Beam Shear and Moment Diagram Calculator

Beam Input Form

Downward loads should be entered as positive values. UDL intensity uses force per length, such as kN/m.

Beam Length

Sample Points

Force Unit

Length Unit

Support A Position

Support B Position

Point Loads

Point Load 1

Position 1

Point Load 2

Position 2

Point Load 3

Position 3

Point Load 4

Position 4

Uniformly Distributed Loads

UDL 1 Intensity

UDL 1 Start

UDL 1 End

UDL 2 Intensity

UDL 2 Start

UDL 2 End

Calculated Station Table

The table uses the selected sample count. Higher sample counts create smoother diagrams and finer station detail.

Station x (m)	Shear V (kN)	Moment M (kN·m)
0.000	14.000	0.000
2.000	2.000	28.000
4.000	-1.000	30.500
6.000	-12.000	24.000
8.000	-12.000	0.000

Example Data Table

Item	Value	Notes
Beam Length	8 m	Simply supported span.
Point Load 1	12 kN at 2 m	Downward load.
Point Load 2	8 kN at 6 m	Downward load.
UDL 1	3 kN/m from 3 m to 5 m	Partial span UDL.
Total Load	26 kN	12 + 8 + (3 × 2).
Reaction A	14 kN	From equilibrium.
Reaction B	12 kN	From equilibrium.

Formula Used

This calculator uses static equilibrium for a simply supported beam. The left support is A. The right support is B.

First, total vertical load is found. Each UDL becomes an equivalent load: W = w × L_segment. Its line of action passes through the segment centroid.

Support reactions come from: ΣF_y = 0 and ΣM_A = 0.

Therefore: R_A + R_B = ΣP + ΣW and R_B = [Σ(Px) + Σ(Wx̄)] / L. Then R_A = Total Load − R_B.

Shear at any section x is: V(x) = R_A − point loads to the left − active UDL load to the left.

Bending moment at any section x is: M(x) = R_Ax − Σ[P(x−a)] − Σ[W_active(x−x̄_active)].

The charts are created from many stations across the beam. More stations usually produce smoother diagrams.

How to Use This Calculator

Enter the beam span using one consistent length unit.
Choose the number of sample points for the station table.
Select the force and length units for labels.
Add point loads and their positions along the beam.
Add one or two UDL ranges with start and end positions.
Click Calculate Diagram to show reactions, plots, and station values.
Use the CSV button to save the station table.
Use the PDF button to export the station table for reports.

Frequently Asked Questions

1. What beam type does this calculator analyze?

It analyzes a simply supported beam with one support at each end. Loads can include point loads and partial or full UDL segments.

2. Can I mix units in one calculation?

No. Use one consistent force unit and one consistent length unit. The tool labels outputs with your selected units but does not convert entered values.

3. What sign convention is used here?

Downward applied loads are entered as positive values. Reactions are calculated upward. Positive bending moments are shown from the formula result across the span.

4. Why does sample point count matter?

The calculator evaluates the beam at many stations. More points improve curve smoothness and help locate peaks more accurately. They also create larger tables.

5. Does the calculator include self weight automatically?

No. Enter self weight manually as a UDL segment if needed. That keeps the model transparent and easy to verify.

6. Can it handle uplift or negative loads?

Yes. Negative values can represent upward forces or opposite effects. Review the resulting diagrams carefully when using mixed load directions.

7. Are the exported files suitable for documentation?

Yes. The CSV file is useful for spreadsheets. The PDF export is useful for quick sharing, classwork, and report appendices.

8. Is this calculator enough for final structural design?

It is excellent for learning, checking, and preliminary sizing. Final structural design should still follow code rules, professional review, and project-specific loading requirements.