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Displacement of the node, superposition of forces

  1. Feb 22, 2017 #1
    1. The problem statement, all variables and given/known data
    Hi,
    I was wondering if anybody has an idea how to devide the forces on this structure to get the dispacement of the node 4.
    upload_2017-2-22_10-49-8.png
    2. Formulas
    I would like to solve this task by superpositioning forces working on different elements of the construction. (note different EI)
    using basic values for basic beams:
    upload_2017-2-22_10-58-51.png


    3. The attempt at a solution
    upload_2017-2-22_10-56-14.png
    ????? should it be devided like this???
    but then, how would i consider displacement at the node 2?
    upload_2017-2-22_10-49-45.png
     

    Attached Files:

  2. jcsd
  3. Feb 22, 2017 #2

    Nidum

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    Proceed in six stages :

    (1) Treat the vertical beam initially as just a lever which is applying a bending moment to the horizontal beam at the point where the two join .

    (2) Work out the slope of the horizontal beam at the point where the two join .

    (3) From that slope work out the displacement of the bottom of the vertical beam using geometry .

    (4) Now treat the vertical beam as a cantilever fixed at the top to some fictional rigid structure .

    (5) Work out the deflection caused by the load applied at the bottom end .

    (6) Add the deflection from (3) to the deflection from (5) to get the total deflection .
     
    Last edited: Feb 22, 2017
  4. Feb 22, 2017 #3
    ok. I understand, however I have a question how to get the slope of the horizontal beam. Can I devide this beam into 4 elements like this: upload_2017-2-22_11-29-15.png
     
  5. Feb 22, 2017 #4

    Nidum

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    You can use superposition for this simple problem .

    Work out the slope due to the distributed load and to the lever moment separately and add them together . Pay attention to signs when doing this .
     
  6. Feb 22, 2017 #5
    I guess I made some wrong superposition assumptions considering case 3,4. Could u please tell me, what kind of assumptions should i do to get the final displacement in this middle node. This task has to be solved using superposition of forces
    upload_2017-2-22_12-21-29.png
     
  7. Feb 22, 2017 #6

    Nidum

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    Your M as shown in top diagram is turning the wrong way .

    You need to work out the slope at the joining point not the vertical deflection .
     
  8. Feb 22, 2017 #7
    Yes. I agree. On the top diagram it is just the exaple of how forces work in case of my beam. In case 2 i take the moment with correct sign.
    i will try to find the formulas for calculating the change of the slope depending on the position of x. cause i need it for my case 3, where i want to calculate the angle in the middle of the beam.
     
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