Structural Engineering & Statics
where the load goes
Concept

Engesser — where it appears

Engesser's formula for a member flexible in shear: its buckling load's reciprocal is the sum of the reciprocals of the Euler load and the shear stiffness. It is exact for some shear models and one of two competing answers for others, such as laminated rubber bearings.

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

A built-up column has a second way to bend. A 12 m column of two chords 300 mm apart, joined by double lacing. On the left it buckles the way a solid column does, by bending; on the right the chords stay straight and the lattice racks, which a solid column cannot do at all. Neither happens alone, and the two flexibilities add rather than the two stiffnesses — so the critical load is 1287 kN against an Euler load of 1341 kN, which is 96% of it, and the column behaves as though its slenderness were 80 rather than 79.

The column made of two columns

A solid column buckles when its bending stiffness runs out. A laced one has a second way to go — the lattice shears, the chords stay straight — and the two flexibilities add rather than the two stiffnesses. A battened column reaches 23% of its own Euler load and behaves as though its slenderness were twice what it is.

stability · Built-up column Two formulas that agree until the shear is soft. The buckling load over the Euler load, by Engesser (dashed) and Haringx (solid), against the shear stiffness over the Euler load on a logarithmic scale. Marked: double lacing, 23.48: Engesser 0.959, Haringx 0.961; battens, 0.30: Engesser 0.232, Haringx 0.419; rubber bearing, 6.6e-4: Engesser 0.001, Haringx 0.025. They agree within 5 per cent while the shear stiffness is more than about 4 times the Euler load, and for a shear stiffness a thousandth of it Haringx's is 31 times Engesser's.

The bearing Engesser says has buckled

A member that is flexible in shear buckles below its Euler load, and there are two classical formulas for how far below. For a laced column they agree to a fraction of a per cent. For a battened column one gives nearly twice the other. For a laminated rubber bearing, Engesser's says it buckles at a fourteenth of the load it carries every day and Haringx's says it is safe by a factor of nearly three. They are not two theories. Put the axial load into Engesser's shear stiffness and it becomes Haringx's, exactly — so the whole disagreement is about which shear stiffness was measured.

stability · Built-up column

Named alongside it

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

BucklingBuilt-up columnEuler loadSeries combinationShear stiffnessBase isolationBattenChordCritical loadEffective slendernessLacingRadius of gyration

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