Bracing
The count that does not see it
A frame can have exactly as many unknowns as equations and fold up anyway. The count asks whether there are enough equations; it never asks whether they are different from one another.
The ends decide the length that matters
Four columns of identical height and section, buckling at loads sixteen times apart. Nothing differs but what is holding the two ends.
The brace that need not be strong
A brace holding a column at mid-height carries almost no force. What it has to be is stiff — and the stiffness required is exact, large, and reached at a knee past which more buys nothing at all.
Named alongside it
The objects these essays reach for when they reach for this one.
Buckled mode shapeEffective lengthCritical formCritical loadEigenvalueEnd restraintEquilibrium matrixImperfectionIndependent equationsLateral restraintMechanismRank deficiency