Shear and Moment Calculator

Model point, uniform, and linear beam loads quickly. Check support reactions and internal demand safely. Export tables for records, lessons, and project reviews today.

Enter Beam Data

Example Data Table

Input Example Value Meaning
Beam Span 10 Total beam length
Point Load 20 at x = 5 Single downward force
Uniform Load 3 from x = 0 to x = 10 Constant distributed load
Station Count 20 Number of sampled beam divisions

Formula Used

Vertical equilibrium: RA + RB = total downward load.

Moment equilibrium for simple support: RB × L = sum of load moments about the left support plus applied couple.

Point load moment contribution: M = P × distance from load to section.

Uniform load resultant: W = w × loaded length.

Linear load resultant: W = loaded length × (start intensity + end intensity) / 2.

Shear at a section: V = left reaction minus loads located to the left of the section.

Moment at a section: M = reaction moment arm minus load moment arms, adjusted by applied couples.

How to Use This Calculator

Choose the beam type first. Enter the span using your preferred units. Use the same unit system for every value. Add a point load and its position if needed. Add uniform load limits when a constant load covers the whole beam or part of it. Use the linear load fields for triangular or trapezoidal loading. Enter an applied couple when a known external moment acts on the beam. Press calculate. Review the reaction values and the station table. Use CSV for spreadsheet work. Use PDF for quick reporting.

About the Shear and Moment Calculator

Purpose

A shear and moment calculator helps you study a beam before detailed design begins. It converts load data into support reactions, shear force values, and bending moment values. These outputs help you see where a beam is likely to experience high internal demand.

Load Options

This page is made for fast checks on simple beam cases. You can select a simply supported beam or a cantilever beam. You can add one point load, one uniform load, one linear distributed load, and one applied couple. The tool then samples the beam at equal stations. It reports shear and moment at each station.

Diagram Behavior

The calculator is useful for learning, estimating, and comparing load positions. A point load creates a jump in the shear diagram. A distributed load creates a sloped shear curve. A bending moment is the area under the shear curve. These patterns help users understand beam behavior without drawing every value by hand.

Static Equilibrium

The reaction calculation uses static equilibrium. For a simply supported beam, the sum of vertical forces and the sum of moments are balanced. For a cantilever, the fixed end carries the total vertical load and the fixed end moment. The calculator assumes downward loads are positive input values.

Reading Results

Use the result table to locate important positions. Large positive moments may show sagging regions. Negative moments may show hogging regions, especially near a fixed end. The maximum absolute moment is often important for beam sizing. The maximum shear is often important for support, web, and connector checks.

Practical Limits

This calculator should not replace a final engineering review. Real structures may include self weight, load combinations, moving loads, partial fixity, settlement, torsion, dynamic effects, and code factors. Material strength and section capacity must also be checked.

Unit Guidance

For best results, enter consistent units. If the span is in meters, use kN and kN per meter. If the span is in feet, use lb and lb per foot. The output will follow the same unit system. Review the example table before using project values. Then export the results for records or further study. Keep entries realistic. Avoid placing loads outside the beam span. Increase the station count when sharper diagrams are needed. Compare the exported table with hand sketches for a safer review process.

FAQs

1. What does this calculator find?

It finds support reactions, shear force values, and bending moment values at sampled beam positions. It also reports maximum and minimum values.

2. Which beam types are supported?

It supports a simply supported beam and a cantilever beam fixed at the left end. These cover many basic learning and checking cases.

3. Can I enter partial uniform loads?

Yes. Enter the uniform load intensity, start position, and end position. The tool converts the load into an equivalent resultant force.

4. Can I model a triangular load?

Yes. Use the linear load fields. Set one end intensity to zero and the other end to the required peak intensity.

5. What sign convention is used?

Downward loads are entered as positive values. Positive bending moments show sagging behavior. Cantilever fixed moments may appear negative.

6. Why should I increase station count?

A higher station count gives more table points. This can show sharper changes near point loads, load starts, and load ends.

7. Are the results suitable for final design?

No. Use them for study and preliminary checks. Final design should include code rules, load factors, material capacity, and professional review.

8. What units should I use?

Use one consistent unit system. For example, use meters with kN and kN per meter, or feet with pounds and pounds per foot.

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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.