Structural Engineering & Statics
where the load goes
Concept

Moment about an axis — where it appears

The component of a moment along a chosen direction, which is what a torque is and what a bolt group's twist is measured as. It is obtained by projecting the moment vector onto the axis, which is how a three-dimensional free body's six equations are reduced to the ones a particular question needs.

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

Three legs, three equations, one answer. A rigid top on three legs carrying 120 kN at (0.3, 0.2) m. The three equilibrium equations available — one vertical and two moments — leave three unknowns, so the system is exactly determinate and the reactions are 56.8, 13.6, 49.6 kN. Move the load anywhere and the answer moves with it; nothing about the legs' stiffness enters.

Six equations, and the drawing shows three

Every essay so far has taken place on a piece of paper, where equilibrium is three equations and a structure is a diagram. The real object has six, the extra three are the ones nobody writes down, and the difference between three legs and four is not a matter of degree.

equilibrium · Three-dimensional equilibrium A general force system is a screw, not a force. Two forces that are neither parallel, nor concurrent, nor coplanar. Their resultant is (30, 0, -60) and no point in space reduces them to it alone: the moment left on the central axis is (14.40, 0.00, -28.80), which is parallel to the resultant and has a pitch of 0.4800. The simplest object equivalent to the system is therefore a force and a couple about the same line — a wrench — and a planar drawing can never produce one, because a coplanar system has its moment perpendicular to its resultant by construction.

Moving a force, and what it costs

Every free body begins by putting a force somewhere convenient. That move is free along the force's own line, costs a couple across it, and in three dimensions leaves behind something no choice of point can remove.

equilibrium · Force couple

Named alongside it

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

Bolt groupDeterminacyEccentricityFree bodyFree body diagramIndeterminacyLever armLine of actionMoment centreMoment equilibriumRankResultant

All concepts