Structural Engineering & Statics
where the load goes
Concept

Cable — where it appears

A member that carries load in tension only, taking the funicular shape of whatever it is holding. Its stiffness comes from its geometry rather than from its material, so a slack cable is not a soft spring but very nearly no spring at all.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

The windward guy tightens, the leeward one gives way. A 120 m mast on three guy levels, at a wind of 3 N/mm, with the deflection drawn 0.54 times its true size. The guys start at 160 kN each and end at 259 against 95, 299 against 83, 221 against 112 kN. The leeward guys still carry a real force — the lowest keeps 28 per cent of its partner's tension — and supply almost none of the restraint, because their tangent modulus has fallen to 54 per cent of the steel's. The mast top moves 100 mm, its worst bending moment is 554 kNm at 40 m, and it is carrying 801 kN of axial load that nothing but the guys put there.

Held by something that goes soft

A guy is a cable, so it has no stiffness of its own — what resists a mast's movement is the guy's geometry changing, and how much of that there is depends on the tension already in it. Wind pushes the mast towards the leeward guy, which is the one losing tension.

structures · Guyed mast Three ways to move the same column, and they are not close. The same 2000 kN moved 3 m across 14 m, built three ways and drawn to one scale. The deep beam is 1.14 m of concrete, 24.1 tonnes, and settles 60.6 mm in the long term. The storey-deep truss takes the same moment as a couple at 3.6 m centres, so its chords carry M/h and it weighs 2.6 tonnes — a fifth of the beam — while settling 15.8 mm, and it does not creep. The wall is 72.8 tonnes and hardly moves at all, 1.71 mm, of which 36% is shear rather than bending — which is what a member as deep as it is long always does, and is why beam theory does not describe one. A wall as a deep beam is the stiffest of the three by a factor of 35.4.

The same span, four ways

A beam, a truss, an arch and a cable can all cross the same gap under the same load, and the choice between them is usually described as a matter of judgement or of taste. It is neither. Each carries the load by a different mechanism, each mechanism has a different exponent, and an exponent decides the ordering at every span rather than at some spans.

structures · Form selection The tendon is a load, pointing the other way. A 14 m beam with a parabolic tendon dropping 260 mm to midspan, stressed to 1440 kN after losses. Its curvature pushes the beam up along its whole length with an intensity of 8Pe/L² = 15.28 kN/m, against an applied 17.63 kN/m — so 2.34 kN/m is left to bend anything, and the beam carries 57.4 kNm where an unstressed one carries 432 kNm. What the section then feels is 6.40 MPa of uniform compression and very little else.

The load that comes from changing direction

A force that travels in a straight line asks nothing of anything. Bend its path and it asks for a transverse load of F over R along every millimetre of the curve, and that load is real, is nowhere on the load schedule, and is the same statement behind a prestressing tendon, a hoop force, an arch thrust and a web that buckles with nothing applied to it.

internal-forces · Deviation force Two curvatures of opposite sign, which is what makes it a structure. A cable net over a 36 m square, drawn as the two families of cables that are also the two rulings of the surface. One family sags and carries downward load by hanging; the other rises and carries upward load — wind uplift, and a load reversal anywhere — by the same mechanism upside down. Neither can do anything alone. A single family of cables is a mechanism: it changes shape freely under any load pattern it was not tensioned for, and the shape it moves to is decided by the load rather than by the designer. Put the two together and each is the other's restraint, but only if they are pulled against one another first — the pretension of 520 kN in the sagging family and 715 in the hogging one is a self-equilibrating state that exists with no load on the roof at all, and it is what turns two mechanisms into one structure. The curvatures are drawn four times their true value: a real net of this span sags 2.2 m over 36, which is flatter than it looks anywhere.

Two curvatures of opposite sign

A single family of cables is not a structure. It is a mechanism that takes whatever shape the load asks for, and it will do that under any load pattern it was not tensioned for. Cross it with a second family curved the other way, pull the two against each other, and the pair becomes stiff — with no bending anywhere and no material property involved in the stiffness at all.

structures · Cable net A hanger that would push is a hanger that is not there. The force in each hanger of a tied arch of 100 m span and 17 m rise on 32 crossed hangers, carrying 60 kN/m of dead load over the span and 120 kN/m of live load over its left half, against the hanger's position along the tie. Solved as though every hanger could push (pale bars), 4 come out in compression, the worst at 185 kN. Solved with those hangers taken out until no remaining one is compressed (dark bars), 8 are slack — more than the linear solution has in compression, because each hanger that goes passes its share to its neighbours and some of them follow.

The deck that keeps the hangers in the truss

Crossing the hangers of a tied arch turns it from a frame that bends into a truss that does not, as long as every hanger is pulling. A hanger cannot push, and under a load on half the span some of them would have to. Solved as it really is — with those hangers taken out, and the ones that follow them — the arch keeps the linear answer exactly until the live load on half its span is about equal to its own dead weight, and past that the tie's moment doubles and then quadruples. The arch's own weight is the pretension nobody had to apply, and a heavier deck is a stiffer network.

structures · Network arch

Named alongside it

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

FunicularLoad pathMembrane actionGeometric stiffnessNonlinearityPrestressPretensionShell actionSlackAnchorAnticlasticArch

All concepts