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Statically Indeterminate Shaft

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Determine the load (vertical only) on the three bearings at A, B and C. The shaft is loaded at one end with force F (see attached diagram).


    2. Relevant equations

    Cantilever Beam Deflection
    Deflection at End = PL^3/(3EI)
    Deflection at Point X = Px^2/(6EI)*(3l-x)


    3. The attempt at a solution

    I'm having a few difficulties remembering the details of solving statically indeterminate problems. My attempt is as follows:

    1. Remove reaction forces B and C. Applying beam deflection formulas I can find the displacement of points B and C due to force F. I called these δB1 and δC1.

    2. Replace the reaction forces at B and C, but remove the force F. I can now find the displacement of points B and C due to the reaction forces, respectively. I called these δB2 and δC2.

    3. Since the actual deflection at the fixed points B and C is zero, I can set:

    δB1 + δB2 = 0

    and similarly

    δC1 = δC2

    This leaves 2 equations and 2 unknowns which may be solved.


    Any hints, comments or corrections would be a world of help :smile:
     

    Attached Files:

    Last edited: Apr 16, 2013
  2. jcsd
  3. Apr 16, 2013 #2

    PhanthomJay

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    All supports take vertical load only (simple supports) and cannot carry moment, so the support at A is not fixed and cannot act that way when supports B and C are removed. The beam is statically indeterminate to the first degree, so you need to initially remove just one support.... like perhaps B.
     
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