{"id":2034,"date":"2024-07-31T21:01:00","date_gmt":"2024-07-31T21:01:00","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2034"},"modified":"2024-07-31T21:01:01","modified_gmt":"2024-07-31T21:01:01","slug":"extension-in-varying-cross-section-or-taper-rod","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/31\/extension-in-varying-cross-section-or-taper-rod\/","title":{"rendered":"EXTENSION IN VARYING CROSS-SECTION OR TAPER ROD"},"content":{"rendered":"\n

A rod of length\u00a0l<\/em>\u00a0tapers uniformly from a diameter\u00a0D<\/em>\u00a0at one end to diameter\u00a0d<\/em>\u00a0at other end as shown in\u00a0Figure 12.8.\u00a0Considering an small element of thickness\u00a0dx<\/em>\u00a0at distance\u00a0x<\/em>\u00a0from the end of diameter\u00a0d<\/em>, the diameter of the element is calculated as\u00a0\"equation\"<\/p>\n\n\n\n

\"equation\"\/<\/figure>\n\n\n\n
\"Figure<\/figure>\n\n\n\n

Figure 12.8<\/strong> Extension in Taper Rod<\/p>\n\n\n\n

Example 12.4:<\/strong> A rod tapers uniformly from 50 to 20 mm diameter in a length of 500 mm. If the rod is subjected to an axial load of 10 kN, find the extension in the rod. Assume E<\/em> = 2 \u00d7 105<\/sup> MPa.<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Example 12.5:<\/strong> Determine the elongation of a conical bar under the action of its own weight, if the length of the bar is L<\/em>, the diameter of the base is D<\/em>, and the weight per unit volume of the material is \u03c1<\/em>.<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Consider a section of small length\u00a0dx<\/em>\u00a0at a height\u00a0x<\/em>\u00a0from the apex cone (as shown in\u00a0Figure 12.9) where the diameter is\u00a0\"equation\", and weight of the cone below the section,\u00a0\"equation\"<\/p>\n\n\n\n

\"Figure<\/figure>\n\n\n\n

Figure 12.9<\/strong> Conical Bar<\/p>\n\n\n\n

<\/a>Elongation in the section \"equation\"<\/p>\n\n\n\n

Total elongation of the bar, \"equation\"<\/p>\n","protected":false},"excerpt":{"rendered":"

A rod of length\u00a0l\u00a0tapers uniformly from a diameter\u00a0D\u00a0at one end to diameter\u00a0d\u00a0at other end as shown in\u00a0Figure 12.8.\u00a0Considering an small element of thickness\u00a0dx\u00a0at distance\u00a0x\u00a0from the end of diameter\u00a0d, the diameter of the element is calculated as\u00a0 Figure 12.8 Extension in Taper Rod Example 12.4: A rod tapers uniformly from 50 to 20 mm diameter in a length […]<\/p>\n","protected":false},"author":1,"featured_media":2035,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[344],"tags":[],"class_list":["post-2034","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-strain-and-stress"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/07\/download-18.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2034","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2034"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2034\/revisions"}],"predecessor-version":[{"id":2036,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2034\/revisions\/2036"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2035"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}