Structural Engineering & Statics
where the load goes
Concept

Joint classification — where it appears

The division of connections into nominally pinned, semi-rigid and rigid by their rotational stiffness relative to the beam's. It is a licence rather than a description: a joint in the first or third class may be modelled as a pin or as fully continuous, and one in the middle has to be modelled as it is.

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

A force may be moved anywhere, at the price of a couple. A 80 kN force applied 250 mm off the centreline of a body, and the same force applied ON the centreline together with a couple of 20 kNm. The two systems are equivalent: they have the same resultant force and the same moment about every point in space, so no equilibrium equation written about the body can tell them apart. What they are not is the same loading — the stresses inside the body differ, and they differ over a distance of about the body's own depth. The offset is drawn to a scale that keeps the arrow on the body; the number beside it is the real one.

The moment the beam left behind

A beam reaction is drawn arriving on a column's centreline. It arrives on a cleat a hundred millimetres out from the face, and the difference is a couple that goes into the column and has to be shared between the lengths above and below it. Nothing about it appears in a frame model whose members meet at nodes.

internal-forces · Column eccentricity Where the span moment and the support moment cross. Span moment and support moment against the joint's stiffness, for a 6 m beam under 30 kN/m. They move in opposite directions because they add to a constant — the simple-span 135 kN·m is fixed by statics and the joint only decides how it is split. They cross at 68 kN·m, where the joint is delivering 75 per cent of the fixed-end moment, and neither the crossing nor the fraction depends on the beam, the span or the load: it is the point where f·wL²/12 equals wL²/8 − f·wL²/12, which is f = 0.75 for every beam there has ever been.

The joint that was chosen

A joint's stiffness decides how a beam's moment divides between its span and its supports, and the two add to a constant. So there is a stiffness at which they are equal, the beam is sized by the smaller of two numbers rather than the larger of one, and the design moment is half what a simple connection leaves behind.

connections · Joint classification

Named alongside it

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

Moment distributionAxial forceBase plateBending momentCompatibilityConnectionConnection designContinuityDesign momentEccentricityEnd plateForce couple

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