Physics

Verified calculator with a transparent formula

Physics

Bending Stress Calculator.

Calculates the maximum bending stress in a beam under a point load, based on load, span, and section modulus.

Results update live as you type.
ƒ

Your inputs

How it works

  1. 1

    Enter the point load applied at the center of the beam.

  2. 2

    Enter the span length between supports.

  3. 3

    Enter the section modulus of the beam cross-section.

  4. 4

    The calculator computes the maximum bending stress using the formula.

(load * span) / (4 * section_modulus)

Frequently asked questions

What is bending stress?

Bending stress is the internal stress that resists bending in a beam. It is maximum at the top and bottom surfaces of the beam.

Why is the formula divided by 4?

For a simply supported beam with a central point load, the maximum bending moment is (load × span) / 4. Dividing by the section modulus gives the stress.

What units should I use?

Use consistent units: newtons for load, millimeters for span, and cubic millimeters for section modulus. The result will be in megapascals (MPa).

Explore this calculator category

PhysicsBrowse all

Results

Formula checked

Maximum Bending Stress

0MPa

Ask Anything

Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the maximum bending stress in a beam under a point load, based on load, span, and section modulus.

  1. Enter the point load applied at the center of the beam.
  2. Enter the span length between supports.
  3. Enter the section modulus of the beam cross-section.
  4. The calculator computes the maximum bending stress using the formula.

Formulas

The math behind this calculator, written out so you can verify the result.

Bending Stress Formula

σ = M / S

Bending stress equals the bending moment divided by the section modulus.

Example:

Input: M = 500,000 N·mm, S = 50,000 mm³

Calculation: 500,000 / 50,000

Result: 10 MPa

Real-world use cases

Where this calculation shows up in everyday life.

Beam Design

Check if a beam can safely carry a load without exceeding its material's yield strength.

Example: Select a steel beam with sufficient section modulus.

Structural Analysis

Evaluate existing structures for load capacity.

Example: Assess a bridge girder under a heavy vehicle.

Mechanical Components

Design shafts, levers, and frames that experience bending.

Example: Calculate stress in a bicycle crank arm.

Tips and common mistakes

Tips

  • Use consistent units to avoid conversion errors.
  • For distributed loads, use a different formula.
  • The section modulus depends on cross-section shape; for a rectangle it is (b×h²)/6.
  • Always compare the calculated stress with the material's allowable stress.

Common Mistakes to Avoid

  • Using the wrong bending moment formula for the load case.
  • Forgetting to convert units (e.g., using meters instead of millimeters).
  • Using the area moment of inertia instead of the section modulus.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.