Structural Engineering & Statics
where the load goes
Concept

Yield criterion — where it appears

The rule deciding when a combination of stresses ends elastic behaviour, which for a ductile metal is about distortion rather than about tension. For a ductile metal it depends on the deviatoric stress alone, so hydrostatic pressure of any size causes no yielding at all — which is the reason confinement works.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

0102030405060708090020406080100120140160angle between the weld and the load, degreescapacity, kN0° · 116.83 kN45° · 127.98 kN90° · 143.09 kN×1.22along

The weld that is stronger across than along

The same fillet weld, the same size, the same steel, carries twenty-two per cent more when the load runs across it than along it. The factor is exactly the square root of three over the square root of two, and it comes out of the yield criterion rather than out of a test.

connections · weld strength στthe x faceσ₁ = 153.2σ₂ = -13.2τ max 83.2the plane turns by 16.4°, the circle by 32.7°von Mises 160.2 N/mm²

The worst stress is not where the worst bending is

Every stress this collection has quoted is a stress on a particular plane, and neither the bending stress nor the shear stress is a property of the point. Turn the plane and both change; one pair of numbers does not, and on a short beam it peaks where neither of them does.

sections · principal stress 00.20.40.60.810%20%40%60%80%100%shear, as a fraction of the web's capacitymoment capacity leftthe sectionthe web alone√(1 − v²)96.5%85.3%web 26.1% of the plastic modulus · M_pl 744 kNm · V_pl 959 kN

Both at once, and neither matters until it does

A section carrying shear has less moment capacity, and the reduction is the web's share of the plastic modulus times one minus the root of one minus the shear ratio squared. On a rolled beam that share is a quarter, so half the shear capacity costs three and a half per cent — and then the last tenth costs more than the first eight.

sections · shear moment interaction -1-0.50.51-1-0.50.51σ₁ ÷ f_yσ₂ ÷ f_yvon MisesTrescapure shearthe widest gap is 2/√3 = 1.1547, at pure shear

The shear strength nobody measured

Every web on this site 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 0102030405060strength (N/mm²)mean 30characteristic 23.2design 15.5one specimen in 155,818 falls below the design value

The strength no specimen had

A material property is written into a calculation as a number, and a material does not have one. It has a population of strengths with a mean and a spread, and the number used is a low fractile of that population — a value that need not have been measured, that most of the material exceeds, and whose distance below the mean is decided entirely by the scatter.

materials · characteristic strength

Named alongside it

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

Von misesDuctilityBending stressFlangePrincipal stressShear stressCharacteristic strengthCoefficient of variationConfinementConnectionContinuous beamDeviatoric stress

All concepts