Module 3 · Lesson 3.2
Parametric structures
Generating grids, trusses, diagrids and tapered towers — and reading the numbers that come with them.
Why 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.
The family of generators
Grids. A floor grid is two spacings and a rule about which direction spans onto which. Changing the spacing changes the beam depths, the number of connections and the slab span, all at once — which is exactly what makes a grid worth parameterising and a floor plan worth not.
Trusses. Span, depth, number of panels, diagonal pattern. Four numbers generate a Warren, a Pratt, a Howe or a K, and the structural volume of each can be compared directly.
Diagrids. A perimeter of nodes, a number of storeys per diagonal module, and a rotation. The diagonal angle that comes out is the parameter that matters structurally: too shallow and the diagonals carry little shear, too steep and they carry little gravity.
Tapered towers. Base radius, top radius, height, node count, and a twist per storey. A pure taper gives straight members; a twist gives a hyperboloid — a doubly-curved surface generated entirely by straight members, which is the reason the form exists at all.
What to report
A generator that returns geometry alone is half a tool. The half that matters returns:
- Total member length — a proxy for material before sections are known.
- Number of distinct member lengths — the repetition measure, and often the one that decides cost.
- Approximate structural volume — force times length summed, once the geometry can be analysed.
- Lateral stiffness proxy — for a tower, the second moment of area of the perimeter about the plan centroid, which falls with the square of the radius as the tower tapers.
- Constructability flags — members shorter than a transportable minimum, angles too acute to connect, nodes with too many members meeting.
Rationalisation
A generated geometry is almost never buildable as generated. Rationalisation is the step that makes it so: snapping members to a set of standard lengths, forcing panels to be planar, limiting the number of distinct node types.
It always costs something structurally and it almost always saves more than it costs. It is a design objective in its own right, and a parametric model that cannot express it — that can only produce the pure form — is producing a shape rather than a structure.
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
- Lateral stiffness of a perimeter structure goes with the square of the radius
- A generated form is not a buildable form until it has been rationalised, and rationalisation is a design objective
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint