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Beam with two supports + spring

  1. Jan 8, 2019 #1
    1. The problem statement, all variables and given/known data

    I have beam supported in three points (one of the support is spring) .
    What i know:
    PR = 100kN/m
    spring constant Z = 10kN/m
    I have to calculate bending moments and shear forces in points A, B and Z.

    20190107_184740.jpg
    2. Relevant equations

    ΣM = 0
    ΣF = 0
    Spring force : Fz=-zx
    This is not enoug to solve the problem. I have two equations and three unknowns (VA, VB, and x)

    3. The attempt at a solution

    I was thinking about finding deflection of the beam in point Z however the shape of the beam between points Z and A is quite complicated. Maybe there is some simpler method and I can't see?

    I will be very gratefull for help/hint with that!
     
    Last edited: Jan 8, 2019
  2. jcsd
  3. Jan 17, 2019 at 5:55 PM #2

    haruspex

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    That is the right approach, but of course it is a bit more complicated here because the deflection and the force at Z depend on each other.
    You will need to step through the usual procedure for figuring out the shape of the beam, but treating the force at Z as an unknown.
     
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