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Compound bars question

  1. Dec 15, 2013 #1
    A concrete column is reinforced with steel bars and carries a load of 20t. The overall cross section area of the column is 0.1m^2 and the steel bars accounts for 3% of this area.
    Find the stress in the concrete
    If the length is 4m< how much does it shorten.

    E of steel 200GN/m^2
    E of concrete 20 GN/m^2

    Load=20*1000=20000*9.81=196200 or 19.6*10^4

    Area of concrete =.1*97%/100=.097m^2
    Area of steel=.1*3%/100=.003m^2
    Area of concrete=.1*97%/100=.097m^2
    steel=s
    concrete=c

    σs/Es=σc/Ec→σs=σc*Es/Ec→σs=σc*200/20→σs=10*σc

    F=σs*As+σc*Ac
    19.6*10^4=(10*σc*.003)+(σc*.097)
    19.6*10^4=σc(10*.003+.097)
    19.6*10^4=σc(.127)

    19.6/.127=154.3*10^4
    σc=154.3*10^4

    My question is, the answer I have in my notes is 1.54MN/m^2. Why is my decimal point wrong?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 15, 2013 #2
    I'm not sure if it isn't. 1.54MN is the same as 1.54 x 10^6. 154.3 x 10^4 is the same as 1.54x10^6
     
  4. Dec 15, 2013 #3
    Would be able to break that down more, still don't understand. Thanks
     
  5. Dec 15, 2013 #4
    I just want to stress I'm not so sure on the physics but I feel it is just a error in standard form

    Your notes give you the answer 1.54MN/m2, which is 1.54 Mega nm2 which is 1.54x106 N/m2 or 1,540,000 n/m2

    Your answer is 154.3x104 N/m2which is 154.3x10,000 which is 1,543,000 N/m2
     
  6. Dec 15, 2013 #5
    Thanks
     
  7. Dec 15, 2013 #6
    Appreciate if someone could check the physics work in my problem.
     
  8. Dec 16, 2013 #7
    Anyone thanks
     
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