{"id":5072,"date":"2025-07-14T10:10:09","date_gmt":"2025-07-14T04:40:09","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=5072"},"modified":"2025-07-18T14:54:38","modified_gmt":"2025-07-18T09:24:38","slug":"analysis-of-stress-in-pure-bending","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/strength-of-materials\/analysis-of-stress-in-pure-bending","title":{"rendered":"Analysis of stress in pure bending"},"content":{"rendered":"<h2>Normal Stresses in beams<\/h2>\n<p>As per Hooke\u2019s law, \u03b5x = \u03c3\/E<\/p>\n<p>Here, \u03c3 is the bending stress in longitudinal direction and E is the Young\u2019s modulus of elasticity.<\/p>\n<p>\u03c3\/E = y\/R<\/p>\n<p>\u03c3\/y = E\/R<\/p>\n<p>In simply supported beam, when subjected to downward loading bending stresses are compressive above neutral axis while these are tensile below the neutral axis.<\/p>\n<p>Due to these stress, a moment is produced which is bending moment for the section and it acts along z-axis.<br \/>\nAs the resultant force in x-direction is zero.<\/p>\n<p>\u222b 0xdA = O [\u2235 There is no other horizontal force]<\/p>\n<p>When dA is small area element on cross-section on section.<\/p>\n<p>\u03c3\/y = E\/R<\/p>\n<p>\u03c3= Ey\/R &#8230;(v)<\/p>\n<p>Putting eq. (v) in (iv), \u222b Ey\/R dA =0<\/p>\n<p>As E and R are constant, \u222bydA=0<\/p>\n<p>Eq. (vi) implies that neutral axis which is in z-direction passes through centroid of section.<br \/>\nAlso, resultant moment acting on section is equal to bending moment say M, then<\/p>\n<p>M= \u222b \u03c3, ydA<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5073 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/07\/Moment-on-section-.jpg\" alt=\"Moment on section \" width=\"540\" height=\"356\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/07\/Moment-on-section-.jpg 540w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/07\/Moment-on-section--300x198.jpg 300w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Normal Stresses in beams As per Hooke\u2019s law, \u03b5x = \u03c3\/E Here, \u03c3 is the bending stress in longitudinal direction<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1619,10],"tags":[1650,1651],"class_list":["post-5072","post","type-post","status-publish","format-standard","hentry","category-strength-of-materials","category-me","tag-moment-on-section-x-x","tag-youngs-modulus-of-elasticity"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5072","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=5072"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5072\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5072"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5072"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5072"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}