Use this beam calculator to generate reaction forces, shear force values, and a bending moment diagram for a simply supported beam with: one point load (at any location) and an optional uniformly distributed load (UDL) over the full span.
Shear Force Diagram (SFD)
Bending Moment Diagram (BMD)
What this moment diagram calculator does
A bending moment diagram calculator helps you understand how internal moments vary along a beam. Instead of hand-plotting every point, this tool computes reactions, evaluates shear and moment equations across the span, and plots the diagrams instantly.
This is especially useful for structural engineering students, civil designers, mechanical engineers, and anyone checking a beam quickly before moving into detailed design software.
Assumptions and sign convention
- The beam is simply supported at both ends.
- The point load acts downward.
- The UDL acts downward over the full span.
- Positive shear and sagging-positive bending moment convention is used.
- Units are assumed consistent: kN, m, and kN·m.
Core equations used
Support reactions:
\( R_B = \dfrac{P a + wL\left(\dfrac{L}{2}\right)}{L} \), \( R_A = P + wL - R_B \)
Shear along beam:
\( V(x) = R_A - wx - P \cdot H(x-a) \)
Moment along beam:
\( M(x) = R_Ax - \dfrac{wx^2}{2} - P\max(0, x-a) \)
Where \(H(x-a)\) is the step function (0 before point load, 1 after).
How to use the calculator
1) Enter beam geometry and loads
Input span L, UDL w, point load P, and location a. If you only need a point-load case, set UDL to zero. If you only need a full-span UDL case, set point load to zero.
2) Click “Calculate Diagram”
The tool computes left and right support reactions, identifies important moment values, and renders both shear force and bending moment diagrams.
3) Review key stations
A station table is generated at quarter points, supports, and the point load position. This is handy when creating design notes or checking hand calculations.
Why the moment diagram matters
The moment diagram tells you where flexural demand is highest. That peak region usually governs beam sizing, reinforcement, section modulus checks, and stress calculations. Pairing shear force and bending moment diagrams gives you a complete view of internal actions.
Common mistakes this tool helps avoid
- Forgetting that point load location strongly affects reaction split.
- Mixing units (for example N vs kN, mm vs m).
- Missing the shear jump at the point load.
- Assuming maximum moment is always at midspan.
- Skipping verification that end moments at simple supports return to zero.
FAQ
Can I use this as a shear force diagram calculator too?
Yes. It computes and plots both shear force and bending moment, so it works as a shear and moment diagram calculator in one page.
Does this handle cantilever beams?
Not in this version. This implementation is for simply supported beams only.
Is this suitable for final design?
Use it for rapid checks, education, and conceptual sizing. Final design should still be validated against your applicable building code and, when needed, a full structural analysis workflow.