Max height of a concrete column

In summary: Well, I am pretty sure they wrote the book.In summary, the maximum possible height for a concrete column of constant cross sectional area with a compressive strength of 2.0 x 107 N/m2 and a density of 2.3 x 103 kg/m3 is approximately 89m. This can be determined by setting the compressive stress equal to the hydrostatic relation ρgh and solving for h. The stress would be located at the bottom of the column, assuming it is standing vertically. Young's modulus is not needed to solve this problem and the book answer may be incorrect.
  • #1

Homework Statement


For a concrete column of constant cross sectional area, what is the maximum possible height if the compressible strength is 2.0 x 107 N/m2? The density of concrete is 2.3 x 103 kg/m3.

Homework Equations


[tex]\frac{F}{A}[/tex]

The Attempt at a Solution


I am not really sure what I am doing wrong, or what I have to do differently, but so far I have tried a few different things.
First I tried setting the force equal to 2*102, and trying to solve for height:
[tex]\frac{2*10^7}{2.3*10^3*9.8}\approx890[/tex]
This was incorrect however. From there, I tried adding a π to the denominator, but that didn't work. I then tried taking the square root because I realized the r term was squared. After that I realized the r term doesn't even really have a place in the equation because I am looking for height, not radius. How do I correctly approach the problem? I honestly have no clue what I am doing here.
 
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  • #2
Your answer looks correct to me.
 
  • #3
Quantum Singularity said:

Homework Statement


For a concrete column of constant cross sectional area, what is the maximum possible height if the compressible strength is 2.0 x 107 N/m2? The density of concrete is 2.3 x 103 kg/m3.

Homework Equations


[tex]\frac{F}{A}[/tex]

The Attempt at a Solution


I am not really sure what I am doing wrong, or what I have to do differently, but so far I have tried a few different things.
First I tried setting the force equal to 2*102, and trying to solve for height:
[tex]\frac{2*10^7}{2.3*10^3*9.8}\approx890[/tex]
This was incorrect however. From there, I tried adding a π to the denominator, but that didn't work. I then tried taking the square root because I realized the r term was squared. After that I realized the r term doesn't even really have a place in the equation because I am looking for height, not radius. How do I correctly approach the problem? I honestly have no clue what I am doing here.
The first thing is to understand what the numbers mean that you are given. In your attempted calculation above, you should always do a check of the units in the result to see if these agree with the answer you are supposed to obtain.

The maximum compressive stress of the concrete is 2.0 × 107 N/m2, which you would presumably obtain from the equation σ = F / A.

It is given that the column is uniform, so this suggests that A is a constant.

What other quantity is needed to give the stress in the column?

Given the density of the concrete (2.3 × 103 kg/m3), how would you determine the maximum stress in the column? Where would this stress be located?
 
  • #4
edit : removed redundant post
 
  • #5
Nidum said:
edit : removed redundant post
The cross sectional areas cancel out. The compressive stress on the bottom is just the hydrostatic relation ##\rho g h##.
 
  • #6
SteamKing said:
The first thing is to understand what the numbers mean that you are given. In your attempted calculation above, you should always do a check of the units in the result to see if these agree with the answer you are supposed to obtain.

The maximum compressive stress of the concrete is 2.0 × 107 N/m2, which you would presumably obtain from the equation σ = F / A.

It is given that the column is uniform, so this suggests that A is a constant.

What other quantity is needed to give the stress in the column?

Given the density of the concrete (2.3 × 103 kg/m3), how would you determine the maximum stress in the column? Where would this stress be located?
I would think that the stress would be located in the center of the column. From the equations in my book, I only see where force and area are the quantities shown. The equation it gives me for force near the beginning of the chapter that this is reviewing equates it to length, a delta l, and a young's modulus number, which I don't think helps me either.

Chestermiller said:
Your answer looks correct to me.

This is a review for my final, so I am able to see the answers, and it shows the answer as being 89m, instead of the 890m that I got, unless I am just missing something on units somewhere. It is really annoying seeing the error like that with it being a factor of 10 off.
 
  • #7
Quantum Singularity said:
I would think that the stress would be located in the center of the column.
This column is presumably standing vertically, as most columns are won't to do.

Why would you think that the stress in a vertical column would occur in the middle? Draw a free body diagram of a vertical column to check.

From the equations in my book, I only see where force and area are the quantities shown. The equation it gives me for force near the beginning of the chapter that this is reviewing equates it to length, a delta l, and a young's modulus number, which I don't think helps me either.
You don't need to know Young's modulus to solve this problem.

This is a review for my final, so I am able to see the answers, and it shows the answer as being 89m, instead of the 890m that I got, unless I am just missing something on units somewhere. It is really annoying seeing the error like that with it being a factor of 10 off.
You can always check the book answer to see if it matches the information given in the problem statement. Answers in the book have been known to be wrong.
 
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  • #8
SteamKing said:
This column is presumably standing vertically, as most columns are won't to do.

Why would you think that the stress in a vertical column would occur in the middle? Draw a free body diagram of a vertical column to check.You don't need to know Young's modulus to solve this problem.You can always check the book answer to see if it matches the information given in the problem statement. Answers in the book have been known to be wrong.

That is what I am thinking might be the case, but that would mean my professor is wrong because it is his final exam review. As for the free body diagram, I have decided to abandon the problem and the rest of the review for now because the exam is tomorrow and this professor hasn't cared enough to actually teach me anything of value. I have some other homework I need to do before the final anyways, and because the final curves and everyone else in the class has the same problems as me, the stuff I am having problems with shouldn't hurt me too bad. Thanks for the help though, hopefully next semester I can get someone who actually wants to teach physics.
 

What is the maximum height of a concrete column?

The maximum height of a concrete column depends on various factors such as the type of concrete used, the dimensions of the column, and the surrounding environmental conditions. Generally, the maximum height of a concrete column can range from 10 feet to 100 feet.

How do you calculate the maximum height of a concrete column?

The maximum height of a concrete column can be calculated by considering the compressive strength of the concrete, the load-bearing capacity of the column, and the safety factor. These calculations can be done using mathematical formulas and structural engineering principles.

What factors affect the maximum height of a concrete column?

The maximum height of a concrete column can be affected by several factors such as the type and quality of concrete used, the dimensions and design of the column, the reinforcement used, and the environmental conditions such as temperature and humidity.

What are the safety considerations for determining the maximum height of a concrete column?

Safety is a crucial factor when determining the maximum height of a concrete column. The column must be designed to withstand the expected loads and should have a sufficient safety margin to account for any unforeseen circumstances. The materials and construction methods used should also adhere to safety standards and codes.

Are there any limitations to the maximum height of a concrete column?

Yes, there are limitations to the maximum height of a concrete column. Factors such as the availability of materials, construction techniques, and budget constraints can limit the height of a concrete column. Additionally, local building codes and regulations may also have specific requirements for the maximum height of a concrete column.

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