{"id":36089,"date":"2024-04-01T10:00:02","date_gmt":"2024-04-01T08:00:02","guid":{"rendered":"https:\/\/arvengtraining.com\/?p=36089"},"modified":"2024-03-27T10:26:56","modified_gmt":"2024-03-27T09:26:56","slug":"asme-section-viii-div-2-part-5-dba-why-is-the-limit-2-x-sy-important-elastic-shakedown","status":"publish","type":"post","link":"https:\/\/arvengtraining.com\/en\/asme-section-viii-div-2-part-5-dba-why-is-the-limit-2-x-sy-important-elastic-shakedown\/","title":{"rendered":"ASME Section VIII Div.2, Part 5 (DBA). Why is the limit 2 x Sy important? Elastic Shakedown"},"content":{"rendered":"<p>Let\u2019s consider, for example, a fully pressurized pressure vessel with a load applied on the nozzle as shown in the picture. This load creates a bending stress (secondary stress) at the nozzle-to-head juncture. In the left-hand side of the nozzle, this load creates a tension strain value \u03b5<sub>1<\/sub> (see below), somewhat beyond the yield strain as shown in the picture<em>. <\/em>Since we are considering the case of a secondary stress, we shall assume that the nature of the loading is such as to cycle the strain from zero to \u03b5<sub>1<\/sub> and back to zero (self-limiting). When the load is removed, a residual compressive stress will be present in the area of the juncture under study.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-36098 aligncenter\" src=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-690x400.png\" alt=\"\" width=\"690\" height=\"400\" srcset=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-690x400.png 690w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-1024x593.png 1024w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-150x87.png 150w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-1536x890.png 1536w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-840x487.png 840w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.2-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png 1881w\" sizes=\"auto, (max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>Let\u2019s give this a closer look. As indicated, the applied load has created a tension strain value \u03b5<sub>1<\/sub>, somewhat beyond the yield strain as shown in the path 0AB (see below). The calculated elastic stress would be S<sub>1<\/sub>=E x \u03b5<sub>1<\/sub>. When the load is removed, a residual compressive stress \u2013S<sub>1<\/sub> will be present. In fact, the magnitude of the residual compressive stress is S<sub>1<\/sub> &#8211; S<sub>y<\/sub>. On any subsequent loading, this residual compression must be removed before the stress goes into tension and thus the elastic range has been increased by the quantity S<sub>1<\/sub> &#8211; S<sub>y<\/sub>. <strong>This is known as Elastic shakedown.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-36100 aligncenter\" src=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.3-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png\" alt=\"\" width=\"214\" height=\"316\" srcset=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.3-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png 214w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.3-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-102x150.png 102w\" sizes=\"auto, (max-width: 214px) 100vw, 214px\" \/><\/p>\n<p>Now, let\u2019s assume that on a subsequent cycle the load applied moves the strain up to point D (see below), this corresponds with \u03b5<sub>2<\/sub>. The calculated elastic stress that corresponds to this strain value would be S<sub>2<\/sub>=E x \u03b5<sub>2<\/sub>. It can be observed that S<sub>2<\/sub> &gt; 2S<sub>y<\/sub>. Since the magnitude of the residual compressive stress will remain the same, now the unloading line arrives to point E, showing that the external fiber of the nozzle yields in compression with the corresponding plastic strain. If the cyclic load is not increased on subsequent cycles, no additional plastic strain will accumulate. <strong>This is known as plastic shakedown.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-36102 aligncenter\" src=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.4-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png\" alt=\"\" width=\"209\" height=\"321\" srcset=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.4-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png 209w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.4-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-98x150.png 98w\" sizes=\"auto, (max-width: 209px) 100vw, 209px\" \/><\/p>\n<p>From this analysis, it can be observed that as long as the stress levels induced by the load (S<sub>1<\/sub>), are lower or equal to two times S<sub>y<\/sub>, the elastic range becomes 2 S<sub>y<\/sub> and the calculated secondary elastic stress will &#8220;shake down&#8221; to purely elastic action. <strong>This explains why the limit imposed by building codes on secondary stresses, or rather their variation, is exactly twice the elastic limit.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-36104 aligncenter\" src=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.5-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png\" alt=\"\" width=\"215\" height=\"316\" srcset=\"https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.5-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown.png 215w, https:\/\/arvengtraining.com\/wp-content\/uploads\/2024\/04\/4.5-ASME-VIII-Div.2-Part-5-DBA.-Why-is-the-limit-2-x-Sy-important-Elastic-Shakedown-102x150.png 102w\" sizes=\"auto, (max-width: 215px) 100vw, 215px\" \/><\/p>\n<p>For more information:<\/p>\n<p><a href=\"https:\/\/arvengtraining.com\/en\/all-courses\/asme-viii-design-pressure-vessels-online\/\">ASME VIII | Design of Pressure Vessels for Industrial Plants<\/a><\/p>\n<p><a href=\"https:\/\/arvengtraining.com\/en\/all-courses\/asme-viii-div-2-design-of-pressure-vessels-by-analysis-live-course\/\">ASME VIII Div. 2 | Design of Pressure Vessels by Analysis<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let\u2019s consider, for example, a fully pressurized pressure vessel with a load applied on the nozzle as shown in the picture. This load creates a bending stress (secondary stress) at the nozzle-to-head juncture. In the left-hand side of the nozzle, this load creates a tension strain value \u03b51 (see below), somewhat beyond the yield strain [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":36107,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[323,325],"tags":[613],"class_list":["post-36089","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-piping-en","category-static-equipment-en","tag-asme-viii-div-2-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>ASME Section VIII Div.2, Part 5 (DBA). Why is the limit 2 x Sy important? 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