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Lame's Equation Maths Problem

  1. Jan 18, 2015 #1

    Jud

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    1. The problem statement, all variables and given/known data
    A steel pipe is 200mm internal diameter and 20mm thick. Calculate the safe internal pressure if the allowable stress is not to exceed 140Mpa.

    2. Relevant equations
    σr = A-B/r^2

    and
    σtheta = A+B/r^2

    3. The attempt at a solution

    Right so, I've got two equations.....

    (eq1)140MPa =A+B/0.1^2
    and
    (eq2)0 = A-B/0.12^2


    I need help getting A and B. Answers (A=57.38)and (B=0.826)

    I know I need to use simultaneous equations. Could someone please give me a step by step solution as I'm stuck.

    I have so far done -(eq2)+(eq1) to cancel out A.
    and got
    ...140MPa = B/0.1^2 + B/0.12^2

    I'm not sure what to do next to get B.
     
  2. jcsd
  3. Jan 18, 2015 #2

    SteamKing

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    Hint: use eq. 2 to get A in terms of B (or vice versa). Substitute back into eq. 1 and solve.
     
  4. Jan 18, 2015 #3

    Jud

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    I don't understand, sorry. Could you elaborate with the values please.
     
  5. Jan 18, 2015 #4

    SteamKing

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    It's very simple. You've got A - B/0.12^2 = 0. Find A in terms of B, or B in terms of A.

    Once you have found an expression for A or B, substitute that expression back into eq. 1, which will then be one equation in one unknown.

    You're in algebra 101 here.
     
  6. Jan 18, 2015 #5

    Jud

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    I.e. B = A/0.12^2

    So,
    140MPa = A + (A/0.12^2)/0.1^2?
     
  7. Jan 18, 2015 #6

    SteamKing

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    Uh, not quite. Remember, you've got

    A - B/0.12^2 = 0

    How did you come up with

    B = A/0.12^2 ?
     
  8. Jan 18, 2015 #7

    Mark44

    Staff: Mentor

    Jud, starting with A - B/0.12^2 = 0, solve for B, without skipping steps.
     
  9. Jan 19, 2015 #8

    Jud

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    A = -B/0.12^2

    A(0.12^2) = -B
     
  10. Jan 19, 2015 #9

    SteamKing

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    So you're saying if A - 5 = 0, then A = -5. Check your work again.
     
  11. Jan 19, 2015 #10

    Jud

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    -A(0.12^2) = -B

    So, 140MPa = A + - A(0.12^2)/0.1^2
     
  12. Jan 19, 2015 #11

    SteamKing

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    You can multiply both sides of the equation by -1 to obtain

    A(0.12^2) = B

    And how would you solve for A?

    Friendly advice: I don't know anything about your academic background, but your apparent lack of understanding of algebra is going to prevent you from solving more complex problems than this. Try to take time and remedy this gap in your mathematical knowledge. ;)
     
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