# [Summary] Bending stress in beams - anamsmind

A beam is said to be in pure bending if is subjected to equal and opposite couples M and M' acting in the same longitudinal plane. The member will then bend under the action of the couples as shown in the following figure:

 Image source: F. Beer. "Mechanics of Materials," Sixth Edition

### The bending stress

The bending stress which is maximum on the surface and minimum in the center can be calculated from the following equation:

### The radius of curvature "R"

The radius of curvature "R" can be calculated from the following equation:

### The Area moment of inertia "I"

• The Area Moment of Inertia for a rectangular section can be calculated from:

• The Area Moment of Inertia for a solid cylindrical section can be calculated from:

• The Area Moment of Inertia for a hollow cylindrical section can be calculated from:

### The Neutral Axis (N.A)

For symmetrical shapes, the neutral axis is the line that passes through the center of the shape as shown below:

If the shape is formed of many unsymmetrical parts or parts of different dimensions - as shown below, we then must use the "Centroid" to locate the position of neutral axis as shown below:
 Image source: F. Beer. "Mechanics of Materials," Sixth Edition

Sample problem 4.2 in the book: F. Beer. "Mechanics of Materials," Sixth Edition, represents a good example of how to use the centroid.

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### Resources:

• F. Beer. "Mechanics of Materials," Sixth Edition