VC-12 — Roof Joist Design through the Service, Eurocode Profile

Module: vernastruct.modules.roofs.service.RoofDesignService with code_profile="EC" (delegating to the VC-10-verified vernastruct.codes.ec5.check_round_timber_beam_ec5) Code basis: EN 1995-1-1 limit-state design of the secondary joists inside the full roof workflow: load takeoff (t/m² layers → kN/m line loads, dead/live kept separate for 1.35G + 1.5Q), smallest-passing-diameter selection, EN 338 characteristic strengths from the material library, EN 1998-3 confidence factor. Completes the roof half of roadmap task 2.1. Status: ✅ PASS — software matches hand calculation exactly.

1. Problem statement

A heritage roof re-joisted in imported pine, assessed to the Eurocode profile. This is the first case exercising the characteristic-strength data added to the timber library:

pine_imported → EN 338:2016 class C22 (f_m,k = 22 MPa, f_v,k = 3.8 MPa, E_0,mean = 10.0 GPa, ρ_k = 340 kg/m³ — values cross-checked against the Holzforschung Austria dataholz.eu datasheet, which reproduces EN 338:2016 Table 1; E_0,mean matches the library's existing mean E).
Heritage species (athel, date palm, acacia) have no EN 338 class; their characteristic values are derived from the allowable stresses via the ASTM D245 derivation factor (f_k ≈ 2.1 × F_allow, applied conservatively to shear too, whose true factor is 4.1) and any EC5 design in them is forced to knowledge level KL1 (CF = 1.35) — verified in the companion test.

Input	Symbol	Value
Dead load (roof layers)	D	0.25 t/m² (25 cm × 1000 kg/m³ fill)
Live load	L	150 kg/m² = 0.15 t/m²
Joist spacing	s	0.40 m
Joist span	ℓ	3.00 m
Timber self-weight	—	excluded (clean hand numbers)
Material	—	`pine_imported` = EN 338 C22
Service class	—	2 (moisture 12% ≤ 20%) → k_mod 0.80, k_def 0.80
Load duration	—	medium
Deflection limits	—	w_inst ≤ ℓ/360, w_fin ≤ ℓ/240 (GUI defaults)
Knowledge level	—	KL3 → CF 1.00

2. Hand calculation

Line loads (TON_TO_KN = 9.80665):

w_G = 0.25 × 0.40 × 9.80665 = 0.980665 kN/m
w_Q = 0.15 × 0.40 × 9.80665 = 0.588399 kN/m
w_d = 1.35 w_G + 1.5 w_Q    = 2.206496 kN/m

First standard diameter d = 150 mm:

W = π·0.15³/32 = 3.31340×10⁻⁴ m³      I = π·0.15⁴/64 = 2.48505×10⁻⁵ m⁴
A = π·0.075²   = 1.76715×10⁻² m²

M_d = w_d ℓ²/8 = 2.482308 kN·m         V_d = w_d ℓ/2 = 3.309744 kN
σ_m,d = M_d/W  = 7.4917 MPa
f_m,d = k_mod·k_h·f_m,k/γ_M = 0.80 × 1.0 × 22/1.3 = 13.5385 MPa   (k_h = 1.0, d ≥ 150)
util_bending = 0.5534 ✓

τ_d = 4V_d/(3·k_cr·A) = 0.37272 MPa   (k_cr = 0.67, §6.1.7 — added after VC-15)
f_v,d = 0.80 × 3.8/1.3 = 2.33846 MPa
util_shear = 0.1594 ✓

w_char = w_G + w_Q = 1.569064 kN/m  (unfactored, characteristic combination)
w_inst = 5·w·ℓ⁴/(384·E·I) = 5×1569.064×81/(384×10×10⁹×2.48505×10⁻⁵)
       = 6.6593 mm   vs ℓ/360 = 8.333 mm   → util 0.799 ✓
w_fin  = w_inst(1 + k_def) = 6.6593 × 1.8 = 11.9868 mm
       vs ℓ/240 = 12.500 mm                → util 0.9589 ✓  ← GOVERNS

Selection: d = 150 mm passes all four checks → chosen (smallest first). Governing utilization 0.959, final (creep) deflection.

Iteration variant (span 4.0 m, same loads): 150 mm fails w_inst (21.05 > 11.11 mm), 180 mm fails w_fin (18.27 > 16.67 mm), 200 mm passes → service must report candidates [150, 180, 200] and choose 200.

3. Software result

RoofDesignService().design(...) with code_profile="EC" reproduces every number above to the stated precision (tests/test_codes.py:: test_vc12_roof_service_ec5_matches_hand_calc and ::test_vc12_ec5_selection_iterates_diameters, pinned as regression tests). Companion tests verify: KL2 divides strength (not stiffness) by 1.20; derived-species designs are forced to CF = 1.35 with an explanatory warning; the default NDS profile is untouched; single-module PDF/Excel reports render the EN 1995-1-1 table.

4. Notes

The main beam intentionally stays on its existing path under the EC profile (AISC 360 LRFD for steel — itself a limit-state format; NDS ASD for bundled timber) and the report says so explicitly. EN 1993 steel is a Phase 2 open decision; a documented boundary beats a half-feature.
The EC5 engine itself (k_mod/k_def/k_h tables, formula-level checks) was verified in VC-10; this case verifies the integration: unit conversion of the load takeoff, dead/live separation, library characteristic data, selection loop, CF plumbing, and reporting.