VC-11 — Masonry Wall Vertical Resistance per Eurocode 6 (EN 1996-1-1)

Module: vernastruct.codes.ec6.check_masonry_wall_ec6 Code basis: EN 1996-1-1 §6.1.2 (N_Rd = Φ·t·f_d), §5.5.1.1 (e_init = h_ef/450), §6.1.2.2 (e ≥ 0.05·t; Φ_i = 1 − 2e/t), Annex G (Φ_m with the actual stiffness ratio f_k/E), γ_M = 2.20; EN 1998-3 CF on f_k. Status: ✅ PASS — software matches hand calculation exactly.

1. Problem statement

An unreinforced masonry bearing wall assessed to the Eurocode profile.

Input	Symbol	Value
Thickness	t	0.30 m
Height (ρ_n = 1.0)	h_ef	2.70 m
Permanent vertical load	G_k	50 kN/m
Variable vertical load	Q_k	15 kN/m
Load eccentricity at top	e_load	5 mm
Characteristic strength	f_k	2.0 MPa (soft stone / lime-brick class)
Stiffness	E	1000·f_k (EN 1996 default)
Partial factor	γ_M	2.20

2. Hand calculation

Design action: N_Ed = 1.35×50 + 1.5×15 = 90.0 kN/m

Slenderness: h_ef/t_ef = 2.70/0.30 = 9.0 ≤ 27 ✓

Eccentricities: e_init = 2700/450 = 6.0 mm → e = 5 + 6 = 11 mm < 0.05t = 15 mm (floor governs) at both locations.

Top/bottom: Φ_i = 1 − 2×15/300 = 0.90

Mid-height (Annex G):

λ_t = 9.0 × √(f_k/E) = 9.0 × 0.0316228 = 0.284605
u   = (0.284605 − 0.063)/(0.73 − 1.17×0.05) = 0.221605/0.6715 = 0.330015
Φ_m = (1 − 2×0.05) · e^(−u²/2) = 0.90 × 0.947001 = 0.85230   ← governs

Resistance: f_d = 2.0/2.2 = 0.909091 MPa

N_Rd = Φ·t·f_d = 0.85230 × 0.30 × 909.091 = 232.446 kN/m
util = 90.0/232.446 = 0.38719 → PASS

3. The heritage nuance — real adobe stiffness

For an adobe wall (t = 0.55, h = 3.0, f_k = 0.5 MPa, minimum eccentricity):

Stiffness assumption	λ_t	Φ_m
EN default E = 1000·f_k	0.1725	0.88812
Measured adobe E = 100 MPa (E/f_k = 200)	0.3857	0.80186

The common European default overstates adobe capacity by ~10% — the module therefore takes the measured E and warns whenever the default is used. This is precisely the correction a heritage assessment needs.

4. Results comparison

Quantity	Hand calc	Software	Match
N_Ed	90.0 kN/m	90.0	✅ exact
e_i = e_mk (floor)	15.0 mm	15.0	✅ exact
Φ_i / Φ_m	0.90 / 0.85230	same	✅ exact
N_Rd	232.446 kN/m	232.446	✅ exact
Utilisation	0.38719	0.38719	✅ exact
Adobe Φ_m (real E / default E)	0.80186 / 0.88812	same	✅ exact
KL2 variant	N_Rd/1.20, Φ unchanged	same	✅ exact

Documented conventions: vertical resistance only (in-plane shear and out-of-plane bending stay on the existing generic/SBC path until the profile switch lands); creep eccentricity e_k = 0 with a warning above λ = 15; CF divides f_k for strength while Annex G keeps the unreduced f_k/E (stiffness is an estimate, not a strength).

5. Reproducing this check

from vernastruct.codes import check_masonry_wall_ec6
r = check_masonry_wall_ec6(
    t_m=0.30, h_m=2.7, N_dead_kN_m=50.0, N_live_kN_m=15.0,
    f_k_MPa=2.0, e_load_mm=5.0,
)
assert r.ok and abs(r.util_vertical - 0.38719) < 1e-4

Pinned in tests/test_codes.py (test_vc11_*, three tests + slenderness/moment behaviour).