Calculate nominal bending stress, allowable stress, utilization, and required section modulus for a beam.
Set the inputs and run the calculation.
Check elastic nominal stress of a section under uniaxial bending.
Bending moment M, elastic section modulus W, allowable stress and safety factor are entered.
W represents how far load-carrying material lies from the neutral axis. The same moment gives lower edge stress with larger W; local notches can remove that benefit in the real part.
Edge stress is σ = M/W. Required W follows from moment and allowable stress.
10 kNm with W = 50 cm³ gives 200 MPa nominal bending stress.
Sources and limits: Dubbel, Mechanical Engineering Handbook, section C 2.4.5, bending stresses in straight beams; linear beam theory. Assess notches, stability, fatigue and combined loading separately.
Check elastic nominal stress of a section under uniaxial bending.
Under simple bending, normal stress is zero at the neutral axis and increases proportionally with distance from it in the linear-elastic model. Under the Bernoulli assumption, cross-sections remain plane. At the extreme fibre, elastic section modulus W = I/e combines second moment of area I and extreme-fibre distance e, giving sigma_b,max = |Mb|/W.
σb,max = |Mb| / W
W = I / eσallow = Re / SUtilization = σb,max / σallowWreq = |Mb| / σallow| Symbol / input | Meaning |
|---|---|
| Mb | Magnitude of the governing internal bending moment at the section checked, not merely an external point load. |
| I | Second moment of area about the centroidal principal axis actually subjected to bending. |
| e | Largest distance of the extreme fibre considered from the neutral axis. |
| W | Elastic section modulus I/e about the bending axis; asymmetric sections can have different values on their tension and compression sides. |
| Re, S | Entered yield strength or Rp0.2 and required safety factor; the calculator forms sigma_allow = Re/S. |
| Utilization | Ratio of calculated nominal bending stress to allowable stress; at most 100% passes this simplified check. |
Bending moment M, elastic section modulus W, allowable stress and safety factor are entered. W represents how far load-carrying material lies from the neutral axis. The same moment gives lower edge stress with larger W; local notches can remove that benefit in the real part.
Enter the bending moment at the section considered and its elastic section modulus W (or carry W over from the section-properties calculator). Compare the result with the material's allowable stress.
10 kNm with W = 50 cm³ gives 200 MPa nominal bending stress.
Bending stress is the magnitude of the largest elastic nominal stress at an extreme fibre. Allowable stress is formed here as Re/S; utilization compares sigma_b with that limit. At 100%, the selected margin to the entered yield strength is just exhausted. Required W is the minimum |Mb|/(Re/S): the actual section must provide at least this elastic section modulus about the axis that is really loaded.
Moment in N·m or kN·m, section modulus in mm³ or cm³, stress in MPa.
Quickly checking whether a beam or girder section withstands a known bending moment with sufficient margin, for example when preselecting a profile.
Dubbel, Mechanical Engineering Handbook, section C 2.4.5, bending stresses in straight beams; linear beam theory. Assess notches, stability, fatigue and combined loading separately.
Common mistake: Don't substitute second moment of area I for section modulus W – only W already accounts for the edge-fiber distance and directly gives a stress. This nominal-stress calculation excludes notch effects; at holes, shoulders or welds, local stress is noticeably higher.
At the section's edge fiber, i.e. the point farthest from the neutral axis in the bending direction – bending stress is highest there in the linear-elastic model.
No, it gives only the nominal bending stress. Transverse shear, notch effects, stability (buckling, lateral-torsional buckling) and fatigue must be checked separately.
Required W follows directly from moment divided by allowable stress; then use the section-properties calculator to find a profile whose W meets or exceeds that value.
The tension and compression edges can have different distances from the neutral axis and therefore different section moduli. The smaller W belonging to the relevant extreme fibre governs the largest stress magnitude.
From the internal-force diagram of the loaded member. Check the governing section using its internal moment; an external force cannot be entered as a moment without its lever arm.
Nominal bending stress then equals Re/S. This is not a general component approval because notches, fatigue, transverse shear and stability are absent from this simplified comparison.
Bending moment M acts about the centroidal axis. Bending stress is zero at the neutral axis and increases linearly in magnitude to σmax at the extreme fibres. Reversing the moment swaps tension and compression.
Bending moment and elastic section modulus give the maximum nominal stress. This is useful for quickly comparing candidate beam sections.
Valid for linear-elastic uniaxial bending. Notches, fatigue, stability, and combined loading require separate checks.