Can somebody point me towards a reference which will let me solve the
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.
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
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]
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Handbook", Tropical Woods no. 95, and unpublished data from the U.S. Forest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.
"Roy Smith" > Can somebody point me towards a reference which will let me
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.
S/A: Challenge, The Bullet Proof Boat, (Under Construction in the Southland)
Cool - that's a really useful page.
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).
Exactly what I was looking for, thanks!
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 :-)
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.
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.
HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.