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Finding load in compound bar

  1. Dec 17, 2013 #1
    A cast iron pipe is filled with concrete and used as a column to support a load W.If the outside diameter of the pipe is 200mm and the inside diameter is 150mm, what is the maximum permissible value for W if the compressive stress in the concrete is limited to 5 KN/m2.
    Take E for concrete as one tenth that of cast iron.

    σc=5KN/m2
    Area of concrete is 3.14*1502/4=17671*10-3mm2
    Area of pipe is 3.14*2002/4=31415-17671=13744*10-3mm2

    σp/Epc/Ec

    σpc*.1N E of concrete one tenth that of cast iron=.1

    σpc*.1N

    σp=5*106N*.1N

    σp=.5*106N

    F=Fc+Fp

    F=σp*Apc*Ac

    F=(.5*106N*17771*10-3mm)+(5*106N*13744*10-3MM2)

    F=8835.5*103N+68720*103N

    F=77555.5N*106

    F=77555.5N/9.81=7905kg=7.9tons

    The answer in my notes is 79tons, where have I gone wrong with my decimal point
     
    Last edited: Dec 17, 2013
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  3. Dec 17, 2013 #2

    SteamKing

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    It's really hard to follow your calculations because you don't indicate the units of your results. You must get into the habit of writing the units along with the magnitudes of your results.
     
  4. Dec 17, 2013 #3
    The units of my result are in tons which is what is asked for in the question and are indicated Do you see something else I m missing?
     
  5. Dec 17, 2013 #4

    SteamKing

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    Yeah, but what about all the calculations it took to get you to the final result? Units are important there, too.
     
  6. Dec 17, 2013 #5
    Just so I understand properly would you expect units in this part of the solution

    F=(.5*106*17771*10-3)+(5*106*13744*10-3)
     
  7. Dec 17, 2013 #6

    SteamKing

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    Yup. And BTW, your area calculations are wrong. 1 m^2 = 10^6 mm^2
     
  8. Dec 18, 2013 #7
    Any help would be appreciated
     
  9. Dec 18, 2013 #8

    SteamKing

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    σc=5KN/m2
    Area of concrete is 3.14*1502/4=17671*10-3mm2
    Area of pipe is 3.14*2002/4=31415-17671=13744*10-3mm2

    Incorrect area calculations. If your dimensions are in mm, then area will be in mm2. 1 m2 = 106 mm2

    σp/Epc/Ec

    σpc*.1N E of concrete one tenth that of cast iron=.1

    σpc*.1N

    σp=5*106N*.1N

    σp=.5*106N

    The units of stress are pascals, not newtons.

    F=Fc+Fp

    F=σp*Apc*Ac

    F=(.5*106N*17771*10-3mm)+(5*106N*13744*10-3MM2)

    Incorrect areas used here.

    F=8835.5*103N+68720*103N

    F=77555.5N*106

    F=77555.5N/9.81=7905kg=7.9tons

    The answer in my notes is 79tons, where have I gone wrong with my decimal point
     
  10. Dec 18, 2013 #9
    σc=5KN/m2
    Area of concrete is 3.14*1502/4=17671mm2
    Area of pipe is 3.14*2002/4=31415-17671=13744mm2

    σp/Epc/Ec

    σpc*.1pa E of concrete one tenth that of cast iron=.1

    σpc*.1pa

    σp=5*106pa*.1pa

    σp=.5*106pa

    F=Fc+Fp

    F=σp*Apc*Ac

    F=(.5*106pa*13744mm2)+(5*106*17671mm2)

    F=(6872*106)+(88355*106)

    F=95227*1012*9.81=934176.87kg/1000=934tons

    Seem to have gone a long way from the correct answer of 79tons
     
  11. Dec 18, 2013 #10

    SteamKing

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    You've got to remember what the definition of a pascal is. 1 Pa = 1 N / m^2

    Check your force calculations. This is why units are important.
     
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