ASTM D5457-23

Standard Specification for Computing Reference Resistance of Wood-Based Materials and Structural Connections for Load and Resistance Factor Design

ABSTRACT
This specification covers procedures for computing the reference resistance of wood-based materials and structural connections for use in load and resistance factor design (LRFD). Parameters required for the derivation of reference resistance are presented. These parameters include the distribution percentile, coefficient of variation, data confidence factor, and reliability normalization factor. The shape and scale parameters of the two-parameter Weibull distribution shall be established to define the distribution of the material resistance. The data confidence factor accounts for uncertainty associated with data sets. This factor, which is a function of coefficient of variation, sample size, and reference percentile, is applied as a multiplier on the distribution estimate. The reliability normalization factor is used to adjust the distribution estimate to achieve a target reliability index. The reliability normalization factor is the ratio of the computed resistance factor to the specified resistance factor, adjusted by a scaling factor.
SCOPE
1.1 This specification covers the format conversion procedure for computing the reference resistance of wood-based materials and structural connections for use in load and resistance factor design (LRFD). The format conversion procedure is outlined in Section 4. The reference resistance derived from this specification applies to the design of structures addressed by the load combinations in ASCE 7-16.  
1.2 A commentary to this specification is provided in Appendix X1.  
1.3 Guidance for users considering test-based derivation of reference resistance is provided in Appendix X2.  
1.4 The values stated in inch-pound units are to be regarded as the standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Apr-2023
• ICS: 35.240.70 - IT applications in science
• Technical Committee: D07 - Wood
• Drafting Committee: D07.02 - Lumber and Engineered Wood Products

Relations

• Refers: ASTM D2718-24 - Standard Test Methods for Structural Panels in Planar Shear (Rolling Shear)
• Effective Date: 15-Feb-2024
• Refers: ASTM D143-23 - Standard Test Methods for Small Clear Specimens of Timber
• Effective Date: 15-Nov-2023
• Refers: ASTM D3737-18(2023)e1 - Standard Practice for Establishing Allowable Properties for Structural Glued Laminated Timber (Glulam)
• Effective Date: 01-Oct-2023
• Refers: ASTM D1761-20 - Standard Test Methods for Mechanical Fasteners in Wood and Wood-Based Materials
• Effective Date: 15-Apr-2020
• Refers: ASTM D1990-19 - Standard Practice for Establishing Allowable Properties for Visually-Graded Dimension Lumber from In-Grade Tests of Full-Size Specimens
• Effective Date: 01-Oct-2019
• Refers: ASTM D4761-19 - Standard Test Methods for Mechanical Properties of Lumber and Wood-Based Structural Materials
• Effective Date: 01-Apr-2019
• Refers: ASTM D5055-19 - Standard Specification for Establishing and Monitoring Structural Capacities of Prefabricated Wood I-Joists
• Effective Date: 01-Mar-2019
• Refers: ASTM D2718-18 - Standard Test Methods for Structural Panels in Planar Shear (Rolling Shear)
• Effective Date: 01-Nov-2018
• Refers: ASTM D3501-05a(2018) - Standard Test Methods for Wood-Based Structural Panels in Compression
• Effective Date: 01-Nov-2018
• Refers: ASTM D4761-18 - Standard Test Methods for Mechanical Properties of Lumber and Wood-Based Structural Materials
• Effective Date: 01-Nov-2018
• Refers: ASTM D5456-18 - Standard Specification for Evaluation of Structural Composite Lumber Products
• Effective Date: 01-Apr-2018
• Refers: ASTM D3737-18 - Standard Practice for Establishing Allowable Properties for Structural Glued Laminated Timber (Glulam)
• Effective Date: 01-Apr-2018
• Refers: ASTM D3737-18e1 - Standard Practice for Establishing Allowable Properties for Structural Glued Laminated Timber (Glulam)
• Effective Date: 01-Apr-2018
• Refers: ASTM D3043-17 - Standard Test Methods for Structural Panels in Flexure
• Effective Date: 15-Nov-2017
• Refers: ASTM D5456-17 - Standard Specification for Evaluation of Structural Composite Lumber Products
• Effective Date: 01-Mar-2017

Overview

ASTM D5457-23 is the standard specification for computing the reference resistance of wood-based materials and structural connections for use in Load and Resistance Factor Design (LRFD). Developed by ASTM International, this standard outlines reliable procedures to ensure consistent calculation of reference resistance values, which are essential for the safety and efficiency of wood-based structural designs. The specification addresses both format conversion from code-recognized allowable stress design (ASD) values and test-based approaches, supporting a unified, reliability-focused method for modern structural engineering.

Key Topics

• Reference Resistance Calculation: Procedures for deriving reference resistance values for wood and wood-based structural materials and connections, vital to the LRFD approach.
• Format Conversion Process: Outlines how to convert ASD values into LRFD values using format conversion factors, creating consistency in design methodologies.
• Statistical Parameters: Includes core parameters such as distribution percentile, coefficient of variation, data confidence factor, and reliability normalization factor, ensuring statistical accuracy in reference resistance.
• Weibull Distribution: Utilizes a two-parameter Weibull distribution to model material resistance distributions, facilitating uniform statistical treatment across product types.
• Test-Based Derivation Guidance: Provides users with insights on conducting test-based resistance derivations, emphasizing appropriate sampling, data confidence, and reliability factors.

Applications

ASTM D5457-23 is essential for professionals involved in the design and evaluation of wood-based structures, particularly when using LRFD. Key practical applications include:

• Structural Engineering Design: Facilitates accurate adjustment of resistance values for beams, columns, shear walls, diaphragms, and mechanical fasteners in wood-based constructions.
• Code Compliance: Ensures wood-based structures are designed in accordance with the load combinations specified in ASCE 7-16, improving safety and regulatory compliance.
• Material Evaluation: Provides manufacturers and engineers with standardized methods for interpreting or developing reference resistance values from both established ASD data and new test results.
• Quality Assurance: Assists quality control programs by defining minimum requirements for sample representativeness, size, and periodic verification.

Engineers, specifiers, and manufacturers benefit from a standardized, statistically robust framework for determining the resistance of wood products-crucial for designing safe and economical buildings.

Related Standards

Several standards are referenced within or related to ASTM D5457-23, enhancing interoperability and consistency across the field:

• ASTM D9: Terminology Relating to Wood and Wood-Based Products
• ASTM D143, D198, D1037, D1761, D2718, D2719, D3043, D3500, D3501, D4761: Various test methods for the physical and mechanical properties of wood products
• ASTM D1990, D3737: Practices for establishing allowable properties for dimension lumber and glued laminated timber
• ASTM D2915: Practice for sampling and data analysis
• ASTM D5055, D5456: Specifications for prefabricated wood I-joists and structural composite lumber
• ASCE 7-16: Minimum Design Loads and Associated Criteria for Buildings and Other Structures

Summary

ASTM D5457-23 underpins the modern reliability-based design of wood structures by standardizing the computation of reference resistance. By detailing statistical treatments, format conversion, and test-based derivation procedures, it ensures that wood-based materials and connections meet safety, performance, and code requirements under LRFD principles. This standard is an indispensable resource for structural engineers and anyone involved in the design or assessment of wood construction, supporting a consistent and scientifically sound approach to structural resistance.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D5457 − 23
Standard Specification for
Computing Reference Resistance of Wood-Based Materials
and Structural Connections for Load and Resistance Factor
Design
This standard is issued under the fixed designation D5457; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
Load and resistance factor design (LRFD) is a structural design method that uses concepts from
reliability theory and incorporates them into a procedure usable by the design community. The basic
design equation requires establishing a reference resistance based on several material property
parameters. A standard method for calculating the required material property input data is critical so
that all wood-based structural materials can be treated equitably. This specification provides the format
conversion procedure that is required for the generation of reference resistance for LRFD. A
non-mandatory appendix of this specification provides broad guidance for users who wish to pursue
the test-based approach for the generation of reference resistance for LRFD.
1. Scope 2. Referenced Documents
1.1 This specification covers the format conversion proce- 2.1 ASTM Standards:
dure for computing the reference resistance of wood-based D9 Terminology Relating to Wood and Wood-Based Prod-
materials and structural connections for use in load and ucts
resistance factor design (LRFD). The format conversion pro- D143 Test Methods for Small Clear Specimens of Timber
cedure is outlined in Section 4. The reference resistance D198 Test Methods of Static Tests of Lumber in Structural
derived from this specification applies to the design of struc- Sizes
tures addressed by the load combinations in ASCE 7-16. D1037 Test Methods for Evaluating Properties of Wood-
Base Fiber and Particle Panel Materials
1.2 A commentary to this specification is provided in
D1761 Test Methods for Mechanical Fasteners in Wood and
Appendix X1.
Wood-Based Materials
1.3 Guidance for users considering test-based derivation of
D1990 Practice for Establishing Allowable Properties for
reference resistance is provided in Appendix X2.
Visually-Graded Dimension Lumber from In-Grade Tests
1.4 The values stated in inch-pound units are to be regarded of Full-Size Specimens
D2718 Test Methods for Structural Panels in Planar Shear
as the standard. The values given in parentheses are mathemati-
cal conversions to SI units that are provided for information (Rolling Shear)
D2719 Test Methods for Wood Structural Panels in Shear
only and are not considered standard.
Through-the-Thickness
1.5 This international standard was developed in accor-
D2915 Practice for Sampling and Data-Analysis for Struc-
dance with internationally recognized principles on standard-
tural Wood and Wood-Based Products
ization established in the Decision on Principles for the
D3043 Test Methods for Structural Panels in Flexure
Development of International Standards, Guides and Recom-
D3500 Test Methods for Wood Structural Panels in Tension
mendations issued by the World Trade Organization Technical
D3501 Test Methods for Wood-Based Structural Panels in
Barriers to Trade (TBT) Committee.
Compression
D3737 Practice for Establishing Allowable Properties for
This specification is under the jurisdiction of ASTM Committee D07 on Wood
and is the direct responsibility of Subcommittee D07.02 on Lumber and Engineered
Wood Products. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved May 1, 2023. Published June 2023. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1993. Last previous edition approved in 2021 as D5457 – 21a. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D5457-23. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5457 − 23
Structural Glued Laminated Timber (Glulam) 3.2.10 resistance factor, ϕ—a factor applied to the resistance
D4761 Test Methods for Mechanical Properties of Lumber side of the LRFD equation.
and Wood-Based Structural Materials
4. Reference Resistance for LRFD
D5055 Specification for Establishing and Monitoring Struc-
tural Capacities of Prefabricated Wood I-Joists
4.1 Reference resistance for LRFD shall be determined
D5456 Specification for Evaluation of Structural Composite
using the format conversion procedure per 4.2.
Lumber Products
NOTE 1—Appendix X2 discusses considerations that should be ad-
E105 Guide for Probability Sampling of Materials
dressed by users considering test-based approaches for the generation of
2.2 ASCE Standard:
reference resistance for LRFD. Appendix X5 provides discussion of
ASCE 7-16 Minimum Design Loads and Associated Criteria
alternative methods to determine reference resistance for LRFD.
for Buildings and Other Structures
4.2 Format Conversion Procedure:
4.2.1 Resistance values for LRFD shall be based on format
3. Terminology
conversion from code-recognized allowable stress design
3.1 Definitions:
(ASD). It shall not be claimed that reference resistance values
3.1.1 For general definitions of terms related to wood, refer
generated in this manner achieve a stated reliability index.
to Terminology D9.
Resistance factors for determining LRFD factored resistance,
3.2 Definitions of Terms Specific to This Standard:
ϕR , are given in Table 1.
n
3.2.1 ASD reference design value, F —the design value at
x
reference conditions used in allowable stress design (ASD) NOTE 2—Examples of standards that are used to generate code-
recognized ASD values include Test Methods D143, D198, D1037,
prior to application of the load duration factor (C ).
D
D1761, D2718, D2719, D3043, D3500, D3501, and D4761; Practices
3.2.2 coeffıcient of variation, CV —the standard deviation
w
D1990 and D3737; and Specifications D5055 and D5456.
divided by the mean of a 2-parameter Weibull distribution.
4.2.2 For standardization purposes, format conversion ref-
3.2.2.1 Discussion—Coefficient of variation, CV , can be
w
erence resistance values shall be based on the arithmetic
calculated three ways: the traditional method of moments;
conversion for a specific design case that results from the
method of maximum likelihood; and method of least squares.
calibration of basic ASD and LRFD equations. Here, the
The method of moments calculates the mean and standard
calibration means providing an identical required section
deviation directly from the data of a complete data set. The
modulus, cross-sectional area, allowable load capacity, and so
methods of maximum likelihood and least squares calculate the
forth. The specific design case was chosen such that changes in
Weibull parameters from complete or incomplete data sets. An
design capacity over the range of expected load cases and load
incomplete data set includes suspended data (for example, data
ratios were minimized.
from proof loading.) Mean and standard deviation (and CV )
w
4.2.3 Values of the format conversion factor, K , are given
F
are then calculated from the Weibull parameters.
in Table 2.
3.2.3 factored resistance—the product of the resistance
4.2.4 The format conversion reference resistance is com-
factor (ϕ) and the reference or nominal resistance (R ).
n
puted by multiplying the ASD resistance by K . For members
F
3.2.4 format conversion factor, K —a factor applied to and connections, the ASD resistance is based on a normal
F
convert resistance from the allowable stress design (ASD) (10-year) load duration. For shear walls and diaphragms, the
format to the LRFD format, equal to the ratio R /F . ASD resistance is based on a 10-min load duration.
n x
4.2.5 For lateral buckling (stability), compression perpen-
3.2.5 lower tail—a portion of an ordered data set consisting
dicular to grain, and rolling shear that is not subject to load
of all test specimens with the lowest property values (for
duration or time effect adjustments, the value of K is based on
F
example, lowest strengths).
the assumption that neither the ASD nor LRFD resistance
3.2.6 nominal resistance—a term equivalent to the reference
values are modified by duration of load or time effect adjust-
resistance used in reliability analysis and LRFD standards.
ments.
3.2.7 reference conditions—the design basis for which all
4.2.6 Format Conversion Example—An ASD bolt design
applicable adjustment factors are equal to unity, except for the
value for a single shear connection, F , is 800 lbf (3.56 kN)
x
load duration factor in ASD or the time effect factor in LRFD.
(based on normal 10-year load duration). From Table 2, the
3.2.8 reference resistance, R —the design value at reference
n
conditions used in LRFD to represent member resistance prior
to application of the resistance factor (ϕ) and the time effect
TABLE 1 Specified LRFD Resistance Factors, ϕ
s
factor (λ).
Application Property ϕ
s
3.2.8.1 Discussion—The reference value represents member
A
Members compression 0.90
resistance at 10-minute load duration.
bending, lateral buckling (stability) 0.85
3.2.9 reliability normalization factor, K —a factor used to tension parallel 0.80
R
shear, radial tension 0.75
establish the reference resistance (R ) to achieve a target
n
Connections all 0.65
reliability index for a specific set of conditions.
Shear Walls, diaphragms shear (wind) 0.80
shear (seismic) 0.50
A
Available from The American Society of Civil Engineers (ASCE), 1801
Compression parallel-to-grain, compression perpendicular-to-grain, and bearing.
Alexander Bell Dr., Reston, VA 20191.
D5457 − 23
TABLE 2 Format Conversion Factor, K
R 5 K F 5 3.32 800 5 2658 lbf 11.82 kN (1)
F ~ !~ ! ~ !~ ! ~ !
n F x
Property K
F
4.2.7 Format Conversion Example for Shear Walls and
Compression Parallel to Grain 2.40
Diaphragms—An ASD shear wall design value, F , is 350 lb/ft
x
Bending 2.54
(5.11 kN/m) for seismic design, and 490 lb/ft (7.15 kN/m) for
Tension Parallel to Grain 2.70
A
Shear 2.88
wind design. From Table 2, the format conversion factor, K , is
F
Radial Tension 2.88
2.8 for seismic design and 2.0 for wind design. The corre-
Connections 3.32
sponding LRFD shear wall reference resistance values for
Lateral Buckling (Stability) 1.76
Compression Perpendicular to Grain 1.67
seismic and wind are as follows:
B
Shear Wall and Diaphragm Shear (wind) 2.00
For seismic:
B
Shear Wall and Diaphragm Shear (seismic) 2.80
A
R 5 ~K !~F ! 5 ~2.8!~350! 5 980 lb/ft ~14.30 kN/m! (2)
The value of the format conversion factor is 2.00 where shear is not subject to
n F x
load duration or time effect adjustments (for example, rolling shear in cross-
laminated timber).
For wind:
B
The format conversion factor for shear wall and diaphragm shear is only intended
to be applied to the design capacity of shear wall or diaphragm assemblies, not to
the design of individual members or subcomponents of these assemblies. R 5 K F 5 2.0 490 5 980 lb/ft 14.30 kN/m (3)
~ !~ ! ~ !~ ! ~ !
n F x
5. Keywords
5.1 format conversion; load and resistance factor design
format conversion factor, K , is 3.32. The corresponding (LRFD); reference resistance; structural connections; test-
F
LRFD bolt reference resistance value is as follows: based derivation; wood-based materials
APPENDIXES
(Nonmandatory Information)
X1. COMMENTARY TO THE TEXT
X1.1 Commentary to the Introduction: reference values and variability) but substantially less than
RBD. In the most advanced LRFD procedures, one needs only
X1.1.1 Load and resistance factor design (LRFD) is a
a distribution type and the parameters that describe that
design format. LRFD is a subset of a broader design method-
distribution. Refinements of these procedures suggest that
ology known as reliability-based design (RBD). The distinc-
estimates of the distribution and its parameters give the most
tion between the two design procedures is significant. RBD
accurate reliability estimates when they represent a tail portion
implies, and often calculates, quantities related to the reliability
of the distribution rather than the full distribution. This reflects
of a member under a given set of conditions. A higher
the fact that, for common building applications, only the lower
reliability corresponds to a lower probability of failure. One
tail of the resistance and upper tail of the load distribution
practical concern that arises when one attempts to apply RBD
contribute to failure probabilities.
to real structural applications is that the calculations must
idealize both the loads and the structural system response to
X1.2 Commentary to Section 1, Scope—Format conversion
reduce it to a mathematically tractable problem. This idealiza-
per 4.2 is the standard method for determination of reference
tion process reduces the final calculation to a theoretically
resistance for LRFD. The test-based approach per Appendix
interesting, but often inapplicable, number. LRFD was devel-
X2 provides broad guidance for users who wish to pursue the
oped by selecting a few of the basic concepts of RBD and using
test-based approach for the generation of reference resistance
them to develop a format that is similar in many ways to
for LRFD. Due to the sensitivity of reliability to changes in
allowable stress design.
some of the parameters, these procedures offer a limited set of
X1.1.2 Previous standards for developing allowable proper- options to ensure that LRFD reference resistances are gener-
ties for many types of wood-based products directed the user to ated in a consistent manner. Other methods for computing
various ways of computing a population lower fifth-percentile reference resistance that are beyond the scope of this standard
estimate. This single number was the basis for an allowable are discussed in Appendix X5.
strength property assignment. At the other extreme, a realistic
X1.3 Commentary to Section 3, Terminology:
RBD would require an accurate definition of a large portion of
the lower tail of the material distribution and a large portion of X1.3.1 The term “factored resistance” is specifically defined
the upper tail of the load distribution. LRFD requires some- as the product of the resistance factor (ϕ) and the nominal
what more information than current procedures (for example, resistance (R ) to differentiate it from the nominal (reference)
n
D5457 − 23
resistance. Users are cautioned to include all applicable adjust- specified values of the resistance factor, ϕ, for LRFD as
ment factors when determining the LRFD adjusted design provided in Table 1.
value.
X1.5 Commentary to Table 2, Format Conversion Factor,
X1.3.2 The term “nominal resistance” is the most widely
K , for Compression Parallel to Grain, Bending,
F
used term in reliability analysis and material specifications. As
Tension Parallel to Grain, Shear, Radial Tension and
described in Ref (1), users are cautioned that the term
Connections:
“nominal” has been defined in various ways over the years.
X1.5.1 The format conversion factors for compression par-
This standard focuses on the term “reference resistance,” used
allel to grain, bending, tension parallel to grain, shear, radial
in the NDS.
tension and connections that are subject to load duration or
X1.3.3 The term “reference conditions” is added to clarify
time effect adjustments, can be obtained from Eq X1.2.
that the design checking equations presented in this specifica-
X1.5.2 The factor of 2.16 is the algebraic solution at the
tion do not include notations for the myriad of potential
calibration point, the ratio of R / F for S/D = 3, λ = 0.80, and
n x
end-use adjustment factors that might be applicable to specific
C = 1.15.
D
designs. The rationale is that all end-use adjustment factors,
with the notable exceptions of the load duration factor in ASD LRFD: λϕR $ 1.2D11.6 L or S (X1.1)
~ !
n
and the time effect factors in LRFD, are identical in both
ASD: C F $ D1~L or S! (X1.2)
D x
design formats and will mathematically cancel in the calcula-
where:
tion of the ratio R / F . Users are cautioned to include all
n x
λ = time effect factor (LRFD),
applicable adjustment factors when determining the LRFD
ϕ = specified resistance factor (LRFD),
adjusted design value.
R = reference resistance value (LRFD),
n
X1.3.4 The term “reference resistance” is retained as the
D, L, S = dead, live, and snow load effects, respectively,
primary terminology in this version of the standard for contin-
C = load duration factor (ASD), and
D
ued compatibility with the NDS (2) and other design
F = ASD design value (ASD).
x
documents, but its definition is clarified to indicate that it does
Substituting and solving for K (= R /F ):
F n x
not include the resistance factor (ϕ), the time-effect factor (λ)
K 5 2.16/ϕ (X1.3)
and other adjustments for end-use conditions that will be
F s
subsequently applied in the design checking equation.
X1.5.3 Use of a single constant for the format conversion
factor, K , is appropriate, based on the judgment of the
X1.3.5 As discussed in Ref (3), an underlying assumption in F
committee, over a broad range of design cases. As shown in
virtually all reliability analyses is that every adjustment factor
Fig. X1.1, this judgment produces exact calibration between
applied in the design checking equation applies equally across
ASD and LRFD for one specific design case (S/D = 3, C =
the entire resistance population. From an analysis standpoint, d
1.15, λ = 0.8). Differences between ASD and LRFD designs
this results in identical reliability indices for the reference and
will result for other design cases. The algebraic format con-
adjusted design cases.
version solution for the precise constant in the numerator of Eq
X1.3.6 Ref (3) also describes the difficulty of applying the
X1.3 is not to be confused as the RBD basis supporting Eq
same judgment to the time effect factor (λ). The time effect
X1.3 (see Appendix X2). The RBD basis of the format
factor is different from other design adjustment factors in two
conversion factor involved first order, second moment reliabil-
respects. First, it represents an interaction between the load
ity methods to graph R /F across a range of load ratios for
n x
side and the resistance side of the design equation. This fact
three distinct live-load cases (occupancy floor, snow roof, and
leads to a dilemma regarding the format of the design checking
non-snow roof), where R and F come directly from the LRFD
n x
equation: should the time effect factor be expressed separately
and ASD design equations. The factor in the numerator of Eq
(that is, λϕ R ) or embedded into the adjusted resistance like
s n
X1.3 is in the range from 2.1 to 2.2 and resulted from the
other adjustment factors? Second, test specimens at the lower
application of engineering judgment as a balance of increases
tail of the strength distribution exhibit shorter times to failure
for floors at low L/D ratios versus decreases for non-snow
under constant load than those higher in the distribution, while
roofs at higher L/D ratios.
most of those at the upper end don’t fail at all, because they are
effectively loaded at a lower stress ratio.
X1.6 Commentary to Table 2, Format Conversion Factor,
K , for Lateral Buckling (Stability), Compression
F
X1.4 Commentary to 4.2, Format Conversion—Format
Perpendicular to Grain, and Rolling Shear not subject
conversion is the method used to develop format conversion
to load duration or time effect adjustments:
factors to adjust reference ASD design values (based on normal
X1.6.1 The format conversion factors for lateral buckling
10-year load duration) to LRFD reference resistances (based on
(stability), compression perpendicular to grain, and rolling
10-min load duration). Format conversion factors in Table 2
shear values that are not subject to load duration or time effect
are developed to provide similar member and connection sizes
adjustments, can be obtained from Eq X1.4:
when considering specific ASD and LRFD load cases and
K 5 1.5/ϕ (X1.4)
F s
X1.6.2 The K of 1.5/ϕ is the algebraic solution at the point
The boldface numbers in parentheses refer to a list of references at the end of F
this standard. of calibration - the ratio of R /F for L/D = 3. Terms λ and C
n x D
D5457 − 23
FIG. X1.1 R /F Producing Exact Calibration Between ASD and LRFD for Bending (ϕ = 0.85; K = 2.16/ϕ = 2.54)
n x s F s
do not appear in the design checking equations because they tabulated E values (fifth percentile shear-free E values
min
are not applicable for modulus of elasticity for beam and divided by a 1.66 safety factor) to simplify design equations for
column stability (E ), compression perpendicular to grain, beam and column stability and to enable use of the same
min
and rolling shear in accordance with the NDS.
equations for both ASD and LRFD.
LRFD: ϕ R $ 1.2D11.6 L or S (X1.5) X1.6.4.1 E values tabulated in the NDS Design Value
~ !
s n min
Supplement for sawn lumber are estimated in accordance with
ASD: F $ D1 L or S (X1.6)
~ !
x
Eq X1.9 where for sawn lumber E = 1.03E(1-1.645(COV )):
05 E
Substituting and solving for K ~ 5 R ⁄ F !:
F n x
1.03E 1 2 1.645 COV
~ ~ !!
E
E 5 (X1.9)
min
1.66
K 5 1.5/ϕ
F s
X1.6.5 Format Conversion for ASD Deformation-Based
X1.6.3 Format Conversion for Lateral Buckling
Compression Perpendicular to Grain Values—Wood compres-
(Stability)—The format conversion factor of 1.76 for stability
is applied to E which is the modulus of elasticity used in sion perpendicular to grain stresses are based on serviceability
min
ASD for beam stability and column stability calculations (not criteria from testing of small specimens (Test Methods D143,
to the average modulus of elasticity, E, used for deflection
square cross-section block, 2 in. loading block). However, in
calculations). Using the format conversion factor of 1.76, E
many cases, these allowable stresses are being applied more
min
for LRFD can be calculated from E as follows:
broadly. In some compression perpendicular to grain
applications, especially where laterally unsupported tall/
For ASD: E 5 E /1.66 (X1.7)
min 05
narrow sections are used, failure modes, such as instability or
where:
splitting, can occur. These failure modes have been demon-
E = fifth percentile shear-free E value, and
strated in short-term tests to occur at compression perpendicu-
1.66 = safety factor for beam and column stability
lar to grain stress levels as low as 1.5 times the ASD value for
calculations.
compression perpendicular to grain. Designers must be certain
For LRFD: Multiply by K 5 1.5/ϕ (X1.8) to check the failure modes of buckling or splitting that may
F s
now control the design. Alternatively, the designer may choose
E 5 E /1.66 1.76
~ !~ !
min 05
to brace the tall/narrow member at the bearing to prevent this
mode from occurring.
5 1.06 E
~ !~ !
X1.6.6 One method to compute buckling capacity in the
X1.6.4 Equations for K and K contained in the 2001
bE cE
perpendicular to grain direction for ASD may be done by using
NDS beam and column stability provisions adjust tabulated
average modulus of elasticity, E, values to fifth percentile an elastic-buckling (Euler) type formula similar to that now
used for visually graded lumber. This calculation could supple-
shear-free E values divided by a 1.66 safety factor. In the 2005
NDS, K and K equations were replaced with a reference to ment the standard ASD compression perpendicular to grain
bE cE
D5457 − 23
calculation. In the calculation, the relevant modulus of elastic- X1.7.4.1 To simplify the initial transition to LRFD in the
ity is the transverse modulus (often assumed to be E/20) and 1990s, Specification D5457 adopted a single resistance factor,
the relevant dimensions (relative to buckling direction) would
ϕ, for shear walls and diaphragms. Subsequently, Special
also be substituted.
Design Provisions for Wind and Seismic (SDPWS) accommo-
dated the use of a single ϕ and differences in historical design
X1.7 Commentary to Table 2, Format Conversion Factor,
levels between seismic design and wind design by tabulating
K , for Shear Walls and Diaphragms:
F
different nominal unit shear capacities for seismic and wind.
X1.7.1 The format conversion factor, K = 2.0 for wind and
F More recently, simplification of the shear wall and diaphragm
K = 2.8 for seismic, for shear walls and diaphragms has been
F tables to utilize a single nominal unit shear capacity value
derived as the algebraic solution (with rounding) at specific
associated with a nominal strength estimate is coupled with
points of calibration. The ratio of R /F for ϕ = 0.80 for wind
n x s
different values of ϕ for seismic design and wind design. For
design, and the ratio of R /F for ϕ = 0.50 for seismic design,
n x s
LRFD, ϕ = 0.5 for seismic design and ϕ = 0.8 for wind design.
and where F is determined in accordance with SDPWS in Ref
x
For ASD, the ASD reduction factor is 2.8 for seismic design
(4). Terms λ and C do not appear in the design checking
D
and 2.0 for wind design. Calibration arithmetic in accordance
equations because design values for wind and seismic load
with 2021 SDPWS follows.
cases in accordance with SDPWS Ref (4) are tabulated based
Allowable nominal unit shear capacity for seismic design and
on a 10-min load duration and require no further designer
wind design in accordance with 2021 SDPWS:
adjustment for short duration wind or seismic loading.
v 5 v⁄2.8 (X1.14)
ASD2SEISMIC
X1.7.2 Design equations for wind load effects based on
v 5 v⁄2.0 (X1.15)
ASD2WIND
wind load factors from ASCE 7–16 are as follows:
where:
LRFD: ϕ R $ 1.0 W (X1.10)
s n
v = nominal unit shear capacity.
ASD: F $ 0.6 W (X1.11)
x
Substituting and solving for K (=R /F ):
F n x
Design checking equations for seismic:
K = 1.0 ⁄(0.6ϕ ) = 2.08
F s
ASD:v⁄2.8 $ 0.7 E (X1.16)
where:
LRFD: ~ϕ !~v! $ 1.0 E (X1.17)
W = wind load effects. seismic
X1.7.3 Design equations for seismic (earthquake) load ef-
Substituting and solving for ϕ :
seismic
fects are as follows:
0.7E~2.8! 5 1.0E⁄ϕ (X1.18)
seismic
LRFD: ϕ R $ 1.0 E (X1.12)
s n
ϕ 5 0.510
seismic
ASD: F $ 0.7 E (X1.13)
x
A rounded value of ϕ = 0.5 for seismic design is specified in
Substituting and solving for K (=R /F ):
F n x
2021 SDPWS.
K =1.43 ⁄ϕ = 2.86
F s
Design checking equations for wind:
where:
ASD:v⁄2.0 $ 0.6 W (X1.19)
E = earthquake load effects.
LRFD: ~ϕ !~v! $ 1.0 W (X1.20)
wind
X1.7.4 The rounded values of the format conversion factor,
Substituting and solving for ϕ wind:
K , in Table 2 are slightly conservative to values derived from
F
exact calibration (that is, approximately 4 % for wind and 2 % 0.6W 2.0 5 1.0W⁄ϕ (X1.21)
~ !
wind
for seismic). Table 1 factors for shear walls and diaphragms are
ϕ 5 0.833 (X1.22)
wind
consistent with those within SDPWS. The following section is
provided to assist users to trace the history of these factors
A rounded value of ϕ = 0.8 for wind design is specified in
within Specification D5457. 2021 SDPWS.
D5457 − 23
X2. USING TEST-DATA TO COMPUTE REFERENCE RESISTANCE VALUES FOR LRFD
X2.1 Overview of this Appendix—The primary purpose of design condition should be used to define the target – since
this specification is to provide users with the ability to generate computed reliability indices are different for various load
reference resistance values for LRFD by applying format
combinations?
conversion factors to generally accepted allowable stress
X2.2.2 Other Data Collection Decisions—Similarly, when a
design (ASD) values. Prior versions of this specification also
production facility wisely chose to include a broad range of
included an annex that permitted users to derive LRFD
potential variability in a candidate data set (such as production
reference resistance values directly from test-data. More
over multiple time periods or multiple manufacturing lines),
recently, the Committee felt that the prior annex had outlived
this decision would penalize that facility with lower computed
its usefulness for several reasons. First, because the field of
reliability indices (because increasing variability leads to
reliability analysis has evolved dramatically since this specifi-
decreasing computed reliability).
cation was originally approved in 1993, the methods embodied
in the annex were outdated. Second, the Committee
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D5457 − 21a D5457 − 23
Standard Specification for
Computing Reference Resistance of Wood-Based Materials
and Structural Connections for Load and Resistance Factor
Design
This standard is issued under the fixed designation D5457; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
Load and resistance factor design (LRFD) is a structural design method that uses concepts from
reliability theory and incorporates them into a procedure usable by the design community. The basic
design equation requires establishing a reference resistance based on several material property
parameters. A standard method for calculating the required material property input data is critical so
that all wood-based structural materials can be treated equitably. This specification provides the
procedures that areformat conversion procedure that is required for the generation of reference
resistance for LRFD. A non-mandatory appendix of this specification provides broad guidance for
users who wish to pursue the test-based approach for the generation of reference resistance for LRFD.
1. Scope
1.1 This specification covers procedures the format conversion procedure for computing the reference resistance of wood-based
materials and structural connections for use in load and resistance factor design (LRFD). The format conversion procedure is
outlined in Section 4. The test-based derivation procedure is outlined in Annex A1. The reference resistance derived from this
specification applies to the design of structures addressed by the load combinations in ASCE 7-16.
1.2 A commentary to this specification is provided in Appendix X1.
1.3 Guidance for users considering test-based derivation of reference resistance is provided in Appendix X2.
1.4 The values stated in inch-pound units are to be regarded as the standard. The values given in parentheses are mathematical
conversions to SI units that are provided for information only and are not considered standard.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
This specification is under the jurisdiction of ASTM Committee D07 on Wood and is the direct responsibility of Subcommittee D07.02 on Lumber and Engineered Wood
Products.
Current edition approved May 1, 2021May 1, 2023. Published May 2021June 2023. Originally approved in 1993. Last previous edition approved in 2021 as
D5457 – 21.D5457 – 21a. DOI: 10.1520/D5457-21A.10.1520/D5457-23.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5457 − 23
2. Referenced Documents
2.1 ASTM Standards:
D9 Terminology Relating to Wood and Wood-Based Products
D143 Test Methods for Small Clear Specimens of Timber
D198 Test Methods of Static Tests of Lumber in Structural Sizes
D1037 Test Methods for Evaluating Properties of Wood-Base Fiber and Particle Panel Materials
D1761 Test Methods for Mechanical Fasteners in Wood and Wood-Based Materials
D1990 Practice for Establishing Allowable Properties for Visually-Graded Dimension Lumber from In-Grade Tests of Full-Size
Specimens
D2718 Test Methods for Structural Panels in Planar Shear (Rolling Shear)
D2719 Test Methods for Wood Structural Panels in Shear Through-the-Thickness
D2915 Practice for Sampling and Data-Analysis for Structural Wood and Wood-Based Products
D3043 Test Methods for Structural Panels in Flexure
D3500 Test Methods for Wood Structural Panels in Tension
D3501 Test Methods for Wood-Based Structural Panels in Compression
D3737 Practice for Establishing Allowable Properties for Structural Glued Laminated Timber (Glulam)
D4761 Test Methods for Mechanical Properties of Lumber and Wood-Based Structural Materials
D5055 Specification for Establishing and Monitoring Structural Capacities of Prefabricated Wood I-Joists
D5456 Specification for Evaluation of Structural Composite Lumber Products
E105 Guide for Probability Sampling of Materials
2.2 ASCE Standard:
ASCE 7-16 Minimum Design Loads and Associated Criteria for Buildings and Other Structures
3. Terminology
3.1 Definitions:
3.1.1 For general definitions of terms related to wood, refer to Terminology D9.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 ASD reference design value, F —the design value at reference conditions used in allowable stress design (ASD) prior to
x
application of the load duration factor (C ).
D
3.2.2 coeffıcient of variation, CV —the standard deviation divided by the mean of a 2-parameter Weibull distribution.
w
3.2.2.1 Discussion—
Coefficient of variation, CV , can be calculated three ways: the traditional method of moments; method of maximum likelihood;
w
and method of least squares. The method of moments calculates the mean and standard deviation directly from the data of a
complete data set. The methods of maximum likelihood and least squares calculate the Weibull parameters from complete or
incomplete data sets. An incomplete data set includes suspended data (for example, data from proof loading.) Mean and standard
deviation (and CV ) are then calculated from the Weibull parameters.
w
3.2.3 data confidence factor, Ω—a factor that is used to adjust member reference resistance for sample variability and sample size.
3.2.4 distribution percentile, R —the value of the distribution associated with proportion, p, of the cumulative distribution
p
function.
3.2.3 factored resistance—the product of the resistance factor (ϕ) and the reference or nominal resistance (R ).
n
3.2.4 format conversion factor, K —a factor applied to convert resistance from the allowable stress design (ASD) format to the
F
LRFD format, equal to the ratio R /F .
n x
3.2.5 lower tail—a portion of an ordered data set consisting of all test specimens with the lowest property values (for example,
lowest strengths).
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from The American Society of Civil Engineers (ASCE), 1801 Alexander Bell Dr., Reston, VA 20191.
D5457 − 23
3.2.6 nominal resistance—a term equivalent to the reference resistance used in reliability analysis and LRFD standards.
3.2.7 reference conditions—the design basis for which all applicable adjustment factors are equal to unity, except for the load
duration factor in ASD or the time effect factor in LRFD.
3.2.8 reference resistance, R —the design value at reference conditions used in LRFD to represent member resistance prior to
n
application of the resistance factor (ϕ) and the time effect factor (λ).
3.2.8.1 Discussion—
The reference value represents member resistance at 10-minute load duration.
3.2.9 reliability normalization factor, K —a factor used to establish the reference resistance (R ) to achieve a target reliability
R n
index for a specific set of conditions.
3.2.10 resistance factor, ϕ—a factor applied to the resistance side of the LRFD equation.
4. Reference Resistance for LRFD
4.1 Reference resistance for LRFD shall be determined using one of the following procedures:the format conversion procedure
per 4.2.
NOTE 1—Appendix X2 discusses considerations that should be addressed by users considering test-based approaches for the generation of reference
resistance for LRFD. Appendix X5 provides discussion of alternative methods to determine reference resistance for LRFD.
4.1.1 Format conversion per Section 4.2; or
4.1.2 Test-based derivation per Annex A1.
4.2 Format Conversion Procedure:
4.2.1 Resistance values for LRFD are permitted to shall be based on format conversion from code-recognized allowable stress
design (ASD). It shall not be claimed that reference resistance values generated in this manner achieve a stated reliability index.
Resistance factors for determining LRFD factored resistance, ϕR , are given in Table 1.
n
NOTE 2—Examples of standards that are used to generate code-recognized ASD values include Test Methods D143, D198, D1037, D1761, D2718, D2719,
D3043, D3500, D3501, and D4761; Practices D1990 and D3737; and Specifications D5055 and D5456.
4.2.2 For standardization purposes, format conversion reference resistance values shall be based on the arithmetic conversion for
a specific design case that results from the calibration of basic ASD and LRFD equations. Here, the calibration means providing
an identical required section modulus, cross-sectional area, allowable load capacity, and so forth. The specific design case was
chosen such that changes in design capacity over the range of expected load cases and load ratios were minimized.
4.2.3 Values of the format conversion factor, K , are given in Table 2.
F
4.2.4 The format conversion reference resistance is computed by multiplying the ASD resistance by K . For members and
F
TABLE 1 Specified LRFD Resistance Factors, ϕ
s
Application Property ϕ
s
A
Members compression 0.90
bending, lateral buckling (stability) 0.85
tension parallel 0.80
shear, radial tension 0.75
Connections all 0.65
Shear Walls, diaphragms shear (wind) 0.80
shear (seismic) 0.50
A
Compression parallel-to-grain, compression perpendicular-to-grain, and bearing.
D5457 − 23
TABLE 2 Format Conversion Factor, K
F
Property K
F
Compression Parallel to Grain 2.40
Bending 2.54
Tension Parallel to Grain 2.70
A
Shear 2.88
Radial Tension 2.88
Connections 3.32
Lateral Buckling (Stability) 1.76
Compression Perpendicular to Grain 1.67
B
Shear Wall and Diaphragm Shear (wind) 2.00
B
Shear Wall and Diaphragm Shear (seismic) 2.80
A
The value of the format conversion factor is 2.00 where shear is not subject to
load duration or time effect adjustments (e.g., (for example, rolling shear in
cross-laminated timber).
B
The format conversion factor for shear wall and diaphragm shear is only intended
to be applied to the design capacity of shear wall or diaphragm assemblies, not to
the design of individual members or subcomponents of these assemblies.
connections, the ASD resistance is based on a normal (10-year) load duration. For shear walls and diaphragms, the ASD resistance
is based on a 10-minute10-min load duration.
4.2.5 For lateral buckling (stability), compression perpendicular to grain, and rolling shear that is not subject to load duration or
time effect adjustments, the value of K is based on the assumption that neither the ASD nor LRFD resistance values are modified
F
by duration of load or time effect adjustments.
4.2.6 Format Conversion Example—An ASD bolt design value for a single shear connection, F , is 800 lbf (3.56 kN) (based on
x
normal 10-year load duration). From Table 2, the format conversion factor, K , is 3.32. The corresponding LRFD bolt reference
F
resistance value is as follows:
R 5 K F 5 3.32 800 5 2658 lbf 11.82 kN (1)
~ !~ ! ~ !~ ! ~ !
n F x
4.2.7 Format Conversion Example for Shear Walls and Diaphragms—An ASD shear wall design value, F , is 350 lb/ft (5.11
x
kN/m) for seismic design, and 490 lb/ft (7.15 kN/m) for wind design. From Table 2, the format conversion factor, K , is 2.8 for
F
seismic design and 2.0 for wind design. The corresponding LRFD shear wall reference resistance values for seismic and wind are
as follows:
For seismic:
R 5 ~K !~F ! 5 ~2.8!~350!5 980lb/ft~14.30kN/m! (2)
n F x
For wind:
R 5 ~K !~F ! 5 ~2.0!~490!5 980lb/ft~14.30kN/m! (3)
n F x
5. Keywords
5.1 format conversion; load and resistance factor design (LRFD); reference resistance; structural connections; test-based
derivation; wood-based materials
D5457 − 23
ANNEX
(Mandatory Information)
A1. TEST-BASED DERIVATION OF REFERENCE RESISTANCE FOR LRFD
A1.1 Parameters required for the derivation of reference resistance are presented in this Annex. These parameters include the
distribution percentile, R , coefficient of variation, CV , data confidence factor, Ω, and reliability normalization factor, K . An
p w R
example derivation of reference resistance is provided in X1.8.5.
A1.2 Sampling:
A1.2.1 Samples selected for analysis and implementation with this specification shall be representative of the population about
which inferences are to be made. Both manufacturing and material source variability shall be considered. The principles of Practice
E105 shall be maintained. Practice D2915 provides methods for establishing a sampling plan. Special attention is directed to
sampling procedures in which the variability is low and results can be influenced significantly by manufacturing variables. It is
essential that the sampling plan addresses the relative magnitude of the sources of variability.
A1.2.1.1 Data generated from a quality control program shall be acceptable if the criteria of A1.2.1 are maintained.
A1.2.1.2 Multiple Data Sets—When data from multiple data sets are compiled or grouped, the criteria used to group such data
shall be in accordance with the provisions of A1.2.1. When such procedures are available in applicable product standards, they
shall be used.
A1.2.2 Sample Size:
A1.2.2.1 For data sets in which all specimens are tested to failure, the minimum sample size shall be 30.
NOTE A1.1—The confidence with which population properties can be estimated decreases with decreasing sample size. For sample sizes less than 60,
extreme care must be taken during sampling to ensure a representative sample.
A1.2.2.2 For lower tail data sets, a minimum of 60 failed observations is required for sample sizes of n = 600 or less. This
represents at least the lower 10 % of the distribution. For sample sizes greater than 600, a minimum of the lowest 10 % of the
distribution is required. For example, sample size, n = 720, 0.10 (720) = 72 failed test specimens in the lower tail. Only parameter
estimation procedures designed specifically for lower tail data sets shall be used (see Appendix X2).
A1.3 Testing:
A1.3.1 Testing shall be conducted in accordance with appropriate standard testing procedures. The intent of the testing shall be
to develop data that represent the capacity of the product under standard conditions.
A1.3.2 Periodic Property Assessment—Periodic testing is recommended to verify that the properties of production material remain
representative of published properties.
D5457 − 23
A1.4 Reference Resistance, R —The following equation establishes reference resistance for LRFD:
n
R 5 ~R !~Ω!~K ! (A1.1)
n p R
where:
R = distribution percentile estimate,
p
Ω = data confidence factor, and
K = reliability normalization factor.
R
A1.4.1 Distribution Percentile Estimate, R :
p
A1.4.2 Eq A1.2 is intended to be used to calculate any percentile of a two-parameter Weibull distribution. The percentile of interest
depends on the property being estimated.
1⁄α
R 5η -ln 1 2 p (A1.2)
@ ~ !#
p
where:
η = Weibull scale parameter,
p = percentile of interest expressed as a decimal (for example, 0.05), and
α = Weibull shape parameter.
A1.4.3 The shape (α) and scale (η) parameters of the two-parameter Weibull distribution shall be established to define the
distribution of the material resistance (1). Algorithms for common estimation procedures are provided in Appendix X2.
A1.4.4 Coeffıcient of Variation, CV —The coefficient of variation of the material is necessary when determining the data
w
confidence factor, Ω, and the reliability normalization factor, K . The CV can be estimated from the shape parameter of the
R w
Weibull distribution as follows:
20.92
CV >α (A1.3)
w
NOTE A1.2—The above approximation is within 1 % of the exact solution for CV values between 0.09 and 0.50. An exact relationship of CV and α
w w
is shown in Appendix X3.
A1.5 Data Confidence Factor, Ω—The data confidence factor accounts for uncertainty associated with data sets (2). This factor,
which is a function of coefficient of variation, sample size, and specified percentile, is applied as a multiplier on the distribution
estimate. Table A1.1 provides data confidence factors appropriate for lower fifth-percentile estimates.
NOTE A1.3—When a distribution tolerance limit is developed on a basis consistent with Ω, the data confidence factor is taken as unity.
A1.6 Reliability Normalization Factor, K —The reliability normalization factor, K , which is a function of CV and is generated
R R w
for specific target reliability indices, is used to adjust the distribution estimate (for example, R ) to achieve a target reliability
0.05
index. The reliability normalization factor is the ratio of the computed resistance factor, ϕ (X1.8.5), to the specified resistance
c
factor, ϕ (Table 1), adjusted by a scaling factor, which is a function of CV and is generated for specific target reliability indices.
s w
The boldface numbers in parentheses refer to a list of references at the end of this standard.
D5457 − 23
The K values presented in Table A1.2 were computed at a live-to-dead load ratio of 3. Computations (FORTRAN code listings
R
reflecting 1980’s methodologies) for determining reliability indices are contained in Refs (3) and (4). Calculations to derive input
parameters for reliability analyses are outlined in Ref (5).
A1.7 Presentation of Results:
A1.7.1 Report the sampling plan and testing in accordance with applicable standards. When lower tail data sets are used, report
the sample size and data used in the calculations. Report the estimated shape and scale parameters along with the calculated
coefficient of variation. When appropriate, also report the mean and standard deviation (derived from the calculated coefficient of
variation). Include a plot showing the data points and fitted Weibull distribution. In addition to these basic parameters, also report
the data confidence factor, Ω, calculated percentile estimate, R , reliability normalization factor, K , and reference resistance, R .
p R n
APPENDIXES
(Nonmandatory Information)
X1. COMMENTARY TO THE TEXT
X1.1 Commentary to the Introduction:
X1.1.1 Load and resistance factor design (LRFD) is a design format. LRFD is a subset of a broader design methodology known
as reliability-based design (RBD). The distinction between the two design procedures is significant. RBD implies, and often
calculates, quantities related to the reliability of a member under a given set of conditions. A higher reliability corresponds to a
lower probability of failure. One practical concern that arises when one attempts to apply RBD to real structural applications is
that the calculations must idealize both the loads and the structural system response to reduce it to a mathematically tractable
problem. This idealization process reduces the final calculation to a theoretically interesting, but often inapplicable, number. LRFD
was developed by selecting a few of the basic concepts of RBD and using them to develop a format that is similar in many ways
to current (allowable stress) design. LRFD provides incremental improvements in the design process in this way. The
improvements provided by LRFD include the following:allowable stress design.
X1.1.1.1 Consideration of the variability of various types of loads when assessing safety factors.
X1.1.1.2 Consideration of the consequences of various potential failure modes in a structure.
X1.1.1.3 Material resistance values that relate more closely to test data (member capacities).
X1.1.1.4 Consideration of resistance variability.
X1.1.2 Previous standards for developing allowable properties for many types of wood-based products directed the user to various
ways of computing a population lower fifth-percentile estimate. This single number was the basis for an allowable strength
property assignment. At the other extreme, a realistic RBD would require an accurate definition of a large portion of the lower tail
of the material distribution and a large portion of the upper tail of the load distribution. LRFD requires somewhat more information
than current procedures (for example, reference values and variability) but substantially less than RBD. In the most advanced
LRFD procedures in use today, procedures, one needs only a distribution type and the parameters that describe that distribution.
Refinements of these procedures suggest that estimates of the distribution and its parameters give the most accurate reliability
D5457 − 23
estimates when they represent a tail portion of the distribution rather than the full distribution. This reflects the fact that, for
common building applications, only the lower tail of the resistance and upper tail of the load distribution contribute to failure
probabilities.
X1.1.3 Simulations have shown that the assumed distribution type can have a strong effect on computed LRFD resistance factors.
However, much of this difference is due to the inability of standard distribution forms to fit the tail data precisely. By standardizing
the distribution type, this procedure provides a consistent means for deriving these factors. In addition, by permitting tail fitting
of the data, it provides a way of fitting data in this important region that is superior to full-distribution types.
X1.1.4 While the two-parameter Weibull distribution is the underlying basis for these calculations, the user of this specification
is not burdened with applying statistical decisions. For LRFD purposes, the user must calculate the shape and scale parameters for
the fitted Weibull distribution using the equations in the specification. All remaining steps in the calculations of a reference
resistance are spelled out in the equations of the specification.
X1.2 Commentary to Section 1, Scope—The calculation procedures identifiedFormat conversion per 4.2 in this specification are
common statistical procedures. This specification gives the user a document for all calculations necessary to develop LRFD
reference resistances. Format conversion per Section is the standard method for determination of reference resistance for LRFD.
The 4.2 and test-based derivationapproach per Annex A1Appendix X2 represent two separate approaches for determination
provides broad guidance for users who wish to pursue the test-based approach for the generation of reference resistance for LRFD.
Due to the sensitivity of reliability to changes in some of the parameters, these procedures offer a limited set of options to ensure
that LRFD reference resistances are generated in a consistent manner. Other methods for computing reference resistance that are
beyond the scope of this standard are discussed in Appendix X4X5.
X1.3 Commentary to Section 3, Terminology:
X1.3.1 Numerical simulations show that, for complete data sets from an underlying 2-paramenter Weibull distribution, all three
methods: method of moments; method of maximum likelihood; and, method of least squares; will estimate mean, standard
deviation, and coefficient of variation with little difference. Reliability analyses benefit from fitting the distribution parameters to
a lower tail subset of the data.
X1.3.1 The term “factored resistance” is specifically defined as the product of the resistance factor (ϕ) and the nominal resistance
(R ) to differentiate it from the nominal (reference) resistance. Users are cautioned to include all applicable adjustment factors
n
when determining the LRFD adjusted design value.
X1.3.2 The term “nominal resistance” is the most widely used term in reliability analysis and material specifications. As described
in Ref (61), users are cautioned that the term “nominal” has been defined in various ways over the years. This standard focuses
on the term “reference resistance,” used in the NDS.
X1.3.3 The term “reference conditions” is added to clarify that the design checking equations presented in this specification do
not include notations for the myriad of potential end-use adjustment factors that might be applicable to specific designs. The
rationale is that all end-use adjustment factors, with the notable exceptions of the load duration factor in ASD and the time effect
factors in LRFD, are identical in both design formats and will mathematically cancel in the calculation of the ratio R / F . Users
n x
are cautioned to include all applicable adjustment factors when determining the LRFD adjusted design value.
X1.3.4 The term “reference resistance” is retained as the primary terminology in this version of the standard for continued
D5457 − 23
compatibility with the NDS (72) and other design documents, but its definition is clarified to indicate that it does not include the
resistance factor (ϕ), the time-effect factor (λ) and other adjustments for end-use conditions that will be subsequently applied in
the design checking equation.
X1.3.5 As discussed in Ref (83), an underlying assumption in virtually all reliability analyses is that every adjustment factor
applied in the design checking equation applies equally across the entire resistance population. From an analysis standpoint, this
results in identical reliability indices for the reference and adjusted design cases.
X1.3.6 Ref (83) also describes the difficulty of applying the same judgment to the time effect factor (λ). The time effect factor is
different from other design adjustment factors in two respects. First, it represents an interaction between the load side and the
resistance side of the design equation. This fact leads to a dilemma regarding the format of the design checking equation: should
the time effect factor be expressed separately (that is, λϕ R ) or embedded into the adjusted resistance like other adjustment factors?
s n
Second, test specimens at the lower tail of the strength distribution exhibit shorter times to failure under constant load than those
higher in the distribution, while most of those at the upper end don’t fail at all, because they are effectively loaded at a lower stress
ratio.
X1.4 Commentary to Section 4.2, Format Conversion—Format conversion is the method used to develop format conversion
factors to adjust reference ASD design values (based on normal 10-year load duration) to LRFD reference resistances (based on
10-minute10-min load duration). Format conversion factors in Table 2 are developed to provide similar member and connection
sizes when considering specific ASD and LRFD load cases and specified values of the resistance factor, ϕ, for LRFD as provided
in Table 1.
X1.5 Commentary to Table 2, Format Conversion Factor, K , for Compression Parallel to Grain, Bending, Tension Parallel to
F
Grain, Shear, Radial Tension and Connections:
X1.5.1 The format conversion factors for compression parallel to grain, bending, tension parallel to grain, shear, radial tension and
connections that are subject to load duration or time effect adjustments, can be obtained from Eq X1.2.
X1.5.2 The factor of 2.16 is the algebraic solution at the calibration point, the ratio of R / F for S/D = 3, λ = 0.80, and C = 1.15.
n x D
LRFD: λϕR $ 1.2D11.6 L or S (X1.1)
~ !
n
ASD: C F $ D1~L or S! (X1.2)
D x
where:
λ = time effect factor (LRFD),
ϕ = specified resistance factor (LRFD),
R = reference resistance value (LRFD),
n
D, L, S = dead, live, and snow load effects, respectively,
C = load duration factor (ASD), and
D
F = ASD design value (ASD).
x
Substituting and solving for K (= R /F ):
F n x
K 5 2.16/ϕ (X1.3)
F s
X1.5.3 Use of a single constant for the format conversion factor, K , is appropriate, based on the judgment of the committee, over
F
a broad range of design cases. As shown in Fig. X1.1, this judgment produces exact calibration between ASD and LRFD for one
specific design case (S/D = 3, C = 1.15, λ = 0.8). Differences between ASD and LRFD designs will result for other design cases.
d
The algebraic format conversion solution for the precise constant in the numerator of Eq X1.3 is not to be confused as the RBD
D5457 − 23
FIG. X1.1 R /F Producing Exact Calibration Between ASD and LRFD for Bending (ϕ = 0.85; K = 2.16/ϕ = 2.54)
n x s F s
basis supporting Eq X1.3 (see Commentary to Annex A1Appendix X2). The RBD basis of the format conversion factor involved
first order, second moment reliability methods to graph R /F across a range of load ratios for three distinct live-load cases
n x
(occupancy floor, snow roof, and non-snow roof), where R and F come directly from the LRFD and ASD design equations. The
n x
factor in the numerator of Eq X1.3 is in the range from 2.1 to 2.2 and resulted from the application of engineering judgment as
a balance of increases for floors at low L/D ratios versus decreases for non-snow roofs at higher L/D ratios.
X1.6 Commentary to Table 2, Format Conversion Factor, K , for Lateral Buckling (Stability), Compression Perpendicular to
F
Grain, and Rolling Shear not subject to load duration or time effect adjustments:
X1.6.1 The format conversion factors for lateral buckling (stability), compression perpendicular to grain, and rolling shear values
that are not subject to load duration or time effect adjustments, can be obtained from Eq X1.4:
K 5 1.5/ϕ (X1.4)
F s
X1.6.2 The K of 1.5/ϕ is the algebraic solution at the point of calibration - the ratio of R /F for L/D = 3. Terms λ and C do
F n x D
not appear in the design checking equations because they are not applicable for modulus of elasticity for beam and column stability
(E ), compression perpendicular to grain, and rolling shear in accordance with the NDS.
min
LRFD: ϕ R $ 1.2D11.6~LorS! (X1.5)
s n
ASD: F $ D1 LorS (X1.6)
~ !
x
Substituting and solving for K 5 R ⁄ F :
~ !
F n x
K 5 1.5/ϕ
F s
X1.6.3 Format Conversion for Lateral Buckling (Stability)—The format conversion factor of 1.76 for stability is applied to E
min
which is the modulus of elasticity used in ASD for beam stability and column stability calculations (not to the average modulus
of elasticity, E, used for deflection calculations). Using the format conversion factor of 1.76, E for LRFD can be calculated from
min
E as follows:
D5457 − 23
For ASD: E 5 E /1.66 (X1.7)
min 05
where:
E = fifth percentile shear-free E value, and
1.66 = safety factor for beam and column stability calculations.
For LRFD: Multiply by K 5 1.5/ϕ (X1.8)
F s
E 5 ~E /1.66!~1.76!
min 05
5 1.06 E
~ !~ !
X1.6.4 Equations for K and K contained in the 2001 NDS beam and column stability provisions adjust tabulated average
bE cE
modulus of elasticity, E, values to fifth percentile shear-free E values divided by a 1.66 safety factor. In the 2005 NDS, K and
bE
K equations were replaced with a reference to tabulated E values (fifth percentile shear-free E values divided by a 1.66 safety
cE min
factor) to simplify design equations for beam and column stability and to enable use of the same equations for both ASD and
LRFD.
X1.6.4.1 E values tabulated in the NDS Design Value Supplement for sawn lumber are estimated in accordance with Eq X1.9
min
where for sawn lumber E = 1.03E(1-1.645(COV )):
05 E
1.03E~121.645~COV !!
E
E 5 (X1.9)
min
1.66
X1.6.5 Format Conversion for ASD Deformation-Based Compression Perpendicular to Grain Values—Wood compression
perpendicular to grain stresses are based on serviceability criteria from testing of small specimens (Test Methods D143, square
cross-section block, 2 in. loading block). However, in many cases, these allowable stresses are being applied more broadly. In some
compression perpendicular to grain applications, especially where laterally unsupported tall/narrow sections are used, failure
modes, such as instability or splitting, can occur. These failure modes have been demonstrated in short-term tests to occur at
compression perpendicular to grain stress levels as low as 1.5 times the ASD value for compression perpendicular to grain.
Designers must be certain to check the failure modes of buckling or splitting that may now control the design. Alternatively, the
designer may choose to brace the tall/narrow member at the bearing to prevent this mode from occurring.
X1.6.6 One method to compute buckling capacity in the perpendicular to grain direction for ASD may be done by using an
elastic-buckling (Euler) type formula similar to that now used for visually graded lumber. This calculation could supplement the
standard ASD compression perpendicular to grain calculation. In the calculation, the relevant modulus of elasticity is the transverse
modulus (often assumed to be E/20) and the relevant dimensions (relative to buckling direction) would also be substituted.
X1.7 Commentary to Table 2, Format Conversion Factor, K , for Shear Walls and Diaphragms:
F
X1.7.1 The format conversion factor, K = 2.0 for wind and K = 2.8 for seismic, for shear walls and diaphragms has been derived
F F
as the algebraic solution (with rounding) at specific points of calibration. The ratio of R /F for ϕ = 0.80 for wind design, and the
n x s
ratio of R /F for ϕ = 0.50 for seismic design, and where F is determined in accordance with SDPWS in Ref (94). Terms λ and
n x s x
C do not appear in the design checking equations because design values for wind and seismic load cases in accordance with
D
SDPWS Ref (94) are tabulated based on a 10-minute10-min load duration and require no further designer adjustment for short
duration wind or seismic loading.
X1.7.2 Design equations for wind load effects based on wind load factors from ASCE 7–16 are as follows:
LRFD: ϕ R $ 1.0 W (X1.10)
s n
D5457 − 23
ASD: F $ 0.6 W (X1.11)
x
Substituting and solving for K (=R /F ):
F n x
K = 1.0 ⁄(0.6ϕ ) = 2.08
F s
where:
W = wind load effects.
X1.7.3 Design equations for seismic (earthquake) load effects are as follows:
LRFD: ϕ R $ 1.0 E (X1.12)
s n
ASD: F $ 0.7 E (X1.13)
x
Substituting and solving for K (=R /F ):
F n x
K =1.43 ⁄ϕ = 2.86
F s
where:
E = earthquake load effects.
X1.7.4 The rounded values of the format conversion factor, K , in Table 2 are slightly conservative to values derived from exact
F
calibration (that is, approximately 4 % for wind and 2 % for seismic). Table 1 factors for shear walls and diaphragms are consistent
with those within SDPWS. The following section is provided to assist users to trace the history of these factors within Specification
D5457D5457.
X1.7.4.1 To simplify the initial transition to LRFD in the 1990s, Specification D5457D5457 adopted a single resistance factor, ϕ,
for shear walls and diaphragms. Subsequently, Special Design Provisions for Wind and Seismic (SDPWS) accommodated the use
of a single ϕ and differences in historical design levels between seismic design and wind design by tabulating different nominal
unit shear capacities for seismic and wind. More recently, simplification of the shear wall and diaphragm tables to utilize a single
nominal unit shear capacity value associated with a nominal strength estimate is coupled with different values of ϕ for seismic
design and wind design. For LRFD, ϕ = 0.5 for seismic design and ϕ = 0.8 for wind design. For ASD, the ASD reduction factor
is 2.8 for seismic design and 2.0 for wind design. Calibration arithmetic in accordance with 2021 SDPWS follows.
Allowable nominal unit shear capacity for seismic design and wind design in accordance with 2021 SDPWS:
v 5 v⁄2.8 (X1.14)
ASD2SEISMIC
v 5 v⁄2.0 (X1.15)
ASD2WIND
where:
v = nominal unit shear capacity.
Design checking equations for seismic:
ASD:v⁄2.8 $ 0.7E (X1.16)
LRFD: ϕ v $ 1.0E (X1.17)
~ !~ !
seismic
Substituting and solving for ϕ :
seismic
0.7E~2.8!5 1.0E⁄ϕ (X1.18)
seismic
ϕ 5 0.510
seismic
A rounded value of ϕ = 0.5 for seismic design is specified in 2021 SDPWS.
Design checking equations for wind:
ASD:v⁄2.0 $ 0.6W (X1.19)
D5457 − 23
LRFD: ϕ v $ 1.0W (X1.20)
~ !~ !
wind
Substituting and solving for ϕ wind:
0.6W~2.0!5 1.0W⁄ϕ (X1.21)
wind
ϕ 5 0.833 (X1.22)
wind
A rounded value of ϕ = 0.8 for wind design is specified in 2021 SDPWS.
X1.8 Commentary to Annex A1, Test-Based Derivation of Reference Resistance for LRFD—The basis for establishing many of the
allowable stresses for wood-based products has traditionally focused on the population lower fifth percentile. The primary
emphasis of this section is on these types of values. Some classes of products or types of stresses (that is, connections and
compression perpendicular to grain) have established stresses based on an average (or mean) value or based on serviceability
criteria rather than an ultimate limit, or both, in the past. Regardless of past procedures, a resistance distribution is necessary for
a reliability-based procedure.
X1.8.1 Commentary to Annex A1.2, Sampling—Some wood-based products exhibit extremely low variability when tested on a
batch basis. On this basis, one would compute, for example, a fifth percentile that may be as high as 90 % of the mean value, as
compared with a computed fifth percentile that may be less than 50 % of the mean value for a product with a substantially higher
variability. The warning provided in this section is intended to caution the user of this specification to be certain that either the
sampling plan or the daily quality control procedures are sufficiently sensitive to reflect population shifts caused by factors such
as subtle manufacturing changes or shifts in material sources.
X1.8.2 Commentary to Annex A1.2.1.2, Multiple Data Sets—Some test programs include a large number of replications of a single
test cell. However, it is more common to develop a testing plan that includes a small number of replications in each test cell,
repeating the testing across several configurations. For example, a joist hanger manufacturer might test less than ten replications
of a given configuration, but the test is repeated across a range of wood species or hanger depths, or both. For such cases, it is
advantageous to be able to pool the data from the various test cells to minimize the data confidence penalty. One technique for
verifying the appropriateness of pooling across several test cells is to conduct pairwise significance tests using the Student “T” test.
For this test, it is proposed that the minimum significance level be established at the 0.10 level. Another technique often used for
data pooling is regression analysis.
X1.8.3 Commentary to Annex A1.3, Testing—While the most desirable and reliable method of defining reference resistance for a
given property is by the direct testing of representative materials, estimation methods may be used when such data are not
available. The preferred method of defining the characteristics for missing data is through the use of a known physical relationship.
For example, Weibull’s theory (2) can be used to estimate reference resistance values for untested sizes of a certain product.
Statistical relationships may be used in the case in which data are missing and no sufficiently reliable physical relationship exists.
Linear or nonlinear curve fitting methods can be applied to define the statistical relationship between a given property and the
influencing variables.
X1.8.4 Commentary to Annex A1.5, Data Confidence Factor, Ω—This factor is based on the ratio of binomial confidence bounds
for the reference resistance. More specifically, it is the ratio of the specified percentile with 75 % confidence to the estimate with
50 % confidence. Note that Ω is chosen based on the sample size of the complete data set, even if tail fitting is used.
X1.8.5 Commentary to Annex A1.6, Reliability Normalization Factor, K :
R
X1.8.5.1 The objective of an LRFD format is to provide the designer with a simple, easy-to-use procedure. For the convenience
of the designer, specified resistance factors, ϕ , are given in the LRFD specification. To keep the number of different ϕ values to
s s
a minimum, an adjustment to the resistance is necessary because the computed resistance factors, ϕ , needed to achieve the specific
c
D5457 − 23
target reliability indices for each product, generally differ from the specified resistance factors assigned to a design property. To
attain the target reliability index, the application of a reliability normalization factor, K , is required in the development of tabulated
R
resistances.
X1.8.5.2 The reliability normalization factor, K , is computed as shown in Eq X1.23, Eq X1.24, and Eq X1.25.
R
X1.8.5.3 Consider the following LRFD design checking load and resistance factor equation:
ϕ R $ γ Q (X1.23)
c p ( i i
where:
ϕ = computed resistance factor to achieve a target reliability index,
c
R = distribution percentile estimate,
p
γ = load factor for load type, i, and
i
Q = load effect for load type, i.
i
X1.8.5.4 When R in Eq X1.23 is fixed as the population 5th percentile (R ), the value of ϕ will vary across a range of
p 0.05 c
coefficients of variation (COVs). If we wish to present resistance factors to the designer that are not product-specific, we would
replace ϕ with ϕ , a single, specified resistance factor for each property:
c s
ϕ R $ γ Q (X1.24)
s 0.05 ( i i
X1.8.5.5 However, Eq X1.24 does not preserve a constant reliability index across a range of COVs. To preserve this constant
reliability index, we introduce the reliability normalization factor, K :
R
K 5ϕ /ϕ (X1.25)
R c s
X1.8.5.6 The designer need not be concerned with the relationship between ϕ and ϕ , since K is incorporated in the tabulated
c s R
reference resistance values.
X1.8.5.7 K equations are generated by applying first-order, second-moment, Level 2 reliability methods using the Rackwitz-
R
Fiessler algorithms (10). The procedure is the following: Choose a target reliability index, β, and conduct the reliability analysis
across a range of CV values. Plot the calculated ϕ versus CV from these results to check for consistency and tabulate the ϕ as
w w c
a function of CV .Table 1 is an example of some specified resistance factors for an LRFD specification. Selected target reliability
w
indices are based on many technical parameters and judgments. For example, the general level of the index is influenced by the
underlying reliability calculation methods and on assumed distribution type. Other parameters that influence the relationship
between calculated ϕ and CV , such as target load cases (for example, live or snow), appropriate load ratios (for example, ratios
w
of live-to-dead or snow-to-dead loads), and tributary areas are also important. The target indices were chosen based on a 50-year
life for a structure. Also examined were a range of commonly used primary structural members. A target reliability index of 2.4
was used for the bending strength properties of fifth-percentile-based products. For the purposes of determining K , the reliability
R
analysis used the dead plus live load case with the load distributions given in Ref (2). This load case and the live-to-dead ratio
of 3 are considered an appropriate basis for evaluating the reliability of wood-based materials used in structures addressed within
the scope of ASCE 7-16.
X1.8.5.8 The target reliability index was computed for bending and tension in which the ASTM-specified divisor is 2.1. For other
cases, in which the ASTM-divisor differs significantly from 2.1, it is believed that these differences attempt to quantify factors to
account for discrepancies between stress calculations in the ASTM test versus those in the structural-size member. An example of
this is the larger divisor for shear, in which the results from the standard test specimen, a 4-in. shear block, do not correlate directly
with those on structural-size members. Thus, for the purposes of this specification, it is assumed that differing ASTM-divisors do
D5457 − 23
not produce differing target reliability indices, but merely adjust for other factors
...