What Is the Optimal Geometry for a Concrete Column Supporting 1250 Tonnes?

In summary, when building a tall support, the self weight must be considered in order to determine the optimal geometry for the support. This is because the volume of material, and hence the cost, will be minimized. In order to achieve this, the maximum allowable stress in concrete, which is 15 MPa, must be considered. By using the shape of the CN tower as a hint, the optimal geometry for a column 100 metres tall made of concrete to support a mass of 1250 tonnes at its top can be determined. This involves finding the stress at different heights and using the maximum stress as a guideline for the design.
  • #1
Dethrone
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When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 15 MPa, determine the optimal geometry of a column 100 metres tall made of concrete to support a mass of 1250 tonnes at its top. Hint: think of the shape of the CN tower
There's no textbook for this course, so we're expected to use common sense to answer these questions...
$$\sigma = \frac{F}{A}=\frac{\pi D^2/4\cdot H\cdot W+1250\cdot 10^3 \cdot 9.81}{\pi D^2/4} $$
W=25 Kn/m, and putting all the information in, I get diameter is 1.1m. Is that right, and I was told that the radius is different at the top, not sure what to do.
 
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  • #2
Rido12 said:
When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 15 MPa, determine the optimal geometry of a column 100 metres tall made of concrete to support a mass of 1250 tonnes at its top. Hint: think of the shape of the CN tower
There's no textbook for this course, so we're expected to use common sense to answer these questions...
$$\sigma = \frac{F}{A}=\frac{\pi D^2/4\cdot H\cdot W+1250\cdot 10^3 \cdot 9.81}{\pi D^2/4} $$
W=25 Kn/m, and putting all the information in, I get diameter is 1.1m. Is that right, and I was told that the radius is different at the top, not sure what to do.

Hey Rido! (Smile)

It appears you have already made the assumption that the support is a massive cylinder.
Suppose we make no assumptions about the shape yet, and just assume a cross section of $A$.
And suppose we do not make the assumption that the cross section is constant, but instead is a function of height. That is $A=A(y)$.

What formula would yet get for the stress at height $y$? (Wondering)

And since we want to use a minimal amount of material, suppose this stress is equal to the maximum stress at each $y$.
What can you deduce from that?
 

FAQ: What Is the Optimal Geometry for a Concrete Column Supporting 1250 Tonnes?

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