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How do I find deflection in this beam?

  1. Sep 19, 2013 #1
    How do I find deflection (displacement) in point C at the end of the beam? Answer is to be given in mm. There is a roller connection (only Fy) in B and an external pin in A (Fy and Fx). The module of elasticity and area moment of inertia is given.

    2vwzre8.jpg

    Relevant equations:
    1. http://en.wikipedia.org/wiki/Deflection_(engineering)
    2. http://www.advancepipeliner.com/Resources/Others/Beams/Beam_Deflection_Formulae.pdf


    Here is a solution to a similar problem: https://dl.dropboxusercontent.com/u/11241083/beer_mecanica_4e_solucionario_c09_a.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 20, 2013 #2

    SteamKing

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    First, you are going to need to know E, I, and LAB and LBC.
     
  4. Sep 21, 2013 #3
    I tried solving this using the unit load method.
    I = 57.9 * 10^6 (mm^4)
    E = 2.1 * 10^5 (N/mm^2)
    AB distance = 3 meters
    BC distance = 2 meters

    https://dl.dropboxusercontent.com/u/11241083/Solution_Beam_Problem.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
  5. Sep 21, 2013 #4

    nvn

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    raymanmusic: I currently got an answer different from your post 3 answer for deflection of point C, using a different method.
     
    Last edited by a moderator: Sep 21, 2013
  6. Sep 22, 2013 #5

    Evo

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    You failed to use the template which was provided. Do not do this again, we have rules for a reason and they must be followed.

    Answers discussed in OP's first thread.

    https://www.physicsforums.com/showthread.php?t=711176
     

    Attached Files:

    Last edited by a moderator: May 6, 2017
  7. Sep 22, 2013 #6

    nvn

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    raymanmusic: I now also used a second method, and I got exactly the same answer I got using a completely different method in post 4. Therefore, I am about 99 % certain I have the correct answer.

    You did excellent work in post 3, but it appears you made one main mistake, as follows. Delete your unit load at x2 = 666,67 mm, and then try your solution again. You do not want to find deflection at x2 = 666,67 mm, and you therefore should not place a unit load at x2 = 666,67 mm. Try again.

    By the way, always maintain four significant digits throughout all your intermediate calculations, then round only the final answer to three significant digits. E.g., -7,556 kN, not -7,56 kN.
     
  8. Sep 22, 2013 #7
    Thanks for helping me out nvn. Do I place the unit load where I want to find deflection? What about the triangle load? Should I ignore it when I calculate mx2? What did you get as your final answer in mm?
     
  9. Sep 22, 2013 #8

    nvn

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    raymanmusic: Yes, place the unit load where you want to find deflection. Yes, ignore the triangular load when you compute mx1 and mx2. I will let you know if you obtain the correct final answer, if this is not a test question.
     
    Last edited: Sep 22, 2013
  10. Sep 23, 2013 #9
    I got approximately 5.922 mm as my final answer. Is this close to the correct answer?
     
  11. Sep 23, 2013 #10

    nvn

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    Excellent work, raymanmusic. Your answer is correct (5.921 54, which rounds to 5.92 mm).

    By the way, N/mm^2 is called MPa. If a derived unit has a standardized special name, then only the standardized special name should be used. E.g., 210 000 MPa, not 210 000 N/mm^2.
     
    Last edited: Sep 23, 2013
  12. Sep 23, 2013 #11
    Thanks for the help nvn. I'll ask you if I have more problems I'm stuck with.
     
  13. Sep 23, 2013 #12
    deflection101 came with a formula for this case,Where is it?
     
  14. Sep 24, 2013 #13
    Yc=[wb^3(5L-2b)+30PLb^2] / 90
     
  15. Sep 24, 2013 #14
    given: w=10kn/m
    p=8kn/m
    a= 3
    b=2
    EI=1 (to simplify)

    Ans.:yc= - 72 (-160/3 - 56/3)
     
    Last edited: Sep 24, 2013
  16. Sep 24, 2013 #15
    it doesn't get any better than this! yc= - 72
     
  17. Sep 24, 2013 #16
    EIy(x)=wx/360b(3x^4-15bx^3+30b^2X^2-30b^3X-20ab^3)+Px/6(x^2-3bx-2ab)
    EIy(2)=-72
    y=- 72/EI EI=read above
     
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