VC-15 — EC5 Joist vs Swedish Wood Vol. 3 (Examples 3.1 + 7.1)

Module: vernastruct.codes.ec5.check_rect_timber_beam_ec5 Cross-check source (task 2.2): Design of timber structures — Volume 3: Examples, 3rd English edition 2022, Swedish Forest Industries Federation (Swedish Wood) — the official companion to the Eurocode 5 textbook used in European university courses; this edition uses original Eurocode values, no national annex. Free download: https://www.swedishwood.com/publications/list_of_swedish_woods_publications/design-of-timber-structures/ Examples used: 3.1 (straight timber joist, ULS bending + shear) and 7.1 (same joist, SLS instantaneous + final deflection). Status: ✅ PASS — and this case caught defect #5: our EC5 checks omitted the EN 1995-1-1 §6.1.7 crack factor k_cr (see §4).

1. Published inputs (both examples, same joist)

Input	Value
Section	45 × 220 mm, strength class C24 (f_m,k = 24, f_v,k = 4.0 MPa — EN 338:2016, E_0,mean = 11 GPa)
Span / spacing	4.5 m / 0.6 m
Ex 3.1 load	q_dim = 3.3 kN/m² already factored → q_d = 0.6 × 3.3 = 2.0 kN/m
Ex 7.1 loads	characteristic g_k = 0.5, q_k = 2.0 kN/m² (ψ₂ = 0.3)
Service class	1, medium-term → k_mod = 0.80, k_def = 0.60; γ_M = 1.3; k_h = 1.0
Shear	k_cr = 0.67 (§6.1.7): V_Rd = (2/3)·k_cr·A·f_v,d

2. Published results vs software — Example 3.1 (ULS)

Quantity	Published	VernaStruct	Note
f_m,d	14.8 MPa	14.769	pub rounds
M_Ed	5.1 kN·m	5.0625	pub uses rounded q_d
W required	345·10⁻⁶ m³	section W = 363·10⁻⁶ passes (σ 13.95 < 14.77)	h_req 214 → 220 chosen
V_Ed	4.5 kN	4.500	exact
f_v,d	2.46 MPa	2.4615	exact
V_Rd (with k_cr)	10.9 kN	util_shear = V_Ed/V_Rd matches to 5 s.f. (0.41342 vs 4.5/10.885 = 0.41341)	the k_cr check

3. Published results vs software — Example 7.1 (SLS)

Quantity	Published	VernaStruct	Note
I	39.93·10⁻⁶ m⁴	39.930·10⁻⁶	exact
w_inst,G	3.6 mm	3.6469	pub rounds
w_inst,Q	14.6 mm	14.5874	pub rounds
w_inst total	≈ ℓ/250 (18.2 mm)	18.234	✓
w_fin = w_G(1+k_def) + w_Q(1+ψ₂k_def)	≈ 22.8 mm (ℓ/200)	23.048	pub sums rounded intermediates (5.8 + 17)

The quasi-permanent creep combination implemented for VC-13 reproduces the Swedish Wood final-deflection method exactly (they present the identical formula, including the E_mean,fin = E/(1+k_def) equivalence).

4. Defect caught: missing k_cr (EN 1995-1-1 §6.1.7, A1:2008)

The published shear capacity V_Rd = (2/3)·k_cr·A·f_v,d uses the crack factor k_cr = 0.67 for solid timber — shear stress must be computed on an effective width b_ef = k_cr·b to account for drying cracks. Both our EC5 checks (round and rectangular) omitted it, understating shear utilisation by 1/0.67 ≈ 1.49×. This never flipped a verdict in our cases (roof-joist shear utilisations are ~0.1–0.4), but it is exactly the kind of unconservative gap the verification library exists to catch — the fifth real defect found this way.

Fix: k_cr parameter on both checks, default 0.67 (EN recommended value, NA-overridable; pass 1.0 to disable). VC-10 and VC-12 pinned shear values updated accordingly (τ_d now on A_ef = k_cr·A); VC-13 passes k_cr = 1.0 because its older UK source predates the amendment — the difference between those two published sources is itself documented here.

Pinned as tests/test_codes.py::test_vc15_uls_matches_swedish_wood_example_3_1 and ::test_vc15_sls_matches_swedish_wood_example_7_1.