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Mechanics Of Materials Stress Problem

  1. Jun 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Here is a link to a picture of the problem:
    http://imgur.com/5nOnpJE Click on the picture to make it bigger, and readable!


    I need to find the angle that the two rods will have the same stress. We are talking about normal stress here!

    2. Relevant equations

    [itex]\sigma[/itex] = Force / Area

    3. The attempt at a solution

    I am using the method of joints to solve for the internal force because they are both two force members. I have the equations for x, and y.

    X:
    -AB + BC cos(θ) = 0

    Y:
    -50 + BC sin(θ) = 0

    Where do I go from here? I want to start solving in terms of something to be able to put them into the stress formula.
     
  2. jcsd
  3. Jun 17, 2013 #2

    SteamKing

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    In order to find the axial stress in each rod, you must first determine the axial force in each rod.
     
  4. Jun 17, 2013 #3
    Steam is correct. However, does the load of 50 kN really matter if you want the stress to be the same? (just use F)
    Draw a "joint diagram" and then find the force in BC as a function of theta, then the force in AB as a function of theta. Then continue.
     
  5. Jun 17, 2013 #4

    You already practically have it solved. Solve your two equations for AB and BC in terms of θ. The tensile stress in each of these members is equal to its tension divided by its cross section area. Set the two stresses equal to one another, and you will get an equation for θ.
     
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