A beam is said to be in ** pure bending** if is subjected to equal and opposite

**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:**

*couples*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
can be calculated from:*Area Moment of Inertia for a rectangular section*

- The
can be calculated from:*Area Moment of Inertia for a solid cylindrical section* - The
can be calculated from:*Area Moment of Inertia for a hollow cylindrical section*

### The Neutral Axis (N.A)

For symmetrical shapes, the

**is the line that passes through the center of the shape as shown below:***neutral axis*If the shape is formed of many unsymmetrical parts or parts of different dimensions - as shown below, we then must use the "

**" to locate the position of***Centroid***as shown below:***neutral axis*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*### [Important] A bonus

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