Calculate the normal stress in a beam resulting from an applied bending moment using the flexure formula.
Last updated: March 2026
Bending stress is the normal stress that an object encounters when it is subjected to a large load at a particular point that causes the object to bend. It is a combination of compressive and tensile stresses that occur simultaneously in different parts of the beam.
When a beam is bent, the fibers at the top are compressed (compressive stress) and the fibers at the bottom are stretched (tensile stress). The "neutral axis" is the theoretical line running through the center of the cross-section where the stress is zero—it's the transition point between compression and tension.
Understanding bending stress is helpful in structural analysis, as it shows how stress varies across a beam's cross-section. Maximum bending stress typically occurs at the points furthest from the neutral axis (the top and bottom surfaces). However, this calculation alone is not sufficient for complete beam design—factors like material yield strength, safety factors, shear stresses, and buckling must also be considered.
Where:
A beam experiences a bending moment of 5,000 lb-in. The neutral axis is 2 inches from the outer fiber. The moment of inertia is 10 in⁴.
Disclaimer: This calculator provides theoretical bending stress values based on the flexure formula and ideal assumptions. It does not account for material imperfections, dynamic loads, combined stresses, stress concentrations, fatigue, or plastic deformation. Use for estimation and educational purposes only. Always consult engineering references or a professional for critical applications and safety-critical structural design.
Maximum bending stress occurs at the fibers furthest from the neutral axis—typically the top and bottom surfaces of the beam. This is why beams often fail by cracking at these outer surfaces first.
The neutral axis is the axis in the cross-section of a beam along which there are no longitudinal stresses or strains. For symmetric beams, it passes through the centroid of the cross-section.
The shape determines the Moment of Inertia (I). A higher I value (like in an I-beam or H-beam) significantly reduces bending stress for the same applied moment. This is why structural beams have flanges far from the neutral axis.
Consistency is critical. In Imperial units, use lb-in for moment, inches for y and I⁴ for inertia—the result will be in psi. In metric, use N-mm, mm, and mm⁴ to get MPa.
Section modulus (S = I/y) is a geometric property that simplifies the flexure formula to σ = M/S. It's commonly tabulated for standard beam shapes.
For standard shapes (rectangles, I-beams, channels), use engineering handbooks or online tables. For complex shapes, calculate using integration or CAD software.
This formula applies to beams in pure bending with elastic behavior. It assumes the material follows Hooke's law and doesn't account for shear stress, local buckling, or plastic deformation.
Allowable stress depends on the material and safety factor. For structural steel, it's typically 0.6 to 0.66 times the yield strength. Always consult building codes and material specifications.
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