Structural Engineering & Statics
where the load goes
Concept

Force method — where it appears

A way of analysing an indeterminate structure by releasing its redundants and restoring compatibility with the forces that requires. Each redundant comes back as a ratio of two flexibility integrals, which makes visible which flexibility in the structure is deciding the answer.

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

real Mpeak 32.0a unit load, here and nowhere elseunit mM × marea ÷ EI = 213.33the unit load is the only place the question 'deflection where?' is asked

One deflection, without solving everything

To find how far one point of a structure moves, put an imaginary force of one unit there, multiply two moment diagrams together, and integrate. The answer arrives without ever solving for the deflected shape.

deflection · virtual work 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.

CompatibilityArchAxial shorteningBending momentDeckFlexibilityFunicularHangerLoad arrangementMoment diagramProduct integralRedundancy

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