[Zumba]

The rebar on the beam is in interesting contraption. It is using the rebar as a tension spring, not as a structural member.

When a beam sags 3", the bottom edge elongates by about 1/8" (the top edge compresses a little bit less than that). So the purpose of the rebar would be to prevent that elongation, and hence prevent sag.

A quick calculation shows that it takes roughly 3000 lbs of tensile force to elongate a 1/2" round x 19 foot bar 1/8 of an inch.

I'm not exactly sure what this means... I can't quite figure how the vertical force of gravity correlates with the horizontal tension force on the rebar. Does anyone know if there are leverage ratios to take into account?

If not, then the rebar is kind of useless. A 2x12 by itself (typical Conifer tree like pine or douglas fir, 1100ksi modulus of elasticity), requires 15000 lbs of force to sag 3". Much more than it what it takes to stretch that wimpy piece of rebar.

[Geof]

The rebar on the beam is in interesting contraption. It is using the rebar as a tension spring, not as a structural member....

That is always how rebar works but it is a but unusual to use it with wood normally it is in concrete. Rebar is strong in tension and weak in compression; because it is small diameter it buckles under compression. Concrete is strong in compression and weak in tension.

In an symmetric beam under load the distribution of stress is maximum compression at the top surface, maximum tension at the bottom surface with a neutral zone which is neither under compression or tension running along the middle. Rebar is placed below the neutral zone in the region that is subjected to tension because that is the type of load it can take. The structural member in this case is the combination of the two materials with different but complementary properties.

A beam with rebar on only one side of the neutral zone must be used in the correct orientation; if it is installed upside down it is no different to unreinforced concrete.

[jsage]

Zumba,

Not sure if you are considering this. The rebar is effectively attached all along the length by the ribs. So the tensioned cable is a bit oversimplified. Also it is more a longer term fatigue of the material I'm concerned with. If this small component prevents the sag to begin with then it a composite effect rather than the individual properties of the materials.


Of course I don't know.

Like Al Gore created the internet. The gougen brothers invented epoxy construction ; )

http://www.westsystem.com/webpages/home/about.htm

jsage

[ger21]

A 2x12 by itself (typical Conifer tree like pine or douglas fir, 1100ksi modulus of elasticity), requires 15000 lbs of force to sag 3".

I wouldn't think a 2x12 could even support 15000 lbs. How long of a 2x12 are we talking about?

[martinw]

The rebar on the beam is in interesting contraption. It is using the rebar as a tension spring, not as a structural member.

Dear Zumba,

All you have to do is analyse the beam by the "lever arm" method.

The lever arm method is one of many ways of looking at the behaviour of beams. There are loads of ways, but they all come up with the same predictions , as regards bending capacity, and deflection within about 15%.

Yep, I will be shot down. I have my tin hat on.

Basically, and simplified, the lever arm analysis says that it is pretty much the properties of the top and bottom parts of the beam that contribute the most to the strength of a beam. The "stuff" in the middle, near the neutral axis, (roughly the point at which the top of the beam is in compression, and at which the bottom is in tension), does not really do much.

If you put a rebar at the bottom of the beam, and it is glued in, the bottom of the beam becomes stronger in tension.

As a result, the neutral axis comes further,vertically down the beam, and the compression forces at the top of the beam become less.

Bingo,

Stronger beam, and less deflection.

Best wishes

Martin

[lgalla]

I would think the 2X12's are doing all the work or carring the load.The rebar may be along for the ride.I did not want to post about this as I don't see any connection or revelence to the thread unless my gantry was 2X12's.:stickpoke
Larry

[ger21]

I don't see any connection or revelence to the thread unless my gantry was 2X12's.:stickpoke
Larry

But wouldn't the rebar stengthen the E/G the same way it stiffens concrete (and the 2x12). That's why I posted that link, as Walter asked about stiffening a 16' beam.

[lgalla]

Agreed Gerry, re-bar may be part of the equasion.Forgive me if I cannot remember[427 posts and growing]but have we decided E/G needs re-bar in certain applications?Is it possible adding re-bar may affect the damping factor in a negative way?The E/G machine builders appear to not use steel reinforcments in their units.It looks like they use hollow sections for coolant,wires,etc.I imagine the hollows reduce the weight of spans and may be stiffer.
Larry

[jsage]

Well folks I enjoy everyone's contribution. Martinw, appreciate the diplomacy. Especially since it isn't a skill I've mastered ; )

I made a mistatement on my own thread. Mostly cause I'm working with concrete on another project and I carried over those concerns to epoxy granite. I was only half right if that.

.

[Zumba]

I wouldn't think a 2x12 could even support 15000 lbs. How long of a 2x12 are we talking about?

19 feet, just like in the article.

That's how much force it would take to make it deflect 3" in the center. Of course, that doesn't mean it won't snap in half long before it actually bends that much. :rainfro:

[Zumba]

Zumba,

Not sure if you are considering this. The rebar is effectively attached all along the length by the ribs. So the tensioned cable is a bit oversimplified.

Yea, but I avoid calculus whenever possible. :rainfro:

[martinw]

Well folks I enjoy everyone's contribution. Martinw, appreciate the diplomacy.

.

Dear jsage,

Thanks for the input.

We all disagree at times, and that is what it is all about.

Bring it on....


Best wishes

Martin

[jsage]

Zumba,

I needed a tutor I slept through math in high school. :rainfro:. I think those aluminum oxide contrails are responsible for my ADD.

[lgalla]

Zunba hope you don't mind me asking direct questions,but you seem to have good answers.On tube filling and deflection.Does the modulas of each material really addup?Example from only a hands on experience.If I fill a 4"X1/16"wall aluinium tube with lightweight urethane foam,you can drive your car over it and not crush it.I would guess the defection is less although the urethane foam only is 15psi.Joining 4 walls of tubing with lightweight filler appears to increase the moment.Any thoughts on the subject?Thanks
Larry

[lgalla]

This is not related to the subject ofE/G but related to damping from a non techinical standpoint on resonance from an audio engineer with no machine experience.Loudspeaker stands are generally hollow steel tubes and we fill them with sand to eliminate resonance.Filling with urethane foam also reduces resonance as there is no airspace for non musical resonances to resonate.I imagine a hollow steel tube router with steppers to resonate [in concert]I am guessing what works in audio to counter act unwanted resonance may apply to machine design.If you eliminate cabinet resonance in audio,all your energy or watts goes into higher sound fidelity.Lack of resonance in a machine frame should result in higher cut quality.Maybe the audio and machine guys can help each other.
Larry

[jsage]

Larry,

As a financial, business, market analyst I can't be of much help. I am wondering how much that urethane foam costs. The catalyzed stuff I have seen is a bit pricey. I still want to find that $30 epoxy too. I'm paying $70 to 100 in gallon quantities.

Outside of that I had a thought that might address beam construction of reasonable length. Rather than maximizing engineering, it focuses a bit more on ease of construction.

You take an EMT pipe and tack weld rebar at 90 degrees. It gives you a space to run wires and ties together the rebar. The welding is less critical in this case. You could position this internal structure with non granite (silica based epoxy filler?, structural microspheres)mounting/connection blocks giving you a bit of flexibility in the future.

The weakness is probably the rebar is not optimally placed. Square tubing might be better with the rebar on the corners. Otherwise spacers of some kind.

I'll put together quick drawing, hopefully. Maybe this will give us something to start with on longer beams. You make the mold maximum length but you can cast shorter versions using the same mold. So you have streamlined the process a bit.

Edit: I attached a mockup realizing this probably isn't what everybody needs or wants but it is a visual concept.

Off the cuff dimensions. ; ) 4"x4"x4' 1" thickness epoxy granite. Rebar is 1/2" Square tubing is 3" x 3" 1/8" thickness. About 5 issues come immediately to mind but not necessarily unresolvable ones.

James (Mike)

As for what I'm working on. It's decorative concrete and stone veneers. Using acid staining for color variations and prototyping textures with silicon casts of real stone. I was looking at fractals for a couple of reasons. The most relevant is how to get a minimal, scaleable, seamless pattern quickly. However I have resorted to imitating some of the better stone work patterns, I have found. There are a number of issues with simplifying the mold making. I wouldn't mind having a finished cnc machine to help with the process but the funds are limited.

[Zumba]

If I fill a 4"X1/16"wall aluinium tube with lightweight urethane foam,you can drive your car over it and not crush it.I would guess the defection is less although the urethane foam only is 15psi.Joining 4 walls of tubing with lightweight filler appears to increase the moment.Any thoughts on the subject?Thanks
Larry

That is interesting. In that particular example, I'm guessing that there are other factors coming into play. Perhaps the top face of the tube deforms, but at the same time, the car tire also deforms. At a certain point, the flat spot on the tire will be wide enough that the vertical sides of the tube begin carrying the weight. If this is the case, then the foam actually has no effect.

As for your main question, "On tube filling and deflection.Does the modulas of each material really addup?", I think yes.

The easiest way to test this would be to get a piece of steel pipe and an aluminum solid round. Turn the aluminum solid so that it fits snugly in the steel pipe. Then perform basic beam deflection experiments and compare to the calculated values. I think they'll match up pretty closely.

If you want to take it a step further, you could get a piece of aluminum pipe and steel solid round. Deflection should definitely be different. How much would depend on the wall thickness of the pipe.

[Zumba]

jsage, I think the steel tube and rebar in the E/G might be overkill. The reason why I like steel so much (in an exoskeleton form) is that I like perfectly ground, relatively hard surfaces with pefectly aligned bolt holes. Some surfaces won't necesssarily be flat... they may be slotted or have a shoulder for set screws.

If you're going to have epoxy as the outer surface, then a much easier way to stiffen a beam would be to simply make it ever so slightly larger. A 5x5 beam should be 2.5 times as stiff as a 4x4.

[vger]

This is not related to the subject ofE/G but related to damping from a non techinical standpoint on resonance from an audio engineer with no machine experience.Loudspeaker stands are generally hollow steel tubes and we fill them with sand to eliminate resonance.Filling with urethane foam also reduces resonance as there is no airspace for non musical resonances to resonate.I imagine a hollow steel tube router with steppers to resonate [in concert]I am guessing what works in audio to counter act unwanted resonance may apply to machine design.If you eliminate cabinet resonance in audio,all your energy or watts goes into higher sound fidelity.Lack of resonance in a machine frame should result in higher cut quality.Maybe the audio and machine guys can help each other.
Larry

I once heard it said that the ideal speaker enclosure would be of solid concrete. I deal with resonances a lot in my work and know that eliminating resonances can be frustrating, especially if you are dealing with variable excitation frequencies.

Steve

[lgalla]

Jsage here is the link.
As a financial, business, market analyst I can't be of much help. I am wondering how much that urethane foam costs. The catalyzed stuff I have seen is a bit pricey. I still want to find that $30 epoxy too. I'm paying $70 to 100 in gallon quantities.
www.shopmaninc.com They are located in Florida.
635 thin epoxy slow kit#epox6355567 15gal $454.00=30/gal
8lbs denisity urethane foam 16lbs kit$54.00 makes 2cuft.
They have a 16lb density foam which would have the properties of pine but lighter.
They also have silicone mold rubbers.
Hope this helps
Larry