Trusses & Space Frames

Take four bars and pin them loosely at the corners into a rectangle, then push sideways on the top. The rectangle instantly folds into a leaning parallelogram - it racks - because the corner angles are free to change and nothing stops them. The same four bars can be pushed into any lopsided shape you like without changing a single bar's length. A pin-jointed rectangle, or any four-or-more-sided figure, is a mechanism, not a structure: it has no shape of its own.

Now do the same with three bars pinned into a triangle. Push on it and it does not budge, because there is no way to change the shape of a triangle without changing the length of at least one of its sides - and the bars resist changing length by their own axial strength. This is the deep reason triangulation works: fixing the three side lengths of a triangle fixes all three of its angles, uniquely and rigidly. It is a fact of geometry, not of engineering, and it is why the triangle appears in every efficient lightweight structure ever built, from a bicycle frame to a transmission tower to the boom of a crane.

A truss is simply a structure assembled entirely from triangles. Because each triangle is rigid, the whole assembly is rigid, and because the joints are treated as pins (they transfer force but not moment), no member is asked to bend - each simply pushes or pulls. If you ever see a large panel in a lattice that is a plain rectangle with no diagonal, be suspicious: either there is hidden stiffness (a rigid joint, a stiff panel) or that bay is a weakness. The habit of looking for the triangles is the fastest way to judge whether a lattice structure is sound.

A typical truss has a recognisable anatomy. The two roughly horizontal lines of members running the full length are the chords: the top chord and the bottom chord. Between them, the shorter members forming the triangles are the web, made up of verticals (posts) and diagonals. Together the chords and web behave, at the large scale, exactly like a very deep beam: the truss as a whole resists the span by bending, but it does so by putting its top chord and bottom chord into opposite axial forces rather than by stressing a solid section.

Here is the key to reading any truss. When a simply supported truss is loaded downwards (the usual case for a roof or floor), it sags very slightly like a beam, so its top chord shortens - it is in compression - and its bottom chord lengthens - it is in tension. The web members then carry the shear, alternating between tension and compression as they zig-zag from top to bottom. Knowing which members push and which pull is not academic: compression members can buckle (fail by bowing sideways) and so must be made stouter - a tube, an angle back-to-back, a fatter section - while tension members cannot buckle and can be as slender as a rod or a cable, because pulling something straight only makes it straighter. So the very shapes of the members tell you the forces: fat struts are usually in compression, thin ties usually in tension.

This is why the truss is such an efficient use of material. In a solid beam every fibre is forced to follow the whole depth of bending stress whether it is useful or not. In a truss the designer places a stout compression member exactly where compression flows and a slim tension member exactly where tension flows, and puts nothing in between. The result is a structure that can be a tenth the weight of an equivalent solid beam - the difference between a spanning member you can lift by hand and one that needs a crane.

Trusses are named mostly by the pattern of their diagonals, and three names cover most of what an architect will meet. The Pratt truss has vertical posts and diagonals that slope down towards the centre. Under normal downward load this arrangement puts the long diagonals into tension and the short verticals into compression - which is efficient, because you keep the buckling-prone compression in the short members and let the long members simply pull. The Pratt was a favourite of the steel age for exactly this reason and remains extremely common in roofs and bridges.

The Howe truss is the Pratt's mirror image: its diagonals slope up towards the centre, which reverses the forces so the long diagonals are in compression and the verticals in tension. This is inefficient for steel (you now have long compression members that must be beefed up against buckling), but it was ideal for timber trusses, where the diagonals could be simple timber struts in compression and the short verticals could be iron rods in tension - a classic nineteenth-century combination. Knowing the difference between Pratt and Howe is really knowing that the direction of the diagonals decides which members push and which pull.

The Warren truss dispenses with the verticals altogether and uses only diagonals in a continuous zig-zag of equilateral or near-equilateral triangles, so its members alternate tension-compression-tension-compression along the span. It is clean, economical and visually calm, which is why it is so often left exposed as an architectural feature. Beyond these three sit many relatives - the Fink and Howe roof trusses of pitched roofs, the bowstring or tied arch (a curved top chord with a straight tension tie), the Vierendeel (a rectangular truss with no diagonals that works only because its joints are rigid, used where a diagonal would block a doorway), and the deep lattice girder. Each is a variation on the same theme: arrange members so the forces stay axial, and keep the compression short and the tension long.

A single truss is a planar or 2D structure: it is very strong in its own plane but flimsy sideways, like a sheet of paper held up on edge, so real roofs use many parallel trusses tied together with bracing to stop them toppling. But if triangulation is good in two dimensions, it is even better in three. A space frame (or space truss) extends the idea into a three-dimensional lattice, most often two horizontal grids of members - a top layer and a bottom layer - linked by a web of diagonals, so the whole assembly is built from tetrahedra and octahedra, the three-dimensional cousins of the triangle.

The payoff of going 3D is that a space frame spans in two directions at once and shares any load among a great many members, so no single member is heavily stressed and the structure becomes both extraordinarily light and extraordinarily robust - if one member is overloaded, dozens of alternative paths remain. This is what lets a space frame roof an exhibition hall, an airport concourse or a sports arena as a shallow, glittering plane of small identical members, often supported on just a few columns or even a single tree-like support. Because the members and the connecting nodes are identical and mass-produced (proprietary systems like MERO use a machined ball node into which struts screw), space frames are highly prefabricated: they arrive as a kit of struts and balls and are bolted together on the ground, then lifted into place.

The honest limits are worth knowing. Space frames are superb for large, roughly square or free-form roofs where their two-way action and light weight shine, but they are fiddly and connection-intensive - the cost lives in the hundreds of nodes, not the struts - so for a simple one-directional span a set of ordinary 2D trusses is often cheaper and quicker. They also demand accurate setting-out and offer little fire resistance without protection, being exposed steel. Used where their geometry pays off, though, a space frame is one of the most efficient long-span roofs available, and one of the most beautiful when left honestly on show.

Three practical instincts turn truss theory into good architecture. The first is depth. A truss behaves like a deep beam, and its efficiency comes almost entirely from its depth: the deeper the truss (the further apart its chords), the smaller the forces in those chords for a given span, because the internal lever arm is longer. A useful rule of thumb is that a truss is typically around a tenth to a fifteenth of its span in depth - so a 30 metre span wants a truss roughly 2 to 3 metres deep. Architects who try to make a long-span truss too shallow to look elegant simply force enormous forces into the chords and heavy, ungainly members; letting a truss be honestly deep is what keeps it light. That depth zone is also a gift, because services can be threaded straight through the open web.

The second instinct concerns joints and loading. Truss theory assumes loads arrive only at the joints (nodes) and that the joints act as pins. Real trusses are usually welded or bolted, so the joints are somewhat rigid and members do pick up small secondary bending - engineers account for this, but the design lesson for an architect is to bring loads to the nodes wherever possible. Hanging a heavy point load from the middle of a chord, between nodes, forces that chord to bend as a beam and defeats the whole point of the truss. Purlins, hangers and applied loads should land on the panel points.

The third instinct is expressive honesty. Because a truss so clearly shows tension and compression, it is one of the most legible structures to leave exposed, and great architecture has always exploited this - the fine tension rods and stout compression struts of a well-detailed truss are a diagram of the forces made visible. The reward for understanding trusses is not only lighter, cheaper long spans but a structure you can put on display, where the honest expression of how the building stands up becomes the architecture itself. That is the spirit in which the next lesson turns from lattices that span with straight members to forms that span with pure curved geometry - the arch, vault, dome and shell.