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Specifying Siding - 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 |
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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