VC-10 — Round Timber Beam per Eurocode 5 (EN 1995-1-1)

Module: vernastruct.codes.ec5.check_round_timber_beam_ec5 Code basis: EN 1995-1-1 — limit-state design: f_d = k_mod·k_h·f_k/γ_M vs stresses from ULS loads (EN 1990 combination 1.35G + 1.5Q); SLS deflections w_inst (L/300) and w_fin = w_inst·(1 + k_def) (L/250). First Eurocode check in the code-profile abstraction (task 2.1). Status: ✅ PASS — software matches hand calculation exactly.

1. Problem statement

A round timber joist assessed to the Eurocode profile — the same physical member type as VC-01, but in the European limit-state format.

Input	Symbol	Value
Diameter	d	200 mm
Span	L	3.50 m
Permanent load	g_k	1.00 kN/m
Variable load	q_k	0.50 kN/m
Characteristic bending strength	f_m,k	16.0 MPa (C16-class)
Characteristic shear strength	f_v,k	1.8 MPa
Mean modulus	E_mean	8.0 GPa
Characteristic density	ρ_k	310 kg/m³
Service class	—	2 (sheltered exterior — heritage typical)
Load-duration class	—	medium (imposed floor/roof load)
Partial factor	γ_M	1.30 (solid timber)
Confidence factor	CF	1.00 (KL3; a KL2 variant is also verified)

2. Hand calculation

ULS actions (1.35G + 1.5Q):

w_d = 1.35 × 1.00 + 1.5 × 0.50 = 2.1000 kN/m
M_d = w_d L²/8 = 2.10 × 3.5²/8  = 3.215625 kN·m
V_d = w_d L/2                    = 3.675 kN

Design stresses (W = πd³/32 = 7.854×10⁻⁴ m³, A = 3.1416×10⁻² m²):

σ_m,d = M_d/W        = 4.0943 MPa
τ_d   = 4V_d/(3·k_cr·A) = 0.2328 MPa   (k_cr = 0.67, EN 1995-1-1 §6.1.7)

Design strengths (k_mod = 0.80 SC2/medium; k_h = 1.0 since d ≥ 150 mm):

f_m,d = 0.80 × 1.0 × 16.0/1.30 = 9.84615 MPa   → util 0.41582
f_v,d = 0.80 × 1.8/1.30        = 1.10769 MPa   → util 0.14081

SLS (characteristic combination g_k + q_k = 1.5 kN/m; I = 7.854×10⁻⁵ m⁴):

w_inst = 5wL⁴/(384·E·I) = 4.6647 mm ≤ L/300 = 11.6667 mm  → util 0.39983
w_fin  = w_inst(1 + k_def) = 4.6647 × 1.8 = 8.3964 mm
       ≤ L/250 = 14.0 mm                                   → util 0.59975 ← governs

KL2 variant (CF = 1.20): f_m,d = 9.84615/1.20 = 8.20513 MPa → util_bending = 0.41582 × 1.20 = 0.49899.

3. Results comparison

Quantity	Hand calc	Software	Match
w_d / M_d / V_d	2.1000 / 3.215625 / 3.675	same	✅ exact
σ_m,d / τ_d	4.0943 / 0.2328 MPa	same	✅ exact
f_m,d / f_v,d	9.84615 / 1.10769 MPa	same	✅ exact
w_inst / w_fin	4.6647 / 8.3964 mm	same	✅ exact
Governing utilisation	0.59975 (w_fin)	0.59975	✅ exact
KL2: f_m,d	8.20513 MPa	8.20513	✅ exact

Final (creep) deflection governs — same engineering conclusion as the NDS path (VC-05), reached through the Eurocode k_def formalism. A good cross-format sanity signal.

Documented conventions: characteristic strengths are explicit inputs (from an EN 338 class or from testing of existing members — VernaStruct does not guess a class); w_fin uses the full characteristic load with k_def (simplified, conservative for dead-load-dominated earth roofs); CF divides characteristic strengths per EN 1998-3 §3.3.

4. Reproducing this check

from vernastruct.codes import check_round_timber_beam_ec5
r = check_round_timber_beam_ec5(
    d_mm=200.0, span_m=3.5, w_dead_kN_m=1.0, w_live_kN_m=0.5,
    f_m_k_MPa=16.0, f_v_k_MPa=1.8, E_mean_GPa=8.0, rho_k_kg_m3=310.0,
    service_class=2, load_duration="medium",
)
assert r.ok and abs(r.utilization_max - 0.59975) < 1e-4

Pinned in tests/test_codes.py (test_vc10_*, four tests covering ULS, strengths, SLS, and the CF variant).

Amendment (2026-07-14, after VC-15)

The VC-15 published cross-check (Swedish Wood Vol. 3) caught that this check originally omitted the EN 1995-1-1 §6.1.7 (A1:2008) crack factor k_cr = 0.67 on the shear width — shear utilisation was understated by 1/0.67. τ_d is now computed on A_ef = k_cr·A (parameter, default 0.67, pass 1.0 to disable) and the hand-calc values above were updated. Bending, strengths and deflections are unchanged.