Add or replace a cross-section on an existing FERS model and optionally assign it to members. Takes the model JSON, mutates model.sections (and model.materials when a new preset is introduced), returns the model.

THREE WAYS TO DEFINE IT:

1. LIBRARY — shape:"library" with library_name (or just name) set to a library profile — European IPE/HEA/HEB/HEM/UPE/RHS/SHS/CHS/L or UK UB/UC/PFC, e.g. "IPE300", "HEB240", "CHS 114.3x5", "RHS 100x50x5", "UB 457x191x67". This is the ONLY way to get exact rolled-profile properties (root fillets included) and it carries every EC3 modulus. Prefer it whenever a standard profile fits.

2. PARAMETRIC — shape:"rect" (h_mm, b_mm), "circle" (d_mm), "chs" (d_mm, t_mm), "rhs"/"shs"/"box" (h_mm, b_mm, t_mm) or "i" (h_mm, b_mm, tf_mm, tw_mm), dimensions in MILLIMETRES. rect/circle/chs are exact and rhs area+inertias are exact (its Bredt torsion J is ~2% low), but the "i" generator assumes SHARP fillets: against a real rolled IPE300 it is 3.6% low on area, 4.3% low on i_z and 22% low on J. Use "i" for WELDED plate girders, not for rolled profiles.

3. CUSTOM — shape:"custom" with your own SI numbers. area, i_y, i_z and j are all MANDATORY and strictly positive; a missing one is a hard parse error and a MISTYPED one is silently ignored (Section has no deny_unknown_fields), giving a wrong answer that still solves.

AXIS CONVENTION: local z is the STRONG axis. For depth h and width b, i_z = b·h³/12 (strong, resists gravity on a horizontal member) and i_y = h·b³/12 (weak). Getting these the wrong way round is the most common authoring error and the solver cannot detect it.

EC3 CHECKS NEED MORE THAN STIFFNESS. An Ec3Steel check on a section lacking wel_y/wpl_y/i_w does not fail — it returns utilization 0.0, status Green and an explanatory message, which reads as a clean pass. So also give wel_y, wel_z, wpl_y, wpl_z and i_w (warping constant, m⁶); the parametric shapes compute these for you. Optionally add ec3 {"section_class":1,"buckling_curve_y":"B","buckling_curve_z":"C","buckling_curve_lt":"B"} — curves A0/A/B/C/D (alpha 0.13/0.21/0.34/0.49/0.76); omitting the block silently uses curve b. Unlike the rest of the section, the ec3 block DOES reject unknown keys, so a typo there is a hard solve-time error.

ASSIGNMENT: apply_to "all" reassigns every member, a JSON array of member ids reassigns those, a classification string reassigns every member in that group. A section whose name already exists is overwritten IN PLACE, keeping its id and all existing member references.