Building a workbench, considering building one.

[woodchucker]

See:

It's all in the engineering.

[Dan Coby]

You correctly point out that using a wide stretcher will make for a stiffer bench. If the stretcher is rigidly connected to the leg, then its contribution to the stiffness of the bench is proportional to the square of its height. So doubling the height of the stretcher will quadruple its effect on the bench's stiffness. However other things like the size of the upper apron, legs, top, and the rigidity of the joints also affect stiffness. Diagonal braces can also have a major impact.

However there are a few problems with your analysis when it comes to the location of the stretcher.

If I am interpreting your video correctly, the magnet represents the stretcher and the bar of the magnetic base represents the leg of the bench. The joint between the stretcher and leg is free to pivot.

Real benches are not normally built with joints that pivot. The rigidity of many bench designs comes from the rigidity of the joints between the legs, aprons, top, and stretchers. If none of these joints were rigid then the bench would simply fall down due to gravity. You can build a bench with flexible joints but you need to have some form of diagonal bracing to convert some of the parallelograms into triangles.

Lets do a simple analysis of a bench leg. To make things very simple, I am going to have a bench with only a single leg and without a top or an apron. Obviously this is not very representative of real benches. However this is somewhat equivalent to what you were showing in your video. I am also going to replace the stretcher with just a couple of forces. When the leg tries to rack (twist) it will apply a force at the top of the stretcher which is trying to push the stretcher to the right and a force at the bottom of the stretcher which is trying to pull the stretcher to the left. The stretcher pushes back on the leg with equal and opposite forces so the stretcher will push back to the left at the top and pull to the right at the bottom. With a rigid joint between the stretcher and leg, the top of the stretcher will be in compression and the bottom will be in tension as the stretcher tries to keep the bench from racking. (In a real joint the forces will be distributed across the joint and vary smoothly from compression at the top to tension at the bottom.)

Fy ----> |---| | | | | | | | | | | | | | | | | | Fst | | | | | | | | | | | | | | | | S | | | | | | | | | |---|

[woodchucker]

Well not exactly the yellow grip tite is the stretcher. But to represent the lever principle simply, they are not connected. The point is that even w/o locking them together solidly, even if you had loose bolts the middle would offer less leverage and the bottom, would be too much leverage.

You are taking this too literally, it's to show the benefit of a middle stretcher vs a bottom stretcher.

That really is not supported in reality. I can take a bench with the same size stretcher and move it from the middle to the bottom and cause the bench to rack. All things being equal.

Certainly it is. I agree that wide stretchers are necessary, but if I put that wide stretcher at the bottom I have more leverage and therefore that joint will fail eventually. It will cause compression of the fibers and the socket will widen if I were to put that stretcher at the very bottom like I have seen on benches.

[woodchucker]

I'll build a small mortise and tenon setup (2) to show middle pressure vs end pressure.

This is about leverage and lever arms. A longer lever has more ability to break the joint down, that a shorter one.

[Dan Coby]

Another way to look at the leverage issue. There are forces from both the your efforts at the top of the bench and counter balancing reaction force from the floor being applied to the bottom of the leg. As you move the location of the stretcher up, you are shortening the lever arm between the top of the bench and the stretcher. However at the same time, you are lengthening the lever arm between the force reaction at the bottom of the leg and stretcher. The decrease in the top torque is balanced by an increase in the bottom torque. The result is the the torque applied to the stretcher/leg joint is constant.

Dan

[Dan Coby]

See my comment in another post about there being two lever arms to consider. The first is the lever arm between the top and the stretcher. The second is the lever arm between the bottom and the stretcher. As you make one shorter, the other is getting longer. The resulting torques remain constant.

Dan

[woodchucker]

Ok, added another video.

you try it.

[Dan Coby]

If the stretcher were attached to something fixed like a wall then I would agree with what you have been showing. Indeed if you are fastening your bench to a wall then you should fasten it near the top of the bench.

However the stretcher is not attached to a fixed object. It is simply attached to another leg of the bench. That leg can also move and flex.

Let me give you another example. Take your argument to the extreme and move the stretcher all the way to the top of the bench. If I understand your arguments then since this would produce a near zero lever arm then the bench would be extremely rigid.

However this is basically the same situation as most tables with an apron around the top. (The stretcher in this case is the same as the apron.) However to make a table rigid, table makers have to go to great lengths to make the leg/apron joint very strong and rigid. The problem is that the table leg makes a very long lever arm connected to the bottom of the apron/stretcher. You have simply shortened one lever arm and lengthened another when you move the stretcher.

Dan

[woodchucker]

A table is not meant to overcome racking forces. A workbench is. The floor is now the top when you put the apron at the top. You are looking to minimize the leverage of the top or the floor. putting it closer to the middle does this.

I don't understand why you say if it is fixed to a wall. I'm at a loss to understand that.

[Dan Coby]

Both benches and table have to overcome racking forces. Take a look at the joints between a table leg and table top and apron sometime. These can be massive on a large heavy table. Check out any book on table construction and you will see the emphasis that is placed on making this joint correctly.

To keep the bench from racking, you have to counteract the torque created when you push on the top. This applied force also creates an equivalent force at the floor. Both of those forces are trying to twist the joint between the stretcher and the leg. You are not including this second force in your demonstrations or in your arguments.

Moving the stretcher up or down simply increases the torque from one force while decreasing the other.

When the stretcher is at the bottom then: torque = F*L + F*0 = F*L Where F is the force applied and L is the length of leg.

When the stretcher is at the top then: torque = F*0 + F*L = F*L

When the stretcher is in the middle then: torque = F*L/2 + F*L/2 = F*L

Please note that the result is the same in each case.

I am trying to say that your analysis would be correct if the other end of your stretcher were connected to a fixed object instead of another bench leg.

Dan