Structural Engineering & Statics
where the load goes
Concept

Lack of fit — where it appears

A member made longer or shorter than the geometry it has to fit, forced into place during erection. A determinate structure simply changes shape to accept it; a redundant one resists it and carries forces before any load arrives, in proportion to its stiffness.

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

Five millimetres short, and a hundred kilonewtons in every member. An X-braced bay 6 m by 4 m in which one diagonal was fabricated 5 mm short, with the force that leaves in every member. Nothing is applied to this frame. The forces are the self-stress state the frame's one redundancy supports, scaled so that the diagonal is pulled back to the length it should have been: tension in both diagonals at 100 kN, compression in the four members round the outside, and the whole set in equilibrium with nothing. That is 25% of the force the diagonal was sized to carry, and it is there for the life of the structure. Take one diagonal out and the frame becomes determinate: the short member then simply puts the joint somewhere else, and the structure is in the wrong place instead of under stress. Redundancy is bought, and this is the price.

Built to the wrong length

A redundant structure's members do not have independent lengths. Choose all but one and geometry decides the last, so a member made a different length has to be pulled or pushed into place — and the force required stays in the structure for as long as the structure does. Nothing has been applied to it, there is no load case and no factor, and the members are carrying real force.

connections · Fit-up 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.

Bolt holeCamberCompatibilityDead loadErectionFabrication toleranceForce methodImposed deformationIndeterminacyPrestressRelaxationResidual stress

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