A chassis is a collection of triangles
Reading a frame as load paths rather than as tubes.
A chassis is best read as a collection of triangles rather than as a collection of tubes, because a triangle is the only simple shape whose corners cannot move relative to each other without a side actually stretching or compressing, while any four-sided panel of tubes can rack sideways into a parallelogram under load even though every individual tube stays exactly the length it started at.
Why three pinned bars hold their shape and four do not
Picture a shape made of rigid bars joined at pinned corners, free to rotate. A three-sided version of that shape, a triangle, has only one possible layout for a given set of side lengths, so pushing sideways on it cannot change its shape at all without a side genuinely growing or shrinking, which for a stiff bar takes enormous force. A four-sided version of the same idea, a simple rectangle of pinned bars, has no such guarantee, and a sideways push can fold it into a slanted parallelogram using nothing but rotation at the corners, with every side staying precisely the length it always was.
A welded chassis behaves a little better than a pin-jointed one, because the welds themselves resist some rotation. That resistance is far weaker than the resistance of a tube being stretched or compressed along its own length, though, so an unbraced rectangular panel of tubes still wants to rack in roughly the same way, just with more force needed and less obvious motion. Adding one diagonal member across that rectangle removes the racking possibility almost entirely, because the rectangle has effectively become two triangles sharing a side, and neither of those triangles can change shape without a tube stretching.
A step-ladder with its brace unlatched
A folding step-ladder shows the same idea outside any workshop. The two front legs and the horizontal steps between them form a shape that, left on its own, could easily splay sideways under someone's weight, exactly the racking a bare rectangle of tubes is prone to. The rear brace strut, hinged to the front legs and locked straight when the ladder is opened, closes off that possibility by turning the whole structure into a pair of triangles, and it does so with a single diagonal member instead of thicker or heavier legs. Anyone who has tried to stand on a step-ladder with that rear brace unlatched knows how differently the same ladder behaves once the triangle is broken, sliding and wobbling sideways under weight that felt completely solid a moment before. Nothing about the legs themselves changed, only whether the shape they formed was allowed to rack.
Turning a bent corner into a pulled tube
A panel of tubes with no diagonal relies entirely on how stiffly its corner joints resist twisting to keep its shape, and that resistance is a small part of what the same tubes would offer if the load instead had to stretch or compress one of them along its length. Adding a single well-placed diagonal converts every load reaching that panel from a bending problem at the corners into a tension or compression problem along the diagonal itself, and tubes are far better at resisting a straight pull or push than a weld is at resisting a twist.
The cost of that diagonal is modest. The diagonal of a square is about 1.4 times the length of one side, so bracing a square panel adds roughly a third to the tube already in its four edges, a small price for turning a panel that folds into one that holds. This is why a chassis designer thinks in terms of which panels have been triangulated and which have not, and pays little attention to total tube length, since two frames using an identical length of the same tube can differ enormously in stiffness depending entirely on where the diagonals were placed.
Reading a drawing, and checking a finished frame
Reading a chassis this way changes what a designer looks for on a drawing. An untriangulated panel, wherever it sits on the frame, is a point where the structure is depending on weld stiffness alone to hold its shape, and it is usually cheaper, in both weight and effort, to close that panel with a diagonal than to compensate for its softness by thickening tubes elsewhere that were never the weak point. It also explains why a drawing that looks dense and complicated near a suspension pickup point may be carrying exactly the triangulation needed there, since that is where a highly loaded panel would otherwise rack under the very forces the suspension is passing into the frame.
It also changes how a finished frame gets checked before it is trusted. Counting triangles is a faster and more reliable way to spot a weak area than counting welds or measuring tube diameters, because a panel can be welded competently at every joint and still be soft overall if nothing was ever added to stop it racking, while a panel with a well-placed diagonal can tolerate a slightly rougher weld and still hold its shape under load. Walking around a completed chassis and asking, panel by panel, whether each face is a genuine triangle or merely a rectangle waiting for a load to find its weakness, catches problems that a purely visual check for straightness or tidiness would miss entirely.
The habit carries over to any welded structure. The same rectangle-and-triangle question decides whether a bicycle rack, a shelving frame or a garden gate stays rigid under a shove or slowly racks itself loose over years of ordinary use, and a gate that sags at its latch corner is usually a rectangle that was never given its diagonal, or was given one running the wrong way so that it pushes where it should pull.