Why a steep timber roof sheds snow load, and what the rafters and walls carry.
-Design load (kN/m2)
-Wall reaction V per rafter (kN)
-Thrust H (kN)
-Tie beam tension (kN)
-Peak rafter moment (N m)
-Peak stress (MPa)
-Strength utilisation
-Snow depth at failure (m)
The science
Each rafter pair acts as a three-hinged frame: pinned at the eave plates and at the ridge. Snow and shingles are loaded per metre of horizontal projection: q = (rho g d + w_dead) a with snow density rho, depth d and rafter spacing a. Because the roof is steep, snow slides off sooner than it would on a shallow one, and the log walls only see the vertical share.
Vertical reactions are V = q B / 2. Taking moments about the ridge hinge (where the bending moment must be zero) gives the horizontal thrust H = q B^2 / (8 f) = q B / (4 tan(alpha)), with rise f = (B/2) tan(alpha). A tie beam at the eaves carries H as tension; without it the log walls must resist the outward push.
Along the rafter, at horizontal distance x from the eave, M(x) = V x - H x tan(alpha) - q x^2 / 2 = (q x / 2)(B/2 - x), peaking at q B^2 / 32 at x = B/4. Stress is sigma = M / W + N / A with W = b h^2 / 6, compared with the timber bending strength.
Honest simplifications: static load only, uniform snow with no drifting or wind, rafters treated as straight beams with ideal pins, no buckling, no creep, no connection slip, and no stability check of the log walls. A teaching model of a traditional roof, not a design code check.