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NATIONAL DESIGN SPECIFICATIONFOR WOOD CONSTRUCTION ยฎ
American Wood Council AssociationAmericanForest &Paper
N D S
2005 EDITION
Approval Date: JANUARY 6, 2005ANSI/AF&PA NDS-
SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION^ WITH COMMENTARY AND
ASD/LRFD
American WAmerican WAmerican WAmerican WAmerican Wood Council
ood Councilood Councilood Councilood Council
BEAM DESIGN FBEAM DESIGN FBEAM DESIGN FORMULASBEAM DESIGN FBEAM DESIGN FORMULASORMULASORMULASORMULAS
WITH SHEAR AND MOMENTWITH SHEAR AND MOMENTWITH SHEAR AND MOMENTWITH SHEAR AND MOMENTWITH SHEAR AND MOMENT
DIADIADIAGRAMSDIADIAGRAMSGRAMSGRAMSGRAMS
AmericanAmericanAmericanAmericanAmerican FFForest &FForest &orest &orest &orest & PPPPPaperaperaperaperaper AssociationAssociationAssociationAssociationAssociation
R w R V Shear^2 2 V
Mmax Moment
x^
DESIGN AID NDESIGN AID NDESIGN AID No DESIGN AID NDESIGN AID Noooo. 6. 6. 6. 6. 6
AMERICAN WOOD COUNCIL
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association 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 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. Those
using this document assume all liability from its use.
American Forest & Paper Association, Inc.^ Copyright ยฉ 2007 1111 19American Wood Councilth^ St., NW, Suite 800 Washington, DC 20036202-463-
awcinfo@afandpa.orgwww.awc.org
BEAM FBEAM FBEAM FORMULAS WITH BEAM FBEAM FORMULAS WITHORMULAS WITHORMULAS WITHORMULAS WITH SHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENTSHEAR AND MOMENT DIADIADIAGRAMSDIADIAGRAMSGRAMSGRAMSGRAMS
AMERICAN WOOD COUNCIL
w R R V Shear^2 2 V
Mmax Moment
x
7-36 A
a b c
V 1 R^1 x R^2 Shear V 2 a + โR w^1
Mmax Moment
wb
7-36 B
Figure 1 Simple Beam โ Uniformly Distributed Load
Figure 2 Simple Beam โ Uniform Load Partially Distributed
AMERICAN FOREST & PAPER ASSOCIATION
R 1 R 2
V 1 V 2
Shear
x R โw (^11)
Mmax Moment
w^ a 1 a b^ wc 2 c
7-37 B
R (^1) x R 2 V 2
V 1
Mmax Moment
Shear R โ w 1
waa
7-37 A
Figure 3 Simple Beam โ Uniform Load Partially Distributed at One End
Figure 4 Simple Beam โ Uniform Load Partially Distributed at Each End
AMERICAN FOREST & PAPER ASSOCIATION
x (^) P R (^1) a R 2 V (^1) V 2 Shear
Mmax Moment
b
7-39-b
x (^) P 2
R R
V Shear V
Mmax Moment
7-39 A
Figure 7 Simple Beam โ Concentrated Load at Center
Figure 8 Simple Beam โ Concentrated Load at Any Point
AMERICAN WOOD COUNCIL
x (^) P R (^1) a R 2 V (^1) Shear V 2
M (^1) Moment
P
b
M 2
7-40 B
x (^) P R (^) a R V Shear
Mmax Moment
P
a
7-40 A
V
Figure 9 Simple Beam โ Two Equal Concentrated Loads Symmetrically Placed
Figure 10 Simple Beam โ Two Equal Concentrated Loads UnsymmetricallyPlaced
AMERICAN WOOD COUNCIL
x a Shear V
Moment
b
Mmax
7-42-b
P^ R
x
R
Shear V
Moment^ Mmax
P
7-42 A
Figure 13 Cantilever Beam โ Concentrated Load at Free End
Figure 14 Cantilever Beam โ Concentrated Load at Any Point
AMERICAN FOREST & PAPER ASSOCIATION
R 1 R^2
V (^1) Shear V 2
M 1
M 2
7-43 B
x P
w R 1
7-43 A
R 2
V 1 V 2
Shear
M (^1) Mmax
x
Figure 15 Beam Fixed at One End, Supported at Other โ Uniformly DistributedLoad
Figure 16 Beam Fixed at One End, Supported at Other โ Concentrated Load atCenter
AMERICAN FOREST & PAPER ASSOCIATION
V 2
Mmax
x x 1 a
Moment
Shear
R 1 R 2
V 1
P
7-45 B
V 2
Mmax
x wa^ x 1 a
Moment
Shear
R 1 R 2
V 1
7-45 A
Figure 19 Beam Overhanging One Support โ Uniformly Distributed Load onOverhang
Figure 20 Beam Overhanging One Support โ Concentrated Load at End ofOverhang
AMERICAN WOOD COUNCIL
R 1 R 2
w a b c V V 21 V V (^43) MM (^) x 11 X^1 M^ M 23
X
7-46 B
x R 1 R 2
x 1 a b V (^1) V 2
Mmax
Shear
Moment 7-46 A
Figure 21 Beam Overhanging One Support โ Concentrated Load at Any PointBetween Supports
Figure 22 Beam Overhanging Both Supports โ Unequal Overhangs โ UniformlyDistributed Load
AMERICAN WOOD COUNCIL
V (^1) Shear
R 2 R 3
M 1
V 2
Moment
Mmax
x
7-48 B
R 1
V 3
w
x
Moment
PPP
V 2
MMa 2
R 2
V 1
M 1
7-48 A
R 1
Shear
a b
Figure 25 Beam Fixed at Both Ends โ Concentrated Load at Any Point
Figure 26 Continuous Beam โ Two Equal Spans โ Uniform Load on One Span
AMERICAN FOREST & PAPER ASSOCIATION
V (^1) Shear
R 2 R 3
M 1 Mmax Moment
PPP
V 2 V^3
R 1
a b
7-49 B
V (^1) Shear
R 2 R 3
M (^1) Moment
PPP
V 2 V^3
R 1
7-49 A
Mmax
Figure 27 Continuous Beam โ Two Equal Spans โ Concentrated Load at Centerof One Span
Figure 28 Continuous Beam โ Two Equal Spans โ Concentrated Load at AnyPoint
AMERICAN FOREST & PAPER ASSOCIATION
R 1 R 2 R 3
x 1
M Mx 12
V 11 2 V 4^ V V 32
w 1 w 2
x 2
Mx 1
V 1
R 2 R 3
P
V 3
R 1
P
a a b b M (^) m 1
V 4
M^ M 1^ m^2
1 2 V 2
P 1 P 2
Figure 31 Continuous Beam โ Two Unequal Spans โ Uniformly Distributed Load
Figure 32 Continuous Beam โ Two Unequal Spans โ Concentrated Load on EachSpan Symmetrically Placed
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