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Homework Help: Making free bodies of a static structure

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data

    The problem is this. We have a structure (see the attached image) and need to make freebodies of all of the members. 150 lbs are applied to the platform being lowered by the strings. We also need to figure internal stresses, but I think I can get those if I can understand this first.


    2. Relevant equations

    ---

    3. The attempt at a solution

    I picked one of the legs, and I idealized it into an elevation. Since each of the legs is equal in all ways, I divided the force applied by three, so 50lbs on the lowered platform.

    Using the properties of similiar triangles, and knowing that the string has to resist 50lbs of downward force, I found that 96.18lbs of force is acting in tension on the string.

    This force is transfered to the tower at a 90 degree angle. I placed a pin at the bottom and a pin at the top. Using the sum of the moments, I found that 35.43 lbs of force were being exherted perpendicular to the top of the tower, and 60.74 to the bottom of the tower.

    I started with the beam at the top of the tower. Again using similar triangles, I found that the forces acting on the end were 30.26lbs going into the beam in the x direction, and 18.42lbs going down. So the forces being applied where the three beams meet (from this beam) is the same, but opposite directions.

    I think I'm wrong there, but I'm not sure how.

    I also tried to figure it going to the base. Using the figures that I had from the tower, it's exherting 31.57lbs of pressure onto the base. That has to be wrong, as each tower needs to support 50 lbs.

    So....I'm really not sure where I'm going wrong. I tried to figure everything more holistically, but I still don't see how the forces are moving, and how the 50lbs are getting to the points of connection. Thanks in advance for your help!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 12, 2009 #2
    Look at your fbd for the tower where you have wrongly assumed that the end forces are at rightangles to the tower. The 35.43 and 60.74 are not wrong but are just components of bigger forces in other directions.. It was good for you to realize that the answer must be wrong.
     
  4. Dec 12, 2009 #3
    Additional comment: When you draw a freebodydiagram, you must state ALL the forces on it before making an equilibrium statement.
     
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