Bound theorems — where it appears
Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.
What is left after the first fibre yields
The elastic section modulus stops at the moment the outermost fibre reaches yield. Nothing else in the section has, so it goes on taking load — and how much more it takes turns out to be a property of the shape alone, with no dimension, no stress and no material anywhere in the answer.
The point the mechanism turns about
A collapsing frame is a chain of rigid pieces, and every piece is rotating about some point. Find those points and the whole collapse load reads off two ratios of lengths, with no trigonometry anywhere — and for a pitched roof the point in question is well above the top of the drawing.
The smallest of six failures
Everything else in this collection that fails does so in one way at a time. A dowel through timber does not — the wood can crush while the steel stays straight, or one plastic hinge can form in it, or two — and the capacity is the smallest of the six, which is the kinematic theorem of plasticity applied to a joint rather than to a frame.
Named alongside it
The objects these essays reach for when they reach for this one.
Plastic hingeCollapse loadDuctilityFree bodyAnisotropyBearingConnection designDeterminacyDowel yieldEmbedment strengthEqual area axisEquilibrium