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 3 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 A bigger top column attracts more moment, and only the joint stops it. The top storey of the edge column of a braced six-storey frame — 4 m storeys, a 254 UC 89 below the splice and a 203 UC 60 above — carrying a 9 m beam at every floor on partial-strength joints of 261 kN·m, with each of seven columns that might be chosen for it: the moment its floor's edge joint delivers at the design load of 60 kN/m (dark) and at the beams' collapse load (light), against what the column can carry at its top end, its plastic moment reduced for the axial force (line). 203×203 UC 46: 148 and 195 against 167; 203×203 UC 60: 171 and 225 against 230; 203×203 UC 71: 189 and 247 against 283; 203×203 UC 86: 205 and 261 against 347; 254×254 UC 73: 218 and 261 against 352; 254×254 UC 89: 232 and 261 against 435; 254×254 UC 107: 243 and 261 against 527. A stiffer column attracts more of the joint's moment until the joint's 261 kN·m caps it; the lightest column that carries what it attracts at collapse is the 203 × 203 UC 60.

The column on the other side of the joint

A partial-strength joint is sold as a fuse: it caps the moment a beam can put into its support at the joint's own resistance. At an interior column that is true. At the edge of a frame the column is not a support that stays still; it is a spring in series with the joint, so the joint delivers less than its resistance in service and almost exactly what a rigid joint would. The column then carries three times the moment the simple-construction rule gave it, and at the top storey, where it stands alone and is lightest, it is weaker than the joint it was meant to be protected by.

connections · Joint classification

Named alongside it

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

ContinuityJoint classificationRotational stiffnessSemi-rigidConnection designEnd plateDuctilityInteractionJoint stiffnessMoment distributionMoment redistributionOptimisation

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