The Round-Log Beam Rule: Span from Diameter for Roof and Floor Loads

A round log used whole, without sawing, is one of the oldest beam forms available to a builder who has trees but no mill. This paper originates a sizing rule for such beams by computing, for a circular cross-section, both the span at which bending strength is exhausted and the span at which sag reaches a stated limit, for two stated load cases and three stated species classes. The study is simulated, not measured, and no beam described here has been load-tested. The central finding is that sag governs everywhere in the range computed: for every diameter from 100 mm to 350 mm, for every species class, and for both the floor case and the roof case, the deflection span is shorter than the strength span, typically by a factor near two. A 200 mm pine-class log, for example, has a strength span of 9.23 m under the floor load but a governing span of only 4.64 m once the floor sag limit of span/360 is applied; a 200 mm oak-class log governs at 4.95 m and a 200 mm light-softwood log at 4.21 m. The rule that follows is stated as a span-from-diameter table in the Results, together with the practical consequence that choosing a stronger species buys surprisingly little extra span — at 200 mm the oak class spans only 1.18 times as far as the light class on a floor — because stiffness, not strength, is the binding property. Anyone using the table must apply it only under the stated assumptions, with the stated factor of 3.0 on bending strength, and with local judgement about taper, defects, supports, and moisture, none of which the arithmetic can see.