Structural Engineering & Statics
where the load goes
Concept

Hoop force — where it appears

The membrane force running round a shell or a pipe, carrying whatever component of pressure the circumferential curvature can take. For a cylinder it is pR and there is nothing along the length; for a sphere the two directions share the pressure equally at pR/2 each.

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

0102030405060-60-40-20020angle from the crown (degrees)membrane force (kN/m)N_θ = 0 at 51.8273°meridional N_φ-60.0 kN/mhoop N_θ15.0 kN/mcompression abovetension below

The surface that carries by being curved

A flat plate spends its thickness on a lever arm of a few millimetres. Curve the same sheet and the load is carried in the surface itself, at a thirtieth of the thickness — and the entire bill is presented at the edges.

structures · shell action 18 kN/m18 kN/mN = 9.3 kN/m1190 Pa121 mm of water60 mtotal uplift 3365 kNworst membrane force when the snow melts

Held up by the air inside

A membrane has no bending stiffness at all, so the only thing that can hold it in tension is a pressure difference. The pressure needed to hold up a roof is smaller than the pressure a closed door makes — and the same pressure arrives at the foundation as hundreds of tonnes of uplift.

structures · pneumatic structure

Named alongside it

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

FunicularMembrane actionAnchorageBoundaryCable netCompatibilityCurvatureEquilibriumFree bodyHorizontal thrustLoad pathPneumatic structure

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