Free-form Structures

What is a free-form structure?

A free-form structure is a building surface whose geometry is defined by a model rather than by a repeating rule. A barrel vault has one radius. A dome has one centre. A free-form surface has neither, so no two panels, no two members and no two nodes are identical unless the geometry is deliberately made to repeat.

Three terms get used for overlapping things, and it helps to separate them:

• Free-form structure — the general case. Any surface not describable by simple geometry.
• Gridshell — a structural surface made of a grid of linear members that carries load primarily through the surface itself rather than through bending. Most free-form steel and glass roofs are gridshells.
• Shell — a continuous surface, usually concrete. Structurally related, built completely differently.

In practice, when an architect asks for a free-form roof, what gets engineered is almost always a single or double-layer steel gridshell.

Typical span range

10 m – Unlimited

Surface tolerance against the control model

± 3 to ± 5 mm

Maximum panel size, typical

1,500 × 3,000 mm

Execution class to EN 1090-2

EXC2 / EXC3

Why double curvature is structurally efficient

This is the part that surprises people: the geometry that looks hardest to build is often the one that needs least material.

A flat roof member resists load in bending, which is the least efficient thing a steel section can do. Stress is concentrated at the extreme fibres and most of the section does very little. To span further you deepen the member, and the steel grows faster than the span. The same effect, measured in tonnes on a 60 m hall, is worked through in space frame vs portal frame.

Curve the surface in two directions and the behaviour changes. Load resolves into membrane action — tension and compression carried within the surface — and every part of the section works. That is why a doubly curved shell can cross a span on a fraction of the steel a flat grid would need.

• Flat: bending Most of the section does very little. To span further the member goes deeper, and the steel grows faster than the span.

• Curved: membrane action Load resolves into tension and compression carried within the surface, so every part of the section works. Curved in two directions, the surface gains this both ways.

Sections. Deflection and curvature exaggerated.

The consequence for design is worth stating plainly: a more sculptural surface is not automatically a more expensive structure. It is often a lighter one. The cost sits somewhere else, which is the subject of the next section.

The decision that sets the budget: how the surface is panelised

The largest cost variables in a free-form envelope are not the span, the steel tonnage or the glass specification. They are how many different panels the surface needs, and how much curvature each panel is asked to carry.

There are four options. The first three are in ascending order of cost; the fourth buys curvature at close to flat-glass cost, within limits.

Planar panels

The surface is approximated by flat facets — usually triangles, or quadrilaterals forced to be planar. The glass is ordinary flat glass. Fabrication is conventional and replacement panels are easy to source for the life of the building.

The trade-off is visible faceting, and on tight curvature the facet lines read clearly across the surface. Triangular panels guarantee planarity but increase node complexity, because six members meet at each node instead of four. Planar quadrilateral meshes reduce node complexity but constrain the geometry — the surface has to cooperate.

• Triangles Every panel is planar by definition, so the glass is flat — but six members meet at each node.

• Planar quadrilaterals Four members at each node, a simpler node — but the surface has to cooperate for every quad to stay flat.

Single-curved panels

Curved in one direction, straight in the other — developable, like a rolled sheet. Metal panels roll easily. Glass can be hot-bent to a single radius at moderate cost, and a family of panels sharing one radius is much cheaper than a family where each has its own.

This is usually the best value for money on a large surface, and it is where rationalisation earns most of its keep: pushing a free-form surface toward a small number of repeated radii.

Double-curved panels

Curved in both directions. Every panel needs its own mould. For glass this means individually formed units; for metal, stretch-forming or explosive forming. The result is a seamless surface with no faceting, at a cost that scales with the number of unique panels rather than the area.

Reserve this for the areas that carry the architecture. Very few projects need it everywhere.

Cold-bent glass

A flat insulating unit is elastically twisted into a warped quadrilateral shape on site or in the frame, and held there. It gives a continuous-looking surface at close to flat-glass cost, with no forming.

It is bounded by what the glass and the interlayer will tolerate as permanent stress. The allowable twist depends on the pane dimensions, glass thickness, build-up and the supplier's own limits, and it has to be confirmed against the specific unit rather than assumed. Where it works, it is the most economical route to a genuinely curved appearance.

• 1 · Planar panels Flat facets of ordinary flat glass. Conventional to make and replace — the facet lines show on tight curvature.

• 2 · Single-curved panels Curved one way, straight the other. Glass hot-bent to one radius — far cheaper when many panels share it.

• 3 · Double-curved panels Curved both ways, so every panel needs its own mould. Cost follows the number of unique panels, not the area.

• 4 · Cold-bent glass A flat insulating unit twisted elastically into a warped shape and held there — close to flat-glass cost, within what the glass allows.

The first three in ascending order of cost. Curvature exaggerated.

Rationalisation: what it is, and when it has to happen

Rationalisation is the process of reducing an unconstrained surface to a set of parts that can actually be manufactured — a limited family of panel types, a limited family of node types, a set of member lengths that can be cut and coated in batches.

An unrationalised surface produces a unique part for every position. Every panel needs its own drawing, its own cutting file, its own quality check and its own place on the scaffold. Panel-set reduction is the single biggest cost lever on this system.

• Unrationalised: 24 positions, 24 parts Every panel has its own drawing, its own cutting file, its own check and its own place on the scaffold.

• Rationalised: three panel families Panels grouped to share a radius, a mould or a cutting pattern within an agreed tolerance — made, checked and fixed in batches.

Illustrative. How many families a real surface needs depends on its geometry and the agreed tolerance.

What rationalisation actually involves:

• Mesh strategy — triangular, quadrilateral, or hybrid, chosen against panel planarity and node complexity together rather than separately.
• Panel family reduction — grouping panels that can share a radius, a mould or a cutting pattern within an agreed tolerance.
• Node family reduction — establishing how many distinct node types the surface needs, and whether one adjustable type can absorb the variation.
• Member standardisation — repeating section sizes and, where possible, lengths.

The timing matters more than the technique. Rationalisation is cheap while the surface is still a model and expensive once it is a set of approved drawings. The right moment is immediately after the geometry is agreed in principle and before it is developed in detail. An architect who brings a surface to a façade engineer at concept stage keeps the design intent. One who brings it after tender usually has to trade some of it away.

Node geometry

On a free-form gridshell, members meet at varying angles in three planes. No two nodes are the same unless the geometry has been made to repeat.

The node family has to absorb that variation without becoming a bespoke fabrication for every junction. Three approaches are in common use, and the specification for this system allows all three:

• Bolted spherical Members thread into a machined ball; the angles are in the drilling. Fast to erect, little adjustment on site.

• Cast One formed body where many members converge, or where the node is seen. High tooling cost, low unit cost at volume.

• Welded plate Members welded to a plate. Keeps a single-layer node slim; the most flexible geometrically and the most demanding to fabricate.

Simplified. Member sections and connection details vary with the geometry.

Fixing the node family early prevents bespoke fabrication later. It also determines the erection method, because a node that is adjustable on site is a different erection sequence from one that is not.

Glazing a curved surface

Once the panel geometry is settled, the glazing detail has to accept it.

• Sealing on a warped surface. A flat gasket profile sits on a plane. On a warped quadrilateral, the frame itself twists, and the gasket has to maintain compression along a line that is no longer straight. This is where water gets in on free-form roofs, and it is a detailing problem rather than a materials problem.
• Drainage direction changes across the surface. On a doubly curved roof the fall direction is different at every point. Drainage has to be resolved against the actual surface model, not against a notional slope — the same discipline as on free-form skylights.
• Support tolerance. Glass is unforgiving of point loads introduced by frames that are out of position. The surface tolerance below is not an aspiration — it is what keeps the glazing from being stressed by its own support.
• Cladding options on this system: insulated and laminated glass, polycarbonate, ETFE and composite panels. ETFE is worth considering where the span is long and the weight budget is tight, since it removes most of the cladding's dead load.

Tolerance and the control model

Every free-form project runs against a control model — the single agreed digital definition of the surface. Drawings, cutting files, survey points and setting-out all derive from it. If there is more than one version of the model, there will be more than one version of the building.

The surface tolerance for this system is ± 3 to ± 5 mm against the control model.

That figure does more work than it looks. It has to absorb, cumulatively:

• fabrication tolerance on members and nodes
• survey and setting-out tolerance on site
• deflection under self-weight once temporary support is released
• thermal position at the moment of measurement

• FabricationTolerance on members and nodes.
• Setting outSurvey and setting-out tolerance on site.
• Self-weightDeflection once temporary support is released.
• TemperatureWhere the structure sits thermally at the moment of measurement.

Band width exaggerated. On a free-form surface, position is measured against the model, not against a straight datum.

Which is why the survey regime is agreed before fabrication starts rather than after erection begins. On a free-form surface there is no straight datum line to measure against — position is only meaningful relative to the model.

What happens when it is not is set out on DOMAINE Shopping Center in Yerevan, where the erected steel was found up to 15 cm high in some areas and 18 cm low in others against its model — and had to be corrected before a single panel could be fixed.

Thermal movement

Curved surfaces expand along their own axes. A flat façade grows in two predictable directions; a doubly curved shell grows along the surface, which means the movement direction rotates from one part of the roof to another.

• Flat façade Grows in two directions, the same everywhere on the elevation — joints can sit on a regular grid.

• Curved shell Grows along its own surface, so the direction of movement turns across the roof. Where it is held and where it slides is a decision, not a default.

Joints must absorb the movement or the glass will find the stress on its own. The practical implications:

• Movement joints are positioned against the geometry, not on a regular grid.
• The restraint strategy has to be explicit — where the structure is held, where it is allowed to slide, and what the resulting forces are at the boundary.
• Interfaces with the primary building structure are where free-form roofs most often go wrong, because the two elements move differently and the tolerance between them is usually the smallest on the project.

Erection and temporary works

Long spans need temporary support planned before the first component is fabricated, not once it arrives.

A gridshell is frequently not stable until it is complete. Until the surface closes, it is a collection of members in bending — the condition it was specifically not designed for. That means:

• The erection sequence is a design case. Partial structures are checked as their own load cases, not assumed safe because the finished structure is.
• Temporary works can govern member sizes. Occasionally a member is sized by an erection condition rather than by the in-service condition.
• Ground assembly and lift, or piecemeal on falsework. The choice depends on crane access, the site below, and whether the building is occupied.
• Release is a calculated event. Removing falsework transfers load in a sequence that is designed, staged and surveyed.

Where the building below is live — a working shopping centre, an occupied concourse — the erection strategy usually drives the programme more than fabrication does.

What to give an engineer, and when

The most common way a free-form project loses money is a façade engineer arriving after the geometry is fixed. This is what is useful at each stage:

1. 01

   Concept

   The surface as a Rhino or equivalent model, the span, where the structure is allowed to land, and what the surface is for — daylight, shelter, enclosure or appearance. At this stage the model does not need to be clean. A conversation here costs nothing and can save a scheme.

2. 02

   Developed design

   The agreed panelisation strategy, glass or cladding performance requirements, site wind and seismic data or just the city, and the interfaces with the primary structure. Rationalisation belongs at the start of this stage, before the surface is developed in detail.

3. 03

   Technical design

   The control model, the node family, the movement and restraint strategy, and the survey regime. Shop drawings follow from these, not the other way round.

4. 04

   Before tender

   A defined panel set and node family. Tendering an unrationalised surface produces prices that are either padded for risk or wrong, and both cost the client money.

Engineering carried out on this system

Form finding. Finite element modelling of the frame, nodes and connections. Computational fluid dynamics for wind pressure across doubly curved surfaces, where standard code pressure coefficients do not apply. Energy calculation for thermal transmittance and condensation risk. Full 3D detail design, and full-scale mock-up testing where the geometry or the risk justifies it.

CORTEX carries design, engineering, shop drawings, fabrication and installation as one scope, with aluminium profiles extruded in-house — so a section can be developed for the surface rather than selected from a catalogue.