Structural Engineering & Statics
where the load goes
Concept

Plasticity — where it appears

Deformation that stays after the load is removed, which in steel begins at yield and in a member lets moment redistribute once a section has yielded. It is what plastic design relies on, and what makes a notch's strain grow faster than its stress.

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

One criterion inside the other, touching at six points. The two yield criteria in principal stress space with the third principal stress zero, both normalised by the yield stress. Von Mises is the ellipse — σ₁² − σ₁σ₂ + σ₂² = f_y², which is a circle seen at an angle — and Tresca is the hexagon inscribed in it, touching at the six points where one principal stress is zero or the two are equal. Everywhere else Tresca is the smaller, by up to 15.5 per cent, and the widest gap is at pure shear, where σ₁ = −σ₂ and the two answers are 205 and 178 N/mm². The ratio there is exactly 2/√3, computed rather than quoted, and it is the whole reason a web is checked against f_y over root three.

The shear strength nobody measured

Every steel web in a design check is checked against the yield stress divided by the square root of three, and no test produced that number. It is a consequence of a decision about what makes a metal yield, and the alternative decision gives a different answer by fifteen per cent.

materials · Yield criterion The forging is a pad nobody designed. For a 2.0 t tup at 7.0 m/s, 49 kJ, on the 150 t foundation with its 30 t anvil on a pad: the largest force through the anvil's pad (solid) against the forging's flow force (logarithmic), with the dies meeting at the right; dashed, the pad force if the same impulse arrived all at once, as a fixed-impulse calculation takes it. Through a forging flowing at 0.1 MN the pad carries 0.15 MN, against 3.70 for the same impulse delivered at once; at 1.5 MN, 2.32 against 3.93; with the dies meeting, 5.86 against 5.93.

The forging that cushions the blow

A forge hammer's foundation is usually designed for a blow treated as a fixed impulse: the tup's momentum, multiplied by a factor for its rebound. The blow is not fixed. Between the tup and the anvil lies a hot forging, a plastic body that flows under the tup, stretches the blow to 48 milliseconds and absorbs nearly all of its 49 kJ, so that the anvil's pad feels 0.46 MN. As the part cools it flows less, the blow shortens, the tup rebounds, and the pad force climbs to 5.86 MN when the dies meet with nothing between them. The foundation is designed by the blow that does no work.

dynamics · Vibration isolation

Named alongside it

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

ConfinementDeviatoric stressDuctilityEnergy absorptionEquivalent stressFoundationHydrostatic stressImpulseInteraction diagramMohr circlePrincipal stressRestitution

All concepts