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Axial Deformation on Statically indeterminate beam

  1. Nov 1, 2014 #1
    1. The problem statement, all variables and given/known data

    I am trying to find a solution to the below attached image.
    The area for AB=CD = 0.8m^2
    Area of BC = 0.3m^2

    Force at B = 140 kN (left)
    Force at C = 60 kN (right)

    AB=CD = Concrete with a E of 25,000N/mm^2
    CD = Steel with an E = 200,000N/mm^2

    2. Relevant equations

    PL/AE

    3. The attempt at a solution


    This is where I get confused because there is a force acting at B and a force acting at C I am not sure if I need to make a cut at say B or make a cut at C.

    I understand the the sum of the forces in X direction have to equal Ax + Dx = 80 kN (As a result of 140 - 60 kN)

    Now taking BC as the redundant section

    PL/AE for section AB should that of section CD?

    I am not sure if I am going about it the right way?

    If it was one continuous section with forces only in one direction or even two I understand but because of that section BC it has thrown me out .
     
  2. jcsd
  3. Nov 1, 2014 #2

    SteamKing

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    There's no image attached to your post.
     
  4. Nov 1, 2014 #3
    Oops... Here we go
     

    Attached Files:

  5. Nov 1, 2014 #4
    Second Attempt at solution

    Taking Section AB

    δA/D = Fab*L(ab)/AE = Fcd*L(cd)/AE

    Now F in AB = 140 kN
    and F in CD = -60 kN

    *** Edit ***

    My compatibility equation of Fab + Fcd = 80 kN?
     
    Last edited: Nov 1, 2014
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