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Simply supported beam reactions

Static reactions and the peak sagging moment. No shear design, deflection limit or steel check.

Load case Uniform load over the whole spanPoint load at midspanPoint load at a set distance from A

Span L (m)

UDL w (kN/m)

Point load P (kN)

Distance a from A (m)

CalculateReset

Method

UDL: R_A = R_B = wL/2, M_max = wL²/8. Midspan point load: R = P/2, M = PL/4. Offset point load: R_A = Pb/L, R_B = Pa/L, M = Pab/L.

Worked UDL: 8 kN/m on 6 m gives reactions of 24 kN each and a midspan moment of 36 kN·m.

Self-weight, partial factors and lateral restraint are not included. Do not use the moment to size a beam without a competent check.

Logic: how this figure is built.

What the reactions are

A simply supported beam with a uniform load has equal reactions of wL/2 and a midspan moment of wL²/8. The worked beam, 8 kN/m on 6 m, has reactions of 24 kN and a moment of 36 kN·m. A central point load has reactions of P/2 and a moment of PL/4.

The supports are a pin and a roller. A fixed end, a cantilever and a continuous beam have different reactions. Putting this number against a continuous model will not match, and the mismatch is the support condition, not a rounding error.

Load and span need consistent units. 8 kN/m on 6 m is 48 kN of total load. The two reactions sum to that. If they do not, the load was not uniform or the span was not the loaded span.

The moment is not a section size. It becomes a stress only after you divide by a section modulus. This page stops at the statics.

• Related: direct stress
• structural logic

Last checked 3 October 2026. Worked figures are scenarios. See methodology and the disclaimer.