[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-665451-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-665451-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","qualitative-sketching-of-displacements-case-study-examples","Qualitative Sketching of Displacements Case Study Examples","","Qualitative Sketching of Displacements presents case study examples and a method for drawing deformed shapes of simple structural members using intuition validated by mechanics. It defines qualitative deformed shapes as neutral-surface sketches under prescribed loading and explains how bending moment determines curvature and deformation profiles. The material covers common structural examples, rules for consistency with boundary constraints, and simplifications such as small displacements, neglecting axial deformation, and ignoring self-weight.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/qualitative-sketching-of-displacements-case-study-examples/665451/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/qualitative-sketching-of-displacements-case-study-examples/665451.png","ImageObject",300,407,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What is a qualitative deformed shape in this material?","Question",{"text":62,"@type":63},"It is a rough sketch of the neutral surface (axis) of a structure in its deformed position under a specified loading condition.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How does mechanics relate beam curvature to bending moment?",{"text":67,"@type":63},"Beam curvature is proportional to bending moment, so positive bending moment produces a concave-up (convex) deflection profile, negative bending moment produces concave-down, and zero bending moment leaves curvature unchanged.",{"name":69,"@type":60,"acceptedAnswer":70},"What rules must the qualitative sketch satisfy?",{"text":71,"@type":63},"The curvature must match the bending-moment profile, the deformed shape must satisfy boundary constraints, rigid joint angles must be preserved, and points of inflection occur when M(x)=0 and V(x)≠0.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},665451,1793304261,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":117,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":103},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Qualitative Sketching of Displacements Case Study Examples  \nQualitative Sketching of Displacements  \nMark A. Austin  \nUniversity of Maryland  \n[austin@umd.edu](austin@umd.edu)[ ](austin@umd.edu)ENCE 353, Fall Semester 2020  \nOctober 18, 2020  \nQualitative Sketching of Displacements Case Study Examples  \nOverview  \n1 Qualitative Sketching of Displacements  \n De􀀍ection of very simple structures  \n Rules and Simpli􀀌cations  Types of Boundary Support  Rigid Corner Points  \n2 Case Study Examples  \nQualitative Sketching of Displacements Case Study Examples  \nQualitative Sketching of Displacements  \nQualitative Sketching of Displacements Case Study Examples  \nQualitative De􀀍ected Shape  \nA rough (usually exaggerated) sketch of the neutral surface (axis) of the structure in the deformed position under the action of a prescribed loading condition.  \nThese sketches provide insight into the behavior of structures, e.g. ,  Is there tension in the top or bottom of the beam?  \n Does the beam move upwards or downwards?  \n Does the beam rotate clockwise or anticlockwise?  \nGood answers to these questions can serve as valuable checks for correctness (catch mistakes) in more complicated approaches to analysis.  \nQualitative Sketching of Displacements Case Study Examples  \nProcedure: Very simple structures ! can rely on intuition. Simple Example 1 . Cantilever Beam  \nSimple Example 2 . Simply Supported Beam  \nQualitative Sketching of Displacements Case Study Examples  \nSimple Example 3 . Cantilevered Simply-Supported Beam  \nPoint of Maximum Curvature  \nBending Moment Diagram  \ny(x )  \nFor more complex cases, intuition starts to fail ... Revised Procedure. Rely on math and mechanics.  \nQualitative Sketching of Displacements Case Study Examples  \nHere's what Mechanics tells us:  \n Beam curvature is proportional to bending moment.  \n􀀞 (x ) = 􀀔 ~~ ~~ME(xI) 􀀕 : (1)  \n Positive bending moment ! de􀀍ection pro􀀌le is concave upward (convex) .  \n Negative bending moment ! de􀀍ection pro􀀌le is concave downward.  \n Zero bending moment ! curvature of beam or frame element remains unchanged.  \nQualitative Sketching of Displacements Case Study Examples  \nThe Rules:  \n The curvature must be consistent with the pro􀀌le of bending moment.  \n The de􀀍ected shape must satisfy the boundary constraints.  \n The original angle at a rigid joint (e.g. , cantilever support) must be preserved.  \n Points of in􀀍ection occur when M (x) = 0 and V (x)  0.  \nSimpli􀀌cations:  \n The length of the deformed member is the same as the original  \nlength of the unloaded member (i.e. , small displacements) .  Neglect axial deformations (i.e. , very close to zero) .  \n Neglect self-weight of the structure.  \nQualitative Sketching of Displacements Case Study Examples  \nTypes of Boundary Support:  \nQualitative Sketching of Displacements Case Study Examples  \nRigid Corner Points: Must keep the same angle as they rotate.","cbCaieea4sTD9ckP","https://ap.wps.com/l/cbCaieea4sTD9ckP","pdf",947505,"English","# Overview\n## Qualitative Sketching of Displacements\n## Procedure: Very Simple Structures\n## Case Study Examples\n## Qualitative Deformed Shape\n## Revised Procedure: Rely on Math and Mechanics\n## The Rules and Simplifications\n## Types of Boundary Support\n## Rigid Corner Points","[{\"question\":\"What is a qualitative deformed shape in this material?\",\"answer\":\"It is a rough sketch of the neutral surface (axis) of a structure in its deformed position under a specified loading condition.\"},{\"question\":\"How does mechanics relate beam curvature to bending moment?\",\"answer\":\"Beam curvature is proportional to bending moment, so positive bending moment produces a concave-up (convex) deflection profile, negative bending moment produces concave-down, and zero bending moment leaves curvature unchanged.\"},{\"question\":\"What rules must the qualitative sketch satisfy?\",\"answer\":\"The curvature must match the bending-moment profile, the deformed shape must satisfy boundary constraints, rigid joint angles must be preserved, and points of inflection occur when M(x)=0 and V(x)≠0.\"}]","Qualitative Sketching of Displacements Case Study Examples | PDF"]