Beam Calculator (Simply Supported)
Calculate reactions, maximum shear force, maximum bending moment, and maximum deflection for a simply supported beam under either a full-span UDL or a point load.
Assumptions: linear elastic behavior, small deflection theory (Euler-Bernoulli), and prismatic member with constant E and I.
Why use an online beam calculator?
A good online beam calculator can save serious time during early design checks. Instead of manually recomputing reactions and deflections each time you tweak span length or loading, you can evaluate alternatives in seconds. This is especially useful for conceptual structural design, framing layouts, and educational work where you need fast feedback.
What this beam calculator computes
This page focuses on a simply supported beam and provides:
- Support reactions at left and right supports
- Maximum shear force
- Maximum bending moment
- Maximum deflection and location
- Optional maximum bending stress if section modulus is supplied
Supported load cases
- Uniformly Distributed Load (UDL) over the full span
- Single Point Load at any distance from the left support
Input guide
1) Geometric input
L is the clear span length in meters. Be careful with unit consistency: all calculations are converted to SI internally.
2) Material stiffness
E is entered in GPa (for example, steel is commonly around 200 GPa). Higher E means lower deflection for the same loading and section.
3) Section property
I is the second moment of area (cm⁴). This strongly affects stiffness: deflection is inversely proportional to I.
4) Optional stress check
If you provide Z (section modulus in cm³), the tool estimates bending stress using σ = M / Z. Leave blank if you only want force/deflection results.
How the math works
Static equilibrium: reactions are computed from force and moment balance.
Internal actions: shear and moment are evaluated from the selected load case.
Deflection: numerical integration of the curvature equation y''(x) = M(x)/(EI) along the span, then boundary conditions are applied for a simply supported beam (y(0)=0 and y(L)=0).
Worked example
Suppose you have a 6 m steel beam with E = 200 GPa and I = 8500 cm⁴ under a 12 kN/m full-span UDL.
- Total load = 72 kN
- Each support reaction = 36 kN
- Maximum bending moment = 54 kN·m (at midspan)
- Maximum deflection is reported directly by the calculator in mm
Now change the UDL to a point load and move it off-center. You will immediately see reaction redistribution and a shift in the critical bending location.
Practical tips for better beam design checks
- Always verify units before comparing with code limits.
- Check both strength (stress/moment) and serviceability (deflection).
- Use realistic stiffness values (especially for timber or composite members).
- For final design, include load combinations, safety factors, and local code requirements.
Limitations and engineering caution
This calculator is intended for quick checks and learning. It does not replace full structural analysis for complex conditions such as multiple spans, non-prismatic members, partial fixity, dynamic effects, shear deformation in deep beams, or nonlinear material behavior.
For permit drawings, fabrication details, and safety-critical work, calculations should be reviewed and stamped by a qualified structural engineer.