The maximum bending moment caused by a truck moving across a bridge depends on the bridge span, support arrangement, axle loads, axle spacing, and the truck’s position. Engineers normally solve this moving-load problem with an influence line rather than treating the truck as one concentrated load.

This calculation must be completed by a qualified structural engineer before deciding whether a bridge, dock plate, or temporary loading structure can safely support a loaded truck.

Start with the Truck’s Axle Loads

A truck’s gross weight alone is insufficient. The required inputs are:

• Front-axle load

• Rear-axle or tandem-axle loads

• Distance between axles

• Bridge span

• Support conditions

• Lane position

• Dynamic allowance required by the applicable code

• Weight added by equipment such as a truck tail lift

A rear-mounted tail lift changes the vehicle’s empty weight and axle-load distribution. Its mass and overhang must therefore be included in the vehicle data supplied to the engineer.

Influence Line for a Simply Supported Bridge

For a simply supported bridge with span (L), the bending-moment influence-line ordinate at section (x) is:

[ y(z)= \begin{cases} \dfrac{z(L-x)}{L}, & z \leq x \ \dfrac{x(L-z)}{L}, & z \geq x \end{cases} ]

Here, (z) is the position of an axle measured from the left support. For several axle loads, the moment at the selected section is:

[ M_x=\sum P_i y_i ]

where (P_i) is an individual axle load and (y_i) is the corresponding influence-line ordinate.

The truck is moved across the span in small position increments. At each position, the contribution from every axle located on the bridge is added. The largest calculated value is the maximum bending moment for that loading arrangement.

A Simplified Single-Load Example

For one point load (P) on a simply supported span, the largest moment occurs when the load is at midspan:

[ M_{\max}=\frac{PL}{4} ]

A real truck has multiple axles, so this equation cannot be used as the final answer. The critical truck position is usually found when one of the heavier axles is near the section being checked and the combined axle group produces the largest influence-line total.

Why Gross Vehicle Weight Can Be Misleading

Two trucks with the same total weight can create different bridge moments.

A truck should therefore be weighed by axle or modeled from verified manufacturer data.

Practical Calculation Sequence

1. Obtain verified axle weights for the fully loaded truck.

2. Add the installed weight and position of the tail lift.

3. Draw the axle group to scale.

4. Define the bridge span and support conditions.

5. Create the bending-moment influence line.

6. Move the axle group across the bridge.

7. Sum (P_i y_i) at every relevant position.

8. Apply code-required dynamic and load factors.

9. Compare the design action with the bridge’s verified capacity.

10. Check shear, local deck loading, deflection, fatigue, and axle limits separately.

The maximum bending moment is only one part of bridge assessment. A satisfactory moment result does not automatically confirm that the deck, beams, bearings, or approaches are safe.

Relationship to Tail Lift Selection

Our factory supplies hydraulic tail lifts for truck loading and unloading. When a buyer specifies a tail lift, we review platform dimensions, rated capacity, truck-bed height, mounting space, equipment weight, and intended cargo.

As a truck tail lift OEM/ODM manufacturer, we can support project-specific platform structures, steel or aluminum options, lifting capacities, hydraulic configurations, and installation requirements. However, bridge capacity and vehicle axle compliance must be verified by qualified vehicle and structural engineers in the destination market.

Engineering Takeaway

The reliable way to solve the maximum moment of a truck moving across a bridge is to combine verified axle loads with the bridge’s influence line. Do not use gross weight alone, and do not ignore the weight or overhang of a rear-mounted tail lift.

For an existing bridge with unknown capacity, restrict access until a competent engineer has reviewed the structure, loading configuration, and applicable local standards.