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)
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