What Is the Maximum Load a Concrete-Filled Cast Iron Pipe Can Support?

[anthonyk2013]

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.

σ_c=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

σ_p/E_p=σ_c/E_c

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

σ_p=σ_c*.1N

σ_p=5*10⁶N*.1N

σ_p=.5*10⁶N

F=F_c+F_p

F=σ_p*A_p+σ_c*A_c

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

 

[SteamKing]

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.

 

[anthonyk2013]

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.

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?

 

[SteamKing]

Yeah, but what about all the calculations it took to get you to the final result? Units are important there, too.

 

[anthonyk2013]

Yeah, but what about all the calculations it took to get you to the final result? Units are important there, too.

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)

 

[SteamKing]

Yup. And BTW, your area calculations are wrong. 1 m^2 = 10^6 mm^2

 

[anthonyk2013]

Any help would be appreciated

 

[SteamKing]

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.

σ_c=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

σ_p/E_p=σ_c/E_c

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

σ_p=σ_c*.1N

σ_p=5*10⁶N*.1N

σ_p=.5*10⁶N

The units of stress are pascals, not Newtons.

F=F_c+F_p

F=σ_p*A_p+σ_c*A_c

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

 

[anthonyk2013]

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

σ_p/E_p=σ_c/E_c

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

σ_p=σ_c*.1pa

σ_p=5*10⁶pa*.1pa

σ_p=.5*10⁶pa

F=Fc+Fp

F=σ_p*A_p+σ_c*A_c

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

 

[SteamKing]

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.