Bending Stress Calculator: worked example
This example is generated from PROFENG's own default input set and the implemented relationship. It is not copied from a cited publication.
Relationship
σ = M c / I
This calculator determines bending stress from bending moment, distance to extreme fibre, second moment of area. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
Inputs
- Bending moment (moment) = 10 kN·m
- Distance to extreme fibre (c) = 50 mm
- Second moment of area (inertia) = 8,000,000 mm⁴
Working
(10)*1000*((50)/1000)/((8000000)*1e-12)/1e6 = 62.5 MPa
Bending stress: 62.5 MPa
Assumptions and limits
- Loads and geometry are represented by the idealized relationship shown.
- Material behavior is treated according to the simple formula, typically linear-elastic where relevant.
- Units and section properties are consistent with the displayed equation.
- Classical linear-elastic beam theory is applicable.
- Section remains elastic and the neutral-axis/section properties correspond to the bending axis.
- Local stress concentrations and lateral-torsional instability are outside this simple stress calculation.
Formula source and acknowledgement
Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek, Mechanics of Materials, 8th, 2020, McGraw Hill. Credit belongs to the cited author(s)/publisher; PROFENG presents its own implementation and does not imply endorsement.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks and an independent implementation where applicable.
This worked example is for engineering screening and education. Replace defaults with traceable project data and confirm the method, assumptions, standards and equipment information before design, procurement or operation.