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Once you have a moment from analysis, bending stress follows in one step. This article gives the relationship, defines the section modulus, and explains where the analysis output ends and the design check begins.

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The formula

Divide the moment by the elastic section modulus: σ = M / S where σ is the bending stress, M is the bending moment, and S is the elastic section modulus.

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What the section modulus is

The elastic section modulus S is the second moment of area I_x divided by c. Here c is the distance from the neutral axis to the extreme fiber: S = I_x / c For a symmetric section, c is half the depth, and the same S applies to the top and bottom fibers. For an unsymmetric section, the two distances differ. Compute S separately for each fiber and use the smaller value where it matters.

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Using the beam calculator output

The Calcs.com beam calculator returns the moment demand M*. Once you know S for your section, the stress follows directly from σ = M / S. Two practical points:
  • Read the moment at the location you care about, not only at midspan. On continuous beams the support moment often controls.
  • Keep units consistent. Mixing kip-ft with in³, or kN·m with mm³, is a common source of error by a factor of 12 or 10⁶.
Section properties including I_x and S can be looked up in the Calcs.com section properties library.

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Stress is not yet a check

Calculating a stress is an analysis result. Checking that stress against an allowable or factored value is a design check rather than an analysis output. That check depends on the standard you design to, the design method, and the section classification. It also depends on limit states the stress figure alone does not capture, lateral-torsional buckling among them. A stress below the allowable value does not by itself confirm the member is adequate. Use the Calcs.com design calculators when you need the code check itself, with the governing standard and the working shown. Responsibility for the design stays with the engineer.