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Stress/Strain with two rods joined together

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data
    A rod is made of two sections joined end to end. The sections are identical, except the one is steel and the other is brass. While one end is held fixed, the other is pulled to result in change in length of 1.20 mm. By how much does the length of each section increase?


    2. Relevant equations
    Strain = stress / E
    Stress = F/A
    delta L = 1/E x L


    3. The attempt at a solution
    I know that E(steel) = 200x10^9 and E(brass) = 100x10^9
    I know that the total length is L= L1 +L2, where L1 is the length of the steel and L2 is the length of the brass
    I know that the force and cross-sectional area is the same, so those don't matter.
    I feel that the delta L = 1/(E(steel)+E(brass))xL would be right, but i dont know where to find the value of L.
    or is it that delta L = 1/E(steel)xL1, where delta L = 1.20mm? but i feel that this is wrong because it says in the question that the whole rod lengthens that much.
    any suggestions?
     
  2. jcsd
  3. Apr 11, 2010 #2

    PhanthomJay

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    the total change in length of the rod is equal to the sum of the change in lengths of its component parts. If E_B = 1/2E_S, which piece deforms more, and how much more?
     
  4. Apr 11, 2010 #3
    the brass deforms and it is double the amount of the steel, so is this right:
    1.2 = x+2x , where x is the length of steel
    x = 0.4mm and the length of brass increases by 0.8mm?
     
  5. Apr 12, 2010 #4

    PhanthomJay

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    Yes, very good.
     
  6. Apr 12, 2010 #5
    thank you :eek:)
     
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