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?
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
Then you have the problem of what would a lot of taper look like.
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.
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.
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.
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.
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.
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.
On Apr 11, 3:08 pm, " email@example.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.
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 ...
There's lots of Idunno, that depends answers.
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.
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