Moment of Inertia of an Area

Second Moment of Area or Area Moment of Inertia

Moment of Inertia of an Area, Area Moment of Inertia, also known as Second Moment of Area - I, is a property of shape that is used to predict deflection, bending and stress in beams.

Note

  • the "Area Moment of Inertia" is analogous to the "Polar Moment of Inertia" as a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque
  • the "Section Modulus" is defined as W = I / y, where I is Area Moment of Inertia and y is the distance from the neutral axis to any given fibre

Area Moment of Inertia - Imperial units

  • inches4

Area Moment of Inertia - 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

Second Moment of Area

can be expressed as

Ix = ∫ y2 dA         (1)

where

Ix = second moment of area

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

area moment of inertia square section

Ix = b4 / 12         (2)

where

b = side

 

Iy = b4 / 12         (2b)

Solid Rectangular Cross Section

area moment of inertia rectangular section

Ix = b h3 / 12         (3)

where

b = width

h = height

 

Iy = b3 h / 12         (3b)

Solid Circular Cross Section

area moment of inertia circular 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

area moment of inertia cylindrical section

Ix = π (do4 - di4) / 64         (5)

where

do = cylinder outside diameter

di = cylinder inside diameter

 

Iy = π (do4 - di4) / 64         (5b)

Area Moment of Inertia vs. Polar Moment of Inertia

  • "Polar Moment of Inertia" as a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque
  • "Area Moment of Inertia" is a property of shape that is used to predict deflection, bending and stress in beams

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

Related Documents

Key Words

  • en: moment inertia plane area
  • es: momento área del plano de inercia
  • de: Trägheitsmoment ebene Fläche

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