Optimizing Support Geometry for Tall Structures: A Civil Engineering Problem

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SUMMARY

The discussion focuses on optimizing the geometry of a concrete support column, specifically a 100m tall structure designed to hold a mass of 1000 tonnes while adhering to a maximum stress limit of 12 MPa. Key factors include the weight of concrete at 24 kN/m³, stiffness of 30,000 MPa, and a cost of $0.05/kg. Participants suggest using stress calculations to determine the radius or diameter of the column and propose a cone shape for optimal material usage. Linear programming is recommended as a method to minimize cost and volume under the given constraints.

PREREQUISITES
  • Understanding of concrete stress limits, specifically 12 MPa
  • Knowledge of weight calculations, particularly 24 kN/m³ for concrete
  • Familiarity with linear programming techniques for optimization
  • Basic principles of structural engineering related to column design
NEXT STEPS
  • Research linear programming applications in structural optimization
  • Study the principles of stress distribution in concrete columns
  • Explore geometric optimization techniques for tall structures
  • Learn about cost analysis in construction materials
USEFUL FOR

Civil engineers, structural designers, and students involved in optimizing support structures for tall buildings will benefit from this discussion.

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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
 
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will3330 said:

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
 

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