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Moment of Inertia  

Moment of Inertia or second moment of area is a geometrical property of a section of structural member which is required to calculate its resistance to bending and buckling. Mathematically, the moment of inertia of a section can be defined as

  Moment of Inertia about x-x axis

   Moment of Inertia about y-y axis

 Moment of Inertia of some standard areas can be found below.

1. Rectangular section;

(a)  Ixx = (bd3)/12

(b) Iyy = (db3)/12

where b= width of the section, and d= depth of section.

The axes x-x and y-y are passing through the centroid and x-x axis is parallel to the width of section and y-y parallel to the depth.

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2. Circular Section

  Ixx = Iyy = (πD4)/64,

where D is the diameter of the section and x-x and y-y axes are passing through the centroid.

We can use parallel axes theorem to find the moment of inertia about an axis parallel to x-x or y-y,

For example if p-q is an axis parallel to x-x and it is at a distance of 'h' from x-x axis. Then the moment of inertia  Ipq  about p-q axis can be determined as given below;

 Ipq = Ixx + Ah2

where A= the area of the section

Moment of inertia of hollow sections can also be determined by subtracting the moment of inertia of the removed area from the moment of inertia of original area.

Polar Moment of inertia is required in case of torsion of structural member.  Polar Moment of Inertia is defined as the Moment of inertia bout an axis perpendicular to the plane of the section and can be calculated by applying perpendicular axes theorem which says that

 Ixx + Iyy = Izz

Use our Moment of Inertia calculator to determine centroid, moment of inertia and section modulus for different sections including angle, circle, rectangle, Channel, I-section and T-section. Moment of inertia is required to determine bending stress and deflection of beam.

You can also use our Deflection Calculator Easy to use calculator for different loads on beams

See more about bending moment and shearing force

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Last updated on Thursday January 31, 2013