Dead load is the weight of the bridge itself and live load is the weight of what crosses it, and both must be counted in newtons, not kilograms: a 6 m timber bridge with four 30 cm logs weighs about 22.1 kN, while a 1,500 kg cart adds 14.7 kN. A crowd can be the worse live load: at 3.6 kPa on a 2.4 m by 6 m deck it gives a midspan moment of 38.9 kN·m against 29.4 kN·m for the cart with a bump allowance. Post both a vehicle limit and a crowd limit.
Part of Bridge Types & Construction
Counting the permanent weight of a bridge and the moving weight of its traffic, converting both to forces, and finding the worst case for the span.
The Worst Case Is Not Always The Heaviest Vehicle
The parent article defines the two terms. Dead load is the weight of the bridge itself: beams, deck, railing, everything permanent, calculated from material weights. Live load is the weight of what crosses; it gives a loaded ox cart as about 1,000-1,500 kg, concentrated on its wheels. The bridge must carry both at the same time, plus dynamic forces: impact from a cart hitting a bump, wind and vibration.
The numbers must be in forces. A kilogram is a mass; the force it exerts is 9.81 N per kilogram. Quoting newtons as kilograms, or the reverse, misstates a load by 9.81 times. In this page 1 kN is 102 kgf.
What You Need
- Material weights — see Common Material Weights.
- The bridge dimensions — span, deck width, number and size of logs.
- The traffic — heaviest cart or wagon, and whether a crowd can gather.
- The dynamic allowance — 1.33 is used here, from the 33% dynamic load allowance in US highway bridge practice, recalled and not checked.
Method: Total The Loads
Step 1: Add the dead load per metre Weigh each permanent part per metre of span: logs, planks, rails. Multiply by 9.81 to get N/m.
Step 2: Choose the live loads Take the heaviest vehicle, one axle at midspan, with the dynamic allowance. Separately take a crowd as a load spread over the deck area.
Step 3: Turn each into a midspan moment For a load w spread along the span: M = w L² / 8. For a point load P at midspan: M = P L / 4.
Step 4: Compare The larger live moment governs the span. Check the deck separately for the heaviest wheel.
Step 5: Post the limits Write both on a sign at each end.
Worked Example: The 6 m Bridge From The Multi-Beam Page
Inputs from Multi-Beam Bridge: four logs of 30 cm, deck 2.4 m wide, span 6 m; dead load 375 kg/m.
Dead load. 375 × 9.81 = 3,679 N/m = 3.68 kN/m. Total over 6 m: 3.68 × 6 = 22.1 kN, which is 22.1 / 9.81 × 1000 = 2,250 kgf. Midspan moment: 3.68 × 6² / 8 = 16.5 kN·m.
Cart. 1,500 kg × 9.81 = 14.7 kN. As one axle at midspan: 14.7 × 6 / 4 = 22.1 kN·m; with 1.33, 29.4 kN·m.
Crowd. Modern pedestrian-bridge loading is 3.6 kPa in the US highway bridge specification (AASHTO LRFD) and 5 kPa in the Eurocode for footbridges; both are recalled and not checked here. At 3.6 kPa, 3.6 kN/m² is about 367 kg/m², or four people of 90 kg per square metre. On 2.4 m × 6 m = 14.4 m²: 3.6 × 14.4 = 51.8 kN, about 5,280 kg. As a load along the span: 3.6 × 2.4 = 8.64 kN/m, so M = 8.64 × 6² / 8 = 38.9 kN·m. At 5 kPa, the force is 72 kN and M = 54.0 kN·m.
Comparison. The crowd at 3.6 kPa gives 38.9 kN·m against 29.4 kN·m for the cart: 32% more. The parent mentions only the cart.
What the bridge can take. Suppose 3 of the 4 logs share the load (an assumption), the bending strength is 30 MPa (a low round figure recalled from the US Forest Products Laboratory Wood Handbook) and the parent’s safety factor for timber is 4, so the allowable stress is 7.5 MPa. One log’s section modulus is π × 0.3³ / 32 = 2.65 × 10⁻³ m³, so its allowable moment is 7.5 × 10⁶ × 2.65 × 10⁻³ = 19.9 kN·m; for 3 logs, 59.6 kN·m. Subtract the dead moment 16.5 to leave 43.1 kN·m for live load.
- As an evenly spread crowd: w = 8 × 43.1 / 6² = 9.58 kN/m, or 9.58 / 2.4 = 4.0 kPa. That just covers 3.6 kPa and does not cover 5 kPa.
- As one axle at midspan: P × 1.33 = 4 × 43.1 / 6 = 28.7 kN, so P = 21.6 kN, about 2,200 kg.
Result: post “one axle 2,200 kg” and “crowd no denser than about 4 people per m²”, and note that the second limit is close to the first. If you want 5 kPa, add logs.
Common Mistakes
- Mixing kg and N — 1,500 kg is 14.7 kN, not 1.5 kN and not 1,500 N.
- Counting the cart only — a crowd at a festival or a flock of animals puts more on the span.
- Ignoring the dead load — in this example it is 16.5 of 45.9 kN·m, over a third of the total.
- Leaving out the bump — a dynamic allowance matters for carts, less for a crowd standing still.
- Not allowing for water, wind or ice — flood debris, wind and snow load add to the parent’s list.
Safety
Overloading a bridge
A bridge that is loaded beyond its design can fail with no warning, and cracks may only show afterward. Post the limits at both ends and enforce them. Allow only one cart at a time. Never let a crowd gather on a timber bridge, and watch for sag and creaking.
What’s Next
- Learn next: Safety Factors — why the parent asks for 4 on timber
- Combine with: Live Loads — loads on buildings