
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 xx axis
Moment of Inertia about yy axis
Moment of Inertia of some standard areas can be found
below.
1. Rectangular section;
(a) I_{xx} = (bd^{3})/12
(b) I_{yy} = (db^{3})/12
where b= width of the section, and d= depth of
section.
The axes xx and yy are passing through the
centroid and xx axis is parallel to the width of section and yy
parallel to the depth.

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2. Circular Section
I_{xx}
= I_{yy} = (πD^{4})/64,
where D is the diameter of the section and xx
and yy axes are passing through the centroid.
We can use parallel axes theorem to find the
moment of inertia about an axis parallel to xx or yy,
For example if pq is an axis parallel to xx
and it is at a distance of 'h' from xx axis. Then the moment of
inertia I_{pq} about pq axis can be determined
as given below;
I_{pq} = I_{xx
}+ Ah^{2}
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
I_{xx}
+ I_{yy} = I_{zz}
Use our
Moment
of Inertia calculator to determine centroid, moment of inertia
and section modulus for
different sections including angle, circle, rectangle, Channel, Isection and Tsection.
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 The links on this page will lead you to available web resources
including Lecture notes, products or services in the field of
Structural Analysis. Visit
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