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Beam deflection integration

  1. Jan 7, 2016 #1
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    Can someone explain why the slope dy/dx = 0 at x = L/2? L/2 is the midpoint and there would be a deflection here so surely the slope of the deflection curve shouldn't be 0? I'm finding it hard to visualise this.

    EDIT: I think I understand the above. The slope of the deflection curve at x = L/2 will be 0 as the slope at this point is a flat line of constant value (due to the symmetry of the diagram). This is correct yes?

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    Is the part circled in red a mistake? There shouldn't be a negative sign after integrating 0 = EI(d^4y/dx^4)? As in it should be just A = EI(d^3y/dx^3) rather than A = -EI(d^3y/dx^3)?

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    Last edited: Jan 7, 2016
  2. jcsd
  3. Jan 7, 2016 #2

    SteamKing

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    The value of the slope of the beam is independent of the value of the deflection at the same location.

    For the simply supported beam, the deflection at x = L/2 will be a maximum, and since the slope curve is the first derivative of the deflection curve, what value will the derivative of the deflection curve have where the deflection is a maximum? This is a basic property of derivatives from intro calculus.
     
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