What is Bending Stress?
Bending stress (or flexural stress) is the internal stress that develops in a beam when it is subjected to a load. [1, 2] When a beam bends, one side is compressed (pushed together) and the opposite side is in tension (pulled apart). The bending stress is highest at the top and bottom surfaces and zero at the center (the "neutral axis").
The fundamental formula for bending stress is σ = M / S, where σ (sigma) is the bending stress, M is the maximum bending moment, and S is the section modulus of the beam's cross-section. [3, 4] This calculator assumes a simply supported beam with a concentrated load at its center, a very common scenario.
Key Concepts
| Concept | Explanation |
|---|---|
| Bending Moment (M) | The internal reaction induced by the load. For a simply supported beam with a center load, M = (Force × Length) / 4. [5] |
| Section Modulus (S) | A property of the beam's cross-sectional shape that measures its resistance to bending. A deeper beam has a much larger section modulus and is stronger. For a rectangle, S = (width × depth²) / 6. [6] |
| Yield Strength | The maximum stress a material can withstand before it starts to permanently deform. The calculated bending stress should always be less than the material's yield strength, with a factor of safety applied. |
How to Use the Calculator
- Select the shape of your beam's cross-section (Rectangle or Round).
- Enter the magnitude of the force (load) applied to the center of the beam.
- Enter the span (length between supports) of the beam.
- Provide the dimensions of the cross-section (width and depth for a rectangle, diameter for a round beam).
- Click "Calculate Stress" to see the results.
Frequently Asked Questions
What if my load isn't at the center?
This calculator is specifically for a load at the center of a simply supported beam. Other loading conditions (e.g., off-center, distributed load, cantilevered beam) create different bending moments and require different formulas. This tool provides a common baseline for analysis.
What unit is the bending stress result in?
The result is in Pounds per Square Inch (PSI), which is the standard unit for stress in the Imperial system. This value can be compared directly to the yield strength of your chosen material (also measured in PSI).