Concept

Collapse load — where it appears

The load at which a structure becomes a mechanism, with enough plastic hinges to move without any further increase. It is the lowest over all mechanisms, and it exceeds the first-yield load by the shape factor on a simple member and by considerably more on a continuous one.

Named by 4 essays across 4 fields — each of them below, with the objects they name alongside it.

the centre200 kN80 kNλ = 1.339 · lowest over the hinge position 1.339 at 100% of the rafterthe centre sits 5.5 m above the ridge

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.

equilibrium · instantaneous centre
a12.12 kNb12.12 kNc5.02 kNd6.86 kNe6.86 kNf9.61 kNgoverning: mode c · 5.02 kN per shear plane

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.

connections · dowel yield
n = 20.138n = 30.367n = 40.689n = 51.102critical pressure in N/mm² · lowest is n = 2

The pressure that needs no direction

Every buckling problem in this collection has had a load with a direction — a column pushed along its axis, a plate along its edge, an arch by what is on it. A buried pipe has none. The pressure is the same everywhere, it stays normal to the wall as the wall moves, and it does work on any change of shape that reduces the area inside.

stability · ring buckling
10^-410^-210^2123456strain rate (per second)strength ÷ its static valuea testing machinean earthquakea vehicle impacta blastconcrete in tensionsteel, yieldsteel, ultimatethe modulus

The steel that is stronger in a millisecond

Every strength quoted anywhere in this collection was measured at about a ten-thousandth of a strain per second, because that is what a testing machine does, and nothing on a drawing says so. Load the same steel a million times faster and its yield stress rises by a third.

materials · strain rate

Named alongside it

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

Free bodyPlastic hingeBound theoremsDuctilityEquilibriumAnisotropyBearingBlastBuckling modeCapacity designConnection designCowper symonds

All concepts