Leg splay or not to splay?

[Giles55]

I am making an assembly table/ lay out table/ finishing table. I am using a four by two piece of mdf for the top and I will use cls studs for the frame beneath. I envisage right angle legs bridle jointed to each end of two rails, or I could move the joints inwards away from the ends of the rails and mortise and tenon slightly splayed legs. My question is, is the table more stable with a splayed leg or with the right angled leg, if the footprint of the feet is exactly the same and sit directly under the corners of the table top? I am hoping to use my assembly bench to hand plane some of the boards for a work bench build, so the loads placed upon the bench will be from end to end. Once I am using the bench as an assembly bench the issue of stability is more or less moot. I am interested in hearing mathematically verifiable answers. I am not particularly interested in people’s intuitive thoughts as I already have my own opinion of that. So if there is a definitive answer I would like to hear it, perhaps a question for someone with formal engineering training.

 

[Yojevol]

Splayed legs do not add to the overall stability. As long as the centre of gravity of the load is inside the footprint of the legs it will be stable no matter what the leg structure is like (assuming the leg structure is well made, ie, good joints and well braced).
However that can't always be said of the table top as an individual component. If the legs are splayed then it will be possible to load the top outside the leg attachment points, thus putting the top under stress. Taking the splayed leg concept to extremes, if the splay angle is so great that the attachment points are near the tabletop centre, you're going to have an extremely stable undercarriage and a very unstable top.
Personally I wouldn't dream of splaying legs of a workshop bench or table, but I would have the top overhanging the rails by a couple of inches to allow clamping.
What is tour opinion?
Brian BSC M,eng

 

[Jacob]

Hmm, can't entirely agree!
In theory splaying will increase stability as it is a move towards triangulating the structure, which makes racking impossible.
But it depends on how it is done and the details.
For your purposes it would be easier to triangulate by adding brackets or diagonal braces, or if you don't want them, to have a deep apron with M&Ts into the legs to resist racking.
Works most brilliantly and noticeably with the common splayed leg saw stool, which is inherently stable and effectively self tightening if there is any slack in the joint. Also benefits if the top is shorter than the splay so that even if you stand on the very tip it can't tip over.
See Robin Clevett's example in this vid. It's a bit of a cheat as the angles are only approximate, but it will work really well.



Wouldn't translate easily into a big table, unless you made a pair with a table top laid across them, which is a very ancient idea still in use - IKEA do a two trestle table.
Single trestle would work for a narrow table for heavy loads - I've got my lathe on one.

 

[Terry - Somerset]

They real issue is the stress on the joints - it may be a good idea to triangulate the corners so the horizontal forces created by planing don't cause a simple right angled joint to fail.

 

[TheTiddles]

Based on your explanation of splayed legs, no. The centre of mass remains the same, the pivot line remains the same and you increase the bending moment on the joints for no benefit…

That’s not really why you splay legs for stability, you do it to move the pivot line out, which does increase stability.

Sounds like you’re overthinking this, a built workbench is more effective than a theoretical one.

 

[Giles55]

Splayed legs do not add to the overall stability. As long as the centre of gravity of the load is inside the footprint of the legs it will be stable no matter what the leg structure is like (assuming the leg structure is well made, ie, good joints and well braced).
However that can't always be said of the table top as an individual component. If the legs are splayed then it will be possible to load the top outside the leg attachment points, thus putting the top under stress. Taking the splayed leg concept to extremes, if the splay angle is so great that the attachment points are near the tabletop centre, you're going to have an extremely stable undercarriage and a very unstable top.
Personally I wouldn't dream of splaying legs of a workshop bench or table, but I would have the top overhanging the rails by a couple of inches to allow clamping.
What is tour opinion?
Brian BSC M,eng

Ok, thanks, I may as well stick to right angled joinery which is easier to set out and cut since the splay option isn’t going to improve stability.

 

[Giles55]

Hmm, can't entirely agree!
In theory splaying will increase stability as it is a move towards triangulating the structure, which makes racking impossible.
But it depends on how it is done and the details.
For your purposes it would be easier to triangulate by adding brackets or diagonal braces, or if you don't want them, to have a deep apron with M&Ts into the legs to resist racking.
Works most brilliantly and noticeably with the common splayed leg saw stool, which is inherently stable and effectively self tightening if there is any slack in the joint. Also benefits if the top is shorter than the splay so that even if you stand on the very tip it can't tip over.
See Robin Clevett's example in this vid. It's a bit of a cheat as the angles are only approximate, but it will work really well.



Wouldn't translate easily into a big table, unless you made a pair with a table top laid across them, which is a very ancient idea still in use - IKEA do a two trestle table.
Single trestle would work for a narrow table for heavy loads - I've got my lathe on one.

Thanks, I am going to stick with right angled joinery, legs directly under the corners, I will add some appropriate bracing to stop any racking.

 

[Giles55]

They real issue is the stress on the joints - it may be a good idea to triangulate the corners so the horizontal forces created by planing don't cause a simple right angled joint to fail.

Thanks, I am going to stick with right angled joinery and add some bracing. A friend of mine recently made a shelf unit, he added two horizontal rails inside the top and bottom shelves, just at the back and it completely cured the racking. I think I will do something similar, adding a second rail beneath the top rail, between the legs on the side which sits against the wall. I am also running a rail down the middle, between the two leg assemblies, at foot height. I think I have just proved that a picture is worth a thousand words.....ha ha ha

 

[Giles55]

Based on your explanation of splayed legs, no. The centre of mass remains the same, the pivot line remains the same and you increase the bending moment on the joints for no benefit…

That’s not really why you splay legs for stability, you do it to move the pivot line out, which does increase stability.

Sounds like you’re overthinking this, a built workbench is more effective than a theoretical one.

Thanks, I am going to stick with the right angled joinery option and keep it nice and simple.

 

[niall Y]

I have a small work bench with splayed legs. It was built to hold a large metal working vice. It is very solid,with 4 inch sectioned legs and comes up to waist height. It is very stable and allows me to give things a lot of 'welly', when they are in the vice.Probably more akin to a sculptors bench.
Something with a small top and tall legs. such as a chair or stool certainly benefits from a small amount of splay, but for a table it's not really needed. However, I do remember my parents having a G-Plan dining table with splayed legs, but this was more for the aesthetic than the structure
Also, anything with a splay to it I invariably end up tripping over in the workshop.

 

[Jameshow]

Add a decent apron say 9" deep minimum and this will counter the main loads of racking from planning..

 

[Giles55]

Add a decent apron say 9" deep minimum and this will counter the main loads of racking from planning..

I am adding a second rail below the top apron which will do the same thing as a deep apron.

 

[Giles55]

I have a small work bench with splayed legs. It was built to hold a large metal working vice. It is very solid,with 4 inch sectioned legs and comes up to waist height. It is very stable and allows me to give things a lot of 'welly', when they are in the vice.Probably more akin to a sculptors bench.
Something with a small top and tall legs. such as a chair or stool certainly benefits from a small amount of splay, but for a table it's not really needed. However, I do remember my parents having a G-Plan dining table with splayed legs, but this was more for the aesthetic than the structure
Also, anything with a splay to it I invariably end up tripping over in the workshop.

I have decided to keep it simple and go with right angled joinery as I believe splay wouldn’t add anything extra to this project, if the footprint of the feet is under the corners of the top( whether splayed or right angled), it’s not going to make a difference to stability with or without splay. It will be interesting to see how it turns out in practice.

 

[D_W]

I can't think of a good reason to have splayed legs sticking out on an assembly table. It may not be often, but there could be a chance that you want to have something run down the side of the table for alignment and splayed legs will get in the way. If strength is an issue, just build the base a little bit more heavily.

I'd bet a lot of people copy Chris Schwarz and others and then end up cutting the legs of their sawhorses and wishing for a wider horse that is straight up and down.