Reasonable deflection for a metal and wood table

**daleacyr** · 05-26-2016, 03:07 PM

I've been tasked with building a couple of tables for a church.
The "customer" is requesting that the tables be made from 3" high x 1.5" wide by 14 ga. tube steel, with a wood plank top.

The table will be 12' long, with a leg (same size tube) in each corner.

I'm prone to 'run the numbers' on pretty much everything I do,
so, using the calculators available on this site, I've come up with various potential deflections.

Which begs the question, "What is a reasonable amount of deflection for this application?".

Without having any good reason, I've chosen L/240.

Comments?

**jboggs** · 05-26-2016, 07:57 PM

A better question to ask yourself might be: how close am I willing to get to the yield stress? Speaking as one who has embarrassed himself significantly by sitting on (and breaking) a long table in a business meeting, picture your face after the wife of one of the bulwarks of the church innocently sits on this table and, well, you get the picture. I would try to creatively envision the worst possible case and build it to handle DOUBLE that! But that's just me. My wife says I build everything to last for the millennium. Why not?

**Kelly_Bramble** · 05-27-2016, 08:34 AM

JBoggs is suggesting that the bench be stiff enough that the deflections are not noticed by the well fed Americans sitting on it. Which I agree with..

Another view is to understand the applied load vs deflection of the bench design. If you know what the stress - strain curve looks like for this bench - then you could then determine what is optimal based on the materials and design.

See Strength of Materials Basics see the Stress Strain Curve.

**daleacyr** · 05-27-2016, 02:01 PM

Thank you for your responses.

I wish I could develop a stress / strain curve for the complete assembly, but the only way that I know how to do that would be to actually stress the assembly and measure the change in length / deflection / whatever.
Since it is not built yet, that is... problematic.

By my calculations, I'm showing that a 500 lb. "load" at center will result in a little less than 0.5" deflection.
That seems reasonable to me. But then, I don't have very much (rather, any) experience with stress analysis in furniture.
Hence my request for comments.

We've added a stretcher between the legs, per the attached drawing.
Any further comments, observations, cautions, advice, review notes?

**Kelly_Bramble** · 05-27-2016, 04:27 PM

Based on the design you have above with the lower center stiffener bar, and if *** you simplified the geometry and calculated the Area moment of inertia..

here: http://www.engineersedge.com/materia...gyration-5.htm

Then using the E from this chart...

http://www.engineersedge.com/lumber.htm

and put the numbers into this calculator:

http://www.engineersedge.com/beam_be...m_bending1.htm

and maybe this one as well..

http://www.engineersedge.com/beam_be..._bending2e.htm

apply a factor of safety that makes you feel good.

You would get a conservative estimate of deflections under load...

All this doing is calculating the deflection and stress of the upper bench seat itself - any additions you do to stiffen the bench helps.

**daleacyr** · 05-27-2016, 06:18 PM

Thanks! I had not thought of the assembly in that way.
Now for a bit more number crunching...

**jboggs** · 05-28-2016, 08:40 AM

Kelly read my mind. I was seeing a leg in the middle also. While the table itself may not fail with .5" deflection in the middle I think it would probably crack or damage the finish of the top cover.

Also, it is tempting to try to calculate the deflection of the whole assembly including the stiffness contributed by the top cover, but it becomes very complex very quickly. It is much simpler, and accepted engineering practice to just analyze the stiffness of the support frame itself with the only contribution of the top cover being its weight. This just increases your safety factor.

**Kelly_Bramble** · 05-28-2016, 09:24 AM

Originally Posted by jboggs

Kelly read my mind. I was seeing a leg in the middle also. While the table itself may not fail with .5" deflection in the middle I think it would probably crack or damage the finish of the top cover.

I think .5" is probably too much at max load. I would target .25" at maximum.

Originally Posted by jboggs

Also, it is tempting to try to calculate the deflection of the whole assembly including the stiffness contributed by the top cover, but it becomes very complex very quickly. It is much simpler, and accepted engineering practice to just analyze the stiffness of the support frame itself with the only contribution of the top cover being its weight. This just increases your safety factor.

Yes, simplicity gets the job done and ensures a healthy FOS. The only engineering designs that we might consider the entire structural system with are those where total mass or costing must be optimized and the structural integrity analytically verified. Like, spacecraft, automotive and other end items that must be light weight, cheap and structurally sound.

Moreover, structural applications that life and death matter should failure occur should be fully understood both analytically and by ATP (Acceptance Testing Procedure). I'm sure some academic is shaking their head at this - but ask yourself do you not remove radii and other details from your FEA model so the analysis will actually run?

**daleacyr** · 05-28-2016, 08:43 PM

Thanks for the input.
I've run the various numbers; a center support fixes a lot of problems.
I'll check with the committee for approval.

**daleacyr** · 05-29-2016, 01:43 AM

Well, we got approval (for aesthetics) regarding the center support.
With a 500 lb load at center, this reduces deflection to less than a tenth of an inch, providing my calculations are correct.

Any comments regarding the most recent revision?

**jboggs** · 05-30-2016, 07:35 AM

I didn't see it that way, but if they're happy and the deflection is good, I'm good.

By the way, you haven't really "added a support at the center". All you have really done is to add a third bending member. A true support at the center would have gone to the floor.

**daleacyr** · 05-31-2016, 11:54 AM

Originally Posted by jboggs

By the way, you haven't really "added a support at the center". All you have really done is to add a third bending member. A true support at the center would have gone to the floor.

Good point.
That's why I ask for input.

**daleacyr** · 06-02-2016, 06:01 PM

If you will indulge me just a bit further...
I've been thinking about the fact that the center support is really just adding a third bending member.

To calculate how much that third member adds to the mix, I've talked myself into two completely plausible, yet different possibilities.

Keeping in mind that the most conservative estimate of strength would be to use only one "beam" (technically called a table skirt, I believe),
and run the numbers on that, ignoring whatever strength the 2x6 top might add, and ignoring the other, parallel skirt entirely.
(I like this; that is how I typically do my load calculations)

So, to still stay on the conservative side of things, and yet add the strength of the bottom stretcher...

would the center support add one more beam height (3") to the I of the table skirt?
(this is my current favorite theory)

or would the center support add 1/2 of a beam height to the I of one of the table skirts?
(my thinking is that the bottom stretcher is sharing the load of both table skirts)

I hope I'm explaining this clearly.
I can probably come up with some kind of picture if that would help.

In any case, we are going to build one, measure the deflection, and act accordingly.

**jboggs** · 06-02-2016, 07:41 PM

It appears to me that you are trying to "combine" the beams so that they can all be analyzed as if they were one beam. Not comfortable with that. Because it probably all gets down to where and how the actual load is applied. If it is evenly spread across the width of the table, then all three beams contribute equally to the stiffness. If however, one of the beams will see more of the load than the other two, load sharing is much less of an issue. Picture a 300 lb man leaning on and then sitting on the table. In that case, the beam immediately under him would see all the load. The middle beam a lot less, and the far beam probably none.

**daleacyr** · 06-02-2016, 08:18 PM

Ok, thanks.
Simple beam calculations I understand very well.
Structures.... less so.

We are still going to build one and let two "big dogs" sit on it.
And adjust to suit.

**daleacyr** · 07-27-2016, 05:56 PM

We built a table, and then performed a real world deflection measurement.
I was getting less and less comfortable with the potential deflection, so we up-sized the beams to .120.

We got an actual 280-300 pound man to sit on one beam at center; it deflected a little less than 3/16" of an inch.
A solid plank top, 2" thick of some exotic hard wood was added. We haven't measured the deflection of the final product yet, but we will, and I'll post a picture of the completed project.
Thanks for all your help.
I appreciate you guys.

**daleacyr** · 10-06-2016, 05:30 PM

Here is a picture of the completed project.
I really appreciate you guys providing your thoughts / notes / conjecture / advice / comments.

It turned out pretty well; the customer wants several more.

**Kelly_Bramble** · 10-06-2016, 07:19 PM

Wow! that's nice, good work!

**Cake of Doom** · 10-07-2016, 04:41 AM

That's a handsome looking table.

**Kelly_Bramble** · 10-07-2016, 08:46 AM

Originally Posted by Cake of Doom

That's a handsome looking table.

with wheels... I want one.

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