Shells & Gridshells

A flat plate resists load by bending, and bending stiffness depends steeply on thickness - halve the depth and you lose most of the stiffness. That is why a flat roof needs beams: depth to fight bending. A shell cheats this entirely. Because it is curved, an applied load is carried mostly by in-plane forces - membrane tension and compression running within the surface - rather than by bending across it. The curvature effectively gives the thin material a structural 'depth' it does not physically have, letting it work like the funicular arch from lesson one, but in two directions at once.

The kind of curvature matters. A surface curved the same way in both directions (a dome, synclastic) and a surface curved oppositely in each direction (a saddle, anticlastic) are both doubly curved, and double curvature is what makes a shell genuinely stiff, because the two curvatures brace each other. A singly curved surface (a cylinder or cone, which can be unrolled flat) is far weaker - it can still buckle or flatten in the uncurved direction. This is why the most efficient shells - Heinz Isler's concrete roofs, form-found domes - are doubly curved: the geometry itself is doing the structural work, and it was frequently found by exactly the hanging-and-inverting method of lesson 7.1.

You can feel all of this with a sheet of paper. Flat, it flops the instant you hold it out; give it the gentlest curl and it stiffens enough to cantilever. Nothing changed but the shape - which is the whole argument in miniature.

So a shell is form-finding's ultimate pay-off. Get the doubly curved, funicular geometry right and a few centimetres of concrete, or a thin timber lattice, can span tens of metres in near-pure compression. Get it wrong - too shallow, singly curved, or not funicular for the load - and the same material bends, buckles and fails. The shape is not styling; it is the structure.

A solid shell is wonderful but hard and expensive to build (formwork, mass, no daylight). A gridshell keeps the curved-surface structural logic but replaces the solid with a network of slender members following the surface, with glazing or cladding in the gaps. You get light, transparency and far less material - at the cost of introducing all the node and member questions from the diagrid lesson.

Parametrically, deriving a gridshell is a direct extension of what you already know. Take the (usually form-found) surface, lay a grid of points across it with Divide Surface, and connect neighbours into a member network - orthogonal, diagonal (a diagrid-shell), or a more relaxed pattern. The members are then given a structural depth: real gridshells are not paper-thin, so you offset the members or add a second layer to create the depth that resists buckling - the dashed rise in the figure. Two families of gridshell are worth knowing. A rigid, pre-shaped gridshell (like the steel-and-glass roof over the British Museum's Great Court) is engineered node by node to its final geometry, every member and joint bespoke - a triumph of computational geometry, since almost every panel and node is unique and had to be individually calculated. A strained / elastic gridshell (the classic being the Mannheim Multihalle by Frei Otto) is assembled as a flat, loose lattice of thin timber laths and then bent into its curved shape, exploiting the timber's flexibility - so the form must be one the flat grid can actually deform into.

That distinction is not trivia; it drives the whole definition. A rigid gridshell can follow almost any found surface but demands that you manage thousands of unique members and nodes. A strained gridshell severely constrains the geometry (the flat grid can only bend so far, and only into developable-ish shapes) but rewards you with near-identical straight laths and simple nodes. Which one you are designing changes what your Grasshopper definition must guarantee.

This is the lesson's heart, because a doubly curved surface is easy to draw and hard to build. Several buildability questions decide whether your shell is architecture or a render. Panel geometry: the cladding in each grid cell is often glass, and flat glass is far cheaper than curved glass - but a flat quad panel cannot sit on a doubly curved surface without gaps or twist. So designers either triangulate (three points always define a flat plane, which is one big reason gridshell-shells are often triangulated), or use the planarization tricks from the Kangaroo lesson to nudge quads flat, or accept cold-bent / curved glass at a cost. Member bending: in a strained gridshell the laths must physically bend to the curvature without snapping, which limits how tight the curvature can be relative to the timber's minimum bend radius.

Nodes return as the dominant problem, just as in diagrids. On a doubly curved surface the angle at which members meet changes from node to node, so unless you constrain the geometry, every node is unique - a fabrication nightmare. Much of advanced gridshell design is really the search for geometry that keeps nodes and panels as repeatable as possible while still spanning and looking right. Concepts like developable surfaces (surfaces that can be unrolled flat without stretching, so they can be made from flat sheet) and planar-quad (PQ) meshes are the geometry world's answers to these fabrication constraints - deep enough to be their own field (see architectural geometry).

And the standing rule of the module applies with full force here. Shells and gridshells are buckling-critical, geometry-sensitive structures where a small change in curvature, support or load can have large consequences - they are among the least forgiving structures to get wrong. Form-finding and parametric modelling give you a superb, efficient, buildable-looking geometry; they do not tell you the shell is safe. Shell thickness, member sections, buckling capacity, connection design and the response to asymmetric and dynamic loads are specialist structural engineering, requiring proper analysis (FEA, Karamba3D as a bridge) and a qualified engineer - ideally one experienced specifically with shells. Design the shape; let them make it stand.

Step back and the four lessons form one arc. Form-finding (7.1) taught the founding idea: let equilibrium choose an efficient shape, hanging for tension, inverting for compression. Kangaroo (7.2) made that idea interactive, relaxing meshes to minimal surfaces and hanging shells inside Grasshopper. Diagrids (7.3) resolved found surfaces into triangulated member networks and exposed the density-versus-node trade. Shells and gridshells (7.4) close the loop: they are what you get when the found surface's own curvature becomes the structure, built either solid or as a member lattice.

The through-line is a single conviction: in structural form, shape and force are the same thing. A well-found shell is efficient not because it is thick but because its geometry keeps the material in the forces it is good at. Computational tools are so powerful here precisely because they let you shape geometry and reason about force paths in the same parametric breath - find a surface, mesh it, pattern it, curve it, and read the consequences instantly.

But the same through-line carries the same discipline, and it is worth stating once more plainly as you leave the module: these tools find and express structure; they do not certify it. Every found shape, relaxed membrane, tuned diagrid and curved gridshell in this module is a hypothesis about how a building might stand - a very good, physics-informed hypothesis, and a far better starting point than a shape drawn by eye. Turning that hypothesis into a safe, sized, code-compliant structure is the work of a structural engineer, and the best computational designers are the ones who make that engineer's job easier by handing over geometry the forces already like. Design the shape the forces want; collaborate on the structure that carries them.