(Copying this image here just to have it as a cover for my Notion page)

2 Units

Stage 1 - Part 1

The goal of this part of the assignment, was to test one of the example conceptual mass forms from the Revit shared library by flexing one input. To do so, I have followed this procedure:

1. To give my building a geographical context, I have first linked the site context data “Burj Khalifa Area.rvt” into my Revit project file and acquired its coordinates as shown in the image below.

3. II have then imported the conceptual mass named “Parametric Tower - Twisting Cog” from the CEE 220C Revit shared library. I have slightly modified this file and named it “Lavinia Custom - Parametric Tower - Twisting Cog”. In this file I have added formulas and locked in parameters. Also, I have slightly modified the cog profile family (used withing the parametric tower family) to be able to enlarge the cog to a outer radius superior to 100’ - now the limit is set at 200’). More in details:
1. I have adjusted instance parameters of the parametric tower to my desired values that will be held constant through testing.
• Base rotation is locked at 0 degrees.
• Base Spread Angle is locked at 50 degrees.
2. I have set up formulas to specify relationships between the parameters that should be maintained as the building form is flexed:
• The middle height is set as half of the top height.
• Middle Rotation and Top Rotation is set at the same value of the Base Rotation (0 degrees). This choice was arbitrary, as I thought that this specific design would look better without a twist.
• Base Outer Radius and Top Outer Radius set as equal.
• Base Spread Angle set equal as the Top Base Angle
4. Parameters that I am planning to adjust are:
• Base Outer Radius (that will affect the Top Outer Radius)
• Mid Outer Radius
• Mid Spread Angle
• Top Height
5. So far, My model looks like this:


It has a Gross Floor area 2.77 million SF (comprised between 2,500,000 and 3,000,000 SF as requested), a height of 742’ (less than 755’ as requested), and base outer radius of 120’, meaning a diameter of 240’ (less than 984’ wide x 328’ deep in plan view as requested).

For Stage 1 Part 1, I have evaluated a single parameter, namely, the “Mid Spread Angle”, i.e. the spread angle of the mid cog profile. I have reported the Gross Floor Area and the Gross Surface Area associated to 7 different designs, where the Mid Spread Angle was Changed to 20, 25, 30, 35, 40, 45, 50. I have included below an illustration of how the design changes by varying the mid spread angle value (for conciseness I have shown only the cases for 20, 30, 40, and 50 degrees).

I have added a node logic to the code to automatically create the following table.

Note that the first three designs (20, 25, 30 degrees) are not complying to the requirements for GFA that should be between 2,500,000 and 3,000,000 SF.

Stage 1 - Part 2

For this part of the assignment, I crafted my own conceptual mass and profile to personalize and refine my design further.

First, I created my custom profile that resembles a simplified form of a clover, named “Lavinia Custom - Profile - Clover.rfa”. 🍀

The adjustable parameters for this family include the square distance and the circle radius, with the condition that the circle radius remains one-fourth of the square distance. This constraint was chosen to maintain the feasibility of the form, while also enhancing its aesthetic appeal. I have then used this profile to craft my own conceptual mass, employing three profiles positioned at varying levels, which were then lofted together. I have added the following parameters to the conceptual mass:

The final design looks like the following:

Note that the mid height was set to be half of the top height, and that the mass can twist thanks to the three rotational parameters (bottom, mid, top). I have included below an illustration of how the design changes by varying the mid rotation angle value (for conciseness I have shown only the cases for 10, 20, 30, and 40 degrees).

By using the same logic of part 1, I have created an Excel Table to show the GFA and the GSA for seven different designs, corresponding to seven different “Mid Rotations”.

Exporting the evaluation metrics to Excel can have several benefits.

• Excel is a great tool for data analysis. By exporting values to Excel, one can perform additional calculations, create charts, and visualize the results / evaluation metrics in various formats. This can be very helpful to gain deeper insights about the performance of the proposed design alternatives.
• Additionally, by using Excel, one can easily compare the performance of different designs. This comparative analysis can help stakeholders make informed decisions about which design options are most effective or cost-efficient, leading to better overall project outcomes.
• Also, Excel facilitates discussions and collaboration among team members by providing a clear and comprehensive overview of the performance differences between various design alternatives.
• Finally, Excel can be used as a central repository for storing evaluation metrics, design iterations, and project-related information. By exporting values to Excel, users can create detailed reports or documentation, which can be shared with stakeholders, archived for future reference, or used for regulatory compliance purposes.

3 Units - Stage 2

For this Stage, I first created a set of adjustable parameters that allow to define the tower shape and dimensions. These parameters are used to firstly create three stars at three different levels (lower, mid, upper). These three stars are then used to create a surface by loft, representative of the tower envelope (walls).

The resulting design, and its adjustable parameters are shown in the images below. For completeness, I have displayed two variations of the input parameters for my new building form created with Dynamo and their corresponding designs.

Note 1: I have used a custom Node named “RegularStar” to create the star shape. I have saved this node in my submission folder.

Note2. I have not used the “List.Map” function because this function takes only one argument, meaning, it works only when flexing a single input parameter. Instead, I have used the “Function Apply” node to iteratively evaluate the combinations of input values for the two input parameters: “Base Star Radius” and “Number of Star’s Mountains”.

For this analysis, I have fixed the following parameters:

• Middle Star Radius = 160’
• Top Star Radius = 150’
• Middle Star Rotation = 0 degrees
• Top Star Rotation = 0 degrees
• Tower - Story Height = 14’

And I have flexed the following parameters (and hence performed a grid search):

• Base Star Radius = 90, 110, 130, 150 degrees
• Number of Star’s Mountains = 5, 6, 7

The analysis produced the following result. I have highlighted in red the results that are not compliant to the GFA requirements for which the GFA should be comprised between 2’500’000 and 3’000’000 SF. All the other requirements are satisfied, as the height is fixed at 742’ (less than 755’ as requested), and the largest radius value among all the radii (bottom, middle, top) employed is of 160’ (the top star radius), meaning a diameter of 320’ (less than 984’ wide x 328’ deep in plan view as requested).

From the table above one can observe that increasing the base star radius generally leads to a larger GFA. Additionally, having more star mountains also contributes to a larger GFA.

However, the Number of Stars’ Mountains emerges as the most influential factor in shaping a desirable building form that satisfies the GFA constraints. In fact, when considering base radii of 90, 110, and 130, feasibility in terms of Gross Floor Area (GFA) compliance is achieved only by increasing the number of stars’ mountains from 5 or 6 to 7.

On the other hand, increasing the base radius in this specific context (i.e., after having fixed certain parameters), does not necessarily ensure compliance with GFA requirements. Despite the increase in radius, achieving GFA compliance relies heavily on adjusting the Number of Stars’ Mountains, indicating the critical role of shape complexity in meeting design specifications.

Note that these observations hold true within the parameters fixed for this specific analysis at their designated values. Further exploration into varying these parameters may highlight additional trends and their impact on GFA compliance!

4 Units - Stage 3

The resulting analysis for this stage is summarized in the Table below:

Minimum GFA/GSA:

• Of all the evaluated combinations, (Base Star Radius = 90’ - Number Star Mountains = 5’) is the pair of input values that gives the minimum value of the GFA/GSA metric. Hower, this combination is not compliant to the requirements regarding the GFA. as it is below 2,500,000 SF.
• Among the combinations that comply to the GFA requirements, the minimum value of the GFA/GSA metric is given by (Base Star Radius = 90’ - Number Star Mountains = 7’).

Maximum GFA/GSA:

• Of all the evaluated combinations, (Base Star Radius = 150’ - Number Star Mountains = 7’) is the pair of input values that gives the maximum value of the GFA/GSA metric. Hower, this combination is not compliant to the requirements regarding the GFA, as it is above 3,000,000 SF.
• Among the combinations that comply to the GFA requirements, the maximum value of the GFA/GSA metric is given by (Base Star Radius = 130’ - Number Star Mountains = 7’).

The two designs are displayed below (considering all the other parameters fixed):

The most desirable result for me is the combination that maximizes the GFA/GSA metric and minimizes the construction cost (tradeoff) while still complying with the GFA requirements.

• In terms of space efficiency, the best solution is represented by the pair of input values (Base Star Radius = 130’ - Number Star Mountains = 7’), as it offers the maximum GFA/GSA metric within the allowable GFA range. This design optimizes the utilization of available space, potentially maximizing revenue potential for the building owner.
• On the other hand, considering economics, the best solution would be the design with the least construction cost while meeting the GFA requirements. From the table, the design with (Base Star Radius = 90’ - Number Star Mountains = 5’) offers the most economical solution in terms of construction cost. This is because, given the assumption of linear growth in construction cost per square foot from USD $500 at ground level to USD $1000 at 750’ above the ground, minimizing the gross floor area results in fewer square feet to be constructed at higher cost levels. Therefore, a design with smaller gross floor area, such as (Base Star Radius = 90’ - Number Star Mountains = 5’), leads to lower overall construction cost compared to designs with larger gross floor areas.

To have a balance between space efficiency and economics, my recommended solution would be the tradeoff between maximizing the GFA/GSA metric and minimizing construction cost. Among the evaluated combinations, (Base Star Radius = 110’ - Number Star Mountains = 7’) achieves this balance, offering a respectable GFA/GSA metric while remaining within reasonable construction cost parameters. Therefore, I would strongly recommend this design to the building owner as it represents the optimal tradeoff between space efficiency and economics, while respecting the GFA constraints.

Final note: the optimization of construction costs could involve varying different parameters beyond just adjusting the number of star mountains and base star radius. For instance, one could instead enlarge the base radius while diminishing the top radius to potentially minimize construction costs by reducing the amount of high-cost construction at greater heights!