BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT

BEAM DESIGN FORMULAS

WITH SHEAR AND MOMENT

DIAGRAMS

2005 EDITION

ANSI/AF&PA NDS-2005

Approval Date: JANUARY 6, 2005

ASD/LRFD

N DS

?

NATIONAL DESIGN SPECIFICATION?

FOR WOOD CONSTRUCTION

WITH COMMENTARY AND

SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION

American

Forest &

Paper

Association

?

x

w?

American W

ood Council

Wood

American Wood Council

R

R

?

2

?

2

V

Shear

V

Mmax

Moment

American

Forest &

DESIGN AID No. 6

Paper

Association

BEAM FORMULAS WITH

SHEAR AND MOMENT

DIAGRAMS

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 .

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-ofthe-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@



AMERICAN WOOD COUNCIL

Notations Relative to ¡°Shear and Moment

Diagrams¡±

Intr

oduction

Introduction

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.

E =

I =

L =

R =

M=

P =

R =

V =

W=

w =

¦¤ =

x =

modulus of elasticity, psi

moment of inertia, in.4

span length of the bending member, ft.

span length of the bending member, in.

maximum bending moment, in.-lbs.

total concentrated load, lbs.

reaction load at bearing point, lbs.

shear force, lbs.

total uniform load, lbs.

load per unit length, lbs./in.

deflection or deformation, in.

horizontal distance from reaction to point

on beam, in.

List of Figur

es

Figures

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Figure 31

Figure 32

Simple Beam ¨C Uniformly Distributed Load ................................................................................................ 4

Simple Beam ¨C Uniform Load Partially Distributed..................................................................................... 4

Simple Beam ¨C Uniform Load Partially Distributed at One End .................................................................. 5

Simple Beam ¨C Uniform Load Partially Distributed at Each End ................................................................ 5

Simple Beam ¨C Load Increasing Uniformly to One End .............................................................................. 6

Simple Beam ¨C Load Increasing Uniformly to Center .................................................................................. 6

Simple Beam ¨C Concentrated Load at Center ............................................................................................... 7

Simple Beam ¨C Concentrated Load at Any Point.......................................................................................... 7

Simple Beam ¨C Two Equal Concentrated Loads Symmetrically Placed....................................................... 8

Simple Beam ¨C Two Equal Concentrated Loads Unsymmetrically Placed .................................................. 8

Simple Beam ¨C Two Unequal Concentrated Loads Unsymmetrically Placed .............................................. 9

Cantilever Beam ¨C Uniformly Distributed Load ........................................................................................... 9

Cantilever Beam ¨C Concentrated Load at Free End .................................................................................... 10

Cantilever Beam ¨C Concentrated Load at Any Point .................................................................................. 10

Beam Fixed at One End, Supported at Other ¨C Uniformly Distributed Load ............................................. 11

Beam Fixed at One End, Supported at Other ¨C Concentrated Load at Center ........................................... 11

Beam Fixed at One End, Supported at Other ¨C Concentrated Load at Any Point ..................................... 12

Beam Overhanging One Support ¨C Uniformly Distributed Load ............................................................... 12

Beam Overhanging One Support ¨C Uniformly Distributed Load on Overhang ......................................... 13

Beam Overhanging One Support ¨C Concentrated Load at End of Overhang ............................................. 13

Beam Overhanging One Support ¨C Concentrated Load at Any Point Between Supports ........................... 14

Beam Overhanging Both Supports ¨C Unequal Overhangs ¨C Uniformly Distributed Load ......................... 14

Beam Fixed at Both Ends ¨C Uniformly Distributed Load ........................................................................... 15

Beam Fixed at Both Ends ¨C Concentrated Load at Center .......................................................................... 15

Beam Fixed at Both Ends ¨C Concentrated Load at Any Point .................................................................... 16

Continuous Beam ¨C Two Equal Spans ¨C Uniform Load on One Span ....................................................... 16

Continuous Beam ¨C Two Equal Spans ¨C Concentrated Load at Center of One Span ................................. 17

Continuous Beam ¨C Two Equal Spans ¨C Concentrated Load at Any Point ................................................ 17

Continuous Beam ¨C Two Equal Spans ¨C Uniformly Distributed Load ....................................................... 18

Continuous Beam ¨C Two Equal Spans ¨C Two Equal Concentrated Loads Symmetrically Placed ............. 18

Continuous Beam ¨C Two Unequal Spans ¨C Uniformly Distributed Load ................................................... 19

Continuous Beam ¨C Two Unequal Spans ¨C Concentrated Load on Each Span Symmetrically Placed ..... 19

AMERICAN FOREST & PAPER ASSOCIATION

Figure 1

Simple Beam ¨C Uniformly Distributed Load

?

x

w?

R

R

?

2

?

2

V

Shear

V

Mmax

Moment

Figure 2

7-36 A

Simple Beam ¨C Uniform Load Partially Distributed

?

a

b

wb

c

R2

R1

x

V1

Shear

V2

R

a + ¡ª1

w

Mmax

Moment

7-36 B

AMERICAN WOOD COUNCIL

Figure 3

Simple Beam ¨C Uniform Load Partially Distributed at One End

?

a

wa

R2

R1

x

V1

Shear

V2

R

¡ª1

w

Mmax

Moment

Figure 4

7-37 ASimple

Beam ¨C Uniform Load Partially Distributed at Each End

?

a

b

w1a

c

w2c

R1

R2

x

V1

Shear

V2

R1

¡ª

w1

Mmax

Moment

7-37 B

AMERICAN FOREST & PAPER ASSOCIATION

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