Structural Engineering & Statics
where the load goes
Concept

Tie — where it appears

A member carrying tension, provided to close a force that would otherwise have to be delivered to a support. An arch's tie carries the whole thrust, its stiffness decides how much thrust the arch develops, and whatever thrust is lost to its stretching arrives as bending in the rib.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

200 kN200 kNthe chord — and the line of action1.20 mbending moment = P × offsetpeak 240 kNmbending stress is 24.0 times the axial stress at the worst section

The member with only one direction

If a body is in equilibrium under forces applied at exactly two points, those forces are equal, opposite and along the line joining the points. It is three conclusions from two equations, it is the shortest real theorem in statics, and nearly everything on this site depends on it without saying so.

equilibrium · two force member 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 load on the top chordthe same load, hung from the soffit600 kN in the hangernothing in the same memberchord forces identical to machine precision · hanger steel 1200 mm², shear steel 96 mm² over the same length

The load that has to be lifted

Every shear calculation on this site assumes the load arrives on the top of the beam and walks down a diagonal to the support. Hang the same load from the soffit and the diagonal cannot start — the load has to be carried up to the compression zone first, by a tie no sectional calculation contains.

internal-forces · indirect support

Named alongside it

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

EquilibriumFree bodyFunicularArchAxial shorteningBending momentCompatibilityCompression strutDeckDetailingEccentricityFlexibility

All concepts