Beam Design Formulas with Shear and Moment Diagrams

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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

Wood
American Wood Council

American Wood Council
R

R
2

2
V
Shear

V

Mmax
Moment

American
Forest &

DESIGN AID No. 6
DESIGN

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 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-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@afandpa.org
www.awc.org
AMERICAN WOOD COUNCIL

Notations Relative to “Shear and Moment
Diagrams”

Introduction
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=
Δ=
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.

Figures
List of 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 – Uniformly Distributed Load ................................................................................................ 4 Simple Beam – Uniform Load Partially Distributed..................................................................................... 4 Simple Beam – Uniform Load Partially Distributed at One End .................................................................. 5 Simple Beam – Uniform Load Partially Distributed at Each End ................................................................ 5 Simple Beam – Load Increasing Uniformly to One End .............................................................................. 6 Simple Beam – Load Increasing Uniformly to Center .................................................................................. 6 Simple Beam – Concentrated Load at Center ............................................................................................... 7 Simple Beam – Concentrated Load at Any Point.......................................................................................... 7 Simple Beam – Two...
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