Step 1 - Generative Design Framework
- Design Decision 1
- Concrete Mix Design - Resistance to Transport of CO2 and H20
- Water to Cement Ratio
- Aggregate Gradation
- Depth of Steel
- Presence of Admixtures
- Evaluators
- Porosity
- Time of Diffusion
- Cost
- Most Important Tradeoffs to Consider
- Cost of concrete dramatically increases with the presence of admixtures and increased cement content.
- City Planning: Grocery Stores
- Design Variables
- Location of Grocery Stores
- Evaluators
- Proximity to most densely populated area
- Proximity to distribution centers
- Most Important Tradeoffs to Consider
- Want to minimize the amount of time necessary for the majority of people to commute to grocery stores, while also minimizing distances to food distribution centers
- Park Planning: Shade and Sun
- Location of Trees
- Location of Benches
- Location of Trails
- Evaluators
- % of park sunny
- % of park in shade
- Distribution of shady and sunny areas with relation to rest areas
- Most Important Tradeoffs to Consider
- This analysis can be used to optimize desired levels of sun and shade in a park, as well as ensure an even distribution of these parameters across the park utilizing tree cover. The location of buildings and paths will need to be considered in this analysis.
Step 2 - Generative Design Study
I decided to do a very simple optimization of a rectangular reinforced concrete beam section with one layer of reinforcing steel. The input variables are the amount of steel reinforcement and the cross-sectional dimensions of the section. The outputs that are being optimized are the cost of the beam materials and the nominal moment capacity of the beam. The following formula was applied to compute the height of the Whitney stress block outlining the portion of the beam that carries the compressive load.
As : Area of Steel (input)
b: width of beam (input)
fy : yield stress of steel at 60000 psi
f’c : compressive stress at 4000 psi
Before actually calculating the nominal strength of the beam another check is necessary to ensure that the beam is tension controlled by applying the following check.
It should be noted that in order to calculate the parameter d from above, I assumed a #8 steel rebar size. The aforementioned calculations are reflected in dynmo as follows:
Finally, the moment capacity of the beam can be calculated utilizing the following formula:
While I want to maximize the moment capacity, I want to minimize the cost of the beam which was found by multiplying the volume of concrete and volume of steel by unit costs.
Step 3 - Generative Design Study Results
Looking back I would have done this a bit differently. The way I set up my dynmo logic there is a linear relationship between my two outputs of strength and cost. There are different combinations of steel and concrete that will yield the same cost/strength but according to these results, if you want to achieve a certain strength, you will have to pay a certain amount, regardless of how you optimize your steel or concrete content. This is demonstrated by the linear relationships displayed below:
Based on these results, it's probably best to choose a geometry with a moment capacity of around 450 k*in and a cost of 600 dollars as this is the middle of the line in terms of generated options. There are a few different steel and width combinations that generate results in this range.