The Mechanics of Joinery

The Mechanics of Joinery:
Douglas Coates looks at how joints work.

In a previous article I discussed the joint as a connector – a component whose job it is to connect two or more structural members together, allowing stress to flow efficiently and completely through the joint and ultimately out of the structure. For this approach to be actually useful in helping us refine how we use and cut joints, we now need to consider the various conditions that will exist inside the joint.
So, we use joints to create spatial structures and in doing so change grain direction – a rail to a stile or stretcher into a leg for example. There are exceptions (a scarf joint) but turning a grain corner is one of the main reasons for joining two components. This results in a composite of our material within the joint which has grain laying at different angles, most usually 90°. That’s quite interesting, it’s how we make plywood. So from the outset there is the potential or even likelihood that the material within the joint structure will be very stiff, and strong.

In the mortise and tenon illustrated here, this assembly is experiencing racking so the stretcher’s tenon is trying to rotate within the mortise. Assuming the cheeks of that tenon are bonded (if not it’s failing already), then there is a notional fulcrum and the stretcher is a very powerful lever. Obviously, quite small loads that try to bend the stretcher convert to huge loads inside the joint.
These loads are concentrated into a very small proportion of the joint’s internal volume. If the bond fails then the fulcrum point is free to move and distortion results, quickly leading to failure.
What we do know is that small areas of any joint are doing most of the work and in a sense the rest of the material is there to connect the hard-working areas to each other. It might be an 80:20 rule – 20% of the joint surfaces or internal volumes are doing 80% of the work (very approximately of course).
It’s difficult to turn away from all that has been learned and passed down over centuries, evolving along the way. This is a temporary call to ignore what we know or accept as given. Keep what we know about wood as a material, just forget what we know about joint design for a moment. Essentially, we are aiming to create the largest possible area of contact between the two components, with minimum structural disruption. We create a number of mating faces, and each face will have a job to do in the joint: reference (locational); bearing (to take main loads), bonding. All contact faces are locational and together they fix the two pieces precisely. It’s easy then to determine what are bearing and bonding faces.

If we take the case of a simple bridle joint, we have the maximum possible bonding area with grain laid at right angles. The sides are the bearing faces and need to be a good close fit. Clamping gets the shoulder tight down, and this forms the third bearing surface. If future movement within the wood is taken into account you may make the side faces a slight interference fit (feather the leading edge for clean assembly).

There’s a concise set of key requirements in any joint:
1. If we think of a joint having a total volume when assembled, then that volume is shared between the two components. It tends towards the 50/50 split but it is adjusted for the application, or compromised because the integrity of the joint is not our only consideration. We often use blind joints for aesthetic reasons for example, but a through tenon will beat a blind one every day.
2. We aim to maximise the mechanical gains of laying grain at 90°, or somewhere close.
3. We need to create reliable bearing surfaces. We know that woods compress most readily across the grain, and are very resistive to compression along the grain. End grain is an excellent bearing surface. It also happens to be a very poor bonding surface – we’ll look for that somewhere else.
4. We want large bonding areas, and these need to be long grain to long grain. These faces will be at angles to each other so if we can bond them well the result will be very strong and stiff. But these faces are not the best bearing surfaces. They are not bad because they are relatively large areas, but they are not fundamentally good as bearing surfaces. All this is general of course – very hard woods like lignum (Guaiacum officinale) are excellent bearing materials in all orientations (tricky to glue though).

Proportions and tolerances
In the previous article I mentioned that we also aim to get the maximum volume of long grain material into the joint. Seen from the receiving component that means removing the minimum long grain we can. It’s the long grain that gives us almost all the good properties we want (strength, stiffness and so on).
It would take far too long to discuss every form of joint in detail, but by thinking about the loads the joint will see in use, then identifying the bearing and bonding faces, and then designing and cutting accordingly – by doing all of this we will improve the long-term performance of the joint. Taking a blind mortise and tenon as an example, deeper tenons are good on every count. Steeper angles on dovetails increase the interlock area (but don’t go too far). Firm contact or even some tightness is good on any bearing surface, where at least one face will be end grain. To go a step further, modified versions of the common joints can offer significant advantages.

Reinforcing joints
Adding a third component to a joint will improve its performance, sometimes quite dramatically. Splines, keys, wedges and pegs (or dowels) are all used to lock joints together, increase bonding area and to tolerate specific loads. An example is the addition of a spline to a simple mitre joint, which is otherwise quite weak. Biscuits are just splines by another name. For any critical applications, the time invested in adding this joint ‘complication’ will be well rewarded.
In some cases the third component is placed under considerable load itself, so choice of material is essential. Pegs must be straight grained and cleaved to ensure grain flows straight along the peg axis. I always use a harder wood for wedges, because I want control of the compression I place into the tenon. If the wedge is also compressing I won’t know or feel what is going on. I’m personally quite wary of draw-bored pegged joints. I think they are fine things in architectural structures (green oak frames for example) but high-risk and a bit brutish for furniture. If at all, I would certainly make the offset small, 0.5mm maybe. I make sure pegs are very dry indeed – using board ends (offcuts) cleaved and then stored indoors. If there is any moisture at all left in the woods, I want the peg to be dryer still so as it equalises it will swell into the joint. We’re talking tiny differentials here because the woods being used are properly dry and stable of course.
I have great faith in wedged tenons. Made with just moderate care they are incredibly strong and stable. Wedges need to be perpendicular to the grain flow of the receiving (mortise) component, because the wedge will apply massive pressure inside the tenon and that must be transferred onto end grain, square-on. I’ve seen round three-legged stools with wedges placed tangentially in the top for visual reasons.
It doesn’t look right because it isn’t right – those wedges are trying to split the top. We have been using wooden wedges to split stone for centuries, maybe millennia. We should know better.
I’ll mention one more example of reinforcement – the square key inserted across a scarf joint. I’ve seen it used in the arch of a Gothic door frame and it acts to pull the two parts together with a lot of force, mating end grain to end grain. I think there is a real beauty in such excellent engineering.

Avoiding failure
The sure way to prevent a future failure is to over-engineer everything, but that is neither efficient or attractive. From race car engineers to bridge designers, the efficient and elegant approach is to design for purpose, and add a safety (or error) margin. In our joinery we are dealing with a huge number of variables and using an inconsistent material so it is beyond our reach to get this close to the margins of possible failure.
By taking a little care in selecting the woods then making the joint with an applied accuracy, we can improve the joint’s future efficiency. None of this really takes longer or costs more. Select workpieces with straight compact grain structure and no flaws, and identify bearing and bonding surfaces. By ‘applied accuracy’, I mean accuracy that is adjusted for the purpose. I want bearing faces to be a really good fit, and bonding faces to be slightly more free with maybe 5 thou clearance. I can’t confidently saw to 5 thou, but I can pare this with a chisel (it looks and feels like a fine shaving off a well-tuned smoother). With this kind of fit and careful use of the adhesive, we are giving any joint the very best chance of a good life that we can. 

About dovetail angles
From a mechanical viewpoint, the dovetail needs to be a tight fit with the pin under very slight compression. This compression applies load into the tail and helps prevent shear along the tail.
The angle is only there to achieve an interlock – less than say 1:10 and we may as well have a finger joint, more than 1:4 is excessive as it begins to actually encourage shear in the tail.
So, using around 1:6 to 1:8 we have it right of course. I think these exact angles have come about because companies can sell us pairs of marking gauges, not because the angles must be these.
A few years ago I was taken to a mothballed joinery shop, full of old Wadkin machines and a few well-used workbenches. On one of them, a strong gouged line was scribed at an angle on the front of the skirt beside the vice. This was certainly a guide to ‘eyeball’ when setting dovetail angles, and it looked to be about what we use. Time was money and I doubt these makers could afford to take the time marking out dovetails the way we might.

Managing movement
We call it movement, but I can’t recall problems arising in a piece of furniture because the woods were too dry. And I have never yet come across a workshop here in the UK that was too dry. I’ve definitely experienced the opposite, and these days I take far more care to manage moisture content before and during build. Our homes have central heating and, increasingly, air conditioning. For the vast majority of applications we are being challenged by shrinkage.

My own approach is:
• Get all the movement you can out of the wood before the build, and keep it that way up to completion. This means getting the wood’s moisture to where it will be in the home, over the long term.
• Rough (over)size every component to release any stresses (often stored in a board from its time in the kiln), then acclimatise down to the target dryness.
• And then, still expect small amounts of shrinkage over the long term but do all you can now to minimise those.

The first and obvious course of action is to get the moisture down to its long-term stable level. If you have a moisture meter (and it is an important investment) you have probably been around your house testing various woods. I generally get about 6%, maybe less. The hardwoods I get from a reputable supplier are generally around 10–12% moisture content which is typical I think, but too high.
So, going back to our joints we need to get as much movement out during the build as we possibly can. I think there is an argument for slightly over-drying, partly because the amounts of movement at these low levels of moisture are very small and a tiny swelling in  a joint is better than shrinkage.

The adhesive interface
This is an extensive topic, but we are considering mechanical properties of joints here. In the previous article I referred to the glue as a membrane or interface between the two components. We want that interface to transmit loads (stresses) through the joint as efficiently as possible – ideally as if it wasn’t there. The joint may be well fitted but if the glue membrane can flex (even very slightly) then mating faces will distort. Distortion increases stress in critical areas and failure will ultimately follow.
Because stress will find the weak point, wherever that is and no matter how small it is – it is important to ensure the entire mating area is connected with glue (the bottom of a blind joint is not mating). If stress is a gremlin looking for a weakness, then a sudden discontinuity in the glue membrane is exactly the kind of place those gremlins will get to work. Stress is looking for the weakest link in our structural chain.

• Glue needs to be low viscosity to flow and penetrate (that’s one advantage of hide / pearl glue, provided the wood isn’t too cold).
• Cover all areas within the joint, on both components. Applying glue thoroughly to both components may take slightly longer but it’s a fraction of the time it took to make the joint. This is to help avoid discontinuities in the bond membrane.
• Apply to end grain (the tenon end for example) – it won’t bond usefully but it’s an end-grain sealer and end grain is mostly where we get movement from.
• Give bonding faces enough clearance for the glue to do its job – I mentioned 5 thou per face but a nice slip fit is about right.
• Listen to the makers. It may be ‘stronger than the wood itself’ but there are terms and conditions in the small print. Working temperature is important and cold winter workshops represent a disclaimer.
• Use a brush or similar – I have a cheap brush stuck into a hole in a pot lid. Keep water in the pot and the brush will last many months (I’m from Yorkshire where these things matter).

In our joinery work we are dealing with such a huge number of variables that mechanical principles can only take us a part of the way. I set out to look at joint-making from a different point of view, in the hope that it gives a broader perspective and helps inform the decisions we make in designing and building joints. I regret to inform you that the answer is not 42.