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Area Moment of Inertia
Second Moment of Inertia or Area Moment of Inertia
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Area Moment of Inertia, also known as Second Moment of Inertia - I, is a property of shape that is used to predict deflection and stress in beams.
Imperial units
- inches4
Metric units
- mm4
- cm4
- m4
Converting between units
- 1 cm4 = 10-8 m = 104 mm
- 1 in4 = 4.16x105 mm4 = 41.6 cm4
- 1 cm3 = 10-6 m = 103 mm
Definition of Second Moment of Inertia
Ix = ∫ y2 dA (1)
where
Ix = second moment of inertia
y = the perpendicular distance from axis x to the element dA
dA = an elemental area
Area Moment of Inertia for some common Cross Sections
Solid Square Cross Section
Ix = b4 / 12 (2)
where
b = side
Iy = b4 / 12 (2b)
Solid Rectangular Cross Section
Ix = b h3 / 12 (3)
where
b = width
h = height
Iy = b3 h / 12 (3b)
Solid Circular Cross Section
Ix = π r4 / 4
= π d4 / 64 (4)
where
r = radius
d = diameter
Iy = π r4 / 4
= π d4 / 64 (4b)
Hollow Cylindrical Cross Section
Ix = π (do4 - di4) / 64 (5)
where
do = cylinder outside diameter
di = cylinder inside diameter
Iy = π (do4 - di4) / 64 (5b)
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