What a Truss Actually Does

A beam resists load by bending: the top shortens, the bottom lengthens, and stress varies linearly between them. At the neutral axis it is zero, so the material there contributes nothing but weight — and over a long span, weight becomes the dominant load.

Move that material to the top and bottom and the bending moment is carried as a couple: compression in one chord, tension in the other. Increasing the depth increases the lever arm, so strength rises with no extra material.

A rectangle of pinned bars is a mechanism — nothing fixes the corner angles, so it folds into a parallelogram. Mobility confirms it: F = 3(4−1) − 2(4) = 1, one degree of freedom.

The triangle is the only polygon whose shape is fixed by its side lengths alone. Deform it and some bar must change length, which a rigid bar will not do. That is why every truss is built from triangles, and why the diagonal is structural rather than decorative.

1. 1Joints are frictionless pins, so they transmit force but not moment.
2. 2Loads are applied only at joints, so no member is loaded along its length.
3. 3Therefore every member is a two-force member: no moment at either end, nothing applied between them.
4. 4A two-force member can only push or pull along its own axis — pure tension or pure compression, with no bending anywhere.

Pure axial stress is uniform across the section, so the whole cross-section works at full capacity. That is the efficiency a beam cannot match.

Real joints are welded or bolted gussets and *do* transmit moment, producing secondary stresses. They stay small — typically a few per cent — because the triangulated axial path is far stiffer than the bending path, so almost all the load takes it. The idealisation is justified rather than merely convenient.

Each pin joint gives two equations — ΣH = 0 and ΣV = 0, and no moment equation, since a pin cannot carry one. With j joints there are 2j equations against m + r unknowns.

As with beams, the count is necessary and not sufficient: a truss can have the right number of members overall and still contain a floppy panel, which no amount of counting will reveal.

Pratt

Diagonals slope toward the centre, so under gravity load they are in tension — and long tension members can be slender, since they cannot buckle.

Howe

The reverse: diagonals in compression, verticals in tension. Suited to timber, where the compression members are short.

Warren

Alternating diagonals with no verticals. Economical, and the diagonals alternate between tension and compression as load moves.

K truss

Shortens the compression members in a deep truss, which is what governs their size.

The recurring design driver is that compression members buckle and tension members do not, so a good layout keeps the compression members short. That, rather than aesthetics, is why these shapes look the way they do.