Structural Engineering & Statics
where the load goes
Concept

Monosymmetric — where it appears

A cross-section with one axis of symmetry, such as a tee or an I-section with unequal flanges. Its shear centre is not at its centroid, so its lateral-torsional buckling moment depends on which flange is in compression, through a term that a doubly symmetric section does not have.

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

The hole in the web pulls the axis down after it. The effective section of a 1,500 × 8 mm web between 400 mm flanges 15.0 mm thick at the top and 25.0 mm at the bottom, in S355, bending with its top in compression, and the elastic stress on it. The top flange's outstands are slender and keep 91% of their width. The web is compressed over 959 mm of its depth and keeps 44% of that, as two strips next to the flange and the neutral axis, leaving a hole of 538 mm. The neutral axis sits 566 mm above the bottom, against 665 mm for the gross section, and the section keeps 78% of its gross elastic modulus: 9.91 × 10⁶ mm³ against 12.76.

The flange a slender web wants heavier

A girder's gross section is strongest with its flange steel shared equally, top and bottom. Its effective section is not, because a slender web loses the middle of whatever part of it is compressed, and moving steel into the compression flange raises the neutral axis and shortens that part. Forty millimetres of flange on a 1,500 by 8 mm web is best split 22 on top and 18 below, and split the other way round — 15 on top and 25 below, the shape of a composite girder's steel before its slab hardens — it keeps 70% of what the best split carries.

sections · Effective cross-section 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.

stability · Lateral-torsional

Named alongside it

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

Composite actionCritical momentEffective widthLateral-torsional bucklingLocal bucklingNeutral axisPlate bucklingPlate girderSection modulusShear centreSlendernessWagner effect

All concepts