Structural Engineering & Statics
where the load goes
Series

Lateral-torsional — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The length at which a beam stops being a beam. Elastic critical moment against the distance between lateral restraints, with the section's plastic capacity drawn across it. The two cross at 3803 — beyond that length the beam buckles sideways before it reaches the strength its cross-section has, and the capacity is set by the restraints rather than by the steel.

    The beam that fails sideways

    A deep narrow beam bending in its strong plane can, at a moment well below its capacity, swing out of that plane and twist. The failure has nothing to do with how much it can carry and everything to do with what is holding it.

    part 1 · stability
  2. The same steel, divided unequally, and the moment either way. The critical moment under uniform moment, on a span of 8.0 m, against the top flange's width, out of 450 mm in all, with the top flange in compression and in tension. At equal flanges both are 534 kN·m. With a top flange of 300 mm they are 1,018 and 283 kN·m, a factor of 3.6.

    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.

    part 2 · stability

All series