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DA6-BeamFormulas.pdf

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  NATIONAL DESIGN SPECIFICATION ® FOR WOOD CONSTRUCTION American Wood CouncilAmericanForest & PaperAssociation N DS 2005 EDITION ® ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005 WITH COMMENTARY AND SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION ASD/LRFD      A   m   e   r   i   c   a   n   W   A   m   e   r   i   c   a   n   W   A   m   e   r   i   c   a   n   W   A   m   e   r   i   c   a   n   W   A   m   e   r   i   c   a   n   W   o   o   d   C   o  u   n   c   i   l   o   o   d   C   o  u   n   c   i   l   o   o   d   C   o  u   n   c   i   l   o   o   d   C   o  u   n   c   i   l   o   o   d   C   o  u   n   c   i   l BEAM DESIGN FBEAM DESIGN FBEAM DESIGN FBEAM DESIGN FBEAM DESIGN FORMULASORMULASORMULASORMULASORMULASWITH SHEAR AND MOMENTWITH SHEAR AND MOMENTWITH SHEAR AND MOMENTWITH SHEAR AND MOMENTWITH SHEAR AND MOMENTDIADIADIADIADIAGRAMSGRAMSGRAMSGRAMSGRAMS AmericanAmericanAmericanAmericanAmericanFFFFForest &orest &orest &orest &orest &PPPPPaperaperaperaperaperAssociationAssociationAssociationAssociationAssociation w RRV V  2 2Shear  M max Moment  x    DESIGN AID NDESIGN AID NDESIGN AID NDESIGN AID NDESIGN AID Nooooo. 6. 6. 6. 6. 6  AMERICAN WOOD COUNCIL The American Wood Council (AWC) is part of the wood products group of the American Forest & Paper Association (AF&PA). AF&PA is the national tradeassociation of the forest, paper, and wood products industry, representing member companies engaged in growing, harvesting, and processing wood and wood fiber,manufacturing pulp, paper, and paperboard products from both virgin and recycled  fiber, and producing engineered and traditional wood products. For more information see www.afandpa.org. While 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. Thoseusing this document assume all liability from its use. Copyright © 2007American Forest & Paper Association, Inc.American Wood Council1111 19 th  St., NW, Suite 800Washington, DC 20036202-463-4713 awcinfo@afandpa.orgwww.awc.org BEAM FBEAM FBEAM FBEAM FBEAM FORMULAS WITHORMULAS WITHORMULAS WITHORMULAS WITHORMULAS WITHSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTDIADIADIADIADIAGRAMSGRAMSGRAMSGRAMSGRAMS  AMERICAN FOREST & PAPER ASSOCIATION Figures 1 through 32 provide a series of shear and moment diagrams with accompanying formulasfor design of beams under various static loadingconditions.Shear and moment diagrams and formulas areexcerpted from the Western Woods Use Book  , 4thedition, and are provided herein as a courtesy of  Western Wood Products ssociation . IntrIntrIntrIntrIntroductionoductionoductionoductionoduction Notations Relative to “Shear and MomentDiagrams”  E  =modulus of elasticity, psi  I  =moment of inertia, in. 4  L =span length of the bending member, ft. R =span length of the bending member, in.  M  =maximum bending moment, in.-lbs.  P  =total concentrated load, lbs.  R =reaction load at bearing point, lbs. V  =shear force, lbs. W  =total uniform load, lbs. w =load per unit length, lbs./in. ∆ =deflection or deformation, in.  x =horizontal distance from reaction to pointon beam, in. List of FigurList of FigurList of FigurList of FigurList of Figureseseseses Figure 1Simple Beam–Uniformly Distributed Load................................................................................................4Figure 2Simple Beam–Uniform Load Partially Distributed.....................................................................................4Figure 3Simple Beam–Uniform Load Partially Distributed at One End..................................................................5Figure 4Simple Beam–Uniform Load Partially Distributed at Each End................................................................5Figure 5Simple Beam–Load Increasing Uniformly to One End..............................................................................6Figure 6Simple Beam–Load Increasing Uniformly to Center..................................................................................6Figure 7Simple Beam–Concentrated Load at Center...............................................................................................7Figure 8Simple Beam–Concentrated Load at Any Point..........................................................................................7Figure 9Simple Beam–Two Equal Concentrated Loads Symmetrically Placed.......................................................8Figure 10Simple Beam–Two Equal Concentrated Loads Unsymmetrically Placed..................................................8Figure 11Simple Beam–Two Unequal Concentrated Loads Unsymmetrically Placed..............................................9Figure 12Cantilever Beam–Uniformly Distributed Load...........................................................................................9Figure 13Cantilever Beam–Concentrated Load at Free End....................................................................................10Figure 14Cantilever Beam–Concentrated Load at Any Point..................................................................................10Figure 15Beam Fixed at One End, Supported at Other–Uniformly Distributed Load.............................................11Figure 16Beam Fixed at One End, Supported at Other–Concentrated Load at Center...........................................11Figure 17Beam Fixed at One End, Supported at Other–Concentrated Load at Any Point.....................................12Figure 18Beam Overhanging One Support–Uniformly Distributed Load...............................................................12Figure 19Beam Overhanging One Support–Uniformly Distributed Load on Overhang.........................................13Figure 20Beam Overhanging One Support–Concentrated Load at End of Overhang.............................................13Figure 21Beam Overhanging One Support–Concentrated Load at Any Point Between Supports...........................14Figure 22Beam Overhanging Both Supports–Unequal Overhangs–Uniformly Distributed Load.........................14Figure 23Beam Fixed at Both Ends–Uniformly Distributed Load...........................................................................15Figure 24Beam Fixed at Both Ends–Concentrated Load at Center..........................................................................15Figure 25Beam Fixed at Both Ends–Concentrated Load at Any Point....................................................................16Figure 26Continuous Beam–Two Equal Spans–Uniform Load on One Span.......................................................16Figure 27Continuous Beam–Two Equal Spans–Concentrated Load at Center of One Span.................................17Figure 28Continuous Beam–Two Equal Spans–Concentrated Load at Any Point................................................17Figure 29Continuous Beam–Two Equal Spans–Uniformly Distributed Load.......................................................18Figure 30Continuous Beam–Two Equal Spans–Two Equal Concentrated Loads Symmetrically Placed.............18Figure 31Continuous Beam–Two Unequal Spans–Uniformly Distributed Load...................................................19Figure 32Continuous Beam–Two Unequal Spans–Concentrated Load on Each Span Symmetrically Placed.....19  AMERICAN WOOD COUNCIL w RRV V  2 2Shear  M max Moment  x  7-36 A   abc  x R 1 R 2 V  1 V  2 Shear a + —R 1 w  M max Moment wb 7-36 B  Figure 1Simple Beam–Uniformly Distributed Load   Figure 2Simple Beam–Uniform Load Partially Distributed
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