[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656417-105":59,"doc-detail-656417-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","shear-force-bending-moment-diagrams-graphical-methods","Shear-Force & Bending-Moment Diagrams - Graphical Methods","","Learning notes on evaluating shear-force and bending-moment diagrams for beams with discrete loads. The material establishes sign conventions for distributed loads, positive internal shear, and positive bending moments, then provides a step-by-step procedure: find support reactions, define section origins between loads, sum vertical forces for V, and sum moments to determine M while eliminating V from moment equations. It includes graphical methods and worked examples for beams with a couple and point load, and for simply supported beams under trapezoidal loading, deriving reactions and expressions for V(x) and M(x).",{"@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":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/shear-force-bending-moment-diagrams-graphical-methods/656417/",{"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/shear-force-bending-moment-diagrams-graphical-methods/656417.png","ImageObject",300,407,{"name":92,"@type":93},"Indoniesian Boy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-10-25",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},"What is the sign convention for distributed load, shear force, and bending moment in these notes?","Question",{"text":112,"@type":113},"A distributed load is positive when the load acts upward. A positive internal shear force produces a clockwise rotation of the beam segment. A positive internal bending moment compresses the top fibers of the segment.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is shear force V determined for a sectioned beam?",{"text":117,"@type":113},"First determine support reactions, then choose beam sections between discrete loads. Sum vertical forces for the section to solve for V, using the requirement that V is shown in its positive sense.",{"name":119,"@type":110,"acceptedAnswer":120},"How are bending moment M expressions obtained using the graphical methods procedure?",{"text":121,"@type":113},"Take moments at the sectioned end to determine M. This approach eliminates V from the moment equation, so M is found by applying the summed moment condition with M shown in its positive sense.","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},656417,1792968315,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"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},962090760608,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","# Shear-Force &Bending-Moment DiagramsGraphical Methods\n\nuse ttltion  \n## Learning Objectives\n\n   \n1)To evaluate the shear-force and bending-moment diagrams for systemswith discrete loads.  \n2)To do an engineering estimate of these quantities.  \nBeam Sign Convention  \n   \nDistributed load -  \nAn upward load is positive  \nShear Force -A positive internal shear force causes a clockwiserotation of beam segment.(i.e.,it pushes a left-facing cross-section upward or a right-facing cross-section downward).  \nBending Moment -A positive internal moment causes compression inthe top fibers of the segment (i.e.,clockwise on aleft-facing cross-section or counter-clockwise on aright-facing cross-section).  \n## Procedure\n\n   \n1.Determine support reactions  \n2.Specify beam sections origin (left end)to between each discrete load(force or moment).Be sure V and M are shown acting in the positivesense.  \n3.Sum forces vertically to determine V  \n4.Sum moments at sectioned end to determine M.(This eliminates Vfrom the moment equation).  \nLeft-facingcross section  \nRight-facingcross sectionPositive shear  \nFIGURE 7a  \nPositive bending moment  \nFIGURE 7b  \nFree-body diagramof segment△x(b)  \n△X-(V+oV=0  \nZy=0  \n∑M=  :  \n△x→      M =MGncendrzted Momtnt:Mx=:  M+-M +M一V_(之×-V+(主)=0长  X-0》从-m=-△X2V+X V-=V   Fy=:从MatV+M+-V-(1)]-V(0x)=三mX=0:△X→0V+-V=0 sx-F=0V-V+F+W(X。)x=M+Concentroted   oad.Fa  \nchange inarea undersheardistributed loading  \nchange inarea undermomentshear diagram  \n(p)  \n## Shear-Force &Bending-Moment DiagramsGraphical MethodsExample 1\n\nGiven:A simply-supported beam is loaded with a 2 kN-m couple and a4kN load as shown.  \nFind:Using graphical methods,draw the shear-force and bending-moment diagrams.  \n=3KN  \neacdion:  \n三MA=0:-2 -4(4)十By(6)=。Ау 48;— 4ва>Ay=1KNZF=:By=  3KN  \n## Shear-Force &Bending-Moment DiagramsGraphical MethodsExample 2\n\nGiven:A simply supported beam is supporting a trapezoidal loading as shown and is in staticequilibrium.  \nFind:  \na)Determine the reactions at supports A and B.  \nb)Write an algebraic expression for the trapezoidal loading shown(w(x)).  \n),determine an expression for the shear force as a function ofc)Using the relationshipx(i.e.,V(x)).  \n,determine an expression for the bending moment as ad)Using the relationship","cbCaio87KjPRU6ZF","https://ap.wps.com/l/cbCaio87KjPRU6ZF","pdf",4553983,23,"English","# Learning Objectives\n## Beam Sign Convention\n## Procedure\n# Shear-Force & Bending-Moment DiagramsGraphical MethodsExample 1\n# Shear-Force & Bending-Moment DiagramsGraphical MethodsExample 2","[{\"question\":\"What is the sign convention for distributed load, shear force, and bending moment in these notes?\",\"answer\":\"A distributed load is positive when the load acts upward. A positive internal shear force produces a clockwise rotation of the beam segment. A positive internal bending moment compresses the top fibers of the segment.\"},{\"question\":\"How is shear force V determined for a sectioned beam?\",\"answer\":\"First determine support reactions, then choose beam sections between discrete loads. Sum vertical forces for the section to solve for V, using the requirement that V is shown in its positive sense.\"},{\"question\":\"How are bending moment M expressions obtained using the graphical methods procedure?\",\"answer\":\"Take moments at the sectioned end to determine M. This approach eliminates V from the moment equation, so M is found by applying the summed moment condition with M shown in its positive sense.\"}]","Shear-Force & Bending-Moment Diagrams - Graphical Methods | PDF",58]