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

• Area Moment of Inertia for typical Cross Sections I

Angle with Equal Legs

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

I_x = 1/3 (2 c⁴ - 2 (c - t)⁴ + t (h - 2 c + 1/2 t)³)                       (1a)

where

c = y_t cos(45^o)                             (1b)

and

y_t = (h² + ht + t²) / (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_d³ - b₁ (y_d - t)³)                            (2a)

I_y = 1/3 (t (b - x_d)³ + h x_d³ - h₁ (x_d - t)³)                            (2b)

where

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

y_d = (h² + b₁ t) / (2 (h + b₁))

 

Triangle

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

I_x =  b h³ / 36                                (3a)

I_y = h b (b² - b_a b_c) / 36                         (3b)

Rectangular Triangle

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

I_x =  b h³ / 36                                (4a)

I_y =h b³ / 36                              (4b)

• Area Moment of Inertia for typical Cross Sections I