Computational Engineering / Parametric thinking
Parametric structures
Generating grids, trusses, diagrids and tapered towers — and reading the numbers that come with them.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Checks needed for project use
- A computational engineering reviewer must check algorithms, convergence claims, statistical assumptions and numerical examples beyond the cases explicitly recorded.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
This lesson is the one where a parametric model stops being a drawing tool. Every geometry generated here carries structural quantities with it: member lengths, an approximate structural volume, a count of distinct member types, and a lateral stiffness proxy. Those are the numbers a design decision is actually made on.
Geometry generators
A floor-grid generator may vary bay spacing and spanning direction. Those choices affect spans, member quantities and connections; the analysis and sizing rules determine the consequences.
A truss generator can use span, depth, panel count and a categorical diagonal pattern. Compare forms using consistent loading, material assumptions and checks.
A diagrid generator can vary perimeter nodes, module height and rotation. With diagonal angle measured from the horizontal, shallow diagonals have a small vertical force component and steep diagonals have a small horizontal component. The balance of gravity, bending and shear stiffness depends on the complete system.
A tower generator can vary base radius, top radius, height, node count and rotation between levels. State how members connect between levels; a general twisted tower should not automatically be described as a hyperboloid.
What to report
Report total member length and the number of distinct lengths to support comparison of quantities and repetition. Once member forces are available, their magnitudes multiplied by member lengths give a load-path measure. Dividing that measure by a common allowable axial stress gives an idealised material volume, subject to separate stability and connection checks.
For perimeter columns, the second moment of their areas about a plan axis can serve as a local stiffness proxy. With column count and area fixed on a uniform ring, that proxy varies with radius squared. It is not a measure of whole-building stiffness on its own.
Include fabrication and erection checks appropriate to the project: transport limits, connection angles, congested nodes and minimum practical member sizes.
Rationalisation
Rationalisation may group member lengths, make panels planar or reduce the number of connection types. Measure the resulting changes in structural performance, fabrication and erection requirements. The most suitable degree of standardisation depends on the project.
Try it
Parametric tower builder
Every change reports member lengths, repetition, a lateral stiffness proxy and what would be difficult to build.
Straight members on a twisted ring generate a doubly-curved surface.
- Storey height
- 4.00 m
- Total column length
- 1442 m
- Total bracing length
- 848 m
- Total member length
- 2290 m
- Distinct member lengths
- 11
- Shortest / longest member
- 4.00 / 8.23 m
- Lateral stiffness proxy, base
- 1176 m²·(unit area)
- Lateral stiffness proxy, top
- 384 m²·(unit area)
- Top / base stiffness ratio
- 0.327
a material proxy before sections are chosen
the repetition measure — often what decides cost
goes with the square of the radius ratio
No constructability flags at this combination. That is not the same as buildable — it means nothing on the short list of automatic checks has fired.
What the proxy is and is not
- The lateral stiffness proxy is ½·n·r² for a uniform ring: the second moment of area of the perimeter about the plan centroid, per unit column area. It is a comparison number, not a stiffness.
- It says nothing about the bracing, which is what actually carries the shear. Two towers with the same proxy and different bracing behave very differently.
- Halving the top radius quarters the proxy. That is why a sharp taper is a structural decision as well as an aesthetic one.
What this shows: A generator that returns geometry alone is half a tool; the half that matters returns the quantities a decision is made on.
Worked example
What a taper costs in lateral stiffness
Given
- A tower with 12 perimeter columns on a circle
- Base radius 12 m, top radius 6 m
- Lateral stiffness proxy taken as the second moment of area of the perimeter columns about the plan centroid
Find
The ratio of the top's lateral stiffness proxy to the base's
Practice
A parametric tower has 16 perimeter columns on a circle of radius 15 m, each of area 0.04 m². Compute the lateral stiffness proxy I = ½·n·A·r², in m⁴.
Check yourself
A generated diagrid produces 340 members of which 289 are distinct lengths. What should happen next?
Check yourself
A parametric study varies span from 6 m to 18 m and reports the lightest scheme at 6 m. What has it shown?
Summary
- A generator should return quantities, not only geometry
- Total length, distinct-length count, structural volume and a stiffness proxy are the numbers a decision uses
- For a fixed number and area of perimeter columns, their second-moment proxy about a plan diameter varies with radius squared
- A generated form is not a buildable form until it has been rationalised, and rationalisation is a design objective