NATIONAL DESIGN SPECIFICATION ® FOR WOOD CONSTRUCTION American Wood Council American Forest & Paper Association NDS 2005 EDITION ® ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005 WITH COMMENTARY AND SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION ASD/LRFD American W American W American W American W American W ood Council ood Council ood Council ood Council ood Council BEAM DESIGN F BEAM DESIGN F BEAM DESIGN F BEAM DESIGN F BEAM DESIGN FORMULAS ORMULAS ORMULAS ORMULAS ORMULAS WITH SHEAR AND MOMENT WITH SHEAR AND MOMENT WITH SHEAR AND MOMENT WITH SHEAR AND MOMENT WITH SHEAR AND MOMENT DIA DIA DIA DIA DIAGRAMS GRAMS GRAMS GRAMS GRAMS American American American American American Forest & orest & orest & orest & orest & Paper aper aper aper aper Association Association Association Association Association w R R V V 2 2 Shear M max Moment x DESIGN AID N DESIGN AID N DESIGN AID N DESIGN AID N DESIGN AID No o o. 6 . 6 . 6 . 6 . 6
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NATIONAL DESIGN SPECIFICATION®
FOR WOOD CONSTRUCTION
American Wood Council
AmericanForest &
PaperAssociation
N D S
2005 EDITION
®
ANSI/AF&PA NDS-2005Approval Date: JANUARY 6, 2005
WITH COMMENTARY AND
SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION
ASD/LRFD
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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
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 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 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.
BEAM FBEAM FBEAM FBEAM FBEAM FORMULAS WITHORMULAS WITHORMULAS WITHORMULAS WITHORMULAS WITHSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENT
DIADIADIADIADIAGRAMSGRAMSGRAMSGRAMSGRAMS
AMERICAN FOREST & PAPER ASSOCIATION
Figures 1 through 32 provide a series of shearand 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 ofWestern Wood Products Association.
IntrIntrIntrIntrIntroductionoductionoductionoductionoduction Notations Relative to “Shear and MomentDiagrams”
E = modulus of elasticity, psiI = 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.Δ = deflection or deformation, in.x = horizontal distance from reaction to point
on beam, in.
List of FigurList of FigurList of FigurList of FigurList of Figureseseseses
Figure 1 Simple Beam – Uniformly Distributed Load ................................................................................................ 4Figure 2 Simple Beam – Uniform Load Partially Distributed..................................................................................... 4Figure 3 Simple Beam – Uniform Load Partially Distributed at One End .................................................................. 5Figure 4 Simple Beam – Uniform Load Partially Distributed at Each End ................................................................ 5Figure 5 Simple Beam – Load Increasing Uniformly to One End .............................................................................. 6Figure 6 Simple Beam – Load Increasing Uniformly to Center .................................................................................. 6Figure 7 Simple Beam – Concentrated Load at Center ............................................................................................... 7Figure 8 Simple Beam – Concentrated Load at Any Point .......................................................................................... 7Figure 9 Simple Beam – Two Equal Concentrated Loads Symmetrically Placed....................................................... 8Figure 10 Simple Beam – Two Equal Concentrated Loads Unsymmetrically Placed .................................................. 8Figure 11 Simple Beam – Two Unequal Concentrated Loads Unsymmetrically Placed .............................................. 9Figure 12 Cantilever Beam – Uniformly Distributed Load ........................................................................................... 9Figure 13 Cantilever Beam – Concentrated Load at Free End .................................................................................... 10Figure 14 Cantilever Beam – Concentrated Load at Any Point .................................................................................. 10Figure 15 Beam Fixed at One End, Supported at Other – Uniformly Distributed Load ............................................. 11Figure 16 Beam Fixed at One End, Supported at Other – Concentrated Load at Center ........................................... 11Figure 17 Beam Fixed at One End, Supported at Other – Concentrated Load at Any Point ..................................... 12Figure 18 Beam Overhanging One Support – Uniformly Distributed Load ............................................................... 12Figure 19 Beam Overhanging One Support – Uniformly Distributed Load on Overhang ......................................... 13Figure 20 Beam Overhanging One Support – Concentrated Load at End of Overhang ............................................. 13Figure 21 Beam Overhanging One Support – Concentrated Load at Any Point Between Supports ........................... 14Figure 22 Beam Overhanging Both Supports – Unequal Overhangs – Uniformly Distributed Load ......................... 14Figure 23 Beam Fixed at Both Ends – Uniformly Distributed Load........................................................................... 15Figure 24 Beam Fixed at Both Ends – Concentrated Load at Center .......................................................................... 15Figure 25 Beam Fixed at Both Ends – Concentrated Load at Any Point .................................................................... 16Figure 26 Continuous Beam – Two Equal Spans – Uniform Load on One Span ....................................................... 16Figure 27 Continuous Beam – Two Equal Spans – Concentrated Load at Center of One Span ................................. 17Figure 28 Continuous Beam – Two Equal Spans – Concentrated Load at Any Point ................................................ 17Figure 29 Continuous Beam – Two Equal Spans – Uniformly Distributed Load ....................................................... 18Figure 30 Continuous Beam – Two Equal Spans – Two Equal Concentrated Loads Symmetrically Placed ............. 18Figure 31 Continuous Beam – Two Unequal Spans – Uniformly Distributed Load ................................................... 19Figure 32 Continuous Beam – Two Unequal Spans – Concentrated Load on Each Span Symmetrically Placed ..... 19