Structural Engineering & Statics
where the load goes
Concept

Rigid joint — where it appears

A beam-to-column connection that keeps the angle between the members unchanged as the frame deflects, so that moment passes fully from beam to column. Real joints rotate a little under moment; a standard calls one rigid when its stiffness is high enough for that rotation to be ignored.

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

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 What leaves the interior panel lands in the span. A frame of two 8 m bays and two 4 m storeys with fixed bases, 457 mm beams and 254 mm columns, with 20 kN/m on the left bay's beams only, against the stiffness of every beam-to-column joint as a multiple of the beam's EI/L, on a logarithmic scale. The shear across the floor interior joint's column-web panel (solid): 154 kN with rigid joints, 146 at EN 1993-1-8's rigid limit of 25 EI/L, 104 at 3.0 EI/L, 23 MN·m/rad, 63 at EI/L. The loaded beam's largest sagging moment (dashed), in kN·m: 71, 76, 102 and 126, against 160 for a simply supported span. The faint lines are EN 1993-1-8's boundaries for a frame that sways: nominally pinned below 0.5 EI/L, rigid above 25.

The panel a soft joint empties into the span

Under a load on one bay, an interior column's web panel carries the difference between the two beams' moments. Make the beam-to-column joints semi-rigid and the panel is relieved — by 5 per cent at the stiffness EN 1993-1-8 still calls rigid, by a third at three times the beam's EI/L — because a softer joint takes less moment. The moment it does not take lands at mid-span, where the beam was not designed for it, and in sway it lands in the columns. And soften only some of a frame's joints, and the sway goes looking for the ones still stiff: their panels carry up to a quarter more than they would in an all-rigid frame.

internal-forces · Corner moment

Named alongside it

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

Joint equilibriumPanel zonePattern loadingPortal frameSwayFlange coupleLoad combination

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