VC-13 — EC5 Rectangular Timber Beam vs Published Worked Example

Module: vernastruct.codes.ec5.check_rect_timber_beam_ec5 Code basis: EN 1995-1-1 — rectangular sawn-timber beam: ULS bending + shear (τ = 1.5V/A), SLS deflection including shear deformation (A_v = A/1.2) and the quasi-permanent creep combination w_fin = w_inst,G·(1+k_def) + w_inst,Q·(1+ψ₂·k_def). Cross-check source (task 2.2): published worked example — Structville, "Structural Design of Timber Beams (EN 1995-1-1)", 2020: 75 × 200 mm C24 floor beam, service class 2. https://structville.com/2020/04/structural-design-of-timber-beams.html Status: ✅ PASS — all published values reproduced within the source's own rounding (≤ 0.3 %); deflections agree to 0.06 %.

1. Why this case matters

VC-10/VC-12 verified the EC5 engine against our own hand calculations. Task 2.2 requires cross-checks against independently published examples — this is the first, and it deliberately exercises two things our round-joist path simplifies away:

Shear deformation in the deflection (standard UK/Irish EC5 practice for solid timber; the published example includes it).
The ψ₂ quasi-permanent creep combination for w_fin (the round-joist engine conservatively applies k_def to the full load).

The rectangular function also gives the product its first sawn-timber EC5 capability (not yet GUI-wired — engine + verification first).

2. Published inputs

Input	Value
Section	75 × 200 mm (breadth × depth)
Design span	2.85 m (2.75 m clear + 100 mm bearings)
Permanent	1.30 kN/m UDL + self-weight (420 kg/m³ → 0.0618 kN/m) + 1.0 kN point at mid-span
Variable	1.50 kN/m UDL
Class	C24 to EN 338:2003 — f_m,k = 24, f_v,k = 2.5 MPa, E_0,mean = 11 GPa, G_mean = 0.69 GPa
Service class	2, medium-term → k_mod = 0.80, k_def = 0.80
γ_M	1.30; k_h = 1.0 (h = 200 ≥ 150 mm); ψ₂ = 0.3
Limits	w_inst ≤ L/300 = 9.5 mm; w_fin ≤ L/150 = 19 mm

(Note the source uses the 2003-edition C24 shear strength f_v,k = 2.5 MPa; EN 338:2016 gives 4.0. Characteristic strengths are explicit inputs to our function, so the cross-check uses the source's values.)

3. Published results vs software

Quantity	Published	VernaStruct	Diff
M_d	5.122 kN·m	5.1129	−0.18 % *
σ_m,d	10.244 MPa	10.2258	−0.18 % *
f_m,d	14.77 MPa	14.7692	−0.01 %
V_d	6.52 kN	6.5010	−0.29 % *
τ_d	0.652 MPa	0.6501	−0.29 % *
f_v,d	1.54 MPa	1.5385	−0.10 %
w_inst	5.765 mm	5.7662	+0.02 %
w_fin	8.963 mm	8.9683	+0.06 %

* The source rounds its total factored UDL to 4.1 kN/m before computing M_d/V_d; our value keeps full precision (w_d = 4.0884 kN/m). The deflection agreement (0.02–0.06 %) is the sharper test: it confirms bending + shear deformation terms and the ψ₂ combination independently.

Pinned as tests/test_codes.py::test_vc13_rect_ec5_matches_published_example (plus companions: shear-deformation toggle, k_h below 150 mm depth).

4. Notes

The published deflection figures can only be reproduced by including shear deformation — a bending-only calculation gives 5.35 mm, not 5.765. This is documented behaviour: pass G_mean_GPa=0 to omit it.
w_fin here uses the proper EN 1990 quasi-permanent combination; the round joist engine's w_fin = w_inst(1+k_def) remains a conservative simplification (heritage earth roofs are dead-load dominated), stated in VC-10.