Traditionally, individual pieces of wood were assigned qualitative ratings by expert “visual graders”, based solely on the outward visual appearance. As a piece of wood gets bigger, the chance of a hidden internal flaw increases, so the American Wood Council’s National Design Specification for Wood Construction assigns penalties to the reference design values as member size increases. Even with modern machine-grading of lumber, larger pieces of wood are better at hiding critical internal flaws, so the practice persists through machine-rated lumber as well.
Wood is a naturally occurring material that contains natural flaws that are progressively more difficult to detect as the size of the member increases.
How Does Member Size Affect Wood Strength?
I actually had a shockingly difficult time researching this one, as every paper seems to point to an earlier one and treat this phenomenon as a given.
Long story short, there are many, many theories all vying for primacy on the concept that a single area of lower strength can handicap a structural member, and the larger the member, the more likely that such an area goes undetected.
The “weakest link” theory made the most intuitive sense to me, basically boiling down to something akin to the Fourth Law of the Navy (drilled into my head during a “summer seminar” at the US Naval Academy):
On the strength of each link of the cable
Fourth Law of the Navy, Admiral R.A. Hopwood
Dependeth the might of the chain.
Who knows when thou may’st be tested?
So live that thou bearest the strain!
A small pocket of lower-density or lower-strength wood can have a significant effect on degrading the strength of the overall member. In four-point bending, for example, the whole middle section of a beam is under uniform bending stresses. Any point within that middle span can cause a failure, much like a weak link in a chain.
Larger member sizes give more bulk material to try to penetrate to find low-density wood areas. Historical visual-grading practices don’t stand a chance of penetrating the outer faces of a member to find internal flaws, and machine-stress grading has a very hard time analyzing every bit of the wood along the full length, so it doesn’t actually do much better at flaw detection.
NDS Size Factors for Design
The only three reference design values that get multiplied by the Size Factor are the reference bending, tension, and ordinary compression values (not perpendicular compression).
The NDS directs us to a few different provisions for design, depending on the size, shape, and classification of the members in question.
Visually-Graded Lumber
For ordinary, visually-graded lumber 2″ to 4″ thick, size factors come directly from Tables 4A and 4B in the NDS Supplement – Design Values for Wood Construction (not a clean table I can easily reproduce for you).
Timbers
For bending members 5″ thick or thicker, with depths exceeding 12″, the equation below is used to derive an appropriate size factor:
where d = beam depth
Large Round or Square Members
For beams with diameters exceeding 13.5″ on circular cross-sections, or square beams with 12″ or larger cross-sections loaded in the plane of the diagonal, the NDS directs us to use the equation above with an ordinary square cross-section of equal area.
Decking (other than Redwood)
Table 4E in the same NDS Supplement – Design Values for Wood Construction contains the relevant size factors for 2″ and 3″ thick decking for all species other than Redwood.
Summary
The size factor acts to help account for the increased probability of difficult-to-detect flaws in members of larger volumes.
For more information about structural wood design, check out my other articles on wood design, or grab a copy of by far the best wood design textbook on the market (I’m entirely self-taught out of this one, having needed to drop my wood design class in favor of Wastewater Treatment Plant Design to get through my Capstone Design project…), “Design of Wood Structures” by Breyer, Fridley, Cobeen, & Pollock.
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