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The lecture reviews how shear stress and shear strain are related, then revisits stress on an inclined plane to decompose normal and tangential stress components for an axially loaded rectangular bar at angle θ. It motivates shear failure, then establishes objectives covering material properties review, material selection trade-offs, and factor-of-safety calculations using tensile testing and ASTM E8 guidance.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/me-323-mechanics-of-materials-lecture-4-introduction-to-design-of-deformable-bodies/665554/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/me-323-mechanics-of-materials-lecture-4-introduction-to-design-of-deformable-bodies/665554.png","ImageObject",300,407,{"name":92,"@type":93},"asba","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does the lecture represent shear stress and define shear strain?","Question",{"text":112,"@type":113},"It asks how shear stress is represented on a stress element and what the shear strain is. The goal is to connect these measures for deformable-body design.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is decomposed when analyzing an axially loaded rectangular bar on an inclined plane?",{"text":117,"@type":113},"The lecture revisits stress on an inclined plane and focuses on the normal and tangential stress components acting on the plane for a given angle θ.",{"name":119,"@type":110,"acceptedAnswer":120},"How are factors of safety used differently for brittle versus ductile materials?",{"text":121,"@type":113},"The lecture states that ductile materials use yield strength or ultimate strength, while brittle materials use ultimate strength. It introduces factor-of-safety expressions separately for different loading cases.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665554,1793304942,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},3985747872567,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","ME 323 – Mechanics of Materials  \nLecture 4: Introduction to design of deformable  \nbodies  \nJoshua Pribe Fall 2019  \nFrom the end of last class…  \nFor the applied shear force V:  \n• How do we represent the shear stress on a stress element?  \n• What is the shear strain?  \n• How are shear stress and strain related?  \nExample from last class: Stress on an inclined plane  \nFor the axially loaded rectangular bar, what are the normal and tangential components of the stress acting  \non the plane given by the angle θ?  \nMotivation: Metals typically fail due to shear stress  \nMotivation: Axial member with a weld line  \nExample from last class: Stress on an inclined plane  \nFor the axially loaded rectangular bar, what are the normal and tangential components of the stress acting  \non the plane given by the angle θ?  \nObjectives for today  \n• Review material properties  \n• Discuss material selection in design  \n• Calculate factors of safety  \n• If time permits: introduce generalized stress and strain Steel:  \nNylon:  \nAluminum:  \nMaterial properties: Tensile testing  \nAmerican Society of Testing and Materials (ASTM) Standard E8 governs tensile testing Measure load and displacement; convert to stress and strain  \nExample: [https://www.youtube.com/watch?v=ipDZska5VN4](https://www.youtube.com/watch?v=ipDZska5VN4)  \nMaterial properties  \nStress-strain curves for two aluminum alloys: How does composition affect the mechanical properties?  \nMaterial properties  \nExamples from the lecture book  \nMaterial selection  \nTypically a trade-off between weight and stiffness or strength  \n9  \n“Ashby diagram” from Shigley’s Mechanical Engineering Design  \nFactors of safety (from pre-week video)  \nUse a factor of safety to account for uncertainty in design  \n10  \nFactor of safety (FS) = Failure~~ ~~loActual~~ ~~loaadd 􀀡 1  \nBrittle  \nDuctile  \nDuctile  \nmaterials (most metals): use the yield strength or ultimate strength  \nFS = 􀁖􀁖acYtual~~ ~~  \nFS = 􀁗~~ ~~􀁗acUtual~~ ~~  \nuse the ultimate strength  \nBrittle materials:  \nAxial loading:  \n􀁖U FS = ~~ ~~  \n􀁖 actual  \nFS = 􀁗~~ ~~􀁗acYtual~~ ~~  \n􀁖U FS = ~~ ~~  \n􀁖 actual  \nShear loading:  \nAxial loading:  \nShear loading:  \nFS = 􀁗~~ ~~􀁗acUtual~~ ~~","cbCaicoSv4fJocXm","https://ap.wps.com/l/cbCaicoSv4fJocXm","pdf",1217133,14,"English","# Objectives for today\n## Review material properties\n## Discuss material selection in design\n## Calculate factors of safety\n## If time permits: generalized stress and strain\n# Motivation and examples\n## Metals fail due to shear stress\n## Axial member with a weld line\n## Stress on an inclined plane\n# Material properties and testing\n## Tensile testing and ASTM E8\n## Stress-strain curves for aluminum alloys\n# Material selection and design trade-offs\n## Ashby diagram reference\n# Factors of safety\n## Using FS to account for uncertainty\n## Brittle vs ductile material approaches","[{\"question\":\"How does the lecture represent shear stress and define shear strain?\",\"answer\":\"It asks how shear stress is represented on a stress element and what the shear strain is. The goal is to connect these measures for deformable-body design.\"},{\"question\":\"What is decomposed when analyzing an axially loaded rectangular bar on an inclined plane?\",\"answer\":\"The lecture revisits stress on an inclined plane and focuses on the normal and tangential stress components acting on the plane for a given angle θ.\"},{\"question\":\"How are factors of safety used differently for brittle versus ductile materials?\",\"answer\":\"The lecture states that ductile materials use yield strength or ultimate strength, while brittle materials use ultimate strength. It introduces factor-of-safety expressions separately for different loading cases.\"}]","ME 323 - Mechanics of Materials - Lecture 4 - Introduction to design of deformable bodies | PDF",35]