{"id":2592,"date":"2024-08-06T17:47:58","date_gmt":"2024-08-06T12:17:58","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=2592"},"modified":"2025-07-16T15:24:56","modified_gmt":"2025-07-16T09:54:56","slug":"composite-beams","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/strength-of-material\/composite-beams","title":{"rendered":"What is a Composite Beam in Strength of Materials?"},"content":{"rendered":"<p style=\"text-align: justify;\">A beam that is built from more than one material is known as composite beams. Example are bimetallic<br \/>\nbeams, flitched beams and reinforced concrete beam as shown.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2531 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/bimetallic-beam.jpg\" alt=\"Bimetallic Beam\" width=\"401\" height=\"144\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/bimetallic-beam.jpg 401w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/bimetallic-beam-300x108.jpg 300w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><strong>The materials in composite beam can be:<\/strong><\/h2>\n<p style=\"text-align: justify;\">(a) Simply placed over one another<br \/>\n(b) Rigidly connected<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/strength-of-material\/composite-beams\/#a-Simply-placed-over-one-another\" >a) Simply placed over one another<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/strength-of-material\/composite-beams\/#b-Rigidly-connected\" >(b) Rigidly connected<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/strength-of-material\/composite-beams\/#FLITCHED-BEAM\" >FLITCHED BEAM<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"a-Simply-placed-over-one-another\"><\/span><strong>a) Simply placed over one another<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Consider a beam section in which two different materials (1) and (2) are used to make the section with their Young\u2019s modulus of elasticity E1 and E2 respectively. There is no bond between material (1) and (2) so they will bend independently about their own neutral axis and their stress distribution diagram is shown in figure.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2532 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/stress-distribution.jpg\" alt=\"Stress Distribution\" width=\"397\" height=\"154\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/stress-distribution.jpg 397w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/stress-distribution-300x116.jpg 300w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/p>\n<p style=\"text-align: justify;\">However, it is assumed that radius of curvature at junctions of both the materials is same So, R1 = R<\/p>\n<p style=\"text-align: justify;\">From flexure formula, R = Ey\/\u03c3<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2534 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/bending-stress-.jpg\" alt=\"Bending Stress \" width=\"636\" height=\"277\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/bending-stress-.jpg 636w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/bending-stress--300x131.jpg 300w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"b-Rigidly-connected\"><\/span><strong>(b) Rigidly connected<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">When different materials are rigidly connected to make the cross-section, then there is a common neutral axis and they behave like a single beam. But the position of neutral axis will not be the centroid of section because materials are different so the assumption of homogeneity does not apply here.<br \/>\nHowever, if by any method, section is converted in terms of any one material, then neutral axis will coincide with the centroid of equivalent section. In such types of beam bending strain diagram is linear hence strain in two material at a given vertical distance from NA will be same which is called strain compatibility condition. To convert one section into other, concept of modular ratio is used which is defined as ratio of modulus of elasticity of both the materials. In this method, width of one material is multiplied by modular ratio. Thus two types of method that can be used to analyse composite beam in which materials are rigidly connected are illustrated below with the help of analysis of flitched beam.<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"FLITCHED-BEAM\"><\/span>FLITCHED BEAM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Top and bottom flitched beam<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Method-1<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2535 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/flitched-beam.jpg\" alt=\"Flitched Beam\" width=\"432\" height=\"232\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/flitched-beam.jpg 432w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/flitched-beam-300x161.jpg 300w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/p>\n<p style=\"text-align: justify;\">By strain compatibility; strain in steel = Strain in wood<\/p>\n<p style=\"text-align: center;\">\u03b5<sub>s<\/sub> = \u03b5<sub>w<\/sub><\/p>\n<p style=\"text-align: center;\">\u03c3<sub>s<\/sub>\/E<sub>s<\/sub> = \u03c3<sub>w<\/sub>\/E<sub>w<\/sub><\/p>\n<p style=\"text-align: center;\">\u03c3<sub>s<\/sub>\/\u03c3<sub>w<\/sub> = E<sub>s<\/sub>\/E<sub>w<\/sub> = m (modular ratio)<\/p>\n<p style=\"text-align: center;\">At same level, if stress in steel is \u03c3<sub>s<\/sub>, then corresponding stress in wood will be<\/p>\n<p style=\"text-align: center;\">\u03c3<sub>w<\/sub> = \u03c3<sub>s<\/sub>\/m<\/p>\n<p style=\"text-align: center;\">\u03c3<sub>s<\/sub> = m\u03c3<sub>w<\/sub><\/p>\n<p style=\"text-align: justify;\">Let permissible stress in wood is \u03c3<sub>w<\/sub><br \/>\nPermissible stress in steel is \u03c3<sub>s&#8217;max<\/sub><br \/>\nStress in steel at junction of wood is \u03c3<sub>s<\/sub><br \/>\nThen, moment of resistance of wood section,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2536 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/permissible-stress.jpg\" alt=\"Permissible Stress\" width=\"568\" height=\"175\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/permissible-stress.jpg 568w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/permissible-stress-300x92.jpg 300w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Method-2<\/strong><br \/>\nMoment of resistance of top and bottom flitched beam can be calculated by converting heterogeneous section into either equivalent wooden section or steel section as shown in figure.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2537 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/equivalent-steel.jpg\" alt=\"Equivalent steel\" width=\"560\" height=\"319\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/equivalent-steel.jpg 560w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/equivalent-steel-300x171.jpg 300w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2538 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/wood-section.jpg\" alt=\"Wood section\" width=\"515\" height=\"280\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/wood-section.jpg 515w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/wood-section-300x163.jpg 300w\" sizes=\"auto, (max-width: 515px) 100vw, 515px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2539 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/steel-section.jpg\" alt=\"Steel section\" width=\"583\" height=\"290\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/steel-section.jpg 583w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/steel-section-300x149.jpg 300w\" sizes=\"auto, (max-width: 583px) 100vw, 583px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Side flitched beam<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2540 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/side-flitched-beam.jpg\" alt=\"Side Flitched Beam\" width=\"501\" height=\"195\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/side-flitched-beam.jpg 501w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/side-flitched-beam-300x117.jpg 300w\" sizes=\"auto, (max-width: 501px) 100vw, 501px\" \/><br \/>\n<\/strong><\/p>\n<p style=\"text-align: justify;\">Moment of resistance of wood, MOR<sub>w<\/sub> = \u03c3w x bd<sup>2<\/sup>\/6<\/p>\n<p style=\"text-align: justify;\">Moment of resistance of steel, MORs = \u03c3s x 2td2\/6<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2542 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/heterogeneous.jpg\" alt=\"Heterogeneous\" width=\"641\" height=\"430\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/heterogeneous.jpg 641w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/heterogeneous-300x201.jpg 300w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/p>\n<p style=\"text-align: justify;\">Modulus of elasticity of aluminium = E<sub>a<\/sub><br \/>\nModulus of elasticity of steel = E<sub>s<\/sub><\/p>\n<p style=\"text-align: justify;\">Modulus ratio, m = E<sub>s\u00a0<\/sub>\/E<sub>a<\/sub><\/p>\n<p style=\"text-align: justify;\">Let the heterogeneous section is converted into equivalent aluminium section by multiplying width of steel section by modulus.<\/p>\n<p style=\"text-align: justify;\">Permissible stress in aluminium = \u03c3<sub>a<\/sub><br \/>\nPermissible stress in steel = \u03c3<sub>s<\/sub><\/p>\n<p style=\"text-align: justify;\">First of all, we have to find moment of inertia of equivalent aluminium section about its neutral axis.<\/p>\n<p style=\"text-align: justify;\">Location of neutral axis from top = \u222bydA\/\u222bdA<\/p>\n<p style=\"text-align: justify;\">After calculating location of neutral axis, let the moment of inertia calculated is I.<\/p>\n<p style=\"text-align: justify;\">Let, the distance of top and bottom fibre of equivalent aluminium section from neutral axis is y<sub>t<\/sub> and y<sub>b<\/sub> respectively as shown.<br \/>\nIts section modulus will be different in tension and compression as the section is unsymmetrical.<\/p>\n<p style=\"text-align: justify;\">Maximum stress at top of section = \u03c3<sub>a<\/sub><br \/>\nMaximum stress at bottom of section,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2543 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/heterogeneous-1.jpg\" alt=\"Heterogeneous\" width=\"477\" height=\"171\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/heterogeneous-1.jpg 477w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/heterogeneous-1-300x108.jpg 300w\" sizes=\"auto, (max-width: 477px) 100vw, 477px\" \/><\/p>\n<p style=\"text-align: justify;\">Moment of resistance of section is taken as lesser of MOR<sub>1<\/sub> and MOR<sub>2<\/sub><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/strength-of-material\/principal-stresses\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/strength-of-material\/beam-of-uniform-strength\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-strength-of-material\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Strength of Material?<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A beam that is built from more than one material is known as composite beams. Example are bimetallic beams, flitched<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[685,2],"tags":[696,710,711],"class_list":["post-2592","post","type-post","status-publish","format-standard","hentry","category-strength-of-material","category-ce","tag-flitched-beam","tag-rigidly-connected","tag-side-flitched-beam"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2592","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=2592"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2592\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=2592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=2592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=2592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}