Distributed Load Calculator for Beam Resultants

Calculator Inputs

Beam Length

Full beam span for reaction calculations.

Load Start Position

Measured from the left beam end.

Load End Position

Must be greater than start position.

Load Profile

Positive values act downward. Use negative values for uplift.

Start Intensity

Intensity at the load start position.

End Intensity

Intensity at the load end position.

Force Unit

Used for force, intensity, and reactions.

Length Unit

Used for beam geometry and moment units.

Support Condition

Adds beam reactions when selected.

Reference Position

Additional moment output about this point.

Plot Stations

Higher values create smoother charts.

Reset

Formula Used

1) Segment length: a = x₂ − x₁

2) Linear load law: intensity changes from w₁ at the segment start to w₂ at the segment end.

3) Resultant force: R = a × (w₁ + w₂) / 2

4) Moment about the segment start: Mlocal = a² × (w₁ + 2w₂) / 6

5) Moment about the left beam end: Mleft = x₁ × R + Mlocal

6) Application point from the left: x̄ = Mleft / R when R ≠ 0

7) Average intensity: wavg = R / a

8) Slope of the load line: m = (w₂ − w₁) / a

9) Simply supported reactions: RB = Mleft / L and RA = R − RB. For a left cantilever, the fixed-end vertical reaction is R, and the fixed-end reaction moment is Mleft.

How to Use This Calculator

Enter the full beam length.
Set the loaded segment start and end positions.
Choose the load profile type.
Enter start and end intensities in your chosen units.
Pick the support condition if reactions are needed.
Choose a reference position for an extra moment report.
Set the number of plot stations.
Click Calculate Distributed Load.
Review the result cards, summary table, and graph above the form.
Use the CSV or PDF buttons to export your results.

Example Data Table

Beam Length	Load Start	Load End	Profile	Start Intensity	End Intensity	Resultant	Application Point	Moment About Left	Left Reaction	Right Reaction
8 m	1.5 m	6.5 m	Trapezoidal	2 kN/m	8 kN/m	25 kN	4.5 m	112.5 kN·m	10.9375 kN	14.0625 kN

FAQs

1) What does this calculator solve?

It finds the equivalent resultant force, application point, moments, average intensity, load slope, and optional beam reactions for a single linear distributed load segment.

2) Can it analyze a partial-span load?

Yes. Enter any start and end positions within the beam. The calculator handles loads that begin and finish anywhere along the span.

3) How are triangular loads entered?

Choose triangular rising or triangular falling. The tool automatically forces one end intensity to zero and keeps the other end as the peak value.

4) What if my load is upward?

Use negative intensity values. Positive values are treated as downward loads, while negative values represent uplift or reverse loading.

5) Why can the application point be undefined?

When the signed distributed load produces zero net force, the system becomes a pure couple. In that case, there is no single point load location.

6) Are the reactions exact?

They are exact for the single linear distributed load described by the form, using standard static equilibrium relations for simply supported and left-fixed beams.

7) Which units are supported?

You can use N, kN, lb, or kip for force and m, ft, or mm for length. The calculator converts internally and reports consistent outputs.

8) What do the CSV and PDF exports contain?

They export the summary table of your entered geometry, computed resultant values, moments, and reactions, which is helpful for reports or design notes.