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Additional sections provide cantilevered beam diagram formulas with moment and reaction coefficients across different numbers of equal load spaces, plus continuous beam shear and moment coefficient data for equal spans under uniform and concentrated loads.",{"@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/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/v-m-d-diagrams-beam-loading-and-momentdeflection-coefficients/656415/",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/v-m-d-diagrams-beam-loading-and-momentdeflection-coefficients/656415.png","ImageObject",300,407,{"name":42,"@type":43},"dabgoudw","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-27","2026-10-25",true,{"@type":52,"interactionType":53,"userInteractionCount":30},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What is included in the V-M-D diagram tables for simple beams?","Question",{"text":62,"@type":63},"The tables provide concentrated-load equivalents, reaction coefficients (pinned and fixed ends), and maximum positive/negative moment coefficients, along with deflection coefficients and maximum deflection expressions.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How are cantilevered beams handled in the document?",{"text":67,"@type":63},"Cantilever sections list beam diagram formulas and provide moment and reaction coefficients across different numbers of spans or equal load spaces, along with dimensional coefficients in terms of beam length.",{"name":69,"@type":60,"acceptedAnswer":70},"What additional coefficients are provided for continuous beams?",{"text":71,"@type":63},"For continuous beams with equal spans, the document provides shear and moment coefficients for uniform loading and for concentrated loads (including values given for different load placements such as center or 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\u003Cbr>Beam   | Beam Fixed One  \u003Cbr>End,Supported  \u003Cbr>at Other   | Beam Fixed  \u003Cbr>Both Ends   |\n| n   | Loading   | Coeff.   | ▲   |  |  |\n| 0   |  | a   | 0.125   | 0.070   | 0.042   |\n|  |  | b   | 一   | 0.125   | 0.083   |\n|  |  | c   | 0.500   | 0.375   | 一   |\n|  |  | d  \u003Cbr>e   | 一  \u003Cbr>0.013   | 0.625  \u003Cbr>0.005   | 0.500  \u003Cbr>0.003   |\n|  |  | f   | 1.000   | 1.000   | 0.667   |\n|  |  | g   | 1.000   | 0.415   | 0.300   |\n| 2   |  | a   | 0.250   | 0.156   | 0.125   |\n|  |  | b   | 一   | 0.188   | 0.125   |\n|  |  | C   | 0.500   | 0.313   | 一   |\n|  |  | d   | 一   | 0.688   | 0.500   |\n|  |  | e   | 0.021   | 0.009   | 0.005   |\n|  |  | f  \u003Cbr>g   | 2.000  \u003Cbr>0.800   | 1.500  \u003Cbr>0.477   | 1.000   |\n|  |  |  |  |  | 0.400   |\n| 3   |  | a   | 0.333   | 0.222   | 0.111   |\n|  |  | D  \u003Cbr>c  \u003Cbr>d   | 一  \u003Cbr>1.000  \u003Cbr>一   | 0.333  \u003Cbr>0.667   | 0.222  \u003Cbr>一   |\n|  |  |  |  |  |  |\n|  |  |  |  | 1.333   | 1.000   |\n|  |  | e   | 0.036   | 0.015   | 0.008   |\n|  |  | f   | 2.667   | 2.667   | 1.778   |\n|  |  | g   | 1.022   | 0.438   | 0.333   |\n| 4   |  | a   | 0.500   | 0.266   | 0.188   |\n|  |  | b   | 一   | 0.469   | 0.313   |\n|  |  | C   | 1.500   | 1.031   | 一   |\n|  |  | d   | 一   | 1.969   | 1.500   |\n|  |  | e   | 0.050   | 0.021   | 0.010   |\n|  |  | f   | 4.000   | 3.750   | 2.500   |\n|  |  | g   | 0.950   | 0.428   | 0.320   |\n| 5   |  | a  \u003Cbr>b  \u003Cbr>c   | 0.600  \u003Cbr>一  \u003Cbr>2.000   | 0.360   | 0.200   |\n|  |  |  |  | 0.600  \u003Cbr>1.400   | 0.400   |\n|  |  |  |  |  | 一   |\n|  |  | d   | 一   | 2.600   | 2.000   |\n|  |  | e   | 0.063   | 0.027   | 0.013   |\n|  |  | f   | 4.800   | 4.800   | 3.200   |\n|  |  | g   | 1.008   | 0.424   | 0.312   |\n| Equivalent simple span uniform load (kips):fP  \u003Cbr>Maximum positive moment(kip-ft):aPL  \u003Cbr>Maximum negative moment(kip-ft):bPL  \u003Cbr>Deflection coeffcient for equivalent simple span uniform load:g  \u003Cbr>Pinned end reaction (kips):cP  \u003Cbr>Number of equal load spaces:n  \u003Cbr>Fixed end reaction(kips):dP  \u003Cbr>Span of beam(ft):L  \u003Cbr>Span of beam(in.):1  \u003Cbr>Maximum deflection(in.):ePI³/EI   |  |  |  |  |  |\n\n\n| Cantilevered Beams  \u003Cbr>Beam Diagrams and Formulas  \u003Cbr>—Equal Loads,Equally Spaced   |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| No.Spans   |  | System   |  |  |  |  |\n| 2   |  |  |  |  |  |  |\n| 3   |  | b  \u003Cbr>b  \u003Cbr>台  \u003Cbr>台  \u003Cbr>5   |  |  |  |  |\n| 4   |  |  |  |  |  |  |\n| 5   |  | M2   |  |  |  |  |\n| ≥6  \u003Cbr>(even)   |  |  |  |  |  |  |\n| ≥7  \u003Cbr>(odd)   |  | 台   |  |  |  |  |\n| n   |  |  | 2   | 3   | 4   | 5   |\n| Typical  \u003Cbr>Span  \u003Cbr>Loading   |  |  | P2  \u003Cbr>P2'  \u003Cbr>P   | P  \u003Cbr>P  \u003Cbr>P2  \u003Cbr>P2   | PG  \u003Cbr>P  \u003Cbr>P2   | 2  \u003Cbr>ND   |\n| Moments   | M₁  \u003Cbr>M₂  \u003Cbr>M₃  \u003Cbr>M₄  \u003Cbr>M₅   | 0.086×PL  \u003Cbr>0.096×PL  \u003Cbr>0.063×PL  \u003Cbr>0.039×PL  \u003Cbr>0.051×PL   | 0.167×PL  \u003Cbr>0.188×PL  \u003Cbr>0.125×PL  \u003Cbr>0.083×PL  \u003Cbr>0.104×PL   | 0.250×PL  \u003Cbr>0.278×PL  \u003Cbr>0.167×PL  \u003Cbr>0.083×PL  \u003Cbr>0.139×PL   | 0.333×PL  \u003Cbr>0.375×PL  \u003Cbr>0.250×PL  \u003Cbr>0.167×PL  \u003Cbr>0.208×PL   | 0.429×PL  \u003Cbr>0.480×PL  \u003Cbr>0.300×PL  \u003Cbr>0.171×PL  \u003Cbr>0.249×PL   |\n| Reactions   | ABCDEFGH   | 0.414×P  \u003Cbr>1.172×P  \u003Cbr>0.438×P  \u003Cbr>1.063×P  \u003Cbr>1.086×P  \u003Cbr>1.109×P  \u003Cbr>0.977×P  \u003Cbr>1.000×P   | 0.833×P  \u003Cbr>2.333×P  \u003Cbr>0.875×P  \u003Cbr>2.125×P  \u003Cbr>2.167×P  \u003Cbr>2.208×P  \u003Cbr>1.958×P  \u003Cbr>2.000×P   | 1.250×P  \u003Cbr>3.500×P  \u003Cbr>1.333×P  \u003Cbr>3.167×P  \u003Cbr>3.250×P  \u003Cbr>3.333×P  \u003Cbr>2.917×P  \u003Cbr>3.000×P   | 1.667×P  \u003Cbr>4.667×P  \u003Cbr>1.750×P  \u003Cbr>4.250×P  \u003Cbr>4.333×P  \u003Cbr>4.417×P  \u003Cbr>3.917×P  \u003Cbr>4.000×P   | 2.071×P  \u003Cbr>5.857×P  \u003Cbr>2.200×P  \u003Cbr>5.300×P  \u003Cbr>5.429×P  \u003Cbr>5.557×P  \u003Cbr>4.871×P  \u003Cbr>5.000×P   |\n| Dimensions  \u003Cbr>Cantilever   | a  \u003Cbr>b  \u003Cbr>C  \u003Cbr>d  \u003Cbr>e  \u003Cbr>f   | 0.172×L  \u003Cbr>0.125×L  \u003Cbr>0.220×L  \u003Cbr>0.204×L  \u003Cbr>0.157×L  \u003Cbr>0.147×L   | 0.250×L  \u003Cbr>0.200×L  \u003Cbr>0.333×L  \u003Cbr>0.308×L  \u003Cbr>0.273×L  \u003Cbr>0.250×L   | 0.200×L  \u003Cbr>0.143×L  \u003Cbr>0.250×L  \u003Cbr>0.231×L ","cbCaiiAC7tD46Vda","https://ap.wps.com/l/cbCaiiAC7tD46Vda","pdf",3499173,"English","# Concentrated Load Equivalents\n# Cantilevered Beams: Beam Diagrams and Formulas\n## Equal Loads, Equally Spaced\n# Continuous Beams: Moments and Shear Coefficients\n## Equal Spans, Equally Loaded\n## Concentrated Loads","[{\"question\":\"What is included in the V-M-D diagram tables for simple beams?\",\"answer\":\"The tables provide concentrated-load equivalents, reaction coefficients (pinned and fixed ends), and maximum positive/negative moment coefficients, along with deflection coefficients and maximum deflection expressions.\"},{\"question\":\"How are cantilevered beams handled in the document?\",\"answer\":\"Cantilever sections list beam diagram formulas and provide moment and reaction coefficients across different numbers of spans or equal load spaces, along with dimensional coefficients in terms of beam length.\"},{\"question\":\"What additional coefficients are provided for continuous beams?\",\"answer\":\"For continuous beams with equal spans, the document provides shear and moment coefficients for uniform loading and for concentrated loads (including values given for different load placements such as center or third points).\"}]","V-M-D-Diagrams - Beam Loading and Moment/Deflection Coefficients | PDF",1792968308,48]