NATIONAL DESIGN SPECIFICATION® FOR WOOD CONSTRUCTION
American Wood Council American Forest &
Paper Association
N D S
2005 EDITION
®
ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005
WITH COMMENTARY AND
SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION
ASD/LRFD
American WAmerican WAmerican WAmerican WAmerican W ood Councilood Councilood Councilood Councilood 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 FFFFForest & orest & orest & orest & orest &
P P P
P Paper aper aper aper aper Association Association Association Association Association
w
R R
V
V
2 2
Shear
Mmax
Moment x
ᐉ ᐉ
ᐉ ᐉ
DESIGN AID N DESIGN AID N DESIGN AID N
DESIGN AID N DESIGN 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 trade association 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 accuracy of the information presented, and special effort has been made to assure that the information reflects the state-of- the-art, neither the American Forest & Paper Association nor its members assume any responsibility for any particular design prepared from this publication. Those using this document assume all liability from its use.
Copyright © 2007
American Forest & Paper Association, Inc.
American Wood Council 1111 19th St., NW, Suite 800
Washington, DC 20036 202-463-4713 awcinfo@afandpa.org
www.awc.org
BEAM F BEAM F BEAM F
BEAM F BEAM FORMULAS WITH ORMULAS WITH ORMULAS WITH ORMULAS WITH ORMULAS WITH SHEAR AND MOMENT SHEAR AND MOMENT SHEAR AND MOMENT SHEAR AND MOMENT SHEAR AND MOMENT
DIA DIA DIA
DIA DIAGRAMS GRAMS GRAMS GRAMS GRAMS
AMERICAN FOREST & PAPER ASSOCIATION
Figures 1 through 32 provide a series of shear and moment diagrams with accompanying formulas for design of beams under various static loading conditions.
Shear and moment diagrams and formulas are excerpted from the Western Woods Use Book, 4th edition, and are provided herein as a courtesy of Western Wood Products Association.
Intr Intr Intr
Intr Introduction oduction oduction oduction oduction
Notations Relative to “Shear and Moment Diagrams”E
= modulus of elasticity, psi
I= moment of inertia, in.
4L
= 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 Figur List of Figur List of Figur List of Figur List of Figures es es es es
Figure 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 ... 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 ... 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 ... 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 COUNCIL w
R R
V
V
2 2
Shear
Mmax
Moment x
7-36 A ᐉ ᐉ
ᐉ ᐉ
a b c
x
R1 R2
V1
V2 Shear
a + —R1 w
Mmax
Moment wb
7-36 B ᐉ
Figure 1 Simple Beam – Uniformly Distributed Load
Figure 2 Simple Beam – Uniform Load Partially Distributed
AMERICAN FOREST & PAPER ASSOCIATION
R1 R2
V1
V2 Shear
x
R1
—w1
M max
Moment
a b c
w2c w1a
7-37 B ᐉ x
R1 R2
V2 V1
Mmax
Moment Shear
R1
—w a wa
7-37 A ᐉ
Figure 3 Simple Beam – Uniform Load Partially Distributed at One End
Figure 4 Simple Beam – Uniform Load Partially Distributed at Each End
AMERICAN WOOD COUNCIL x
W
2
R R
V
Shear V
Mmax
Moment 2
7-38 B ᐉ
ᐉ ᐉ
W
R1 R2
V1
V2 Shear
Mmax
Moment x
.57741
7-38 A ᐉ
Figure 5 Simple Beam – Load Increasing Uniformly to One End
Figure 6 Simple Beam – Load Increasing Uniformly to Center
AMERICAN FOREST & PAPER ASSOCIATION
x P
a
R1 R2
V1
V2 Shear
M max
Moment b
7-39-b ᐉ
x P
2
R R
V
Shear V
M max
Moment 2
7-39 A ᐉ ᐉ
ᐉ
Figure 7 Simple Beam – Concentrated Load at Center
Figure 8 Simple Beam – Concentrated Load at Any Point
AMERICAN WOOD COUNCIL
x P
a
R1 R2
V1
V2 Shear
M1
Moment P
b
M2
7-40 B ᐉ
x P
a
R R
V
Shear
Mmax
Moment P
a
7-40 A
V ᐉ
Figure 9 Simple Beam – Two Equal Concentrated Loads Symmetrically Placed
Figure 10 Simple Beam – Two Equal Concentrated Loads Unsymmetrically Placed
AMERICAN FOREST & PAPER ASSOCIATION a
R1 R2
V1
V2 Shear
M 1
Moment b
M2
7-41-a x
P1 P2 ᐉ
Figure 11 Simple Beam – Two Unequal Concentrated Loads Unsymmetrically Placed
Figure 12 Cantilever Beam – Uniformly Distributed Load
x
R
Shear V
Moment w
Mmax
7-41- B ᐉ ᐉ
AMERICAN WOOD COUNCIL x
a
V Shear
Moment b
Mmax
7-42-b P
R ᐉ
x
R
V Shear
Moment
Mmax P
7-42 A ᐉ
Figure 13 Cantilever Beam – Concentrated Load at Free End
Figure 14 Cantilever Beam – Concentrated Load at Any Point
AMERICAN FOREST & PAPER ASSOCIATION R1
R2
V1
V2 Shear
M1 2
M2
—3 11
7-43 B 2
x P
ᐉ
ᐉ ᐉ
ᐉ w
R1
7-43 A
R2
V1
V2
—4 Shear
M1
Mmax 3
8 x
ᐉ ᐉ
ᐉ
ᐉ
Figure 15 Beam Fixed at One End, Supported at Other – Uniformly Distributed Load
Figure 16 Beam Fixed at One End, Supported at Other – Concentrated Load at Center
AMERICAN WOOD COUNCIL
a b
R1
V2 Shear
x
Pa— R2 M 1
Moment
R2
V 1
P
M2
7-44 A
Figure 17 Beam Fixed at One End, Supported at Other – Concentrated Load at Any Point
Figure 18 Beam Overhanging One Support – Uniformly Distributed Load
x1
Shear
M2 M1
R1
(1 – a2)
Moment
V 3 V 2
(1 – a2)
2 2
2
x
a w( + a)
R2
V1
7-44 B ᐉ
ᐉ
ᐉ ᐉ
ᐉ ᐉ
AMERICAN FOREST & PAPER ASSOCIATION V2
Mmax x1
x
a
Moment Shear
R1 R2
V 1
P
7-45 B ᐉ
V2
Mmax x1
x
a wa
Moment Shear
R1 R2
V1
7-45 A ᐉ
Figure 19 Beam Overhanging One Support – Uniformly Distributed Load on Overhang
Figure 20 Beam Overhanging One Support – Concentrated Load at End of Overhang
AMERICAN WOOD COUNCIL
R1 R2
w
a b c
V2 V1
V4 V3
Mx
1
M2 M1
M3 X1
X
7-46 B ᐉ
ᐉ x
R1 R2
x1
a b
V1
V2
Mmax
Shear
Moment
7-46 A ᐉ
Figure 21 Beam Overhanging One Support – Concentrated Load at Any Point Between Supports
Figure 22 Beam Overhanging Both Supports – Unequal Overhangs – Uniformly Distributed Load
AMERICAN FOREST & PAPER ASSOCIATION x
V
V
2 2
Shear
Moment
R R
Mmax P
P P
Mmax 4
7-47 B ᐉ
ᐉ ᐉ
ᐉ x
V
V
2 2
Shear
M1
Moment w
R R
Mmax .2113
7-47 A ᐉ
ᐉ
ᐉ ᐉ
ᐉ
Figure 23 Beam Fixed at Both Ends – Uniformly Distributed Load
Figure 24 Beam Fixed at Both Ends – Concentrated Load at Center
AMERICAN WOOD COUNCIL Shear
V1
R3 R2
16 7
M1 V2
Moment Mmax x
7-48 B R1
V3 w
ᐉ ᐉ
ᐉ ᐉ x
Moment P P P
V2
Ma M2 R2
V1
M1
7-48 A R1
Shear
a b
ᐉ
Figure 25 Beam Fixed at Both Ends – Concentrated Load at Any Point
Figure 26 Continuous Beam – Two Equal Spans – Uniform Load on One Span
AMERICAN FOREST & PAPER ASSOCIATION Shear
V1
R3 R2
M1
Moment Mmax
P P P
V3 V2
R1
b a
7-49 B
ᐉ ᐉ
Shear V1
R3 R2
M1
Moment P
P P
V3 V2
R1
2 2
7-49 A Mmax
ᐉ ᐉ
ᐉ ᐉ
Figure 27 Continuous Beam – Two Equal Spans – Concentrated Load at Center of One Span
Figure 28 Continuous Beam – Two Equal Spans – Concentrated Load at Any Point
AMERICAN WOOD COUNCIL
7-50 A
R1 R2 R3
3l/8
0.4215 0.4215
M1
w w
Δmax
V2 V3
l l
l l
l l
M2
3l/8 V1
V2
V1
R3 R2
P P P
V2
R1
P P P
a a a a
Mx x
V2 V3
M1 M2
l l
Figure 29 Continuous Beam – Two Equal Spans – Uniformly Distributed Load
Figure 30 Continuous Beam – Two Equal Spans – Two Equal Concentrated Loads Symmetrically Placed
AMERICAN FOREST & PAPER ASSOCIATION
R1 R2 R3
x1
Mx
2
M1 V1
V4 V3 V2
1 2
1 2
w w
x2
Mx
1
l l
l l
V1
R3 R2
P
V3
R1
P
a a b b
Mm1
V4
M1 Mm
2 2
1
V2
P2 P1
l l
Figure 31 Continuous Beam – Two Unequal Spans – Uniformly Distributed Load
Figure 32 Continuous Beam – Two Unequal Spans – Concentrated Load on Each Span Symmetrically Placed
A F & P A®
American F
American F American F American F
American Forest & P orest & P orest & P orest & P orest & Paper Association aper Association aper Association aper Association aper Association American W
American W American W American W
American Wood Council ood Council ood Council ood Council ood Council 1111 19th S
1111 19th S 1111 19th S 1111 19th S
1111 19th Stree tree tree tree treet, NW t, NW t, NW t, NW t, NW Suit
Suit Suit Suit Suite 800 e 800 e 800 e 800 e 800 W
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Washingt ashingt ashingt ashingt ashington, DC 20036 on, DC 20036 on, DC 20036 on, DC 20036 on, 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: 202-463-2797979791791111 a
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wwwwww www
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