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Design Aid 6 Beam Design Formulas with Shear and Moment ...

NATIONAL Design SPECIFICATION FOR WOOD CONSTRUCTIONA merican Wood CouncilAmericanForest & PaperAssociationNDS2005 EDITION ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005 WITH COMMENTARY AND SUPPLEMENT: Design VALUES FOR WOOD CONSTRUCTIONASD/LRFDA merican WAmerican WAmerican WAmerican WAmerican Wood Councilood Councilood Councilood Councilood CouncilBEAM Design FBEAM Design FBEAM Design FBEAM Design FBEAM Design FORMULASORMULASORMULASORMULASORMULASWITH Shear AND MOMENTWITH Shear AND MOMENTWITH Shear AND MOMENTWITH Shear AND MOMENTWITH Shear AND MOMENTDIADIADIADIADIAGRAMSGRAMSGRAMSGRAM SGRAMSA mericanAmericanAmericanAmericanAmericanF FFFF orest &orest &orest &orest &orest &PPPPP aperaperaperaperaperAssociationAssociati onAssociationAssociationAssociationwRRVV 22 ShearMmaxMomentx Design AID NDESIGN AID NDESIGN AID NDESIGN AID NDESIGN AID Nooooo.

AMERICAN WOOD COUNCIL w R V V 2 2 Shear M max Moment x 7-36 A ab c x R 1 R 2 V 1 V 2 Shear a + — R 1 w M max Moment wb 7-36 B Figure 1 Simple Beam–Uniformly Distributed Load

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Transcription of Design Aid 6 Beam Design Formulas with Shear and Moment ...

1 NATIONAL Design SPECIFICATION FOR WOOD CONSTRUCTIONA merican Wood CouncilAmericanForest & PaperAssociationNDS2005 EDITION ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005 WITH COMMENTARY AND SUPPLEMENT: Design VALUES FOR WOOD CONSTRUCTIONASD/LRFDA merican WAmerican WAmerican WAmerican WAmerican Wood Councilood Councilood Councilood Councilood CouncilBEAM Design FBEAM Design FBEAM Design FBEAM Design FBEAM Design FORMULASORMULASORMULASORMULASORMULASWITH Shear AND MOMENTWITH Shear AND MOMENTWITH Shear AND MOMENTWITH Shear AND MOMENTWITH Shear AND MOMENTDIADIADIADIADIAGRAMSGRAMSGRAMSGRAM SGRAMSA mericanAmericanAmericanAmericanAmericanF FFFF orest &orest &orest &orest &orest &PPPPP aperaperaperaperaperAssociationAssociati onAssociationAssociationAssociationwRRVV 22 ShearMmaxMomentx Design AID NDESIGN AID NDESIGN AID NDESIGN AID NDESIGN AID Nooooo.

2 6. 6. 6. 6. 6 AMERICAN WOOD COUNCILThe American Wood Council (AWC) is part of the wood products group of theAmerican Forest & Paper Association (AF&PA). AF&PA is the national tradeassociation of the forest, paper, and wood products industry, representing membercompanies engaged in growing, harvesting, and processing wood and wood fiber,manufacturing pulp, paper, and paperboard products from both virgin and recycledfiber, and producing engineered and traditional wood products. For more informationsee every effort has been made to insure the accuracyof the information presented, and special effort has beenmade to assure that the information reflects the state-of-the-art, neither the American Forest & Paper Associationnor its members assume any responsibility for anyparticular Design prepared from this publication.

3 Thoseusing this document assume all liability from its 2007 American Forest & Paper Association, Wood Council1111 19th St., NW, Suite 800 Washington, DC FBEAM FBEAM FBEAM FBEAM Formulas WITHORMULAS WITHORMULAS WITHORMULAS WITHORMULAS WITHSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTDIADIADIADIADIAGRAMSGRAMSGRAMSGRAM SGRAMSAMERICAN FOREST & PAPER ASSOCIATIONF igures 1 through 32 provide a series of shearand Moment diagrams with accompanying formulasfor Design of beams under various static and Moment diagrams and Formulas areexcerpted from the Western Woods Use Book, 4thedition, and are provided herein as a courtesy ofWestern Wood Products Relative to Shear and MomentDiagrams E= modulus of elasticity, psiI= Moment of inertia, span length of the bending member, span length of the bending member.

4 Maximum bending Moment , total concentrated load, reaction load at bearing point, Shear force, total uniform load, load per unit length, = deflection or deformation, horizontal distance from reaction to pointon beam, of FigurList of FigurList of FigurList of FigurList of FiguresesesesesFigure 1 Simple Beam Uniformly Distributed Load .. 4 Figure 2 Simple Beam Uniform Load Partially Distributed .. 4 Figure 3 Simple Beam Uniform Load Partially Distributed at One End .. 5 Figure 4 Simple Beam Uniform Load Partially Distributed at Each End .. 5 Figure 5 Simple Beam Load Increasing Uniformly to One End .. 6 Figure 6 Simple Beam Load Increasing Uniformly to Center .. 6 Figure 7 Simple Beam Concentrated Load at Center.

5 7 Figure 8 Simple Beam Concentrated Load at Any Point .. 7 Figure 9 Simple Beam Two Equal Concentrated Loads Symmetrically Placed .. 8 Figure 10 Simple Beam Two Equal Concentrated Loads Unsymmetrically Placed .. 8 Figure 11 Simple Beam Two Unequal Concentrated Loads Unsymmetrically Placed .. 9 Figure 12 Cantilever Beam Uniformly Distributed Load .. 9 Figure 13 Cantilever Beam Concentrated Load at Free End .. 10 Figure 14 Cantilever Beam Concentrated Load at Any Point .. 10 Figure 15 Beam Fixed at One End, Supported at Other Uniformly Distributed Load .. 11 Figure 16 Beam Fixed at One End, Supported at Other Concentrated Load at Center .. 11 Figure 17 Beam Fixed at One End, Supported at Other Concentrated Load at Any Point.

6 12 Figure 18 Beam Overhanging One Support Uniformly Distributed Load ..12 Figure 19 Beam Overhanging One Support Uniformly Distributed Load on Overhang .. 13 Figure 20 Beam Overhanging One Support Concentrated Load at End of Overhang .. 13 Figure 21 Beam Overhanging One Support Concentrated Load at Any Point Between Supports .. 14 Figure 22 Beam Overhanging Both Supports Unequal Overhangs Uniformly Distributed Load .. 14 Figure 23 Beam Fixed at Both Ends Uniformly Distributed Load .. 15 Figure 24 Beam Fixed at Both Ends Concentrated Load at Center .. 15 Figure 25 Beam Fixed at Both Ends Concentrated Load at Any Point .. 16 Figure 26 Continuous Beam Two Equal Spans Uniform Load on One Span .. 16 Figure 27 Continuous Beam Two Equal Spans Concentrated Load at Center of One Span.

7 17 Figure 28 Continuous Beam Two Equal Spans Concentrated Load at Any Point .. 17 Figure 29 Continuous Beam Two Equal Spans Uniformly Distributed Load .. 18 Figure 30 Continuous Beam Two Equal Spans Two Equal Concentrated Loads Symmetrically Placed .. 18 Figure 31 Continuous Beam Two Unequal Spans Uniformly Distributed Load .. 19 Figure 32 Continuous Beam Two Unequal Spans Concentrated Load on Each Span Symmetrically Placed .. 19 AMERICAN WOOD COUNCILwRRVV22 ShearMmaxMomentx7-36 A ab cxR1R2V1V2 Sheara + R1wMmaxMomentwb7-36 B Figure 1 Simple Beam Uniformly Distributed LoadFigure 2 Simple Beam Uniform Load Partially DistributedAMERICAN FOREST & PAPER ASSOCIATIONR1R2V1V2 ShearxR1 w1M maxMomentabcw2cw1a7-37 B xR1R2V2V1 MmaxMomentShearR1 wawa7-37 A Figure 3 Simple Beam Uniform Load Partially Distributed at One EndFigure 4 Simple Beam Uniform Load Partially Distributed at Each EndAMERICAN WOOD COUNCILxW2 RRVVS hearMmaxMoment27-38 B A Figure 5 Simple Beam Load Increasing Uniformly to One EndFigure 6 Simple Beam Load Increasing Uniformly to CenterAMERICAN FOREST & PAPER ASSOCIATIONxPaR1R2V1V2 ShearM maxMomentb7-39-b xP2 RRVVS hearM

8 MaxMoment27-39 A Figure 7 Simple Beam Concentrated Load at CenterFigure 8 Simple Beam Concentrated Load at Any PointAMERICAN WOOD COUNCILxPaR1R2 V1V2 ShearM1 MomentPbM27-40 B xPaRR VShearMmaxMomentPa7-40 A V Figure 9 Simple Beam Two Equal Concentrated Loads Symmetrically PlacedFigure 10 Simple Beam Two Equal Concentrated Loads UnsymmetricallyPlacedAMERICAN FOREST & PAPER ASSOCIATIONaR1R2 V1V2 ShearM 1 MomentbM27-41-axP1P2 Figure 11 Simple Beam Two Unequal Concentrated Loads UnsymmetricallyPlacedFigure 12 Cantilever Beam Uniformly Distributed LoadxRVShearMomentwMmax7-41- B AMERICAN WOOD COUNCILxaV ShearMomentbMmax7-42-bPR xRVShearMomentMmaxP7-42 A Figure 13 Cantilever Beam Concentrated Load at Free EndFigure 14 Cantilever Beam Concentrated Load at Any PointAMERICAN FOREST & PAPER ASSOCIATIONR1R2V1V2 ShearM12M23 117-43 B2xP wR17-43 AR2V1V2 4 ShearM1 Mmax38x Figure 15 Beam Fixed at One End, Supported at Other Uniformly DistributedLoadFigure 16 Beam Fixed at One End, Supported at Other Concentrated Load atCenterAMERICAN WOOD COUNCILabR1V2 ShearxPa R2M 1 MomentR2V 1PM27-44 AFigure 17 Beam Fixed at One End, Supported at Other Concentrated Load atAny PointFigure 18 Beam Overhanging One Support Uniformly Distributed Loadx1 ShearM2M1R1(1 a2)MomentV 3V 2(1 a2)2 2 2xaw( + a)

9 R2V17-44 B AMERICAN FOREST & PAPER ASSOCIATIONV2 Mmaxx1xaMomentShearR1R2 V 1P7-45 B V2 Mmaxx1xawaMomentShearR1R2V17-45 A Figure 19 Beam Overhanging One Support Uniformly Distributed Load onOverhangFigure 20 Beam Overhanging One Support Concentrated Load at End ofOverhangAMERICAN WOOD COUNCILR1R2wabcV2V1V4V3Mx1M2M1M3X1X7-46 B xR1R2x1abV1V2 MmaxShearMoment7-46 A Figure 21 Beam Overhanging One Support Concentrated Load at Any PointBetween SupportsFigure 22 Beam Overhanging Both Supports Unequal Overhangs UniformlyDistributed LoadAMERICAN FOREST & PAPER ASSOCIATIONxVV22 ShearMomentR RMmaxPPPMmax47-47 B xVV22 ShearM1 MomentwR A Figure 23 Beam Fixed at Both Ends Uniformly Distributed LoadFigure 24 Beam Fixed at Both Ends Concentrated Load at CenterAMERICAN WOOD COUNCILS hearV1R3R2167M1V2 MomentMmaxx7-48 BR1V3w xMomentPPPV2 MaM2R2V1M17-48 AR1 Shearab Figure 25 Beam Fixed at Both Ends Concentrated Load at Any PointFigure 26 Continuous Beam Two Equal Spans Uniform Load on One SpanAMERICAN FOREST & PAPER ASSOCIATIONS hearV1R3R2M1 MomentMmaxPPPV3V2R1ba7-49 B ShearV1R3R2M1 MomentPPPV3V2R1227-49 AMmax Figure 27 Continuous Beam Two Equal Spans Concentrated Load at Centerof One SpanFigure 28 Continuous Beam Two Equal Spans Concentrated Load at AnyPointAMERICAN WOOD COUNCIL7-50

10 AR1R3R23 V2V3 M23 /8V1V2V1R3R2 PPPV2R1 PPPaaaaMxxV2V3M1M2 Figure 29 Continuous Beam Two Equal Spans Uniformly Distributed LoadFigure 30 Continuous Beam Two Equal Spans Two Equal Concentrated LoadsSymmetrically PlacedAMERICAN FOREST & PAPER ASSOCIATIONR1R3R2x1Mx2M1V1V4V3V21212wwx2 Mx1 V1R3R2PV3R1 PaabbMm1V4M1Mm221V2P2P1 Figure 31 Continuous Beam Two Unequal Spans Uniformly Distributed LoadFigure 32 Continuous Beam Two Unequal Spans Concentrated Load on EachSpan Symmetrically PlacedAF&PA American FAmerican FAmerican FAmerican FAmerican Forest & Porest & Porest & Porest & Porest & Paper Associationaper Associationaper Associationaper Associationaper AssociationAmerican WAmerican WAmerican WAmerican WAmerican Wood Councilood Councilood Councilood Councilood Council1111 19th S1111 19th S1111 19th S1111 19th S1111 19th Streetreetreetreetreet, NWt, NWt, NWt, NWt, NWSuitSuitSuitSuitSuite 800e 800e 800e 800e 800 WWWWW ashingtashingtashingtashingtashington, DC 20036on, DC 20036on, DC 20036on, DC 20036on, DC 20036 Phone: 202-463-4 Phone: 202-463-4 Phone: 202-463-4 Phone: 202-463-4 Phone: 202-463-4777771111133333 FFFFFax: 202-463-2ax: 202-463-2ax: 202-463-2ax: 202-463-2ax.


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