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