Calculator Inputs
Formula Used
For a linearly varying distributed load, the equivalent load is W = (w1 + w2) × l / 2.
The centroid from the load start is x̄ = l × (w1 + 2w2) / [3 × (w1 + w2)].
For a simply supported beam, reactions are found from equilibrium. The formulas are RB = Σ(Wx) / L and RA = ΣW - RB.
Moment at a section is found by subtracting load moments from reaction moments. The stress check uses fb = M / S.
How To Use This Calculator
Enter beam span, support model, and distributed load limits. Use zero start intensity for a triangular load rising rightward.
Enter equal start and end intensities for a uniform load. Enter different values for a trapezoidal load.
Add an optional point load when one exists. Use the load factor field for factored design checks.
Enter section modulus and allowable stress. Submit the form to view reactions, shear, moment, stress, and utilization.
Example Data Table
| Case | Span | Load type | w1 | w2 | Load range | Use case |
|---|---|---|---|---|---|---|
| Floor beam | 8 m | Uniform | 8 kN/m | 8 kN/m | 0 to 8 m | Slab dead load |
| Retaining edge | 5 m | Triangular | 0 kN/m | 18 kN/m | 0 to 5 m | Soil pressure |
| Roof purlin | 6 m | Partial uniform | 4 kN/m | 4 kN/m | 1 to 5 m | Patch load |
| Transfer beam | 10 m | Trapezoidal | 6 kN/m | 14 kN/m | 2 to 9 m | Variable wall load |
Understanding Distributed Load Moments
Distributed loads represent weight spread along a beam. They may come from slabs, walls, soil, roofing, or stored materials. A uniform load has one constant intensity. A triangular load changes from zero to a larger value. A trapezoidal load has different start and end intensities.
The main task is replacing that spread load with one resultant force. The resultant acts at the load centroid. For a uniform load, the centroid is at mid length. For a triangular load, it sits one third from the heavy end. For a trapezoidal load, the centroid moves toward the larger intensity.
Why Moment Checks Matter
Bending moment controls beam stress and deflection. A high moment can crack concrete or overstress steel. It can also increase timber bending strain. Support reactions must be known first. Then shear and moment can be traced along the span.
A simply supported beam usually has a sagging peak near zero shear. A cantilever often has its largest moment at the fixed end. Partial loads can shift the critical point. Point loads can change both reaction and peak moment.
Useful Site Practice
This calculator helps with early construction checks. It does not replace code based structural design. Real beams may need live load factors, dead load factors, impact allowance, and lateral stability checks. Concrete members also need reinforcement detailing. Steel beams need section classification and lateral bracing review.
Use consistent units for every value. Enter length in meters and load in kilonewtons per meter. The result then gives kilonewton meters. Section modulus in cubic centimeters gives stress in megapascals.
Design Interpretation
A low utilization ratio suggests reserve bending capacity. A ratio near one needs careful review. A ratio above one means the selected section is not enough. Increase section size, reduce span, add support, or lower the applied load.
Distributed load moments are simple in concept. They become complex with partial spans and varying intensity. This tool organizes those steps. It shows resultant load, centroid, reactions, moment, shear, and stress. Keep notes for load sources and assumed combinations. Review drawings when slab thickness or wall position changes. Recalculate after any field change before ordering steel on site. Use the outputs to compare beam options before final design. Always confirm members with qualified structural guidance before construction.
Frequently Asked Questions
What is a distributed load?
A distributed load is force spread along beam length. It is usually shown in kN/m. Slabs, walls, roofing, storage, soil, and finishes can create distributed loads.
What load shapes can this tool handle?
It handles uniform, triangular, trapezoidal, and partial distributed loads. It also includes one optional point load for combined construction checks.
How is the resultant load calculated?
The tool multiplies average load intensity by loaded length. For a varying load, it also locates the centroid toward the heavier end.
Why does centroid location matter?
Centroid location controls the load moment about supports. Reaction values change when the same load shifts closer to one support.
Can I calculate partial distributed loads?
Yes. Enter the load start and end positions. The calculator applies the load only across that part of the beam span.
What does positive moment mean?
For simply supported beams, positive moment means sagging. Cantilever results may show negative hogging moments near the fixed support.
How do I model a triangular load?
Set one intensity to zero. Use the larger value at the heavy end. The tool will calculate the correct resultant centroid.
What units should I use?
Use meters for length and kN/m for distributed load. Use kN for point load, cm³ for section modulus, and MPa for stress.
What is utilization ratio?
Utilization ratio compares calculated bending stress with allowable stress. Values below one are usually acceptable for the selected input assumptions.
Can this replace structural design?
No. It supports early checks only. Final beam selection must follow local codes, load combinations, bracing rules, and professional engineering review.
Why are load factors included?
Load factors help compare service loads and factored design loads. Enter 1.0 for service checks or a higher value for design combinations.