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Factor of safety question

  1. Dec 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Two overlapping metal plates are bolted together with 12 bolts. The diameter of each bolt is 8mm. If the ultimate shear stress of the bolt material is 300MPa determine what factor of safety applies if the total force to be carries by the joint is 20kN.


    2. Relevant equations
    Stress = force/area
    factor of safety = ultimate stress/actual stress (I think)


    3. The attempt at a solution
    stress=force/area
    stress=20kn/∏r^2 x 12
    stress=20,000N / (∏ X 0.004)^2 X 12
    = 10.55 MN/m^2

    factor of safety = ultimate stress/actual stress
    factor of safety = 300MPa/10.55 MN/m^2
    = 300 x 10^6 / 10.55 x 10^6
    = 28.42

    Is this correct, cause im not that confident? also what is the unit? is there one?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 5, 2013 #2

    PhanthomJay

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    Your equations are good but you squared Pi in error. Would you expect the safety factor to have units? The stress unit N/ m^2 is called a Pascal (Pa).
     
  4. Dec 5, 2013 #3
    Thanks for the reply, I thought that to work out the area of a circle which in this case is the bolt, the equation is ∏r^2? or are you saying I only need to square the radius first then times it by pi?

    and no I assume there's no units as its a ratio
     
  5. Dec 5, 2013 #4
    ok think ive sussed it:

    300,000,000 x ∏ x 0.004^2 x 12 = 180,955 = max force

    max force / actual force = factor of safety

    180,955 / 20000 = 9.05

    I sure that's the final answer!
     
  6. Dec 5, 2013 #5

    PhanthomJay

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    Yes, you have to be careful with use (or non-use) of parentheses when writing equations. The area of a circle is ∏r^2 or ∏(r^2) or (∏)r^2 or (∏)(r^2) or ∏*r^2, but it is not (∏r)^2. Also when you wrote "stress=20kn/∏r^2 x 12" , that should have read ""stress=20kN/12∏r^2" or some correct variation thereof. The way you wrote it implies you are multiplying by 12 instead of dividing by 12.
    correct
     
  7. Dec 5, 2013 #6

    PhanthomJay

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    Well, OK, but you should round it off to 9 (one significant figure).
     
  8. Feb 12, 2016 #7
    Did you ever find the correct solution to this question? I am currently stuck on the same one
     
  9. Feb 12, 2016 #8

    Nidum

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    sl8rbaby never came back again so you are unlikely to get a direct answer .

    You can have some help on this problem though - ask the question afresh in a new thread here on homework section .
    Best to give us your own statement of the question and your own attempts at solution rather than just copy what was originally posted .
     
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