Example Data Table
| Input |
Example value |
Meaning |
| Beam length |
8 m |
Total span length. |
| Support type |
Simply supported |
Two vertical reactions. |
| Point load P1 |
12 kN at 3 m |
Concentrated downward load. |
| UDL 1 |
2 kN/m from 1 m to 5 m |
Distributed downward load. |
| Self weight |
0.25 kN/m |
Uniform beam weight. |
Formula Used
The calculator uses static equilibrium for reaction forces.
Vertical equilibrium: ΣFy = 0
Moment equilibrium: ΣM = 0
Shear force: V(x) = Σ reactions left of x − Σ point loads left of x − Σ distributed loads left of x
Bending moment: M(x) = Σ R(x − xR) − Σ P(x − xP) − Σ w a(x − xc) − Σ applied moments
For a uniform load, its resultant is w multiplied by loaded length. Its action point is the loaded segment centroid.
How to Use This Calculator
Enter the beam length first. Select a support condition. Use simply supported for pin and roller beams. Use cantilever options for fixed end beams.
Add point loads with their positions. Add distributed loads with start and end points. Add applied moments when needed. Use positive values for downward loads. Press calculate. The result appears above the form.
Review reactions, maximum shear, and maximum bending moment. Check the plotted diagrams. Download CSV for spreadsheets. Download PDF for a compact report.
Shear Force and Moment Diagram Guide
What the Diagram Shows
A shear force moment diagram explains how a beam carries loads. It shows internal shear force and bending moment at many positions. These values help students and engineers understand beam behavior. The shear diagram changes when a load is crossed. The moment diagram changes slope according to shear force.
Why Reactions Matter
Every beam calculation starts with support reactions. A simply supported beam has two vertical reactions. A cantilever has one vertical reaction and one fixed moment. The calculator balances vertical forces and moments. This gives the unknown support actions before diagram values are plotted.
Point Loads and Distributed Loads
A point load acts at one exact position. It creates a jump in the shear diagram. A uniform distributed load acts over a length. It creates a sloped shear line. Its resultant equals intensity multiplied by loaded length. The resultant acts at the middle of that loaded part.
Bending Moment Meaning
Bending moment measures the turning effect inside the beam. High bending moment often controls beam size. Positive and negative values show different bending directions. The largest absolute value is important for design checks. It helps compare stress demand with material capacity.
Good Input Practice
Use consistent units for all inputs. If length is in meters, use kilonewtons and kilonewton meters. Keep load positions within the beam length. Use enough stations for a smooth graph. More stations give a clearer curve, but they also make a longer result table.
Physics Use
This tool is useful for physics, mechanics, and strength of materials. It supports classroom examples and early design checks. It is not a replacement for code based structural design. Real structures need load combinations, safety factors, deflection checks, and professional review.
FAQs
1. What is shear force?
Shear force is the internal vertical force at a beam section. It balances loads and reactions on one side of the cut.
2. What is bending moment?
Bending moment is the internal turning effect at a beam section. It shows how strongly the beam bends at that point.
3. Which sign convention is used?
Downward loads are entered as positive values. Upward reactions are calculated by equilibrium. Applied moments are treated as clockwise positive in reaction equations.
4. Can I calculate cantilever beams?
Yes. Select fixed left or fixed right. The calculator finds vertical reaction and fixed support moment for the cantilever case.
5. What does UDL mean?
UDL means uniform distributed load. It spreads load evenly over a selected beam length, such as beam self weight or floor load.
6. Why does shear jump at point loads?
A point load acts at one location. When the section passes that point, the shear value changes suddenly by the load amount.
7. Why is the moment diagram curved under UDL?
A uniform load makes shear vary linearly. Since moment slope equals shear, the bending moment diagram becomes curved.
8. Can I export the results?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a compact printable report.