What is Bending Stress?
Bending stress (also called flexural stress) is the internal stress induced in a structural member when an external force or moment causes it to bend. It is a normal stress that varies linearly from the neutral axis of the beam, with maximum values occurring at the outermost fibers.
Formula
The bending stress formula is:
$$\sigma = \frac{M \cdot c}{I}$$
Where:
- ฯ = bending stress (N/mยฒ or Pa)
- M = bending moment (Nm)
- c = distance from the neutral axis to the outermost fiber (m)
- I = moment of inertia of the cross-section (mโด)
How to Calculate Bending Stress
Step-by-Step Example:
Given:
- Bending Moment: 200 Nm
- Distance from the Neutral Axis: 0.05 meters
- Moment of Inertia: 0.001 mโด
Calculate the Bending Stress:
$$\sigma = \frac{200\ \text{Nm} \cdot 0.05\ \text{m}}{0.001\ \text{m}^4} = 10{,}000\ \text{N/m}^2$$
So, our bending stress turns out to be 10,000 N/mยฒ or 10 kPa.
Applications
- Structural Engineering: Designing beams, columns, and other load-bearing elements
- Mechanical Design: Analyzing shafts, axles, and machine components
- Material Selection: Determining if a material can withstand applied bending loads
- Failure Analysis: Identifying potential points of failure in structures
- Civil Engineering: Bridge design, building frames, and cantilever structures
Key Concepts
- Neutral Axis: The line within a beam where stress is zero during bending
- Moment of Inertia: A geometric property representing resistance to bending
- Maximum Stress: Occurs at the point furthest from the neutral axis
- Sign Convention: Tensile stress (positive) on one side, compressive stress (negative) on the other
- Elastic Limit: Bending stress must remain below material yield strength to avoid permanent deformation