Simply Supported Beam Calculator
Estimate support reactions, maximum shear, maximum bending moment, and maximum deflection for two common load cases: a center point load and a full-span uniform load.
For conceptual sizing only. Verify with code checks and a licensed engineer before construction.
How to use this beam calculator
- Select a load case: center point load or full-span uniform load.
- Enter the span length L in meters.
- Enter the load magnitude (either P in kN or w in kN/m).
- Enter material stiffness E and section property I.
- Click Calculate to get reactions, shear, moment, and deflection.
What the results mean
1) Support reactions
These are the vertical forces carried by each support. For both load cases in this tool, the beam is symmetric, so left and right reactions are equal.
2) Maximum shear force
The maximum internal vertical force in the beam. Shear is often critical near supports, especially for short and heavily loaded beams.
3) Maximum bending moment
The peak internal bending demand. This value is used with section modulus and yield stress to evaluate bending capacity.
4) Maximum deflection
Estimated vertical displacement at midspan for these load cases. Serviceability limits (for example L/360) are commonly used to keep floors and roofs feeling stiff enough.
- Center point load:
R = P/2,Mmax = P·L/4,δmax = P·L³/(48·E·I) - Uniform load:
R = w·L/2,Mmax = w·L²/8,δmax = 5·w·L⁴/(384·E·I)
Key assumptions and limitations
This beam calculator is intentionally focused on common textbook cases. The results are useful for quick checks and learning, but they are not a full structural design package.
- Beam is simply supported at both ends.
- Material behavior is linear elastic.
- Deflections are small.
- No axial force, torsion, or lateral buckling effects included.
- No partial load patterns, multiple point loads, or varying stiffness along span.
Worked example
Example A: Center point load
Suppose a beam has a 6 m span and a 20 kN point load at midspan. Reactions are 10 kN each, maximum moment is 30 kN·m, and deflection depends on E and I. If E = 200 GPa and I = 85,000,000 mm⁴, expected deflection is modest and easy to check against a serviceability criterion.
Example B: Uniform load
For a 6 m span carrying 8 kN/m, each support reaction becomes 24 kN. Maximum moment is 36 kN·m at midspan. Deflection rises more quickly than in many point-load scenarios because of the L⁴ term in the equation.
Practical tips for better preliminary beam sizing
- Start by checking both strength (moment/shear) and serviceability (deflection).
- If deflection is too high, increasing section depth is often more effective than adding material width.
- Keep units consistent. This calculator converts internally, but your downstream checks must also align.
- Use conservative live-load assumptions early, then refine with project-specific criteria.
Final note
Use this beam calculator for fast decision support in concept design, comparisons between sections, and educational analysis. For permit drawings, final member sizing, and code compliance, always complete a full engineering review.