I think what he demonstrated must have been different than what you
recall or mine is all awash...see my note to Edwin.
As a practical thought experiment, if it were as you say, you could
continue to reduce the wall thickness of the tube until it was paper
thin and the result wouldn't be different--that obviously wouldn't be
true in reality.
Sounds like an urban legend to me. Kinda like hot water freezes faster
than cold water.
The wikipedia says stiffness is a measure of resistance to deformation.
Solid rod resists deformation more than a hollow rod. It makes no
sense that boring out a steel rod would make it stronger. How thin
should I make it? The thinner the stronger? And the opposite is true
too? The more I fill it, the less stiff it becomes?
Well, it's true that water w/ less entrained air will freeze faster than
that w/ more entrained air--and, heating water will drive out some of
the entrained air so there's a kernel of truth in the saw...
I'm not sure what laws you're thinking of...let's see--if we consider a
simple beam w/ uniform load w/ simple support at both ends the maximum
deflection at the center is 5/384 (W*l^3)/(EI) where
E = modulus of elasticity (material property only)
I = moment of inertia (dependent on geometry)
W = applied load
l = length
Now for a rod Irod = MR^2
where M = mass of beam and R = radius
and for a hollow tube it is Itube = M(R1^2 + R2^2) where
R1,R2 are inner/outer radii, respectively.
This superficially makes it look like Itube>Irod for R2 = R, but that
doesn't include the mass which will be less for a hollow tube than for a
Since we're after comparing two geometries of the same material, we can
consider the density of the two to be the same as well as the length.
On that basis, for the rod the weight/unit length is
mRrod = density*pi*R^2/4
mTube = density*pi*(R2^2-R1^2)
Substituting into the formulae for I the geometrical terms for each M we
get that for each the moment of inertia is proportional to
iRod ~ R^4
iTube ~ (R2^2 - R1^2)*(R1^2 + R2^2) = R2^4 - R1^4
Thus, it can be seen that the moment of inertia for the tube section is
always slightly smaller than that of the solid rod and since I is in the
denominator of the deflection, the larger deflection will occur for the
tube, not the rod for R2==R (the outer diameters equal).
If you figure on an equivalent weight basis, the tube will be stronger
as the same amount material will be located at a farther distance from
the neutral axis.
I = bd^3/12 in^4, for a b" wide x d" deep beam.
I = 2x6^3/12 = 36 in^4 for a rough-sawn (real) 2x6.
....the total load. Say W = 400 lb.
....in inches. So a 10' rough-sawn 2x6 beam would have
a D = 5W(10x12)^3/(384EI) = 0.23" max deflection.
You may be confusing something like the polar moment of inertia (including
mass, for dynamics) with the geometric moment of inertia about the neutral
axis, eg the horizontal diameter x-axis. That's the sum of the products of
each tiny area and the square of the perpendicular distance from that area
to the axis. Ix = Pir^4/4 for a disk of radius r, eg Pi2^4/4 = 12.57 in^4
for a 2" radius rod, IMO.
....with the same axis, consider the rod to be a composite area and subtract
I = Pi1^4/4 = 0.79 in^4 for the 1" radius bore from 12.57 to get 11.78 in^4
for a 2" radius rod with a 1" radius bore.
So a 10'x2" radius Eastern hemlock rod with a 400 pound total load would
have D = 5x400(10x12)^3/(384x1.1x10^6x12.57) = 0.650" max, and the hollow
version would have D = 5x400(10x12)^3/(384x1.1x10^6x11.78) = 0.695" max.
If the hemlock weighs 30 lb/ft^3 and the solid rod weighs 26.2 pounds,
a 26.2 pound 4" radius rod with a 3.46" radius bore with I = 201.1-113.1
= 88 in^4 would have D = 5x400(10x12)^3/(384x1.1x10^6x88) = 0.093" max.
And a 26.2 pound 4"x8" hemlock "I beam" with 2 4"x1.6" boards bolted onto
a 4"x4.9" foamboard sandwich and I = 4x8^3/12-4x4.9^3/12 = 133 in^4 might
have D = 5x400(10x12)^3/(384x1.1x10^6x133) = 0.062" max, if nothing slips.
I'm not going to comment about the pipe/rod issue because I was not
familiar with that. However, as far as putting two (or more) timbers
together, a good part of the reason is the same as plywood. A natural
board has all the grain running a certain way, and that allows for
weak spots, such as when you buy a board with a crack in it. (a weak
spot). So, with two boards, it's highly unlikely that you will end up
with the weak spot in the same place as the other board. Thus one
compensates for the weak spot on the other. Then adding the plywood
down the center, which is mainly just a spacer, that too adds quite a
bit. If the boards were glued together they would be stronger still.
Look at the beams they make now. They are simply plywood beams made
to be a 2X12 or whatever, and are 2 or 4 inches thick. They are
supposed to be considerably stronger, yet each layer is less than 1/4
inch thick. Alone, the pieces would not hold up anything, but
together, they are very strong. I used to think that was bogus till I
read up on it. As for the particle board type beams, I still find
them inferior, regardless what is said about them. Many will disagree
with me, but I wont use them.
One final note. I spoke with someone that was building a huge barn at
a county fairgrounds. Instead of using solid posts (uprights), like
in the old days where they used a "power pole". Instead they used
three 2X8's nailed together. Treated lumber below ground, non treated
above, and they consist of pieces with the joints at different spots.
The builder said they are stronger than single posts, and because of
the height of the building, it's next to impossible to get solid poles
amout of steel as a solid rod would have more resistance to bending
force, but a solid tube of the same diameter as a hollow tube will be
stronger. If you don't believe that, try bending a lenght of 1/2" EMT
over your knee, then try with a solid 1/2" steel bar.
No, 4x12 is not common. Making up your own as suggested will make a
far stronger and straighter header. When making it, try to pick fairly
straight stock and if it is a faily long header, lay it out so the
curves are opposite, i.e., if the top one curves left, the bottom one
curves right. Start nailing from one end and keep pulling the other
end together. That makes for a nice straight beam. You might
(probably will) need clamps to draw the ends together when you get
near. I have done that often with stock up to 2x10, haven't tried with
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