Scale changes everything — page 8
Sections and stress
The section stronger for being cut
Take a square bar standing on its corner, and saw a ninth off its top and bottom tips. It has lost material from the places where material does most for bending, and its first-yield moment has gone up by 5.35 per cent. Nothing has gone wrong with the arithmetic. The bar's plastic moment has gone down in the same cut, and at every curvature the whole bar still carries more than the cut one. What the cut exposes is that a first-yield moment was never a measure of how much a section can hold. It is a measure of how far its furthest fibre stands out.
Stability
The beam that is a different beam upside down
Share the same flange steel unequally between the top and the bottom of a girder and it has two buckling moments, depending on which way the moment bends it: 1,018 kN·m one way up and 283 the other, where the equal-flanged beam from the same steel had 534 both ways. The term responsible was found by Herbert Wagner and is usually left out of beam formulas, on the grounds that most beams are symmetric. It has one simple physical reading. Every fibre leans as the section twists, and it matters whether the compressed ones are near the centre of twist or far from it.