{"id":2531,"date":"2026-10-14T08:19:42","date_gmt":"2026-10-14T07:19:42","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/inzynieria\/wskaznik-wytrzymalosci-przekroju\/"},"modified":"2026-10-14T08:19:42","modified_gmt":"2026-10-14T07:19:42","slug":"wskaznik-wytrzymalosci-przekroju","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/inzynieria\/wskaznik-wytrzymalosci-przekroju\/","title":{"rendered":"Wska\u017anik wytrzyma\u0142o\u015bci przekroju belki"},"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\">Wyznaczanie charakterystyk przekroju belki przy zginaniu<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2531\" data-favorite-title=\"Wska\u017anik wytrzyma\u0142o\u015bci\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/inzynieria\/wskaznik-wytrzymalosci-przekroju\/\" data-favorite-excerpt=\"Oblicz spr\u0119\u017cysty wska\u017anik wytrzyma\u0142o\u015bci i moment bezw\u0142adno\u015bci dla przekroj\u00f3w prostok\u0105tnych, ko\u0142owych, rurowych oraz dwuteowych. Wpisz wymiary, wybierz kszta\u0142t i poznaj charakterystyki wzgl\u0119dem mocnej osi zginania.\" aria-label=\"Dodaj do ulubionych\" 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\/pl\/inzynieria\/wskaznik-wytrzymalosci-przekroju\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2531\" data-post=\"2531\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Kszta\u0142t przekroju<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"ksztat_przekroju\"><option value=\"rect\" selected>Prostok\u0105t<\/option><option value=\"circle\">Ko\u0142o pe\u0142ne<\/option><option value=\"tube\">Rura ko\u0142owa<\/option><option value=\"isec\">Przekr\u00f3j dwuteownikowy (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\">Szeroko\u015b\u0107 (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=\"szeroko_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=\"jednostka\" aria-label=\"Jednostka\"><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\">Wysoko\u015b\u0107 (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=\"wysoko_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=\"jednostka\" aria-label=\"Jednostka\"><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\">Wysoko\u015b\u0107 mierzona r\u00f3wnolegle do osi zginania<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">\u015arednica (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=\"rednica_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=\"jednostka\" aria-label=\"Jednostka\"><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\">\u015arednica zewn\u0119trzna (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=\"rednica_zewntrzna_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=\"jednostka\" aria-label=\"Jednostka\"><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\">\u015arednica wewn\u0119trzna (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=\"rednica_wewntrzna_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=\"jednostka\" aria-label=\"Jednostka\"><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\">Wysoko\u015b\u0107 ca\u0142kowita (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=\"wysoko_cakowita_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=\"jednostka\" aria-label=\"Jednostka\"><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\">Szeroko\u015b\u0107 p\u00f3\u0142ki (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=\"szeroko_pki_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=\"jednostka\" aria-label=\"Jednostka\"><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\">Grubo\u015b\u0107 p\u00f3\u0142ki (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=\"grubo_pki_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=\"jednostka\" aria-label=\"Jednostka\"><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\">Grubo\u015b\u0107 \u015brodnika (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=\"grubo_rodnika_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=\"jednostka\" aria-label=\"Jednostka\"><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=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2531\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/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> Charakterystyki przekroju<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Moment bezw\u0142adno\u015bci przekroju<\/span><span class=\"result-term\">Ixx<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Wska\u017anik wytrzyma\u0142o\u015bci spr\u0119\u017cystej<\/span><span class=\"result-term\">Sxx<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Wz\u00f3r i uwagi<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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\">Kopiuj link do tego obliczenia<\/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>Zostaw komentarz<\/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=\"2531\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/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\">Lubi\u0119 to <\/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\">Pomocne <\/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\">Niejasne <\/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\">Rozczarowanie <\/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\">Niedok\u0142adne <\/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>Wska\u017anik wytrzyma\u0142o\u015bci<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/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{(prostok\u0105t)} \\qquad I_{xx} = \\frac{\\pi d^{4}}{64} \\ \\text{(ko\u0142o pe\u0142ne)} \\\\ I_{xx} = \\frac{\\pi \\left(D^{4} - d^{4}\\right)}{64} \\ \\text{(rura)} \\qquad I_{xx} = \\frac{b h^{3} - \\left(b - t_{w}\\right)\\left(h - 2 t_{f}\\right)^{3}}{12} \\ \\text{(dwuteownik \/ profil H)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Obja\u015bnienie symboli:<\/strong><\/p>\n<ul>\n<li>\\(S_{xx}\\) \u2014 spr\u0119\u017cysty wska\u017anik wytrzyma\u0142o\u015bci wzgl\u0119dem poziomej osi centralnej x\u2013x (mm\u00b3 lub in\u00b3)<\/li>\n<li>\\(I_{xx}\\) \u2014 moment bezw\u0142adno\u015bci wzgl\u0119dem tej samej osi (mm\u2074 lub in\u2074)<\/li>\n<li>\\(c\\) \u2014 odleg\u0142o\u015b\u0107 od osi oboj\u0119tnej do skrajnego w\u0142\u00f3kna: \\(c = h\/2\\) lub \\(c = D\/2\\)<\/li>\n<li>\\(b\\) \u2014 szeroko\u015b\u0107 (lub szeroko\u015b\u0107 p\u00f3\u0142ki dwuteownika)<\/li>\n<li>\\(h\\) \u2014 ca\u0142kowita wysoko\u015b\u0107 przekroju<\/li>\n<li>\\(d\\) \u2014 \u015brednica (ko\u0142o pe\u0142ne) lub \u015brednica wewn\u0119trzna (rura)<\/li>\n<li>\\(D\\) \u2014 \u015brednica zewn\u0119trzna rury<\/li>\n<li>\\(t_{f},\\ t_{w}\\) \u2014 grubo\u015b\u0107 p\u00f3\u0142ki i \u015brodnika dwuteownika \/ profilu H<\/li>\n<li>\\(M\\) \u2014 dzia\u0142aj\u0105cy moment zginaj\u0105cy; \\(\\sigma_{max}\\) \u2014 maksymalne napr\u0119\u017cenie zginaj\u0105ce<\/li>\n<\/ul>\n<p>Wska\u017anik wytrzyma\u0142o\u015bci opisuje, jak skutecznie dany przekr\u00f3j przeciwstawia si\u0119 zginaniu: im wi\u0119ksze \\(S_{xx}\\), tym mniejsze napr\u0119\u017cenia zginaj\u0105ce wywo\u0142uje zadany moment.<\/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>Wska\u017anik wytrzyma\u0142o\u015bci \u2013 przyk\u0142ad obliczeniowy<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> drewniana belka o przekroju prostok\u0105tnym, szeroko\u015bci 100 mm i wysoko\u015bci 200 mm, obci\u0105\u017cona tak, \u017ce ugina si\u0119 wzgl\u0119dem osi mocnej.<\/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>Wynik:<\/strong> \\(I_{xx} \\approx 6.67 \\times 10^{7}\\) mm\u2074 oraz \\(S_{xx} \\approx 6.67 \\times 10^{5}\\) mm\u00b3 (40,68 in\u00b3). Moment zginaj\u0105cy 10 kN\u00b7m wywo\u0142a\u0142by wi\u0119c maksymalne napr\u0119\u017cenie \\(\\sigma = 10^{7} \/ 666{,}667 \\approx 15.0\\) N\/mm\u00b2 (MPa).<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Wybierz <strong>kszta\u0142t przekroju<\/strong>: prostok\u0105t, ko\u0142o pe\u0142ne, rura ko\u0142owa lub dwuteownik \/ profil H. Widoczne pozostaj\u0105 tylko pola wymiar\u00f3w istotne dla danego kszta\u0142tu.<\/li>\n<li>Wpisz wymiary w widocznych polach \u2014 na przyk\u0142ad <strong>Szeroko\u015b\u0107 (b)<\/strong> i <strong>Wysoko\u015b\u0107 (h)<\/strong> dla prostok\u0105ta albo <strong>\u015arednica zewn\u0119trzna (D)<\/strong> i <strong>\u015arednica wewn\u0119trzna (d)<\/strong> dla rury.<\/li>\n<li>Dobierz jednostk\u0119 (mm, cm, m lub in) dla ka\u017cdego wymiaru. Wyniki podawane s\u0105 w Twoim uk\u0142adzie jednostek, a w nawiasach widnieje przeliczenie na drugi uk\u0142ad.<\/li>\n<li>Odczytaj z panelu wynik\u00f3w <strong>moment bezw\u0142adno\u015bci<\/strong> oraz <strong>spr\u0119\u017cysty wska\u017anik wytrzyma\u0142o\u015bci<\/strong>, wraz z dok\u0142adnym wzorem zastosowanym dla wybranego kszta\u0142tu.<\/li>\n<\/ol>\n<h2>Czym jest wska\u017anik wytrzyma\u0142o\u015bci?<\/h2>\n<p>Gdy belka si\u0119 ugina, najbardziej obci\u0105\u017cony jest materia\u0142 po\u0142o\u017cony najdalej od osi oboj\u0119tnej, natomiast materia\u0142 przy samej osi przenosi niemal \u017cadnych napr\u0119\u017ce\u0144 zginaj\u0105cych. <strong>Spr\u0119\u017cysty wska\u017anik wytrzyma\u0142o\u015bci<\/strong> \\(S\\) pokazuje, ile \u201eskutecznego\u201d materia\u0142u przekr\u00f3j rozmieszcza daleko od tej osi. Definiuje si\u0119 go jako moment bezw\u0142adno\u015bci podzielony przez odleg\u0142o\u015b\u0107 do skrajnego w\u0142\u00f3kna, \\(S = I\/c\\), i \u0142\u0105czy on moment zginaj\u0105cy z napr\u0119\u017ceniem w wzorze \\(\\sigma = M\/S\\).<\/p>\n<p>Praktyczny wniosek jest prosty: przy tym samym momencie wi\u0119kszy wska\u017anik wytrzyma\u0142o\u015bci oznacza mniejsze maksymalne napr\u0119\u017cenie zginaj\u0105ce. Dlatego dwuteowniki i profile H s\u0105 tak powszechne \u2014 koncentruj\u0105c materia\u0142 w p\u00f3\u0142kach, daleko od osi oboj\u0119tnej, osi\u0105gaj\u0105 wysokie \\(S\\) przy relatywnie niewielkiej ilo\u015bci materia\u0142u. Podwojenie wysoko\u015bci belki prostok\u0105tnej mno\u017cy jej wska\u017anik wytrzyma\u0142o\u015bci mniej wi\u0119cej czterokrotnie.<\/p>\n<p>Wszystkie charakterystyki obliczane s\u0105 tu wzgl\u0119dem <strong>mocnej osi x\u2013x<\/strong> (poziomej osi przechodz\u0105cej przez \u015brodek ci\u0119\u017cko\u015bci przekroju), a tak belki uk\u0142ada si\u0119 zwykle w stropach i dachach. Przekr\u00f3j mo\u017cna te\u017c obci\u0105\u017ca\u0107 wzgl\u0119dem s\u0142abej osi y\u2013y \u2014 wtedy wska\u017anik wytrzyma\u0142o\u015bci b\u0119dzie wyra\u017anie mniejszy; dla prostok\u0105ta \\(S_{yy} = h b^{2}\/6\\).<\/p>\n<p>Aby zamieni\u0107 wynik w sprawdzenie no\u015bno\u015bci, po\u0142\u0105cz go z momentem zginaj\u0105cym z Twojego schematu obci\u0105\u017ce\u0144. Je\u015bli znasz obci\u0105\u017cenie belki, nasi kalkulatory dla <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-uniform-load\/\">belki swobodnie podpartej z obci\u0105\u017ceniem r\u00f3wnomiernym<\/a> lub <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-center-point-load\/\">obci\u0105\u017ceniem skupionym w \u015brodku<\/a> wyznacz\u0105 maksymalny moment; podziel go przez \\(S_{xx}\\), aby otrzyma\u0107 napr\u0119\u017cenie szczytowe, i por\u00f3wnaj z napr\u0119\u017ceniem dopuszczalnym materia\u0142u.<\/p>\n<h2>Za\u0142o\u017cenia, ograniczenia i praktyczne wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Wy\u0142\u0105cznie zakres spr\u0119\u017cysty.<\/strong> Wyniki zak\u0142adaj\u0105, \u017ce materia\u0142 pozostaje poni\u017cej granicy plastyczno\u015bci. W projektowaniu plastycznym nale\u017cy zamiast tego u\u017cy\u0107 plastycznego wska\u017anika wytrzyma\u0142o\u015bci (wi\u0119kszego ni\u017c spr\u0119\u017cysty).<\/li>\n<li><strong>Przekroje jednorodne i symetryczne.<\/strong> Wzory zak\u0142adaj\u0105 jeden materia\u0142 i kszta\u0142t podw\u00f3jnie symetryczny, wi\u0119c o\u015b oboj\u0119tna przechodzi przez \u015brodek ci\u0119\u017cko\u015bci. Belki zespolone (np. stalowo-betonowe) wymagaj\u0105 analizy przekroju zamienionego.<\/li>\n<li><strong>Promienie zaokr\u0105gle\u0144 i detale pomini\u0119to.<\/strong> Rzeczywiste walcowane dwuteowniki maj\u0105 promienie\u8fc7\u6e21owe przy \u015brodniku i p\u00f3\u0142ki nier\u00f3wnomiernie grubo\u015bci, wi\u0119c warto\u015bci katalogowe r\u00f3\u017cni\u0105 si\u0119 od idealizowanego obliczenia o kilka procent.<\/li>\n<li><strong>Orientacja ma znaczenie.<\/strong> Wpisuj wysoko\u015b\u0107 mierzon\u0105 r\u00f3wnolegle do kierunku zginania. Prostok\u0105t 100 \u00d7 200 u\u0142o\u017cony p\u0142asko (zginanie wzgl\u0119dem osi s\u0142abej) ma tylko jedn\u0105 czwart\u0105 wska\u017anika wytrzyma\u0142o\u015bci tego samego przekroju postawionego pionowo.<\/li>\n<li><strong>Sprawdzenie rury.<\/strong> Dla rury \u015brednica wewn\u0119trzna musi by\u0107 mniejsza od zewn\u0119trznej; przy bardzo cienkich \u015bciankach kryterium decyduj\u0105cym mo\u017ce by\u0107 dodatkowo niestateczno\u015b\u0107 lokalna, a nie napr\u0119\u017cenie zginaj\u0105ce.<\/li>\n<li><strong>Zginanie to nie wszystko.<\/strong> Belka mo\u017ce ulec zniszczeniu r\u00f3wnie\u017c przez \u015bcinanie, przemieszczenia (ugi\u0119cia) lub wyboczenie skr\u0119tno-zginaj\u0105ce. Smuk\u0142e elementy \u015bciskane warto dodatkowo sprawdzi\u0107 <a href=\"https:\/\/wpcalc.com\/en\/engineering\/euler-buckling-load\/\">kalkulatorem obci\u0105\u017cenia krytycznego Eulera<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz spr\u0119\u017cysty wska\u017anik wytrzyma\u0142o\u015bci i moment bezw\u0142adno\u015bci dla przekroj\u00f3w prostok\u0105tnych, ko\u0142owych, rurowych oraz dwuteowych. Wpisz wymiary, wybierz kszta\u0142t i poznaj charakterystyki wzgl\u0119dem mocnej osi zginania.<\/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":[8],"tags":[84],"class_list":["post-2531","post","type-post","status-publish","format-standard","hentry","category-inzynieria","tag-belki"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=2531"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2531\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}