Optimizing Support Geometry for Tall Structures: A Civil Engineering Problem

[will3330]

Homework Statement

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 12 MPa, determine the optimal geometry of the column 100m tall made of concrete to support a mass of 1000 tonnes at its top (like the CN tower).

Homework Equations

Weight concrete: 24Kn/m^3
Stiffness: 30000MPa
Cost: $0.05/kg

The Attempt at a Solution

well I guess I can find the total force = 1000(#tonnes) x 9.81.

Also Stress = Force/Area and from that I can find the radius/diameter of the cylinder.

But the cylinder is suppose to be sort of "cone" shaped I think for optimal geometry (like the CN Tower)

Also, would there have to be a function to find the minimum cost and volume of building this structure?

Thanks

 

[niteman555]

Homework Statement

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 12 MPa, determine the optimal geometry of the column 100m tall made of concrete to support a mass of 1000 tonnes at its top (like the CN tower).

Homework Equations

Weight concrete: 24Kn/m^3
Stiffness: 30000MPa
Cost: $0.05/kg

The Attempt at a Solution

well I guess I can find the total force = 1000(#tonnes) x 9.81.

Also Stress = Force/Area and from that I can find the radius/diameter of the cylinder.

But the cylinder is suppose to be sort of "cone" shaped I think for optimal geometry (like the CN Tower)

Also, would there have to be a function to find the minimum cost and volume of building this structure?

Thanks

I can't say much, but as for the minimum cost, you might want to try some linear programming given your constraints

 

[Mene]

for your question!

my first step in solving this problem would be to gather all the necessary information, such as the weight and stiffness of concrete, the maximum allowable stress, and the cost per kilogram. From there, I would use the given information to calculate the total force and stress on the column, as you have mentioned.

Next, I would consider the shape and design of the column. As you mentioned, a "cone" shape may be more optimal for this type of structure. This could potentially reduce the volume of concrete needed while still providing enough support for the given mass. I would also consider other factors such as wind and seismic loads, as these could also impact the optimal geometry.

Once I have a general idea of the shape and design, I would then use mathematical models and simulations to determine the exact dimensions of the column. This could involve optimizing the shape and dimensions to minimize cost while still meeting all necessary structural requirements. This would likely involve creating a function to find the minimum cost and volume, as you mentioned.

In addition to mathematical models, I would also consider real-world factors such as construction methods and materials availability. It may also be beneficial to consult with other civil engineers and experts in the field to ensure the most optimal and practical solution is found.

Overall, optimizing support geometry for tall structures is a complex and important problem in civil engineering. It requires a combination of scientific knowledge, mathematical modeling, and practical considerations to find the most efficient and cost-effective solution.