1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Given Moment about a Pin and a Roller

  1. Mar 2, 2015 #1
    1. The problem statement, all variables and given/known data
    For my statics homework, we are directed to:
    Draw the free body diagram and use the force and moment equilibrium to determine the support reactions for the following systems

    I'm having a bunch of trouble with problem 4.10, which is displayed in the following picture
    HW4:4-10.png

    I'm really stuck so if someone could kind of guide me in the correct direction, I'd really appreciate it.

    2. Relevant equations
    ΣFx=0
    ΣFy=0
    ΣM=0

    3. The attempt at a solution

    IMG_2756.JPG
     
  2. jcsd
  3. Mar 2, 2015 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The diagram alone is not clear to me. Any words to go with it?
     
  4. Mar 2, 2015 #3
    no there were not, simply the moment is acting on that point at the rigid body between the roller, A, and the pin, B. It's then necessary to find the support reactions at A and B, which are RAY, RBY, and RBX
     
  5. Mar 2, 2015 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The beam appears to be pinned and simply supported at the ends. Pin connections typically cannot support a moment (i.e., the ends of the beam are free to rotate), therefore MA = MB = 0.

    You have written several different moment equations for this beam. There is only one correct equation.
     
  6. Mar 2, 2015 #5
    okay, so if the moments at the ends are 0, how does that help me get to the support reactions at each point?
     
  7. Mar 2, 2015 #6

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Like I said at the end of my post, you can have only one correct moment equation, but you have written at least two. Knowing what I said, is one of your moment equations invalid?

    Write the correct moment equation, and you can find the reactions at the supports.

    (Hint: There's nothing especially tricky about this problem, if you write the correct equilibrium equations.)
     
  8. Mar 2, 2015 #7
    okay... I think the correct momentum equation is going to have to do with the sum of moments... so
    ΣM=0 : 0 = |MA+MB| - |M2|
    is this the correct one?
     
  9. Mar 2, 2015 #8

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I already told you what MA and MB were.

    How is this moment equation going to give you the reactions?

    Try again. (You had written the correct equation down already. I thought you would recognize it once I told you about pinned connections.)
     
  10. Mar 2, 2015 #9
    okay, my bad. I'm not very good with moment problems yet, but I am trying. I see that if what I wrote last post was true, then M2 would be equal to zero, which is not the case.

    the equation you must be referring to is 0=M2-(a+b)RBY, but if that's that case, aren't we supposed to get the thing in terms of both support reactions? so.. 0=M2-(a⋅RAY+b⋅RBY)
     
  11. Mar 2, 2015 #10

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    If you select one of the supports as the reference point for calculating moments, the resulting moment equation will contain only the other support reaction. Once you obtain this support reaction, then the sum of the forces equation is used to find the other reaction.
     
  12. Mar 2, 2015 #11
    okay, I think I'm starting to see it now...
    @A, ΣM=0: M2-(a+b)RBY -> RBY=M2 / (a+b)
    and also
    @B, ΣM=0: M2-(a+b)RAY -> RAY=M2 / (a+b)
    yeah?
     
  13. Mar 2, 2015 #12

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You can only write one moment equation. You can use this equation to solve for one reaction. As I explained, you use the sum of the forces to find the remaining reaction.
     
  14. Mar 2, 2015 #13
    I really appreciate your time and patience, thank you so much.

    now.. I have a solution for RBX and RBY, but something tells me that RAY is opposite to RBY... whether or not I am correct in that feeling how do I determine their directions mathematically?
     
  15. Mar 2, 2015 #14

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    This is a consequence of the sum of the forces being equal to zero. Since the only forces acting on this beam are the reactions, they must sum to zero.
     
  16. Mar 2, 2015 #15
    right.. but is the support reaction at A the same direction as the support reaction at B? How to write out this equation properly
     
  17. Mar 2, 2015 #16

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Ask yourself, if the two reactions are in the same direction, can they ever sum to zero?
     
  18. Mar 2, 2015 #17
    no, so they must be in opposite directions...
    must you determine the force from the moment? I'm trying to figure out how the distances come into play, because my next problem has two moments at different distances along the rigid body.
     
  19. Mar 2, 2015 #18

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    A moment is a force multiplied by a distance. If you divide a moment by a distance, you get a force. You can check the units.

    As for your second problem, just write the equations of static equilibrium and solve for the unknown reactions. That's all there is to it.
     
  20. Mar 2, 2015 #19
    right.. so is this or is this not correct,
    ΣFy = 0: 0 = RBY + RAY -(Force determined from Moment)
    Force determined from moment = M2/b
    RAY=M2/b - RBY
     
  21. Mar 2, 2015 #20

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    It's not clear what these equations represent. Are they supposed to show the solution to the reactions for the OP?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted