Load a beam and its top is squeezed, its bottom stretched, its middle nearly idle in bending. The I-section is that sentence rolled in steel: two flanges far from the middle take the bending; a thin web holds them apart and carries the shear. Division of labour in cross-section — Adam Smith’s pin, split into “about eighteen distinct operations”, read as metaphor, not audit.

A beam’s bottom is in tension, where cast iron fails with little warning, so beams went to wrought iron, then steel. Rolled double-T irons were in use in France by 1845–46, Bertrand Lemoine documents, and carried a Paris floor by February 1849; on 1 March 1849 Alphonse Halbou of the Belgian Forges de la Providence patented an improved, lighter one. In 1901–02 Differdange, Luxembourg, first rolled Henry Grey’s wide, parallel-flanged beams in one piece.

Zurich was in the room. Karl Culmann, professor at the new Polytechnikum from 1855, replaced equations with drawn forces in Die graphische Statik (1866); on 6 June 1884 his student Maurice Koechlin sketched the 300 m tower Eiffel’s company would build, a sheet now in the ETH archives.

In 1881, after German architects’ and engineers’ associations and the VDI had fixed the profiles, Heinzerling and Intze published the Deutsches Normalprofil-Buch für Walzeisen, the IPN’s ancestor; IPE and HE became European standards in 1957 and 1962, all now in EN 10365. A named section is specified in one city, rolled in another, erected without redrawing. That was the speed: in July 1930, Engineering News-Record reported, “22 stories of steel were placed in 22 working days” at the Empire State Building.

PAZ’s reading, not a historian’s claim: the Industrial Revolution’s structural invention was not only a material or a shape but a table — and the table is what lets the future reuse the past, because a section with a name can be checked again by someone who never met the engineer who first specified it.

←TODAY: EN 10365 holds IPN, IPE and HE in one European norm.
→3012: Zurich lends its frames like library books, catalogued by section.
Fulcrum: A beam earns a second life only if its first one left a name.

Winterthur, unbolted

K.118 in Winterthur, by baubüro in situ (2021), stands mainly on about 60 t of IPE and HEA beams unbolted from a 15-year-old Coop distribution centre in Basel. Per SZS, the Swiss steel construction centre, reuse emitted 91% less CO2 than the recycled steel mostly used in Switzerland, and the extension cut construction emissions by about 60% against new build. SZS’s “Re-Use” guidance points to SIA 269/3 and SN EN 1090. Steel is 7–8% of global greenhouse-gas emissions, per worldsteel; a reuse checklist is climate policy that fits in a tender annex.

What the sketch checks

The ACTION sketch travelling with this post holds six families and 129 real sections, and paints stress cyan where squeezed, magenta where stretched. It never looks properties up: it walks each outline, recomputes them and compares with the catalogue — 387 checks, median deviation 0.05%, 385 within 1%. On the default job (IPE 300, 6 m, 20 kN/m), switch S235 to S460 and the sag holds at 19.62 mm, because E is 210,000 MPa for every structural steel. The “same steel, solid” bar is 34.6 times floppier. “Lightest that works” gives IPE 300 the kilograms (42.3 kg/m) and HEM 200 the depth (220 mm). Elastic, unfactored, no buckling, no torsion: it teaches a section and will never design your floor.

First lesson: a steady error is a convention you have not read. Measuring the tapered IPN flange mid-outstand inflated every area by about 1.25%; the catalogue measures at b/4 from the tip, and IPN 300 then lands on 69.00 cm² against 69.0. Second: the table can disagree with itself, printing channel radii rounded up to whole millimetres while computing from the exact ones.

Hack: Walk a section’s outline once and make it report its own area, centroid and stiffness. With P a closed, counter-clockwise outline of [x, y] points, run the sketch’s own Green’s-theorem loop:

let A = 0, Sy = 0, J = 0;
for (let i = 0; i < P.length; i++){ const [xa, ya] = P[i], [xb, yb] = P[(i+1) % P.length];
  const c = xa*yb - xb*ya; A += c; Sy += (ya+yb)*c; J += (ya*ya + ya*yb + yb*yb)*c; }
A /= 2; const cy = Sy/(6*A), Iy = J/12 - A*cy*cy;

For IPE 300 it returns 53.82 cm² and 8,358 cm⁴ against the table’s 53.8 and 8,356. Port it to GhPython and any closed Rhino curve becomes a checkable section.

Atelier: Teams asking an AI assistant for section properties get fluent numbers with no visible source; the catalogue is the source, and the machine answers to it. Monday move: add one component to your Grasshopper template that recomputes every catalogue section you use and flags any deviation above 1%.

From the late 2070s, my advice is small: named sections come back. Before the next demolition in your Gemeinde is tendered, ask for the section list of the frame coming down, then check one beam in the sketch yourself.