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 deflections and stresses in beams.

Imperial units

Metric units

Converting between units

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

Rectangular Cross Section

Ix = b h3 / 12 (2)

where

b = width

h = height

Circular Cross Section

Ix = π r4 / 4

    = π d4 / 64 (3)

where

r = radius

d = diameter

Cylindrical Cross Section

Ix = π (do4 - di4) / 64 (3)

where

do = cylinder outside diameter

di = cylinder inside diameter

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Related Topics

  • Mechanics Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
  • Beams and Columns Deflection and stress, moment of inertia, section modulus and technical information of beams and columns

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