A common problem faced by engineers when designing structures is identifying relevant information from standards and applying them to their projects. Each design standard contains a vast amount of information; therefore, time and resources may be wasted in searching and selecting bits that are useful for design. This article aims to aid engineers in such a situation by providing a guideline on the design procedure of timber structures according to the American standard 2018 NDS. Fundamental equations, calculation methods for different timber materials and important design parameters are explained in the following sections. Ultimate strength and serviceability limit state designs are extensively discussed, and any shortfalls in the standards that need improvement are pointed out. 

ASD vs. LRFD

LRFD (load and resistance factor design) or limit state design is the dominant design method for structural design in the Australian standards and Eurocode 5. LRFD is used in the American standards alongside ASD (allowable stress design), which is a method unique to American Standards. 

The general equation for LRFD/LSD and ASD can be expressed as:

Loads acting on a structure do not act in isolation; they usually act in combination (for example, a skyscraper experiencing live loads from human activities and wind loads at the same time). Also, these loads usually do not act on the structure at their maximum values. Hence, load combinations are provided to account for the most critical loading case by amplifying the applied loads by “load factors". Loads at their actual magnitude are referred to as “service loads”, and their values in the most critical case are the “design loads”. Load combinations are calculated according to ASCE 7 in the American standards.

In LRFD, there are essentially two “layers’ of safety produced by the resistance and load factors. The resistance factor reduces the theoretical capacity of the structure, and the load factor increases effects due to design loads such that the member is adequate at the ultimate limit state. In contrast, service loads are used instead of design loads in ASD. The rationale behind this is that load factors can be neglected if the applied loads are predictable and vary insignificantly.

ASCE 7 - Clause 2.3.2 and 2.4.1

What LRFD/LSD provides through the use of load factors (which ASD doesn’t) is the consideration for the variability of the applied loads. LRFD targets a statistically consistent structural reliability by requiring higher load factors for loads with greater variance. Live loads like vehicles and occupants, snow loads and wind loads are examples of varying loads, and their variance is treated with more importance in LRFD than ASD calculations. This can be clearly seen in the load combinations provided in ASCE 7 shown above.

Traditionally, steel and structures were designed using ASD until the introduction of LRFD in 1986 and 2005 to respective design standards. Due to the complex behaviour and difficulty of stress analysis, concrete structures are designed using LRFD only.

Adjustment Factors

Load Duration Factor, C(ASD only)

2018 NDS uses the load duration factor to convert the stresses for a “normal duration” to design stress values for other load durations. Clause 2.3.2 defines a normal load duration as 10 years, which means that the load is applied to the structure for a cumulative maximum duration of 10 years. Timber has a unique characteristic of carrying substantially higher loads for short durations than long durations. In other words, the strength of a timber member is the function of load duration. Therefore, the load duration factor upscales/downscales the strengths of materials based on how long the load lasts. For short-duration loads, timber performs relatively well thus higher CD is used; conversely, lower CD is used for high-duration loads like dead loads.

2018 NDS Table 2.3.2

It should be noted that the shortest duration load is used for load combinations. For example, if the load combination is D + L, then 1.0 is used as it corresponds to the load duration for a live load, which is shorter than the load duration of a dead load. 

Wet Service Factor, C(ASD and LRFD)

CM accounts for the variance in strength due to moisture content. In 2018 NDS, the maximum allowable moisture content for all timber materials except for sawn lumber is 16%. For sawn lumber, the maximum moisture content is 19%. At the maximum moisture content, CM = 1; if any higher, engineers must refer to tables in the Appendix for specific values.

Size Factor, CF (ASD and LRFD)

CF accounts for the variance in the strength due to size. For some timber materials, as the dimensions of the timber member increase, its strength (per unit area) changes. The size factor is applicable to some types of timber, not all.

Repetitive Member Factor, Cr (ASD and LRFD)

Under special circumstances, a failed member can transfer loads to adjacent members and the structure may function without any trouble. Cr accounts for this redistribution of stresses between timber members and is only applicable to members deemed repetitive. A member is repetitive if:

• Minimum three adjacent parallel members

• Member spacing is less than 24 inches between the centroid of the members

• The members are connected together by a sheathing

For repetitive members, Cr = 1.15; for all other cases, Cr = 1.

Flat-use Factor, Cfu (ASD and LRFD)

Cfu accounts for members stressed in their minor axis. Most members in design bend about their major axis, however, in rare situations like stair treads they may bend about the minor axis.

(L) Bending about the major axis (C) bending about the minor axis (R) stair treads

For members bending about the strong axis, Cfu = 1; for bending about the weak axis, engineers must refer to the NDS supplement.

Incising Factor, Ci

To ensure that the timber does not rot and weaken during its service life, chemical preservatives can be added. This process is known as pressure treatment, and some incisions parallel to the grain may be made in the timber to increase the effectiveness of the treatment. The incising factor is only applicable for sawn lumber, and its design values are provided in Table 4.3.8:

2018 NDS Table 4.3.8

Temperature Factor, Ct

For timber, temperature increases beyond 100 degrees Fahrenheit (~37.8 degrees Celsius) lead to a decrease in strength. Ct accounts for this effect using values in Table 2.3.3:

2018 NDS Table 2.3.3

Beam Stability Factor, CL

CL accounts for the effect of lateral-torsional buckling, the twisting of beams that occur due to the movement of the compressive and tensile edges in opposite directions. Lateral-torsional buckling only occurs in members that are restrained at ends. For members that are fully braced by decking or sheathing, lateral-torsional buckling will not occur and CL = 1. For other cases, Table 3.3.3 and the equations given in Clause 3.3.3 must be followed.

Column Stability Factor, Cp

Similar to CL, Cp accounts for the buckling stability of columns which is a function of the column stiffness, fixity (e.g. are the ends pinned, fixed, etc.), section size and effective length. For members that are braced or restrained about their buckling axis by sheathing or walls, Cp = 1. For other cases, engineers must refer to equations given in Clause 3.7.1.

Format Conversion Factor, KF (LRFD only)

All reference design values for different timber materials such as material strengths and moduli in 2018 NDS and its supplementary data are only applicable to ASD calculations, as they are based on a normal load duration of 10 years. KF converts these values for LRFD calculations and is provided in Table 2.3.5:

2018 NDS Table 2.3.5

Time Effect Factor, λ (LRFD only)

Lambda accounts for the effect of load duration and is dependent on the load combination applied to the timber member. These factors have been derived based on a probability-based approach and are provided in Table N3:

2018 NDS Table N3

Standard Structure

Chapters 2 and 3 provide design provisions and equations for flexure, shear, and deflection of bending members, followed by members in compression, tension, and combined actions of bending and axial loading. Guidelines for solid columns and design for bearing are also included. 

Chapters 4 to 10 focus on different timber materials and provide material-specific design provisions and equations. The selection of adjustment factors is also discussed. Chapters 11 to 14 are dedicated to timber connections and follow the same format as previous chapters.

In each of the chapters between 4 and 14, the standard includes a table that outlines which material strengths are to be considered in calculation and the consequent applicability of adjustment factors. Examples are shown below:

2018 NDS Table 4.3.1 and 7.3.1

The leftmost columns include the strengths that are used to calculate the capacity of members and the first row shows the adjustment factors that are considered. These vary depending on the material type.

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References

[1] "2018 NDS", American Wood Council, 2018. [Online]. Available: https://awc.org/publications/2018-nds/.

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Published:
Oct 3, 2022
Edited:
September 19, 2022