{"id":156720,"date":"2023-09-01T14:51:55","date_gmt":"2023-09-01T09:21:55","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156720"},"modified":"2023-09-01T14:54:24","modified_gmt":"2023-09-01T09:24:24","slug":"consider-a-linear-elastic-rectangular-thin-sheet-of-metal-subjected-to-uniform-uniaxial","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-a-linear-elastic-rectangular-thin-sheet-of-metal-subjected-to-uniform-uniaxial\/","title":{"rendered":"Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction"},"content":{"rendered":"\n<p>Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young\u2019s modulus <em>E <\/em>= 200 MPa and Poisson\u2019s ratio <em>\u03bd <\/em>= 0.3 are given. The principal strains in the plane of the sheet are<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>(A) (0.35, \u22120.15)<\/td><td>(B) (0.5, 0.0)<\/td><td>(C) (0.5, \u22120.15)<\/td><td>(D) (0.5, \u22120.5)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Ans: (0.5, &#8211; 0.15)<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Given E = 200 MPa<br>\u03c3<sub>x<\/sub>&nbsp;= 100 MPa<br>\u03c3<sub>y<\/sub>&nbsp;= 0<br>Principal strain in x-direction<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"186\" height=\"299\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/image-2.png\" alt=\"\" class=\"wp-image-156721\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young\u2019s modulus E = 200 MPa and Poisson\u2019s ratio \u03bd = 0.3 are given. The principal strains in the plane of [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156722,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-156720","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156720","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156720"}],"version-history":[{"count":2,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156720\/revisions"}],"predecessor-version":[{"id":156724,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156720\/revisions\/156724"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156722"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156720"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156720"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}