{"id":479,"date":"2021-06-01T09:00:14","date_gmt":"2021-06-01T07:00:14","guid":{"rendered":"http:\/\/www.jureknawrocki.com\/?p=479"},"modified":"2026-03-14T08:14:48","modified_gmt":"2026-03-14T07:14:48","slug":"linearyzacja-naprezenia-po-co","status":"publish","type":"post","link":"https:\/\/jureknawrocki.com\/en\/linearyzacja-naprezenia-po-co\/","title":{"rendered":"Linearyzacja napr\u0119\u017cenia &#8211; po co to jest ?"},"content":{"rendered":"<p>Metoda ta jest stosowana do oceny ryzyka lokalnego uplastycznienia si\u0119 materia\u0142u elementu ci\u015bnieniowego. Punktem wyj\u015bcia jest dobrze znane kryterium energii podkszta\u0142cenia postaciowego Hubera-Misesa-Hencky\u2019ego (HMH), kt\u00f3rego og\u00f3lna formu\u0142a jest przedstawiona poni\u017cej:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1802\" src=\"https:\/\/jn.proklik.pl\/wp-content\/uploads\/Linearyzacja-naprezenia-1.webp\" alt=\"\" width=\"476\" height=\"80\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Linearyzacja-naprezenia-1.webp 476w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/Linearyzacja-naprezenia-1-300x50.webp 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>W wypadku aparat\u00f3w ci\u015bnieniowych napr\u0119\u017cenia g\u0142\u00f3wne u\u017cywane w tej metodzie to:<\/p>\n<ul>\n<li>Napr\u0119\u017cenie pow\u0142okowe g\u0142\u00f3wne ( general primary membrame equivialen stress P<sub>m<\/sub>)<\/li>\n<li>Napr\u0119\u017cenie pow\u0142okowe lokalne ( local primary membrame equivialen stress P<sub>L<\/sub>)<\/li>\n<li>Napr\u0119\u017cenie zginaj\u0105ce g\u0142\u00f3wne (primary bending stress P<sub>B<\/sub>)<\/li>\n<li>Napr\u0119\u017cenie szczytowe (peak stress P<sub>F<\/sub>)<\/li>\n<\/ul>\n<p>W miejscach krytycznych wyznacza si\u0119 p\u0142aszczyzny przeci\u0119cie prostopad\u0142e do dzia\u0142ania napr\u0119\u017cenia pow\u0142oki i\/lub zginaj\u0105cego. Na tej p\u0142aszczy\u017anie wyznacza si\u0119 nast\u0119pnie lini\u0119, na kt\u00f3rej b\u0119dzie prowadzona linearyzacja z regu\u0142y wed\u0142ug norm WRC.<\/p>\n<p>W nast\u0119pnych pi\u0119ciu krokach wyznacza si\u0119: tensory napr\u0119\u017cenia pow\u0142okowego, zginaj\u0105cego, szczytowego, trzy napr\u0119\u017cenia g\u0142\u00f3wne na linii linearyzacji oraz kryterium HMH wed\u0142ug powy\u017cszego wzoru.<\/p>\n<p>W ko\u0144cu por\u00f3wnuje si\u0119 otrzymane wyniki z ka\u017cdej \u015bcie\u017cki z napr\u0119\u017ceniem dopuszczalnym pochodz\u0105cym z normy przyj\u0119tej do oblicze\u0144.<\/p>\n<p>Tak to wygl\u0105da w praktyce:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1801\" src=\"https:\/\/jn.proklik.pl\/wp-content\/uploads\/Linearyzacja-naprezenia-2.webp\" alt=\"\" width=\"924\" height=\"1048\" srcset=\"https:\/\/jn.proklik.pl\/wp-content\/uploads\/Linearyzacja-naprezenia-2.webp 924w, https:\/\/jn.proklik.pl\/wp-content\/uploads\/Linearyzacja-naprezenia-2-480x544.webp 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 924px, 100vw\" \/><\/p>","protected":false},"excerpt":{"rendered":"<p>Metoda ta jest stosowana do oceny ryzyka lokalnego uplastycznienia si\u0119 materia\u0142u elementu ci\u015bnieniowego. Punktem wyj\u015bcia jest dobrze znane kryterium energii podkszta\u0142cenia postaciowego Hubera-Misesa-Hencky\u2019ego (HMH), kt\u00f3rego og\u00f3lna formu\u0142a jest przedstawiona poni\u017cej: W wypadku aparat\u00f3w ci\u015bnieniowych napr\u0119\u017cenia g\u0142\u00f3wne u\u017cywane w tej metodzie to: Napr\u0119\u017cenie pow\u0142okowe g\u0142\u00f3wne ( general primary membrame equivialen stress Pm) Napr\u0119\u017cenie pow\u0142okowe lokalne ( [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1800,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[123,15],"tags":[32,16],"class_list":["post-479","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-obliczenia-wytrzymalosciowe-rur-i-aparatow","category-projekty","tag-mes","tag-naprezenia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Linearyzacja napr\u0119\u017cenia - po co to jest ? - Jerzy Nawrocki<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jureknawrocki.com\/en\/linearyzacja-naprezenia-po-co\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Linearyzacja napr\u0119\u017cenia - po co to jest ? - Jerzy Nawrocki\" \/>\n<meta property=\"og:description\" content=\"Metoda ta jest stosowana do oceny ryzyka lokalnego uplastycznienia si\u0119 materia\u0142u elementu ci\u015bnieniowego. Punktem wyj\u015bcia jest dobrze znane kryterium energii podkszta\u0142cenia postaciowego Hubera-Misesa-Hencky\u2019ego (HMH), kt\u00f3rego og\u00f3lna formu\u0142a jest przedstawiona poni\u017cej: W wypadku aparat\u00f3w ci\u015bnieniowych napr\u0119\u017cenia g\u0142\u00f3wne u\u017cywane w tej metodzie to: Napr\u0119\u017cenie pow\u0142okowe g\u0142\u00f3wne ( general primary membrame equivialen stress Pm) Napr\u0119\u017cenie pow\u0142okowe lokalne ( [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jureknawrocki.com\/en\/linearyzacja-naprezenia-po-co\/\" \/>\n<meta property=\"og:site_name\" content=\"Jerzy Nawrocki\" \/>\n<meta property=\"article:published_time\" content=\"2021-06-01T07:00:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-14T07:14:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Linearyzacja-naprezenia-3.webp\" \/>\n\t<meta property=\"og:image:width\" content=\"316\" \/>\n\t<meta property=\"og:image:height\" content=\"630\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/webp\" \/>\n<meta name=\"author\" content=\"Jerzy Nawrocki\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Jerzy Nawrocki\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/linearyzacja-naprezenia-po-co\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/linearyzacja-naprezenia-po-co\\\/\"},\"author\":{\"name\":\"Jerzy Nawrocki\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#\\\/schema\\\/person\\\/b2567f392defa8e7698c6813f7930563\"},\"headline\":\"Linearyzacja napr\u0119\u017cenia &#8211; po co to jest ?\",\"datePublished\":\"2021-06-01T07:00:14+00:00\",\"dateModified\":\"2026-03-14T07:14:48+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/linearyzacja-naprezenia-po-co\\\/\"},\"wordCount\":211,\"publisher\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/linearyzacja-naprezenia-po-co\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/Linearyzacja-naprezenia-3.webp\",\"keywords\":[\"MES\",\"Napr\u0119\u017cenia\"],\"articleSection\":[\"Obliczenia wytrzyma\u0142o\u015bciowe rur i aparat\u00f3w\",\"Z \u017cycia rzeczoznawcy\"],\"inLanguage\":\"en-GB\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/linearyzacja-naprezenia-po-co\\\/\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/linearyzacja-naprezenia-po-co\\\/\",\"name\":\"Linearyzacja napr\u0119\u017cenia - po co to jest ? 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