Bending Stress Calculator NZ

This calculator finds the bending stress in a beam using the flexure formula, the relationship at the heart of structural and mechanical engineering. When a beam bends under load, one face is stretched in tension and the other is compressed, while a neutral axis through the middle feels no stress. The bending stress at any point is greatest at the surfaces farthest from the neutral axis and is given by the flexure formula: the bending moment times the distance from the neutral axis, divided by the second moment of area of the cross-section. This tells engineers whether a beam will safely carry its load or be overstressed, and it governs the design of joists, shafts, bridges and machine parts. This tool computes it. You enter the bending moment, the distance from the neutral axis to the point of interest, usually the outer surface for the maximum stress, and the second moment of area of the cross-section, and the calculator returns the bending stress in megapascals, the value in pascals, the section modulus, and the bending moment for reference. The results update as you type. Use it for engineering study, for checking a beam against its material's strength, or for understanding how section shape resists bending. The stress is the moment times the distance over the second moment of area. The combination of the second moment of area divided by the distance to the surface is called the section modulus, and dividing the moment by it gives the surface stress directly, which is why the section modulus is the key shape property for bending. A deeper section has a much larger second moment of area and section modulus, so it carries the same moment at far lower stress, which is why beams are made deep rather than wide. Compare the result against the material's allowable stress to judge safety.

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Bending moment (N·m)

Distance from neutral axis (m)

Second moment of area I (m⁴)

62.5 MPa

bending stress

In pascals62,500,000 Pa

Section modulus8.000e-5 m3

Bending moment5,000 N·m

Flexure formula: stress = moment x distance / second moment of area. Section modulus = I / distance. A deeper section greatly lowers the stress for the same moment.

How it works

The flexure formula gives the bending stress as the bending moment multiplied by the distance from the neutral axis, divided by the second moment of area of the cross-section. The section modulus is the second moment of area divided by the distance to the outer surface; dividing the moment by it gives the maximum surface stress directly.

Worked example

For a bending moment of 5,000 newton metres, with the outer surface 0.1 metres from the neutral axis and a second moment of area of 8 times 10 to the minus 6 metres to the fourth, the stress is 5,000 times 0.1 divided by 0.000008, which is 62,500,000 pascals, or 62.5 megapascals.

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Frequently asked questions

What is the flexure formula?

It gives the bending stress in a beam as the bending moment times the distance from the neutral axis, divided by the second moment of area. The maximum stress occurs at the surfaces farthest from the neutral axis, which is where a beam is most likely to fail.

What is section modulus?

The section modulus is the second moment of area divided by the distance from the neutral axis to the outer surface. Dividing the bending moment by it gives the maximum bending stress directly. It is the key shape property describing a section's resistance to bending.

Why are beams made deep rather than wide?

Because the second moment of area, and so the section modulus, grows with the cube of the depth but only linearly with the width. A deeper section therefore resists bending far more effectively, carrying the same moment at much lower stress, which is why I-beams are tall.