Structural Engineering & Statics
where the load goes
Concept

Statical determinacy — where it appears

The condition in which the equations of equilibrium are exactly enough to find every force. It makes the structure insensitive to settlement, temperature and fabrication error, and it leaves it with no alternative path if a member is lost.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The plan a straight beam does not have. A beam of radius 12 m turning through 60°, seen from above, with bending drawn outward from the axis in one colour and torsion in the other. The load is vertical and uniform and nothing is applied off the axis. Bending reaches 446 and torsion 155; the two peaks are in different places, which is why the section has to be chosen for a combination rather than for either.

Bending that arrives as twist

A straight beam under a vertical load carries no torsion unless something applies one. A beam whose axis curves on plan carries torsion everywhere, from the same load, with nothing applied off the axis — and it cannot be simply supported at all.

internal-forces · Curved in plan A frame with no plane to be drawn in. The tetrahedron, solved: three equations at every free joint, one axial force in every member. Members drawn heavy carry more; tension and compression are separated by the sign that came back from the solve rather than by inspection. The count is m + r = 12 against 3j = 12, which makes it exactly determinate, and joint equilibrium closes to 1.8e-15.

Three equations at every joint

A plane truss is determinate when m + r = 2j. A space frame needs 3j, and that one changed digit is why a cube of twelve bars is six mechanisms short while looking perfectly solid — and why every three-dimensional frame ever built is made of triangles in several planes at once.

structures · Space frame

Named alongside it

The objects these essays reach for when they reach for this one.

MechanismBending momentCompatibilityCurved in planDouble-layer gridEquilibrium matrixFree bodyLoad pathLoad-sharingMatrix rankMaxwell ruleMoment vector

All concepts