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# Lect9 Moment of Inertia

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### Lect9 Moment of Inertia

1. 1. Mindanao State UniversityIligan Institute of Technology College of EngineeringMoment of Inertia a ForceGevelyn Bontilao Itao, MOE
2. 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.gsbitao_2013
3. 3. Moment of Inertia Polar Moment of Inertia, Jo The second moment of dA about pole O.gsbitao_2013
4. 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 in4gsbitao_2013
5. 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.gsbitao_2013
6. 6. Moment of Inertia Parallel Axis Theorem:gsbitao_2013
7. 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.gsbitao_2013
8. 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.gsbitao_2013
9. 9. Mindanao State University Iligan Institute of Technology College of EngineeringMoment of Inertiaafor Composite Bodies Force Gevelyn Bontilao Itao, MOE
10. 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.gsbitao_2013
11. 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.gsbitao_2013
12. 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.gsbitao_2013
13. 13. Moment of Inertia for Composite Bodies Example 1: Compute the moment of inertia of the composite shown.gsbitao_2013
14. 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’ axisgsbitao_2013