Results
Sign convention uses positive downward load intensity. Cantilever fixed-end moment is reported by magnitude.
Calculator Inputs
Summary Table
| Metric | Value |
|---|---|
| Beam length | 10 m |
| Loaded segment | 2 to 8 m |
| Loaded length | 6 m |
| Start intensity | 5 kN/m |
| End intensity | 5 kN/m |
| Equivalent resultant | 30 kN |
| Centroid from left end | 5 m |
| Average intensity | 5 kN/m |
| Left reaction | 15 kN |
| Right reaction | 15 kN |
| Fixed-end moment | Not applicable |
| Maximum shear magnitude | 15 kN at x = 0 m |
| Maximum bending moment magnitude | 52.5 kN-m at x = 5 m |
Example Data Table
| x | w(x) | V(x) | M(x) |
|---|---|---|---|
| 0.0000 | 0.0000 | 15.0000 | 0.0000 |
| 0.8333 | 0.0000 | 15.0000 | 12.5000 |
| 1.6667 | 0.0000 | 15.0000 | 25.0000 |
| 2.5000 | 5.0000 | 12.5000 | 36.8750 |
| 3.3333 | 5.0000 | 8.3333 | 45.5556 |
| 4.1667 | 5.0000 | 4.1667 | 50.7639 |
| 5.0000 | 5.0000 | 0.0000 | 52.5000 |
| 5.8333 | 5.0000 | -4.1667 | 50.7639 |
| 6.6667 | 5.0000 | -8.3333 | 45.5556 |
| 7.5000 | 5.0000 | -12.5000 | 36.8750 |
| 8.3333 | 0.0000 | -15.0000 | 25.0000 |
| 9.1667 | 0.0000 | -15.0000 | 12.5000 |
| 10.0000 | 0.0000 | -15.0000 | 0.0000 |
Formula Used
The calculator models a linearly varying distributed load between the selected start and end positions.
Loaded length, l = b − a.
Equivalent resultant load, R = l × (w1 + w2) / 2.
Average intensity, wavg = R / l.
Centroid from the load start, x̄local = l × (w1 + 2w2) / [3 × (w1 + w2)].
Centroid from the beam left end, x̄ = a + x̄local.
For a simply supported beam, RB = R × x̄ / L and RA = R − RB.
For a left fixed cantilever, vertical reaction = R and fixed-end moment = R × x̄.
Shear comes from reaction minus accumulated load up to the section.
Moment comes from reaction effects minus the first moment of accumulated load.
How to Use This Calculator
Choose the support type first. Select simply supported or a left fixed cantilever.
Pick the load profile. Use uniform, triangular, trapezoidal, or custom linear loading.
Enter total beam length. Then enter the load start and load end positions.
Provide the start and end load intensities. The page uses those values to build the load shape.
Set your preferred force and length units. The output labels update with those units.
Press the calculate button. The result cards appear above the input form, directly below the header.
Review the summary table and the example section data. Download CSV or PDF when needed.
Distributed Load on Beam Guide
Why distributed loads matter
Distributed loads appear in floors, bridges, racks, and machine frames. They spread force over length. That changes reactions, shear, and bending moment. A good calculator helps students, designers, and inspectors read those effects quickly. It also helps compare alternate loading zones before a detailed structural check.
What this calculator evaluates
This tool handles partial span loading and full span loading. It also supports uniform, triangular, trapezoidal, and custom linear distributions. Those options cover many practical beam problems. You can place the load anywhere along the beam. That makes the result more useful for real support layouts.
How the physics is applied
The method converts the distributed load into one equivalent resultant. It then locates the centroid of that resultant. Static equilibrium gives the support reactions. After that, accumulated load creates the shear diagram. The first moment of load creates the bending moment diagram. These steps follow standard beam mechanics.
Why centroid location changes results
Two loads can share the same total magnitude but act at different centroids. When that happens, reactions and moments change. A triangular load near one side can produce different behavior than a uniform load with the same resultant. That is why the calculator reports load shape and centroid position clearly.
Using the outputs well
Start with the equivalent resultant load. Then inspect the support reactions. Next, check maximum shear and maximum bending moment. Those values guide sizing, comparison, and verification. The example data table also gives section values along the beam. That helps with plotting, reporting, and homework cross checking.
Best practice for interpretation
Keep units consistent at every step. Confirm that the load segment stays within the beam length. Use realistic start and end intensities. For cantilevers, pay close attention to the fixed-end moment. Exporting the summary to CSV or PDF makes documentation easier during reviews, class notes, and design records.
Applications and limits
Use this calculator for conceptual analysis, study examples, maintenance checks, and quick report preparation. It is not a substitute for full code compliance, deflection review, material verification, or professional approval.
Choosing the right load shape
Choosing the correct load shape improves accuracy. Use uniform loading for constant pressure or weight. Use triangular loading for ramped intensity. Use trapezoidal loading when the beam starts and ends with different nonzero values. Custom linear input is useful for measured field conditions during maintenance reviews.
FAQs
1. What is a distributed load on a beam?
A distributed load acts over a length instead of one point. It may be uniform or vary from one end to the other. Engineers convert it into an equivalent resultant for reaction and moment calculations.
2. What is the difference between UDL and UVL?
A UDL has constant intensity over the loaded length. A UVL changes intensity along the span. Triangular and trapezoidal loads are common UVL cases in beam analysis.
3. Why does the centroid matter?
The centroid gives the location of the equivalent resultant load. Reactions and bending moments depend on both load magnitude and where that resultant acts along the beam.
4. Can this calculator handle partial span loading?
Yes. Enter the start and end positions of the load segment. The calculator applies the load only across that region, then computes reactions, shear, and bending moment from that placement.
5. Does the tool support cantilever beams?
Yes. Select the left fixed cantilever option. The tool returns the vertical reaction and fixed-end moment, along with section shear and moment values along the span.
6. What units should I enter?
You can enter any consistent force and length units. Common choices are kN and m, or N and mm. The output labels follow your chosen unit text.
7. Are the shear and moment values exact?
The reaction, resultant, and centroid values use closed-form expressions. The sample table values are generated from those equations at selected beam positions for clear reporting.
8. When should I export CSV or PDF?
Use CSV for spreadsheets, plotting, or later calculations. Use PDF for quick sharing, project files, class notes, and printable records during design review work.