Snow on a Cheap Roof: A Load Bound by Climate and Density, and a Rafter Sizing Rule That Follows From It

Roof failures under snow are usually described after the event as the result of an exceptional winter. This study shows that, for the light timber roofs commonly built on sheds, workshops, and low-cost houses, many failures are contained in the arithmetic of an ordinary winter in the wrong climate class. Snow pressure is computed as density times depth for five stated climate classes, from 0.88 kN/m² for a mild lowland roof (0.45 m of settled snow at 200 kg/m³) to 9.81 kN/m² for a high-mountain roof (2.00 m of ice-crusted layered snow at 500 kg/m³), with a stated drift multiplier of 1.8 where a roof steps down, raising the worst case to 17.66 kN/m². Simply supported timber rafters spanning 4.0 m are then checked in bending, shear, and deflection against stated allowable stresses. The smallest sections that pass at 0.40 m spacing form a sizing ladder: 45×145 mm for the mildest class, 45×195 mm for the cold continental class, 45×245 mm for the maritime class, 75×245 mm for the mountain class, and 75×295 mm for the high-mountain class. The drifted worst case passes on no section examined at a 4.0 m span; at a 3.0 m span a 75×295 mm rafter at 0.40 m spacing carries it. Common cheap construction fails outright: a 45×145 mm rafter at 0.60 m spacing already fails the mildest class in bending (9.72 MPa against an allowable 8.0 MPa), a 45×95 mm rafter at 0.60 m spacing reaches 22.38 MPa under the mildest class, and a 38×89 mm rafter at 0.90 m spacing reaches 44.79 MPa — more than five times the allowable stress — under the mildest class examined. Snow load is governed at least as much by density as by depth: 0.30 m of ice-crusted snow loads a roof as heavily as 1.47 kN/m², the same as about 0.75 m of settled snow. A builder who knows the climate class and the pack density can size the rafter from the ladder given here; a builder who copies a roof from a milder climate imports its failure load along with its dimensions.