Calculating beam strength

[Roy Smith]

Can somebody point me towards a reference which will let me solve the following problem:

I've got a beam of 5/8" thick by 3-3/4" deep walnut, 28 inches long, supported only at the ends. There is a 150 lb point load at center span. What is the deflection of the beam?

Stated this way, it sounds like a civil engineering problem, but of course what I'm really trying to do is figure out if the rails on a bench I'm building are big enough. I know a true craftsman would just look at it and say, "yeah, that looks strong enough", but the engineer in me us just itching to crunch numbers.

[DanG]

Knock yourself out . . . . ..

[Lew Hodgett]

"Roy Smith" > Can somebody point me towards a reference which will let me solve the

Any basic Strength of Materials text will give you what you want.

I'm do damn tired and also lazy to dig out my old text book and post the beam deflection formula.

In the above, if the 5/8" is vertical, forget it, if it is horizontal, you're good to go.

HTH

[Mark]

[Bay Area Dave]

So you are working in the Sears tool department now?

dave

Mark wrote:

[Mark]

[Luigi Zanasi]

On Wed, 17 Dec 2003 22:13:35 -0500, Roy Smith scribbled

Check out the "sagulator"

"no" with "yk" for real email address

[todd]

Well, the engineer in me had to work the numbers. I come up with about

1/64" of deflection at the center. Not something that would keep me up nights. Keep in mind that the equations I used for the calculations assume a material that is isotropic, and wood is decidedly anisotropic, but even if we're off by a factor of 2 or even 4, we're still not talking about much in the way of movement.

todd

[Me]

Engineers are such dorks...

yes... i'm an engineer too.. :-)

[Mark & Juanita]

... snip

Are you supporting the board at the two ends by the 3 3/4" width of the rails, or the 5/8" thickness? If the latter, 1/64" seems very small over a two foot section with a 150# load. Also, I believe that, at least from the standpoint of aircraft loading, 170# is considered the "average" human weight. You might also want to compute for worst-case (say 220 to 250#) just in case.

No, I haven't run the numbers (I'm an EE doing Systems Engineering (rocket scientist SE, not computer SE), and am too lazy to do the research right now), 1/64" just doesn't sound right.

[John McCoy]

Luigi Zanasi wrote in news: [e-mail]:

FWIW, it also appears to give right (or at least credible) answers for unusual dimensions, such as a shelf .625 wide and 3.75 deep. (it gave .01, which agrees with Todd's 1/64 if we assume it truncates the display).

John

[Roy Smith]

I plugged in my numbers and came out with a sag of 0.54 inches! Then I realized what the program was calling "depth" and "thickness" is the inverse of how I was using the terms (not surprising, since they're thinking book shelves and I'm thinking beams). Once I flipped the numbers around, I got 0.01, which agrees pretty well with todd's estimate of 1/64.

BTW, the 150 lbs is 300 lbs of loading divided by 2 rails (front and back). Of course, depending on how you sit on the bench, you might put more load on one rail than the other, and it's not really a point load, and the M-T joints at the ends provide some rotational moment (i.e. they're not the pinned end joints I'm assuming the sagulator uses). But, at least it gives me a good feeling that it's the right size :-)

[Mike Hide]

Actually wood beams are quite different othe manmade engineering materials . Manmade materials are for the most part homogenious whereas wood is not due to its grain characteristics . For instance wood has several moduluses [sp] . quite a bit of research has been done by the goverment wood testing labs in Madison .They have published many technical manuals on wood characteristics .

As an exengineer with some structural experience , I think you will find wood is a rather complex engineering material and in the end it might be best to conduct simple bending tests on the material you are using rather than trying to run the numbers [which could in the end drive you batty]

-- mike hide

[Mike Hide]

From an

-- mike hide

[JackD]

If you have the beam like you say, and you weigh somewhere at or above

150lbs, you can measure it. I suspect you won't easily be able to measure it though as the deflection will be quite small.

-JAck

[todd]

I pointed out that the normal bending equations don't match the performance of wood exactly due to the anisotropy of wood, but it's not going to be that far off. Deflection is inversely proportional to modulus of elasticity, so even if you're off by a factor of 2 on the modulus, the deflection will only be twice what was calculated. FWIW, I used a value for modulus from Marks Standard Handbook for Mechanical Engineers, whose source was "Wood Handbook", Tropical Woods no. 95, and unpublished data from the U.S. Forest Products Laboratory. So, I think I'm pretty close.

todd