# Area Moment of Inertia - Typical Cross Sections II

## Area Moment of Inertia, Moment of Inertia for an Area or Second Moment of Area for typical cross section profiles

**Area Moment of Inertia **or** Moment of Inertia for an Area - **also known as **Second Moment of Area** - *I*, is a property of shape that is used to predict deflection, bending and stress in beams.

### Area Moment of Inertia for typical Cross Sections II

#### Angle with Equal Legs

The Area Moment of Inertia for an angle with equal legs can be calculated as

*I _{x} = 1/3 [2c^{4} - 2 (c - t)^{4} + t (h - 2 c + 1/2 t)^{3}] (1a)*

*where *

*c = y _{t} cos 45^{o } (1b)*

*and *

*y*

_{t}= (h^{2}+ ht + t^{2}) / [2 (2 h - t ) cos 45^{o}]*(1c)*#### Angle with Unequal Legs

The Area Moment of Inertia for an angle with unequal legs can be calculated as

*I _{x} = 1/3 [t (h - y_{d})^{3} + b y_{d}^{3} - b_{1} (y_{d} - t)^{3}] (2a)*

*I _{y} = 1/3 [t (b - x_{d})^{3} + h x_{d}^{3} - h_{1} (x_{d} - t)^{3}] (2b)*

*where *

*x _{d} = (b^{2} + h_{1} t) / (2 (b + h_{1})) (2c) *

*y _{d} = (h^{2} + b_{1} t) / (2 (h + b_{1}))*

* *

#### Triangle

The Area Moment of Inertia for a triangle can be calculated as

*I _{x} = b h^{3} / 36 (3a)*

*I _{y} = h b (b^{2} - b_{a} b_{c}) / 36 (3b)*

#### Rectangular Triangle

The Area Moment of Inertia for a rectangular triangle can be calculated as

*I _{x} = b h^{3} / 36 (4a)*

*I _{y} =h b^{3} / 36 (4b)*