To be able to determine the strength of wood, first, we need to define what strength is.
The most common definition of strength is the yield point which is where the stress-strain
curve becomes non-linear or materials are no longer elastic.
Alternatively, the ultimate load of the material is also a good reference point for measuring
strength.
However, since wood is an anisotropic material, it has different strength and elasticity properties
depending on the direction of loading . The reason for this is the nature of the material
or in essence the direction of the wood grains.
The grains consist of cellulose chains that are longitudinally connected with strong covalent
bonds [1].
In contrast, the chains are laterally connected with hydrogen bonds which are much weaker.
For that reason, wood pieces are much easier to separate in the direction perpendicular
to grain compared to the direction parallel to grain.
Because of this intrinsic difference, wood exhibits different strengths for different
loading types and directions.
For this video, for simplicity we will only consider the compression strength of wood
and its influence factors.
The compression stress capacity is simply the applied load at failure divided by the
cross-sectional area of the member usually measured in Newtons per mm squared (MPa) or
pounds per squared inch (PSI).
Distinguishing between a force and stress is absolutely crucial to avoid confusion so
keep this in mind.
The key information about the capacity of a particular species is obtained through destructive
testing.
This is performed by testing structural size members with short enough length such that
buckling is not an issue.
Originally small-clear test specimens (20mm x 20mm) were used for obtaining the working
stress of wood members.
However, in the mid-1970s, this practice was replaced with structural size specimens [1]
and soon we will see why.
When the samples get loaded they exhibit loading curves as shown here.
For each sample, the maximum achieved loading stress is recorded which we will refer to
here as the strength of the material.
The Modulus of Elasticity is also of significant importance but we will leave that for another
video.
This experiment has to be repeated for different species and with many samples such that the
variability in the material is well captured.
The data presented here is for 538 small clear samples of Western Hemlock obtained from the
excellent book by Dinwoodie, Timber: Its nature and behavior [1].
The strength data fits a normal distribution fairly nicely with the mean value at 25.4
MPa (3600 PSI) and a standard deviation of 4.6 MPa.
However, if we look up the design value for the combined class of Hemlocks and Firs in
a wood design manual, we can notice design values much lower than the experimental failure
stresses.
In fact, the Canadian Wood Design Manual recommends unfactored design strength values that vary
from 6.1 MPa (885 PSI) for the poorest grade to 11.3 MPa (1640 PSI) for the best grade
[2].
There are 2 main reasons why manuals use far lower values.
The first and more obvious reason is that we would like to select a value that would
ensure almost all members achieve at the very least the graded strength value.
This is usually done by selecting the 5th percentile value.
The 5th percentile value ensures that 95% of the wood members would be able to carry
higher stresses than graded load.
In contrast, selecting the average value for design would mean that every second member
would not be able to reach its strength value and that would produce significantly increased
collapse probability (or significantly decreased structural reliability).
But in this case, you can see that the poorest grade is way on the left of the curve at a
value that is half of the weakest sample.
This may seem like an overkill, but it is absolutely necessary due to the high variability
of wood.
In fact, this data is obtained for small, clear specimens.
If we were to perform the same experiment for structural size members (as the design
manuals do) [2] [3], we would obtain a curve that is shifted to the left and justifies
the lower values.
Based on the discussion so far, it follows that as wood members get larger, they would
become weaker?
This is actually true and now we will see why.
Keep in mind that by weaker we don’t mean that a larger member can carry less force
than a smaller-sized member, that wouldn’t make any sense.
By weaker, we mean that it will fail at a lower stress level.
The main reason for the lower failure stress is a phenomenon known as size-effects or the
weakest-link theory [4] and can be best described with an example of a chain.
Imagine two chains of identical size but different lengths carrying a load W. Now imagine the
weight being increased until one of the two chains fails.
Pause the video here and think which rope do you think would fail first:
write your guess and supporting theory in the comment section and stay tuned for the
answer.
If you guessed the longer chain then you guessed right.
The main reason for this is the weakest-link model.
The chain, like any other material, has micro-fractures that are randomly distributed along its length.
These micro-fractures have different sizes and cause every link of the chain to have
a slightly different strength.
Statistically, this can be described with a distribution similar to the one we saw earlier.
The key idea of size-effects is that as we keep increasing the length of the chain i.e.
adding more links we keep taking random samples from the strength distribution.
Logically, it follows that with each next link we risk sampling on the lower tail of
the distribution and therefore making the whole chain weaker.
Sampling on the high side does not influence the strength of the chain since the chain
is as strong as its weakest link right?
Therefore, statistically speaking, the longer chain is more likely to possess a weaker link
and therefore fail at a lower load.
Leonardo da Vinci was the first to make note of this phenomenon more than 5 centuries ago.
He tested ropes and realized that the longer rope fails at a lower load but he did not
have the necessary mathematics to explain his observation.
The explanation came in the 20th century when Weibull provided a mathematical model describing
this phenomenon.
Weibull’s model is also applicable to wood just instead of micro-fractures the flaws
are randomly distributed like knots in the wood.
Imagine a block of wood with a 1% chance of having a knot that translates into 1% chance
of failure.
Now imagine a larger member composed of 8 of these blocks.
The chances of having a knot now increase to about 8% which also translates to a weaker
section since knots are discontinuities in the material and cannot transfer loads.
With this logic, increasing the volume causes a decrease in the strength of the member.
The wood design manual has a formula for correcting for different size members such that these
effects are accounted for.
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