Shear Force and Bending Moment Calculator

Calculator Input

Beam span

Support type

Diagram intervals

Force unit

Length unit

Sign rule

Point Loads

Point load P1

Position of P1

P1 note

Point load P2

Position of P2

P2 note

Point load P3

Position of P3

P3 note

Point load P4

Position of P4

P4 note

Uniform Distributed Loads

UDL w1

UDL 1 start

UDL 1 end

UDL w2

UDL 2 start

UDL 2 end

Formula Used

Total point load	W = P1 + P2 + ...
Uniform load result	Wudl = w × (b - a), acting at (a + b) / 2
Simply supported reactions	RB = Σ(W × x) / L, and RA = ΣW - RB
Cantilever reactions	RA = ΣW, and fixed end moment MA = -Σ(W × x)
Shear at section x	V(x) = left reaction - loads acting left of x
Moment at section x	M(x) = support moment + RA × x - load moments left of x

How to Use This Calculator

Enter the full beam span.
Select a simply supported or cantilever beam.
Choose matching force and length units.
Add point loads and their positions from the left end.
Add uniform loads with start and end distances.
Use negative values for upward loads.
Press Calculate to view reactions, shear, and moment values.
Use CSV or PDF export for reports and records.

Example Data Table

Input	Example value	Meaning
Span	6 m	Beam length from left support to right support
Support type	Simply supported	Pin and roller reaction model
P1	12 kN at 3 m	Single downward point load
UDL 1	4 kN/m from 1 m to 5 m	Partial uniform distributed load
Expected reactions	RA = 14 kN, RB = 14 kN	Balanced vertical support forces
Expected peak moment	About 34 kN-m	Largest sagging value near the point load

Beam Shear And Moment Guide

Shear force and bending moment describe how a beam carries load. They are used in physics, mechanics, and structural design. A shear diagram shows the vertical force inside the beam. A moment diagram shows the turning effect at each section. Together, they explain where a beam is most stressed.

Why The Calculation Matters

A beam may look safe by size alone. It can still fail when reactions, shear, or moments are ignored. This calculator builds values from equilibrium. It adds point loads and distributed loads. It then samples the span. The largest bending moment is important for section strength. The largest shear value is important near supports and heavy loads.

Supported Load Behavior

Point loads create sudden jumps in shear. They also change the slope of the moment curve. Uniform loads create sloping shear lines. They create curved moment changes. A simply supported beam has two vertical reactions. A cantilever has one fixed reaction and one fixed end moment.

Reading The Results

Positive load means downward load in this tool. Negative load means upward load. Positive shear follows the left segment convention. Positive moment means sagging behavior. For many classroom beams, the maximum moment appears where shear changes sign. It may also appear at a support, free end, or load break.

Practical Workflow

Start with the span and support type. Add loads from left to right. Keep every distance measured from the left end. Use the same force unit for every input. Use the same length unit for every distance. Run the form. Then compare reactions with the total load. If they do not balance, review signs and positions. Export the table when you need a record.

Design Notes

The output is a calculation aid. It does not replace code based design. Real beams can include self weight, load factors, connection stiffness, lateral torsion, and deflection limits. Always compare final results with the required standard for your project. Check units before using any exported report. Use the diagrams for insight, not final approval. Review boundary conditions before sizing material.

Accuracy Tips

Small input mistakes can move the peak moment. Use decimal values carefully. Use exact start and end distances when possible. Round only after exporting.

FAQs

What is shear force?

Shear force is the internal vertical force at a beam section. It shows how loads are transferred across the beam. Support reactions and loads on the left side control its value.

What is bending moment?

Bending moment is the internal turning effect at a beam section. It helps show where the beam may bend most. Larger moment values often require stronger sections.

Can this tool handle upward loads?

Yes. Enter upward loads as negative values. Downward loads are positive by default. This sign rule works for both point loads and distributed loads.

Does the calculator support cantilever beams?

Yes. Select the cantilever option when the beam is fixed at the left end. The tool reports the fixed reaction and fixed end moment.

How are distributed loads calculated?

A uniform load is converted to one equivalent load. Its value equals intensity times loaded length. Its position is the midpoint of the loaded section.

Why does shear jump at point loads?

A point load acts at one exact position. It changes shear instantly by the load amount. The moment curve stays continuous at that point.

Where does maximum bending moment occur?

It often occurs where shear changes sign. It may also occur at a support, fixed end, free end, or load boundary. Always review the full table.

Is this enough for final beam design?

No. It is a calculation aid. Final design should include material strength, deflection, safety factors, load combinations, connection behavior, and local building rules.