Step 1 - Generative Design Framework
Step 2 - Generative Design Study
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.