Typical A Frame Cabin
For this assignment I chose to study a simply A frame wood cabin design. I had recently watched a couple of really cool videos regarding the construction of some really beautiful designs and took inspiration from these in deciding to optimize my own A Frame Cabin. Below is an example image which I took inspiration from.
For this assignment I made a very simple rendition of an A frame cabin with four walls, a floor, and two sloping roofs. This would allow me to have all the necessary things to create a generative design study for my building.
Step 1 - Generative Design Framework
I am a Structural Engineer/Civil Engineer so I chose the design decisions that are most reflective of what I have studied and learned in both my undergraduate and graduate education.
- Structural Design
- Design Variables
- Type of Lateral Resisting Frame
- Type of Materials Used
- Number of Floors
- How tall the first floor is and if it has any columns
- The type of bracing systems
- Spacing of beams, girders, columns
- The shape of the building
- Architectural Form
- Evaluators
- Deflections under gravity loads
- Deflections under lateral loads
- How long the building lasts
- How modular the design is and if it can be fixed or repaired easily
- Resiliency under extreme events
- Cost of structure
- Most Important Tradeoffs to Consider
- Cost vs resistance to extreme events
- Amount of concrete used vs sustainability
- Open uninterrupted space vs strength of building
- Safety vs Cost
- Materials vs Cost
- Construction Design
- Design Variables
- Constructibility of the building
- Typical or new Construction Techniques
- Location of construction site
- When construction is occurring
- How many subcontractors on site
- Quality subcontractors and General Contractor
- Evaluators
- Adherence to the schedule
- Adherence to the budget/How much Rework Occurs
- Quality of work
- If the General Contractor or subcontractor is recommended
- Most Important Tradeoffs to Consider
- Cost of construction vs time to completion
- Very complicated and unique building vs constructibility
- Quality of Construction vs Time of Completion
- Sustainable Design
- Design Variables
- The amount of green materials used
- The least amount of concrete used
- Renewable resources used
- Recyclable resources used
- Location on a green site or brown site
- Amount of windows and natural light
- Amount of natural ventilation/heating
- Renewable System
- Evaluators
- Embodied Carbon
- Destruction of habitats
- Materials diverted from waste
- Service life of building
- Amount of energy needed to maintain building
- Energy given back from renewables
- LCA
- Rating Systems: Leed, LBC, ENVISION, WELL, etc
- Most Important Tradeoffs to Consider
- Cost vs Renewables
- Cost vs Recyclables
- Cost vs LCA
- Cost vs Rating Systems
Step 2 - Generative Design Study
I decided in the end to create a study of my A frame roof with both structural design decisions and construction design decisions as these are what I know the most about and what I am the most passionate about. When building an A frame cabin, like any other structure one of the biggest factors is the cost of the building. For my A frame a taller roof with more structural beams would be better but more expensive and a tradeoff to consider. Most A frame cabins are located in very snowy areas and the angle of the roofs are made so as to minimize the amount of snow on the roof to minimize deflections and potentials for cave in. As a result I decided to weight the factors of cost and structural deflections. The location of study for my structure was Tahoe California. Both construction cost and deflections are inversely related and provide a great optimization study.
- Objective: What is the ideal roof height to minimize the amount of deflections under large snow loads but also minimize the cost of construction?
- Model: In creating this model as mentioned previously, I first created the walls and floor of my structure and then went about creating an A frame roof which could be flexed and changed in height. I also wanted to be able to change the number of structural beams that are located on the roof. The basic Framework of building my dynamo geometry is creating the roof with an input of roof height and creating the structural beams along the roof with an input of the number of structural beams. With the building built, I then went about making two analysis nodes which compute the cost of the roof as this is what is changing. I also computed the max deflection of the middle roof span under a snow load typical in Tahoe.
- Design Variables: The design variables chose was the roof height, and the number of beams.
- Constants: The constants used was the building width, length, and height. There were other material constants utilized in determination of the evaluators. For the cost evaluator the cost per sf of wooden roof was used and the cost per length of 2x4 was used. For the deflection evaluator the snow load of Tahoe was determined as well as the moment of inertia and elastic modulus of the 2x4 beams.
- Interpretation: With a higher roof which has a higher angle, the amount of snow on the roof will be much less and as a result there will be little to no deflections due to the snow loads. However a large number of beams will need to be utilized and these will create a large cost for the structure. In the end I think the study will converge on a medium height with a medium number of beams to both satisfy deflections and material cost. The optimized structure will lie somewhere in the middle and the extremes of no beams and no roof height or many beams and very large roof height will not be very optimal.
Completion of the Dynamo Logic:
Below is the logic used to create the A frame roof with the beams:
Evaluator Nodes:
Cost:
Deflections:
Notes: the constants used for the evaluator nodes can be easily changed an manipulated. The constants used were:
- Snow Load Tahoe: 419lb/ft^2
- Moment of Inertia of 2x4: 5.36 in^4
- Modulus of Elasticity of 2x4: 2.5*10^6 psi
- Cost of 2x4 per ft: $3
- Cost of wood roof per sf: $15
Step 3 - Generative Design Study Results
- The screenshot of the Scatterplot or Parallel Coordinates Graph illustrating the tradeoff that you chose to model and study.
- Provide a brief explanation of what’s being shown in the Scatterplot or Parallel Coordinates Graph and how the tradeoff being illustrated would impact the design decision. What would you do with this info?
- An image of your Dynamo Study Graph (showing all your nodes and the connecting logic) -- You can use the File > Export Workspace As Image... command in Dynamo to save a PNG image to upload with your posting.
With the dynamo logic created, I then ran a generative design study with the following as inputs and constants:
I also set a maximum on the deflection of 15” as anymore than this would be completely unreasonable and this 15” is already on the larger amount. After setting the inputs and constants, I then generated the study and observed my results. Below are images of the results of my study:
There is a highly non linear relationship between all these variables. On the x axis is the number of beams and on the y axis is the height of the roof. The size corresponds to the deflections and the color to the cost. We can see that the smallest deflections are centralized where there are the most number of beams and the largest height of the roof. The largest deflections are present near the origin. However, these deflections are actually quite manageable at around 1”(Note when varying some of the material properties of the wood this number can increase to around 5”). We find that in this instance the cost dominates the deflections due to the deflections being quite small. As a result the most optimal structure is one with a pretty small roof and a medium number of beams. This is quite surprising as I wold have expected the roof to be taller. I suspect the reason for this not being the case is my approximate calculations for deflection underestimate the actual deflection under the same loads. I will also include some screenshots which demonstrate the relationship between cost vs height vs number beams and deflections vs height vs number beams.
Cost vs Height vs Number Beams:
Deflections vs Height vs Number Beams
With this information, I would be able to easily design the best type of A frame which is the most cost effective and also the most structurally sound to bear the snow loads of the tough Tahoe winters.
Dynamo Script:
