Structural Engineering & Statics
where the load goes
Concept

Network arch — where it appears

A tied arch whose hangers lean and cross each other several times instead of hanging vertically. The arch, the tie and the crossed hangers act as a truss, so a load on part of the span barely bends the tie, but the hangers carry the load's shear and their forces swing widely as traffic passes.

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

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 A crossed hanger swings through nearly all of its force. The largest and smallest force in each crossed hanger of a tied arch of 100 m span and 17 m rise on 32 hangers, with 60 kN/m of dead load and a live load of 60 kN/m running on from either end, each bar running from the one to the other. The worst range is 678 kN, from 49 to 727, in hanger 11; the largest force anywhere is 756 kN. 6 of the 32 go slack at some stage, and the worst range is 90% of the largest force anywhere: the live load's shear passes through the crossed hangers as through a truss's web, and swings them from nearly nothing to nearly their most.

The hangers that carry the shear twice

Crossing a tied arch's hangers turns them into the web of a truss, which is why the tie stops bending. It also means a live load's shear passes through them, so as a load runs on from either end each crossed hanger swings from nearly nothing to nearly its most: on a 100 m arch the worst swings through 678 kN, 90% of the largest force in any hanger, where a vertical hanger swings through 194, half of its own. More dead load raises the force and leaves the range alone. The arrangement that is best for strength is the one that hands its hangers to fatigue.

structures · Network arch

Named alongside it

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

Dead loadHangerCableFatigueInfluence lineLive loadLoad arrangementNonlinearityStress rangeTied archTruss

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