Bifurcation — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
The column that was never straight
Euler's load is the load at which a perfectly straight column becomes indifferent to being bent. No column is perfectly straight, so no column ever reaches it — and the load it never reaches can still be measured.
The roof that jumps
Every stability failure in this collection so far has been a bifurcation — a straight thing discovering it can be bent. A shallow frame does something else entirely. It stays perfectly symmetric, deforms steadily, and at some point the load it can carry starts to fall while it is still moving in the direction it was pushed.
A third of what the theory promised
A column with a small crookedness reaches almost its full Euler load. A cylinder with the same relative crookedness reaches a third of its classical one, and the theory is not wrong — what separates them is the slope of the path just past the critical load, which no calculation of the critical load itself can see.
Named alongside it
The objects these essays reach for when they reach for this one.
BucklingEquilibrium pathStabilityAmplification factorCritical loadEuler bucklingGeometric nonlinearityImperfectionImperfection sensitivityKnockdown factorLimit pointPost buckling