Step 1 - Generative Design Framework
- Design Decision 1 — Slab-on-Ground Thickness vs. Joint Spacing Objective: What slab thickness and contraction joint spacing minimize total in-place cost per SF while keeping the joint-spacing-to-slab-thickness ratio within practical limits?
- Design Variables
- Slab thickness (t): 4 – 10 inches
- Contraction joint spacing (s): 10 – 25 feet
- Evaluators
- Concrete material cost per SF: increases linearly with thickness — minimize
- Joint system cost per SF: sawcutting + sealant + dowel cost, distributed across the slab area — decreases as spacing widens but requires a thicker slab to remain structurally viable — minimize
- Most Important Tradeoffs to Consider
- A thinner slab reduces concrete cost directly but requires closer joint spacing to control cracking — more joints per SF raises sawcut, seal, and dowel costs
- A thicker slab allows wider joint spacing and smaller total joint-system cost per SF, but the concrete volume cost increase must be weighed against those joint savings
- Dowel diameter is tied to slab thickness (ACI 360R approximation: d ≈ t/8); thicker slabs don't just cost more in concrete — each joint also requires larger, more expensive dowels, which partially erodes the joint-spacing savings
- The practical maximum joint spacing is approximately 2.5× the slab thickness in feet-per-inch (e.g., a 6-inch slab should not exceed ~15-foot spacing); GD alternatives that violate this ratio are structurally inadmissible regardless of cost
- Design Decision 2 — Concrete Mix Design Objective: What water-cement ratio and cement content produce the highest compressive strength at lowest material and constructability cost per cubic yard?
- Design Variables
- Water-cement ratio (w/c): 0.35 – 0.65, dimensionless
- Cement content (C): 250 – 450 kg/m³
- Evaluators
- Compressive strength (MPa): estimated via simplified Abrams-like relationship — maximize
- Material and constructability cost per m³: cement cost + water cost + admixture/workability penalty at low w/c — minimize
- Most Important Tradeoffs to Consider
- Reducing w/c increases predicted strength exponentially but below roughly 0.45 the mix becomes difficult to place without chemical admixtures — this constructability cost penalty grows nonlinearly and partially offsets the strength gain
- Increasing cement content raises strength with diminishing returns above ~350 kg/m³ while cost increases linearly per kilogram added
- The useful design region is neither the strongest mix nor the cheapest mix, but the portion of the Pareto frontier where strength gains remain cost-efficient before the penalty and cement cost curves steepen
- Design Decision 3 — Pile Quantity and Diameter for a Single Column Foundation Objective: What combination of pile quantity and pile diameter provides enough axial capacity for a single column load while minimizing installed foundation cost and pile-cap complexity?
- Design Variables
- Number of piles per cap (n): 1 – 12, integer
- Pile diameter (d): 24 – 48 inches
- Evaluators
- Capacity adequacy ratio: total group capacity ÷ required column load — maximize
- Installed foundation cost: pile installation cost + pile-cap complexity proxy — minimize
- Most Important Tradeoffs to Consider
- A single large pile simplifies the pile cap and reduces the number of drilling operations, but it concentrates the foundation demand into one element and may require larger equipment, deeper drilling, or a larger diameter than is practical.
- Adding piles increases total group capacity and redundancy, but each additional pile adds drilling time, layout coordination, inspection points, reinforcement congestion, and pile-cap complexity.
- Smaller-diameter piles may be cheaper individually, but a larger quantity can erase those savings through repeated installation operations and a more complex cap.
- Larger-diameter piles provide more capacity per pile, but their cost does not scale gently because drilling effort, spoil volume, reinforcement, and equipment requirements increase with diameter.
- The useful design region is the lowest-cost pile group that clears the required capacity without creating unnecessary pile count, oversized diameter, or excessive pile-cap complexity.
Step 2 - Generative Design Study
- Selected Decision: Slab-on-Ground Thickness vs. Contraction Joint Spacing
- Objective Identify slab configurations on the Pareto frontier between concrete volume cost and joint system cost per square foot. The specific question: at what slab thickness does the reduction in joint system cost no longer offset the increase in concrete cost — and where does that crossover sit in the design space?
- Model The Dynamo graph is organized into four groups. Two sliders drive all computation; two Watch nodes report the GD outputs. A separate geometry branch produces a 3D visualization of one 40ft × 40ft industrial bay (a concrete slab solid and overlapping joint solids) that updates live as slider values change. All model logic lives in code blocks. Visual nodes handle only geometry creation, color assignment, and GD input/output wiring.
- Cost branch A feasibility penalty activates when joint spacing exceeds 2.5× the slab thickness — the practical ACI 360R crack-control threshold. Without it, GD drives to thin slabs with wide spacing, which is structurally inadmissible. The penalty makes that region costly enough that GD avoids it without a hard constraint.
- Geometry branch
The slab solid is a Cuboid centered on the world origin, sitting on Z=0, with plan dimensions fixed at 40ft × 40ft and height driven by the thickness slider. The 40ft bay dimension was chosen so the full slider range (10–25ft spacing) always produces at least one internal joint per direction in the model.
Joint positions are computed using
Math.Ceilingto determine internal joint count from spacing and bay size. Joint solids are 0.5-inch-wide Cuboids spanning the full bay depth or width at each joint location, placed with a +0.01ft Z offset to prevent z-fighting against the slab face. CB4 produces Y-running joints (parallel to the Y axis), CB5 produces X-running joints. Both lists merge viaList.Joinbefore the color node. - Design Variables
- Constants Ready-mix unit cost $8.00/CF, sawcut $0.75/LF, sealant $1.50/LF, dowel cost coefficient $0.25/LF·in, feasibility penalty coefficient 0.50, max spacing ratio 2.5 ft/in, joint width 0.5 in, bay 40ft × 40ft.
- Evaluators
- The Tradeoff Thinner slab → lower concrete cost → feasibility penalty activates unless spacing tightens → higher joint cost per SF. Thicker slab → higher concrete cost → wider spacing is admissible → lower joint cost. The two outputs move in opposite directions across the feasible design space. The concrete cost term is linear in thickness; the joint cost term is nonlinear due to the quadratic penalty, producing a curved rather than straight Pareto frontier.
Input | Node | Range | Step |
Slab thickness | Number Slider (Is Input) | 4–10 in | 0.5 in |
Joint spacing | Number Slider (Is Input) | 10–25 ft | 0.5 ft |
Output | Node | Direction |
concrete_cost_per_SF | Watch (Is Output) | Minimize |
joint_cost_per_SF | Watch (Is Output) | Minimize |
Step 3 - Generative Design Study Results
- Scatterplot & Parallel Coordinates Graph
- What You Do With This The scatter plot answers a concrete specification question that comes up early in industrial floor design: if a project budget requires cost reduction, where does the cut come from — slab thickness or joint frequency? The Pareto curve shows these are not symmetric choices. In the middle band, reducing slab thickness by 1 inch saves roughly $0.53/SF in concrete but increases joint cost by a smaller amount — net savings are positive. Past the lower-left inflection, thinning the slab further triggers the feasibility penalty and joint cost rises sharply, erasing the concrete savings. The curve locates that inflection without requiring a structural calculation. For a project team, the actionable output is: specify in the 5–7 inch range with 12–18ft spacing. That band captures most of the joint system savings while keeping concrete cost at a moderate premium over the minimum. Going thinner saves little and risks cracking; going thicker adds concrete cost with diminishing joint savings return.
- Image of the Dynamo Study Graph
What it shows: Each point is one generated slab configuration. X-axis is concrete cost per SF ($2.67–$6.67 range across the thickness input). Y-axis is joint system cost per SF ($0.40–$0.65 range). Point size encodes slab thickness (larger dots are thicker slabs. Point color encodes joint spacing) red at 10ft, blue at 25ft. The Pareto frontier runs diagonally from upper-left to lower-right and is visibly curved, not linear. This confirms the nonlinear interaction between the penalty term and the joint cost formula is doing real work in the model. Three zones in the cloud: - The upper-left cluster (red, small dots) represents thin slabs with close joint spacing. Concrete cost is minimal but joint system cost is at its highest; frequent joints, smaller dowels, but high total LF of sawcut and sealant per SF. These are cost-effective in concrete but labor-intensive in joint work. - The middle band is where the Pareto frontier is most informative. Moving from a 4-inch to a 6-inch slab (left to center of the X-axis) produces a proportionally larger drop in joint cost than the increase in concrete cost. This is the efficient region; small increases in slab thickness buy disproportionate reductions in joint system cost because joint LF per SF decreases as 1/s while concrete cost increases linearly. - The lower-right cluster (blue, large dots) represents thick slabs with wide joint spacing. Joint cost approaches its minimum and is nearly flat across this zone; further spacing increases yield negligible savings. Concrete cost dominates and continues rising. These configurations are structurally overbuilt relative to what the remaining joint savings justify.
What it shows:
The parallel coordinates graph displays all four variables simultaneously. The crossing of lines between the concrete_cost_per_SF and joint_cost_per_SF axes is the visual proof of the tradeoff — alternatives that perform well on one output perform poorly on the other, with no single configuration dominating both.
The right two axes (slab_thickness_in and joint_spacing_ft) show near-parallel lines, indicating that GD sampling tended to pair thick slabs with wide spacing and thin slabs with close spacing — the structurally coherent region of the input space. This is the feasibility penalty working as intended: combinations outside the 2.5× ratio are penalized out of the efficient region.
