Beam Analysis Simulator
Configure a beam, supports, material, section, and loads to visualize deflection, shear force, bending moment, and stress checks.
What this beam calculator computes
Enter a span, support condition, load, material, and cross-section, and the tool solves the closed-form Euler–Bernoulli beam equations at 200 stations along the beam. It reports the deflection curve, the shear-force diagram, the bending-moment diagram, the maximum bending stress, and the factor of safety against the material's yield strength.
- Support conditions: simply supported, cantilever, and fixed-fixed.
- Loading: a point load at any position, or a uniformly distributed load.
- Cross-sections: rectangular, circular, and I-section, with the second moment of area computed from the entered dimensions.
- Materials: steel, aluminium, concrete, oak, titanium, or a custom material defined by elastic modulus, density, and yield strength.
Equations used
The model is linear-elastic small-deflection beam theory. For a simply supported beam with a central point load P over span L, the standard results are:
- Maximum deflection: δmax = P·L³ / (48·E·I)
- Maximum bending moment: Mmax = P·L / 4
- Bending stress: σ = M·c / I, where c is the distance to the extreme fibre
- Second moment of area, rectangular section: I = b·h³ / 12
- Factor of safety: FoS = σyield / σmax
How to use it
Set the beam type and load type first, because they determine which closed-form solution applies. Enter the span, load magnitude, and load position, then pick the material and section. Press Analyze to redraw the diagrams and update the summary values. Switch between the deflection, moment, and shear views to read each diagram; the deflection view exaggerates the deformed shape by the amplification factor shown on the plot so that a sub-millimetre deflection is still visible.
Frequently asked questions
- How do you calculate maximum beam deflection?
- For a simply supported beam carrying a point load P at midspan, the maximum deflection is δmax = P·L³ / (48·E·I), where L is the span, E is the elastic modulus, and I is the second moment of area of the cross-section. For a cantilever with a point load at the free end it is δmax = P·L³ / (3·E·I), and for a simply supported beam under a uniformly distributed load w it is 5·w·L⁴ / (384·E·I). This calculator evaluates the appropriate closed-form solution for the support and load case you select.
- What is a safe factor of safety for a beam?
- The factor of safety is the yield strength of the material divided by the maximum bending stress. General structural practice looks for a factor of safety of at least 1.5 to 2 against yield for static loads, with higher values where loads are uncertain, fatigue is a concern, or a governing design code demands it. This tool reports the ratio so you can compare it against the code that applies to your work.
- What is the difference between shear force and bending moment?
- Shear force is the internal transverse force at a section of the beam, and bending moment is the internal couple at that section. They are linked: the bending moment is the integral of the shear force along the beam, so the moment reaches an extreme wherever the shear diagram crosses zero. The moment governs bending stress; the shear governs shear stress and web design.
- Does this beam calculator account for self-weight?
- No. It solves the applied load case you enter. The summary reports the beam's own mass so you can decide whether self-weight matters, and you can add it as an equivalent uniformly distributed load if it does.