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Find reactions at supports and bending/shear/axial diagrams

  1. Sep 19, 2015 #1
    1. The problem statement, all variables and given/known data
    0aac393504.png
    Force by uniform loading = 20(5) = 100kN
    Vertical component of the uniform loading = 20(5)(3/5) = 60kN
    Horizontal component of the loading = 20(5)(4/5) = 80kN
    vertical reaction at roller support = Vr
    vertical reaction at pin support = Vp
    2. Relevant equations
    Fx=0, Fy=0, M=0

    3. The attempt at a solution

    Finding reactions

    Horizontal reaction is only at pin support. Let it be Hp. As Fx=0
    Hp=80-40=40kN (to the left)
    So I take moment at pin support first so as to find out Vr
    Vr=[40(1)+50(3)+60(7.5)-80(2)] / 9 = 160/3 kN (upwards)
    take moment at roller support to find Vp
    Vp=[100(2.5)+50(6)-40(1)] / 9 = 170/3 kN (upwards)

    Attempt to find out the equations for diagrams
    for the left part of the frame (free body)
    9f4498861d.jpg
    Resolving Vr into two component
    let the one perpendicular to frame be Rp, Rp = 32 kN
    the other one along the frame be Ra, Ra = 128/3 kN
    distance from roller be x
    Axial force = Ra = 128/3 kN
    Shear force = 32-20x,
    M=32x-10x2

    But for the middle part and right part of the frame, how do I consider the free body? and the segments divided by the point loading?
    I tried thinking to cut at the top-right corner to consider the right part of the frame as a free body but then what should I do for the segment between the P2 loading and the corner?
    The middle part is even more messy to me.
    Thanks!
     
  2. jcsd
  3. Sep 20, 2015 #2

    SteamKing

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    The idea behind the free body is that you can separate a particular member from the rest of the structure as long as you include the loads at the ends as well as any loads applied directly to that member.

    You've started your calculation of the reaction forces and moments with the sloped member on the left of the frame. Figure out which loads from the sloped member are transmitted into the top member, thence to the vertical member on the RHS of the frame.

    Remember, the frame as a whole remains static, so the individual members must be static as well.
     
  4. Sep 20, 2015 #3
    Thanks for your reply! Before I proceed, I want to make sure something.
    In my calculation for the left body, I resolve vertical reaction into two components. One is used to find out the shear force and one is the axial force along the beam.
    Is my concept here correct? If this is the case, how do I balance Rh here?
    a6bd24c976.jpg
     
  5. Sep 20, 2015 #4

    SteamKing

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    You've calculated the reactions on the sloped member in a coordinate system which is aligned with that member. What you need to find is how these forces are transmitted into the other member(s)of this frame. IOW, you need to find the components of the forces which are aligned with the other member attached to the sloped member.
     
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