Wood vs metal in compression -- specs for columns - Woodworking Talk - Woodworkers Forum

 
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post #1 of 15 Old 05-21-2009, 03:34 AM Thread Starter
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Wood vs metal in compression -- specs for columns

How does one determine the minimum gauge/diameter of stainless steel legs for a table? And diameter of a given species of wood legs?

I've searched for this answer quite a bit, and even asked a couple engineer friends, and it seems that furnituremakers merely use intuition, based on rules of thumb derived from existing furniture. Is there a more exact way to figure out the minimum specs to support a given load? Perhaps software or a good website where you can specify load, column length and diameter, species/gauge, etc and see if you get crushing?

For example, I'm looking at making a large elliptical wood tabletop, and using 5 stainless steel legs to support it. I can see that commercial table legs are often 14-ga, ~2"dia, but what if I want to make sure that my heavy top will be adequately supported, that my kids can crawl on the table safely, that I can go thinner on the legs and still be over-engineered, and take into account that I will have 5 legs in a certain configuration?

If someone could explain how one would go about figuring this out, I would be grateful!
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post #2 of 15 Old 05-21-2009, 06:54 AM
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Strength of Materials

Having had the above class in college eons ago, I mostly remember that it requires a force and vector diagram which would analyize the forces and moments at the joints. Either steel or wood will support the weight of the table and most additional loads in compression, but the real issue is the type and strength of the joints and that is the "design/engineering problem" as I see it. The joints are subject to torque, bending and shear depending on the various loading conditions, IE straight down or laterally, etc. So, the attachment method to the table and whether the legs are attached to each other or are at angle all come into play. We were taught as Design students to make mockups of our ideas, then start reducing the dimensions of the materials until something failed....that being the limiting factor for that material. Then increase, the number or size of that member to accomodate and prevent the failure. I don't really think "intuition" plays a big role in furniture design, except at the appearance level. They make the stuff and if it breaks they make it stronger or bigger based on experience and failure reports. Well, those are my thoughts, Good Luck, bill

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post #3 of 15 Old 05-21-2009, 10:06 PM Thread Starter
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Thanks!

I agree on the attachment mechanism being key. Having a large enough flange at the top of the legs so that torque is reduced, and enough attachment points with the right hardware, etc.

But, say I can't afford to build a full-scale prototype of a dining table and jump up and down on it to break it over and over again? (Who can?) In reality, someone who builds a table is referencing typical dimensions of members to make it stable. Perhaps a commerical manufacturer is using a structural engineer to come up with an official weight tolerance that they mention in the product description.

But what about people making bench-made furniture, who are not big commercial outfits? And if you want to do something where there aren't readily accessible examples to copy ou there the market? e.g., stainless steel metal legs that have a larger diameter, like say 4-5", and then what gauge is necessary? How do I make sure I've engineered it to withstand a certain amount of weight (the tabletop itself, plus fullly loaded with food and dishes, plus a possible human sitting on it, plus a big safety margin)?

I am hoping that there is some downloadable software, or an easy reference chart that shows metal tubing compression tolerance based on gauge, diameter, and slenderness ratio... (Since I have no structural engineer friends)
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post #4 of 15 Old 05-22-2009, 07:01 AM
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As Bill states, virtually anything will withstand the compression loads. Both steel and wood are very good in compression. The problem is the loads applied to the interfaces.

Design the legs so that they will look aesthetically appropriate with the table. Then work to provide an interface (joint) with the table that is as strong as possible.

George
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post #5 of 15 Old 05-22-2009, 11:21 AM
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I know there are a few civil engineers prowling around here who could chime in, but Wood is right. You shouldn't really be worried about compression loads. I think the problem you are having in finding an equation to match material vs. compression load vs. shear load is b/c of variability in cross section design. Cylindrical xsection vs. square vs. honeycomb-esuqe will all perform differently. Like Wood said, compression really isn't the issue. Its at the top and bottom of the legs where shear load is acting. This is why mortise and tenon joints work so well with table aprons; the shear is spread out over a large vertical area on the leg. If you just bolt the leg to the table top, all the shear is focused right at the top of the leg and the joint will be weak, regardless of how large of a flange (the torque is resulting from the bottom of the leg, ~3 feet away. that's a big lever arm). My thinking, as an engineer, not an experienced woodworker, is that if you are attaching with flanges to the table top, the wood's elasticity to shear force would work in your favor. The metal's inability to flex in this manner might put too much of a strain on the fasteners. ahhh... stress vs. strain, bringing back memories....
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post #6 of 15 Old 05-22-2009, 11:55 AM
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Quote:
Originally Posted by timbrennan01824 View Post
I know there are a few civil engineers prowling around here who could chime in, but Wood is right. You shouldn't really be worried about compression loads. I think the problem you are having in finding an equation to match material vs. compression load vs. shear load is b/c of variability in cross section design. Cylindrical xsection vs. square vs. honeycomb-esuqe will all perform differently. Like Wood said, compression really isn't the issue. Its at the top and bottom of the legs where shear load is acting. This is why mortise and tenon joints work so well with table aprons; the shear is spread out over a large vertical area on the leg. If you just bolt the leg to the table top, all the shear is focused right at the top of the leg and the joint will be weak, regardless of how large of a flange (the torque is resulting from the bottom of the leg, ~3 feet away. that's a big lever arm). My thinking, as an engineer, not an experienced woodworker, is that if you are attaching with flanges to the table top, the wood's elasticity to shear force would work in your favor. The metal's inability to flex in this manner might put too much of a strain on the fasteners. ahhh... stress vs. strain, bringing back memories....
Actually a Mechanical Engineer would be the one for this type work.

The Civil Engineer would survey the land and lay out your drainage field, but the Mechanical Engineer is the one who designs mechanical items.

Just for the inquiring mind.

G
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post #7 of 15 Old 05-22-2009, 12:14 PM
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A 1" by 1" square leg that is 36" long made of southern pine should buckle at around 2000 lbs. As others have pointed out, the joint is going to probably be the weak link. You can always test a single leg mockup instead of making the whole table.

If you want to see how to calculate it (or you are just having trouble sleeping) keep reading...


in addition to failures due to the connection method, you can have two additional failure modes when talking about compression collumns. The first is when the stress (load divided by area) exceeds the capacity of the material and the material crushes... for table legs this is rare. The more likely is buckling (especialy with steel legs) Immagine pushing on a very long spring, the spring wants to pop out to the side instead of staying straight up and down.

The formula is this: Fcrit=PI^2*E*I/(K*L^2)
Fcrit = load where buckling can occur
PI ~ 3.14
E = modulus of elasticity for the material (wood is around 1 * 10^6 PSI Steel is closer to 30 * 10 ^6 psi)
I = is the moment of inertia for the shape (for a solid rectangle I= width*(thickness^3)/12 circle is I=PI*(r^4)/4 for others you will need to look it up or ask me)
K = .7 (this is a factor based on how the ends are restrained)
L = Length of leg
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post #8 of 15 Old 05-22-2009, 12:18 PM
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Quote:
Originally Posted by GeorgeC View Post
Actually a Mechanical Engineer would be the one for this type work.

The Civil Engineer would survey the land and lay out your drainage field, but the Mechanical Engineer is the one who designs mechanical items.

Just for the inquiring mind.

G
Mechanical engineers design weapons... Civil Engineers design targets
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post #9 of 15 Old 05-22-2009, 12:33 PM
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I'm not an engineer, but I did stay at a Motel 6....

Or was that a Holiday Inn Express? Anyhow, if you look at a Mission style table or most any workbench, there is a perimeter frame to which the legs are attached, screwed, mortised, or by other means secured, as opposed to just screwing a flange to the underside of the table surface. There is a reason for the frame, it triangulates, to a small degree the lateral forces applied when bumped or in moving the table. While not having very long "legs" on the triangle, the frame still constrains the movement and changes the forces from tension on the screws of the flange to a distributed load on the frame members, thereby increasing the rigidity greatly. So, without a Sketch or a Drawing it's difficult to know what the OP is proposing with his legs. Any bracing from leg to leg will help greatly and the further down the better, to increase the "triangulation" As most engineers and savy woodworkers know a Triangle is unmovable unless the joints fail. A Rectangle, whose joints act like hinges, is far less stable and relies solely on the ridgidity of the joints themselves, not the strongest method, but in some designs the only one. Even less rigid is the flange and post leg where all the forces are concentrated at the screws into the table. So, based on all this a mock up in scale will tell you alot unless your design is the flange and post. In that case make one leg and flange and screw it to a suitable wood plank and try to bend it or "rip" it off. Design by failure will tell you alot. See what bends, strips, shears etc.then make it bigger, use fatter/larger screws and try again. Unless you want the thing to fail while in use this is the only way I know, but maybe there is a software program to meet your specific design, tubing and size specifications. Beats me.
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post #10 of 15 Old 05-24-2009, 11:59 PM Thread Starter
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Wow, thanks for all the info!

Aprons and stretchers: I hear what you are saying about the virtues of triangulation for stability. What about a more contemporary table style, where you have a slab top and feet attached directly to the slab, and dont want the visual fuss of either apron or stretcher bars?
See this example:
http://www.hudsonfurnitureinc.com/2007/
I have seen this table in person, and as I recall, there is no stretcher bar, even tucked flush to the tabletop underneath. They are just two separate sets of legs bolted up into the tabletop.

Buckling and crushing: So, if I made my metal legs thin enough, they certainly could crush... are we saying that if I make them aesthetically pleasing, its unlikely they would have a high enough slenderness ratio to crush or buckle? Because what we humans tend to find aesthetically pleasing would naturally be overengineered for crushing and that one wouldn't imagine me putting spindly little metal stick legs under my heavy wood slab top? And therefore I'm really just worried about shearing off at the joint? Because I would think that if I make my metal legs with a big diameter, and my metal gauge isnt thick enough, then I have a leg that's weaker than I think (most metal legs out there are pretty small diameter -- think an IKEA type style).
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post #11 of 15 Old 05-25-2009, 12:16 AM Thread Starter
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Quote:
Originally Posted by daxinarian View Post
A 1" by 1" square leg that is 36" long made of southern pine should buckle at around 2000 lbs.

The formula is this: Fcrit=PI^2*E*I/(K*L^2)
Fcrit = load where buckling can occur
PI ~ 3.14
E = modulus of elasticity for the material (wood is around 1 * 10^6 PSI Steel is closer to 30 * 10 ^6 psi)
I = is the moment of inertia for the shape (for a solid rectangle I= width*(thickness^3)/12 circle is I=PI*(r^4)/4 for others you will need to look it up or ask me)
K = .7 (this is a factor based on how the ends are restrained)
L = Length of leg
OK, I'm really interested in this, and want to make sure I have it right. I'm having trouble replicating the 2000lb result with the 1x1 square profile 36" long leg...

pi^2 * 1000000 * 0.083 / (0.7 * 36^2) = 136000

what units do i have wrong?
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post #12 of 15 Old 05-25-2009, 01:27 AM Thread Starter
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http://www.grainofthought.com/ct7.html

And here's another table suspiciously lacking in apron or stretcher bars... what's the key to stability here?
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post #13 of 15 Old 05-26-2009, 08:05 AM
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I spent several years working for a office furniture company. The Key is having a big enough bracket between the leg and the worksurface.



The top of those legs are about 3" across there's a metal plate that's about 6" in diameter. (the legs were bieng developed about the time I left the company)
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post #14 of 15 Old 02-17-2010, 04:56 PM
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Quote:
Originally Posted by haley View Post
OK, I'm really interested in this, and want to make sure I have it right. I'm having trouble replicating the 2000lb result with the 1x1 square profile 36" long leg...

pi^2 * 1000000 * 0.083 / (0.7 * 36^2) = 136000

what units do i have wrong?
Your math is wrong. The above first reduces to:
9.87 * 1000000 * 0.083 / (0.7 * 1296)

Then:
819210 / 907.2 = 903

Which still isn't 2000, but it's very close to 1/2 of 2000. So I suspect one of the constants are off or an additional constant is missing.
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post #15 of 15 Old 02-17-2010, 09:07 PM
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I think you all mean Structural Engineers. They are the ones responsible for making sure structures don't topple and actually remember and can use Euler famous column formula. But generally the load carrying capacity of a table leg will have as much to do with its slenderness ration as its material. Structurally speaking table legs are columns and looking back at an old text book I was reminded that a column is defined as a compressive structural member that is long enough to fail by buckling... Buckling is feared because it happens without warning as an axial load is carried in bending rather than pure compression. Bang, it falls down.

The loads carried in most furniture are relatively small compared to the structural members used. That is why intuitive design works. By now you have a real feeling of how strong some materials are and what will cause a problem and what wont. Your body tells you a lot about weight bearing. And you probably get why splayed legs where loads are taken in bending tend to be less stable over time than ones with legs going straight down. Just like tipping back in a chair, similar racking loads are carried by a tables joint as you shove a heavy box of books across the surface.

Minimal material use usually comes in designing structures where the materials are very expensive or cost of making many items and driving it through space makes reducing sizes and weight important. If you are really at that point, hire a structural engineer. They could use the work right now.

Otherwise use the time honored trial and error method. As others have said the ability to hold the legs together to the top is probably more of a concern than their ultimate load capacity. You never ever want to get close to those numbers.

Peter
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