I want to make a beam that will be triangular, rather than rectangular, and hollow.
Does anyone know a source or have the knowledge to work out how strong such a beam would be. It sort of feels as if it would be prop. to the sin of the agles of the sides, or whatever, but I am not sure, and it probably gets more complex than that.
Any advice appreciated.
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"Properties of Sections" is what you want, here's the first two Google hits...
Strength will be proportional to Z (section modulus), stiffness proportional to I (moment of inertia). Use superposition (subtract the properties of the "missing" material from that of a solid prism) to account for your hollow setion. If you want to do this analytically, the subject you're looking for is "Strength of Materials". That's also the name of the classic college text by Timoshenko.
This is all you need to compare the strength or stiffness of various sections. If you want the actual numbers you of course need to account for beam material, span, type of support(s), and load distribution.
Ned Simmons
I'm sure one of the kids here has one of those new fangled programs to figure out such things. As for me, your question almost makes me want to take my mechanics of materials book off the shelf and see how much I forgot!
You should probably specify the material and all dimensions though...
One more thing, these properties depend on the orientation of the beam relative to the loading, for example, whether the load is acting parallel or perpendicular to a side of your triangle.
p.s.s. "Roark's Formulas for Stress and Strain" is the Cliff Notes version for all this stuff, but probably not very useful on its own unless you already have a pretty good understanding of the subject.
Ned Simmons
I'm assuing you are looking for bending strength (the usual for a beam)? If so, when beams resist bending loads/moments, one outside surface/edge is in max compression and the opposite surface/edge is in max tension. So you want the beam to have maximum material on those opposite surfaces, which led to the development of the I-beam (though these are only strong for bending in 1 plane--for bending in 2 planes a square tube is much better). So the problem w/ triangles for bending is that there isn't much material where the stress is highest--one of the corners of the triangle. If you can reinforce the weak edge with more material (e.g., weld on a solid bar) with the same area as the bottom flange, the problem is fixed and it's about as good as an I beam. In ascii:
------- | | ------- //\\ // \\ // \\ // \\ // \\ // \\ -------------- --------------
Check out these links:
The second step is to plug it into....... f sub b = M c / eye
On 31 Jul 2004 12:22:50 -0700, snipped-for-privacy@ku.edu (David Malicky) vaguely proposed a theory ......and in reply I say!:
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hmm OK. Thanks. I can see where that makes sense. I will certainly look at that. I assumed though that a lot of the strength would also come from the tension and compression of the "webbing", or vertical sides of the beam. I sort of thought that the top and bottom flange were to stop the I-beams being "floppy" sideways.
***************************************************** It's not the milk and honey we hate. It's having it rammed down our throats.On Sat, 31 Jul 2004 07:06:32 -0700, "larsen-tools" vaguely proposed a theory ......and in reply I say!:
remove ns from my header address to reply via email I did ask for "any advice"
Appreciated.
***************************************************** It's not the milk and honey we hate. It's having it rammed down our throats.On Sat, 31 Jul 2004 11:12:51 -0400, Ned Simmons vaguely proposed a theory ......and in reply I say!:
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Nice. Thank you. That will give me something to chew on.
And not an Epsilon, Sigma or Rho in sight!
***************************************************** It's not the milk and honey we hate. It's having it rammed down our throats.On Sat, 31 Jul 2004 11:44:25 -0400, Ned Simmons vaguely proposed a theory ......and in reply I say!:
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Yes. Thanks. That will be awkward, and I probably have to allow for worst case. It's for a loader rake bucket. So the direction of roces could be anywhere.
Maybe I should just go to round, and work that way? Problem is I am using an alloy for lightweight strength. You can't get tube, and making it would cost a fortune.
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Need moment of inertia (I), radius of gyration (r), locations and nature of loads and supports and material.
Need dimensions of cross section to calculate I and r.
Ted
Advice......... You are in over your head.
What alloy? Are you thinking of welding it up out of flat stock? If so, consider square. Square tube is a very efficient shape for bending strength and also has excellent resistance to twisting. If you give me dimensions, I can run the beam calc on my software. Otherwise, if you give position of support(s) and load(s) with amount of load and material strength, I could give you dimensions for an appropriate square tube.
Ted
On Sun, 01 Aug 2004 00:43:22 GMT, Ted Edwards vaguely proposed a theory ......and in reply I say!:
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It's Bisalloy. Pre tempered etc.
I can do square / rect no problems. IT was the triangular that was a problem. I want it mainly to allow better sheeding of soil, when dealing with rock or logs etc. Maybe I should just shake the oil off and go square!
***************************************************** It's not the milk and honey we hate. It's having it rammed down our throats.On Sat, 31 Jul 2004 17:27:19 -0700, "larsen-tools" vaguely proposed a theory ......and in reply I say!:
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Which is how we all learned to swim....
***************************************************** It's not the milk and honey we hate. It's having it rammed down our throats.On Sun, 01 Aug 2004 00:43:22 GMT, Ted Edwards vaguely proposed a theory ......and in reply I say!:
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I am going to look hardf at the sites Ned gave. They are interesting. I know the principles, but had not dealt with triangular.
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The web contributes very little to bending strength. It's primary purpose is to put as much distance as possible between the flanges. But there are limits on how thin it can be because of instabilities and other failure modes.
You mentioned that your beam can be loaded from any direction. If you mean that the maximum load could come from any direction, then your beam should ideally be equally strong in any direction, which means a circular section. Any section other than circular will add weight. If you can't make it circular, make it as close as possible. An octagonal section would be better than hexagonal, which would be better than square, which would be better than triangular, which would be better than a flat plate.
Bert
That's true, the web can and does contribute some of the strength, %wise depending of course on how big the flanges are. And in a triangular shape you have two webs so that helps. Another way to achieve the added area on the corners is to reinforce the inside of each corner, retaining the o/s triangular profile. Unlikely you'll get the optimum reinforcement, but it's an improvement.
And yes, the flanges do keep the beam from being "floppy" (good observation, it's called "lateral torsional buckling"--in an I shape the compression flange helps that, in a closed section the whole section stops it.), but mainly they are there to improve the bending properties.
Also, as Bert mentioned, triangles carry bending loads, just not as efficiently (strength/weight and stiffness/weight) as an round, square... Given that every design has it's tradeoffs, a triangle may indeed be best if its soil shedding properties outweigh the lower efficiency of the triangle, compared to the performance of a square. I don't know much about shedding of soil so cant' help there.
Also, I also don't know much about bisalloy--how do you weld it and retain the props?
David
On 1 Aug 2004 10:24:02 -0700, snipped-for-privacy@ku.edu (David Malicky) vaguely proposed a theory ......and in reply I say!:
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Great! I actually sat down last night and looked at "filleting" the cormers with pieces. The major loss, givne that the "flanges" are a great strength in tension, is of course that the strongest part of the flange will be well inside the full depth of the triangle. SO you lose a lot of working depth.
a la "sandwich construction", bascially. Or like a roof truss.
This is what I was looking to fond out, in a rough way for a start. What were the losses vs gains?
Very carefully. It is quite weldable, being euivalent to about .3% carbon steel, in the grade I am using.
But a lot of small passes are needed. Check temp between passes. Keep it warm but below a reccommended max. Obviously don't weld across a piece that will be under stress. Use the correct welding wires. And don't breathe the fumes.
If you welded it to _their_ specs, you would be in a hospital clean room, completely controlled up to 300C, and able to be heated and cooled anywhere within that range withon 30 seconds, but up to 1 hour on thermostat!
IN reality, is weldable in the field with care. My results are far from ideal, but still spectacular, AFAIAC.
Cutting it's a PITA, especially if you get down to fine scantlings. It's where you get into at least plasma, and even better, laser or water. It's a bitch to cut with an abrasive wheel, as it seems to clog very badly. I have been told that you can cut it on a bandsaw with the right bimetal bands (at about 60-75 FPM) and a lot of patience, but again, not good with the carbide grit belts.
Its beauty is that its Yield Strength is about 3.5-4 times that of structural steel (Yield = 1190 MPa. Tensile = 1260 MPa). So I figure I can "over engineer" (I actually reckon it's UNDER engineering and over building, but anyway) a little and still get a lighter product of usable porportions.
I actually built some hollow tines for a smaller FEL, using a rectanuglar shape and my own floundering engineering. They were still completely unmovable and unbendable at a very acceptable length, depth and width. The strength of this stuff is phenomenal.
Ironically, the thing that will damage tines, IME, is not the hydraulics, but the force of something jamming in between two tines, and being rammed down between them. Enormous forces can happen there, and are alomost unpredictable.
However.
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