Structural Engineering & Statics
where the load goes
Concept

Sag ratio — where it appears

3 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
cable: pure tensionreflected herearch: pure compression

The shape that carries itself, and the arch that is its reflection

Hang a chain and it takes the one shape that carries its load in pure tension. Turn the shape upside down and it carries the same load in pure compression. That is what an arch is.

structures · funicular 10148126H = 27.9, the same at every stationeach vertex is a load; each slope is the running vertical sum ÷ H

The polygon that finds the shape

A hanging string under five loads has no smooth curve in it — it has five vertices and six straight segments, and every slope in it is a running sum divided by one number.

structures · funicular 00.20.40.60.811.2020406080100120140160midspan sag (m)total load on the cable (kN)the design load, 150 kNsolved 0.740 m1.125 mtangent here 341.2 kN/mk₀ = 8T₀/L = 133.3 kN/mthe flat-cable law

The stiffness that comes from the shape

A cable has no bending stiffness whatever, and it still holds up a roof. What resists the load is the change of its own geometry, so its stiffness is a function of the tension already in it — and prestress buys stiffness that no change of material could.

structures · cable stiffness

Named alongside it

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

FunicularHorizontal thrustForm findingThrust lineCable netCatenaryCompatibilityFunicular polygonGeometric stiffnessPole diagramPrestressSelf weight

All concepts