Structural Engineering & Statics
where the load goes
Concept

Thrust — where it appears

The compressive force running along an arch, whose horizontal component is constant when the shape is the funicular of the load. It is wL squared over 8f for a parabolic arch under a uniform load, and what receives it - a foundation or a tie - is usually what decides the form.

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

first · antisymmetric · C 49.7second · symmetric · C 117.1dashed is the rib before it moved · drawn hugely exaggerated

The arch that leans instead of squashing

A masonry arch is asked whether a line of thrust fits inside it. A steel rib is asked a different question entirely: it is a column carrying an axial force along its whole length, and the mode it buckles in puts one half up and the other half down while the crown moves sideways.

stability · arch buckling 0.10×0.32×3×10×00.20.40.60.81tie stiffness, relative to the one drawnthrust ÷ its rigid-tie value, and bending ÷ its worstthrustbending, to 7422 kNmas built: 2168 kN, tie stretches 68 mmfunicular wL²/8f = 2250 kN · rigid tie 2229 · the difference is the rib's own shortening

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

Named alongside it

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

ArchAntisymmetric modeAxial shorteningBending momentBracingBucklingCompatibilityCritical loadDeckEffective lengthEigenvalueFlexibility

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