{"id":2041,"date":"2024-07-31T21:07:41","date_gmt":"2024-07-31T21:07:41","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2041"},"modified":"2024-07-31T21:07:42","modified_gmt":"2024-07-31T21:07:42","slug":"temperature-stress","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/31\/temperature-stress\/","title":{"rendered":"\u00a0TEMPERATURE STRESS"},"content":{"rendered":"\n

If the temperature of a material is increased, there will be expansion in the material (except ice) and if the temperature is decreased, there will be contraction in the material. If these expansion and contraction occur freely there will be no stress in the material and if these expansion or contraction is prevented then stress will be setup in the material which is known as temperature of thermal stress.<\/p>\n\n\n\n

 <\/p>\n\n\n\n

\u03b4l<\/em> = l<\/em>0<\/sub>\u03b1<\/em>\u0394t<\/em><\/p>\n\n\n\n

 <\/p>\n\n\n\n

where \u03b4l<\/em> is change in length; l<\/em>0<\/sub> is original length; \u03b1<\/em> is coefficient of linear expansion; and \u0394t<\/em> is change in temperature.<\/p>\n\n\n\n

 <\/p>\n\n\n\n

Thermal stress = E<\/em>\u03b1\u0394t<\/em><\/p>\n\n\n\n

Example 12.11:<\/strong>\u00a0A composite bar consisting of aluminium and steel components as shown in\u00a0Figure 12.19\u00a0is connected to two grips at the ends at a temperature of 100\u00b0C. Find the stress in the two rods when the temperature falls to 60\u00b0C (i) if ends do not yields, and (ii) if ends yield by 0.5 mm. Assume\u00a0E<\/em>steel<\/sub>\u00a0= 2 \u00d7 105<\/sup>\u00a0MPa,\u00a0E<\/em>Al<\/sub>\u00a0= 0.7 \u00d7 105<\/sup>\u00a0MPa,\u00a0\u03b1<\/em>steel<\/sub>\u00a0= 1.17 \u00d7 10\u22125<\/sup>\u00a0per degree centigrade,\u00a0\u03b1<\/em>Al<\/sub>\u00a0= 2.34 \u00d7 10\u22125<\/sup>\u00a0per degree centigrade. Cross-sectional areas of aluminium and steel bars are 400 and 250 mm2<\/sup>, respectively.<\/p>\n\n\n\n

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

Figure 12.19<\/strong> Compositer Bars with Fixed Ends<\/p>\n\n\n\n

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

There is contraction in the bars due to decrease in temperature.<\/p>\n\n\n\n

If contraction is free change in length,<\/p>\n\n\n\n

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

When contraction is prevented tensile stress are produced in the rod.<\/p>\n\n\n\n

Loads in two rods will be same.<\/p>\n\n\n\n

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

Case I:<\/em><\/strong> When ends do not yield.<\/p>\n\n\n\n

Total contraction = Contraction in aluminium + Contraction in steel<\/p>\n\n\n\n

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

Case II:<\/em><\/strong> When the ends yield by 0.5 mm.<\/p>\n\n\n\n

\"equation\"\/<\/figure>\n\n\n\n
12.9  STRESS AND STRAIN DUE TO SUDDENLY APPLIED LOAD<\/h5>\n\n\n\n

Suppose\u00a0W<\/em>\u00a0is a load suddenly applied on the collar of a rod and extension due to the load application is\u00a0\u03b4l<\/em>\u00a0as shown in\u00a0Figure 12.20 (a). The original length of the rod is\u00a0l<\/em>. The work done by the load\u00a0W<\/em>\u00a0is\u00a0U<\/em>\u00a0=\u00a0W<\/em>\u00a0\u00d7\u00a0\u03b4l<\/em><\/p>\n\n\n\n

Now consider the equivalent weight for same work is P<\/em> which is applied gradually.<\/p>\n\n\n\n

Work done by gradually applied load\u00a0P<\/em>\u00a0[Figure 12.20 (b)],<\/p>\n\n\n\n

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

Figure 12.20<\/strong> (a) Suddenly Applied Load W on a Rod and (b) Load and Deflection Graph for Equivalent Gradually Applied Load<\/p>\n\n\n\n

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

Hence, gradually applied load for same work done is equal to two times of suddenly applied load.<\/p>\n\n\n\n

Stress produced, \"equation\"<\/p>\n","protected":false},"excerpt":{"rendered":"

If the temperature of a material is increased, there will be expansion in the material (except ice) and if the temperature is decreased, there will be contraction in the material. If these expansion and contraction occur freely there will be no stress in the material and if these expansion or contraction is prevented then stress […]<\/p>\n","protected":false},"author":1,"featured_media":2042,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[344],"tags":[],"class_list":["post-2041","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-19.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2041","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=2041"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2041\/revisions"}],"predecessor-version":[{"id":2043,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2041\/revisions\/2043"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2042"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}