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Thread: Calculating flexion in curved tube

  1. #1
    Associate Engineer
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    Sep 2013
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    Confused Calculating flexion in curved tube

    Hi all,
    I rolled a 3" tube (plain steel) with .1" wall thickness, 15' long
    I rolled it to form a 'C' shape of about 10' diameter with a tighter radius in the middle.
    Unfortunately it have too much flex in it. So I need to go thicker.

    I would like to know if there is some calculation to help find a "perfect" thickness.
    I still what some flexion but not as much as the 0.1" is currently giving. And don't have time and money to try each available thickness!!!

    thanks in advance

    Alexandre B.ing

  2. #2
    Lead Engineer
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    Aug 2013
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    USE WITH CAUTION: WHILE I BELIEVE THE BELOW METHOD TO BE ACCURATE I STRONGLY RECOMMEND THAT YOU REVIEW IT FOR YOURSELF BEFORE PURCHASING ANY NEW TUBING OR TAKING ANY FINAL ACTION; AND, I ENCOURAGE ANY OTHER FORUM MEMBERS TO COMMENT ON THEIR VIEWS OF THE CORRECTNESS OF THE BELOW SOLUTION I HAVE GIVEN.

    If all other factors are kept equal then it appears that the deflection of your curved tubing is inversely proportional to the I (Moment of Inertia) of the X-section of the tubing you use; and, by using your existing tubing I and deflection and your desired acceptable deflection values, you should be able to determine the new minimum wall thickness for the tubing by the following:

    The simplified equation for solving this is:

    deflection2 = deflection1 * [ (D1^4 - d1^4) / (D2^4 - d2^4) ]

    Where: deflection1 = your current curved beam deflection
    deflection2 = your desired new curved beam deflection
    D1 = your current tubing O.D. (10 in)
    d1= your current tubing I.D. (9.80 in)
    D2 = your new tubing O.D.
    d2= your new tubing I.D.

    This is going to be a trial and error solution by varying d2 to achieve your desired deflection2 (assuming your tubing O.D. will be same on the new tubing) My preferred method for solving this would be to use MS Excel and its “Goal Seeking” function.
    Last edited by JAlberts; 09-10-2013 at 11:47 AM. Reason: Symbol for deflection did not copy over from MS Word

  3. #3
    Lead Engineer Cake of Doom's Avatar
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    I know a little equation for finding the required I value but I have never tried it on tube, so I'm not sure how accurate it will be but I'll throw it out there:-

    Irqd = 0.62 x 10^-2 x aWL^2

    a is achieved from dividing the length by a number untill the deflection limit is where you want it eg: L/360 = deflection (in). In this case a = 360. It may be easier to treat it as a cantilever.

    From that you can use the formula from the post above to tweek it and then use the basic defelction methods until it's where you want it. You'll need to convert any point loads to equivalent UDLs for it to work.

    Working on the same assumption as JAlberts (that you want use the original OD); the tube could get really thick (depending on what you're required defelction is) and could get tough to bend. It may also increase the spring action and not hold the desired curve.

    I suppose it may be more accurate to go down the spring theory route but that can get pretty long winded.

    This comes with all the usual caveats about internet advice so good luck.

    EDIT: Once you find an acceptable value for a, you can then take this and divide it by 161.3. this will then give you another value: K. This can then be used to simplify the sum to I req = KWL^2.

    It's also a good idea to record a and it's corresponding K value for later use, to save a bit of work.
    Last edited by Cake of Doom; 09-11-2013 at 06:24 AM. Reason: Daemonic interference

  4. #4
    Lead Engineer RWOLFEJR's Avatar
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    Sounds like your load on this C-shaped piece is at the ends? Or is it at the middle? guess I'm wondering how is this thing loaded?

    If it's being loaded as if to try to close the C further... My guess for a simple way to get close would be to compare your results from what you've already made to a beam deflection formula. Hop over to the calculators section on this site and find the moment (I) of the tube you used. Think the calculator is called section properties. Then hop onto a calculator for beam bending and insert the value I from your part and see if the deflection is close to what you had. If it is close... you picked a formula that'll get you close. Then just keep bumping up the value for I until you get your desired deflection. Once you know this new value for I that you need you simply bump your tube wall up until you reach that moment on the previous calculator.

  5. #5
    Associate Engineer
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    Sep 2013
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    Thanks guys, was not sure if the curved was modifying the values.

    So for the record, I am trying to close the C, it is sitting upright and there going to be something hung inside.
    The outside diameter have to stay at 3.0" don't want to redo the dies (30hrs of work :P)

    Will calculate with each proposed solution (and see if they all end-up with similar result)
    Then I'll go live!!!

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