How do I calculate bending moment on a simply supported beam?
Design & Analysis
For a simply supported beam of span L with a uniformly distributed load w (kN/m), the maximum bending moment is M = wL²/8 at midspan. For a single concentrated load P at midspan, M = PL/4. For a concentrated load P at distance a from one support (where b = L-a), M = Pab/L. For multiple loads, sum the contributions. The maximum shear is at supports: V = wL/2 for uniform load, V = P/2 for central point load. In CalcSteel, you don't need to compute this manually — the FEM solver produces the full bending moment and shear diagrams when you run an analysis. Just model the beam, define the support conditions (pin + roller), apply the load, and click Calculate.
Key takeaways
- For a simply supported span, max moment is PL/4 (central point load) or wL²/8 (uniform load), each at midspan — derived from statics alone.
- Galileo published the first beam-strength theory in 1638 but put the neutral axis at the base, overestimating capacity ~3×; Coulomb (1773) and Navier (1826) gave the modern correct treatment.
- Finding the moment (demand) and proving the section is safe (capacity) are two separate steps — the second one depends entirely on your design code.
- Modern browser tools reduce the moment via finite elements, then auto-verify φMn ≥ Mu against AISC 360, Eurocode 3, NBR 8800 or IS 800.
Full guide
Bending Moment in a Simply Supported Beam
Step-by-step with figures and sources — 9 min read
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