{"id":2828,"date":"2025-03-20T12:23:11","date_gmt":"2025-03-20T11:23:11","guid":{"rendered":"https:\/\/jureknawrocki.com\/?p=2828"},"modified":"2026-02-24T12:07:51","modified_gmt":"2026-02-24T11:07:51","slug":"sztywnosc-kroccow-cz-ii","status":"publish","type":"post","link":"https:\/\/jureknawrocki.com\/en\/sztywnosc-kroccow-cz-ii\/","title":{"rendered":"Nozzel's stiffness II"},"content":{"rendered":"<p>When modernizing old installations, exceedances on the nozzles very often occur. Usually, on such occasions we hear: \"<em>Why do you want to strengthen the nozzle on the equipment? After all, the installation is working several dozen years and nothing has happened<\/em>\"The secret lies primarily in the much lower stiffness <strong>nozzle-equipment-foundation system <\/strong>than it is assumed in pipe stress programs, i.e. in the phenomenon <strong>compound stiffness. <\/strong><\/p>\n\n\n\n<p>Let's consider the composite stiffness itself. In pipeline technology, it is used in the case of equipment on flexible support structures, such as those shown below. The stiffness determined for the equipment's nozzles in isolation from the entire device is a mistake. In an ideal situation, the stiffness of the nozzles should be issued by the manufacturer. Of course, this is a very rare case. If someone is interested in how to determine the stiffness of the nozzle themselves, I encourage you to read Part I - <a href=\"https:\/\/jureknawrocki.com\/en\/sztywnosc-kroccow-pomijany-ale-wazny-temat\/\">HERE<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"737\" height=\"524\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Sztywnosc-kroccow-cz-II.jpg\" alt=\"\" class=\"wp-image-2830\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Sztywnosc-kroccow-cz-II.jpg 737w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/Sztywnosc-kroccow-cz-II-480x341.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 737px, 100vw\" \/><\/figure>\n\n\n\n<p>Due to lack of time I will not model such a complex support structure, which can be seen in the above photo. Let's assume that we have a much simplified support structure of the camera, as in the drawing below. For the description of the concept of complex stiffness it does not matter.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"582\" height=\"514\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-2.jpg\" alt=\"\" class=\"wp-image-2842\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-2.jpg 582w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-2-480x424.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 582px, 100vw\" \/><\/figure>\n\n\n\n<p>From the above figure, the directional stiffness of the equipment's frame can be determined, e.g. KFx = 1 kN\/mm. We proceed in this way for all six degrees of freedom. For example, in the X direction, the stiffness KNx = 3 kN\/mm.<\/p>\n\n\n\n<p>Compound stiffness <strong>nozzle-equipment-foundation system <\/strong>is the equation of a simple relationship. For each degree of freedom, it is the reciprocal of the sum of the reciprocals of the stiffness of the stub pipe and the frame.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"171\" src=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-3.jpg\" alt=\"\" class=\"wp-image-2849\" srcset=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-3.jpg 400w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-3-300x128.jpg 300w, https:\/\/jureknawrocki.com\/wp-content\/uploads\/sztywnosc-zlozona-II-3-18x8.jpg 18w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/figure>","protected":false},"excerpt":{"rendered":"<p>Przy modernizacjach starych instalacji bardzo cz\u0119sto wychodz\u0105 przekroczenia na kr\u00f3\u0107cach. Zwykle przy takiej okazji s\u0142yszymy: &#8222;Czemu Pan chce wzmacnia\u0107 kr\u00f3\u0107ce na aparacie? Przecie\u017c instalacja chodzi o kilkudzeisieciu lat i nic si\u0119 nie dzieje&#8222;. Tajeminca tkwi przede wszystkim w znacznie ni\u017cszej sztywno\u015bci uk\u0142adu kr\u00f3ciec-aparat-fundament ni\u017c to jest przyjmowane w programach pipe stresowych czyli w zjawisku sztywno\u015bci [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":2830,"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":[32,16],"class_list":["post-2828","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>Sztywno\u015b\u0107 kr\u00f3\u0107c\u00f3w cz II - 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\/sztywnosc-kroccow-cz-ii\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sztywno\u015b\u0107 kr\u00f3\u0107c\u00f3w cz II - Jerzy Nawrocki\" \/>\n<meta property=\"og:description\" content=\"Przy modernizacjach starych instalacji bardzo cz\u0119sto wychodz\u0105 przekroczenia na kr\u00f3\u0107cach. Zwykle przy takiej okazji s\u0142yszymy: &#8222;Czemu Pan chce wzmacnia\u0107 kr\u00f3\u0107ce na aparacie? Przecie\u017c instalacja chodzi o kilkudzeisieciu lat i nic si\u0119 nie dzieje&#8222;. Tajeminca tkwi przede wszystkim w znacznie ni\u017cszej sztywno\u015bci uk\u0142adu kr\u00f3ciec-aparat-fundament ni\u017c to jest przyjmowane w programach pipe stresowych czyli w zjawisku sztywno\u015bci [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jureknawrocki.com\/en\/sztywnosc-kroccow-cz-ii\/\" \/>\n<meta property=\"og:site_name\" content=\"Jerzy Nawrocki\" \/>\n<meta property=\"article:published_time\" content=\"2025-03-20T11:23:11+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-24T11:07:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/jureknawrocki.com\/wp-content\/uploads\/Sztywnosc-kroccow-cz-II.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"737\" \/>\n\t<meta property=\"og:image:height\" content=\"524\" \/>\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=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/sztywnosc-kroccow-cz-ii\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/sztywnosc-kroccow-cz-ii\\\/\"},\"author\":{\"name\":\"Jerzy Nawrocki\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#\\\/schema\\\/person\\\/b2567f392defa8e7698c6813f7930563\"},\"headline\":\"Sztywno\u015b\u0107 kr\u00f3\u0107c\u00f3w cz II\",\"datePublished\":\"2025-03-20T11:23:11+00:00\",\"dateModified\":\"2026-02-24T11:07:51+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/sztywnosc-kroccow-cz-ii\\\/\"},\"wordCount\":280,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/sztywnosc-kroccow-cz-ii\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/jureknawrocki.com\\\/wp-content\\\/uploads\\\/Sztywnosc-kroccow-cz-II.jpg\",\"keywords\":[\"MES\",\"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\\\/sztywnosc-kroccow-cz-ii\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/jureknawrocki.com\\\/sztywnosc-kroccow-cz-ii\\\/\",\"url\":\"https:\\\/\\\/jureknawrocki.com\\\/sztywnosc-kroccow-cz-ii\\\/\",\"name\":\"Sztywno\u015b\u0107 kr\u00f3\u0107c\u00f3w cz II - 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