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Engineering
Data
Section Properties
Section properties are used in various
design calculations. For convenience,
the following are formulas to calculate
the section properties of rectangular
beam cross sections.
Definitions
Neutral axis, in the cross
section of a beam, is the line in
which there is neither tension nor
compression stress.
Moment of Inertia (I) of the cross
section of beam is the sum of the
products of each of its elementary
areas multiplied by the square of
their distance from the neutral axis
of the section.
Section Modulus (S) is the moment
of inertia divided by the distance
from the neutral axis to the extreme
fiber of the section.
Cross Section is a section taken
through the member perpendicular to
its longitudinal axis.
Formulas
The following symbols and formulas
apply to rectangular beam cross sections:
 X-X= neutral axis for edgewise bending
(load applied to narrow face)
Y-Y= Neutral axis for flatwise
bending (load applied to narrow face)
b= breadth of rectangular bending
member(in.)
d= depth of rectangular bending
member(in.)
A= bd=area of cross section (in.2)
c= distance from neutral axis
to extreme fiber of cross section
(in.)
Ixx= bd3/12 = moment
of inertia about the X-X axis (in.4)
Iyy= db3/12 = moment
of inertia about the Y-Y axis (in.4)
rxx= Square root
of (Ixx/A) = d/Square
root of 12 = radius of gyration about
the X-X axis (in.)
ryy= Square root
of (Iyy/A) = b/Square
root of 12 = radius of gyration about
the Y-Y axis (in.)
sxx= Ixx
/c = bd2/6 = section modulus about
the X-X axis (in.3)
syy= Iyy
/c = db2/6 = section modulus about
the Y-Y axis (in.3)
Sizes of rough and dressed Western
Red Cedar are shown in Tables 5 and
6.
Base Design Values
(United States Only)
Since different sizes of visually-graded
lumber have different values, the design
values shown in Table 8 are tabulated
in a base value approach. Base values
are provided for a base size that depends
on the grade. For Select Structural,
No.1, No.2 and No.3 grades, the base
strength values are published on a 2x12
basis. For Construction Standard and
Utility grades, the base strength values
are published on a 2x4 basis (the size
factor is always 1.0). For Stud grade,
the base strength values are published
on a 2x6 basis. These values are for
use in the United States only.
To determine the value for a given
size, the designer selects a base
value for a given grade then multiplies
the base value by a size factor from
Table 9.
The base design values apply to Western
Red Cedar manufactured by members
of the Western Red Cedar Lumber Association
and graded to National Lumber Grading
Authority Rules (NLGA). Grades and
sizes of Canadian dimension lumber
are identical to those in use throughout
the United States and conform to the
requirements of applicable American
Standards. Tabulated values are from
The U.S. Span Book for Canadian
Lumber published by the Canadian
Wood Council (1-800-463-5091).
Span Tables
Spans for Western Red Cedar dimension
lumber used as joists and rafters in
residential and commercial structures
are available from the Western Red Cedar
Lumber Association, the Canadian Wood
Council and the National Association
of Home Builders. Please request publication
The U.S Span Book for Canadian Lumber.
Cost $10.
Table 1. Base Design
Values For Use In The U.S.A. For Western
Red Cedar - 2-4" Thick 2"
and Wider
Base values in pounds per square inch
(psi) - Use with Adjustment Factors
(see Tables 9-13)
Grade
Fb |
Extreme
Fiber Stress in Bending
Ft |
Tension
Parallel Parallel to Grain
Fv |
Horizontal
Shear Fv |
Compression
|
Modulus
of Elasticity (million psi)
E |
| Perpendicular
To Grain Fc(perp) |
Parallel To Grain
Fc |
Select
Structural
No.1/No.2
No.3
|
950
575
350
|
450
275
150
|
65
65
65
|
350
350
350
|
1,100
825
475
|
1.1
1.1
1.0 |
Construction
Standard
Utility
|
675
375
175
|
300
175
75
|
65
65
65
|
350
350
350
|
1,050
850
550
|
1.0
0.9
0.9 |
| Stud
|
450
|
200
|
65
|
350
|
525
|
1.0
|
Notes:
- No.1/No.2 applies to either No.1
or No.2 grades.
- Values for Utility grade apply
only to 2" and 4" lumber.
- For studs wider than 6"
bearing the "Stud" grademark,
use the property values and size
factors for No.3 grade.
Table 2. Size Factors (CF) For Tabulated
Design Values
| Grades |
Nominal Width (depth)(in) |
Fb less than 4 in. thick |
Fb
4 in. thick nominal |
Ft |
Fc |
Other Properties |
Select Structural
No.1
No.2
& No.3
|
4 & less
5
6
8
10
12
14 & wider
|
1.5
1.4
1.3
1.2
1.1
1.0
0.9
|
1.5
1.4
1.3
1.3
1.2
1.1
0.9
|
1.5
1.4
1.3
1.2
1.1
1.0
0.9
|
1.15
1.1
1.1
1.05
1.0
1.0
0.9
|
1.0
1.0
1.0
1.0
1.0
1.0
1.0 |
| Construction &
Standard |
4
& less |
1.0
|
1.0
|
1.0
|
1.0
|
1.0
|
| Utility |
4 |
1.0 |
1.0 |
1.0 |
1.0 |
1.0 |
| Stud* |
4 &less
5&6 |
1.1
1.0 |
1.1
1.0 |
1.1
1.0 |
1.05
1.0 |
1.0
1.0 |
| MSR and plank decking
All grades & sizes |
|
1.0
|
1.0
|
1.0
|
1.0
|
1.0
|
Note: Factors are for Stud grade widths
6" and less. For studs wider than
6", use the design values and size
factors for No.3 grade.
Table 3. Wet Use Factors (CM) For Tabulated
Design Values
The recommended design values
are for applications where the moisture
content of the wood does not exceed
19%. For use conditions where the moisture
content of dimension lumber will exceed
19%, the Wet Use Adjustment Factors
below are recommended:
| Property |
Adjustment Factor |
| Fb Extreme Fiber
Stress in Bending |
0.85*
|
| Ft Tension Parallel to Grain
|
1.0 |
| Fc Compression Parellel to Grain
|
0.8** |
| Fv Horizontal Shear |
0.97 |
| Fc(perp) Compresion Perpendicular
to Grain |
0.67 |
| E Modulus of Elasticity |
0.9 |
Notes:
- Bending Wet Use Factor = 1.0 where
Fb Cf (base value size factor) does
not exceed 1,150 psi.
- Compression Parallel Wet Use
Factor=1.0 where Fc Cf (base value
size factor) does not exceed 750
psi.
Table 4. Flat Use
Factors (Cfu)
Apply to Tabulated Design Values for
Extreme Fiber Stress in Bending Where
Lumber is used Flatwise Rather than
on Edge.
| Nominal Width (inches)
|
Nominal Thickness
(inches) |
|
less than 4 |
4 |
| less than 4 |
1.00
|
|
| 4 |
1.10
|
1.00
|
| 5 |
1.10
|
1.05
|
| 6 |
1.15
|
1.05
|
| 8 |
1.15
|
1.05
|
| 10 & Wider |
1.20
|
1.10
|
Note: These factors apply to all
dimension lumber except tongue-and-grove
decking grades. For T & G decking,
the following adjustments may be used:
| Nominal thickness |
2"
|
3"
|
4"
|
| Flat use factor |
1.10 |
1.04
|
1.00 |
Table 5. Repetitive
Member Factor (Cr)
Applies to Tabulated Design Values
for Extreme Fiber Stress in Bending
when members are used as joists, truss
chords, rafters, studs, planks, decking
or similar members which are in contact
or spaced not more than 24" on
centers, are not less than 3 in number
and are joined by floor, roof or other
load distributing elements adequate
to support the design load.
Table 6. Duration
of Load Adjustment (CD) For Tabulated
Design Values
| Load Duration |
Factor |
| Permanent |
0.9 |
| Ten Years (normal load) |
1.0 |
| Two Months (snow load) |
1.15 |
| Seven Days |
1.25 |
| Ten Minutes (wind, earthquake)
|
1.6 |
| Impact |
2.0 |
Note: Confirm load requirements with
local codes. Refer to Model Building
Codes or the National Design Specification
for high-temperature or fire-retardant
treated adjustment factors.
Table 7. Horizontal
Shear Adjustment For Tabulated Design
Values (CH)
All horizontal shear base values
are established as if a piece were split
full length and as such the values are
reduced from those permitted to be assigned
in accordance with ASTM standards. This
reduction is made to compensate for
any degree of shake, check or split
that might develop in a piece.
| 2 inches Thick (Nominal)
Lumber |
3 inches Thicker
(Nominal) Lumber |
| For
convenience, the table below may
be used to determine horizontal
shear values for any grade of
2" thick lumber in any species
when the length of split or check
is known: |
Horizontal shear
values for 3" and thicker
lumber also are established as
if a piece were split full length.
When specific lengths of splits
are known and any increase in
them is not anticipated, the following
adjustments may be applied: |
| When length of split
on wide face does not exceed:
|
Multiply
tabulated FV value by: |
When length of split
on wide face does not exceed |
Multiply
tabulated FV value by: |
No
split
1/2 wide face
3/4 wide face
1 x wide face
1-1/2 wide face or more
|
2.00
1.67
1.50
1.33
1.00 |
No
split
1/2 x narrow face
1 x narrow face
1-1/2 x narrow face or more
|
2.00
1.67
1.33
1.00 |
Table 8. Adjustments
for Compression Perpendicular To Grain
To Deformation Basis of 0.02"
| Design values for compression
perpendicular to grain are established
in accordance with the procedures
set forth in ASTM D 2555 and D
245. ASTM procedures consider
deformation under bearing loads
as a serviceability limit state
comparable to bending deflection
because bearing loads rarely cause
structural failures. Therefore,
ASTM procedures for determining
compression perpendicular to grain
values are based on a deformation
of 0.04" and are considered
adequate for most classes of structures.
Where more stringent measures
need be taken in design, the following
permits the designer to adjust
design values to a more conservative
deformation basis of 0.02".
|
| Y02=0.73Y04+5.60
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Table 9. Design
Values For Use In the U.S.A. For Visually
Graded (NLGA) Western Red Cedar Timbers
(5" 5" and Larger)
| Grade
|
Size
Class-ification |
Design
Values in pounds per square inch
(psi) |
Extreme
Fiber Stress in Bending
Fb |
Tension
Parallel to Grain
F1 |
Shear
Parallel to Grain
FV |
Compression
Perpendicular to Grain
Fc(perp) |
Compression
Parallelto Grain
Fc |
Modulus
of Elasticity
E |
Select
Strctl.
No.1
No.2
|
Beams
and Stringers |
1,150
925
625
|
675
475
300
|
65
65
65
|
425
425
425
|
850
700
450
|
1,000,000
1,000,000
800,000 |
Select
Strctl.
No.1
No.2
|
Posts
and Timber |
1,050
875
500
|
700
575
350
|
65
65
65
|
425
425
425
|
900
800
550
|
1,000,000
1,000,000
800,000 |
Notes:
- Allowable Extreme Fiber Stress
in Bending applies only when Beams
and Stringers are loaded on narrow
face.
- Where applicable see Tables 9
through 13 for conditions of use
and adjustment factors.
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