Structural Engineering & Statics
where the load goes
Concept

Design moment — where it appears

The moment a member or joint is sized for, taken from an analysis under factored loads rather than from what the member can resist. On a beam with semi-rigid joints it depends on how stiff the joints are, and a balanced joint makes the end and span moments equal, each half the simply supported value.

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

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 The joint yields first and the span takes the rest. The end and span moments of a beam of span 9 m and flexural rigidity 61,700 kN·m², with a plastic moment of 522 kN·m, on joints of rotational stiffness 41,133 kN·m/rad, 6.00 EI/L, and resistance 261 kN·m, as a uniform load rises to collapse. While elastic the joints carry 0.75 of the fixed-end moment. The joints reach their resistance first, at 51.6 kN/m, and from there every further increment of load goes to the span, which reaches 522 kN·m at 77.3 kN/m. The collapse load is 8(Mp + Mj)/L² = 77.3 kN/m, between the 51.6 at which the beam would collapse on pins and the 103.1 it would reach on rigid full-strength ends, and it contains the joint's strength and not its stiffness.

The joint that has to keep turning

A beam on partial-strength joints collapses at 8(Mp + Mj)/L² however stiff the joints are. Stiffness decides only which yields first, and a joint that yields first has to go on rotating at full moment until the span catches up. A weak joint on a stiff connection has the most turning to do — more than a rigid full-strength one.

connections · Joint classification

Named alongside it

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

Connection designContinuityEnd plateJoint classificationRotational stiffnessSemi-rigidDuctilityJoint stiffnessMoment distributionMoment redistributionOptimisationRedistribution

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