{"id":3418,"date":"2026-03-20T08:10:40","date_gmt":"2026-03-20T07:10:40","guid":{"rendered":"https:\/\/jureknawrocki.com\/?p=3418"},"modified":"2026-03-20T08:10:41","modified_gmt":"2026-03-20T07:10:41","slug":"dynamika-autopipe-caesar-ii-time-history-cz-vi","status":"publish","type":"post","link":"https:\/\/jureknawrocki.com\/en\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/","title":{"rendered":"Dynamics: AutoPipe Time History. part VI"},"content":{"rendered":"<p>Time history analysis is the most advanced dynamic analysis method, allowing us to study a pipeline's response to loads that vary over time. Unlike static analysis, where the force is constant, we examine what happens to the system second by second or millisecond by millisecond. It's like recording a video of the pipeline's behavior instead of taking a single photo.<br>The most commonly used method is modal superposition. The program first calculates the natural vibration modes (frequencies) and then \"assembles\" the response of the entire system based on how individual modes respond to a given excitation over time. The essence of the analysis is to solve the following equation, where the following matrices are: M for mass, C for damping, K for stiffness, and F for the excitation force vector.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"37\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/9-4.jpg\" alt=\"\" class=\"wp-image-3420\" style=\"width:352px;height:auto\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/9-4.jpg 246w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/9-4-18x3.jpg 18w\" sizes=\"(max-width: 246px) 100vw, 246px\" \/><\/figure>\n\n\n\n<p>When is time history used? We use this method to simulate short-term, rapid events. Below is an example of analyzing a bank of 4x6-inch natural gas safety valves at pressures of 6.4 MPa\/1.15 MPa. Determining the force profile: <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>T=0.00 s: Force = 0 Valve closed<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>T=0.01 s: Force = 35 kN<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>T=0.50 s: Force = 35 kN<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>T=0.51 s: Force=0 Valve closing<\/li>\n<\/ul>\n\n\n\n<p>The AutoPipe model shows the following static analysis results. Ideally, 100% of the B31.3 code stress <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"678\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8-1024x678.jpg\" alt=\"\" class=\"wp-image-3421\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8-1024x678.jpg 1024w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8-980x649.jpg 980w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8-480x318.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) 1024px, 100vw\" \/><\/figure>\n\n\n\n<p>A force of 35 kN is applied to the centers of the arches. This force is absorbed by the triunion supports with the LS function. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"823\" height=\"732\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/2-10.jpg\" alt=\"\" class=\"wp-image-3422\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/2-10.jpg 823w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/2-10-480x427.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 823px, 100vw\" \/><\/figure>\n\n\n\n<p>To demonstrate how the presence or absence of the first support downstream of the PSV valve affects the dynamic results, it was removed from the first set from the top. The absence of the support causes the displacement to dampen the oscillations. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"545\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/3-9-1024x545.jpg\" alt=\"\" class=\"wp-image-3423\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/3-9-980x521.jpg 980w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/3-9-480x255.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) 1024px, 100vw\" \/><\/figure>\n\n\n\n<p>Also, very large force oscillations, which significantly exceed the recoil force of 35 kN, can now be calculated as the actual DLF factor of 61 \/ 35 = 1.85. This shows that frequently assuming a maximum DLF value of 2.0 can sometimes be justified. In this case, it can be justified by the support failure scenario. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"493\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/4-9-1024x493.jpg\" alt=\"\" class=\"wp-image-3425\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/4-9-980x472.jpg 980w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/4-9-480x231.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) 1024px, 100vw\" \/><\/figure>\n\n\n\n<p>It's interesting to see how the oscillations develop further along the pipeline. For example, at the first elbow of the collector, the force is significantly lower, only 18 kN.  <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"442\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/8-7-1024x442.jpg\" alt=\"\" class=\"wp-image-3428\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/8-7-980x423.jpg 980w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/8-7-480x207.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) 1024px, 100vw\" \/><\/figure>\n\n\n\n<p>For comparison, in a situation where the support is working properly, the pipeline and the support are so stiff that no oscillation occurs. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"527\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/6-11-1024x527.jpg\" alt=\"\" class=\"wp-image-3427\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/6-11-980x504.jpg 980w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/6-11-480x247.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) 1024px, 100vw\" \/><\/figure>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>Analiza time history to najbardziej zaawansowana metoda analizy dynamicznej, kt\u00f3ra pozwala na badanie odpowiedzi ruroci\u0105gu na obci\u0105\u017cenia zmieniaj\u0105ce si\u0119 w czasie. W przeciwie\u0144stwie do analizy statycznej, gdzie si\u0142a jest sta\u0142a, tutaj sprawdzamy, co dzieje si\u0119 z uk\u0142adem sekunda po sekundzie lub milisekunda po milisekundzie. Mo\u017cna to por\u00f3wna\u0107 do nagrywania filmu z zachowania ruroci\u0105gu, zamiast robienia [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":3421,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[123,15],"tags":[105,122,16],"class_list":["post-3418","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-obliczenia-wytrzymalosciowe-rur-i-aparatow","category-projekty","tag-autopipe","tag-caesar-ii","tag-naprezenia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Dynamika: AutoPipe \/ Caesar II Time History cz.VI - 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\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dynamika: AutoPipe \/ Caesar II Time History cz.VI - Jerzy Nawrocki\" \/>\n<meta property=\"og:description\" content=\"Analiza time history to najbardziej zaawansowana metoda analizy dynamicznej, kt\u00f3ra pozwala na badanie odpowiedzi ruroci\u0105gu na obci\u0105\u017cenia zmieniaj\u0105ce si\u0119 w czasie. W przeciwie\u0144stwie do analizy statycznej, gdzie si\u0142a jest sta\u0142a, tutaj sprawdzamy, co dzieje si\u0119 z uk\u0142adem sekunda po sekundzie lub milisekunda po milisekundzie. Mo\u017cna to por\u00f3wna\u0107 do nagrywania filmu z zachowania ruroci\u0105gu, zamiast robienia [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jureknawrocki.com\/en\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/\" \/>\n<meta property=\"og:site_name\" content=\"Jerzy Nawrocki\" \/>\n<meta property=\"article:published_time\" content=\"2026-03-20T07:10:40+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-20T07:10:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1213\" \/>\n\t<meta property=\"og:image:height\" content=\"803\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\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=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/\"},\"author\":{\"name\":\"Jerzy Nawrocki\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#\\\/schema\\\/person\\\/b2567f392defa8e7698c6813f7930563\"},\"headline\":\"Dynamika: AutoPipe \\\/ Caesar II Time History cz.VI\",\"datePublished\":\"2026-03-20T07:10:40+00:00\",\"dateModified\":\"2026-03-20T07:10:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/\"},\"wordCount\":389,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/1-8.jpg\",\"keywords\":[\"AutoPipe\",\"Caesar II\",\"Napr\u0119\u017cenia\"],\"articleSection\":[\"Obliczenia wytrzyma\u0142o\u015bciowe rur i aparat\u00f3w\",\"Z \u017cycia rzeczoznawcy\"],\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/\",\"name\":\"Dynamika: AutoPipe \\\/ Caesar II Time History cz.VI - Jerzy Nawrocki\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/1-8.jpg\",\"datePublished\":\"2026-03-20T07:10:40+00:00\",\"dateModified\":\"2026-03-20T07:10:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#primaryimage\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/1-8.jpg\",\"contentUrl\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/1-8.jpg\",\"width\":1213,\"height\":803},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/dynamika-autopipe-caesar-ii-time-history-cz-vi\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/jureknawrocki.com\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Dynamika: AutoPipe \\\/ Caesar II Time History cz.VI\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#website\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/\",\"name\":\"Jerzy Nawrocki\",\"description\":\"dr in\u017c., Rzeczoznawca Izby In\u017cynier\u00f3w, SIMP, NOT || Ruroci\u0105gi i aparaty ci\u015bnieniowe || Uprawnienia budowalne HVAC i Gaz || Spawalnictwo IWE&amp;I || Certyfikat LE w\\\/g EN 13313-Ch\u0142odnictwo i Pompy ciep\u0142a\",\"publisher\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/jureknawrocki.com\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#organization\",\"name\":\"Jerzy Nawrocki\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/Jerzy-Nawrocki-favicon.webp\",\"contentUrl\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/Jerzy-Nawrocki-favicon.webp\",\"width\":210,\"height\":211,\"caption\":\"Jerzy Nawrocki\"},\"image\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.linkedin.com\\\/in\\\/jerzy-nawrocki-a41259105\\\/?locale=pl_PL\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#\\\/schema\\\/person\\\/b2567f392defa8e7698c6813f7930563\",\"name\":\"Jerzy Nawrocki\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/7b00a3b1c70bebf45771a7abe522610a06106bc0b683d081ec8844ee1be51f5d?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/7b00a3b1c70bebf45771a7abe522610a06106bc0b683d081ec8844ee1be51f5d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/7b00a3b1c70bebf45771a7abe522610a06106bc0b683d081ec8844ee1be51f5d?s=96&d=mm&r=g\",\"caption\":\"Jerzy Nawrocki\"},\"sameAs\":[\"https:\\\/\\\/jureknawrocki.com\"],\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/en\\\/author\\\/admin-jn242\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Dynamika: AutoPipe \/ Caesar II Time History cz.VI - Jerzy Nawrocki","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jureknawrocki.com\/en\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/","og_locale":"en_GB","og_type":"article","og_title":"Dynamika: AutoPipe \/ Caesar II Time History cz.VI - Jerzy Nawrocki","og_description":"Analiza time history to najbardziej zaawansowana metoda analizy dynamicznej, kt\u00f3ra pozwala na badanie odpowiedzi ruroci\u0105gu na obci\u0105\u017cenia zmieniaj\u0105ce si\u0119 w czasie. W przeciwie\u0144stwie do analizy statycznej, gdzie si\u0142a jest sta\u0142a, tutaj sprawdzamy, co dzieje si\u0119 z uk\u0142adem sekunda po sekundzie lub milisekunda po milisekundzie. Mo\u017cna to por\u00f3wna\u0107 do nagrywania filmu z zachowania ruroci\u0105gu, zamiast robienia [&hellip;]","og_url":"https:\/\/jureknawrocki.com\/en\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/","og_site_name":"Jerzy Nawrocki","article_published_time":"2026-03-20T07:10:40+00:00","article_modified_time":"2026-03-20T07:10:41+00:00","og_image":[{"width":1213,"height":803,"url":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8.jpg","type":"image\/jpeg"}],"author":"Jerzy Nawrocki","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Jerzy Nawrocki","Estimated reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#article","isPartOf":{"@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/"},"author":{"name":"Jerzy Nawrocki","@id":"https:\/\/jureknawrocki.com\/#\/schema\/person\/b2567f392defa8e7698c6813f7930563"},"headline":"Dynamika: AutoPipe \/ Caesar II Time History cz.VI","datePublished":"2026-03-20T07:10:40+00:00","dateModified":"2026-03-20T07:10:41+00:00","mainEntityOfPage":{"@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/"},"wordCount":389,"commentCount":0,"publisher":{"@id":"https:\/\/jureknawrocki.com\/#organization"},"image":{"@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#primaryimage"},"thumbnailUrl":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8.jpg","keywords":["AutoPipe","Caesar II","Napr\u0119\u017cenia"],"articleSection":["Obliczenia wytrzyma\u0142o\u015bciowe rur i aparat\u00f3w","Z \u017cycia rzeczoznawcy"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/","url":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/","name":"Dynamika: AutoPipe \/ Caesar II Time History cz.VI - Jerzy Nawrocki","isPartOf":{"@id":"https:\/\/jureknawrocki.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#primaryimage"},"image":{"@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#primaryimage"},"thumbnailUrl":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8.jpg","datePublished":"2026-03-20T07:10:40+00:00","dateModified":"2026-03-20T07:10:41+00:00","breadcrumb":{"@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#primaryimage","url":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8.jpg","contentUrl":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/1-8.jpg","width":1213,"height":803},{"@type":"BreadcrumbList","@id":"https:\/\/jureknawrocki.com\/dynamika-autopipe-caesar-ii-time-history-cz-vi\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/jureknawrocki.com\/"},{"@type":"ListItem","position":2,"name":"Dynamika: AutoPipe \/ Caesar II Time History cz.VI"}]},{"@type":"WebSite","@id":"https:\/\/jureknawrocki.com\/#website","url":"https:\/\/jureknawrocki.com\/","name":"Jerzy Nawrocki","description":"dr in\u017c., Rzeczoznawca Izby In\u017cynier\u00f3w, SIMP, NOT || Ruroci\u0105gi i aparaty ci\u015bnieniowe || Uprawnienia budowalne HVAC i Gaz || Spawalnictwo IWE&amp;I || Certyfikat LE w\/g EN 13313-Ch\u0142odnictwo i Pompy ciep\u0142a","publisher":{"@id":"https:\/\/jureknawrocki.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/jureknawrocki.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/jureknawrocki.com\/#organization","name":"Jerzy Nawrocki","url":"https:\/\/jureknawrocki.com\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/jureknawrocki.com\/#\/schema\/logo\/image\/","url":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Jerzy-Nawrocki-favicon.webp","contentUrl":"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Jerzy-Nawrocki-favicon.webp","width":210,"height":211,"caption":"Jerzy Nawrocki"},"image":{"@id":"https:\/\/jureknawrocki.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.linkedin.com\/in\/jerzy-nawrocki-a41259105\/?locale=pl_PL"]},{"@type":"Person","@id":"https:\/\/jureknawrocki.com\/#\/schema\/person\/b2567f392defa8e7698c6813f7930563","name":"Jerzy Nawrocki","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/secure.gravatar.com\/avatar\/7b00a3b1c70bebf45771a7abe522610a06106bc0b683d081ec8844ee1be51f5d?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/7b00a3b1c70bebf45771a7abe522610a06106bc0b683d081ec8844ee1be51f5d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/7b00a3b1c70bebf45771a7abe522610a06106bc0b683d081ec8844ee1be51f5d?s=96&d=mm&r=g","caption":"Jerzy Nawrocki"},"sameAs":["https:\/\/jureknawrocki.com"],"url":"https:\/\/jureknawrocki.com\/en\/author\/admin-jn242\/"}]}},"_links":{"self":[{"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/posts\/3418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/comments?post=3418"}],"version-history":[{"count":5,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/posts\/3418\/revisions"}],"predecessor-version":[{"id":3432,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/posts\/3418\/revisions\/3432"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/media\/3421"}],"wp:attachment":[{"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/media?parent=3418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/categories?post=3418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jureknawrocki.com\/en\/wp-json\/wp\/v2\/tags?post=3418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}