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If I'm looking for a type of wood that has very little flexibility (or one that has a lot), what wood metrics should I look for in tables / charts / lists to judge relative flexibility?

Is the Janka hardness scale a good indicator of flexibility as well or is dent resistance an independent thing?

By flexibility I mean e.g. how much will a shelf of a given thickness and grain orientation bend when a load is placed on it. I don't really care about max load or breaking point, just a way to compare wood types of the same thickness under the same load.

I'm just not sure what to look for. Most searches for flexibility yield hardness scale tables but I don't understand enough material science to know if this is what I'm looking for.

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Let us not perpetuate a misconception of what is stiffness. Indeed, the modulus of elasticity (Young's modulus), as mentioned in your citation, is important to stiffness. But stiffness of beams (structural elements that bend) it is also dependent on the moment of inertia (second moment of area) which for a rectangular cross-section varies as the third power of thickness. (If the thickness doubles, the stiffness is multiplied by eight.) See this article.

Of course, a thick board is stiffer than a thin board. Using "stiffness" is an error by the citation.

The answer to your question

By flexibility I mean e.g. how much will a shelf of a given thickness and grain orientation bend

is actually: modulus of elasticity.

For more information on the bending characteristics of wood, you could look at this article. It shows how wood beams typically act under loads and eventually break.

Further research on the net reveals that the MOE grows larger as the moisture content lessens (moist beams sag more than dry beams). MOE can actually increase by 50% between green wood and wood dried to 12% moisture content.

The MOE also varies greatly from species to species and greatly affects the amount of deflection in a beam or shelf. See this to see that MOE for western red cedar is about 2/3 of that for red oak and only 1/2 of that for shag bark hickory. A book shelf made of the cedar will sag 50% more than one of the same dimensions made from oak.

And then there's the issue of wood continuing to sag with no increase in load over a long period of time. We have all seen book shelves that continue to sag even when all of the books are removed and there is no load on the shelves. This can happen even if the shelf was not loaded beyond its elastic limit. Wood behaves differently from metals, which, incidentally, behave differently from one another.

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  • I'm a little confused. The cited article does say that by stiffness it means modulus of elasticity. Since that varies with thickness the assumption is that it's only useful for relative comparison when all samples are the same thickness and are deflected by the same amount, which I presume is normally the case when many samples are compared in a single table. Are you saying "stiffness" is different than what I asked about? Or are you saying that the articles' choice of the word "stiffness" to mean "modulus of elasticity" (or my choice to cite "stiffness") was colloquial and not a good choice?
    – Jason C
    Nov 6, 2015 at 4:51
  • Ah you are saying that "stiffness" is an actual thing, related but different, and that it was unfortunate that the article interchanged this with "modulus of elasticity", and even more unfortunate that of the two choices I chose "stiffness" when reading. That makes sense, thanks. Still, either choice, when listed in a table, gives the same relative end result. But I see what you mean about keeping terms straight.
    – Jason C
    Nov 6, 2015 at 5:01
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    Everything that YOU said is correct. The article that you cited misused the expression of stiffness to mean only the modulus of elasticity. I am simply saying don't equate modulus of elasticity with stiffness - it is only one component of stiffness.
    – Ast Pace
    Nov 6, 2015 at 5:03
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    @JasonC, The cited article does say that by stiffness it means modulus of elasticity. Since that varies with thickness the assumption is that... Maybe I'm reading this incorrectly, but modulus of elasticity of a material is not dependent on thickness. Moment of inertia, however, is. Just wanted to clear that up.
    – grfrazee
    Nov 6, 2015 at 14:44
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Found it. The metric is "modulus of elasticity" (which the cited article below incorrectly equates with "stiffness" -- yeah, laugh it up), and the unit is Mpsi. It is separate from bending strength. It is also independent of hardness. It measures the force required to deflect a sample some specified distance, so higher numbers are stiffer.

Source: http://workshopcompanion.com/KnowHow/Design/Nature_of_Wood/3_Wood_Strength/3_Wood_Strength.htm

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    Worth noting that the relative differences in Young's modulus of elasticity for various species of wood is comparatively trivial when compared against other material types like steel. Wood deflection is going to be affected more by the shape and size of the part than by the species of wood.
    – user2
    Nov 6, 2015 at 14:53
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If I'm looking for a type of wood that has very little flexibility (or one that has a lot), what wood metrics should I look for in tables / charts / lists to judge relative flexibility?

Some background: I am a structural engineer by profession, have taken structural wood design classes in college, and wrote my graduate thesis on a topic of structural wood design.

As @ASTPace said, the stiffness of a structural member is dependent on both its modulus of elasticity (Young's modulus) and its moment of inertia (second moment of area). I have no idea of your level of engineering knowledge, so I'll explain a little about each below.

Modulus of Elasticity

This is a measurement of a material's resistance to strain given an applied stress. Strain is a proportionate displacement. For example, if a member stretches to 110% of its original length under load, its strain is 0.10. Most structural material exhibit strains much less than this before failure, so this is just a numerical example to illustrate.

Modulus of elasticity, E, is usually found by stretching a test coupon in an apparatus and charting the coupon's displacement vs. the applied load. For example, the image below shows the stress-strain curve for mild steel. The initial linear segment is what's used to determine the modulus of elasticity since that is the elastic deformation of the coupon. The modulus of elasticity is simply the slope of the initial segment. The stiffer the material, the steeper the line.

stress-strain
(source)

Moment of Inertia

This is a property of the cross-section of the structural shape and is independent of the material (assuming the material is essentially isotropic, or the appropriate corrections have been made for anisotropy).

For simple rectangular sections, the moment of inertia, I, is found as bt3/12, where b is the width and t is the thickness. As you can see, a change in the thickness has a much larger impact on the moment of inertia than a change in the width since the change is cubed. For example, doubling the thickness increases the moment of inertia eightfold.

Considerations for Wood Design

In reality, the stiffness of a material is measured by the product of E and I. Consider the image below, taken from the AISC Steel Construction Manual, 7th Edition. The equation for delta (deflection) is a function of 1/EI. As the stiffness increases (product of EI gets larger), deflection decreases.

deflection

If you truly want to compare two woods, you have to isolate one of the variables. For example, to determine which wood is stiffer, you will want to test two samples of the same cross-section. The stiffer one will be the one that deflects less.

The opposite is also true. If you have a wood with a lower modulus of elasticity, you can create a member of equivalent stiffness by changing its moment of inertia. For example, if Wood #1 has half of the E that Wood #2 has, Wood #1 must have twice the I of Wood #2 to be of an equivalent stiffness (so that the product of EI for each is the same).

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    Off topic, I read the source trying to get my head around why there are peaks in the stress-strain curve for steel. Colloquially, is this what shows that I have to try really hard to get steel to start to bend permanently, but as soon as I do cross that hump I can ease off but still be bending it (even if that same force didn't bend it before I reached that hump)? So the downward slope after the yield point is a period of temporary weakening unless I apply even more force to get it to harden in its new shape?
    – Jason C
    Nov 6, 2015 at 16:22
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    After you yield, you have permanently deformed the steel and you can't recover the strain that occurred (i.e., it won't go back to zero). And since the modulus of elasticity changes after you yield, the steel essentially becomes less still. This is why it takes less force to keep bending the steel after you've yielded it. However, once you let off the force entirely, you will be back to the elastic regime, and you will find that you need that same initial high force to bend the steel.
    – grfrazee
    Nov 6, 2015 at 16:27
  • Science sure is weird. So basically if I wanted to permanently bend steel by a large amount I have to have good control over the force to cross the yield point, keep it moving at a constant force, then ramp up to finish at the ultimate strength point?
    – Jason C
    Nov 6, 2015 at 16:31
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    @JasonC, ultimate strength is the point where the steel fails. You don't want to get to that point. All you have to do to bend steel permanently is surpass the yield point.
    – grfrazee
    Nov 6, 2015 at 16:35
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    Thickness is in the dimension along the line of applied force. For example, stand a 2x4 on edge and put a load on it. In this case, the 4" dimension is the thickness. If I'm understanding you correctly, the cross section plane is the nominal 2x4 cross section.
    – grfrazee
    Aug 16, 2018 at 1:54

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