Beam Deflection — validation & limitations

What it calculates

• Deflection, bending moment and shear for 6 closed-form load cases (EN 1993-1-1 / Euler-Bernoulli)
• One governing verdict folding bending (§6.2.5), shear (§6.2.6) and serviceability deflection (§7.2)
• Selectable deflection limit — L/200, L/250, L/300, L/360 or L/500 per your National Annex
• Bending and shear stress with safety factors for solid, hollow, rectangular and I-section cross-sections
• Natural frequency of the first three vibration modes (SS, cantilever, fixed-fixed) with a Rayleigh added-mass correction
• Fatigue safety factor using the Goodman criterion for cyclic loading, with a mean-stress-corrected Basquin S-N life
• Two-span continuous beam analysis via the 3-moment (Clapeyron) equation with bending moment diagram
• Section efficiency comparison — second moment of area for equal-weight cross-sections
• Combined loading superposition (simultaneous point load + UDL)

Standards this tool applies

• EN 1993-1-1 — Closed-form Euler-Bernoulli deflection, bending stress and yield safety factor for six load cases against a selectable deflection limit (not an EN 1993-1-1 member check), plus Goodman fatigue and natural frequency.
• EN 1993-1-8 — Closed-form Euler-Bernoulli beam analysis for the structural members framing into EN 1993-1-8 weld connections — deflection, moment, shear and fatigue safety factor.

Validation evidence — independent reference cases (1)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• I-section bending, web shear and deflection for three load cases

  Conservative

  Source: Gere & Goodno, Mechanics of Materials, Ch. 12 / App. E and §5.5, §5.10; Roark 8e Table 8.1 cases 1a, 1d, 2e; EN 1993-1-1 §6.2.6(2) and Table 5.2

  Inputs: IPE 300 plates h 300, b 150, tf 10.7, tw 7.1 mm, S235, E 210 GPa; cantilever 20 kN/2 m, fixed-fixed 150 kN/4 m, SS UDL 20 N/mm over 6 m

  Quantity	Reference value	Tolerance
  I	79 989 869.5 mm4	1e-6 relative
  Bending SF, cantilever (A)	3.1329	1e-6 relative
  Bending SF, fixed-fixed (B)	1.6709 (CHECK)	1e-6 relative
  Deflection ratio, SS UDL (C)	1.00459 (SLS FAIL)	1e-6 relative

  Conservative simplification: The engine models the section with sharp corners (root radius r = 0), so its moment of inertia reads about 4 % below the published IPE 300 value that includes the fillets.

  tests/golden/REF-beams-i-section-uls-sls.golden.test.ts

Limitations

Conservative simplifications

• I-section bending, web shear and deflection for three load cases — The engine models the section with sharp corners (root radius r = 0), so its moment of inertia reads about 4 % below the published IPE 300 value that includes the fillets.

Not checked by this tool

• Lateral-torsional buckling (EN 1993-1-1 section 6.3.2) — Not checked here; check an unrestrained compression flange with /steel (I-sections) or /buckling
• Web shear buckling (EN 1993-1-5 section 5) — Not checked; for a slender web (h_w/t_w above 72 epsilon / eta) apply EN 1993-1-5 section 5
• Web patch loading under a concentrated load or reaction (EN 1993-1-5 section 6) — Add stiffeners or check the transverse-force resistance per EN 1993-1-5 section 6
• Class 4 effective section (EN 1993-1-5 section 4.4) — Bending of a Class 4 section is not proven; compute the effective section or choose a stockier section
• Axial force combined with bending — Bending only; check beam-columns with /steel (compression + bending) or /buckling
• Partial safety factors (limit-state format) — Characteristic values in and out; apply your own load factors and the material factor for an EN 1993 design
• End connections and support bearing — Size the connections with /bolts or /welds