Free Beam Calculator: Shear Force and Bending Moment Diagrams
Model your beam with fixed, pinned and roller supports and internal hinges, apply point loads, moments and distributed loads, and get the support reactions and the shear force and bending moment diagrams in seconds. It solves simply supported, cantilever and multi-span continuous beams, determinate or indeterminate.
- ✓Reactions at every support, including fixed-end moments
- ✓Shear force (SFD) and bending moment (BMD) diagrams with values
- ✓Continuous beams, overhangs and internal hinges
- ✓Uniform, triangular and trapezoidal loads, point loads and moments
- ✓Metric, MKS and imperial units · save and share your beams
Free with a Google account · daily free credits · Premium for unlimited use
Worked example: continuous beam with a hinge and an overhang
This is the example that opens in the calculator: a 14 m beam, fixed at A, on rollers at B and D, with an internal hinge at C and a 2 m overhang. It carries a triangular load from 0 to 12 kN/m over the first 4 m, a 30 kN·m moment at 6 m, a 30 kN point load at 10 m and a uniform load of 8 kN/m on the overhang.
Support reactions
| Support | Position | Reaction |
|---|---|---|
| A (fixed) | 0 m | Ay = 5.55 kN · M = 4.20 kN·m |
| B (roller) | 4 m | By = 29.45 kN |
| D (roller) | 12 m | Dy = 35.00 kN |
Check: the reactions add up to 70 kN, the total load (24 kN triangular + 30 kN point load + 16 kN on the overhang).
What the diagrams show
- The bending moment is zero at the hinge (x = 8 m), as it must be.
- The largest sagging moment, +22.00 kN·m, is under the point load at 10 m.
- The applied 30 kN·m moment makes the diagram jump from 8.00 to −22.00 kN·m at 6 m.
- Hogging moments over the supports: −14.00 kN·m at B and −16.00 kN·m at D.
- The shear jumps by the reaction at each support and drops by 30 kN under the point load.
Video tutorial: model this beam step by step
Supports, the hinge, every load type and how to read the results, in about two minutes.
How to use the beam calculator
1. Choose units and set the length
Pick metric (kN, m), MKS (ton, m) or imperial (kip, ft) units, and enter the total length of the beam. Overhangs are just parts of the beam beyond the last support.
2. Add supports and hinges
Place fixed, pinned or roller supports at any position. Add internal hinges where the beam should not transmit moment. If the supports cannot hold the beam (it would move as a mechanism), the calculator warns you instead of returning wrong results.
3. Apply the loads
Point loads and concentrated moments at any position, and distributed loads defined by a start and end value over any range: equal values give a uniform load, different values a triangular or trapezoidal one.
4. Calculate and read the results
Press calculate to get the reactions, the free body diagram and the shear force and bending moment diagrams. Save the beam to your account or share it with a link.
Continuous and indeterminate beams
Equilibrium alone solves simply supported beams and cantilevers. Beams with more supports than needed (propped cantilevers, fixed-fixed beams and continuous beams over several supports) are statically indeterminate: their reactions also depend on how the beam bends. The calculator solves them with the matrix stiffness method, using the section and material of the beam, so you get the same results as structural analysis software.
For a quick check of a standard case, the beam formulas tables give the closed-form reactions and maximum shear and moment for 37 common load cases:
Frequently Asked Questions
Can this beam calculator solve continuous and statically indeterminate beams?
Yes. It uses the stiffness method, so it solves simply supported, cantilever, propped, fixed and continuous beams with any number of spans and supports. Internal hinges are supported too, as in Gerber beams.
Which supports and loads can I use?
Fixed, pinned and roller supports, plus internal hinges. Loads can be point loads, concentrated moments and distributed loads that vary linearly between any two points, so uniform, triangular and trapezoidal loads are all covered.
What results does it give?
The support reactions (forces and the moment at fixed supports), the free body diagram and the shear force and bending moment diagrams with their values at every key point.
Which units can I work in?
Metric (kN, m, kN·m), MKS (ton, m, ton·m) and imperial (kip, ft, kip·ft). The diagrams and reactions are shown in the units you choose.
Is the beam calculator free?
Yes. Sign in with your Google account and calculate for free with daily credits: you start with 7 and get 3 more every 24 hours after you run out. Premium removes the limit if you need unlimited calculations.
Can I save and share my beam?
Yes. Save your models to your account and reopen them later, or share a link so a classmate or colleague can open the same beam.