Why steep roofs are better
Looking at snow on various roofs, I decided to settle a question that had puzzled me for a long time.
It's clear that steep roofs are better in snowy places.
One reason is obvious but not very important. When snow is 'shed-able', steep roofs will shed it faster. Powdery snow is inclined to fall or blow off, and it falls faster from a steep roof. However, most snow doesn't blow or slide easily. It sticks equally on all roofs. (This year's Spokane snow is especially glue-like, presumably because the temperature has been especially steady at 20 degrees.)
The other reason is more general, but I couldn't wrap my mind around it properly: Steep roofs can hold the load better. This is usually described in terms of pounds per square foot, but that doesn't hit the mark. The important variable for breaking or weakening a roof
is the bending force applied at the middle of the rafters.
I could sense that the bending force was different for a steep roof, but I needed a diagram to pin it down.
Here's the diagram. The animation varies the roof from steep to nearly flat. Three vector arrows represent the relevant forces felt by the middle of a rafter. The black arrow, always pointing straight down and always the same strength, is the pull of gravity on the snow. The green arrow represents the component of gravity along
the rafter. This force tends to pull the house apart, and it is actually worse** for the steep roof. Most important is the red arrow, the component that tries to bend the rafters. This force is weak on a steep roof, strong on a flat roof.
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**Footnote: If you take the green along-rafter force and vectorize its effects on the top of the wall, you see that it comes out roughly the same for all roofs. The force along the rafter is strongest for a steep roof, but most of it goes into downward compression, which is the safest kind of force. For a low roof the along-rafter force goes mainly into sideways pull-apart, but it's a weak force.
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March 2017: a more precise observation
of actual roofs. Steep is definitely better. Steep with occupied (warm) attic is best of all. No doubt about it. The Cape Cod was deaigned by experience in snowy New England, and it's still the winner.