Set one wheel pair
Enter the two downward wheel forces and their fixed spacing. This tool supports a spacing no greater than the beam span.
BEAMS & SECTIONS / TOOL 13
Two-Wheel Moving Load Beam Calculator
Use this to explore how a fixed pair of wheel forces changes the actions on a simple beam as the wheels enter, cross and leave the span.
Before you start: required inputs
- Obtain individual wheel forces for the selected load condition rather than deriving them by dividing total crane weight equally.
- Measure the wheel spacing along the travel direction and the distance between the two beam support lines.
Calculation diagram
A PRACTICAL WALKTHROUGH
How to use this calculator
Follow the first-wheel coordinate
The first wheel is at s and the second at s + spacing. A negative s means the first wheel has not yet entered the span while the second may already be on it.
Review the envelope and its locations
The program moves the pair through sampled travel positions, then reports maximum moment, reactions and internal shear with their corresponding first-wheel coordinates.
Two 50 kN wheels, 2 m apart, on a 10 m span
THE INPUTS
Span 10 m; P1 = 50 kN; P2 = 50 kN; wheel spacing 2 m.
THE RESULT
The sampled maximum sagging moment is 202.5 kN·m. One maximum occurs with the first wheel at 3.5 m and the critical section at 5.5 m. Maximum support reactions are 90 kN; the sampled internal shear maximum is 89.95 kN.
What does the result mean?
01
The plotted curve shows the maximum bending moment at each wheel-pair travel position; it is not beam deflection or the bending diagram for one position.
02
Moment, reaction and shear maxima can occur at different wheel positions. Use the location reported with each result.
03
The envelope uses 2,401 uniform travel positions plus exact entry and exit positions. Internal-action maxima are numerical approximations.
Watch for this
Treating the 100 kN total of two wheels as one centred force, or using the crane span as the wheel spacing along the runway.
Formula & model conditions +
For wheels on the span: RA = Σ[P × (L − x) / L]; RB = Σ[P × x / L]
M(z) = RA × z − Σ[P × max(z − x, 0)]
Maximum positive moment occurs at a wheel or a support for each sampled travel position.
- A single simple span carries two downward point forces at x = s and x = s + spacing. Only forces on the span are included.
- The first-wheel coordinate s runs from −spacing to span. Forces may enter or leave the beam independently.
- The calculation uses 2,401 travel positions plus exact entry/exit positions; intermediate maxima are numerical approximations.
- Wheel spacing must not exceed the span. No uniform beam weight, impact factor, lateral load, continuity or code load combination is included.
Common questions
Why is sampled internal shear slightly below the maximum reaction?
A force placed exactly at a support contributes to the reaction but not the internal shear just inside the span. Nearby sampled positions approach the limiting internal value.
Does the calculation include beam self-weight or impact?
No. It includes only the two entered downward forces on a simple span. Uniform weight, dynamic factors, lateral effects and design combinations are separate.