Built-Up Member Generative Design
Example of Built-Up I-Beam
Intended users
For the final project, I wanted to create a user-friendly Dynamo generative design tool for architects and engineers that want to optimize their design of built-up girders or members.
Need you’re trying to provide a solution or support for
Sometimes at the beginning of schematic design, the building plans will call for specific steel members that are not standard sizes within the AISC manual. Such members are called “built-up members” or “built-up girders”, and are most simply constructed by welding two plates acting as “flanges” to a “web” plate, as shown above. However, a lot of times these specific steel members are wasteful, and BIM designers have to manually calculate what is the optimal shape that achieves the desired structural strength while lowering cost. In practice, most designers do not optimize and are wasteful in their drawings, as this process can get tedious, and multiple shapes could be required in a project. Moreover, other valid factors could prevent a designer from choosing the most structurally efficient design, such as an architecturally desired flange, web width, or height, the carbon emissions resulting from a beam section, or the increasing cost of a plate as its thickness increases.
Thus, I want to create a simple built-up girder generative design tool using Dynamo. In this tool, the user can choose to input or vary key dimensions, such as the total height or flange thickness, and constrain the outputs, including the maximum budget, area, and the minimum required plastic section modulus. In turn, the user receives outputs of multiple iterations of beams that fit these requirements. While there are many ways to configure a built-up member with C-channels and L-shapes, I will code the tool such that the built-up member is made out of three simple rectangles, indicating the web of the beam and its two flanges. With this tool, designers can introduce themselves to new shapes that fulfill their design criteria with faster and greater insight.
Inputs
From a relatively short set of inputs, one can construct a simple built-up member section and produce a wealth of structural and architectural information. Thus, I limited the number of inputs to make this tool as intuitive and simple as possible.
- Total Beam Height H
- Total Beam Width Bf
- Thickness of Flange tf
- Thickness of Web tw
- Yield Strength of Steel Fy
Underlying logic of the model you’ll implement
- Create H-Shape Profile of Built-Up Girder
- First, I will construct the section with Dynamo geometry nodes using the dimensions inputted.
- Calculate Section Properties of Built-Up Girder
- From this section, I can use mathematical nodes to extract important section details, including the beam plastic section modulus and its area. For instance, the second moment of area Ixx can be calculated using the formula below:
Source: www.sciencedirect.com
- Calculate Strength Properties of Built-Up Girder
- If the user inputs the yield strength of steel Fy, I can also calculate the axial, shear, and moment capacity of the beam, assuming it remains elastic. All of these calculations can be found in the AISC Steel Manual.
- For example, the plastic moment capacity of a beam Mp is equal to Mp = Fy * Zx (steel yield strength * section modulus Zx).
- The nominal shear capacity of a beam Vn is equal to Vn = 0.6 * Fy * Aw * Cv1.
- Calculate Other Important Factors of Built-Up Girder
- Finally, I can calculate the cost of the beam section / length, assuming that the price of steel increases if its thickness increases, and the resulting carbon emissions from producing such a beam section.
- From a simple search, a 1’ x 1’ square of 1/4” inch A36 steel costs approximately $30, while a 1’ thick square costs approximately $110. Thus, to find the cost per length of A36 steel, we can equate the cost per unit length of steel for a single plate to be equal to Cost / Length = ($0.208 + $0.556 * thickness ) * width.
Steel Plate - A36
- From another simple search, the CO2 emissions per ton of steel is equal to approximately 3 tons. https://8billiontrees.com/carbon-offsets-credits/carbon-footprint-of-steel/#:~:text=How Much CO2 Is Produced Per Ton of Steel%3F,how the steel is produced.
- These values can be set as limits, as well as the strength and section properties, during the generative design study.
Outputs
- Section Area
- Beam Moment of Inertia
- Beam Elastic Section Modulus
- Beam Plastic Section Modulus
- Nominal Flexural Strength of Beam Mn
- Nominal Axial Strength of Beam Pn
- Nominal Shear Strength of Beam Vn
- Cost of Beam Section / Length
- Carbon Emissions of Beam Section / Length