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Homework Help: Direct stress

  1. Dec 9, 2007 #1
    1. The problem statement, all variables and given/known data

    1. A steel bar 375mm long is machined to give a diameter of 75mm for the first 175mm length, a diameter of 45mm for the next 100mm length and a diameter of 37mm for the final 100mm length. Determine:

    (i) The total extension of the bar when it’s subjected to an axial tensile load of 84 kN.

    (ii) The tensile stress in each portion of the bar.
    Assume E = 200 GN/m2

    2. Relevant equations

    3. The attempt at a solution

    can this be solved by working out each part as if it were 3 seperate bars ?
  2. jcsd
  3. Dec 9, 2007 #2
    The simple answer is yes. A bar with varing diameter as noted is nothing more that 3 springs in "series" with 3 different spring constants "k". An axial force applied to springs in series would be equal to the sums of the [itex] k_i \cdot x_i [/itex].

    [tex] k_i [/tex] in this problem would be [itex] \frac{A_{i}E}{L_i} [/itex]
  4. Dec 9, 2007 #3
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