This week I am building a Hobbit-y chair for a customer in black cherry instead of white oak. Is cherry strong enough for a stick chair such as this? Of course. How do I know? I added 1/8” in diameter and thickness to some key components. So now I can sleep without worry.

If the above paragraph makes little sense, then you haven’t read my chapter on wood in “The Stick Chair Book.” No, this isn’t an advertisement to twist your arm into buying the book. Instead, I hope to help you think about the strength of wood in a different way.

First, I think we can agree that when we increase the thickness of a tenon, that it will be stronger. Right? So let’s say we have a 1/2”-thick tenon and we decide to double its thickness to 1”. Because we have doubled the thickness, that should double its strength. Right?

Wrong.

When we double the thickness of that 1/2” tenon, it can increase the strength of the component by four-fold or eight-fold. How much additional strength you get depends on the component – whether you are testing its “modulus of rupture” or its “shear strength” (this is covered in detail in the book – this is still not a commercial, I promise!).

The bottom line is this: small increases in the size of components can increase their strength dramatically. This is hugely important when building chairs, stools, benches, workbenches or any object that will see abuse.

Let’s get back to this Hobbit-y chair for a moment. Cherry is weaker than oak. But if I increase the diameter of the leg tenons or the thickness of the seat by a mere 1/8”, I will more than make up for the difference between the two species. And the 1/8” added thickness isn’t really noticeable to the naked eye.

Take a look at these charts for some details.

These formulas are not my doing. They are created using the formulas from the “Wood Handbook” from the U.S. Department of Agriculture (a free download). For me, they help me design furniture that is strong without being bulky. I know that I can increase the thickness of a tenon by 1/8” and get a disproportionate increase in strength. I can do the math to prove it to myself.

Or, as I discussed before, I can prove it with a sledgehammer.

Chris, Using cherry for a ADB welsh stick chair, I should either increase the thickness of the seat by 1/8 when using 5/8″ leg tenons OR I can make the leg tenons 3/4″?
Many thanks,
Glnn

There are many options. If your chair has strut legs, those legs need to resist shear forces. So the increase in strength needs to come from the tenon. If you are using cylindrical tenons, increase their diameter by 1/8″. If you are using tapered tenons, you can increase their diameter or increase the thickness of the seat (or both).

If you add an undercarriage to the chair, then you start using “modulus of rupture” forces for the legs and stretchers. In my experience, adding an undercarriage is enough for a cherry chair without changing tenon sizes.

There are lots of makers who make reamers with matching tenon cutters. Elia Bizzari is one. His are excellent. Kelly Harris makes a nice tenon cutter (8°). https://studiohappis.com/shop/tenon-cutter

I am trying to suppress my inner math nerd (minored it in it college because it was easy and yes, it made me really popular with the ladies – not). Small increases in radius add a lot of volume of wood due to volume of say a cylinder be 3.14 x radius squared x length. To find the percentage increase you would set up a ratio and length and pi disappear. So, for going from a 1/2″ to 5/8″ diameter (1/4″ and 5/16″ radius respectively) you end up with: ((5/16)/(1/4))squared = 1.56. This means that that one eighth increase in diameter results in a 56 percent increase in volume of wood. A way to cross check this to see if I have lost my marbles is to take some of the values above and see what percentage increases they get. For example, the sheer strength of cherry is 499 and 320 for 5/8 and 1/2″ cherry respectively. If you do the math, 499/320 = 1.56. This is a 56% increase in value which matches the volume calculation. I didn’t crunch the numbers for any of the other measurements because that would be too nerdy. My math geeking done for the day.

Putting on my engineering hat, I’ll tell you that the shear strength is directly proportional to cross sectional area, so yes this math is correct for shear strength. For bending loads, the calculation uses the moment of inertia or second moment of area which is proportional to r^4 so even more benefit.

Thanks for the pointer to the freely downloadable Wood Handbook !
After adding it to my ever expanding library of wood-related information I recon I now have enough reading material to last me two dozen lifetimes. I will never get through it all, let alone understand or digest it. Does that make me some kind of hoarder ? Perhaps. Will I stop aquiring this kind of stuff ? Not on your nelly !

The nerd engineer in me also want to point out the length of a column also has an impact on how much the diameter needs to be increased. For a chair, likely negligible. But for something of significantly longer lengths, the safe diameter may be much larger. But who in their right mind will be constructing barn columns out of valuable cherry wood. Oh wait, there are some ancient barns constructed out of walnut.

This is totally not the point of your post, but did the chair you were making last week get sold? I was hoping to see it come up on the blog.

It did sell. I received an offer for it before it was finished that was too good to pass up.

Makes sense! My wife loves that design. Lucky for me I bought this great digital book about how to make any vernacular chair I could ever want.

Chris, Using cherry for a ADB welsh stick chair, I should either increase the thickness of the seat by 1/8 when using 5/8″ leg tenons OR I can make the leg tenons 3/4″?

Many thanks,

Glnn

Hi Glenn,

There are many options. If your chair has strut legs, those legs need to resist shear forces. So the increase in strength needs to come from the tenon. If you are using cylindrical tenons, increase their diameter by 1/8″. If you are using tapered tenons, you can increase their diameter or increase the thickness of the seat (or both).

If you add an undercarriage to the chair, then you start using “modulus of rupture” forces for the legs and stretchers. In my experience, adding an undercarriage is enough for a cherry chair without changing tenon sizes.

Thank you very much. This is very helpful and have a great day. Glenn

The strength difference between 1/2″ and 5/8″ demonstrates why one has to be very careful not to overcut when sawing the tenon shoulders.

Given that Lee Valley are out of the ⅝ tapered tenon cutters until February, can you recommend a different tool for creating tapered tenons?

There are lots of makers who make reamers with matching tenon cutters. Elia Bizzari is one. His are excellent. Kelly Harris makes a nice tenon cutter (8°). https://studiohappis.com/shop/tenon-cutter

I am trying to suppress my inner math nerd (minored it in it college because it was easy and yes, it made me really popular with the ladies – not). Small increases in radius add a lot of volume of wood due to volume of say a cylinder be 3.14 x radius squared x length. To find the percentage increase you would set up a ratio and length and pi disappear. So, for going from a 1/2″ to 5/8″ diameter (1/4″ and 5/16″ radius respectively) you end up with: ((5/16)/(1/4))squared = 1.56. This means that that one eighth increase in diameter results in a 56 percent increase in volume of wood. A way to cross check this to see if I have lost my marbles is to take some of the values above and see what percentage increases they get. For example, the sheer strength of cherry is 499 and 320 for 5/8 and 1/2″ cherry respectively. If you do the math, 499/320 = 1.56. This is a 56% increase in value which matches the volume calculation. I didn’t crunch the numbers for any of the other measurements because that would be too nerdy. My math geeking done for the day.

Putting on my engineering hat, I’ll tell you that the shear strength is directly proportional to cross sectional area, so yes this math is correct for shear strength. For bending loads, the calculation uses the moment of inertia or second moment of area which is proportional to r^4 so even more benefit.

This is probably how the table was put together. The Department of Agriculture will not have been testing all the possible cross sections.

Sydney Miyakawa (comment further down) is alluding to “buckling” (think about Charlie Chaplin’s cane).

Thanks for the pointer to the freely downloadable Wood Handbook !

After adding it to my ever expanding library of wood-related information I recon I now have enough reading material to last me two dozen lifetimes. I will never get through it all, let alone understand or digest it. Does that make me some kind of hoarder ? Perhaps. Will I stop aquiring this kind of stuff ? Not on your nelly !

Good stuff. I’m betting a lot of folks don’t know this info. I know I didn’t.

The nerd engineer in me also want to point out the length of a column also has an impact on how much the diameter needs to be increased. For a chair, likely negligible. But for something of significantly longer lengths, the safe diameter may be much larger. But who in their right mind will be constructing barn columns out of valuable cherry wood. Oh wait, there are some ancient barns constructed out of walnut.