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Analysis of complicated lever

  1. Jun 22, 2015 #1
    Hi guys,

    I'm new here and this is my first post so apologies if its in the wrong location or anything.

    My post is not in regards to a direct question as such but i am more looking for general advice and guidance on how to tackle a problem. I am working on a project that involves lifting equipment to pick up an object.

    One of the components is a clamping arm with a single pivot point shown below. Image_zpsp5mxzqrc.png

    The arm is constant width and constant thickness and the shape is approximately what is shown ie the point load F will cause counter clockwise rotation of the lever arm about point A.

    What i need assistance with is how calculate the maximum deflection, maximum direct and shear stresses and what the relevant equations are. How do i go about breaking the problem down into manageable chunks?

    Dimensions and forces are not important as it is the principles of how to calculate stresses etc which i am looking for.

    Any help would be great. Let me know if you need any more info.

  2. jcsd
  3. Jun 22, 2015 #2


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    The general process for calculating stresses is along these lines:
    1, Treating the whole body as rigid, calculate the angular acceleration for the body;
    2. Next, create an imaginary cut through the body at some point;
    3. For the body above (or below, either one) the cut, write the equations of motion. Remember that you now know the angular acceleration from step 1;
    4. Solve the equations of motion (step 3) for the forces on the cut face. In general, these will be an axial force, a shear force, and a bending moment;
    5. Apply the standard stress formulas to the cut section:
    primary normal stress = P/A
    shear stress = Fshear/A
    bending stress = Mc/I
    6. Combine the stresses from 5 to get max and min stress on the section.
    7. Repeat steps 2 through 6 at every section of interest.
  4. Jun 23, 2015 #3
    Thanks OldEngr63,

    How does calculating the angular acceleration help me resolve the equations of motion?

    Also say for example i take a cut through the vertical part of the lever and look at the bottom L section, if i know the applied force F how would i go about calculating forces on the cut face?

  5. Jun 23, 2015 #4


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    In step 3 above, I told you to write the equations of motion for the section on one side of the cut. The angular acceleration of the body appears in the moment equation. Since the angular acceleration of a part of the body is the same as the angular acceleration of the entire body, this term is known. That is why it is useful to have from step 1.

    If you take a cut through the vertical section (or anywhere else), you have to write the equations of motion for the body on one side of the cut. These equations will include the forces acting on the cut, and can be solved for them.
  6. Jul 5, 2015 #5
    The diagram is not in equilibrium, which is why the first respondent thinks there could be angular acceleration. But, given the questions that follow, the diagram is probably incorrect in concept. For static equilibrium, the applied force and the reaction should lie in the same line. So the lever needs to rotate a bit anticlockwise until the forces line up. Then draw bending, shear and normal force diagrams. the rest follows.
  7. Jul 5, 2015 #6


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    pongo38, your comments may, or may not, be correct. Stresses and deflections exist within an accelerating body just as well as within on at equilibrium. I assumed that the OP knew what his system was when he asked the questions; you are assuming that he does not understand his system. Either of us could be correct.
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