Structural Engineering & Statics
where the load goes
Concept

Moment frame — where it appears

A frame that resists sideways load by bending its beams and columns through stiff joints rather than by bracing or walls. It sways by racking, its storeys shearing like a stack of parallelograms, and its beams and joints are what limit how far.

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

One drift, two motions, opposite curvatures. The sideways movement of a 120 m building under a uniform wind, drawn as the sum of the two mechanisms that produce it. The bending curve is a cantilever's: flat at the base, steepening upward, concave one way. The racking curve is a stack of parallelograms: steepest at the base and flattening, concave the other. They add to 366 mm at the roof, of which 61% is bending. The one group that decides the split is αH = H√(GA/EI) = 2.48: below one the racking dominates and the building behaves as a frame, above about six the bending does and it behaves as a cantilever, and everything interesting is in between.

Two motions with one name

A tall building's sway is two movements added. A frame racks like a stack of parallelograms, worst at the bottom; a cantilever bends about its base, worst at the top. The total at roof level says nothing about which storey is worst, and on this building it is neither.

deflection · Drift components The column line's sum agrees with every analysis, because it cannot see the beams. The roof sway of a 4-bay, 10-storey concrete frame, 8 m bays and 3.5 m storeys, 600 mm columns and 400 × 700 mm beams, 40 kN/m on every beam and 40 kN of wind at every floor, against the beams' stiffness as a share of their gross value, from the whole frame (line) and from the windward column line's integral of the moments that analysis gives it (dots). At the gross stiffness, 15.7 mm; at 0.5, 25.4; at 0.35, the usual allowance for cracked beams, 33.3; at 0.2, 52.0. The windward column's base moment moves from 126 to 235 kN·m, and the line's integral follows the sway exactly at every one.

The check that cannot see the beams

The unit load that finds a frame's sway may be carried on any structure that can carry it, and in a frame of four bays and ten storeys it can be carried down one line of columns alone. Then the roof sway is that line's real moments against the unit load's, a few dozen products by hand — exact for the frame as drawn, for its beams cracked to a third of their stiffness, for its joints made springs and for its bases made springs, the last only once the bases' rotation is given its own term. It is exact because the unit load never enters a beam. Which makes it a check on the analysis's arithmetic that cannot say anything about the analysis's beams.

deflection · Virtual work

Named alongside it

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

DriftBending stiffnessCantilever actionCladdingCompatibilityDeflected shapeIndeterminacyLateral systemRackingReleased structureSecond-orderServiceability

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