Structural Engineering & Statics
where the load goes
Concept

Hanger — where it appears

A member that carries load upward from a deck to a structure above it, and which can only pull. Its inability to push is what decides the arrangement of any system that relies on it: a hanger whose computed force turns negative has gone slack and taken its triangle out of the structure.

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

Also named here as tied arch — the same set of essays touches all of them, so they are one junction rather than several.

The tie is a redundancy, so its stiffness decides the thrust. Thrust and rib bending for a 60 m tied arch of 0.15 rise ratio, against the stiffness of its tie. Cut the tie and the structure is a curved simply supported beam, so the tie force is the one redundant and the force method gives it: with a rigid tie the answer is 2229 kN, within 0.9 per cent of the funicular wL²/8f, and the shortfall is the arch's own axial shortening. A real tie stretches 68 mm and returns 2168 kN — 2.7 per cent of the flexibility is the tie — and whatever thrust the arch does not get, it carries as bending: 739 kNm at 30 m. A tenth of the tie stiffness is not a tenth of the problem; it is a different structure.

The thrust that never reaches the ground

Every arch on this site has ended at the same sentence — the foundation is where an arch is really decided. A tie changes the sentence without changing the arithmetic: the horizontal force is still there, still the same size, and it now closes on itself through a bar at deck level.

structures · Tied arch Cross the hangers and the chords stop bending. The same tied arch, the same twelve hangers, the same load on half the span — hung vertically and hung as a network. Vertical hangers make the two chords a Vierendeel frame, which has no truss action at all, so a partial load is carried by bending: 14827 kNm in the tie and 24213 in the arch. Inclined hangers can carry the shear between the chords axially, and the same load gives 5852 and 7484 — factors of 2.5 and 3.2. The thrust is identical in both, because that is decided by the span and the rise and nothing else.

Cross the hangers and the bending goes

A tied arch with vertical hangers is a Vierendeel frame with a curved top chord — it has no truss action at all, so a load on half the span is carried by bending. Incline the hangers so they cross and the same two chords become a truss.

structures · Network arch

Named alongside it

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

Load arrangementThrustTied archArchAxial shorteningBending momentCompatibilityDeckFlexibilityForce methodFunicularRedundancy

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