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Stresses and change in length in a compound bar

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the stresses and the change in length of the compound bar.

    compressive load F = 40kN
    Length L = 0.25m
    material (a) mild steel E = 205 GPa
    material (a) area = 0.04m^2
    material (b) concrete E = 10 GPa
    material (b) area = 0.16m^2

    For a similar example see example 2 of this PDF:
    http://fetweb.ju.edu.jo/staff/che/ymubarak/Strength-lectures/chapter2.pdf [Broken]

    My calculations so far are:
    (a) σ = 40/0.04 = 1000kNm^2
    (b) σ = 40/0.16 = 250kNm^2

    E=σ/ε → ε=σ/E

    (a) ε = 1000*10^3/205*10^9
    = 4.9*10^-6

    (b) ε = 250*10^3/10*10^9
    = 25*10^-6

    Free change in length = ΔL = ε*L

    (a) ΔL = 4.9*10^-6*0.25
    = 1.2*10^-6m

    (b) ΔL = 25*10^-680.25
    = 6.25*10^-6m

    After those calculations I am unsure what to do next to find the change in length in a joined compound bar.

    2. Relevant equations
    See PDF


    3. The attempt at a solution
    See above

    Thanks a lot for any help in improving my understanding of this.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 16, 2012 #2
    Does the following help? I think you have figured out what I call k1 and k2.
     
  4. Jan 16, 2012 #3

    I forgot the following,
     

    Attached Files:

  5. Jan 18, 2012 #4
    It may be related but I can't deduce anything from it.
     
  6. Jan 20, 2012 #5
    Can anybody else offer a solution?
     
  7. Jan 22, 2012 #6
    Young's modulus, Y = Stress/Strain = (F/A)/(ΔL/L)

    So F = (Y*A*ΔL)/L = kΔL which is the relationship between the applied force on a "spring" and the distance it compresses. In your problem both the steel and concrete are compressed the same distance, they each have an effective spring constant for the problem as stated. So in your case you know k_steel and k_concrete as given above so,

    ΔL = F/(k_steel + k_concrete)

    Good luck!
     
    Last edited: Jan 22, 2012
  8. Jan 22, 2012 #7
    After another reading of your link it probably makes sense that the concrete is under compression and the steel is under tension which is a common configuration of those materials, so in that case,

    F = k_steel*ΔL_steel = - k_concrete*ΔL_concrete

    the concrete gets shorter and the steel gets longer.
     
  9. Jan 24, 2012 #8
    Thanks a lot for the replies spinnor, what is it that you are referring to with k btw? is it the Young's Modulus of the materials? concrete E = 10 GPa and mild steel E = 205 GPa

    Thanks a lot again
     
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