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

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Homework Help Overview

The discussion revolves around determining the maximum load a concrete-filled cast iron pipe can support, given specific dimensions and material properties. The problem involves calculating compressive stress and areas related to the pipe and concrete, with a focus on ensuring the calculations adhere to unit consistency.

Discussion Character

  • Mathematical reasoning, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore calculations related to the areas of the concrete and pipe, as well as the relationship between compressive stress and material properties. There are questions about unit consistency and the correctness of area calculations.

Discussion Status

Several participants have pointed out issues with unit usage and area calculations. There is ongoing clarification regarding the importance of maintaining consistent units throughout the calculations. Some participants express confusion about the discrepancies in results, while others seek to understand the implications of their calculations.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance they can provide. There is a noted emphasis on ensuring calculations are presented with appropriate units, as well as the need to verify assumptions made in the problem setup.

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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/Ep=σc/Ec

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

σp=σc*.1N

σp=5*106N*.1N

σp=.5*106N

F=Fc+Fp

F=σp*Ap+σc*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
 
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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.
 
SteamKing said:
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?
 
Yeah, but what about all the calculations it took to get you to the final result? Units are important there, too.
 
SteamKing said:
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)
 
Yup. And BTW, your area calculations are wrong. 1 m^2 = 10^6 mm^2
 
Any help would be appreciated
 
anthonyk2013 said:
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

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

σp/Ep=σc/Ec

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

σp=σc*.1N

σp=5*106N*.1N

σp=.5*106N

The units of stress are pascals, not Newtons.

F=Fc+Fp

F=σp*Ap+σc*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
 
σc=5KN/m2
Area of concrete is 3.14*1502/4=17671mm2
Area of pipe is 3.14*2002/4=31415-17671=13744mm2

σp/Ep=σc/Ec

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

σp=σc*.1pa

σp=5*106pa*.1pa

σp=.5*106pa

F=Fc+Fp

F=σp*Ap+σc*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
 
  • #10
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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