Step 1 - Generative Design Framework
A very brief description of the design decisions from Step 1 following the Generative Design Framework.
- Design Decision 1 - Beam Depth vs. Span Length
- Design Variables
- Beam depth
- Beam width
- Section wall thickness
- Material strength
- Section geometry
- Load on beam
- Evaluators
- Maximum beam span length
- Material cost
- Midspan deflection
- Most Important Tradeoffs to Consider
- Allowable midspan deflection
- Beam depth
- Beam span length
- Design Decision 2 - Bay Size vs. Material Cost
- Design Variables
- Slab thickness (concrete)
- Column Spacing
- Material strength (concrete)
- Rebar size
- Bay length and width
- Evaluators
- Maximum slab deflection
- Bay size (area)
- Material cost
- Most Important Tradeoffs to Consider
- Material cost
- Bay size (area)
- Design Decision 3 - Lateral Deformations vs. Ductility
- Design Variables
- Natural period of building
- Mass of building
- Lateral loading
- Building material (strength)
- Evaluators
- Lateral stiffness
- Lateral deformation
- Ductility
- Most Important Tradeoffs to Consider
- Lateral deformation
- Ductility
Step 2 - Generative Design Study
Beam Depth vs. Span Length
- Overview
- A steel HSS rectangular beam with a fixed load and fixed material strength is being selected
- The beam length is determined by the beam depth, beam width, material thickness, and loading on the beam
- Objective
- Find a beam size that will minimize the deflection, maximize the span length, and minimize the material cost of the beam
- Variable Inputs
- Beam depth
- Beam width
- Section wall thickness
- Fixed Inputs / Constants
- Section type - HSS rectangular
- Material strength
- Gravity load on beam
- Design type - LRFD
- Outputs / Evaluators
- Span length
- Material cost
- Midspan vertical deflection of beam
Step 3 - Generative Design Study Results
Scatterplot:
Description of scatterplot:
The scatterplot shows that as the maximum beam length increases, the beam depth must also increase. The size and color of the data points correspond to the maximum amount of deflection at the midspan of the beam. The deflection also increases as the beam length increases.
This scatterplot only shows the maximum length that the beam can span, so it can be very useful when making decision decisions. If there is a limitation on the depth of the beam, or any other parameter, the designer can use this study to see what beam span length is possible and can choose that length or a length that is shorter. Or if there is a minimum length the beam needs to be, the designer can use this study to see what the required depth of the beam needs to be. They can also see how thick the walls of the beam need to be, and how much the beam will deflect. If they need to use a longer beam length, then they will know that they will have to size up from the current beam size. This study also evaluates the cost of each design decision, so this can give the designer an estimation of whether the design will be in the budget of the project.
Dynamo Study Graph:
Description of Dynamo Study Graph:
Inputs (pink groups):
- The inputs that will vary during the study are the beam depth, beam width, and section wall thickness. The limitations on each of these inputs are based off of real world HSS rectangular beam dimensions, but the combinations of these three inputs are not controlled by the dimensions of HSS beams that are actually manufactured / listed in the steel manual. This study serves more as a guide to what combinations will work, and then the designer can pick a specific beam size that is close to the dimensions from the study and double check that they will work.
- The inputs that are fixed in this study are the material strength (A992 steel, Fy=50ksi), the modulus of elasticity (E=29000ksi), and the loading on the beam (uniform dead load = 1 kip). For simplicity, the self weight of the beam is ignored, but this could be implemented in the future. The LRFD design method is used for this study.
Actions / Computations (green groups):
- First I created the beam cross section in dynamo using the beam depth, beam width, and wall thickness inputs. I modeled the HSS beam as hollow rectangle by offsetting the outer rectangle dimensions (depth and width) by the wall thickness. for simplicity, I did not round the corners of the HSS beam, but if I did this would reduce the volume of steel (and material cost) of the design.
- Next I computed the section properties that will be needed to compute the maximum length of the beam. These properties are the strong axis moment of inertia, section modulus, and design strength (LRFD).
- Next I computed the maximum length of the beam based on the LRFD equation: ϕMn≥Mu. I computed ϕMn using the section properties and then set that equal to the the maximum moment of a uniformly loaded, simply supported beam, Mu = w*L^2 / 8. I then rearranged the equation to solve for length, L. I then computed the maximum deflection, that occurs at the midspan of the beam.
- For simplicity, I did not consider any deflection limitations, and will leave it up to the designer to determine whether the computed deflection is acceptable.
- After the beam length was calculated, I could then extrude the cross section that I created earlier. I extruded both the outer and inner rectangles and then subtracted the inner rectangle from the outer rectangle to get the hollow HSS beam.
- I then estimated the material cost of the beam by first multiplying the volume of the HSS solid by the weight of ASTM A572 Grade 50 steel to get the total weight of the beam. Then I multiplied the total weight by the cost of steel, that I found from an online source, to get the material cost of the beam. This was a pretty rough estimate of the material cost, but it can still be helpful to the designer to know the different volumes of the beam sizes, which corresponds to the cost.
Outputs (orange group):
- The outputs are the evaluators of the study. They are the material cost ($), the maximum beam length (ft), and the maximum deflection (in).