Single Log Bridge

A single log bridge is limited by bending in the lower fibres at midspan, not by shear: at a safety factor of 4, a 20 cm log over 4 m carries about 2 bunched people, a 30 cm log over 6 m about 5, and a 40 cm log over 8 m about 9. The span rules of 3-4 m, 5-6 m and 7-8 m for 20, 30 and 40 cm logs therefore leave a wide margin in bending, and that margin is spent on knots, rot, wet slipperiness and unknown timber. Do not stretch the spans.

Part of Bridge Types & Construction

A round log laid across a gap as a pedestrian beam, checked against bending, shear and deflection.

Bending In The Bottom Fibres Governs A Log, Not Shear

A log across a gap is a simple beam. A load at the middle bends it so that the top fibres are squeezed and the bottom fibres are stretched. Timber is weaker in tension than in compression, and a knot or crack on the underside starts the failure. Shear along the grain is checked below and is small. Sag is also small for these logs, but a sag of 2-3 cm gives the bounce that makes walkers refuse to cross.

The parent article gives the rule: a 20 cm log spans 3-4 m, a 30 cm log spans 5-6 m and a 40 cm log spans 7-8 m for foot traffic, and the span is cut by 30-40% for animals or carts. This page tests that rule against beam arithmetic.

What You Need

• A tape and a way to measure log diameter at the thin end, the midpoint and the ends.
• A knife or spike to probe for rot at the bearing ends.
• The parent’s safety factor for timber: 4.

Method: Check A Log Before You Trust It

Step 1: Measure the thin end Use the smallest diameter along the log, not the butt. A tapered log is only as strong as its thin part near midspan.

Step 2: Check the underside at midspan Roll or lift the log. A knot, check (split) or rot pocket on the bottom face at midspan is a failure starter. Turn a log so the defect is on top. Reject it if there are defects on both faces.

Step 3: Probe the bearing ends Push a spike 3-5 cm into the end grain and into the underside where the log rests. It should meet hard resistance. A spike that sinks easily means decay.

Step 4: Flatten the top and test Flatten the top with an axe or adze, then walk one person across while another watches the sag.

Worked Example: Three Parent Spans Checked In Bending

Assumptions, which are mine and not the parent’s:

• Green softwood weighs 1,000 kg/m³, the top of the 800-1000 kg/m³ range for green wood in Common Material Weights.
• Bending strength 30 MPa, a deliberately low round figure for green softwood. I am recalling it from the US Forest Products Laboratory Wood Handbook, which lists roughly 30-55 MPa for common softwoods; I have not checked it against the book here.
• Modulus of elasticity 9 GPa, also recalled.
• One person of 100 kg with a dynamic factor of 2 for a stride: 100 × 9.81 × 2 = 1,962 N at midspan.

Formulas: section modulus of a round log S = π d³ / 32; self-weight per metre w = (π d² / 4) × 1,000 × 9.81; midspan moment from self-weight = w L² / 8; midspan moment from a point load = P L / 4; stress = M / S. Allowable stress = 30 MPa / 4 = 7.5 MPa.

20 cm log over 4 m.

• S = π × 0.2³ / 32 = 7.85 × 10⁻⁴ m³.
• w = 0.0314 m² × 1,000 × 9.81 = 308 N/m; M(self) = 308 × 4² / 8 = 616 N·m.
• M(person) = 1,962 × 4 / 4 = 1,962 N·m. Total M = 2,578 N·m.
• Stress = 2,578 / 7.85 × 10⁻⁴ = 3.3 MPa, against 7.5 MPa allowable.
• Capacity: M(allowable) = 7.5 × 10⁶ × 7.85 × 10⁻⁴ = 5,890 N·m. Minus 616 leaves 5,274 N·m, so P = 5,274 × 4 / 4 = 5,274 N, about 538 kgf. At 1,962 N per person that is 2.7, so 2 people bunched, not 3.

30 cm log over 6 m. S = 2.65 × 10⁻³ m³; w = 693 N/m; M(self) = 3,120 N·m; M(allowable) = 19,880 N·m. P = (19,880 − 3,120) × 4 / 6 = 11,173 N, which is 5.7, so about 5 people.

40 cm log over 8 m. S = 6.28 × 10⁻³ m³; w = 1,233 N/m; M(self) = 9,862 N·m; M(allowable) = 47,124 N·m. P = (47,124 − 9,862) × 4 / 8 = 18,631 N, which is 9.5, so about 9 people.

Shear. The largest shear stress in a round section is 4V / (3A). For the 20 cm log V is about 1.5 kN, so τ = 4 × 1,500 / (3 × 0.0314) = 64 kPa, about 0.06 MPa. Timber shear strength along the grain is several MPa (recalled, not checked), so shear is not a concern.

Sag. One person plus the log’s own weight sags the 20 cm log by about 5 mm, which is L/776 for 4 m. That is stiff.

Result: in bending the parent’s spans have room to spare for one walker, and the crowd the log allows is small. The margin exists for the things the formula cannot see.

What Actually Kills A Log Bridge

• A knot or check on the underside at midspan — it cuts local tensile strength sharply and the fibres tear from there.
• Rot at the bearing — the log is sound in the middle and soft at the ends, and it fails by crushing or by slipping off the bank. This is why the parent asks for 60 cm of bearing.
• A wet round surface — the commonest injury is a slip, not a break.
• Flood and drift — water above the log pushes it off the abutments.

For animals or carts the parent cuts the span by 30-40%. For a 30 cm log that is 3.5-4.2 m when 30% comes off 5-6 m. A 500 kgf loaded mule with a 1.33 impact allowance on 3.6 m of 30 cm log gives about 2.6 MPa, so the cut span is conservative in bending. Animals rarely walk willingly onto a round log, which is the practical reason not to try.

Common Mistakes

• Reading the table as a measured strength — the spans are margins, not the point where the log breaks.
• Using the butt diameter — measure the thin end.
• Putting the defect face down — check the underside before laying.
• Skipping the handrail — see Log & Beam Bridges.

Safety

A fall from a log bridge

A wet or frosted round log is extremely slippery, and a drop onto rock or into fast water is serious. Flatten the top, add a rail, and keep the load to what the calculation allows: no more than 2 people together on a 20 cm log over 4 m.

What’s Next

• Learn next: Multi-Beam Bridge — when one log is not enough
• Combine with: Safety Factors — why the parent asks for 4 on timber