Advanced Bending Moment Diagram Calculator

Analyze beam loads with fast visual results. Track reactions, shear force, and bending moments clearly. Build safer beam checks using organized, exportable engineering insights.

Beam Input and Load Definition

Use the form below to model a simply supported beam or a cantilever beam. Add as many point loads, distributed loads, and applied moments as needed.

Point Loads

Uniformly Distributed Loads

Applied Moments

Example Data Table

These sample values show how to organize typical entries before calculation.

Beam Type Span Point Load UDL Applied Moment Expected Use
Simply supported 8 m 20 kN downward at 3 m 5 kN/m downward from 4 m to 7 m 10 kN·m clockwise at 6.5 m General beam design review
Cantilever 5 m 12 kN downward at 4 m 2 kN/m downward from 1 m to 5 m 6 kN·m counterclockwise at 2 m Fixed-end support check
Simply supported 10 ft 8 lb upward at 2 ft 3 lb/ft downward from 3 ft to 9 ft 0 Mixed load comparison

Formula Used

1. Signed vertical load = point loads + distributed load resultants.

2. Distributed load resultant = intensity × loaded length.

3. Distributed load centroid = (start + end) ÷ 2.

4. Simply supported reactions use equilibrium:

RA + RB = ΣV

RB × L = Σ(Moments about A)

5. Cantilever reactions use:

Vfixed = ΣV

Mfixed = Σ(Moments about fixed end)

6. Internal shear at any section subtracts loads already passed.

7. Internal moment at any section equals support effects minus the moment contribution from each load and applied moment to the left.

This calculator treats downward loads as positive and clockwise applied moments as positive input values. Positive bending moment is plotted as sagging.

How to Use This Calculator

  1. Select the beam type and enter the beam length.
  2. Choose the length and force units that match your problem.
  3. Add point loads, distributed loads, and applied moments as needed.
  4. Use positions measured from the left end of the beam.
  5. Press Calculate Diagram to show reactions, critical values, the graph, and the detailed table.
  6. Use the CSV or PDF buttons to export your results.

Frequently Asked Questions

1. What does this calculator compute?

It computes support reactions, shear force values, bending moment values, critical peaks, and a full diagram along the beam span.

2. Can I use more than one load type?

Yes. You can combine multiple point loads, multiple uniformly distributed loads, and multiple applied moments in one beam model.

3. Which beam supports are available?

This version supports simply supported beams and cantilever beams. Those two cases cover many common classroom and design-check situations.

4. What sign convention does the calculator use?

Downward loads are treated as positive inputs. Clockwise applied moments are positive. Positive plotted bending moment represents sagging behavior.

5. Why are there both shear and moment values?

The bending moment diagram comes from the load distribution through the beam. Shear force helps explain slope changes and important turning points.

6. How accurate is the plotted curve?

Accuracy depends on the selected divisions. A higher division count creates a denser set of points and a smoother plotted response.

7. Does the export include detailed data?

Yes. The CSV export includes the x-position, shear value, and moment value for every calculated point. The PDF summarizes the same analysis.

8. Can this replace full structural design software?

No. It is useful for beam analysis, quick checks, and learning. Final structural design should still follow code requirements and professional review.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.