1. Mindanao State University
Iligan Institute of Technology
College of Engineering
Moment of Inertia
a Force
Gevelyn Bontilao Itao, MOE

2. Moment of Inertia
Inertia
That property of matter by virtue of which any physical
body persist to remain at rest or in a state of uniform
motion unless acted upon by external forces.
Moment of Inertia, I
 Integral of the second moment of an area.
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3. Moment of Inertia
Polar Moment of Inertia, Jo
The second moment of dA about pole O.
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4. Moment of Inertia
NOTE: Ix , Iy , and Jo will always be positive since they
involve the product of distance squared and area
Units for Inertia
 m4 , mm4 , ft4, or in4
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5. Moment of Inertia
Parallel Axis Theorem:
 Most often, the moment of inertia for an area is known
about an axis passing through its centroid. But it is
convenient to determine the moment of inertia of the
area about a corresponding parallel axis.
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6. Moment of Inertia
Parallel Axis Theorem:
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7. Moment of Inertia
Parallel Axis Theorem:
 In general, the moment of inertia of an area about an
axis is equal to the moment of inertia of an area about a
parallel axis passing through the area’s centroid plus the
product of the area and the square of the perpendicular
distance between the axes.
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8. Internal Forces
Example 1:
The beam is supports the loading shown. Determine the
internal normal force, shear force and bending moment
acting just to the left of point C and just to the right of
point C.
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9. Mindanao State University
Iligan Institute of Technology
College of Engineering
Moment of Inertiaafor Composite Bodies
Force
Gevelyn Bontilao Itao, MOE

10. Moment of Inertia for Composite Bodies
Moment of Inertia of the Composite Bodies
 can be determined about a common axis. It is just the
algebraic sum of the moments of inertia of all its parts or
common shapes.
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11. Moment of Inertia for Composite Bodies
Procedure for Analysis:
1. Sketch and divide the area into its composite parts and
indicate the perpendicular distance from the centroid
of each part to the reference axis.
2. Determine the moment of inertia of each part about
its centroidal axis which is parallel to the reference
axis.
3. If the centroidal axis does not coincide with the
reference axis, the Parallel-Axis Theorem should be
used to determine the moment of inertia of the part
about the reference axis.
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12. Moment of Inertia for Composite Bodies
Procedure for Analysis:
4. The moment of inertia of the entire area about the
reference axis is determined by summing the results of
its composite parts. If a composite part has a “hole”,
subtract its moment of inertia from the entire area.
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13. Moment of Inertia for Composite Bodies
Example 1:
Compute the moment of inertia of the composite shown.
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14. Moment of Inertia for Composite Bodies
Example 2:
Compute the moment of inertia of the area shown with
respect to its:
a. centroidal axis
b. x - y axis
c. x’ – y’ axis
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