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Forces/Moments on Complex Beam System

  1. Aug 26, 2016 #1
    To give a bit of context, I am doing my final year university project on micro-mechanical interactions between an AFM probe and a sample surface. I do not have notes for a system this complicated, as we always considered our systems to be rigid bodies. I was always relatively clueless at mechanics so this particular small part of my project is a nightmare for me!

    I have labelled the Free Body Diagram attached, but the following information should help to explain further:

    Section A has a downwards-vertical displacement being applied, and can be considered a rigid body, fixed in all other DOFs.
    A key feature of this system is the bending cantilever beam (Section B as marked in FBD).
    It begins with an angle of 13 degrees from the horizontal axis, the inclined beam can be seen on the image FBD.
    Section C (probe tip) can also be assumed to be a rigid body.
    Section D is the sample surface which can be assumed rigid and fixed in all DOFs.

    How do I get to the solution for finding Fz/Fy components and moments on the sample surface from the probe tip?

    I have not given values for the system because I want to use the help provided to work through it myself.

    As I say, this is a relative nightmare for me and I don't really know where to start, so all help will be greatly appreciated.

    I'm sure I'll need to provide more information to helpers, so these will be answered in EDITS below.

    Attached Files:

    • FBD.jpg
      File size:
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  2. jcsd
  3. Aug 28, 2016 #2


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    The diagram looks a bit odd because you show a straight and bent version of the beam yet A is in the same place. In consequence, the angle at which B joins A seems to change. I assume that is not the case.
    You show Fy. Is there friction to be taken into account at the probe? If not, there will be no Fy; if there is it is going to complicate matters.
  4. Aug 29, 2016 #3
    Hi haruspex,

    You're right, my diagram is incorrect with respect to the illustrated bending section. Linked to this, I am not sure if the probe tip will move in the negative y-direction (horizontal) to accommodate for the horizontal component of the length being decreased due to the bending? If this question doesn't make sense then please let me know and I will try to clarify.

    With regards to your question about friction: I am still questioning whether friction shall be taken into account. I want to study the system in static equilibrium, so I think that friction might need to be included, otherwise the beam would straighten itself by moving the probe tip (Section C) in the positive y-direction as Section A is displaced downwards (unless my intuition is incorrect?).

    I should add, I posted this question in the Homework forum and Nidum is kindly trying to help me so would you be inclined to join the discussion there? Might be best to finish the clarifications here before moving to the other thread. However, it is here for your interest: https://www.physicsforums.com/threa...al-eng-forces-moments-on-complex-beam.883145/

    Thanks for you reply! I would appreciate any further input, or if you have any other questions then please feel free to ask.
    Last edited: Aug 29, 2016
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