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Thread: Steel tube strength charts

  1. #1
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    Steel tube strength charts

    I've looked for awhile but can't find the info I need. My design uses some steel and aluminum tubing. An aluminum tube for the main spar and some steel tubes for subframes, these will not be truss structures but simple cantilever beams.

    What I'm looking for is some kind of a chart or graph that will show the cantilever and beam bending strength of different diameter and wall thickness tubes.

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    Registered User wsimpso1's Avatar
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    Re: Steel tube strength charts

    Starman,

    Tubes in cantilever loading is too complicated to present in charts, and is taught in Mechanics of Materials. Timoshenko and Gere is an excellent text.

    Bending and shear loads carried by a structure are entirely a result of the load distributions and geometry used. Stresses are then a result of the shear and bending loads and the beam section chosen. And maximum stresses that the section can carry are based in the metals chosen.

    First - determine shear and bending moment on beam. For cantilever beams, the shear at any point along the beam is equal to all of the accumulated load from that point towards the free end. In a cantilever beam, this load varies from zero at the very tip to huge at the built in end. The bending moment is the sum of each of the loads times the distance from the point in question to the load. With distributed loads, calculas is the way to do it.

    Second - For a given metal, you have to find the section that allows the beam to carry the load while stresses are kept within bounds. Max tensile stress in a tube is sigma = (32*M*D)/(PI*(D^4-d^4), where M is bending moment, D is the major diameter, and d is the minor diameter. Max compressive stress is the negative of the tensile. Shear stress in tubes is another matter and the texts will help with that one. I do not have it off the top of my head. Shear and tensile/compressive stresses interact heavily in tubes as beams - you can not simply calculate each and compare them to some limit. For yield, von Mises works nicely, for ultimate, it is back to the books for you.

    More efficient beams (lighter for the same load carrying) have their own calculations and limitations. Beams with flanges (caps) and webs separate the stresses more cleanly and are more easily checked in these ways.

    Third - Check that the stresses are below limits for the material in question. The most appropriate means for checking yield at limit stresses is to use von Mises total stress. Its application requires calculation of principle stresses via Mohr's circle and is beyond the scope of a forum. For metals, you will have several criteria: Stress under ultimate load (from FAR Part 23) can be no higher than ultimate strength; Stress under limit load can be no higher than yield strength; tension, compression, and shear must all be checked, with all being safe.

    Evans carries a lot of this in his Lightplane Designer's Handbook. It may be a useful introduction to all of this stuff, as well as charts of column loads that can be carried by standard tubes (a far simpler situation than cantilever beams).

    Billski

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    Registered User LArzfromarz's Avatar
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    Re: Steel tube strength charts

    You materials guys are full of good stuff!
    L

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    Re: Steel tube strength charts

    Thanks Billski, unfortunately I'm too old and set in my way to get into books like that. What I'll do instead is some destruction testing of some different tubes to get an idea of what I'll be needing for tube sizes. I have a twenty ton hydraulic jack and a nice piece of I beam just made for a hold down. What I need now is a separate compression gage or get a setup with a gage added to the cylinder or pump.

    The wing spar on my design is going to have a torque of about 50,000 foot pounds trying to bend it. I designed a wing fold hinge like the Grumman Cats use and was aiming at 1" diameter bearings and shaft separated 6" for 100,000 lb/ft. at each bearing.

    I want to use a 2.5" diameter steel tube to carry the hinge so I can insert that tube inside my main spar center section, which is a 4.5" diameter 6061 tube with 1/2" wall thickness for a 3.5" ID. The steel tube will also carry the outer wing spars.

    I'm pretty sure that a 1/4" wall section on the 2.5" steel tube wont take 100,000 pounds at one foot of bending force so I'll have to use a thicker tube, just guessing, but I'll test it. If anyone here has any seat of the pants ideas on this then let me know.

    Two foot pieces of steel tube don't cost all that much for destruction testing.

    By the way, the wing hinge is something "for later" that I may or may not decide to use depending on the compromise of weight versus coolness factor. at first I'll just slide the outer wing spar over the center section wing spar.

    What I do need right from the start is a steel tube subframe which holds the tails to the cockpit tub.

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    Registered User wsimpso1's Avatar
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    Re: Steel tube strength charts

    You can do a lot of checking equations and calculations for the cost of just one test. And if you are just sizing the root structure we can make it simpler...

    Shear load at the root is your design g loading times the weight of the airplane divided by two. Multiply this by your factor of saftey, and that is the limit load. This is conservative in that it over estimates the real number, but not hugely.

    Bending moment at the root is your shear load times 0.42 times the half span. That is where the center of lift is with eliptical span loading. Since the shear load is slightly high, so will your moment.

    Now, once you know those things, you can estimate the shear and bending stresses in the tube. Mohr's circle and von Mises stress calcs are not hard or complicated, and will lead to a lot less trial and error.

    I am visiting with family, but I can run a quick check on these numbers for your size tubing when I get home... What are your g-loading, airplane weight, and wing span?

    Billski

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    Re: Steel tube strength charts

    Thanks Billski, I don't mind working with equations, I just didn't want to read a couple of big engineering books in order to find those equations. So if you can post some equations that would be great!

    Using nice rounded numbers, I used 2000lb gross, which adds about an 80% safety margin, and ten Gs, which adds more safety margin, and assuming a 5 foot semispan on the wings, which is how I arrived at 50,000 lb force at one foot, the force trying to bend the tubes which carries the hinge, which gives the 100,000lb force at the 6" wide wing hinge. I called it torque. This is assuming ten foot wings are being added to a six foot center section for a span of 26 ft. Actually I'm planning on starting with very large wings and then making smaller ones, possibly in several stages. The first wings will be like hang glider type ultralight wings.

    Actually the wing hinge is for later. First I need to figure out what size steel tube I need for the rear subframe, which attaches the vertical and horizontal tails, the engine, and the landing gear to the cockpit tub.

    If the CG is six inches ahead of the CL and the gross weight is 2000lb at ten Gs that gives a required download of 10,000 pounds at one foot. There are two of these tubes (2 tails) so each needs to carry 5000 lb force at one foot, or about 700lb at 7 feet. I hope you can understand my terminology because even though I've heard all the words I'm not familiar with how a couple of them are commonly used by engineers
    Last edited by Starman; August 27th, 2009 at 01:34 AM.

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    Registered User wsimpso1's Avatar
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    Re: Steel tube strength charts

    Starman,

    OK, let's get grounded here.

    Engineering is about applying the appropriate math to a problem, making judgements about what is and is not appropriate, figuring out how to make it go together, and weighing risks. You are asking for us to provide you with the math. The trouble with skipping the knowledge is that you are asking someone else to make your choices on what is appropriate and what is not for you. Unfortunately, in this society, if you use my math and assumptions and hurt someone, and the math gets run back to me, I can get dragged into the fuss. I am disinclined to cooperate with such a plan... In addition, most of us are accustomed to getting paid for what we do professionally. As a educated professional on the topic of designing structures, I may share some knowledge, but I am not inclined to give away the whole party for free... Your toy, your plan, you may have to get educated or pay folks to get your answers. And no, I am not hanging out my shingle, but Orion does.

    Now beam theory is just a couple chapters of Timoshenko and a couple chapters of Shigley, and stress/strength relationships is only a couple more. The only mathematical prerequisite is understanding what integral calculus is. Get the books off the web (used copies are usually cheap), and we will help you understand this stuff, and even check your work... You can probably find Wikipedia pages on each of the topics too. I can also supply you with my spreadsheet for calculating shear and bending moment at any place along a cantilever wing. PM me for that and the text that describes what it is doing.

    Semi-span is the distance from the centerline to the wingtip. 26 foot wingspan leaves you with 156" semispan. A gross of 2000lb and 10g means each wing will be designed to carry 10000 pounds.

    Bending moment at the centerline is approximately 0.42*shear*semispan, assumming eliptical lift distribution. To be more conservative, change the 0.42 to 0.46 or even 0.50. The shear at the centerline is 10,000 pounds, and moment at the centerline is 665,000 in-lb. In my first note of this thread, I gave the equation for max tensile stress. I started at your 4.5" aluminum tube and checked stresses against the yield strength I know for 6061-T6, which is 35 kpsi. It is way too puny. Strength of tubes goes with the third power of diameter, so grow your diameter... Once your half inch wall tube is big enough in diameter to get tensile stresses below yield, you might calculate its weight, and then figure out if thinner walls and bigger diameters would still fit inside your wing and be lighter too.

    Then there is combined stress to really know that the tubes will be OK. Next step after knowing the tensile/compressive stresses is shear stress. In wide flange beams, tau is approximated by V/A with A being the area of the web only. In simle beam shapes, shear is a parabola with the max shear at the center of the beam depth at 4V/3A. This too is in Timoshenko in the chapters on beam theory. I do not know how shear stress is distributed in tubes, but the basics are in Timoshenko. Maybe you can Google the topic... Then for each of several places around the tube, you tabulate sigma and tau, and roll out Mohr's circle. Mohr's circle lets you figure out the principle stresses at each of the places. Mohr's circle is in Timoshenko too. Just an equation with principle stresses output. Those principle stresses are put into von Mises stress equation. It is in Shigley, and it too is easy. Probably Wiki pages out there too. Anyway, check Von Mises stress against yield. If it yields, bump the diameter or the materials or both... Iterate as necessary. Excel is your friend.

    Once you have that tube rough sized, you have to remember that another tube telescoped inside of it has to carry the shear and moment developed in the outer panel into the center section. Hmmm. Figure out the loads at the contacts between the tubes are, and those go into a third direction locally in both tubes as a compression normal to the tube surfaces... This is a third stressor on Mohr's circle and the von Mises stresses. If the compression stresses are small, they might be ignored, but then, what is small? Or you can just go through the math and find out.

    You may have a problem. I used 35 kpsi for yield strength of 6061-T6. If you weld that tube into your fuselage, the strength near those welds will drop to 10-12 kpsi, so your stresses at those locations have to go below 10 kpsi. If instead you weld in a couple saddles that clamp the tube in, and the clamps will carry 10,000 pounds each, it will work. If you are clamping the center section beam into the fuselage, maybe it could be 4130 normalized tubing with a 70 kpsi tensile/compressive yield, and all worries over galvanic corrosion and fretting between the steel and aluminum tubes will fade. Then you will still have to isolate the steel tube from the aluminum structure...

    So, you can begin to see that this requires more than elementary fussing with a couple equations. And you can get into weight and how to reduce it economically. And avoid multiple design/build/test iterations too. And if you have a capable mind, this stuff can get interesting...

    One other topic. The shear web and cap beams are used because they are efficient in terms of strength/weight ratio, and because you can tailor the web and cap areas, reducing them as appropriate as you move outboard. The web might be four thicknesses of alloy at the root through the hinge, then go to three then two then just one in the last couple feet. Likewise, the caps will start out with many plies through the fuselage, and then go down to just a couple at the tip. They also make the mounting of hinge mechanisms and getting the loads from beam to hinge to beam a lot more straightforward.

    Tube spars are only attractive until you get into the rest of the stuff.

    Billski

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    Re: Steel tube strength charts

    Quote Originally Posted by wsimpso1 View Post
    I started at your 4.5" aluminum tube and checked stresses against the yield strength I know for 6061-T6, which is 35 kpsi. It is way too puny. Strength of tubes goes with the third power of diameter, so grow your diameter... Once your half inch wall tube is big enough in diameter to get tensile stresses below yield, you might calculate its weight, and then figure out if thinner walls and bigger diameters would still fit inside your wing and be lighter too.
    Thanks for checking that for me Billski. My original idea was to make a giant aluminum I beam for a main spar center section (18" deep at the center and 9" at the ends) but I had this aluminum pipe lying around and assumed it would be much stronger than needed, but see, i asked before using it so it's back to the drawing board.

    For the wing spars my idea was to use aluminum tubes for the fabric wings but then use a composite spar for the later versions.

    I like the idea of using a steel tube main spar center section and attaching it with saddles

    I will reread what you've written in your last post to better digest it and read your first post too, and get those books. I'll ask some people at the local chapters to help me with the figuring if need be.

    For the steel tube subframe shown in my design I was just going to make a wild guess and test it to destruction (mild steel is cheap) because in addition to bending there will be strong twisting forces on those tubes which will make calculations even more difficult. When I get the sizes right I'll build it out of 4130 for that nice safety margin. Thanks to your motivation I'll figure out how to do the calculations in order to get a starting size.

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    Re: Steel tube strength charts

    Billski, thanks to your advice I'm now leaning toward making a fabricated steel I beam for the main spar center section. It will be easy for me to calculate the stresses in that and to connect it to the steel subframe. Now the problem is how to connect it to the aluminum fuselage tub. My choice is a few big connectors or many smaller connectors spread out over a larger area, I'm leaning towards the later.

    I'm also aware of the corrosion potential between the steel and aluminum and the need for protecting against that. I assume there's been discussion in this forum already about that so I'll do a search.

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