Connect with us

Column Critical Buckling Loads

Discussion in 'Home Power and Microgeneration' started by Curbie, Jul 2, 2009.

Scroll to continue with content
  1. Curbie

    Curbie Guest

    I went back after the math behind calculating loads exerted on wind
    turbine tower masts and I'm still having trouble converting the
    formulas to a spread-sheet so the results match the examples given.

    The formula I'm having trouble converting is:
    (34,000/1.9)[1 - (1/2)(101.8/132)^2] = 10,994

    My question is how do I convert the contents of the left square
    bracket "[" and right square bracket "]" to spread-sheet expression?
    Or maybe just what is the purpose of the brackets.

    Thanks for any help.

    Curbie
     
  2. vaughn

    vaughn Guest

    Just change those square brackets to round ones. They were probably only
    made square to help us humans keep track of things. Computers (even cheap
    scientific calculators) can handle multiple nested round brackets just fine.

    Vaughn
     
  3. Curbie

    Curbie Guest

    Vaughn,
    That worked for me in the past but using this spread-sheet expression:
    (34000 / 1.9) * (1 - (1 / 2) * (101.8 / 132)^2) = 12,573

    where their example is:
    (34,000/1.9)[1 - (1/2)(101.8/132)^2] = 10,994

    Different results, and since these formulas where taken from some
    college physics department, I have to be interpreting that formula
    incorrectly.

    http://physics.uwstout.edu/StatStr/Statics/Columns/colse62c.htm

    I always look for examples with results so I can check my math for
    just this sort of mis-interpretation.

    Curbie
     
  4. Neon John

    Neon John Guest

    I worked this out by hand on a calculator to make sure I got my
    operator precedence correct and got your answer of 12,573. I can't
    get 10,994 using any combination of the numbers, even abusing
    precedence rules.

    I ran the formula using square root instead of square, figuring that
    the guy might have hit the wrong key on his calculator. That produces
    10,037. Closer but no cigar. I think that he made a math error. Why
    not drop him a note and ask?

    John

     
  5. Curbie

    Curbie Guest

    I'm sorry John, I didn't mean for anyone to run the calculations, just
    explain the use of the "[ ]".

    Do you think those "[ ]" could be replaced with "( )", it seems there
    has to be more than that and that one of the students would have run
    the math and gleefully pointed out the error (seems that would to be
    worth some extra credit)?
    I'll try, I've never had any luck doing that, their pretty busy.

    Thanks,

    Curbie
     
  6. vaughn

    vaughn Guest

    You have been rare lately John. Good to see you back.

    Vaughn
     
  7. Curbie

    Curbie Guest

    z,

    On a side note, have you ever visited OtherPower.com hydro page?

    I read over there a lot and someone asked if anyone was using a
    WindBlue generator, so I pointed him at your site and you.

    Vaughn,

    You where right about just replacing the square brackets with
    parentheses (see below) thanks for your help.

    Neon John,

    You where right about the formula being wrong, I was really wrong in
    thinking a university physics department couldn't post simple math
    errors, I can't believe one of the student haven't pointed that out.

    The next example that they give uses a larger column with the same
    formula:

    (34000 / 1.85) * (1 - (1 / 2) * (69.3 / 132)^2) = 15,845

    My spread-sheet agrees those results using the same formula with new
    variables so it seems that the results given for the first formula
    (the one you hand calculated) was wrong. I sent the instructor an
    email like you suggested before I ran into this latest discovery. Be
    interesting to see how they handle this?

    Thanks Neon John,

    Curbie
     
  8. Curbie

    Curbie Guest

    So:
    (34,000/1.9)[1 - (1/2)(101.8/132)^2] = 12,578 and NOT 10,994

    and

    (34,000/1.85)[1 - (1/2)(69.3/132)^2] = 15,845

    2:36 and I'm still at it too.

    Get sleep that's what I'm going to do. zzzzzzzzz

    Curbie
     
  9. Neon John

    Neon John Guest

    Kewl. Be sure to post the reply. Interesting to see if he weasles or
    admits the mistake.
    You be welcome.
     
  10. daestrom

    daestrom Guest

    Working it backwards to find the 'error',

    (34000/1.9)*(1-0.5*X) = 10994
    -.5*X = 10994*(1.9/34000)-1

    X = .771259

    Which is almost exactly 101.8/132

    So in order to get the 'answer' of 10994, the original calculation would
    have to have been...

    (34,000/1.0)(1 - (1/2)(101.8/132)) = 10994.42

    Without the square.

    So now you'll have to decide if the 'error' was in the calculation and
    the right answer should have been 12,573, or the 'error' was in putting
    the superscript '2' indicating the quotient of (101.8/132) is supposed
    to be squared.

    Probably the person working the example simply forgot to square the
    quotient and came up with the wrong answer and the right answer is
    12,573. Does the rest of the text show that that term is supposed to be
    squared?

    daestrom
     
  11. Curbie

    Curbie Guest

    z,
    When it come to DIY wind turbines OtherPower has some people with lots
    of experience, big brains, I've read the posts there for years (good
    wind forum) although I rarely post there, my first two posts where
    pulled there I E-mailed both times to fine out why, but they never
    told me what I was doing wrong.

    They have a hydro forum I was hoping you aware of, I can't really tell
    how good it is, but alternative energy forums are so rare I read it
    anyway.

    Have fun.

    Curbie
     
  12. Curbie

    Curbie Guest

    daestrom,
    The next two examples that they give uses a larger columns with the
    same formula (Ys / FS) * (1 - (1 / 2) * (S / SC)^2)
    Ys = Yield Strength
    FS = Factor of Safety
    S = Slenderness Ratio
    SC = Slenderness Ratio Critical

    My spread-sheet agrees those results using the same formula with their
    new variables so it seems the results given for the first expression
    was wrong.

    I'm easily confused so when something doesn't make sense my mind seems
    to fixate on it to the exclusion of all else that is related. I
    generally don't pursue information posted on a site that contains an
    error; my mind fixates on the error and questions the validity of
    everything else. I've decided to press on with that site, the subject
    has such specialized and limited interest that I've only found four
    other sites with examples (and issues of their own) to learn from
    (beggars can't choosers).

    Hopefully between the four incomplete spread-sheets I'll be able to
    fill in the blanks to make one complete sheet that both make sense to
    me and can be verified with on-line calculators?

    Neon John suggested I email them and ask for clarification (this was
    before I knew it was an error), hopefully they can clean it up for
    future readers.

    Before I can play with wind-turbines I need to understand this stuff,
    kind of a slugfest, but "welcome to my life".

    Thanks for the math check.

    Curbie
     
Ask a Question
Want to reply to this thread or ask your own question?
You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Electronics Point Logo
Continue to site
Quote of the day

-