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# Area Moment of Inertia - Typical Cross Sections II

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

Ix = 1/3 [2c4 - 2 (c - t)4 + t (h - 2 c + 1/2 t)3]                       (1a)

where

c = yt cos 45o                             (1b)

and

yt = (h2 + ht + t2) / [2 (2 h - t ) cos 45o]                               (1c)

#### Angle with Unequal Legs

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

Ix = 1/3 [t (h - yd)3 + b yd3 - b1 (yd - t)3]                            (2a)

Iy = 1/3 [t (b - xd)3 + h xd3 - h1 (xd - t)3]                            (2b)

where

xd = (b2 + h1 t) / (2 (b + h1))                                 (2c)

yd = (h2 + b1 t) / (2 (h + b1))

#### Triangle

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

Ix =  b h3 / 36                                (3a)

Iy = h b (b2 - ba bc) / 36                         (3b)

#### Rectangular Triangle

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

Ix =  b h3 / 36                                (4a)

Iy =h b3 / 36                              (4b)

## Related Topics

### • Beams and Columns

Deflection and stress, moment of inertia, section modulus and technical information of beams and columns.

### • Mechanics

Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

## Related Documents

### American Standard Beams - S Beam

American Standard Beams ASTM A6 - Imperial units.

### American Standard Steel C Channels

Dimensions and static parameters of American Standard Steel C Channels

### American Wide Flange Beams

American Wide Flange Beams ASTM A6 in metric units.

### Area Moment of Inertia - Typical Cross Sections I

Typical cross sections and their Area Moment of Inertia.

### Area Moment of Inertia Converter

Convert between Area Moment of Inertia units.

### British Universal Columns and Beams

Properties of British Universal Steel Columns and Beams.

### Center Mass

Calculate position of center mass.

### Euler's Column Formula

Calculate buckling of columns.

### HE-A Steel Beams

Properties of HE-A profiled steel beams.

### HE-B Steel Beams

Properties of HE-B profiled steel beams.

### HE-M Steel Beams

Properties of HE-M profile steel beams.

### Mass Moment of Inertia

The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration.

### Normal Flange I-Beams

Properties of normal flange I profile steel beams.

### Steel Angles - Equal Legs

Dimensions and static parameters of steel angles with equal legs - metric units.

### Steel Angles - Unequal Legs

Dimensions and static parameters of steel angles with unequal legs - imperial units.

### W-Beams - American Wide Flange Beams

Dimensions of American Wide Flange Beams ASTM A6 (or W-Beams) - Imperial units.

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