, tubos ou perfis I\/H. Digite as dimens\u00f5es, escolha o formato e obtenha as propriedades em rela\u00e7\u00e3o ao eixo forte de flex\u00e3o.<\/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-2063","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\/2063","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=2063"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2063\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}