========================================================================================== Zomes PU dome — STRUCTURAL SANITY CHECK ========================================================================================== This is a SANITY CHECK, not a stamped engineering review. It uses conservative hand-calc envelopes and lab-measured material values to detect gross under-design. A licensed PE must sign off before construction. Building ------------------------------------------------------------------------------------------ Footprint diameter (avg) : 6.69 m Height : 3.97 m Footprint area : 35.2 m^2 Panel count (structural) : 94 Base-ring panels : 11 Panel thickness : 76.2 mm (3.00 in) Total panel area : 75.0 m^2 Total foam volume : 5.71 m^3 Total foam dead weight : 13.44 kN (3023 lbf) Unique panel shapes: # count edge mm acute deg short diag long diag area m^2 1 11 1011.2 80.37 1305.0 1545.0 1.0081 2 12 1004.2 77.40 1255.7 1567.4 0.9841 3 20 1017.1 63.75 1074.2 1727.4 0.9278 4 11 1019.2 57.15 975.0 1790.1 0.8727 5 12 1002.7 52.49 886.8 1798.7 0.7975 6 11 862.5 52.77 766.6 1545.3 0.5923 7 4 703.0 81.15 914.5 1067.9 0.4883 8 1 808.9 45.77 629.1 1490.5 0.4688 9 12 1004.6 26.50 460.5 1955.7 0.4503 Material ------------------------------------------------------------------------------------------ Zomes PU foam (240 kg/m^3 rigid, ASTM-tested) density : 240 kg/m^3 E (worst dir) : 70.8 MPa poisson : 0.30 ULTIMATE -- compression (worst): 2.47 MPa ULTIMATE -- bending (worst) : 2.17 MPa ULTIMATE -- parent shear : 0.584 MPa ULTIMATE -- joint shear : 0.410 MPa ULTIMATE -- joint tension : 0.270 MPa Safety factors : {'compression': 2.5, 'tension': 2.5, 'shear': 2.5, 'bending': 2.5, 'buckling': 3.0, 'joint': 2.5} ALLOWABLE compression (worst) : 0.988 MPa ALLOWABLE bending (worst) : 0.868 MPa ALLOWABLE joint shear : 164.0 kPa ALLOWABLE joint tension : 108.0 kPa Site & code-prescribed loads ------------------------------------------------------------------------------------------ Site: severe US envelope V (3-s gust) : 160 mph (71.5 m/s) Exposure : D Ground snow p_g : 100 psf (4788 Pa) Mean roof height : 3.97 m q_z @ roof : 3232 Pa Flat roof snow p_f : 3352 Pa C&C suction (worst) : -8984 Pa C&C inward (worst) : 5429 Pa Panel dead load : 179 Pa Load cases (signed; +=inward): D = +179 Pa (Dead only (panel self weight)) D + L = +1137 Pa (Dead + roof live) D + S (balanced snow) = +3531 Pa (Dead + balanced snow at crown) D + S_unb (peak) = +6883 Pa (Dead + unbalanced snow on leeward 30-deg band) D + W_inward = +5609 Pa (Dead + worst inward wind (windward panel)) 0.6 D + W_uplift = -8877 Pa (Reduced dead + worst wind suction (uplift)) D + 0.75 (S + 0.6 W_inward) = +5136 Pa (Combined gravity case) 1.2 D + 1.6 S = +5578 Pa (Strength factored gravity) 0.9 D + 1.0 W_uplift = -8823 Pa (Strength factored uplift) Sanity-check results ------------------------------------------------------------------------------------------ [PLATE BENDING] [FAIL] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 1.10 demand= 0.9555 MPa capacity= 0.868 MPa load case='0.6 D + W_uplift' [FAIL] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 1.09 demand= 0.9497 MPa capacity= 0.868 MPa load case='0.9 D + 1.0 W_uplift' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.85 demand= 0.7408 MPa capacity= 0.868 MPa load case='D + S_unb (peak)' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.70 demand= 0.6037 MPa capacity= 0.868 MPa load case='D + W_inward' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.69 demand= 0.6004 MPa capacity= 0.868 MPa load case='1.2 D + 1.6 S' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.64 demand= 0.5528 MPa capacity= 0.868 MPa load case='D + 0.75 (S + 0.6 W_inward)' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.44 demand= 0.3801 MPa capacity= 0.868 MPa load case='D + S (balanced snow)' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.14 demand= 0.1224 MPa capacity= 0.868 MPa load case='D + L' [PASS] Panel plate bending (worst panel, diags=1305x1545 mm) D/C = 0.02 demand= 0.0193 MPa capacity= 0.868 MPa load case='D' WORST in 'plate bending': D/C = 1.10 (FAIL) [JOINT TENSION] [PASS] Joint TENSION (peeling) edge=1011 mm D/C = 0.27 demand= 0.02903 MPa capacity= 0.108 MPa load case='0.6 D + W_uplift' [PASS] Joint TENSION (peeling) edge=1011 mm D/C = 0.27 demand= 0.02886 MPa capacity= 0.108 MPa load case='0.9 D + 1.0 W_uplift' WORST in 'joint tension': D/C = 0.27 (PASS) [JOINT SHEAR] [PASS] Joint SHEAR (in-plane) edge=1011 mm D/C = 0.18 demand= 0.02903 MPa capacity= 0.164 MPa load case='0.6 D + W_uplift' [PASS] Joint SHEAR (in-plane) edge=1011 mm D/C = 0.18 demand= 0.02886 MPa capacity= 0.164 MPa load case='0.9 D + 1.0 W_uplift' WORST in 'joint shear': D/C = 0.18 (PASS) [COMPRESSION] [PASS] Base-ring axial compression (11 panels share 131.3 kN) D/C = 0.21 demand= 0.2031 MPa capacity= 0.988 MPa load case='D + S (cumulative)' WORST in 'compression': D/C = 0.21 (PASS) [BUCKLING] [PASS] Panel local buckling (simply-supported plate) D/C = 0.70 demand= 0.2031 MPa capacity= 0.2909 MPa load case='D + S' WORST in 'buckling': D/C = 0.70 (PASS) [SHELL BUCKLING] [PASS] Global shell snap-through (R=3.39 m) D/C = 0.23 demand= 3352 Pa capacity=1.439e+04 Pa load case='D + S' WORST in 'shell buckling': D/C = 0.23 (PASS) [BEARING] [PASS] Foundation bearing (footprint 35.2 m^2) D/C = 0.04 demand= 3.734 kPa capacity= 100 kPa load case='D + S' WORST in 'bearing': D/C = 0.04 (PASS) ========================================================================================== OVERALL: FAILS one or more checks ========================================================================================== Notes & out-of-scope items ------------------------------------------------------------------------------------------ - Creep at sustained dead+snow load NOT modelled (PU foam creeps). - Cyclic wind fatigue NOT modelled. - Thermal & UV degradation of joints NOT modelled. - Door / window cut-outs NOT modelled (panels with cutouts will have higher stress concentrations than the rhombic-plate envelope here). - The non-structural exterior fibre cement shell is excluded by request. - Snow drift on dome saddles between adjacent zomes (not applicable here) is NOT considered.