# How tapered can you make a leg?

What are the limits of tapering for a leg that will be part of a small bench, i.e how thin can the end be without the thing breaking when you sit on it. The leg will be walnut and about 18" long, 1 1/2 x 1 1/2 at the top. How would you go about calculating such a value?
Thanks :)
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Depending on your weight and how gently you sit, you could probably taper to almost a triangle. That said, with the information that you provided it would be hard to tell what would be safe. The intended use has a lot to do with how much taper. If building a bench that holds 3 people, not so much taper. If building a small stool that is narrow you could probably go to 3/4" square with out any problems. Then you have the problem of what would a lot of taper look like.
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I've had this discussion before and the consensus was that the leg is only as strong as it's weakest point. If you go down to 3/4" you need to picture the whole leg being 3/4", tapering the leg wider at the top just allows you to limit the wobble factor.

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That doesn't really make sense to me; you could balance on a cone of say steel that ended up pin sharp without breaking the cone, but there is no way you could stand on a pin without bending it. Height has to enter the equation.
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Indirectly. Height makes movement more likely, and it's the movement that makes the pin bend. (Hey, the real world is very complex.)
Puckdropper
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Wise is the man who attempts to answer his question before asking it.

To email me directly, send a message to puckdropper (at) fastmail.fm
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For what it's worth, I too agree that the idea that a tapered leg is only as strong as its thinnest point doesn't make sense. Clearly the greatest stresses will occur at the top. Picture someone wobbling on such a bench, the breaking point will be at the joint, or near the top of the leg. I like the suggestion of 3/4" at the bottom, I would bet you could go even smaller.
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Doug wrote:

Consider the surface it's going to be sitting on as well. The compression strength of the leg, which is loaded parallel to the grain, will be higher than the compression strength of a wood floor of the same species, which is loaded perpendicular to the grain. So it's quite possible that a leg that is adequately strong will nonetheless knock a divot in the floor when someone heavy sits on it. If you have concrete or tile floors it's less of an issue.
--
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--John
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damian penney wrote:
> > That doesn't really make sense to me; you could balance on a cone of > say steel that ended up pin sharp without breaking the cone, but there > is no way you could stand on a pin without bending it. Height has to > enter the equation.
The reader is referred to the column design section of any decent Strength of Materials text.
I'm to damn lazy to dig it out for you.
Lew
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wrote:

I probably would not go under 3/4" square for each leg. This would hold a heavy person but if that person started swaying back and forth it's a different situation.
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Is there a reason you would want the end of the leg so small? From all of my reading, and actually making tapered legs for tables, aesthetics are what you must focus on. Too much taper looks bad. You want enough taper so it has the hint/look of being tapered but not tapered so much it shouts at you that it is tapered. Make some mockups from 2x4s. Easy since your real legs are 1.5x1.5, just rip a 2x4 to 1.5 and cut to 18" long. Make several test legs and taper them differently. Little taper to a lot of taper. You will easily see which look good and which do not. Maybe even paint them brown to simulate the walnut.
I made a coffee table with tapered legs. Short legs like you are talking about. Thick 2" walnut top. Maple legs. Maybe 2" square at the top of the legs. I tapered them too much. Maybe 1" or 1.25" at the bottoms. They looked/look wrong. I built an oak kitchen/dining table. Small, 3 feet by 4 feet maybe. 28" tall legs. Slight taper. Mabye 1.5" square at top to 1.25" at bottom. Tapered on two sides of course. Legs look right with the slight, almost imperceptible taper.
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On Apr 11, 3:08 pm, " snipped-for-privacy@yahoo.com"

Mocking them up using 2x4's is a great idea :) In reality I wouldn't make them crazy skinny, but in researching designs I've seen some very pointy looking things (usually on desks) and I wondered how you could calculate how much weight they could handle.
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"damian penney" wrote in message

It is pretty safe to say that depending upon various factors, each leg would have a different value for the force necessary to break/shear/shatter, but there would probably be an average figure that could be calculated, which is nigh impossible to say without more input, as in density, grain direction/pattern, knots, defects in wood, etc.
This would be a job for a testing lab.
That said, and for that size/length leg, a fairly standard, two inside faces taper would be from the bottom of the bench apron to 1" square.
"Standard" in this case is strictly YMMV ...
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There's lots of Idunno, that depends answers.
Me too.
Since calculating it is pertty much impossible, I suggest prototyping it. Start with 2x4 material and test the shape for aesthics. Once you get a taper than you like, beat on it. That is, bend twist and push. If it feels weak, beef it up and try again.
The differnce between pine and walnu can be your safety factor.
-Steve
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