{"id":559862,"date":"2024-11-05T18:25:24","date_gmt":"2024-11-05T18:25:24","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-tm-1192002\/"},"modified":"2024-11-05T18:25:24","modified_gmt":"2024-11-05T18:25:24","slug":"esdu-tm-1192002","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-tm-1192002\/","title":{"rendered":"ESDU TM 119:2002"},"content":{"rendered":"<p><strong>INTRODUCTION<\/strong><\/p>\n<p>Stress analysis and rigid body motion are just two of the fields<br \/>\nof mechanics in which area and area moment properties are<br \/>\nfrequently required. Such properties.<\/p>\n<p>where distances are measured from some moment axis to the<br \/>\nelemental area and the integration is applied over the whole of the<br \/>\narea of interest (the zero<sup>th<\/sup> moment when <i>n<\/i> =<br \/>\n0\u00a0gives the area).<\/p>\n<p>In the numerous text books that derive the various moments, a<br \/>\ncartesian approach is invariably taken whereby the shape of<br \/>\ninterest is decomposed into essentially rectangular elements in<br \/>\norder for the integration to be applied. This approach is perfectly<br \/>\nacceptable for the relatively simple shapes that are normally<br \/>\nconsiderd but becomes less so when the shape is complex. The<br \/>\napproach becomes particularly messy when shapes with re-entrant<br \/>\nboundaries are to be analysed.<\/p>\n<p>In this note an alternative, pseudo polar, approach is developed<br \/>\nin which a triangular &#034;slice&#034; element is used for the required<br \/>\nintegration. It is demonstrated that such an approach leads to<br \/>\neasily implemented computational algorithms that are general and<br \/>\ncan cope with shapes of arbitrary complexity. Having obtained the<br \/>\narea and moment properties, the mass-based properties can be easily<br \/>\ncalculated for a real shape, or plate, of finite thickness.<\/p>\n","protected":false},"excerpt":{"rendered":"<p><b>Calculation of Planar Area and Moment Properties &#8211; Theoretical Background<\/b><\/p>\n<table style=\"width: 100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td>Published By<\/td>\n<td>Publication Date<\/td>\n<td>Number of Pages<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/pdfstandards.shop\/product-category\/publishers\/esdu\/\"><b>ESDU<\/b><\/a><\/td>\n<td>2002-05<\/td>\n<td>16<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":559872,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-559862","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-esdu","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/559862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/559872"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=559862"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=559862"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=559862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}