Structural Engineering & Statics
where the load goes
Concept

Joint equilibrium — where it appears

The requirement that the forces and moments every member applies to a joint sum to nothing, the joint being a free body in its own right. Written for a rigid joint it gives the panel shear that no member diagram shows.

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

The section, once the joint has supplied the fourth equation. Everything above a cut through panel 3. Four severed members; three equations. Moments about the mid-joint of the horizontal remove both diagonals and leave both legs. Moments about the point where the legs' lines meet, 36.0 m up, remove both legs and leave both diagonals. With the joint's result that the diagonals are equal and opposite, that second equation has one unknown: 20.83 kN in each diagonal. The legs follow: 26.1 T and 86.3 C.

The cut that needs a joint first

The method of sections works because a cut through three members leaves three unknowns and a point about which two of them have no moment. A K-braced tower has no such cut anywhere: every section severs two legs and two diagonals. One joint in the middle of a horizontal supplies the missing equation, and only in that order does each step have one unknown — after which the diagonals turn out to be carrying not the shear but the moment about the point where the legs would meet.

equilibrium · Method of sections The interior panel is designed by the case that designs nothing else. The shear across the column-web panel at each kind of joint of a frame of two 8 m bays and two 4 m storeys with fixed bases, 457 mm beams and 254 mm columns with 8.6 mm webs, under five load cases, the worse direction of sway taken where there is one. Full gravity: roof corner 106, roof interior 0, floor exterior 143, floor interior 0 kN; One bay loaded: roof corner 115, roof interior 117, floor exterior 150, floor interior 154 kN; Sway: roof corner 25, roof interior 40, floor exterior 53, floor interior 89 kN; Gravity + sway: roof corner 131, roof interior 40, floor exterior 196, floor interior 89 kN; Pattern + sway: roof corner 141, roof interior 157, floor exterior 203, floor interior 242 kN. The floor interior panel is empty under full gravity and carries 89 kN under gravity with sway, the case that governs the members; under one bay loaded with sway it carries 242 kN — 2.7 times as much, more than any exterior panel's 203 kN, and 70 per cent of the web's shear resistance.

The panel that gravity leaves empty

A corner joint's panel carries the difference between a beam's flange couple and half a column's shear, and full gravity load is what makes that large. An interior joint has a beam on each side, and under full gravity their two couples cancel: the panel between them carries nothing at all, in the load case that sizes every member around it. It fills under the two loads that are not symmetric. A pattern load hands it one beam's moment, and sway hands it two beams' moments turning the same way. Together they put more shear through it than through any exterior joint, in a combination that governs no member.

internal-forces · Corner moment

Named alongside it

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

Bending momentDeterminacyEquilibriumFlange coupleFree bodyLattice towerLoad combinationMethod of sectionsMoment centrePanel zonePattern loadingPortal frame

All concepts