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Homework Help: Shear and Bending Moment Diagrams for a Ski

  1. Jul 20, 2010 #1
    1. The problem statement, all variables and given/known data

    The ski supports the 900N weight of a person. If the snow loading on its bottom surface is trapezoidal determine the intensity w (N/m). Draw the shear and bending moment diagrams for the ski.
    The ski has an overall length of 2m. The force arrows 'hang' of the bottom of the ski, sloping downwards for .5m then horizontal for 1m and then joining back to the other end of the ski.
    Sorry but I ain't very good with descriptions.

    3. The attempt at a solution

    To be brutally honest I don't a clue how to tackle this question. I've done other shear and bending moment diagrams before but the trapezoid has really thrown me. Any help would be greatly appreciated.
  2. jcsd
  3. Jul 20, 2010 #2
    Clue: The area of the trapezoid is equal to the applied load.
  4. Jul 22, 2010 #3
    Here's the original question and what I think is how the point loads will look.

    Am I on the right track?

    Attached Files:

  5. Jul 22, 2010 #4
    Your values correctly sum up the areas. So, now you can deduce the value of w. However, to obtain the shear and bending moment diagrams, you must express these functions based on the distributed nature of the loads, not the point loads you have shown. A good beginning would be: Let x be the distance from the left hand end. Derive a function of x that represents the loading w(x) in the first 0.5 m Then you are in a good position to develop expressions for shear and moment.
  6. Jul 26, 2010 #5
    Here is my latest attempt. After several tries I think this is the closest I've gotten. Seems pretty wrong to me tho

    Attached Files:

  7. Jul 26, 2010 #6
    You need to show your working if you are to receive more detailed criticism. You seem to be unaware of the definitions of shear force and bending moment. Take shear first. There are two definitions of shear, and each one can be proved from the other. The simplest is to imagine a section through the ski blade. In this case, a vertical section. The first definition of shear is that it is the algebraic sum of forces on one side of the section and which are parallel to it. In other words (the alternative definition) the integral or area of the loading diagram on one side of the section. In the toe zone, the loading diagram is a function of x to the power 1. Therefore in that zone, one must expect a shear function of x to the power 2. In the central zone, the loading is a constant value up to the central load, (a function of x to the power zero) and therefore one expects the expression for shear force in that zone to be straight line (x to power 1). In your diagram for shear, you seem to have these two qualities interchanged for the two zones. When you draw the diagrams, you should put on the leading values. If you get this right, the bending moment diagram will seem easier.
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