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Bending Stress In Beam Calculator

Work out bending stress in beam instantly with clear inputs, formula shown and shareable results.

About Bending Stress In Beam Calculator

Bending stress is moment divided by section modulus, sigma = M / Z. Keeping units consistent, a moment in kilonewton metres becomes newton millimetres by multiplying by a million, and a modulus in cubic centimetres becomes cubic millimetres by multiplying by a thousand. Allowable stress in working stress design is conventionally 0.66 times yield.

Formulas

Bending stress

sigma = M / Z

Capacity

M capacity = 0.66 x fy x Z

Worked example

With the default values below, Bending Stress In Beam Calculator returns Bending stress of 56.25. Change any input above and every figure here is recalculated in your browser.

Inputs used

Applied bending momentminimum 0 kN·m
45 kN·m
Elastic section modulusminimum 0.1 cm³
800 cm³
Steel yield strengthminimum 10 MPa
250 MPa

Results

Bending stress
56.25 MPa
Allowable bending stress
165.00 MPa
Utilisation
34.1% %
Moment capacity of the section
132.00 kN·m

Step by step

  1. 1Values used
  2. 2Bending stress
  3. 3Capacity
  4. 4Bending stress= 56.25 MPa
  5. 5Allowable bending stress= 165.00 MPa
  6. 6Utilisation= 34.1 %
  7. 7Moment capacity of the section= 132.00 kN·m

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Preliminary estimate only. Member design must be verified by a qualified structural engineer including lateral torsional buckling, shear and deflection checks.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Member design must be verified by a qualified structural engineer including lateral torsional buckling, shear and deflection checks.

Frequently Asked Questions

How is the Bending Stress In Beam figure worked out?

sigma = M / Z. Bending stress is moment divided by section modulus, sigma = M / Z.

When is the plastic modulus used instead?

In limit state design, where the section is compact enough to develop a full plastic hinge. The plastic modulus is typically 10-20 percent larger than the elastic value for a rolled I section.

What values do I need to enter?

This calculator takes 3 inputs: Applied bending moment, Elastic section modulus, Steel yield strength. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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Bending Stress In Beam Calculator – Calculate Bending stress