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Stress in compound bar

  1. Dec 17, 2013 #1
    A concrete column having a modulus of elasticity of 20GN/m2 is reinforced by two steel bars of 25mm diameter having modulus of 200GN/m2.
    Calculate the dimensions of a square section strut if the stress in the concrete is not to exceed 7MN/m2 and the load is to be 400KN.

    σ in conctete not to exceed 7*106
    Load =400KN
    E of steel=200GN/m2
    E of concrete=20GN/m2

    Area of steel=3.14*252/4*2=982*10-3m2
    Area of concrete=?

    σc/Ecs/Es

    σcs*Ec/Es

    σcs*20/200

    σcs*.1


    7*106s*.1

    7/.1*106s

    σs=70*106MN/M2

    Wondering if I m on the right track?
     
    Last edited: Dec 17, 2013
  2. jcsd
  3. Dec 17, 2013 #2

    SteamKing

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    You could indicate the units of your calculations.
     
  4. Dec 17, 2013 #3
    Well do. Bad habit
     
  5. Dec 18, 2013 #4
    Any help would be appreciated
     
  6. Dec 18, 2013 #5
    Let S be the side of the square cross section column. What is the total area of the cross section. What is the cross sectional area of the steel rods (this time calculate it correctly, taking into account that 1 mm = 0.001 m)? In terms of S, what is the cross sectional area of the concrete?
     
  7. Dec 18, 2013 #6
    Area of the steel is 3.14*.0252/4=.0004908
    Because there is two rods I multiply .0004908*2=.000981747m2

    S=L*B
     
  8. Dec 18, 2013 #7
    What are L and B?

    For the cross sectional area of the concrete, I get (S - 0.000981747) m2.
     
  9. Dec 18, 2013 #8
    Yes S-0.000981747
     
  10. Dec 18, 2013 #9
    Actually, S2-0.000981747. What is your recommendation as to what to do next in this problem?
     
  11. Dec 18, 2013 #10
    I need the get area using the values I have.

    do I use σc/Ecs/Es

    σcs=Ec/Es

    σc=Fc/Ac and σs=Fs/As

    THEN Fc/Ac*As/Fs=Ec/Es
     
    Last edited: Dec 18, 2013
  12. Dec 18, 2013 #11
    Let ε be the compressive strain in the steel and concrete. What value of ε causes the stress in the concrete to equal 7MN/m2? What is the stress in the bars? In terms of S, what is the compressive force in the bars and in the concrete? What are the sum total of the compressive forces? What value of S causes this total compressive force to equal 400 kN.
     
  13. Dec 18, 2013 #12
    ε of concrete=ε in steel?

    σ=E*ε

    ε=σ/E ε=7MN/m2/20N/m2

    Would the correct way the write this be ε=7*106/20*109=.35*10-3

    σ in steel=.35*200=70MN

    Total force is 400KN so I need to find what load is on the steel.
     
    Last edited: Dec 18, 2013
  14. Dec 18, 2013 #13
    So far, so good. Now, you know the stress in the steel. What is the load carried by the two steel bars?
     
  15. Dec 18, 2013 #14
    σ=F/A→F=σ*A→F=70*106*0.000981747m2=.06872MN/m2

    or 69KN/m2
     
  16. Dec 18, 2013 #15
    Total force is 400KN, force in steel is 69KN so 400KN-69KN=331KN

    Force in concrete=331KN
    σ in concrete=7MN/m2

    Area=f/σ A=331*103/7*106=47.285*103 or 47285

    [itex]\sqrt{}47285[/itex]=217.45mm2

    Answer in my notes is 220mm2
     
  17. Dec 18, 2013 #16
    You're still not being careful about units. You made two errors that cancelled each other out. Incidentally, the length of the side of the square cannot be in mm2. It has to be mm.
     
  18. Dec 18, 2013 #17
    217.45mm is what should have wrote?
     
  19. Dec 18, 2013 #18
    Not exactly. You had to add the area of the bars back to get the total area. Then take the square root. That's probably why you got 217 and the book had 220.
     
  20. Dec 18, 2013 #19
    To get the dimensions I need to find the total area. Concrete +steel and square root that.

    Thanks for your help Chester, big help again.
     
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