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Tapered cantilever beam deflection and stress distribution

  1. Oct 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A positive moment of 12000Nmm at the tip applied as two equal and opposite point loads of 1000N in the x direction at C and D.
    The beam is fully fixed along AB. Young's modulus E = 200*(10^3) MPa and the poisson's ratio = 0.3.
    Geometric Properties: Width, b=10mm... Length, L=200mm
    Depth, d at AB = 36mm
    d at CD = 12mm
    Using the formulae provided, confirm that the theoretical tip displacement of the beam is 0.3241mm. In addition, calculate the σ_xx stress distribution along the top edge of the beam.

    (see attached image)

    2. Relevant equations
    I = [b*{36-(48x/L)}^3]/12 for x≤ L/2 and I'=[b*(12^3)]/12 for x> L/2
    v=1/E ( ∫∫M(x)I(x)dx dx ) the integration for both integrals is from 0 to L
    σ_xx = (-My)/I



    3. The attempt at a solution
    I attached my attempted solution as a document.
     

    Attached Files:

  2. jcsd
  3. Oct 20, 2013 #2
    kindly, what is the analysis of the load boundary condition in the problem specification.and the stress distribution along the top edge of the beam
     
  4. Oct 21, 2013 #3

    SteamKing

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    Necropost. OP is more than a year old.
     
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