Structural Engineering & Statics
where the load goes
Concept

Constraint — where it appears

A condition that removes a degree of freedom, imposed by a support, a connection or a compatibility requirement rather than by a load. Constraints decide how many equations a structure's analysis has and whether statics alone can solve it.

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

The same steel, brittle in January. Fracture toughness against temperature for a 25 mm ferritic plate, from Wallin's master curve — 30 + 70·exp(0.019(T − T₀)) in MPa√m, whose shape is the same for every ferritic steel and whose only free parameter is the reference temperature T₀ = -60 °C. Beside it, and on its own scale, is the crack length that toughness will tolerate at 200 N/mm², which goes as the square of it. At +20 °C this plate carries a 764 mm flaw and at -20 °C it carries 199 mm — a factor of 3.8 for a forty-degree change in the weather, in a steel that met its specification on both days. Thickness moves the curve as well, and the wrong way: constraint at a crack tip suppresses the yielding that would have blunted it, so a 100 mm plate of this steel tolerates 27% of the flaw a 10 mm plate does. Loading it in a millisecond shifts the whole curve another forty degrees.

The same steel, brittle in January

Every other material property in this collection is a number. Toughness is a curve, and the axis it runs along is temperature. Between twenty degrees and minus twenty a structural steel does not get gradually weaker — it changes the mechanism by which it fails, and the flaw it will tolerate falls by a factor of four.

materials · Transition temperature The crack length at which the strength stops mattering. Failure stress against crack length for a toughness of 100 MPa√m, with three steel grades drawn. The falling curve is fracture — Kc divided by Y times the root of pi a — and it does not know what the yield stress is. The horizontal lines are the grades. At 275 N/mm² the two cross at a crack 33.5 mm long; At 355 N/mm² the two cross at a crack 20.1 mm long; At 460 N/mm² the two cross at a crack 12.0 mm long. The stronger grade's transition is the shorter one — raising the yield stress does not raise the strength of a cracked member, it only shortens the crack that takes it away. At a working stress of 120 N/mm² the critical crack is 176.0 mm.

Designed to be found in time

A fatigue design that promises a detail will not crack is making a claim about a hundred years of traffic. A damage-tolerant one assumes it will crack, and sets the inspection interval from how long a crack takes to grow from the smallest size anybody can find to the largest the section can survive.

materials · Fatigue The weakest weld is not the one straight across. The ultimate strength of a member of 6082-T6 (parent ultimate 310 N/mm², zone 185) whose heat-affected zone crosses it at every angle from along the load (0) to straight across it (90 degrees), as load over the gross section. Across the load the zone's neighbours stop it contracting, and it carries 214 N/mm², 15 per cent above its own uniaxial 185. At 54.7 degrees, the angle a free sheet necks along, they give it nothing and the member carries 185. Below 24.2 degrees the zone's own neck would need more than a section through the parent can carry, and the member reaches 278 — the strength it has with the zone, 25 per cent of the section, running along it. At 30 degrees, 237; at 70, 196.

The weld that is weakest at fifty-five degrees

A soft heat-affected zone that the load crosses fails by necking along its own line, and it can do that only if nothing along the line has to stretch. Straight across the load, the parent on either side stops the zone contracting and lends it 15 per cent. At 54.7 degrees — the angle a free sheet necks along — it lends nothing, and the member carries the zone's own strength. Below 24 degrees the zone cannot neck alone at all, and a weld running along the member costs a tenth of its strength while adding to its stretch.

materials · Heat-affected zone What a 60-degree seam leaves of the wall. The combinations of axial stress σa and hoop stress σh that a tube of 6082-T6 (parent ultimate 310 N/mm², softened zone 185) carries, with its seam at 60° to the axis (solid), inside the parent wall's von Mises ellipse (dashed). Where the solid line falls inside the ellipse the seam's zone fails first. axial tension: 60 per cent of the parent; closed pressure: 78 per cent of the parent; hoop alone: 76 per cent of the parent. The seam is weakest, at 60 per cent, along the loadings whose unstretched line lies on it.

The seam that pressure protects

A soft weld zone pulled at 55 degrees to the load gets no help from the metal around it, because 55 degrees is the line a plate under uniaxial tension does not stretch. A spiral-welded tube winds its seam at about that angle. Pressurise the tube and the line that does not stretch moves to the tube's own axis, so the spiral seam is suddenly well protected and the longitudinal seam is the exposed one. The soft zone's weakness belongs to the loading as much as to the weld: a seam is in danger only where the field around it leaves its line unstretched.

materials · Heat-affected zone

Named alongside it

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

Crack growthDuctilityFatigueHeat-affected zoneNeckingTransition temperatureVon misesWeldYield criterionAluminiumBiaxial stressBrittle failure

All concepts