The blind-check duel

Two checkers solve the same beam. Checker A uses closed-form equations; checker B builds and solves its own stiffness matrix. Neither sees the other’s answer. Change the beam and compare their results, then plant an error in A and watch the comparison flag it.

Set the problem

All loads act downward. Self-weight is included only if you add it to w. Supports are idealised. This is a deterministic demonstration of independent checking.

The answers, side by side

A Equations B 60 elements

Maximum absolute values along the beam
Quantity	Checker A	Checker B	Agreement

Disagreement = |A − B| / max(|A|, |B|) × 100; zero against zero = 0%. Agreement = 100% − disagreement. A disagreement of 2% or more is flagged for investigation.

Agreement tests consistency, not the adequacy of a real structure.

One page to validate

Illustrative S355 elastic bending screen

Assumptions that travel with the answer

Straight, prismatic beam; linear elastic Euler–Bernoulli theory; small deflection; constant E and I; no shear deformation or axial effects. Ideal pins/rollers/fixity; continuous full-span UDL and one point load.
Major-axis bending; E = 210,000 N/mm²; assumed f_y = 355 N/mm² and assumed γ_M0 = 1.00 for this educational elastic screen. Listed flanges are below 16 mm thick. Loads are entered directly, with no load factors or combinations applied.
M_el = W_elf_y/γ_M0 assumes an effective elastic section and full lateral restraint. No section classification, local or lateral-torsional buckling, shear resistance/interaction, connections, bearing, vibration, fire or serviceability limit check. This is not a code-compliant design or approval and does not establish Irish National Annex compliance.
Deflection is reported for the same entered loads, without a pass/fail limit. Large deflections invalidate the small-deflection assumption. A chartered engineer must establish the model, loads and applicable checks for real work.

Properties: Steel for Life / SCI Blue Book, Steel material properties, Textbook verification cases

The section properties used

Published rounded major-axis values, used exactly as listed. 1 cm⁴ = 10⁴ mm⁴; 1 cm³ = 10³ mm³.

UB designation	I (cm⁴)	W_el (cm³)	Flange (mm)
203 × 133 × 25	2,340	230	7.8
254 × 146 × 31	4,410	351	8.6
305 × 165 × 40	8,500	560	10.2