Structural Engineering & Statics
where the load goes
Concept

Fabrication tolerance — where it appears

The permitted departure of a manufactured part from its drawn dimensions, such as a member's length or a hole's position. In a truss each millimetre of length error reaches a joint multiplied by that member's unit-load force, so small tolerances decide a camber.

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

A weld is a force, and it is applied where the weld is. The bow a welded girder leaves the shop with, against how far its welds sit from the section's centroid. A weld cannot contract while the plate holds it, so it yields in tension and what is left when everything is cold is a locked-in force at about the yield stress: 312 kN for the 1.2 kJ/mm of heat drawn, over a shrinkage zone of 439 mm². Applied 210 mm off the centroid that is a moment, and a moment applied along a member is a curvature: the 12 m girder comes out bowed 12.5 mm, which is L/962 against a fabrication tolerance of L/1000. It also comes out 1.2 mm shorter. Welding symmetrically about the centroid puts the resultant on the neutral axis and the bow becomes 0.00 mm — the same heat, the same force, and no moment at all.

The shape that came out of the shop

A weld cools by seven hundred degrees while the plate holds it, so it yields in tension and stays that way. What is left is a locked-in force of three hundred kilonewtons applied where the weld is, and if that is not on the centroid the member leaves the shop bent.

connections · Weld distortion What a millimetre on each member does at mid-span. A Pratt truss of eight panels, 24.0 m long and 2.4 m deep, carrying 60 kN of dead load at each top node, drawn with its depth exaggerated. Each member is drawn as thick as, and labelled with, the distance mid-span moves for a millimetre's change in that member's length: its force under a unit load at mid-span. The middle top-chord members move it 2.50 mm per mm — the span over four depths — and the chord members fall off towards the supports: 1.25, 1.88, 2.50, 2.50, 1.88, 1.25 along the top chord. The diagonals move it 0.80 per mm and most verticals 0.50; three verticals — the one at mid-span and the two beside the supports — carry nothing under a load at mid-span and move it not at all (dashed). A truss's shape is its members' lengths, weighted like this.

The camber that lives in the member lengths

A beam is cambered by bending it; a truss cannot be, because it has no curvature to bend — its shape is nothing but the lengths of its members. So a truss's camber is a cutting list, and each millimetre on that list arrives at mid-span multiplied by the member's force under a unit load there: two and a half for the middle chords of a truss ten times as long as it is deep, nothing at all for some verticals. Build only the chords to their dead-load strain and a quarter of the sag stays, the webs' share. Cut every member to a millimetre of scatter and the mid-span misses by six, an eighth of the camber.

deflection · Camber

Named alongside it

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

CamberCurvatureDead loadEccentricityHeat inputImperfectionLack of fitResidual stressSecond-orderThermal gradientTruss deflectionUnit load method

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